Identifier
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0002;cc-rep-3
[1,0]=>[1]=>[1]=>[1]
[1,0,1,0]=>[1,1]=>[2]=>[2]
[1,1,0,0]=>[2]=>[1,1]=>[1,1]
[1,0,1,0,1,0]=>[1,1,1]=>[3]=>[3]
[1,0,1,1,0,0]=>[1,2]=>[2,1]=>[2,1]
[1,1,0,0,1,0]=>[2,1]=>[1,2]=>[2,1]
[1,1,0,1,0,0]=>[2,1]=>[1,2]=>[2,1]
[1,1,1,0,0,0]=>[3]=>[1,1,1]=>[1,1,1]
[1,0,1,0,1,0,1,0]=>[1,1,1,1]=>[4]=>[4]
[1,0,1,0,1,1,0,0]=>[1,1,2]=>[3,1]=>[3,1]
[1,0,1,1,0,0,1,0]=>[1,2,1]=>[2,2]=>[2,2]
[1,0,1,1,0,1,0,0]=>[1,2,1]=>[2,2]=>[2,2]
[1,0,1,1,1,0,0,0]=>[1,3]=>[2,1,1]=>[2,1,1]
[1,1,0,0,1,0,1,0]=>[2,1,1]=>[1,3]=>[3,1]
[1,1,0,0,1,1,0,0]=>[2,2]=>[1,2,1]=>[2,1,1]
[1,1,0,1,0,0,1,0]=>[2,1,1]=>[1,3]=>[3,1]
[1,1,0,1,0,1,0,0]=>[2,1,1]=>[1,3]=>[3,1]
[1,1,0,1,1,0,0,0]=>[2,2]=>[1,2,1]=>[2,1,1]
[1,1,1,0,0,0,1,0]=>[3,1]=>[1,1,2]=>[2,1,1]
[1,1,1,0,0,1,0,0]=>[3,1]=>[1,1,2]=>[2,1,1]
[1,1,1,0,1,0,0,0]=>[3,1]=>[1,1,2]=>[2,1,1]
[1,1,1,1,0,0,0,0]=>[4]=>[1,1,1,1]=>[1,1,1,1]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]=>[5]=>[5]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]=>[4,1]=>[4,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>[3,2]=>[3,2]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]=>[3,2]=>[3,2]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]=>[3,1,1]=>[3,1,1]
[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>[2,3]=>[3,2]
[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>[2,2,1]=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]=>[2,3]=>[3,2]
[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]=>[2,3]=>[3,2]
[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]=>[2,2,1]=>[2,2,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>[2,1,2]=>[2,2,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]=>[2,1,2]=>[2,2,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]=>[2,1,2]=>[2,2,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,4]=>[2,1,1,1]=>[2,1,1,1]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>[1,4]=>[4,1]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]=>[1,3,1]=>[3,1,1]
[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>[1,2,2]=>[2,2,1]
[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]=>[1,2,2]=>[2,2,1]
[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>[1,2,1,1]=>[2,1,1,1]
[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]=>[1,4]=>[4,1]
[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]=>[1,3,1]=>[3,1,1]
[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]=>[1,4]=>[4,1]
[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]=>[1,4]=>[4,1]
[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]=>[1,3,1]=>[3,1,1]
[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]=>[1,2,2]=>[2,2,1]
[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]=>[1,2,2]=>[2,2,1]
[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]=>[1,2,2]=>[2,2,1]
[1,1,0,1,1,1,0,0,0,0]=>[2,3]=>[1,2,1,1]=>[2,1,1,1]
[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>[1,1,3]=>[3,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>[1,1,2,1]=>[2,1,1,1]
[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]=>[1,1,3]=>[3,1,1]
[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]=>[1,1,3]=>[3,1,1]
[1,1,1,0,0,1,1,0,0,0]=>[3,2]=>[1,1,2,1]=>[2,1,1,1]
[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]=>[1,1,3]=>[3,1,1]
[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]=>[1,1,3]=>[3,1,1]
[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]=>[1,1,3]=>[3,1,1]
[1,1,1,0,1,1,0,0,0,0]=>[3,2]=>[1,1,2,1]=>[2,1,1,1]
[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>[1,1,1,2]=>[2,1,1,1]
[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>[1,1,1,2]=>[2,1,1,1]
[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>[1,1,1,2]=>[2,1,1,1]
[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>[1,1,1,2]=>[2,1,1,1]
[1,1,1,1,1,0,0,0,0,0]=>[5]=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]=>[6]=>[6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]=>[5,1]=>[5,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>[4,2]=>[4,2]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]=>[4,2]=>[4,2]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]=>[4,1,1]=>[4,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>[3,3]=>[3,3]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]=>[3,2,1]=>[3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]=>[3,3]=>[3,3]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]=>[3,3]=>[3,3]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]=>[3,2,1]=>[3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>[3,1,2]=>[3,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]=>[3,1,2]=>[3,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]=>[3,1,2]=>[3,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]=>[3,1,1,1]=>[3,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>[2,4]=>[4,2]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]=>[2,3,1]=>[3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>[2,2,2]=>[2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]=>[2,2,2]=>[2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]=>[2,2,1,1]=>[2,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]=>[2,4]=>[4,2]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]=>[2,3,1]=>[3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]=>[2,4]=>[4,2]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]=>[2,4]=>[4,2]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]=>[2,3,1]=>[3,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]=>[2,2,2]=>[2,2,2]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]=>[2,2,2]=>[2,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]=>[2,2,2]=>[2,2,2]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]=>[2,2,1,1]=>[2,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>[2,1,3]=>[3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>[2,1,2,1]=>[2,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]=>[2,1,3]=>[3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]=>[2,1,3]=>[3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]=>[2,1,2,1]=>[2,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]=>[2,1,3]=>[3,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]=>[2,1,3]=>[3,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]=>[2,1,3]=>[3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]=>[2,1,2,1]=>[2,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>[2,1,1,2]=>[2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>[2,1,1,2]=>[2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>[2,1,1,2]=>[2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>[2,1,1,2]=>[2,2,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]=>[2,1,1,1,1]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[1,5]=>[5,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]=>[1,4,1]=>[4,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>[1,3,2]=>[3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]=>[1,3,2]=>[3