Identifier
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]
[1,0,1,0]=>[2,1]=>[1,1]=>[1,1]
[1,1,0,0]=>[1,2]=>[2]=>[2]
[1,0,1,0,1,0]=>[2,1,3]=>[1,2]=>[2,1]
[1,0,1,1,0,0]=>[2,3,1]=>[2,1]=>[1,2]
[1,1,0,0,1,0]=>[3,1,2]=>[1,2]=>[2,1]
[1,1,0,1,0,0]=>[1,3,2]=>[2,1]=>[1,2]
[1,1,1,0,0,0]=>[1,2,3]=>[3]=>[3]
[1,0,1,0,1,0,1,0]=>[2,1,4,3]=>[1,2,1]=>[1,2,1]
[1,0,1,0,1,1,0,0]=>[2,4,1,3]=>[2,2]=>[2,2]
[1,0,1,1,0,0,1,0]=>[2,1,3,4]=>[1,3]=>[3,1]
[1,0,1,1,0,1,0,0]=>[2,3,1,4]=>[2,2]=>[2,2]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[3,1]=>[1,3]
[1,1,0,0,1,0,1,0]=>[3,1,4,2]=>[1,2,1]=>[1,2,1]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,2]=>[2,2]
[1,1,0,1,0,0,1,0]=>[3,1,2,4]=>[1,3]=>[3,1]
[1,1,0,1,0,1,0,0]=>[1,3,2,4]=>[2,2]=>[2,2]
[1,1,0,1,1,0,0,0]=>[1,3,4,2]=>[3,1]=>[1,3]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[1,3]=>[3,1]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[2,2]=>[2,2]
[1,1,1,0,1,0,0,0]=>[1,2,4,3]=>[3,1]=>[1,3]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4]=>[4]
[1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>[1,2,2]=>[2,2,1]
[1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>[2,3]=>[3,2]
[1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>[1,3,1]=>[1,3,1]
[1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>[2,2,1]=>[1,2,2]
[1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>[3,2]=>[2,3]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>[1,2,2]=>[2,2,1]
[1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>[2,3]=>[3,2]
[1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>[1,3,1]=>[1,3,1]
[1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>[2,2,1]=>[1,2,2]
[1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[3,2]=>[2,3]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>[1,4]=>[4,1]
[1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>[2,3]=>[3,2]
[1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>[3,2]=>[2,3]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[4,1]=>[1,4]
[1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>[1,2,2]=>[2,2,1]
[1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>[2,3]=>[3,2]
[1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>[1,3,1]=>[1,3,1]
[1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>[2,2,1]=>[1,2,2]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[3,2]=>[2,3]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>[1,2,2]=>[2,2,1]
[1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>[2,3]=>[3,2]
[1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>[1,3,1]=>[1,3,1]
[1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>[2,2,1]=>[1,2,2]
[1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[3,2]=>[2,3]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>[1,4]=>[4,1]
[1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>[2,3]=>[3,2]
[1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>[3,2]=>[2,3]
[1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>[4,1]=>[1,4]
[1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>[1,2,2]=>[2,2,1]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[2,3]=>[3,2]
[1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>[1,3,1]=>[1,3,1]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>[2,2,1]=>[1,2,2]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>[3,2]=>[2,3]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>[1,4]=>[4,1]
[1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>[2,3]=>[3,2]
[1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>[3,2]=>[2,3]
[1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>[4,1]=>[1,4]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[1,4]=>[4,1]
[1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>[2,3]=>[3,2]
[1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>[3,2]=>[2,3]
[1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>[4,1]=>[1,4]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>[1,2,2,1]=>[1,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>[2,3,1]=>[1,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>[1,3,2]=>[2,3,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>[2,2,2]=>[2,2,2]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>[3,3]=>[3,3]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[1,2,3]=>[3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>[2,4]=>[4,2]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[1,3,2]=>[2,3,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>[2,2,2]=>[2,2,2]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[3,3]=>[3,3]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>[1,4,1]=>[1,4,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>[2,3,1]=>[1,3,2]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>[3,2,1]=>[1,2,3]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>[4,2]=>[2,4]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>[1,2,2,1]=>[1,2,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[2,3,1]=>[1,3,2]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>[1,3,2]=>[2,3,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>[2,2,2]=>[2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>[3,3]=>[3,3]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>[1,2,3]=>[3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>[2,4]=>[4,2]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>[1,3,2]=>[2,3,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>[2,2,2]=>[2,2,2]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[3,3]=>[3,3]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>[1,4,1]=>[1,4,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>[2,3,1]=>[1,3,2]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>[3,2,1]=>[1,2,3]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>[4,2]=>[2,4]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>[1,2,3]=>[3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>[2,4]=>[4,2]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>[1,3,2]=>[2,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>[2,2,2]=>[2,2,2]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>[3,3]=>[3,3]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>[1,4,1]=>[1,4,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>[2,3,1]=>[1,3,2]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>[3,2,1]=>[1,2,3]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>[4,2]=>[2,4]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>[1,5]=>[5,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>[2,4]=>[4,2]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>[3,3]=>[3,3]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>[4,2]=>[2,4]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[5,1]=>[1,5]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>[1,2,2,1]=>[1,2,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>[2,3,1]=>[1,3,2]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>[1,3,2]=>[2,3,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>[2,2,2]=>[2,2,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>[3,3]=>[3,3]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[1,2,3]=>[3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>[2,4]=>[4,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[1,3,2]=>[2,3,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>[2,2,2]=>[2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[3,3]=>[3,3]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>[1,4,1]=>[1,4,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>[2,3,1]=>[1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>[3,2,1]=>[1,2,3]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[4,2]=>[2,4]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>[1,2,2,1]=>[1,2,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>[2,3,1]=>[1,3,2]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>[1,3,2]=>[2,3,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>[2,2,2]=>[2,2,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>[3,3]=>[3,3]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>[1,2,3]=>[3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>[2,4]=>[4,2]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>[1,3,2]=>[2,3,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>[2,2,2]=>[2,2,2]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[3,3]=>[3,3]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>[1,4,1]=>[1,4,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>[2,3,1]=>[1,3,2]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>[3,2,1]=>[1,2,3]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>[4,2]=>[2,4]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[1,2,3]=>[3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>[2,4]=>[4,2]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>[1,3,2]=>[2,3,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>[2,2,2]=>[2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>[3,3]=>[3,3]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>[1,4,1]=>[1,4,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>[2,3,1]=>[1,3,2]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>[3,2,1]=>[1,2,3]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>[4,2]=>[2,4]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>[1,5]=>[5,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>[2,4]=>[4,2]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>[3,3]=>[3,3]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>[4,2]=>[2,4]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>[5,1]=>[1,5]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>[1,2,2,1]=>[1,2,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>[2,3,1]=>[1,3,2]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>[1,3,2]=>[2,3,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>[2,2,2]=>[2,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[3,3]=>[3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>[1,2,3]=>[3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>[2,4]=>[4,2]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[1,3,2]=>[2,3,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>[2,2,2]=>[2,2,2]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[3,3]=>[3,3]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>[1,4,1]=>[1,4,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>[2,3,1]=>[1,3,2]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>[3,2,1]=>[1,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>[4,2]=>[2,4]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>[1,2,3]=>[3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>[2,4]=>[4,2]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>[1,3,2]=>[2,3,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>[2,2,2]=>[2,2,2]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>[3,3]=>[3,3]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>[1,4,1]=>[1,4,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>[2,3,1]=>[1,3,2]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>[3,2,1]=>[1,2,3]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>[4,2]=>[2,4]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>[1,5]=>[5,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>[2,4]=>[4,2]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>[3,3]=>[3,3]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>[4,2]=>[2,4]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>[5,1]=>[1,5]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>[1,2,3]=>[3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[2,4]=>[4,2]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>[1,3,2]=>[2,3,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>[2,2,2]=>[2,2,2]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>[3,3]=>[3,3]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>[1,4,1]=>[1,4,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>[2,3,1]=>[1,3,2]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>[3,2,1]=>[1,2,3]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>[4,2]=>[2,4]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[1,5]=>[5,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>[2,4]=>[4,2]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>[3,3]=>[3,3]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>[4,2]=>[2,4]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>[5,1]=>[1,5]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[1,5]=>[5,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>[2,4]=>[4,2]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[3,3]=>[3,3]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>[4,2]=>[2,4]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>[5,1]=>[1,5]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6]=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[2,3,2]=>[2,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>[1,3,3]=>[3,3,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>[2,2,3]=>[3,2,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>[3,4]=>[4,3]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[1,2,3,1]=>[1,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>[2,4,1]=>[1,4,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[1,3,2,1]=>[1,2,3,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>[3,3,1]=>[1,3,3]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>[1,4,2]=>[2,4,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>[2,3,2]=>[2,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[3,2,2]=>[2,2,3]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[4,3]=>[3,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>[2,3,2]=>[2,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>[1,3,3]=>[3,3,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>[2,2,3]=>[3,2,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>[3,4]=>[4,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>[1,2,3,1]=>[1,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[2,4,1]=>[1,4,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[1,3,2,1]=>[1,2,3,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>[3,3,1]=>[1,3,3]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>[1,4,2]=>[2,4,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>[2,3,2]=>[2,3,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>[3,2,2]=>[2,2,3]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[4,3]=>[3,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[1,2,4]=>[4,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>[2,5]=>[5,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>[1,3,3]=>[3,3,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>[2,2,3]=>[3,2,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>[3,4]=>[4,3]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>[1,4,2]=>[2,4,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>[2,3,2]=>[2,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>[3,2,2]=>[2,2,3]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>[4,3]=>[3,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>[1,5,1]=>[1,5,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>[2,4,1]=>[1,4,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>[3,3,1]=>[1,3,3]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>[4,2,1]=>[1,2,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>[5,2]=>[2,5]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[2,3,2]=>[2,3,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>[1,3,3]=>[3,3,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>[3,4]=>[4,3]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[1,2,3,1]=>[1,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>[2,4,1]=>[1,4,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[1,3,2,1]=>[1,2,3,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>[3,3,1]=>[1,3,3]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>[1,4,2]=>[2,4,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>[2,3,2]=>[2,3,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[3,2,2]=>[2,2,3]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[4,3]=>[3,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>[2,3,2]=>[2,3,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>[1,3,3]=>[3,3,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>[3,4]=>[4,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>[1,2,3,1]=>[1,3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[2,4,1]=>[1,4,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[1,3,2,1]=>[1,2,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>[3,3,1]=>[1,3,3]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>[1,4,2]=>[2,4,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>[2,3,2]=>[2,3,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>[3,2,2]=>[2,2,3]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[4,3]=>[3,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[1,2,4]=>[4,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>[2,5]=>[5,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>[1,3,3]=>[3,3,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>[2,2,3]=>[3,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>[3,4]=>[4,3]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>[1,4,2]=>[2,4,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>[2,3,2]=>[2,3,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>[3,2,2]=>[2,2,3]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>[4,3]=>[3,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>[1,5,1]=>[1,5,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>[2,4,1]=>[1,4,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>[3,3,1]=>[1,3,3]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>[4,2,1]=>[1,2,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>[5,2]=>[2,5]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>[2,3,2]=>[2,3,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>[1,3,3]=>[3,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>[2,2,3]=>[3,2,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>[3,4]=>[4,3]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>[1,2,3,1]=>[1,3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[2,4,1]=>[1,4,2]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[1,3,2,1]=>[1,2,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>[2,2,2,1]=>[1,2,2,2]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>[3,3,1]=>[1,3,3]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>[1,4,2]=>[2,4,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>[2,3,2]=>[2,3,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[3,2,2]=>[2,2,3]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[4,3]=>[3,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>[1,2,4]=>[4,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>[2,5]=>[5,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>[1,3,3]=>[3,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>[2,2,3]=>[3,2,2]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>[3,4]=>[4,3]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>[1,4,2]=>[2,4,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>[2,3,2]=>[2,3,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>[3,2,2]=>[2,2,3]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>[4,3]=>[3,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>[1,5,1]=>[1,5,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>[2,4,1]=>[1,4,2]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>[3,3,1]=>[1,3,3]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>[4,2,1]=>[1,2,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>[5,2]=>[2,5]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>[1,2,4]=>[4,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>[2,5]=>[5,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>[1,3,3]=>[3,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>[2,2,3]=>[3,2,2]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>[3,4]=>[4,3]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>[1,4,2]=>[2,4,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[2,3,2]=>[2,3,2]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>[3,2,2]=>[2,2,3]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[4,3]=>[3,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[1,5,1]=>[1,5,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>[2,4,1]=>[1,4,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>[3,3,1]=>[1,3,3]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>[4,2,1]=>[1,2,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>[5,2]=>[2,5]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>[1,6]=>[6,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>[2,5]=>[5,2]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>[3,4]=>[4,3]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>[4,3]=>[3,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[5,2]=>[2,5]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[6,1]=>[1,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[2,3,2]=>[2,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>[1,3,3]=>[3,3,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>[2,2,3]=>[3,2,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>[3,4]=>[4,3]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[1,2,3,1]=>[1,3,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>[2,4,1]=>[1,4,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[1,3,2,1]=>[1,2,3,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>[3,3,1]=>[1,3,3]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>[1,4,2]=>[2,4,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>[2,3,2]=>[2,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[3,2,2]=>[2,2,3]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[4,3]=>[3,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>[2,3,2]=>[2,3,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>[1,3,3]=>[3,3,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>[2,2,3]=>[3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>[3,4]=>[