Identifier
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,0]=>[1]=>[1]
[1,0,1,0]=>[1,0,1,0]=>[1,1]=>[1,1]
[1,1,0,0]=>[1,1,0,0]=>[2]=>[2]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[1,1,1]=>[1,1,1]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2,1]=>[1,2]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[1,2]=>[2,1]
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[2,1]=>[1,2]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[3]=>[3]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1]=>[1,1,1,1]
[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[2,1,1]=>[1,1,2]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[1,2,1]=>[1,2,1]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[2,1,1]=>[1,1,2]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[3,1]=>[1,3]
[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[1,1,2]=>[2,1,1]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,2]=>[2,2]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[1,2,1]=>[1,2,1]
[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[2,1,1]=>[1,1,2]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[3,1]=>[1,3]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[1,3]=>[3,1]
[1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[2,2]=>[2,2]
[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[3,1]=>[1,3]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[4]=>[4]
[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]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>[1,1,1,2]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>[1,1,2,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]=>[1,1,1,2]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>[1,1,3]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>[1,2,1,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>[1,2,2]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]=>[1,1,2,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]=>[1,1,1,2]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]=>[1,1,3]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>[1,3,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]=>[1,2,2]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]=>[1,1,3]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>[1,4]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]=>[2,1,1,1]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]=>[2,1,2]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>[2,2,1]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]=>[2,1,2]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>[2,3]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]=>[1,2,1,1]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]=>[1,2,2]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]=>[1,1,2,1]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]=>[1,1,1,2]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]=>[1,1,3]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]=>[1,3,1]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]=>[1,2,2]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]=>[1,1,3]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>[1,4]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]=>[3,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>[3,2]
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]=>[2,2,1]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]=>[2,1,2]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2]=>[2,3]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]=>[1,3,1]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]=>[1,2,2]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]=>[1,1,3]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>[1,4]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,4]=>[4,1]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[2,3]=>[3,2]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[3,2]=>[2,3]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>[1,4]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[5]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>[1,1,1,3]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>[1,1,2,2]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]=>[1,1,1,3]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>[1,1,3,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]=>[1,1,2,2]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]=>[1,1,1,3]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>[1,1,4]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>[1,2,1,2]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]=>[1,2,1,2]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>[1,2,3]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]=>[1,1,2,2]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]=>[1,1,1,3]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]=>[1,1,3,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]=>[1,1,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]=>[1,1,1,3]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>[1,1,4]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>[1,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>[1,3,2]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]=>[1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]=>[1,2,1,2]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>[1,2,3]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]=>[1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]=>[1,1,2,2]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]=>[1,1,1,3]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>[1,1,4]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>[1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>[1,3,2]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>[1,2,3]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>[1,1,4]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>[1,5]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]=>[2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]=>[2,1,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]=>[2,1,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>[2,1,3]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]=>[2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]=>[2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]=>[2,1,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]=>[2,1,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]=>[2,1,3]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>[2,3,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]=>[2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]=>[2,1,3]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>[2,4]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]=>[1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]=>[1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]=>[1,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]=>[1,2,3]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]=>[1,1,2,2]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]=>[1,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]=>[1,1,3,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]=>[1,1,2,2]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]=>[1,1,1,3]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>[1,1,4]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]=>[1,3,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]=>[1,3,2]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]=>[1,2,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]=>[1,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>[1,2,3]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]=>[1,1,3,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]=>[1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]=>[1,1,1,3]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>[1,1,4]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>[1,4,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>[1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>[1,2,3]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1,4]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>[1,5]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]=>[3,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]=>[3,1,2]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]=>[3,1,2]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]=>[3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]=>[2,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]=>[2,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]=>[2,1,1,2]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]=>[2,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]=>[2,3,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]=>[2,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]=>[2,1,3]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]=>[2,4]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]=>[1,3,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]=>[1,3,2]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]=>[1,2,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]=>[1,2,1,2]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>[1,2,3]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]=>[1,1,3,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]=>[1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]=>[1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>[1,1,4]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>[1,4,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>[1,3,2]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>[1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>[1,1,4]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>[1,5]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]=>[4,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]=>[4,2]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]=>[3,2,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]=>[3,1,2]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]=>[3,3]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]=>[2,3,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]=>[2,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]=>[2,1,3]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]=>[2,4]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>[1,4,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>[1,3,2]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>[1,2,3]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>[1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>[1,5]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]=>[5,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]=>[4,2]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]=>[3,3]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]=>[2,4]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>[1,5]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]=>[6]
[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]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[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]=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>[1,1,3,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>[1,1,4,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>[1,1,3,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>[1,1,5]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>[1,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[1,2,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>[1,1,4,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]=>[1,1,5]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>[1,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>[1,3,3]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>[1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>[1,2,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>[1,1,4,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]=>[1,1,5]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>[1,4,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>[1,4,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>[1,3,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>[1,3,1,2]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>[1,3,3]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>[1,2,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>[1,2,1,3]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>[1,2,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>[1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>[1,1,3,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>[1,1,2,3]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1,5]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>[1,4,2]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>[1,3,3]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>[1,2,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]=>[1,1,5]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>[1,6]
[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]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[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]=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[2,1,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>[2,2,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]=>[2,1,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>[2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]=>[2,2,1,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]=>[2,2,3]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]=>[2,1,3,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]=>[2,1,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]=>[2,1,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>[2,4,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]=>[2,3,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]=>[2,2,3]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]=>[2,1,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>[2,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]=>[1,2,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>[1,2,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>[1,1,4,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]=>[1,1,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]=>[1,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>[1,3,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>[1,2,3,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>[1,2,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>[1,1,4,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]=>[1,1,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>[1,4,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>[1,4,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>[1,3,2,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>[1,3,1,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>[1,3,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>[1,2,3,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>[1,2,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>[1,1,4,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>[1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]=>[1,1,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>[1,5,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>[1,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>[1,3,3]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>[1,2,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1,5]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1,6]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[3,1,1,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]=>[3,1,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[3,1,1,2]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>[3,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]=>[3,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]=>[3,1,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]=>[3,1,1,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]=>[3,1,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]=>[3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]=>[3,2,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]=>[3,1,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>[3,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>[2,2,1,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>[2,2,1,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]=>[2,2,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>[2,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]=>[2,1,3,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>[2,1,2,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]=>[2,1,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]=>[2,3,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]=>[2,3,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]=>[2,2,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]=>[2