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]=>[1,3,1,1]=>[3,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>[1,2,3]=>[3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]=>[1,2,3]=>[3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]=>[1,2,3]=>[3,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[1,5]=>[5,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]=>[1,4,1]=>[4,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]=>[1,3,2]=>[3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]=>[1,3,2]=>[3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]=>[1,3,1,1]=>[3,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]=>[1,5]=>[5,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]=>[1,4,1]=>[4,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]=>[1,5]=>[5,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]=>[1,5]=>[5,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]=>[1,4,1]=>[4,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]=>[1,3,2]=>[3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]=>[1,3,2]=>[3,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]=>[1,3,2]=>[3,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]=>[1,3,1,1]=>[3,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]=>[1,2,3]=>[3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]=>[1,2,3]=>[3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]=>[1,2,3]=>[3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]=>[1,2,3]=>[3,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]=>[1,2,3]=>[3,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]=>[1,2,3]=>[3,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>[1,1,3,1]=>[3,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]=>[1,1,3,1]=>[3,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]=>[1,1,3,1]=>[3,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]=>[1,1,3,1]=>[3,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]=>[1,1,3,1]=>[3,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]=>[1,1,4]=>[4,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]=>[1,1,3,1]=>[3,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]=>[7]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]=>[6,1]=>[6,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]=>[5,2]=>[5,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]=>[5,2]=>[5,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]=>[5,1,1]=>[5,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]=>[4,3]=>[4,3]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]=>[4,2,1]=>[4,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]=>[4,3]=>[4,3]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]=>[4,3]=>[4,3]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]=>[4,2,1]=>[4,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>[4,1,2]=>[4,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]=>[4,1,2]=>[4,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]=>[4,1,2]=>[4,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]=>[4,1,1,1]=>[4,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]=>[3,4]=>[4,3]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]=>[3,3,1]=>[3,3,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>[3,2,2]=>[3,2,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]=>[3,2,2]=>[3,2,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]=>[3,2,1,1]=>[3,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]=>[3,4]=>[4,3]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]=>[3,3,1]=>[3,3,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]=>[3,4]=>[4,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]=>[3,4]=>[4,3]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]=>[3,3,1]=>[3,3,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]=>[3,2,2]=>[3,2,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]=>[3,2,2]=>[3,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]=>[3,2,2]=>[3,2,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]=>[3,2,1,1]=>[3,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>[3,1,3]=>[3,3,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>[3,1,2,1]=>[3,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]=>[3,1,3]=>[3,3,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]=>[3,1,3]=>[3,3,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]=>[3,1,2,1]=>[3,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]=>[3,1,3]=>[3,3,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]=>[3,1,3]=>[3,3,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]=>[3,1,3]=>[3,3,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]=>[3,1,2,1]=>[3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>[3,1,1,2]=>[3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>[3,1,1,2]=>[3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>[3,1,1,2]=>[3,2,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>[3,1,1,2]=>[3,2,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]=>[3,1,1,1,1]=>[3,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>[2,5]=>[5,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[2,4,1]=>[4,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[2,3,2]=>[3,2,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>[2,3,2]=>[3,2,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]=>[2,3,1,1]=>[3,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>[2,5]=>[5,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[2,4,1]=>[4,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[2,3,2]=>[3,2,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>[2,3,2]=>[3,2,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]=>[2,3,1,1]=>[3,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]=>[2,5]=>[5,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]=>[2,4,1]=>[4,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]=>[2,5]=>[5,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]=>[2,5]=>[5,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]=>[2,4,1]=>[4,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]=>[2,3,2]=>[3,2,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]=>[2,3,2]=>[3,2,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]=>[2,3,2]=>[3,2,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]=>[2,3,1,1]=>[3,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[3,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[3,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[3,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]=>[2,1,4]=>[4,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>[2,1,1,3]=>[3,2,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]=>[2,1,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,6]=>[6,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[1,5,1]=>[5,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,4,2]=>[4,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,4,2]=>[4,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[1,4,1,1]=>[4,