4,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>[1,2,3,1]=>[1,3,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[2,4,1]=>[1,4,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[1,3,2,1]=>[1,2,3,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>[3,3,1]=>[1,3,3]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[1,4,2]=>[2,4,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>[2,3,2]=>[2,3,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>[3,2,2]=>[2,2,3]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[4,3]=>[3,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[1,2,4]=>[4,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>[2,5]=>[5,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>[1,3,3]=>[3,3,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>[2,2,3]=>[3,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>[3,4]=>[4,3]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>[1,4,2]=>[2,4,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>[2,3,2]=>[2,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>[3,2,2]=>[2,2,3]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>[4,3]=>[3,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>[1,5,1]=>[1,5,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>[2,4,1]=>[1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>[3,3,1]=>[1,3,3]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>[4,2,1]=>[1,2,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[5,2]=>[2,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[2,3,2]=>[2,3,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>[2,2,3]=>[3,2,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>[3,4]=>[4,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[1,2,3,1]=>[1,3,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>[2,4,1]=>[1,4,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[1,3,2,1]=>[1,2,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>[3,3,1]=>[1,3,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>[1,4,2]=>[2,4,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>[2,3,2]=>[2,3,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[3,2,2]=>[2,2,3]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[4,3]=>[3,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>[2,3,2]=>[2,3,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>[2,2,3]=>[3,2,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>[3,4]=>[4,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>[1,2,3,1]=>[1,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[2,4,1]=>[1,4,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[1,3,2,1]=>[1,2,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>[3,3,1]=>[1,3,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>[1,4,2]=>[2,4,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>[2,3,2]=>[2,3,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>[3,2,2]=>[2,2,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[4,3]=>[3,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[1,2,4]=>[4,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>[2,5]=>[5,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>[1,3,3]=>[3,3,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>[2,2,3]=>[3,2,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>[3,4]=>[4,3]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>[1,4,2]=>[2,4,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>[2,3,2]=>[2,3,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>[3,2,2]=>[2,2,3]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>[4,3]=>[3,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>[1,5,1]=>[1,5,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>[2,4,1]=>[1,4,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>[3,3,1]=>[1,3,3]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>[4,2,1]=>[1,2,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>[5,2]=>[2,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>[2,3,2]=>[2,3,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>[1,3,3]=>[3,3,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>[2,2,3]=>[3,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>[3,4]=>[4,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>[1,2,3,1]=>[1,3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>[2,4,1]=>[1,4,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[1,3,2,1]=>[1,2,3,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>[2,2,2,1]=>[1,2,2,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>[3,3,1]=>[1,3,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>[1,4,2]=>[2,4,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>[2,3,2]=>[2,3,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[3,2,2]=>[2,2,3]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[4,3]=>[3,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>[2,5]=>[5,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>[1,3,3]=>[3,3,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>[2,2,3]=>[3,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>[3,4]=>[4,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>[1,4,2]=>[2,4,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>[2,3,2]=>[2,3,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>[3,2,2]=>[2,2,3]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>[4,3]=>[3,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>[1,5,1]=>[1,5,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>[2,4,1]=>[1,4,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>[3,3,1]=>[1,3,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>[4,2,1]=>[1,2,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>[5,2]=>[2,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[1,2,4]=>[4,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>[2,5]=>[5,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>[1,3,3]=>[3,3,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>[2,2,3]=>[3,2,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>[3,4]=>[4,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>[1,4,2]=>[2,4,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[2,3,2]=>[2,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>[3,2,2]=>[2,2,3]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[4,3]=>[3,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[1,5,1]=>[1,5,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>[2,4,1]=>[1,4,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>[3,3,1]=>[1,3,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>[4,2,1]=>[1,2,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>[5,2]=>[2,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>[1,6]=>[6,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>[2,5]=>[5,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>[3,4]=>[4,3]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>[4,3]=>[3,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>[5,2]=>[2,5]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>[6,1]=>[1,6]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[2,3,2]=>[2,3,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>[1,3,3]=>[3,3,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>[2,2,3]=>[3,2,2]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>[3,4]=>[4,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[1,2,3,1]=>[1,3,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>[2,4,1]=>[1,4,2]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[1,3,2,1]=>[1,2,3,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>[2,2,2,1]=>[1,2,2,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>[3,3,1]=>[1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>[1,4,2]=>[2,4,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>[2,3,2]=>[2,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[3,2,2]=>[2,2,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[4,3]=>[3,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>[2,3,2]=>[2,3,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>[1,3,3]=>[3,3,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>[2,2,3]=>[3,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>[3,4]=>[4,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>[1,2,3,1]=>[1,3,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[2,4,1]=>[1,4,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[1,3,2,1]=>[1,2,3,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>[2,2,2,1]=>[1,2,2,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>[3,3,1]=>[1,3,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[1,4,2]=>[2,4,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>[2,3,2]=>[2,3,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>[3,2,2]=>[2,2,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[4,3]=>[3,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[1,2,4]=>[4,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>[2,5]=>[5,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>[1,3,3]=>[3,3,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>[2,2,3]=>[3,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>[3,4]=>[4,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>[1,4,2]=>[2,4,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>[2,3,2]=>[2,3,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>[3,2,2]=>[2,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>[4,3]=>[3,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>[1,5,1]=>[1,5,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>[2,4,1]=>[1,4,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>[3,3,1]=>[1,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>[4,2,1]=>[1,2,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>[5,2]=>[2,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>[2,3,2]=>[2,3,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>[1,3,3]=>[3,3,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>[2,2,3]=>[3,2,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>[3,4]=>[4,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>[1,2,3,1]=>[1,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>[2,4,1]=>[1,4,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[1,3,2,1]=>[1,2,3,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>[2,2,2,1]=>[1,2,2,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>[3,3,1]=>[1,3,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>[1,4,2]=>[2,4,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>[2,3,2]=>[2,3,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[3,2,2]=>[2,2,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[4,3]=>[3,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>[1,2,4]=>[4,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>[2,5]=>[5,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>[1,3,3]=>[3,3,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>[2,2,3]=>[3,2,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>[3,4]=>[4,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>[1,4,2]=>[2,4,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>[2,3,2]=>[2,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>[3,2,2]=>[2,2,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>[4,3]=>[3,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>[1,5,1]=>[1,5,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>[2,4,1]=>[1,4,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>[3,3,1]=>[1,3,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>[4,2,1]=>[1,2,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>[5,2]=>[2,5]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>[1,2,4]=>[4,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>[2,5]=>[5,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>[1,3,3]=>[3,3,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>[2,2,3]=>[3,2,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>[3,4]=>[4,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>[1,4,2]=>[2,4,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[2,3,2]=>[2,3,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>[3,2,2]=>[2,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[4,3]=>[3,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[1,5,1]=>[1,5,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>[2,4,1]=>[1,4,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>[3,3,1]=>[1,3,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>[4,2,1]=>[1,2,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>[5,2]=>[2,5]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>[1,6]=>[6,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>[2,5]=>[5,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>[3,4]=>[4,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>[4,3]=>[3,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>[5,2]=>[2,5]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>[6,1]=>[1,6]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>[2,3,2]=>[2,3,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>[1,3,3]=>[3,3,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>[2,2,3]=>[3,2,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[3,4]=>[4,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>[1,2,3,1]=>[1,3,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>[2,4,1]=>[1,4,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[1,3,2,1]=>[1,2,3,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>[2,2,2,1]=>[1,2,2,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>[3,3,1]=>[1,3,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>[1,4,2]=>[2,4,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>[2,3,2]=>[2,3,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[3,2,2]=>[2,2,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[4,3]=>[3,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>[1,2,4]=>[4,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>[2,5]=>[5,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>[1,3,3]=>[3,3,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>[2,2,3]=>[3,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>[3,4]=>[4,3]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>[1,4,2]=>[2,4,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>[2,3,2]=>[2,3,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>[3,2,2]=>[2,2,3]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>[4,3]=>[3,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>[1,5,1]=>[1,5,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>[2,4,1]=>[1,4,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>[3,3,1]=>[1,3,3]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>[4,2,1]=>[1,2,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>[5,2]=>[2,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>[1,2,4]=>[4,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>[2,5]=>[5,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>[1,3,3]=>[3,3,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>[2,2,3]=>[3,2,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>[3,4]=>[4,3]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>[1,4,2]=>[2,4,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[2,3,2]=>[2,3,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>[3,2,2]=>[2,2,3]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[4,3]=>[3,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[1,5,1]=>[1,5,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>[2,4,1]=>[1,4,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>[3,3,1]=>[1,3,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>[4,2,1]=>[1,2,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>[5,2]=>[2,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>[1,6]=>[6,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>[2,5]=>[5,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>[3,4]=>[4,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>[4,3]=>[3,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>[5,2]=>[2,5]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>[6,1]=>[1,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>[1,2,4]=>[4,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[2,5]=>[5,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>[1,3,3]=>[3,3,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>[2,2,3]=>[3,2,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>[3,4]=>[4,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>[1,4,2]=>[2,4,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[2,3,2]=>[2,3,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[3,2,2]=>[2,2,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[4,3]=>[3,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[1,5,1]=>[1,5,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[2,4,1]=>[1,4,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>[3,3,1]=>[1,3,3]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>[4,2,1]=>[1,2,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>[5,2]=>[2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[1,6]=>[6,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>[2,5]=>[5,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>[3,4]=>[4,3]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>[4,3]=>[3,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>[5,2]=>[2,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>[6,1]=>[1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[1,6]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]=>[2,5]=>[5,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>[3,4]=>[4,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[4,3]=>[3,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>[5,2]=>[2,5]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>[6,1]=>[1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[7]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,8,7]=>[3,4,1]=>[1,4,3]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,8,5,7]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7]=>[2,4,2]=>[2,4,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,8,5,7]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,8,5,7]=>[3,3,2]=>[2,3,3]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,8,3,5,7]=>[1,4,3]=>[3,4,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,8,3,5,7]=>[2,3,3]=>[3,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>[3,2,3]=>[3,2,3]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[4,4]=>[4,4]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[1,2,2,3]=>[3,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7,8]=>[2,3,3]=>[3,3,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7,8]=>[1,3,4]=>[4,3,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7,8]=>[2,2,4]=>[4,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7,8]=>[3,5]=>[5,3]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5,8]=>[2,4,2]=>[2,4,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5,8]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5,8]=>[3,3,2]=>[2,3,3]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5,8]=>[2,3,3]=>[3,3,2]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>[4,4]=>[4,4]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,7,8,5]=>[2,5,1]=>[1,5,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,6,3,7,8,5]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,6,1,3,7,8,5]=>[3,4,1]=>[1,4,3]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,3,8,5]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,6,1,7,3,8,5]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,8,5]=>[4,3,1]=>[1,3,4]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,6,7,8,3,5]=>[1,5,2]=>[2,5,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>[2,4,2]=>[2,4,2]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,8,3,5]=>[3,3,2]=>[2,3,3]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,8,3,5]=>[4,2,2]=>[2,2,4]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,7,8,1,3,5]=>[5,3]=>[3,5]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,8,6]=>[3,4,1]=>[1,4,3]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,7,8,5,6]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,7,8,5,6]=>[2,4,2]=>[2,4,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,7,3,8,5,6]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4,7,1,3,8,5,6]=>[3,3,2]=>[2,3,3]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,7,8,3,5,6]=>[1,4,3]=>[3,4,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,8,3,5,6]=>[2,3,3]=>[3,3,2]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]=>[3,2,3]=>[3,2,3]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[4,4]=>[4,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6,8]=>[2,3,3]=>[3,3,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6,8]=>[1,3,4]=>[4,3,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6,8]=>[3,5]=>[5,3]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6,8]=>[2,4,2]=>[2,4,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,8]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6,8]=>[3,3,2]=>[2,3,3]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>[3,2,3]=>[3,2,3]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,8,6]=>[2,5,1]=>[1,5,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,7,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,7,8,6]=>[3,4,1]=>[1,4,3]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,7,3,8,6]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,8,6]=>[4,3,1]=>[1,3,4]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,7,8,3,6]=>[1,5,2]=>[2,5,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,7,8,3,6]=>[2,4,2]=>[2,4,2]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,7,8,3,6]=>[3,3,2]=>[2,3,3]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,5,7,1,8,3,6]=>[4,2,2]=>[2,2,4]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,7,8,1,3,6]=>[5,3]=>[3,5]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,6,7]=>[1,2,2,3]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,8,5,6,7]=>[2,3,3]=>[3,3,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