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]=>[2,1,3,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]=>[2,1,2,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]=>[2,1,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]=>[2,4,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]=>[2,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]=>[2,2,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]=>[2,1,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]=>[2,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]=>[1,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>[1,3,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>[1,2,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>[1,2,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]=>[1,1,3,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>[1,1,4,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>[1,1,3,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]=>[1,1,5]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>[1,4,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>[1,4,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>[1,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>[1,3,1,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>[1,3,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>[1,2,3,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>[1,2,2,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>[1,2,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>[1,1,4,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>[1,1,3,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]=>[1,1,5]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>[1,5,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>[1,4,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>[1,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>[1,2,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1,5]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>[1,6]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]=>[4,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[4,1,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]=>[4,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[4,1,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>[4,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]=>[3,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]=>[3,2,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]=>[3,1,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]=>[3,1,1,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]=>[3,1,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]=>[3,3,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]=>[3,2,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]=>[3,1,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]=>[3,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]=>[2,3,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]=>[2,3,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]=>[2,2,1,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]=>[2,2,3]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]=>[2,1,3,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]=>[2,1,2,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]=>[2,1,1,3]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]=>[2,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]=>[2,4,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]=>[2,3,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]=>[2,2,3]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]=>[2,1,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]=>[2,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>[1,4,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>[1,4,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>[1,3,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>[1,3,1,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>[1,3,3]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>[1,2,3,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>[1,2,2,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>[1,2,1,3]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>[1,2,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>[1,1,4,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>[1,1,3,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[1,1,2,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]=>[1,1,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>[1,5,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>[1,4,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>[1,3,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>[1,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]=>[1,1,5]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>[1,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]=>[5,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]=>[5,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]=>[4,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]=>[4,1,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]=>[4,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]=>[3,3,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]=>[3,2,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]=>[3,1,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]=>[3,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]=>[2,4,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]=>[2,3,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]=>[2,2,3]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]=>[2,1,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]=>[2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>[1,5,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>[1,4,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>[1,3,3]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>[1,2,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]=>[1,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>[1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]=>[5,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]=>[4,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]=>[3,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]=>[2,5]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>[1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]=>[7]
[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]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[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]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[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]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[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]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[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]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[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]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[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]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[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]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[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]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>[1,1,1,3,2]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[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]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[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]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[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]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[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]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[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]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[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]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[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]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[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]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[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]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[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]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>[1,1,4,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[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]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[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]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[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]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[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]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[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]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[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]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>[1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>[1,1,4,2]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,1,6]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[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]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[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]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[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]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[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]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[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]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[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]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[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]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[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]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[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]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[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]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[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]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[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]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[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]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[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]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[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]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[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]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[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]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,2,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[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]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[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]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[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]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>[1,1,2,1,3]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[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]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[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]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[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]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[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]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[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]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[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]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[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]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[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]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[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]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[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]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[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]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[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]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[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]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[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]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[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]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[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]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,5,1,1]=>[1,1,5,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1]=>[1,1,6]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[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]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[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]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[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]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[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]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[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]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[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]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[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]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[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]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]=>[1,2,5]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[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]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[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]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[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]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[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]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,5,1,1]=>[1,1,5,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,1]=>[1,1,6]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[1,4,1,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[1,4,1,2]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[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]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[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]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[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]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[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]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]=>[1,2,5]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[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]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[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]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[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]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[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]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[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]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[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]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[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]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,5,1,1]=>[1,1,5,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]=>[1,1,6]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]=>[1,5,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]=>[1,4,1,2]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]=>[1,3,1,3]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,1]=>[1,2,1,4]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,2,1]=>[1,2,5]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,5,1,1]=>[1,1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,4,1,1]=>[1,1,4,2]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