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[1,3,2,1]=>[3,2,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>[1,3,2,1]=>[3,2,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[1,3,1,1,1]=>[3,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]=>[3,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]=>[3,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>[1,2,3,1]=>[3,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,6]=>[6,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[1,5,1]=>[5,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,4,2]=>[4,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,4,2]=>[4,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[1,4,1,1]=>[4,1,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[1,3,2,1]=>[3,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>[1,3,2,1]=>[3,2,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[1,3,1,1,1]=>[3,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,6]=>[6,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[1,5,1]=>[5,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,4,2]=>[4,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,4,2]=>[4,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]=>[1,4,1,1]=>[4,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,6]=>[6,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]=>[1,5,1]=>[5,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1]=>[1,6]=>[6,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1]=>[1,6]=>[6,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]=>[1,5,1]=>[5,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]=>[1,4,2]=>[4,2,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]=>[1,4,2]=>[4,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]=>[1,4,2]=>[4,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]=>[1,4,1,1]=>[4,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]=>[1,3,2,1]=>[3,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]=>[1,3,2,1]=>[3,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]=>[1,3,2,1]=>[3,2,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[3,2,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]=>[1,3,1,1,1]=>[3,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]=>[3,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]=>[3,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>[1,2,3,1]=>[3,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]=>[1,2,3,1]=>[3,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]=>[1,2,3,1]=>[3,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]=>[1,2,3,1]=>[3,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>[1,2,1,3]=>[3,2,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>[1,1,3,1,1]=>[3,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]=>[1,1,3,1,1]=>[3,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]=>[1,1,3,1,1]=>[3,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]=>[1,1,3,1,1]=>[3,1,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]=>[1,1,3,1,1]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,5]=>[5,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]=>[1,1,4,1]=>[4,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>[1,1,3,2]=>[3,2,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]=>[1,1,3,1,1]=>[3,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]=>[1,1,1,3,1]=>[3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1]=>[8]=>[8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]=>[7,1]=>[7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>[6,2]=>[6,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]=>[6,2]=>[6,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]=>[6,1,1]=>[6,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]=>[5,3]=>[5,3]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]=>[5,2,1]=>[5,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]=>[5,3]=>[5,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]=>[5,3]=>[5,3]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]=>[5,2,1]=>[5,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>[5,1,2]=>[5,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]=>[5,1,2]=>[5,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]=>[5,1,2]=>[5,2,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]=>[5,1,1,1]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>[4,4]=>[4,4]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]=>[4,3,1]=>[4,3,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]=>[4,2,2]=>[4,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]=>[4,2,2]=>[4,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]=>[4,2,1,1]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>[4,4]=>[4,4]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]=>[4,3,1]=>[4,3,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]=>[4,4]=>[4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]=>[4,4]=>[4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]=>[4,3,1]=>[4,3,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,2,2,1]=>[4,2,2]=>[4,2,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]=>[4,2,2]=>[4,2,2]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]=>[4,2,2]=>[4,2,2]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]=>[4,2,1,1]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>[4,1,3]=>[4,3,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]=>[4,1,2,1]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]=>[4,1,3]=>[4,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]=>[4,1,3]=>[4,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]=>[4,1,2,1]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]=>[4,1,3]=>[4,3,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]=>[4,1,3]=>[4,3,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]=>[4,1,3]=>[4,3,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]=>[4,1,2,1]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]=>[4,1,1,2]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]=>[4,1,1,2]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]=>[4,1,1,2]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]=>[4,1,1,2]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]=>[4,1,1,1,1]=>[4,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[3,5]=>[5,3]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>[3,4,1]=>[4,3,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>[3,3,2]=>[3,3,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>[3,3,2]=>[3,3,2]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>[3,3,1,1]=>[3,3,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]=>[3,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]=>[3,2,2,1]=>[3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]=>[3,3,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>[3,2,3]=>[3,3,2]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]=>[3,2,2,1]=>[3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]=>[3,2,1,2]=>[3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