,4,8,3,5,6,7]=>[1,3,4]=>[4,3,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,5,6,7]=>[2,2,4]=>[4,2,2]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,8,1,3,5,6,7]=>[3,5]=>[5,3]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,8,6,7]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,8,6,7]=>[2,4,2]=>[2,4,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,4,5,8,3,6,7]=>[1,4,3]=>[3,4,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,5,8,3,6,7]=>[2,3,3]=>[3,3,2]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]=>[3,2,3]=>[3,2,3]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,8,1,3,6,7]=>[4,4]=>[4,4]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,8,7]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,8,7]=>[2,5,1]=>[1,5,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,8,7]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,8,7]=>[4,3,1]=>[1,3,4]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,8,3,7]=>[1,5,2]=>[2,5,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,8,3,7]=>[2,4,2]=>[2,4,2]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>[3,3,2]=>[2,3,3]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,8,3,7]=>[4,2,2]=>[2,2,4]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,5,6,8,1,3,7]=>[5,3]=>[3,5]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[1,2,5]=>[5,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8]=>[2,6]=>[6,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7,8]=>[1,3,4]=>[4,3,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7,8]=>[2,2,4]=>[4,2,2]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7,8]=>[3,5]=>[5,3]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7,8]=>[1,4,3]=>[3,4,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7,8]=>[2,3,3]=>[3,3,2]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>[3,2,3]=>[3,2,3]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>[4,4]=>[4,4]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3,8]=>[1,5,2]=>[2,5,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3,8]=>[2,4,2]=>[2,4,2]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3,8]=>[3,3,2]=>[2,3,3]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3,8]=>[4,2,2]=>[2,2,4]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3,8]=>[5,3]=>[3,5]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,3]=>[1,6,1]=>[1,6,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>[2,5,1]=>[1,5,2]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,5,1,6,7,8,3]=>[3,4,1]=>[1,4,3]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,5,6,1,7,8,3]=>[4,3,1]=>[1,3,4]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,5,6,7,1,8,3]=>[5,2,1]=>[1,2,5]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,3]=>[6,2]=>[2,6]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,8,7]=>[3,4,1]=>[1,4,3]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,8,4,7]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,8,4,7]=>[2,4,2]=>[2,4,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,8,4,7]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,8,4,7]=>[3,3,2]=>[2,3,3]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,8,3,4,7]=>[1,4,3]=>[3,4,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,8,3,4,7]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,8,3,4,7]=>[3,2,3]=>[3,2,3]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>[4,4]=>[4,4]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7,8]=>[1,2,2,3]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7,8]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7,8]=>[1,3,4]=>[4,3,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7,8]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7,8]=>[3,5]=>[5,3]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4,8]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4,8]=>[2,4,2]=>[2,4,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4,8]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4,8]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4,8]=>[3,3,2]=>[2,3,3]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4,8]=>[1,4,3]=>[3,4,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4,8]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4,8]=>[3,2,3]=>[3,2,3]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4,8]=>[4,4]=>[4,4]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,7,8,4]=>[2,5,1]=>[1,5,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,8,4]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5,6,1,3,7,8,4]=>[3,4,1]=>[1,4,3]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,3,8,4]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,7,3,8,4]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,6,7,1,3,8,4]=>[4,3,1]=>[1,3,4]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,5,6,7,8,3,4]=>[1,5,2]=>[2,5,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>[2,4,2]=>[2,4,2]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]=>[3,3,2]=>[2,3,3]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,5,6,7,1,8,3,4]=>[4,2,2]=>[2,2,4]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>[5,3]=>[3,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,8,6]=>[3,4,1]=>[1,4,3]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,7,8,4,6]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,8,4,6]=>[2,4,2]=>[2,4,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,7,3,8,4,6]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,7,3,8,4,6]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,7,1,3,8,4,6]=>[3,3,2]=>[2,3,3]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,7,8,3,4,6]=>[1,4,3]=>[3,4,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,7,8,3,4,6]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,7,1,8,3,4,6]=>[3,2,3]=>[3,2,3]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>[4,4]=>[4,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6,8]=>[1,2,2,3]=>[3,2,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6,8]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6,8]=>[1,3,4]=>[4,3,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6,8]=>[2,4,2]=>[2,4,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6,8]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,8]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6,8]=>[3,3,2]=>[2,3,3]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6,8]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6,8]=>[4,4]=>[4,4]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,8,6]=>[2,5,1]=>[1,5,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,7,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,7,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,7,8,6]=>[3,4,1]=>[1,4,3]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,7,4,8,6]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,8,6]=>[4,3,1]=>[1,3,4]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,7,8,4,6]=>[1,5,2]=>[2,5,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,7,8,4,6]=>[2,4,2]=>[2,4,2]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,7,8,4,6]=>[3,3,2]=>[2,3,3]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,7,1,8,4,6]=>[4,2,2]=>[2,2,4]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,7,8,1,4,6]=>[5,3]=>[3,5]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,8,4,6,7]=>[1,2,2,3]=>[3,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,8,4,6,7]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,8,3,4,6,7]=>[1,3,4]=>[4,3,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,8,3,4,6,7]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,5,8,1,3,4,6,7]=>[3,5]=>[5,3]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,8,6,7]=>[2,4,2]=>[2,4,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,8,6,7]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]=>[3,3,2]=>[2,3,3]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,5,8,4,6,7]=>[1,4,3]=>[3,4,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,5,8,4,6,7]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]=>[3,2,3]=>[3,2,3]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,8,1,4,6,7]=>[4,4]=>[4,4]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,8,7]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,8,7]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,8,7]=>[4,3,1]=>[1,3,4]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,8,4,7]=>[2,4,2]=>[2,4,2]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,8,4,7]=>[3,3,2]=>[2,3,3]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,8,4,7]=>[4,2,2]=>[2,2,4]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,6,8,1,4,7]=>[5,3]=>[3,5]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7,8]=>[1,2,5]=>[5,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7,8]=>[2,6]=>[6,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7,8]=>[1,3,4]=>[4,3,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7,8]=>[2,2,4]=>[4,2,2]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7,8]=>[3,5]=>[5,3]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7,8]=>[1,4,3]=>[3,4,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7,8]=>[2,3,3]=>[3,3,2]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7,8]=>[3,2,3]=>[3,2,3]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]=>[4,4]=>[4,4]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4,8]=>[2,4,2]=>[2,4,2]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8]=>[3,3,2]=>[2,3,3]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4,8]=>[4,2,2]=>[2,2,4]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4,8]=>[5,3]=>[3,5]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,5,6,7,8,4]=>[1,6,1]=>[1,6,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[2,5,1]=>[1,5,2]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,8,4]=>[3,4,1]=>[1,4,3]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,7,8,4]=>[4,3,1]=>[1,3,4]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,7,1,8,4]=>[5,2,1]=>[1,2,5]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,6,7,8,1,4]=>[6,2]=>[2,6]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,8,5]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,8,5]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,8,5]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,6,3,7,8,4,5]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,6,1,3,7,8,4,5]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,6,7,3,8,4,5]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,6,1,7,3,8,4,5]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,6,7,1,3,8,4,5]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,6,7,8,3,4,5]=>[1,4,3]=>[3,4,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,6,1,7,8,3,4,5]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,6,7,1,8,3,4,5]=>[3,2,3]=>[3,2,3]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>[4,4]=>[4,4]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5,8]=>[1,2,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5,8]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5,8]=>[1,3,4]=>[4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5,8]=>[2,2,4]=>[4,2,2]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5,8]=>[3,5]=>[5,3]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5,8]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5,8]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,8]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5,8]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5,8]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5,8]=>[3,2,3]=>[3,2,3]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5,8]=>[4,4]=>[4,4]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,7,8,5]=>[2,5,1]=>[1,5,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,8,5]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,7,8,5]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,4,8,5]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,3,6,1,7,4,8,5]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,3,6,7,1,4,8,5]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,6,7,8,4,5]=>[1,5,2]=>[2,5,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,8,4,5]=>[4,2,2]=>[2,2,4]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,6,7,8,1,4,5]=>[5,3]=>[3,5]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,8,4,5,7]=>[1,2,2,3]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,8,4,5,7]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,8,3,4,5,7]=>[1,3,4]=>[4,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,8,3,4,5,7]=>[2,2,4]=>[4,2,2]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,6,8,1,3,4,5,7]=>[3,5]=>[5,3]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,8,5,7]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,8,5,7]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,8,5,7]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,8,5,7]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,8,4,5,7]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]=>[3,2,3]=>[3,2,3]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,8,1,4,5,7]=>[4,4]=>[4,4]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,8,7]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,8,7]=>[2,5,1]=>[1,5,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,8,7]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,8,7]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,8,5,7]=>[1,5,2]=>[2,5,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,8,5,7]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,8,5,7]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,8,5,7]=>[4,2,2]=>[2,2,4]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,8,1,5,7]=>[5,3]=>[3,5]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7,8]=>[1,2,5]=>[5,2,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7,8]=>[2,6]=>[6,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7,8]=>[1,3,4]=>[4,3,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7,8]=>[2,2,4]=>[4,2,2]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7,8]=>[3,5]=>[5,3]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7,8]=>[1,4,3]=>[3,4,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7,8]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[3,2,3]=>[3,2,3]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]=>[4,4]=>[4,4]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5,8]=>[1,5,2]=>[2,5,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5,8]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5,8]=>[4,2,2]=>[2,2,4]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5,8]=>[5,3]=>[3,5]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,6,7,8,5]=>[1,6,1]=>[1,6,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[2,5,1]=>[1,5,2]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,6,1,7,8,5]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,6,7,1,8,5]=>[5,2,1]=>[1,2,5]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,7,8,1,5]=>[6,2]=>[2,6]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,7,3,8,4,5,6]=>[1,2,2,3]=>[3,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,7,1,3,8,4,5,6]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,7,8,3,4,5,6]=>[1,3,4]=>[4,3,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>[2,2,4]=>[4,2,2]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,7,8,1,3,4,5,6]=>[3,5]=>[5,3]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,1,7,3,4,8,5,6]=>[1,2,3,2]=>[2,3,2,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,7,1,3,4,8,5,6]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,7,4,8,5,6]=>[1,3,2,2]=>[2,2,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,1,4,8,5,6]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,1,3,7,8,4,5,6]=>[1,4,3]=>[3,4,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,1,7,8,4,5,6]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,7,1,8,4,5,6]=>[3,2,3]=>[3,2,3]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[4,4]=>[4,4]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,8,6]=>[1,2,4,1]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>[2,5,1]=>[1,5,2]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,8,6]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,8,6]=>[1,4,2,1]=>[1,2,4,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,8,6]=>[3,2,2,1]=>[1,2,2,3]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,8,6]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,7,8,5,6]=>[1,5,2]=>[2,5,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,4,7,1,8,5,6]=>[4,2,2]=>[2,2,4]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,4,7,8,1,5,6]=>[5,3]=>[3,5]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6,8]=>[1,2,5]=>[5,2,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6,8]=>[2,6]=>[6,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6,8]=>[1,3,4]=>[4,3,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6,8]=>[2,2,4]=>[4,2,2]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6,8]=>[3,5]=>[5,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6,8]=>[1,4,3]=>[3,4,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6,8]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6,8]=>[3,2,3]=>[3,2,3]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>[4,4]=>[4,4]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[1,5,2]=>[2,5,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6,8]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6,8]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6,8]=>[4,2,2]=>[2,2,4]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6,8]=>[5,3]=>[3,5]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,8,6]=>[1,6,1]=>[1,6,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[2,5,1]=>[1,5,2]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,7,8,6]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,7,8,6]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,6]=>[5,2,1]=>[1,2,5]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,7,8,1,6]=>[6,2]=>[2,6]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7]=>[1,2,5]=>[5,2,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7]=>[2,6]=>[6,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,8,4,5,6,7]=>[1,3,4]=>[4,3,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,1,8,4,5,6,7]=>[2,2,4]=>[4,2,2]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,8,1,4,5,6,7]=>[3,5]=>[5,3]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,4,8,5,6,7]=>[1,4,3]=>[3,4,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,7]=>[2,3,3]=>[3,3,2]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>[3,2,3]=>[3,2,3]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[4,4]=>[4,4]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,8,6,7]=>[1,5,2]=>[2,5,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]=>[2,4,2]=>[2,4,2]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>[3,3,2]=>[2,3,3]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,8,6,7]=>[4,2,2]=>[2,2,4]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,8,1,6,7]=>[5,3]=>[3,5]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[1,6,1]=>[1,6,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,8,7]=>[2,5,1]=>[1,5,2]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,8,7]=>[3,4,1]=>[1,4,3]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,8,7]=>[4,3,1]=>[1,3,4]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7]=>[5,2,1]=>[1,2,5]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,7]=>[6,2]=>[2,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8]=>[1,7]=>[7,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8]=>[2,6]=>[6,2]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8]=>[3,5]=>[5,3]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[4,4]=>[4,4]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[5,3]=>[3,5]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[6,2]=>[2,6]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[7,1]=>[1,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,8,7]=>[3,4,1]=>[1,4,3]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,8,5,7]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,8,5,7]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,8,5,7]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,8,2,5,7]=>[1,4,3]=>[3,4,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,8,2,5,7]=>[2,3,3]=>[3,3,2]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,8,2,5,7]=>[3,2,3]=>[3,2,3]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[4,4]=>[4,4]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7,8]=>[2,3,3]=>[3,3,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7,8]=>[1,3,4]=>[4,3,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7,8]=>[2,2,4]=>[4,2,2]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7,8]=>[3,5]=>[5,3]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5,8]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5,8]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5,8]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5,8]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5,8]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5,8]=>[1,4,3]=>[3,4,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5,8]=>[2,3,3]=>[3,3,2]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5,8]=>[3,2,3]=>[3,2,3]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5,8]=>[4,4]=>[4,4]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,7,8,5]=>[2,5,1]=>[1,5,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,6,2,7,8,5]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,2,7,8,5]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,6,1,2,7,8,5]=>[3,4,1]=>[1,4,3]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,6,7,2,8,5]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,6,7,2,8,5]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,6,1,7,2,8,5]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,6,7,1,2,8,5]=>[4,3,1]=>[1,3,4]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,6,7,8,2,5]=>[1,