Identifier
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-3
[1,0]=>[1]=>[1]=>[1,0]
[1,0,1,0]=>[1,1]=>[1,1]=>[1,0,1,0]
[1,1,0,0]=>[2]=>[2]=>[1,1,0,0]
[1,0,1,0,1,0]=>[1,1,1]=>[1,1,1]=>[1,0,1,0,1,0]
[1,0,1,1,0,0]=>[1,2]=>[2,1]=>[1,1,0,0,1,0]
[1,1,0,0,1,0]=>[2,1]=>[1,2]=>[1,0,1,1,0,0]
[1,1,0,1,0,0]=>[2,1]=>[1,2]=>[1,0,1,1,0,0]
[1,1,1,0,0,0]=>[3]=>[3]=>[1,1,1,0,0,0]
[1,0,1,0,1,0,1,0]=>[1,1,1,1]=>[1,1,1,1]=>[1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0]=>[1,1,2]=>[2,1,1]=>[1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0]=>[1,2,1]=>[1,2,1]=>[1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0]=>[1,2,1]=>[1,2,1]=>[1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0]=>[1,3]=>[3,1]=>[1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0]=>[2,1,1]=>[1,1,2]=>[1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0]=>[2,2]=>[2,2]=>[1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0]=>[2,1,1]=>[1,1,2]=>[1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0]=>[2,1,1]=>[1,1,2]=>[1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0]=>[2,2]=>[2,2]=>[1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0]=>[3,1]=>[1,3]=>[1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0]=>[3,1]=>[1,3]=>[1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0]=>[3,1]=>[1,3]=>[1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0]=>[4]=>[4]=>[1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]=>[1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]=>[2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]=>[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]=>[3,1,1]=>[1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>[2,2,1]=>[1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]=>[2,2,1]=>[1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0]=>[1,4]=>[4,1]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>[3,2]=>[1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0]=>[2,3]=>[3,2]=>[1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0]=>[3,2]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0]=>[3,2]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0]=>[5]=>[5]=>[1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]=>[2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]=>[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]=>[3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]=>[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]=>[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]=>[4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]=>[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]=>[5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]=>[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]=>[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]=>[3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]=>[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]=>[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]=>[4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]=>[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]=>[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]=>[5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]=>[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]=>[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]=>[6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]=>[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]=>[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]=>[4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]=>[3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]=>[3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]=>[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]=>[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]=>[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>[3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]=>[4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>[3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]=>[3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]=>[4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>[3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]=>[3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]=>[3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]=>[2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]=>[2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]=>[2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]=>[2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]=>[5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]=>[3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]=>[4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]=>[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]=>[5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>[4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]=>[4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]=>[4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]=>[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]=>[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]=>[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]=>[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]=>[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]=>[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]=>[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>[7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]=>[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]=>[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]=>[5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,5,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]=>[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]=>[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,2]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]=>[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,7,1]=>[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>[1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,2,1]=>[1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,7,1]=>[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,2]=>[2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,8,1]=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,7,1]=>[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,6,1,1]=>[1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,8,1]=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,5,3]=>[3,5,1]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,7,2]=>[2,7,1]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,2,1]=>[1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,4,1]=>[1,4,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,7,1]=>[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,8,1]=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,6,2]=>[2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,4]=>[4,4,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,6,3]=>[3,6,1]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,7,1]=>[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,8,1]=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,6,1,1]=>[1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,5,2,1]=>[1,2,5,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,5,1,2]=>[2,1,5,1]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,7,2]=>[2,7,1]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5]=>[5,3,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,5,4]=>[4,5,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,6,1]=>[1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>[2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,1]=>[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,8,1]=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,6,1,1]=>[1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,7,1,1]=>[1,1,7,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,4,2,2]=>[2,2,4,1]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,1,2]=>[2,1,6,1]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,7]=>[7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,6]=>[6,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,4,5]=>[5,4,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]=>[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2]=>[2,1,6]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,8,1]=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,4,3,1]=>[1,3,4,1]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,5,1,2]=>[2,1,5,1]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,5,2,1]=>[1,2,5,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,6,1]=>[1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,6]=>[6,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,2]=>[2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,6,1,1]=>[1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,8,1]=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,2,2]=>[2,2,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,6,1]=>[1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,5,2]=>[2,5,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,6,1]=>[1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,8]=>[8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,7]=>[7,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,6,1,1]=>[1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,5,2,1]=>[1,2,5,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,1]=>[1,4,3,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1]=>[1,1,1,5,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[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]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,5,1,1]=>[1,1,5,2]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,6,1]=>[1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,7,1]=>[1,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,8]=>[8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[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]=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,1,3]=>[3,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,1,2,2]=>[2,2,1,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,4]=>[4,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,1,2,3]=>[3,2,1,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,1,5]=>[5,1,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,1,2,4]=>[4,2,1,