]=>[3,2,1,2]=>[3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]=>[3,2,1,2]=>[3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]=>[3,2,1,1,1]=>[3,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[3,5]=>[5,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>[3,4,1]=>[4,3,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>[3,3,2]=>[3,3,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>[3,3,2]=>[3,3,2]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>[3,3,1,1]=>[3,3,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[3,5]=>[5,3]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]=>[3,4,1]=>[4,3,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]=>[3,5]=>[5,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]=>[3,5]=>[5,3]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]=>[3,4,1]=>[4,3,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]=>[3,3,2]=>[3,3,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]=>[3,3,2]=>[3,3,2]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]=>[3,3,2]=>[3,3,2]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]=>[3,3,1,1]=>[3,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]=>[3,3,2]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]=>[3,2,2,1]=>[3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]=>[3,3,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>[3,2,3]=>[3,3,2]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]=>[3,2,2,1]=>[3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]=>[3,2,3]=>[3,3,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]=>[3,2,3]=>[3,3,2]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]=>[3,2,3]=>[3,3,2]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]=>[3,2,2,1]=>[3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]=>[3,2,1,2]=>[3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]=>[3,2,1,2]=>[3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]=>[3,2,1,2]=>[3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]=>[3,2,1,2]=>[3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]=>[3,2,1,1,1]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>[3,1,3,1]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>[3,1,2,2]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]=>[3,1,2,2]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>[3,1,2,1,1]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]=>[3,1,3,1]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]=>[3,1,3,1]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]=>[3,1,2,2]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]=>[3,1,2,2]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]=>[3,1,2,2]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]=>[3,1,2,1,1]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]=>[3,1,3,1]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]=>[3,1,3,1]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]=>[3,1,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]=>[3,1,3,1]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,1]=>[3,1,2,2]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]=>[3,1,2,2]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]=>[3,1,2,2]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]=>[3,1,2,2]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]=>[3,1,2,1,1]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]=>[3,1,1,2,1]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]=>[3,1,1,2,1]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]=>[3,1,1,2,1]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]=>[3,1,1,3]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]=>[3,1,1,2,1]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>[3,1,1,1,2]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]=>[3,1,1,1,2]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]=>[3,1,1,1,2]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]=>[3,1,1,1,2]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]=>[3,1,1,1,2]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]=>[3,1,1,1,1,1]=>[3,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]=>[6,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,5,1]=>[5,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[2,4,2]=>[4,2,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>[2,4,2]=>[4,2,2]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[2,4,1,1]=>[4,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,3,2,1]=>[3,2,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>[2,3,2,1]=>[3,2,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[2,3,1,1,1]=>[3,2,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>[2,2,3,1]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]=>[6,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,5,1]=>[5,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[2,4,2]=>[4,2,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>[2,4,2]=>[4,2,2]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[2,4,1,1]=>[4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,3,2,1]=>[3,2,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>[2,3,2,1]=>[3,2,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[2,3,1,1,1]=>[3,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]=>[6,2]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,5,1]=>[5,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[2,4,2]=>[4,2,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>[2,4,2]=>[4,2,2]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[2,4,1,1]=>[4,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]=>[6,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,5,1]=>[5,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]=>[2,6]=>[6,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]=>[2,6]=>[6,2]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]=>[2,5,1]=>[5,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]=>[2,4,2]=>[4,2,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,2,1]=>[2,4,2]=>[4,2,2]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]=>[2,4,2]=>[4,2,2]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]=>[2,4,1,1]=>[4,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,3,2,1]=>[3,2,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]=>[2,3,2,1]=>[3,2,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]=>[2,3,2,1]=>[3,2,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]=>[2,3,1,2]=>[3,2,2,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]=>[2,3,1,1,1]=>[3,2,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]=>[3,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]=>[3,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>[2,2,3,1]=>[3,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,3,1]=>[3,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]=>[2,2,3,1]=>[3,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]=>[2,2,3,1]=>[3,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]=>[2,2,1,