5,2]=>[2,5,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,6,7,8,2,5]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,8,2,5]=>[4,2,2]=>[2,2,4]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,7,8,1,2,5]=>[5,3]=>[3,5]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,8,6]=>[3,4,1]=>[1,4,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,7,8,5,6]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,7,2,8,5,6]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,7,1,2,8,5,6]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,7,8,2,5,6]=>[2,3,3]=>[3,3,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>[3,2,3]=>[3,2,3]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>[4,4]=>[4,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6,8]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6,8]=>[2,3,3]=>[3,3,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6,8]=>[1,3,4]=>[4,3,1]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6,8]=>[3,5]=>[5,3]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6,8]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6,8]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6,8]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6,8]=>[1,4,3]=>[3,4,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6,8]=>[2,3,3]=>[3,3,2]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6,8]=>[3,2,3]=>[3,2,3]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6,8]=>[4,4]=>[4,4]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,8,6]=>[2,5,1]=>[1,5,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,7,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,7,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,7,8,6]=>[3,4,1]=>[1,4,3]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,7,2,8,6]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,7,2,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,7,2,8,6]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,8,6]=>[4,3,1]=>[1,3,4]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,8,2,6]=>[1,5,2]=>[2,5,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,7,8,2,6]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,7,1,8,2,6]=>[4,2,2]=>[2,2,4]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,7,8,1,2,6]=>[5,3]=>[3,5]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,6,7]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,8,5,6,7]=>[2,3,3]=>[3,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,8,2,5,6,7]=>[1,3,4]=>[4,3,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,8,2,5,6,7]=>[2,2,4]=>[4,2,2]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,8,1,2,5,6,7]=>[3,5]=>[5,3]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,8,6,7]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,8,6,7]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,8,6,7]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,4,5,8,2,6,7]=>[1,4,3]=>[3,4,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,5,8,2,6,7]=>[2,3,3]=>[3,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,1,8,2,6,7]=>[3,2,3]=>[3,2,3]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[4,4]=>[4,4]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,8,7]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,8,7]=>[2,5,1]=>[1,5,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,8,7]=>[3,4,1]=>[1,4,3]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,8,7]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,8,7]=>[4,3,1]=>[1,3,4]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>[1,5,2]=>[2,5,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,8,2,7]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,8,2,7]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,8,2,7]=>[4,2,2]=>[2,2,4]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,6,8,1,2,7]=>[5,3]=>[3,5]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>[1,2,5]=>[5,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8]=>[2,6]=>[6,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7,8]=>[1,3,4]=>[4,3,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7,8]=>[2,2,4]=>[4,2,2]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7,8]=>[3,5]=>[5,3]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7,8]=>[1,4,3]=>[3,4,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7,8]=>[2,3,3]=>[3,3,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>[3,2,3]=>[3,2,3]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[4,4]=>[4,4]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2,8]=>[1,5,2]=>[2,5,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2,8]=>[2,4,2]=>[2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2,8]=>[3,3,2]=>[2,3,3]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,8]=>[4,2,2]=>[2,2,4]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[5,3]=>[3,5]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2]=>[1,6,1]=>[1,6,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1,5,6,7,8,2]=>[2,5,1]=>[1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,5,1,6,7,8,2]=>[3,4,1]=>[1,4,3]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,5,6,1,7,8,2]=>[4,3,1]=>[1,3,4]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2]=>[5,2,1]=>[1,2,5]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[6,2]=>[2,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,8,7]=>[3,4,1]=>[1,4,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,8,4,7]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,8,4,7]=>[2,4,2]=>[2,4,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,8,4,7]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,8,4,7]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]=>[3,3,2]=>[2,3,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,8,2,4,7]=>[1,4,3]=>[3,4,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,8,2,4,7]=>[2,3,3]=>[3,3,2]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>[3,2,3]=>[3,2,3]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[4,4]=>[4,4]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7,8]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7,8]=>[2,3,3]=>[3,3,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7,8]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7,8]=>[2,2,4]=>[4,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7,8]=>[3,5]=>[5,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4,8]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]=>[2,4,2]=>[2,4,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4,8]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4,8]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4,8]=>[3,3,2]=>[2,3,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4,8]=>[1,4,3]=>[3,4,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4,8]=>[2,3,3]=>[3,3,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>[3,2,3]=>[3,2,3]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4,8]=>[4,4]=>[4,4]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,7,8,4]=>[2,5,1]=>[1,5,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,5,6,2,7,8,4]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5,6,1,2,7,8,4]=>[3,4,1]=>[1,4,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,7,2,8,4]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5,6,7,1,2,8,4]=>[4,3,1]=>[1,3,4]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,5,6,7,8,2,4]=>[1,5,2]=>[2,5,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>[2,4,2]=>[2,4,2]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>[3,3,2]=>[2,3,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,8,2,4]=>[4,2,2]=>[2,2,4]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>[5,3]=>[3,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,8,6]=>[3,4,1]=>[1,4,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,7,8,4,6]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,7,8,4,6]=>[2,4,2]=>[2,4,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,7,2,8,4,6]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,7,1,2,8,4,6]=>[3,3,2]=>[2,3,3]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,7,8,2,4,6]=>[1,4,3]=>[3,4,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,7,8,2,4,6]=>[2,3,3]=>[3,3,2]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,7,1,8,2,4,6]=>[3,2,3]=>[3,2,3]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[4,4]=>[4,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,8]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6,8]=>[2,3,3]=>[3,3,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6,8]=>[2,2,4]=>[4,2,2]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6,8]=>[3,5]=>[5,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,8]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>[2,4,2]=>[2,4,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,8]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,8]=>[3,3,2]=>[2,3,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>[1,4,3]=>[3,4,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6,8]=>[2,3,3]=>[3,3,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>[3,2,3]=>[3,2,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>[4,4]=>[4,4]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,7,8,6]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,8,6]=>[2,5,1]=>[1,5,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,7,8,6]=>[3,4,1]=>[1,4,3]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,8,6]=>[4,3,1]=>[1,3,4]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,7,8,4,6]=>[1,5,2]=>[2,5,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>[2,4,2]=>[2,4,2]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,7,8,4,6]=>[3,3,2]=>[2,3,3]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,6]=>[4,2,2]=>[2,2,4]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>[5,3]=>[3,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,8,4,6,7]=>[2,3,3]=>[3,3,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,8,2,4,6,7]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,8,2,4,6,7]=>[2,2,4]=>[4,2,2]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,5,8,1,2,4,6,7]=>[3,5]=>[5,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,8,6,7]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,8,6,7]=>[2,4,2]=>[2,4,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]=>[3,3,2]=>[2,3,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,5,8,4,6,7]=>[1,4,3]=>[3,4,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,5,8,4,6,7]=>[2,3,3]=>[3,3,2]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>[3,2,3]=>[3,2,3]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[4,4]=>[4,4]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,8,7]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>[2,5,1]=>[1,5,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,8,7]=>[3,4,1]=>[1,4,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,8,7]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,8,7]=>[4,3,1]=>[1,3,4]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,8,4,7]=>[1,5,2]=>[2,5,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,8,4,7]=>[2,4,2]=>[2,4,2]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,8,4,7]=>[3,3,2]=>[2,3,3]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,8,4,7]=>[4,2,2]=>[2,2,4]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,6,8,2,4,7]=>[5,3]=>[3,5]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7,8]=>[1,2,5]=>[5,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7,8]=>[2,6]=>[6,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7,8]=>[1,3,4]=>[4,3,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7,8]=>[2,2,4]=>[4,2,2]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7,8]=>[3,5]=>[5,3]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7,8]=>[1,4,3]=>[3,4,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7,8]=>[2,3,3]=>[3,3,2]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7,8]=>[3,2,3]=>[3,2,3]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>[4,4]=>[4,4]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4,8]=>[1,5,2]=>[2,5,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4,8]=>[2,4,2]=>[2,4,2]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4,8]=>[3,3,2]=>[2,3,3]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,8]=>[4,2,2]=>[2,2,4]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4,8]=>[5,3]=>[3,5]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,5,6,7,8,4]=>[1,6,1]=>[1,6,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>[2,5,1]=>[1,5,2]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,5,2,6,7,8,4]=>[3,4,1]=>[1,4,3]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,5,6,2,7,8,4]=>[4,3,1]=>[1,3,4]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,5,6,7,2,8,4]=>[5,2,1]=>[1,2,5]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,6,7,8,2,4]=>[6,2]=>[2,6]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,8,5]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,8,5]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,8,5]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,7,8,4,5]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,6,1,2,7,8,4,5]=>[2,4,2]=>[2,4,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,6,7,2,8,4,5]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,6,7,8,2,4,5]=>[1,4,3]=>[3,4,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,8,2,4,5]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,6,7,1,8,2,4,5]=>[3,2,3]=>[3,2,3]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[4,4]=>[4,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5,8]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5,8]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>[1,3,4]=>[4,3,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5,8]=>[2,2,4]=>[4,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5,8]=>[3,5]=>[5,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5,8]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>[2,4,2]=>[2,4,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5,8]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5,8]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5,8]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5,8]=>[1,4,3]=>[3,4,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5,8]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5,8]=>[3,2,3]=>[3,2,3]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5,8]=>[4,4]=>[4,4]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,8,5]=>[2,5,1]=>[1,5,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,8,5]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,7,8,5]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,4,8,5]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,6,2,7,4,8,5]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,6,7,2,4,8,5]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,6,7,8,4,5]=>[1,5,2]=>[2,5,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,6,7,8,4,5]=>[2,4,2]=>[2,4,2]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,8,4,5]=>[4,2,2]=>[2,2,4]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,6,7,8,2,4,5]=>[5,3]=>[3,5]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,8,4,5,7]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,8,4,5,7]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,8,2,4,5,7]=>[1,3,4]=>[4,3,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,8,2,4,5,7]=>[2,2,4]=>[4,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,6,8,1,2,4,5,7]=>[3,5]=>[5,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,8,5,7]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,8,5,7]=>[2,4,2]=>[2,4,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,8,5,7]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,8,4,5,7]=>[1,4,3]=>[3,4,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,8,4,5,7]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,8,4,5,7]=>[3,2,3]=>[3,2,3]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,8,2,4,5,7]=>[4,4]=>[4,4]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,8,7]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,8,7]=>[2,5,1]=>[1,5,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,8,7]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,8,7]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,8,7]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,8,7]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,8,5,7]=>[1,5,2]=>[2,5,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>[2,4,2]=>[2,4,2]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,8,5,7]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,8,5,7]=>[4,2,2]=>[2,2,4]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,8,2,5,7]=>[5,3]=>[3,5]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7,8]=>[2,6]=>[6,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7,8]=>[1,3,4]=>[4,3,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7,8]=>[2,2,4]=>[4,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7,8]=>[3,5]=>[5,3]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7,8]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7,8]=>[4,4]=>[4,4]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8]=>[1,5,2]=>[2,5,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5,8]=>[4,2,2]=>[2,2,4]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5,8]=>[5,3]=>[3,5]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,8,5]=>[1,6,1]=>[1,6,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[2,5,1]=>[1,5,2]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,6,7,8,5]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,6,2,7,8,5]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,6,7,2,8,5]=>[5,2,1]=>[1,2,5]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,6,7,8,2,5]=>[6,2]=>[2,6]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,7,2,8,4,5,6]=>[1,2,2,3]=>[3,2,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,7,1,2,8,4,5,6]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,7,8,2,4,5,6]=>[1,3,4]=>[4,3,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,7,1,8,2,4,5,6]=>[2,2,4]=>[4,2,2]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,7,8,1,2,4,5,6]=>[3,5]=>[5,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,7,2,4,8,5,6]=>[1,2,3,2]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,7,1,2,4,8,5,6]=>[2,4,2]=>[2,4,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,7,4,8,5,6]=>[1,3,2,2]=>[2,2,3,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,7,8,4,5,6]=>[1,4,3]=>[3,4,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,3,2,7,8,4,5,6]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>[3,2,3]=>[3,2,3]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,3,7,8,2,4,5,6]=>[4,4]=>[4,4]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,8,6]=>[1,2,4,1]=>[1,4,2,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,8,6]=>[2,5,1]=>[1,5,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,8,6]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>[1,4,2,1]=>[1,2,4,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,8,6]=>[3,2,2,1]=>[1,2,2,3]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,8,6]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,7,8,5,6]=>[1,5,2]=>[2,5,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>[2,4,2]=>[2,4,2]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,7,8,5,6]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,3,4,7,2,8,5,6]=>[4,2,2]=>[2,2,4]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,3,4,7,8,2,5,6]=>[5,3]=>[3,5]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6,8]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6,8]=>[2,6]=>[6,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6,8]=>[1,3,4]=>[4,3,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6,8]=>[2,2,4]=>[4,2,2]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6,8]=>[3,5]=>[5,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>[1,4,3]=>[3,4,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6,8]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6,8]=>[3,2,3]=>[3,2,3]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]=>[4,4]=>[4,4]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6,8]=>[1,5,2]=>[2,5,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]=>[2,4,2]=>[2,4,2]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6,8]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6,8]=>[4,2,2]=>[2,2,4]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6,8]=>[5,3]=>[3,5]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,8,6]=>[1,6,1]=>[1,6,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[2,5,1]=>[1,5,2]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,7,8,6]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,7,8,6]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,7,2,8,6]=>[5,2,1]=>[1,2,5]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,7,8,2,6]=>[6,2]=>[2,6]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[1,2,5]=>[5,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,8,1,2,4,5,6,7]=>[2,6]=>[6,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,8,4,5,6,7]=>[1,3,4]=>[4,3,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,2,8,4,5,6,7]=>[2,2,4]=>[4,2,2]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,3,8,2,4,5,6,7]=>[3,5]=>[5,3]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,7]=>[1,4,3]=>[3,4,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,3,2,4,8,5,6,7]=>[2,3,3]=>[3,3,2]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>[3,2,3]=>[3,2,3]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[4,4]=>[4,4]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]=>[1,5,2]=>[2,5,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>[2,4,2]=>[2,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>[3,3,2]=>[2,3,3]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,8,6,7]=>[4,2,2]=>[2,2,4]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,3,4,5,8,2,6,7]=>[5,3]=>[3,5]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]=>[1,6,1]=>[