1]=>[1,1,3,3]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1]=>[1,1,2,4]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1,5]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>[1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,5,1]=>[1,5,2]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,2,1]=>[1,2,5]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1,6]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>[1,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[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]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[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]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[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]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[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]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[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]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[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]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[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]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[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]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[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]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[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]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[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]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[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]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[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]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[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]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[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]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[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]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[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]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[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]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[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]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[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]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[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]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[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]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[2,1,5]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[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]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[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]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[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]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[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]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[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]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[2,2,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[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]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[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]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[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]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[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]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[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]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[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]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[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]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[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]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[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]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]=>[2,1,5]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]=>[2,2,4]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[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]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]=>[2,1,5]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]=>[2,2,4]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,2]=>[2,1,5]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>[2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]=>[2,2,4]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]=>[2,1,5]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]=>[2,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[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]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[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]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[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]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[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]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>[1,2,1,1,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[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]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[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]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[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]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[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]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[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]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[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]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[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]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[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]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[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]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[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]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[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]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]=>[1,2,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[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]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>[1,1,2,1,3]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[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]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[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]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[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]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[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]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[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]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[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]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[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]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[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]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[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]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[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]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[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]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[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]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1]=>[1,1,6]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[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]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[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]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[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]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[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]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[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]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[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]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[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]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,2,1]=>[1,2,5]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[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]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[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]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[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]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[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]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[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]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[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]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[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]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[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]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[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]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[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]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[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]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]=>[1,1,6]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[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]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]=>[1,2,5]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[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]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[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]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[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]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[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]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[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]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[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]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[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]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,1]=>[1,1,6]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]=>[1,5,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]=>[1,5,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,2,1]=>[1,2,5]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1,6]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]=>[1,6,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]=>[1,5,2]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,2,1]=>[1,2,5]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1,6]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1,7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[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]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[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]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[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]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>[3,1,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[3,2,1,2]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[3,2,1,2]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>[3,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>[3,1,3,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[3,2,1,2]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>[3,2,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>[3,1,3,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,1,2,2]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>[3,2,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[3,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[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]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[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]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[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]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[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]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[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]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[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]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[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]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[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]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[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]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[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]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[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]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[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]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[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]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[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]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[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]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[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]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[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]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]=>[2,4,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]=>[2,5,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]=>[2,6]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[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]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[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]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[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]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[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]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[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]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[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]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[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]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[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]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[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]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[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]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[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]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[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]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[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]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[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]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[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]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[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]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[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]