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]=>[3,2,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]=>[3,2,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]=>[3,2,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]=>[3,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]=>[3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]=>[2,1,5]=>[5,2,1]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]=>[2,1,4,1]=>[4,2,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]=>[2,1,3,2]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]=>[2,1,3,1,1]=>[3,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]=>[2,1,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]=>[2,1,1,4]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]=>[2,1,1,3,1]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]=>[2,1,1,1,3]=>[3,2,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]=>[7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]=>[6,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]=>[5,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[1,4,2,1]=>[4,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]=>[4,2,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[1,4,1,1,1]=>[4,1,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]=>[3,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]=>[3,2,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[1,3,1,1,1,1]=>[3,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]=>[7,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]=>[6,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]=>[5,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[1,4,2,1]=>[4,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]=>[4,2,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[1,4,1,1,1]=>[4,1,1,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]=>[3,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]=>[3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[1,3,1,1,1,1]=>[3,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]=>[7,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]=>[6,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]=>[5,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[1,4,2,1]=>[4,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]=>[4,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[1,4,1,1,1]=>[4,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]=>[7,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]=>[6,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]=>[5,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]=>[7,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,6,1]=>[6,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1]=>[1,7]=>[7,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1]=>[1,7]=>[7,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]=>[1,6,1]=>[6,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]=>[1,5,2]=>[5,2,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]=>[1,5,1,1]=>[5,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]=>[1,4,2,1]=>[4,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]=>[4,2,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1]=>[1,4,3]=>[4,3,1]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]=>[1,4,2,1]=>[4,2,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]=>[1,4,1,2]=>[4,2,1,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]=>[1,4,1,1,1]=>[4,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]=>[1,3,3,1]=>[3,3,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]=>[1,3,2,2]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]=>[1,3,2,1,1]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]=>[1,3,1,3]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]=>[1,3,1,1,1,1]=>[3,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,2]=>[1,2,4,1]=>[4,2,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]=>[1,2,3,2]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]=>[1,2,1,4]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,5,1]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]=>[3,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]=>[3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]=>[3,1,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1]=>[1,1,6]=>[6,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,2]=>[1,1,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]=>[1,1,4,2]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]=>[1,1,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]=>[1,1,3,1,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]=>[1,1,3,1,1,1]=>[3,1,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]=>[1,1,2,3,1]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,7,1]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,9]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,2,1]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,7,1]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,2]=>[2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,8,1]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,7,1]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,6,1,1]=>[2,1,1,1,1,3]=>[3,2,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,8,1]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,5,3]=>[2,1,1,1,2,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,7,2]=>[2,1,1,1,1,1,2,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,2,1]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,4,1]=>[1,1,1,2,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,7,1]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,8,1]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,6,2]=>[2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,4]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,6,3]=>[2,1,1,1,1,2,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,7,1]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,8,1]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,6,1,1]=>[2,1,1,1,1,3]=>[3,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,5,2,1]=>[2,1,1,1,2,2]=>[2,2,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,5,1,2]=>[2,1,1,1,3,1]=>[3,2,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,7,2]=>[2,1,1,1,1,1,2,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5]=>[2,1,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,5,4]=>[2,1,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,6,1]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,1]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,8,1]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,6,1,1]=>[2,1,1,1,1,3]=>[3,2,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,7,1,1]=>[2,1,1,1,1,1,3]=>[3,2,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,4,2,2]=>[2,1,1,2,2,1]=>[2,2,2,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,1,2]=>[2,1,1,1,1,3,1]=>[3,2,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,7]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