1,6,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,8,7]=>[2,5,1]=>[1,5,2]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,8,7]=>[3,4,1]=>[1,4,3]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,8,7]=>[4,3,1]=>[1,3,4]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,8,7]=>[5,2,1]=>[1,2,5]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,8,2,7]=>[6,2]=>[2,6]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8]=>[1,7]=>[7,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8]=>[2,6]=>[6,2]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8]=>[3,5]=>[5,3]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[4,4]=>[4,4]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7,8]=>[5,3]=>[3,5]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,8]=>[6,2]=>[2,6]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,2]=>[7,1]=>[1,7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7]=>[3,4,1]=>[1,4,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,8,3,7]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,8,3,7]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,8,3,7]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,8,3,7]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,8,2,3,7]=>[1,4,3]=>[3,4,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,8,2,3,7]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]=>[3,2,3]=>[3,2,3]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[4,4]=>[4,4]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7,8]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7,8]=>[1,3,4]=>[4,3,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7,8]=>[2,2,4]=>[4,2,2]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8]=>[3,5]=>[5,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3,8]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3,8]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3,8]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3,8]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3,8]=>[1,4,3]=>[3,4,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3,8]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3,8]=>[3,2,3]=>[3,2,3]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[4,4]=>[4,4]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,7,8,3]=>[2,5,1]=>[1,5,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,6,1,2,7,8,3]=>[3,4,1]=>[1,4,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5,6,1,7,2,8,3]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,8,3]=>[4,3,1]=>[1,3,4]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,5,6,7,8,2,3]=>[1,5,2]=>[2,5,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,5,6,1,7,8,2,3]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,3]=>[4,2,2]=>[2,2,4]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[5,3]=>[3,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,8,6]=>[3,4,1]=>[1,4,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,7,8,3,6]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,7,8,3,6]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,7,2,8,3,6]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,7,8,2,3,6]=>[1,4,3]=>[3,4,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,7,8,2,3,6]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,5,7,1,8,2,3,6]=>[3,2,3]=>[3,2,3]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[4,4]=>[4,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6,8]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6,8]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6,8]=>[1,3,4]=>[4,3,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6,8]=>[2,2,4]=>[4,2,2]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6,8]=>[3,5]=>[5,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6,8]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6,8]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,8]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6,8]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6,8]=>[1,4,3]=>[3,4,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6,8]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6,8]=>[3,2,3]=>[3,2,3]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>[4,4]=>[4,4]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,8,6]=>[2,5,1]=>[1,5,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,7,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,7,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,7,8,6]=>[3,4,1]=>[1,4,3]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,7,3,8,6]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,7,3,8,6]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,8,6]=>[4,3,1]=>[1,3,4]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,7,8,3,6]=>[1,5,2]=>[2,5,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,7,8,3,6]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,7,8,3,6]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,7,2,8,3,6]=>[4,2,2]=>[2,2,4]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,7,8,2,3,6]=>[5,3]=>[3,5]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,8,3,6,7]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,8,3,6,7]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,8,2,3,6,7]=>[1,3,4]=>[4,3,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,8,2,3,6,7]=>[2,2,4]=>[4,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,8,1,2,3,6,7]=>[3,5]=>[5,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,8,6,7]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,8,6,7]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,8,6,7]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,8,3,6,7]=>[1,4,3]=>[3,4,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,8,3,6,7]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]=>[3,2,3]=>[3,2,3]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,8,2,3,6,7]=>[4,4]=>[4,4]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,8,7]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,8,7]=>[2,5,1]=>[1,5,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,8,7]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,8,7]=>[4,3,1]=>[1,3,4]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[1,5,2]=>[2,5,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,8,3,7]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,8,3,7]=>[4,2,2]=>[2,2,4]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,6,8,2,3,7]=>[5,3]=>[3,5]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7,8]=>[1,2,5]=>[5,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7,8]=>[2,6]=>[6,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7,8]=>[1,3,4]=>[4,3,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7,8]=>[2,2,4]=>[4,2,2]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7,8]=>[3,5]=>[5,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7,8]=>[1,4,3]=>[3,4,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7,8]=>[2,3,3]=>[3,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>[3,2,3]=>[3,2,3]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7,8]=>[4,4]=>[4,4]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3,8]=>[1,5,2]=>[2,5,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3,8]=>[2,4,2]=>[2,4,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3,8]=>[3,3,2]=>[2,3,3]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3,8]=>[4,2,2]=>[2,2,4]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3,8]=>[5,3]=>[3,5]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,3]=>[1,6,1]=>[1,6,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,5,6,7,8,3]=>[2,5,1]=>[1,5,2]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,5,2,6,7,8,3]=>[3,4,1]=>[1,4,3]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,5,6,2,7,8,3]=>[4,3,1]=>[1,3,4]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,5,6,7,2,8,3]=>[5,2,1]=>[1,2,5]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,5,6,7,8,2,3]=>[6,2]=>[2,6]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,8,5]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,8,5]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,8,5]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,8,5]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,6,2,7,8,3,5]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,6,1,2,7,8,3,5]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,6,7,2,8,3,5]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,6,1,7,2,8,3,5]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,6,7,1,2,8,3,5]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,6,7,8,2,3,5]=>[1,4,3]=>[3,4,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,6,1,7,8,2,3,5]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[3,2,3]=>[3,2,3]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>[4,4]=>[4,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5,8]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5,8]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5,8]=>[1,3,4]=>[4,3,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8]=>[2,2,4]=>[4,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5,8]=>[3,5]=>[5,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5,8]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5,8]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5,8]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]=>[1,4,3]=>[3,4,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5,8]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>[3,2,3]=>[3,2,3]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]=>[4,4]=>[4,4]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,7,8,5]=>[2,5,1]=>[1,5,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,8,5]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,7,8,5]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,7,8,5]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,5]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,6,7,3,8,5]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,2,7,3,8,5]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,8,5]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,8,3,5]=>[4,2,2]=>[2,2,4]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,6,7,8,2,3,5]=>[5,3]=>[3,5]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,5,7]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,8,3,5,7]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,8,2,3,5,7]=>[1,3,4]=>[4,3,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,8,2,3,5,7]=>[2,2,4]=>[4,2,2]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,8,1,2,3,5,7]=>[3,5]=>[5,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,8,5,7]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,8,5,7]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,8,3,5,7]=>[1,4,3]=>[3,4,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,8,3,5,7]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]=>[3,2,3]=>[3,2,3]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[4,4]=>[4,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,8,7]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,8,7]=>[2,5,1]=>[1,5,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,8,7]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,8,7]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,8,5,7]=>[1,5,2]=>[2,5,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,8,5,7]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,8,5,7]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,8,5,7]=>[4,2,2]=>[2,2,4]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,8,3,5,7]=>[5,3]=>[3,5]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7,8]=>[1,2,5]=>[5,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7,8]=>[2,6]=>[6,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7,8]=>[1,3,4]=>[4,3,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7,8]=>[2,2,4]=>[4,2,2]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7,8]=>[3,5]=>[5,3]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7,8]=>[1,4,3]=>[3,4,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7,8]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[3,2,3]=>[3,2,3]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]=>[4,4]=>[4,4]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>[1,5,2]=>[2,5,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5,8]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5,8]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5,8]=>[4,2,2]=>[2,2,4]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5,8]=>[5,3]=>[3,5]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,6,7,8,5]=>[1,6,1]=>[1,6,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,6,7,8,5]=>[2,5,1]=>[1,5,2]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,6,7,8,5]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,6,3,7,8,5]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,6,7,3,8,5]=>[5,2,1]=>[1,2,5]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,6,7,8,3,5]=>[6,2]=>[2,6]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,7,2,8,3,5,6]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,7,1,2,8,3,5,6]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,7,8,2,3,5,6]=>[1,3,4]=>[4,3,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,7,1,8,2,3,5,6]=>[2,2,4]=>[4,2,2]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,7,8,1,2,3,5,6]=>[3,5]=>[5,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,7,2,3,8,5,6]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,7,1,2,3,8,5,6]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,7,3,8,5,6]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,7,2,3,8,5,6]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,7,8,3,5,6]=>[1,4,3]=>[3,4,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,7,8,3,5,6]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,7,2,8,3,5,6]=>[3,2,3]=>[3,2,3]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,7,8,2,3,5,6]=>[4,4]=>[4,4]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,8,6]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,8,6]=>[2,5,1]=>[1,5,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,8,6]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,8,6]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,8,6]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,7,8,5,6]=>[1,5,2]=>[2,5,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,4,7,3,8,5,6]=>[4,2,2]=>[2,2,4]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>[5,3]=>[3,5]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6,8]=>[1,2,5]=>[5,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6,8]=>[2,6]=>[6,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6,8]=>[1,3,4]=>[4,3,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6,8]=>[2,2,4]=>[4,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6,8]=>[3,5]=>[5,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>[1,4,3]=>[3,4,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6,8]=>[3,2,3]=>[3,2,3]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]=>[4,4]=>[4,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>[1,5,2]=>[2,5,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6,8]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6,8]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6,8]=>[4,2,2]=>[2,2,4]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6,8]=>[5,3]=>[3,5]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,8,6]=>[1,6,1]=>[1,6,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>[2,5,1]=>[1,5,2]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,7,8,6]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,7,8,6]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,7,3,8,6]=>[5,2,1]=>[1,2,5]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,7,8,3,6]=>[6,2]=>[2,6]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,8,2,3,5,6,7]=>[1,2,5]=>[5,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,8,1,2,3,5,6,7]=>[2,6]=>[6,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,7]=>[1,3,4]=>[4,3,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,4,2,8,3,5,6,7]=>[2,2,4]=>[4,2,2]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,4,8,2,3,5,6,7]=>[3,5]=>[5,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]=>[1,4,3]=>[3,4,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,4,2,3,8,5,6,7]=>[2,3,3]=>[3,3,2]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>[3,2,3]=>[3,2,3]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[4,4]=>[4,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,8,6,7]=>[1,5,2]=>[2,5,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>[2,4,2]=>[2,4,2]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>[3,3,2]=>[2,3,3]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,8,6,7]=>[4,2,2]=>[2,2,4]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,4,5,8,3,6,7]=>[5,3]=>[3,5]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>[1,6,1]=>[1,6,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,8,7]=>[2,5,1]=>[1,5,2]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,8,7]=>[3,4,1]=>[1,4,3]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,8,7]=>[4,3,1]=>[1,3,4]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,8,7]=>[5,2,1]=>[1,2,5]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,8,3,7]=>[6,2]=>[2,6]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8]=>[1,7]=>[7,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8]=>[2,6]=>[6,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8]=>[3,5]=>[5,3]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[4,4]=>[4,4]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7,8]=>[5,3]=>[3,5]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3,8]=>[6,2]=>[2,6]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,3]=>[7,1]=>[1,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4]=>[1,2,2,2,1]=>[1,2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,8,4]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,8,4]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,1,6,2,7,8,3,4]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[5,6,1,2,7,8,3,4]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[5,1,6,7,2,8,3,4]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,6,1,7,2,8,3,4]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,1,6,7,8,2,3,4]=>[1,4,3]=>[3,4,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,6,1,7,8,2,3,4]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[4,4]=>[4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4,8]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4,8]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4,8]=>[1,3,4]=>[4,3,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4,8]=>[2,2,4]=>[4,2,2]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4,8]=>[3,5]=>[5,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4,8]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4,8]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4,8]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4,8]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4,8]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4,8]=>[1,4,3]=>[3,4,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4,8]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4,8]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4,8]=>[4,4]=>[4,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,7,8,4]=>[2,5,1]=>[1,5,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,8,4]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,7,8,4]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,5,2,6,7,3,8,4]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,5,6,2,7,3,8,4]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,8,4]=>[4,3,1]=>[1,3,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[5,1,2,6,7,8,3,4]=>[1,5,2]=>[2,5,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,5,2,6,7,8,3,4]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,5,6,2,7,8,3,4]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,5,6,7,2,8,3,4]=>[4,2,2]=>[2,2,4]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>[5,3]=>[3,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,8,3,4,7]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,8,3,4,7]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,1,6,8,2,3,4,7]=>[1,3,4]=>[4,3,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[5,6,1,8,2,3,4,7]=>[2,2,4]=>[4,2,2]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,8,1,2,3,4,7]=>[3,5]=>[5,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,8,4,7]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,8,4,7]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,8,4,7]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,8,3,4,7]=>[1,4,3]=>[3,4,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,8,3,4,7]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>[4,4]=>[4,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,8,7]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,8,7]=>[2,5,1]=>[1,5,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,8,7]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,8,7]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,8,7]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,8,7]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,8,7]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,8,7]=>[4,3,1]=>[1,3,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[1,5,2]=>[2,5,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,8,4,7]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,8,4,7]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,8,4,7]=>[4,2,2]=>[2,2,4]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,8,3,4,7]=>[5,3]=>[3,5]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7,8]=>[1,2,5]=>[5,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7,8]=>[2,6]=>[6,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7,8]=>[1,3,4]=>[4,3,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7,8]=>[2,2,4]=>[4,2