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,6]=>[6,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1]=>[1,1,1,2,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[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]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,5]=>[5,2,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>[1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[2,4,3]=>[3,4,2]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,5,2]=>[2,5,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,7]=>[7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>[1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,5,1]=>[1,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,6]=>[6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,1,2,1]=>[1,2,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,1,2,1,1]=>[1,1,2,1,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>[1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,4,2]=>[2,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,6]=>[6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,3,2]=>[2,3,4]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[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]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4]=>[4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[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]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[5,3,1]=>[1,3,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,1,1,1]=>[1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[6,1,1,1]=>[1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[6,3]=>[3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,3]=>[3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,2,1]=>[1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[7,2]=>[2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,2]=>[2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,2]=>[2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,1]=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,1]=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,1]=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,1]=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1]=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,1]=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[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]=>[1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[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]=>[1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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]=>[1,1,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,4]=>[4,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[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]=>[1,1,3,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[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]=>[1,1,1,3,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[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]=>[1,1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,1,2]=>[2,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1,1,1]=>[1,1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,6]=>[6,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[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]=>[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[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]=>[1,1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,1,1,2]=>[2,1,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[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]=>[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,2,3]=>[3,2,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,2,5]=>[5,2,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]=>[1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,6]=>[6,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,2,2]=>[2,2,1,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[5,1,3]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]=>[6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,7]=>[7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,6]=>[6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]=>[5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,4]=>[4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,3]=>[3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[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]=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[2,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,8]=>[8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>[1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]=>[6,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[5,1,3]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>[4,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,3]=>[3,1,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>[1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[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]=>[3,1,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]=>[1,1,1,4,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,4,1]=>[1,4,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,2,1]=>[1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,3,1]=>[1,3,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,5,1]=>[1,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[6,1,2]=>[2,1,6]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[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]=>[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,7]=>[7,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,1,6]=>[6,1,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]
[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]=>[5,1,1,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[4,1,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,2,1,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[8,2]=>[2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[8,2]=>[2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[7,3]=>[3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[7,3]=>[3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,4]=>[4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[6,4]=>[4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[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]=>[2,2,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>[1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,1,1]=>[1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[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]=>[1,1,2,1,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,1,3,1]=>[1,3,1,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,1,3]=>[3,1,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[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]=>[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[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]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,5,3]=>[3,5,1]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1,1]=>[1,1,1,1,5,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[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]=>[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[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]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,1,1]=>[1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,1,1,1]=>[1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,3,1,1,1]=>[1,1,1,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,7,1,1]=>[1,1,7,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[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]=>[2,1,1,1,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,1,2]=>[2,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,1,2]=>[2,1,1,2,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]=>[1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,2,1,1,1]=>[1,1,1,2,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[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]=>[1,1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[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]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]=>[1,3,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,7,1]=>[1,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[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]=>[1,1,2,1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,2,1,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,6,1,1]=>[1,1,6,2]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,5,1,1]=>[1,1,5,2]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[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]=>[1,1,1,5,2]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,4,1,1,1]=>[1,1,1,4,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[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]=>[1,1,1,1,4,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>[1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[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]=>[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,1,2]=>[2,1,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>[1,2,1,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]=>[1,1,2,1,4]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[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]=>[1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[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]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>[1,1,1,3,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[5,1,3]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>[4,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,1,3]=>[3,1,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,2,3]=>[3,2,4]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[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]=>[1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,5,1]=>[1,5,2,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
reverse
Description
Return the reversal of a composition.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
Map
bounce path
Description
The bounce path determined by an integer composition.
searching the database
Sorry, this map was not found in the database.