,6]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,4,5]=>[2,1,1,2,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2]=>[1,1,1,1,1,3,1]=>[3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,8,1]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,4,3,1]=>[2,1,1,2,1,2]=>[2,2,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,5,1,2]=>[2,1,1,1,3,1]=>[3,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,5,2,1]=>[2,1,1,1,2,2]=>[2,2,2,1,1,1]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,6,1]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,7]=>[3,1,1,1,1,1,1]=>[3,1,1,1,1,1,1]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,6]=>[2,1,2,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,2]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,6,1,1]=>[2,1,1,1,1,3]=>[3,2,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,8,1]=>[2,1,1,1,1,1,1,2]=>[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]=>[5,2,2]=>[1,1,1,1,2,2,1]=>[2,2,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,6,1]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,5,2]=>[1,2,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,6,1]=>[3,1,1,1,1,2]=>[3,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,8]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,7]=>[2,2,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,6,1,1]=>[2,1,1,1,1,3]=>[3,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,5,2,1]=>[2,1,1,1,2,2]=>[2,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,1]=>[2,1,2,1,1,2]=>[2,2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1]=>[2,1,1,1,4]=>[4,2,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,1,2]=>[2,1,1,4,1]=>[4,2,1,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,5,1,1]=>[1,2,1,1,1,3]=>[3,2,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,6,1]=>[3,1,1,1,1,2]=>[3,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,7,1]=>[1,2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,8]=>[3,1,1,1,1,1,1,1]=>[3,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1,1]=>[1,8]=>[8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,2]=>[1,7,1]=>[7,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,1,2,1]=>[1,6,2]=>[6,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,1,2,1]=>[1,6,2]=>[6,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,1,3]=>[1,6,1,1]=>[6,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,1,2,2]=>[1,5,2,1]=>[5,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,4]=>[1,5,1,1,1]=>[5,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]=>[1,4,4]=>[4,4,1]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,1,2,3]=>[1,4,2,1,1]=>[4,2,1,1,1]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,1,5]=>[1,4,1,1,1,1]=>[4,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]=>[1,3,5]=>[5,3,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]=>[1,3,5]=>[5,3,1]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,1,2,4]=>[1,3,2,1,1,1]=>[3,2,1,1,1,1]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,6]=>[1,3,1,1,1,1,1]=>[3,1,1,1,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1]=>[1,2,2,4]=>[4,2,2,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1]=>[1,2,6]=>[6,2,1]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,5]=>[1,2,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>[1,2,1,5]=>[5,2,1,1]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[2,4,3]=>[1,2,1,1,2,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,5,2]=>[1,2,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,7]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>[1,1,6,1]=>[6,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>[1,1,2,5]=>[5,2,1,1]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,5,1]=>[1,1,2,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,6]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,1,2]=>[1,1,6,1]=>[6,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,1,2,1]=>[1,1,5,2]=>[5,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,1,2,1,1]=>[1,1,4,3]=>[4,3,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>[1,1,3,4]=>[4,3,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>[1,1,2,5]=>[5,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[1,1,2,5]=>[5,2,1,1]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,4,2]=>[1,1,2,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,6]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,3,2]=>[1,1,1,2,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1,5]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1,5]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[5,3,1]=>[1,1,1,1,2,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,1,1,1]=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[6,1,1,1]=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[6,3]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,3]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,2,1]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[7,2]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,2]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,1,1]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,2]=>[1,1,1,1,1,1,2,1]=>[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]=>[8,1]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,1]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,1]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,1]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,1]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,1]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1]=>[9]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,2]=>[8,1]=>[8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,2,1]=>[7,2]=>[7,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,2,1,1]=>[6,3]=>[6,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1,1]=>[5,4]=>[5,4]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1,1]=>[4,5]=>[5,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1,1]=>[3,6]=>[6,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1]=>[2,7]=>[7,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1]=>[10]=>[10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,2]=>[9,1]=>[9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,3]=>[7,1,1]=>[7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,2,1]=>[8,2]=>[8,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,3,1]=>[6,1,2]=>[6,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,2,1,1]=>[7,3]=>[7,3]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,3,1,1]=>[5,1,3]=>[5,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,2,1,1,1]=>[6,4]=>[6,4]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,3,1,1,1]=>[4,1,4]=>[4,4,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1,1,1]=>[5,5]=>[5,5]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1,1]=>[3,1,5]=>[5,3,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1,1,1]=>[4,6]=>[6,4]