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7,8]=>[3,5]=>[5,3]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7,8]=>[1,4,3]=>[3,4,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7,8]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7,8]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[4,4]=>[4,4]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4,8]=>[1,5,2]=>[2,5,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4,8]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4,8]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4,8]=>[4,2,2]=>[2,2,4]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4,8]=>[5,3]=>[3,5]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,6,7,8,4]=>[1,6,1]=>[1,6,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,6,7,8,4]=>[2,5,1]=>[1,5,2]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,6,7,8,4]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,5,6,3,7,8,4]=>[4,3,1]=>[1,3,4]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,5,6,7,3,8,4]=>[5,2,1]=>[1,2,5]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,5,6,7,8,3,4]=>[6,2]=>[2,6]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,7,2,8,3,4,6]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,7,1,2,8,3,4,6]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,7,8,2,3,4,6]=>[1,3,4]=>[4,3,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,7,1,8,2,3,4,6]=>[2,2,4]=>[4,2,2]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,7,8,1,2,3,4,6]=>[3,5]=>[5,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,7,2,3,8,4,6]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,7,1,2,3,8,4,6]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,7,3,8,4,6]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,7,2,3,8,4,6]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,7,8,3,4,6]=>[1,4,3]=>[3,4,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,7,8,3,4,6]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>[4,4]=>[4,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,8,6]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,8,6]=>[2,5,1]=>[1,5,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,8,6]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,8,6]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,8,6]=>[4,3,1]=>[1,3,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,7,8,4,6]=>[1,5,2]=>[2,5,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,8,4,6]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,7,8,4,6]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,3,8,4,6]=>[4,2,2]=>[2,2,4]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,7,8,3,4,6]=>[5,3]=>[3,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6,8]=>[1,2,5]=>[5,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6,8]=>[2,6]=>[6,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>[1,3,4]=>[4,3,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6,8]=>[2,2,4]=>[4,2,2]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6,8]=>[3,5]=>[5,3]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6,8]=>[1,4,3]=>[3,4,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6,8]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6,8]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>[4,4]=>[4,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6,8]=>[1,5,2]=>[2,5,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6,8]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6,8]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,8]=>[4,2,2]=>[2,2,4]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6,8]=>[5,3]=>[3,5]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,8,6]=>[1,6,1]=>[1,6,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>[2,5,1]=>[1,5,2]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,7,8,6]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,7,8,6]=>[4,3,1]=>[1,3,4]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,7,4,8,6]=>[5,2,1]=>[1,2,5]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,7,8,4,6]=>[6,2]=>[2,6]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,8,2,3,4,6,7]=>[1,2,5]=>[5,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[5,8,1,2,3,4,6,7]=>[2,6]=>[6,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,6,7]=>[1,3,4]=>[4,3,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,2,8,3,4,6,7]=>[2,2,4]=>[4,2,2]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,8,2,3,4,6,7]=>[3,5]=>[5,3]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,3,8,4,6,7]=>[1,4,3]=>[3,4,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,2,3,8,4,6,7]=>[2,3,3]=>[3,3,2]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>[3,2,3]=>[3,2,3]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>[4,4]=>[4,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,8,6,7]=>[1,5,2]=>[2,5,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>[2,4,2]=>[2,4,2]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>[3,3,2]=>[2,3,3]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,8,6,7]=>[4,2,2]=>[2,2,4]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>[5,3]=>[3,5]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>[1,6,1]=>[1,6,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,8,7]=>[2,5,1]=>[1,5,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,8,7]=>[3,4,1]=>[1,4,3]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,8,7]=>[4,3,1]=>[1,3,4]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,8,7]=>[5,2,1]=>[1,2,5]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,8,4,7]=>[6,2]=>[2,6]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8]=>[1,7]=>[7,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7,8]=>[2,6]=>[6,2]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7,8]=>[3,5]=>[5,3]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[4,4]=>[4,4]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7,8]=>[5,3]=>[3,5]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4,8]=>[6,2]=>[2,6]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4]=>[7,1]=>[1,7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,4,5]=>[1,2,2,3]=>[3,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,7,1,2,8,3,4,5]=>[2,3,3]=>[3,3,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,1,7,8,2,3,4,5]=>[1,3,4]=>[4,3,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,7,1,8,2,3,4,5]=>[2,2,4]=>[4,2,2]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[3,5]=>[5,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,7,2,3,8,4,5]=>[1,2,3,2]=>[2,3,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,7,1,2,3,8,4,5]=>[2,4,2]=>[2,4,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[6,1,2,7,3,8,4,5]=>[1,3,2,2]=>[2,2,3,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,6,7,2,3,8,4,5]=>[3,3,2]=>[2,3,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[6,1,2,7,8,3,4,5]=>[1,4,3]=>[3,4,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,6,2,7,8,3,4,5]=>[2,3,3]=>[3,3,2]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]=>[3,2,3]=>[3,2,3]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[4,4]=>[4,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,8,5]=>[1,2,4,1]=>[1,4,2,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,8,5]=>[2,5,1]=>[1,5,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,8,5]=>[1,3,3,1]=>[1,3,3,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,8,5]=>[2,2,3,1]=>[1,3,2,2]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,8,5]=>[3,4,1]=>[1,4,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,8,5]=>[1,4,2,1]=>[1,2,4,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>[2,3,2,1]=>[1,2,3,2]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,8,5]=>[3,2,2,1]=>[1,2,2,3]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,8,5]=>[4,3,1]=>[1,3,4]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[6,1,2,3,7,8,4,5]=>[1,5,2]=>[2,5,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,6,2,3,7,8,4,5]=>[2,4,2]=>[2,4,2]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>[3,3,2]=>[2,3,3]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,8,4,5]=>[4,2,2]=>[2,2,4]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,7,8,3,4,5]=>[5,3]=>[3,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5,8]=>[1,2,5]=>[5,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5,8]=>[2,6]=>[6,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5,8]=>[1,3,4]=>[4,3,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5,8]=>[2,2,4]=>[4,2,2]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5,8]=>[3,5]=>[5,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5,8]=>[1,4,3]=>[3,4,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5,8]=>[2,3,3]=>[3,3,2]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5,8]=>[3,2,3]=>[3,2,3]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5,8]=>[4,4]=>[4,4]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5,8]=>[1,5,2]=>[2,5,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5,8]=>[2,4,2]=>[2,4,2]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5,8]=>[3,3,2]=>[2,3,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,8]=>[4,2,2]=>[2,2,4]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5,8]=>[5,3]=>[3,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,8,5]=>[1,6,1]=>[1,6,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,8,5]=>[2,5,1]=>[1,5,2]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,7,8,5]=>[3,4,1]=>[1,4,3]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,7,8,5]=>[4,3,1]=>[1,3,4]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,6,7,4,8,5]=>[5,2,1]=>[1,2,5]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,6,7,8,4,5]=>[6,2]=>[2,6]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,8,2,3,4,5,7]=>[1,2,5]=>[5,2,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,8,1,2,3,4,5,7]=>[2,6]=>[6,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,5,7]=>[1,3,4]=>[4,3,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,8,3,4,5,7]=>[2,2,4]=>[4,2,2]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,6,8,2,3,4,5,7]=>[3,5]=>[5,3]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,8,4,5,7]=>[1,4,3]=>[3,4,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,8,4,5,7]=>[2,3,3]=>[3,3,2]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>[3,2,3]=>[3,2,3]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>[4,4]=>[4,4]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>[1,5,2]=>[2,5,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>[2,4,2]=>[2,4,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,8,5,7]=>[3,3,2]=>[2,3,3]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,8,5,7]=>[4,2,2]=>[2,2,4]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,8,4,5,7]=>[5,3]=>[3,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>[1,6,1]=>[1,6,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,8,7]=>[2,5,1]=>[1,5,2]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,8,7]=>[3,4,1]=>[1,4,3]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,8,7]=>[4,3,1]=>[1,3,4]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7]=>[5,2,1]=>[1,2,5]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7]=>[6,2]=>[2,6]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8]=>[1,7]=>[7,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7,8]=>[2,6]=>[6,2]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8]=>[3,5]=>[5,3]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>[4,4]=>[4,4]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8]=>[5,3]=>[3,5]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5,8]=>[6,2]=>[2,6]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,5]=>[7,1]=>[1,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,8,2,3,4,5,6]=>[1,2,5]=>[5,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[2,6]=>[6,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1,2,8,3,4,5,6]=>[1,3,4]=>[4,3,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,7,2,8,3,4,5,6]=>[2,2,4]=>[4,2,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,8,2,3,4,5,6]=>[3,5]=>[5,3]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1,2,3,8,4,5,6]=>[1,4,3]=>[3,4,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,7,2,3,8,4,5,6]=>[2,3,3]=>[3,3,2]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]=>[3,2,3]=>[3,2,3]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[4,4]=>[4,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,1,2,3,4,8,5,6]=>[1,5,2]=>[2,5,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>[2,4,2]=>[2,4,2]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>[3,3,2]=>[2,3,3]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,6]=>[4,2,2]=>[2,2,4]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>[5,3]=>[3,5]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>[1,6,1]=>[1,6,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,8,6]=>[2,5,1]=>[1,5,2]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,8,6]=>[3,4,1]=>[1,4,3]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,8,6]=>[4,3,1]=>[1,3,4]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6]=>[5,2,1]=>[1,2,5]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,6]=>[6,2]=>[2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>[1,7]=>[7,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8]=>[2,6]=>[6,2]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6,8]=>[3,5]=>[5,3]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>[4,4]=>[4,4]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,8]=>[5,3]=>[3,5]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8]=>[6,2]=>[2,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,6]=>[7,1]=>[1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[1,7]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7]=>[2,6]=>[6,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,8,3,4,5,6,7]=>[3,5]=>[5,3]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[4,4]=>[4,4]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>[5,3]=>[3,5]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,7]=>[6,2]=>[2,6]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7]=>[7,1]=>[1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[8]=>[8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[1,8]=>[8,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[8,1]=>[1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,9]=>[1,8]=>[8,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[7,2]=>[2,7]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[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]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,10]=>[10,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8,10]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>[1,7,1]=>[1,7,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8,9]=>[1,8]=>[8,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[6,3]=>[3,6]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,1,8]=>[7,2]=>[2,7]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[8,2]=>[2,8]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[10,1]=>[1,10]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[1,10]=>[10,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>[1,8,1]=>[1,8,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,9,10]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,9,6,7]=>[1,6,2]=>[2,6,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>[1,7,1]=>[1,7,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8,9]=>[1,8]=>[8,1]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[5,4]=>[4,5]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,9,8]=>[6,2,1]=>[1,2,6]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[7,3]=>[3,7]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,8,9,1,7]=>[7,2]=>[2,7]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[8,2]=>[2,8]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[9,2]=>[2,9]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[1,9,1]=>[1,9,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,10,7,8]=>[1,7,2]=>[2,7,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,10,9]=>[1,8,1]=>[1,8,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8,9,10]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[8,1,2,3,4,9,5,6,7]=>[1,5,3]=>[3,5,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]=>[1,6,2]=>[2,6,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,9,6]=>[1,7,1]=>[1,7,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8,9]=>[1,8]=>[8,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[4,5]=>[5,4]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[6,4]=>[4,6]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,9,1,7,8]=>[6,3]=>[3,6]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,9,7]=>[6,2,1]=>[1,2,6]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,10,9]=>[7,2,1]=>[1,2,7]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,7,8,9,1,6]=>[7,2]=>[2,7]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,10,1,8]=>[8,2]=>[2,8]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[9,2]=>[2,9]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8,11,10]=>[1,9,1]=>[1,9,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,10,6,7,8]=>[1,6,3]=>[3,6,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,10,7,9]=>[1,7,2]=>[2,7,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8,9,10]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,1,2,3,9,4,5,6,7]=>[1,4,4]=>[4,4,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6,9]=>[1,6,2]=>[2,6,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,9,7,8]=>[1,6,2]=>[2,6,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,9,7]=>[1,7,1]=>[1,7,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8,9]=>[1,8]=>[8,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[3,6]=>[6,3]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,9,8]=>[4,4,1]=>[1,4,4]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[5,5]=>[5,5]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,9,7,8]=>[5,2,2]=>[2,2,5]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,9,7]=>[5,3,1]=>[1,3,5]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,7,9]=>[6,3]=>[3,6]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,10,1,8,9]=>[7,3]=>[3,7]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,7,8,1,9,6]=>[6,2,1]=>[1,2,6]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>[7,2,1]=>[1,2,7]
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,11,10]=>[8,2,1]=>[1,2,8]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,6,7,8,9,1,5]=>[7,2]=>[2,7]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,8,9,10,1,7]=>[8,2]=>[2,8]
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,10,11,1,9]=>[9,2]=>[2,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[9,1,2,3,4,10,5,6,7,8]=>[1,5,4]=>[4,5,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7,10]=>[1,7,2]=>[2,7,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8,9,10]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,1,2,9,3,4,5,6,7]=>[1,3,5]=>[5,3,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7,9]=>[1,6,2]=>[2,6,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9]=>[1,8]=>[8,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[2,7]=>[7,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8,9]=>[2,7]=>[7,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[4,6]=>[6,4]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,9,1,6,7,8]=>[5,4]=>[4,5]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7,9]=>[5,2,2]=>[2,2,5]
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,9,10,8]=>[6,3,1]=>[1,3,6]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[7,2]=>[2,7]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,6,7,8,9,1,4]=>[7,2]=>[2,7]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,7,8,9,10,1,6]=>[8,2]=>[2,8]
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,10,11,1,8]=>[9,2]=>[2,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[9,1,2,3,10,4,5,6,7,8]=>[1,4,5]=>[5,4,1]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,9,10,6]=>[1,8,1]=>[1,8,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8,9,10]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,9,2,3,4,5,6,7]=>[1,2,6]=>[6,2,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,9,6,7,8]=>[1,5,3]=>[3,5,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[1,8]=>[8,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,9,1,2,3,4,5,6,8]=>[2,7]=>[7,2]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,9,8]=>[2,6,1]=>[1,6,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[3,7]=>[7,3]
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,9,6,7,8]=>[4,2,3]=>[3,2,4]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,8,7,9]=>[4,3,2]=>[2,3,4]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,7,8,9,6]=>[4,4,1]=>[1,4,4]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,10,1,7,8,9]=>[6,4]=>[4,6]
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,8,1,9,6,7]=>[5,2,2]=>[2,2,5]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,9,8,10]=>[6,2,2]=>[2,2,6]
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,7,9,1,6,8]=>[6,3]=>[3,6]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,9,2]=>[6,2,1]=>[1,2,6]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,1,3]=>[7,2]=>[2,7]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,6,7,8,9,10,1,5]=>[8,2]=>[2,8]
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,8,9,10,11,1,7]=>[9,2]=>[2,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[9,1,2,10,3,4,5,6,7,8]=>[1,3,6]=>[6,3,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9,10]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[2,8]=>[8,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,9,2,3,4,5,6,8]=>[1,2,6]=>[6,2,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7,9]=>[1,6,2]=>[2,6,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[1,7,1]=>[1,7,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[2,8]=>[8,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6,9]=>[2,7]=>[7,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,9,1,2,3,4,5,7,8]=>[2,7]=>[7,2]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,9,10,7]=>[5,4,1]=>[1,4,5]