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[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]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[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]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[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]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]=>[1,5,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]=>[1,5,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]=>[1,6,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]=>[1,5,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]=>[1,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[4,1,1,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[4,1,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[4,1,1,2]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[4,1,3]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[4,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[4,1,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[4,1,1,2]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[4,1,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[4,2,2]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[4,1,3]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[3,2,1,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[3,2,1,2]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[3,1,2,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>[3,1,3,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[3,1,2,2]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>[3,2,1,2]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>[3,1,3,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>[3,1,2,2]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]=>[3,4,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]=>[3,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[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]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[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]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]=>[2,4,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]=>[2,5,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]=>[2,6]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[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]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[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]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[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]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[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]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[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]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[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]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[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]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[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]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[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]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[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]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[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]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[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]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]=>[1,5,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]=>[1,5,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]=>[1,6,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]=>[1,5,2]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]=>[1,7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[5,1,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]=>[5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[5,1,2]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>[5,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]=>[4,2,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>[4,2,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]=>[4,1,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]=>[4,1,1,2]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>[4,1,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]=>[4,3,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>[4,2,2]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>[4,1,3]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]=>[4,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]=>[3,3,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>[3,3,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]=>[3,2,1,2]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>[3,2,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]=>[3,1,3,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]=>[3,1,2,2]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]=>[3,4,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>[3,3,2]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>[3,2,3]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]=>[3,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]=>[2,4,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]=>[2,4,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]=>[2,3,1,2]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[2,3,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]=>[2,2,1,3]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]=>[2,1,4,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]=>[2,1,3,2]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]=>[2,1,1,4]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]=>[2,5,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]=>[2,4,2]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]=>[2,3,3]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]=>[2,6]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]=>[1,5,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]=>[1,5,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]=>[1,4,1,2]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]=>[1,4,3]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]=>[1,3,1,3]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]=>[1,2,1,4]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]=>[1,1,5,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]=>[1,1,4,2]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]=>[1,1,2,4]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]=>[1,1,1,5]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]=>[1,6,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]=>[1,5,2]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]=>[1,4,3]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]=>[1,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]=>[6,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]=>[5,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]=>[5,1,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]=>[5,3]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]=>[4,3,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]=>[4,2,2]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]=>[4,1,3]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]=>[4,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]=>[3,4,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]=>[3,3,2]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]=>[3,2,3]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]=>[3,1,4]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]=>[3,5]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]=>[2,5,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]=>[2,4,2]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>[2,3,3]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]=>[2,2,4]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]=>[2,1,5]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]=>[2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]=>[1,6,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,5,1]=>[1,5,2]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]=>[1,4,3]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[1,3,4]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]=>[1,2,5]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]=>[1,1,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]=>[1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]=>[6,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]=>[5,3]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]=>[4,4]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]=>[3,5]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]=>[2,6]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]=>[1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]=>[8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]=>[8,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]=>[1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,7,1]=>[1,7,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1,7]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[1,9]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,2]=>[2,6,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,7,1]=>[1,7,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,2,1]=>[1,2,6]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1,7]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>[1,1,8]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>[1,10]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,5,3]=>[3,5,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,7,1]=>[1,7,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,4]=>[4,4,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,6,2]=>[2,6,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,4,1]=>[1,4,4]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,2,1]=>[1,2,6]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5]=>[5,3,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,6]=>[6,2,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,1]=>[1,7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,7]=>[7,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,6,1]=>[1,6,2]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>[2,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,6]=>[6,3,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,7]=>[7,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]=>[1,7,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,6,1]=>[1,6,2]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2]=>[2,1,6]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[1,1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,8]=>[8,2]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,6,1,1]=>[1,1,6,1]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,2,2]=>[2,2,5]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,2]=>[2,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[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]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>[1,8,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,5,2,1]=>[1,2,5,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[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]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,1,1,1]=>[1,1,1,6]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[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]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,1,1]=>[1,1,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,1,1]=>[1,1,7]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>[1,1,7]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[1,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[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]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,1]=>[1,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[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]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,1]=>[1,8]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4]=>[4,5]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[7,1,1]=>[1,1,7]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,1]=>[1,8]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,3]=>[3,6]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[7,1,1]=>[1,1,7]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,1]=>[1,8]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,2]=>[2,7]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,2,1]=>[1,2,6]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,1,1]=>[1,1,7]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1]=>[1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,7]=>[7,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,6]=>[6,3]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,2]=>[2,7]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,1]=>[1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9]=>[9]
[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]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]=>[1,6,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[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]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[3,6]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[4,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[5,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]=>[6,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[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]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,3]=>[3,7]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,4]=>[4,6]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]=>[5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,6]=>[6,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,7]=>[7,3]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10]=>[10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[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]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,1]=>[1,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1]=>[1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,8]=>[8,2]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,1]=>[1,9]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,1]=>[1,9]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,1]=>[1,9]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,1]=>[1,9]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,1]=>[1,9]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,1]=>[1,9]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,1]=>[1,10]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,2,1]=>[1,2,6]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,3,1]=>[1,3,5]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,4,1]=>[1,4,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,5,1]=>[1,5,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[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]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[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]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[6,1,2]=>[2,1,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>[4,1,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]=>[6,1,2]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[5,1,3]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,3]=>[3,1,5]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,1,1]=>[1,1,8]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,1,1,1]=>[1,1,1,7]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1,6]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[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]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[8,2]=>[2,8]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[7,3]=>[3,7]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,4]=>[4,6]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11]=>[11]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[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]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[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]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[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]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,2,3]=>[3,2,4]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]=>[1,3,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[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]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[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]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
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 $(i_k, i_{k-1}, \ldots, i_1)$.
searching the database
Sorry, this map was not found in the database.