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1]=>[2,1,6]=>[6,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1,1,1]=>[3,7]=>[7,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1,1]=>[2,8]=>[8,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1,1,1]=>[1,9]=>[9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,3]=>[8,1,1]=>[8,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,3,1]=>[6,1,2]=>[6,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,4]=>[6,1,1,1]=>[6,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,3,1]=>[7,1,2]=>[7,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,3,1,1]=>[5,1,3]=>[5,3,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,4]=>[7,1,1,1]=>[7,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1]=>[2,1,6]=>[6,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,7]=>[7,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,3,1,1]=>[6,1,3]=>[6,3,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1,1]=>[4,1,4]=>[4,4,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,7]=>[7,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,3,1,1,1]=>[5,1,4]=>[5,4,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1,1]=>[3,1,5]=>[5,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,5]=>[6,1,1,1,1]=>[6,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,6]=>[6,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,7]=>[7,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1,1,1]=>[4,1,5]=>[5,4,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1,1]=>[2,1,6]=>[6,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,1,2]=>[2,1,5,1]=>[5,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,6]=>[4,1,1,1,1,1]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,7]=>[7,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1,1,1]=>[3,1,6]=>[6,3,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,6]=>[5,1,1,1,1,1]=>[5,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,7]=>[7,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1,1,1]=>[2,1,7]=>[7,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,1,1,2]=>[2,1,6,1]=>[6,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,7]=>[7,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,2,1]=>[7,2]=>[7,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,2,1,1]=>[6,3]=>[6,3]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,2,2]=>[6,2,1]=>[6,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,3,1]=>[6,1,2]=>[6,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1]=>[5,4]=>[5,4]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,2,3]=>[5,2,1,1]=>[5,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]=>[4,5]=>[5,4]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,2,4]=>[4,2,1,1,1]=>[4,2,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]=>[3,6]=>[6,3]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,2,5]=>[3,2,1,1,1,1]=>[3,2,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]=>[3,1,1,1,1,2]=>[3,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]=>[2,7]=>[7,2]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,6]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,8]=>[8,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>[1,7,1]=>[7,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]=>[1,6,2]=>[6,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]=>[1,5,3]=>[5,3,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,2,2]=>[1,5,2,1]=>[5,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>[1,4,4]=>[4,4,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>[1,3,5]=>[5,3,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>[1,2,6]=>[6,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[1,1,3,1,1,1,1]=>[3,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,2,1]=>[8,2]=>[8,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,2,1,1]=>[7,3]=>[7,3]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,2,1,1,1]=>[6,4]=>[6,4]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1,1]=>[5,5]=>[5,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1,1]=>[4,6]=>[6,4]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,7]=>[4,1,1,1,1,1,1]=>[4,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1,1]=>[3,7]=>[7,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]=>[2,8]=>[8,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]=>[1,9]=>[9,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>[1,8,1]=>[8,1,1]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,7]=>[1,1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,6]=>[1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,4]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,3]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,8]=>[8,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,8]=>[8,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,8]=>[8,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,8]=>[8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,8]=>[8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,8]=>[8,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]=>[1,9]=>[9,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>[1,2,6]=>[6,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]=>[1,9]=>[9,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>[1,3,5]=>[5,3,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]=>[1,9]=>[9,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>[1,4,4]=>[4,4,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]=>[1,9]=>[9,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]=>[1,5,3]=>[5,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]=>[1,9]=>[9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,1,2,1]=>[1,6,2]=>[6,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]=>[1,9]=>[9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1,1]=>[1,9]=>[9,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]=>[1,6,2]=>[6,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,1,2]=>[1,8,1]=>[8,1,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,1]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,1,2,1]=>[1,7,2]=>[7,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,8]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,1]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,1,2]=>[1,1,6,1]=>[6,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>[1,2,1,5]=>[5,2,1,1]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]=>[1,3,1,1,1,1,1]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[1,1,3,1,1,1,1]=>[3,1,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>[1,1,1,3,1,1,1]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,3]=>[1,1,1,1,3,1,1]=>[3,1,1,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>[2,1,1,5]=>[5,2,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>[1,7,1]=>[7,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1]=>[1,2,6]=>[6,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,1,1,3]=>[1,7,1,1]=>[7,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