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6,8,9]=>[5,4]=>[4,5]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,9,2]=>[5,3,1]=>[1,3,5]
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,8,10,1,7,9]=>[7,3]=>[3,7]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[6,3]=>[3,6]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,9,3]=>[6,2,1]=>[1,2,6]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[8,2]=>[2,8]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,5,6,7,8,9,10,1,4]=>[8,2]=>[2,8]
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,7,8,9,10,11,1,6]=>[9,2]=>[2,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,1,10,2,3,4,5,6,7,8]=>[1,2,7]=>[7,2,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[1,9]=>[9,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,10,1,2,3,4,5,6,7,9]=>[2,8]=>[8,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[7,1,8,2,3,4,5,6,9]=>[1,2,6]=>[6,2,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,9,5,6,7,8]=>[1,4,4]=>[4,4,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,9,7,8]=>[1,6,2]=>[2,6,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,9,7]=>[1,7,1]=>[1,7,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,9,6]=>[2,6,1]=>[1,6,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,9,1,2,3,4,6,7,8]=>[2,7]=>[7,2]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,9,5]=>[3,5,1]=>[1,5,3]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,8,6,9,7]=>[4,2,2,1]=>[1,2,2,4]
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6,8,9]=>[4,2,3]=>[3,2,4]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2,9]=>[5,2,2]=>[2,2,5]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,5,6,7,1,8,4,9]=>[5,2,2]=>[2,2,5]
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,9,1,2,8]=>[6,3]=>[3,6]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,3,9]=>[6,3]=>[3,6]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,10,2]=>[7,2,1]=>[1,2,7]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,10,1,3]=>[8,2]=>[2,8]
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,6,7,8,9,10,11,1,5]=>[9,2]=>[2,9]
[]=>[]=>[]=>[]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,9,8]=>[3,3,2,1]=>[1,2,3,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6,9,8]=>[2,3,3,1]=>[1,3,3,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6,9,8]=>[3,2,3,1]=>[1,3,2,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,9,8]=>[4,4,1]=>[1,4,4]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,9,6,8]=>[3,2,2,2]=>[2,2,2,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,7,9,4,6,8]=>[3,3,3]=>[3,3,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,9,4,6,8]=>[4,2,3]=>[3,2,4]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,9,2,4,6,8]=>[5,4]=>[4,5]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,8,9]=>[2,2,2,3]=>[3,2,2,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,9,6]=>[3,2,3,1]=>[1,3,2,3]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,5,2,7,8,4,9,6]=>[3,3,2,1]=>[1,2,3,3]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,9,6]=>[4,2,2,1]=>[1,2,2,4]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,5,2,7,8,9,4,6]=>[3,4,2]=>[2,4,3]
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,8,2,4,6,7,9]=>[4,5]=>[5,4]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,8,7,9]=>[2,2,3,2]=>[2,3,2,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,8,7,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,9,7,8]=>[3,2,2,2]=>[2,2,2,3]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7,9,8]=>[3,2,3,1]=>[1,3,2,3]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,9,8]=>[4,2,2,1]=>[1,2,2,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7,8,9]=>[3,6]=>[6,3]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7,8,9]=>[3,2,4]=>[4,2,3]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,3,2,5,6,7,8,9,4]=>[2,6,1]=>[1,6,2]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5,6,7,8,9,2,4]=>[7,2]=>[2,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5,9,8]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5,8,9]=>[2,3,4]=>[4,3,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5,8,9]=>[4,5]=>[5,4]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,6,7,8,9,2,4,5]=>[6,3]=>[3,6]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,8,7,9]=>[2,3,2,2]=>[2,2,3,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,8,7,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,8,6,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,9,6,8]=>[3,2,2,2]=>[2,2,2,3]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6,9,8]=>[4,2,2,1]=>[1,2,2,4]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,8,5,9,6,7]=>[3,2,2,2]=>[2,2,2,3]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,3,8,2,4,5,6,7,9]=>[3,6]=>[6,3]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,8,9,2,7]=>[7,2]=>[2,7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,3,2,9,4,5,6,7,8]=>[2,2,5]=>[5,2,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[3,6]=>[6,3]
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,3,4,9,2,5,6,7,8]=>[4,5]=>[5,4]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,3,4,5,9,2,6,7,8]=>[5,4]=>[4,5]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,9,2,7,8]=>[6,3]=>[3,6]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[2,6,1]=>[1,6,2]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,9,8]=>[6,2,1]=>[1,2,6]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,9,2,8]=>[7,2]=>[2,7]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,9]=>[2,7]=>[7,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[3,6]=>[6,3]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7,8,9]=>[5,4]=>[4,5]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,8,9]=>[6,3]=>[3,6]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,2,9]=>[7,2]=>[2,7]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,2]=>[8,1]=>[1,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,9,8]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6,9,8]=>[3,3,2,1]=>[1,2,3,3]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,5,7,8,2,3,9,6]=>[5,3,1]=>[1,3,5]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7,8,9]=>[2,2,5]=>[5,2,2]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,5,6,7,8,9,3]=>[2,6,1]=>[1,6,2]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,4,5,6,7,8,2,9,3]=>[6,2,1]=>[1,2,6]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,5,6,7,8,9,2,3]=>[7,2]=>[2,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5,9,8]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7,9]=>[2,3,2,2]=>[2,2,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,8,7,9]=>[4,3,2]=>[2,3,4]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,8,3,5,7,9]=>[5,4]=>[4,5]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8,9]=>[3,2,4]=>[4,2,3]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6,9,8]=>[5,3,1]=>[1,3,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,4,8,2,3,5,6,9,7]=>[3,5,1]=>[1,5,3]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,8,9,7]=>[4,4,1]=>[1,4,4]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,4,9,3,5,6,7,8]=>[4,5]=>[5,4]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8,9]=>[2,7]=>[7,2]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[3,6]=>[6,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7,8,9]=>[4,5]=>[5,4]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7,8,9]=>[5,4]=>[4,5]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,9,3]=>[8,1]=>[1,8]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4,8,9]=>[2,2,2,3]=>[3,2,2,2]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,6,7,8,9,3,4]=>[2,5,2]=>[2,5,2]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,5,6,7,8,9,2,3,4]=>[6,3]=>[3,6]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,8,7,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4,9,8]=>[4,2,2,1]=>[1,2,2,4]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,5,7,8,9,2,3,4,6]=>[5,4]=>[4,5]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,8,6,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,9,8]=>[4,4,1]=>[1,4,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6,9,8]=>[3,3,2,1]=>[1,2,3,3]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,9,8]=>[4,2,2,1]=>[1,2,2,4]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6,9,8]=>[5,3,1]=>[1,3,5]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,7,9,4,6,8]=>[6,3]=>[3,6]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]=>[5,4]=>[4,5]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7,8,9]=>[2,7]=>[7,2]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[4,5]=>[5,4]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4,9]=>[7,2]=>[2,7]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,9,4]=>[8,1]=>[1,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,9,5]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,6,7,8,2,9,3,4,5]=>[4,2,3]=>[3,2,4]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,6,7,8,9,2,3,4,5]=>[5,4]=>[4,5]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5,9]=>[2,3,2,2]=>[2,2,3,2]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,8,5,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5,9,8]=>[3,3,2,1]=>[1,2,3,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,9,8]=>[4,2,2,1]=>[1,2,2,4]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7,9]=>[5,2,2]=>[2,2,5]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7,9]=>[6,3]=>[3,6]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,9,5,7,8]=>[6,3]=>[3,6]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,9,5,8]=>[7,2]=>[2,7]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7,8,9]=>[2,7]=>[7,2]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8,9]=>[3,6]=>[6,3]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[5,4]=>[4,5]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5,8,9]=>[6,3]=>[3,6]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,5,9]=>[7,2]=>[2,7]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,9,5]=>[8,1]=>[1,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,7,2,8,3,9,4,5,6]=>[2,2,2,3]=>[3,2,2,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,7,8,9,2,3,4,5,6]=>[4,5]=>[5,4]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,9,6]=>[4,2,2,1]=>[1,2,2,4]
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,7,8,4,5,9,6]=>[5,3,1]=>[1,3,5]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,8,6,9]=>[4,3,2]=>[2,3,4]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6,9]=>[5,2,2]=>[2,2,5]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,6,9]=>[6,3]=>[3,6]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,9,6]=>[5,3,1]=>[1,3,5]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,9,6]=>[6,2,1]=>[1,2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[3,6]=>[6,3]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,9,5,6,8]=>[6,3]=>[3,6]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,9,8]=>[2,6,1]=>[1,6,2]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,9,8]=>[5,3,1]=>[1,3,5]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,9,8]=>[6,2,1]=>[1,2,6]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,9,6,8]=>[7,2]=>[2,7]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8,9]=>[2,7]=>[7,2]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[6,3]=>[3,6]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,6,9]=>[7,2]=>[2,7]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,6]=>[8,1]=>[1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,8,2,9,3,4,5,6,7]=>[2,2,5]=>[5,2,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[3,6]=>[6,3]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,9,6,7]=>[2,5,2]=>[2,5,2]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[1,2,8,3,4,5,9,6,7]=>[3,4,2]=>[2,4,3]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,9,6,7]=>[5,2,2]=>[2,2,5]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,8,9,5,6,7]=>[6,3]=>[3,6]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,9,7]=>[2,6,1]=>[1,6,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[1,2,8,3,4,5,6,9,7]=>[3,5,1]=>[1,5,3]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,6,9,7]=>[5,3,1]=>[1,3,5]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,9,7]=>[6,2,1]=>[1,2,6]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,8,9,6,7]=>[7,2]=>[2,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7,9]=>[2,7]=>[7,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7,9]=>[4,5]=>[5,4]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,7,9]=>[6,3]=>[3,6]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,9]=>[7,2]=>[2,7]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,7]=>[8,1]=>[1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,9,2,3,4,5,6,7,8]=>[2,7]=>[7,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>[3,6]=>[6,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>[4,5]=>[5,4]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>[5,4]=>[4,5]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>[6,3]=>[3,6]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,8]=>[7,2]=>[2,7]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,8]=>[8,1]=>[1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[9]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7,9]=>[2,3,2,2]=>[2,2,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7,9]=>[2,2,3,2]=>[2,3,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7,9]=>[2,2,2,3]=>[3,2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,9,8]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,9,8]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7,10,9]=>[2,3,2,2,1]=>[1,2,2,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,8,7,9]=>[3,4,2]=>[2,4,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7,10,9]=>[2,2,3,2,1]=>[1,2,3,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,8,3,5,7,9]=>[2,3,4]=>[4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7,10,9]=>[2,2,2,3,1]=>[1,3,2,2,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,8,9,5,7]=>[2,2,3,2]=>[2,3,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,10,7,9]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8,9]=>[2,2,2,3]=>[3,2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,9,7,10]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,9,7]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,9,8,10]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,9,8]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,9,8,10]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7,9]=>[4,5]=>[5,4]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,7,9]=>[2,2,2,3]=>[3,2,2,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,9,5]=>[2,2,4,1]=>[1,4,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,9,8,10]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,8,7,9]=>[2,2,3,2]=>[2,3,2,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,8,5,7,9]=>[2,2,2,3]=>[3,2,2,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,8,9,7]=>[2,2,4,1]=>[1,4,2,2]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,6,7,8,3,9,5]=>[2,4,2,1]=>[1,2,4,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,8,9,7]=>[2,2,4,1]=>[1,4,2,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7,8,9]=>[2,2,5]=>[5,2,2]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,5,6,8,3,9,7]=>[2,4,2,1]=>[1,2,4,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,1,8,3,9,5,10,7]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>[5,5]=>[5,5]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,8,7,9]=>[2,3,2,2]=>[2,2,3,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,10,7,9]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7,8,9]=>[2,2,5]=>[5,2,2]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,8,5,9,7]=>[2,4,2,1]=>[1,2,4,2]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3,8,9]=>[2,4,3]=>[3,4,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,9,5,10]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7,9]=>[3,2,2,2]=>[2,2,2,3]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,6,7,8,9,1,3,5]=>[6,3]=>[3,6]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8,9]=>[2,4,3]=>[3,4,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,3,1,9,4,5,6,7,8]=>[2,2,5]=>[5,2,2]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6,9,8]=>[4,2,2,1]=>[1,2,2,4]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,7,2,8,3,9,4,10,5,6]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7,10,9]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7,10,9]=>[2,3,2,2,1]=>[1,2,2,3,2]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6,9,8,10]=>[4,2,2,2]=>[2,2,2,4]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7,9]=>[2,4,3]=>[3,4,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,8,9,5,7]=>[2,5,2]=>[2,5,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,9,5,7,8]=>[2,4,3]=>[3,4,2]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,6,9,1,3,5,7,8]=>[4,5]=>[5,4]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8,9]=>[1,2,2,4]=>[4,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7,8,9]=>[3,6]=>[6,3]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,8,9,5,6,7]=>[2,4,3]=>[3,4,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[1,2,6]=>[6,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8,9]=>[2,7]=>[7,2]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[1,7,1]=>[1,7,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,8,7,9]=>[2,3,2,2]=>[2,2,3,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,9,4,7,8]=>[2,4,3]=>[3,4,2]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,6,7,8,9,3,4]=>[1,6,2]=>[2,6,1]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,5,6,7,8,9,1,3,4]=>[6,3]=>[3,6]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,7,8,9,4,5]=>[2,5,2]=>[2,5,2]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,6,7,8,9,1,3,4,5]=>[5,4]=>[4,5]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,7,8,9,1,3,4,5,6]=>[4,5]=>[5,4]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,1,8,3,9,4,5,6,7]=>[1,2,2,4]=>[4,2,2,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,8,9,1,3,4,5,6,7]=>[3,6]=>[6,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,1,9,3,4,5,6,7,8]=>[1,2,6]=>[6,2,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,8]=>[2,7]=>[7,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7,9]=>[2,3,2,2]=>[2,2,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,8,7,9]=>[1,3,3,2]=>[2,3,3,1]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,6,7,8,9,1,2,5]=>[6,3]=>[3,6]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,8,9,6]=>[1,3,4,1]=>[1,4,3,1]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,7,8,9,1,2,5,6]=>[5,4]=>[4,5]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,8,9,2,5,6,7]=>[1,4,4]=>[4,4,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,4,9,1,2,5,6,7,8]=>[3,6]=>[6,3]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9]=>[1,2,6]=>[6,2,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8,9]=>[2,7]=>[7,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,2]=>[1,7,1]=>[1,7,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7,9]=>[3,4,2]=>[2,4,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,9,3,7,8]=>[2,4,3]=>[3,4,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7,8,9]=>[1,2,2,4]=>[4,2,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[3,6]=>[6,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,6,7,8,9,3]=>[2,6,1]=>[1,6,2]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,5,6,7,8,9,2,3]=>[1,6,2]=>[2,6,1]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[6,3]=>[3,6]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[4,5]=>[5,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,6,7,8,9,2,3,4]=>[1,5,3]=>[3,5,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[5,4]=>[4,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,9,4,5]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[6,1,7,8,9,2,3,4,5]=>[1,4,4]=>[4,4,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[4,5]=>[5,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,8,2,9,3,4,5,6]=>[1,2,2,4]=>[4,2,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,1,8,9,2,3,4,5,6]=>[1,3,5]=>[5,3,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[3,6]=>[6,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7,10,9]=>[2,4,3,1]=>[1,3,4,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,9,10]=>[1,2,2,2,3]=>[3,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7,9,10]=>[2,4,4]=>[4,4,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,9,10,7]=>[1,2,2,4,1]=>[1,4,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,9,7,10,8]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,9,10,7,8]=>[1,2,2,3,2]=>[2,3,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,10,7,8,9]=>[1,2,2,2,3]=>[3,2,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,7,8,5,6,9,10]=>[2,4,4]=>[4,4,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,9,6,10,7]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,10,5,6,7,8,9]=>[1,2,2,5]=>[5,2,2,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8,9,10]=>[2,8]=>[8,2]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,9,10,3]=>[1,8,1]=>[1,8,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7,10,9]=>[1,3,3,2,1]=>[1,2,3,3,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,9,7,10,8]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,9,10,7,8]=>[1,3,4,2]=>[2,4,3,1]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,5,6,7,8,9,10,1,3,4]=>[7,3]=>[3,7]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,9,10,5]=>[3,6,1]=>[1,6,3]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6,7,8,9,10,1,3,4,5]=>[6,4]=>[4,6]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,7,3,8,4,9,5,10,6]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,7,8,9,10,1,3,4,5,6]=>[5,5]=>[5,5]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