]=>[1,2,1,1,4]=>[4,2,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,7]=>[7,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,4,1]=>[1,1,1,2,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,2,1]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,1]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,3,1]=>[1,1,1,1,2,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,1]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,1]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,5,1]=>[1,1,2,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,1]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,1]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[6,1,2]=>[1,1,1,1,1,3,1]=>[3,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]=>[1,6,2]=>[6,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]=>[1,5,3]=>[5,3,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>[1,4,4]=>[4,4,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>[1,3,5]=>[5,3,1]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,7]=>[1,3,1,1,1,1,1,1]=>[3,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,1,6]=>[1,4,1,1,1,1,1]=>[4,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,1,1,5]=>[1,5,1,1,1,1]=>[5,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,1,4]=>[1,6,1,1,1]=>[6,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,1,1,2,1,1]=>[1,6,3]=>[6,3,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[8,2]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[8,2]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[7,3]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[7,3]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,4]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[6,4]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,2,2]=>[6,2,1]=>[6,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>[1,1,2,5]=>[5,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]=>[2,7]=>[7,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1,1]=>[1,2,7]=>[7,2,1]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,1,1]=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>[1,6,3]=>[6,3,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,1,3,1]=>[1,1,4,1,2]=>[4,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,2,1,1]=>[6,3]=>[6,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1,1]=>[2,7]=>[7,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,1,3]=>[1,1,5,1,1]=>[5,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]=>[1,5,3]=>[5,3,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,1,2,1,1]=>[1,5,3]=>[5,3,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1,1]=>[2,2,5]=>[5,2,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1,1]=>[4,6]=>[6,4]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]=>[1,5,3]=>[5,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1,1,1]=>[2,8]=>[8,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]=>[2,8]=>[8,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1,1]=>[3,7]=>[7,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>[1,2,6]=>[6,2,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,5,3]=>[2,1,1,1,2,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1,1]=>[1,1,1,6]=>[6,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1]=>[1,2,6]=>[6,2,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1,1]=>[2,1,1,1,5]=>[5,2,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]=>[1,5,3]=>[5,3,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1,1]=>[1,2,1,6]=>[6,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1]=>[1,2,6]=>[6,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,1,1]=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,1,1,1]=>[1,1,1,1,1,1,4]=>[4,1,1,1,1,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,3,1,1,1]=>[2,2,1,4]=>[4,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1,1]=>[2,2,5]=>[5,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,1,1,2,1]=>[1,7,2]=>[7,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,7,1,1]=>[2,1,1,1,1,1,3]=>[3,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>[1,4,4]=>[4,4,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>[1,3,5]=>[5,3,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,1,1,2]=>[2,1,1,5,1]=>[5,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,1,2]=>[2,1,5,1]=>[5,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,1,2]=>[2,2,4,1]=>[4,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]=>[2,1,1,5]=>[5,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,2,1,1,1]=>[2,1,2,4]=>[4,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1,1]=>[2,1,1,6]=>[6,2,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]=>[1,1,8]=>[8,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>[1,2,6]=>[6,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]=>[1,5,1,2]=>[5,2,1,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,7,1]=>[1,2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1,2,1,1]=>[2,4,3]=>[4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>[1,6,3]=>[6,3,1]
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,6,1,1]=>[1,2,1,1,1,1,3]=>[3,2,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,5,1,1]=>[1,2,1,1,1,3]=>[3,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,5,1,1,1]=>[1,2,1,1,1,4]=>[4,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,4,1,1,1]=>[1,2,1,1,4]=>[4,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1,1]=>[1,2,1,1,5]=>[5,2,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>[1,2,1,5]=>[5,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>[1,3,5]=>[5,3,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,1,2]=>[1,1,1,5,1]=>[5,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>[1,1,1,4,2]=>[4,2,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]=>[1,1,1,3,3]=>[3,3,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>[1,1,3,4]=>[4,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>[1,2,6]=>[6,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]=>[2,1,6]=>[6,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,1,3,1,1]=>[1,1,3,1,3]=>[3,3,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>[1,1,2,1,4]=>[4,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[1,1,3,1,1,1,1]=>[3,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>[1,1,1,3,1,1,1]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,1,3]=>[1,1,1,1,3,1,1]=>[3,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,2,3]=>[1,1,1,2,2,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1,1]=>[2,2,5]=>[5,2,2]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1,1,1]=>[2,2,6]=>[6,2,2]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,5,1]=>[2,2,1,1,1,2]=>[2,2,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>[1,6,3]=>[6,3,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]=>[1,1,7]=>[7,1,1]
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
searching the database
Sorry, this map was not found in the database.