,8,9,10,1,3,4,5,6,7]=>[4,6]=>[6,4]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,1,10,3,4,5,6,7,8,9]=>[1,2,7]=>[7,2,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[2,8]=>[8,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7,10,9]=>[2,3,2,2,1]=>[1,2,2,3,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,8,10,1,2,5,7,9]=>[5,5]=>[5,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,9,7,10,8]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,6,7,8,9,10,1,2,5]=>[7,3]=>[3,7]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6,10,9]=>[2,4,3,1]=>[1,3,4,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6,9,10]=>[2,4,4]=>[4,4,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,9,6,10,7]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,8,9,10,5,6,7]=>[2,5,3]=>[3,5,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9,10]=>[1,2,7]=>[7,2,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[2,8]=>[8,2]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]=>[1,8,1]=>[1,8,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,9,7,10,8]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,9,10,7,8]=>[3,5,2]=>[2,5,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[3,7]=>[7,3]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,5,6,7,8,9,10,2,3]=>[1,7,2]=>[2,7,1]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[7,3]=>[3,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4,10,9]=>[4,5,1]=>[1,5,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[4,6]=>[6,4]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,6,7,8,9,10,2,3,4]=>[1,6,3]=>[3,6,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[6,4]=>[4,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,9,4,10,5]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,1,2,8,3,9,4,10,5]=>[2,3,2,2,1]=>[1,2,2,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,1,7,8,9,2,3,4,10,5]=>[1,4,4,1]=>[1,4,4,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,10,5]=>[4,5,1]=>[1,5,4]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[6,1,7,8,2,3,9,10,4,5]=>[1,3,4,2]=>[2,4,3,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,1,7,8,9,10,2,3,4,5]=>[1,5,4]=>[4,5,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[5,5]=>[5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,1,8,2,9,3,10,4,5,6]=>[1,2,2,2,3]=>[3,2,2,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,1,2,9,3,10,4,5,6]=>[2,3,2,3]=>[3,2,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[7,1,8,9,2,3,10,4,5,6]=>[1,3,3,3]=>[3,3,3,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,10,4,5,6]=>[3,4,3]=>[3,4,3]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[7,1,8,9,10,2,3,4,5,6]=>[1,4,5]=>[5,4,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[4,6]=>[6,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,1,9,2,10,3,4,5,6,7]=>[1,2,2,5]=>[5,2,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[8,1,9,10,2,3,4,5,6,7]=>[1,3,6]=>[6,3,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[3,7]=>[7,3]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[10]=>[10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,9,8]=>[1,2,2,3,1]=>[1,3,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,9,8]=>[1,2,3,2,1]=>[1,2,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8]=>[1,3,2,2,1]=>[1,2,2,3,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,8,4,9,6,7]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,9,6,10,8]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,8,9]=>[1,2,2,4]=>[4,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,9,6,8,10]=>[1,2,2,2,3]=>[3,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,7,9,6,8]=>[1,2,4,2]=>[2,4,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,9,8,10]=>[1,2,2,3,2]=>[2,3,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,9,8]=>[1,4,3,1]=>[1,3,4,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,9,8,10]=>[1,2,3,2,2]=>[2,2,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8,10]=>[1,3,2,2,2]=>[2,2,2,3,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7,10,9]=>[6,3,1]=>[1,3,6]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6,10,9]=>[5,2,2,1]=>[1,2,2,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6,9,8,10]=>[5,3,2]=>[2,3,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,9,8,10]=>[4,2,2,2]=>[2,2,2,4]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,8,7,9]=>[2,2,3,2]=>[2,3,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,9,8,10]=>[3,3,2,2]=>[2,2,3,3]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[9,1]=>[1,9]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[8,2]=>[2,8]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[10,1]=>[1,10]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,10,7,9]=>[8,2]=>[2,8]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,10,8]=>[7,2,1]=>[1,2,7]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,11,9,10]=>[9,2]=>[2,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,8,7,10,9]=>[2,2,3,2,1]=>[1,2,3,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7,9]=>[2,2,3,2]=>[2,3,2,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,8,7,9]=>[2,2,3,2]=>[2,3,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,8,7,9]=>[2,3,2,2]=>[2,2,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7,9]=>[1,4,2,2]=>[2,2,4,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,8,7,9]=>[1,2,4,2]=>[2,4,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,5,7,9]=>[1,2,2,4]=>[4,2,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,9,5,7]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[9,1]=>[1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[2,8]=>[8,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>[2,9]=>[9,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,9,2,3,4,5,6,7,8,10]=>[2,8]=>[8,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,8,2,3,9,4,5,6]=>[1,2,3,3]=>[3,3,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,4,9,5]=>[1,2,2,3,1]=>[1,3,2,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,9,4,8]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6,9]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[9,1]=>[1,9]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[9,1]=>[1,9]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[9,1]=>[1,9]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[9,1]=>[1,9]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[9,1]=>[1,9]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[9,1]=>[1,9]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,8,7,9]=>[2,5,2]=>[2,5,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,8,7,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,8,7,9]=>[1,4,2,2]=>[2,2,4,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,8,7,10,9]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[10,1]=>[1,10]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,5,6,7,8,9,1,2,4]=>[6,3]=>[3,6]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,6,7,8,9,1,2,3,5]=>[5,4]=>[4,5]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,7,8,9,1,2,3,4,6]=>[4,5]=>[5,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,8,9,1,2,3,4,5,7]=>[3,6]=>[6,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,10,8,9]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7,10,9]=>[5,2,2,1]=>[1,2,2,5]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,8,6,9]=>[3,2,2,2]=>[2,2,2,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6,9,8]=>[1,3,2,2,1]=>[1,2,2,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6,9,8]=>[3,3,2,1]=>[1,2,3,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,9,8]=>[2,4,2,1]=>[1,2,4,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6,9,8]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6,9,8]=>[3,5,1]=>[1,5,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,9,8,10]=>[4,4,2]=>[2,4,4]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,7,9,1,2,4,6,8]=>[4,5]=>[5,4]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,9,4,6,8,10]=>[4,2,4]=>[4,2,4]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5,7,8,1,9,2,4,6]=>[4,2,3]=>[3,2,4]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,7,2,9,4,10,6,8]=>[4,2,2,2]=>[2,2,2,4]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,1,8,2,9,4]=>[4,2,2,1]=>[1,2,2,4]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,9,6,10]=>[4,2,2,2]=>[2,2,2,4]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,9,8]=>[4,2,2,1]=>[1,2,2,4]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,9,8,10]=>[4,2,2,2]=>[2,2,2,4]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6,9,8,10]=>[4,2,2,2]=>[2,2,2,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[4,2,2,2]=>[2,2,2,4]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,7,8,9,1,2,6]=>[6,3]=>[3,6]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[4,9,1,2,3,5,6,7,8]=>[2,7]=>[7,2]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3,9]=>[5,4]=>[4,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,8,9,1,2,3,4,6,7]=>[3,6]=>[6,3]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,6,7,8,1,9,2,3,4]=>[4,2,3]=>[3,2,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,8,1,9,2,3,4,5,6]=>[2,2,5]=>[5,2,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[3,7]=>[7,3]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,7,8,1,9,2,3,4,5]=>[3,2,4]=>[4,2,3]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[4,6]=>[6,4]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,10,5,6,7,8,9]=>[5,5]=>[5,5]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,5,6,7,8,1,9,2,3]=>[5,2,2]=>[2,2,5]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[6,4]=>[4,6]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[7,3]=>[3,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,7,3,8,5,6,9]=>[2,2,2,3]=>[3,2,2,2]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5,9]=>[3,6]=>[6,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,9,6,10,8]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,9,6,10,8]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,9,6,10,8]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[2,2,2,3,1]=>[1,3,2,2,2]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,10,2,3,4,5,6,7,8,9,11]=>[2,9]=>[9,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7,10,9]=>[2,7,1]=>[1,7,2]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,2,10,9]=>[7,2,1]=>[1,2,7]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,10,2,11]=>[9,2]=>[2,9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6,9,8]=>[1,3,4,1]=>[1,4,3,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,7,9,4,6,8]=>[1,2,3,3]=>[3,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,9,6]=>[1,2,2,3,1]=>[1,3,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,9,7,8]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,8,9,5]=>[1,3,4,1]=>[1,4,3,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5,8,9]=>[1,3,5]=>[5,3,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5,8,9]=>[1,4,4]=>[4,4,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8,9]=>[2,4,3]=>[3,4,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,6,1,2,7,9,4,5,8]=>[2,4,3]=>[3,4,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,9,4,7,8]=>[2,4,3]=>[3,4,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,6,1,2,7,8,4,5,9,10]=>[2,4,4]=>[4,4,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,7,8,2,4,5,6,9]=>[1,3,5]=>[5,3,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,6,1,2,7,10,4,5,8,9]=>[2,4,4]=>[4,4,2]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,6,7,4,8,9,5]=>[1,4,3,1]=>[1,3,4,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,10,5,8,9]=>[2,5,3]=>[3,5,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,7,10,5,8,9]=>[3,4,3]=>[3,4,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5,8,9]=>[1,2,3,3]=>[3,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,10,5,8,9]=>[1,3,3,3]=>[3,3,3,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,9,2,4,5,8]=>[2,3,4]=>[4,3,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5,10,8,9]=>[1,3,4,2]=>[2,4,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4,8,9]=>[2,4,3]=>[3,4,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,9,10,5,8]=>[1,3,4,2]=>[2,4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,6,1,3,7,9,4,5,8]=>[2,4,3]=>[3,4,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,9,10,7,8]=>[1,3,4,2]=>[2,4,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,7,9,10,2,4,6,8]=>[6,4]=>[4,6]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,9,2,4,6,8,10]=>[5,5]=>[5,5]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6,9]=>[2,2,2,3]=>[3,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6,9,8,10]=>[3,2,3,2]=>[2,3,2,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,9,6,8,10]=>[3,2,2,3]=>[3,2,2,3]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6,10,9]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,8,7,10,9]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,7,9,4,6,8,10]=>[3,3,4]=>[4,3,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,9,10,6,8]=>[3,2,3,2]=>[2,3,2,3]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6,9,10]=>[3,2,2,3]=>[3,2,2,3]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,9,7,10,8]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,8,6,10,9]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,8,7,10,9]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,10,7,8]=>[8,2]=>[2,8]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,7,8,9,10,2,3,4,5,6]=>[5,5]=>[5,5]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,8,1,9,4,7,10]=>[5,2,3]=>[3,2,5]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,8,9,4,10,7]=>[4,3,2,1]=>[1,2,3,4]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,9,4,7,8,10]=>[4,2,4]=>[4,2,4]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,9,4,10,8]=>[3,4,2,1]=>[1,2,4,3]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8,10,9]=>[3,3,3,1]=>[1,3,3,3]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,6,8,1,9,4,5,10,7]=>[4,2,3,1]=>[1,3,2,4]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,1,8,9,4,10,5,7]=>[3,3,2,2]=>[2,2,3,3]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,9,4,5,7,8,10]=>[3,2,5]=>[5,2,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,7,1,9,4,5,6,10,8]=>[3,2,4,1]=>[1,4,2,3]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,9,5,10,8]=>[2,5,2,1]=>[1,2,5,2]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8,10,9]=>[2,4,3,1]=>[1,3,4,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,7,9,5,10,6,8]=>[2,4,2,2]=>[2,2,4,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6,8,10,9]=>[2,3,4,1]=>[1,4,3,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,10,7,9]=>[2,3,3,2]=>[2,3,3,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,9,2,4,10,8]=>[4,2,3,1]=>[1,3,2,4]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,9,2,10,4,8]=>[3,3,2,2]=>[2,2,3,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8,10,9]=>[3,2,4,1]=>[1,4,2,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,10,4,9]=>[2,4,2,2]=>[2,2,4,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,9,4,10]=>[2,3,3,2]=>[2,3,3,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,6,8,1,9,2,4,10,5,7]=>[3,2,3,2]=>[2,3,2,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,6,1,8,9,2,10,4,5,7]=>[2,3,2,3]=>[3,2,3,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,6,7,1,9,2,3,10,5,8]=>[3,2,3,2]=>[2,3,2,3]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,6,1,7,9,2,10,3,5,8]=>[2,3,2,3]=>[3,2,3,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,6,1,9,2,4,5,7,8,10]=>[2,2,6]=>[6,2,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[3,7,1,9,2,4,5,6,10,8]=>[2,2,5,1]=>[1,5,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8,10,9]=>[2,2,5,1]=>[1,5,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,7,1,9,2,3,5,10,6,8]=>[2,2,4,2]=>[2,4,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,7,1,8,2,3,4,10,6,9]=>[2,2,4,2]=>[2,4,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,9,5,10,8]=>[1,6,2,1]=>[1,2,6,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8,10,9]=>[1,5,3,1]=>[1,3,5,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,7,9,5,10,6,8]=>[1,5,2,2]=>[2,2,5,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8,10,9]=>[1,4,4,1]=>[1,4,4,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,10,7,9]=>[1,4,3,2]=>[2,3,4,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,6,7,8,3,10,5,9]=>[1,5,2,2]=>[2,2,5,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,9,5,10]=>[1,4,3,2]=>[2,3,4,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,7,9,3,10,5,6,8]=>[1,4,2,3]=>[3,2,4,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,7,8,3,10,4,6,9]=>[1,4,2,3]=>[3,2,4,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6,8,10,9]=>[1,3,5,1]=>[1,5,3,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,10,7,9]=>[1,3,4,2]=>[2,4,3,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,9,6,10]=>[1,3,4,2]=>[2,4,3,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,10,6,7,9]=>[1,3,3,3]=>[3,3,3,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,9,5,7,10]=>[1,3,3,3]=>[3,3,3,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[2,3,5,6,8,1,9,11,4,12,7,10]=>[5,3,2,2]=>[2,2,3,5]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,8,1,9,4,7,10,12,11]=>[5,2,4,1]=>[1,4,2,5]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[2,3,5,6,1,8,9,10,4,12,7,11]=>[4,4,2,2]=>[2,2,4,4]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,8,9,4,10,11,7,12]=>[4,3,3,2]=>[2,3,3,4]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,9,1,11,4,7,12,8,10]=>[5,2,3,2]=>[2,3,2,5]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,9,11,4,12,7,8,10]=>[4,3,2,3]=>[3,2,3,4]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,9,4,7,8,10,12,11]=>[4,2,5,1]=>[1,5,2,4]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,10,4,7,8,12,9,11]=>[4,2,4,2]=>[2,4,2,4]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,9,10,4,12,8,11]=>[3,5,2,2]=>[2,2,5,3]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,9,4,10,11,8,12]=>[3,4,3,2]=>[2,3,4,3]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,10,4,12,8,9,11]=>[3,4,2,3]=>[3,2,4,3]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8,10,11,9,12]=>[3,3,4,2]=>[2,4,3,3]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8,11,9,10,12]=>[3,3,3,3]=>[3,3,3,3]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,6,8,9,1,10,4,5,12,7,11]=>[5,2,3,2]=>[2,3,2,5]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,6,8,1,9,10,4,12,5,7,11]=>[4,3,2,3]=>[3,2,3,4]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,6,8,1,9,4,5,10,11,7,12]=>[4,2,4,2]=>[2,4,2,4]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,6,1,8,9,10,4,11,5,7,12]=>[3,4,2,3]=>[3,2,4,3]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[2,3,6,1,8,9,4,10,11,5,12,7]=>[3,3,3,2,1]=>[1,2,3,3,3]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,6,9,1,11,4,5,12,7,8,10]=>[4,2,3,3]=>[3,3,2,4]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,1,9,11,4,12,5,7,8,10]=>[3,3,2,4]=>[4,2,3,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,7,9,1,10,4,5,12,6,8,11]=>[4,2,3,3]=>[3,3,2,4]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,7,1,9,10,4,12,5,6,8,11]=>[3,3,2,4]=>[4,2,3,3]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,10,4,5,7,8,12,9,11]=>[3,2,5,2]=>[2,5,2,3]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,7,1,9,4,5,6,10,11,8,12]=>[3,2,5,2]=>[2,5,2,3]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,7,1,10,4,5,6,12,8,9,11]=>[3,2,4,3]=>[3,4,2,3]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,8,1,10,4,5,6,11,7,9,12]=>[3,2,4,3]=>[3,4,2,3]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,9,10,5,12,8,11]=>[2,6,2,2]=>[2,2,6,2]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,9,5,10,11,8,12]=>[2,5,3,2]=>[2,3,5,2]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,10,5,12,8,9,11]=>[2,5,2,3]=>[3,2,5,2]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8,10,11,9,12]=>[2,4,4,2]=>[2,4,4,2]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8,11,9,10,12]=>[2,4,3,3]=>[3,3,4,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,7,9,10,5,11,6,8,12]=>[2,5,2,3]=>[3,2,5,2]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,7,9,5,10,11,6,12,8]=>[2,4,3,2,1]=>[1,2,3,4,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,7,10,5,12,6,8,9,11]=>[2,4,2,4]=>[4,2,4,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,8,10,5,11,6,7,9,12]=>[2,4,2,4]=>[4,2,4,2]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6,8,10,11,9,12]=>[2,3,5,2]=>[2,5,3,2]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6,8,11,9,10,12]=>[2,3,4,3]=>[3,4,3,2]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,10,11,7,12,9]=>[2,3,4,2,1]=>[1,2,4,3,2]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,11,7,9,10,12]=>[2,3,3,4]=>[4,3,3,2]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,9,5,6,11,7,8,12,10]=>[2,3,3,3,1]=>[1,3,3,3,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,6,7,9,1,10,2,4,12,8,11]=>[5,2,3,2]=>[2,3,2,5]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,5,6,7,1,9,10,2,12,4,8,11]=>[4,3,2,3]=>[3,2,3,4]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,9,2,4,10,11,8,12]=>[4,2,4,2]=>[2,4,2,4]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[3,5,6,1,7,9,10,2,11,4,8,12]=>[3,4,2,3]=>[3,2,4,3]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,9,2,10,11,4,12,8]=>[3,3,3,2,1]=>[1,2,3,3,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,10,2,4,12,8,9,11]=>[4,2,3,3]=>[3,3,2,4]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,10,2,12,4,8,9,11]=>[3,3,2,4]=>[4,2,3,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8,10,11,9,12]=>[3,2,5,2]=>[2,5,2,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8,11,9,10,12]=>[3,2,4,3]=>[3,4,2,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[3,5,1,6,7,8,10,2,11,4,9,12]=>[2,5,2,3]=>[3,2,5,2]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,10,11,4,12,9]=>[2,4,3,2,1]=>[1,2,3,4,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,11,4,9,10,12]=>[2,4,2,4]=>[4,2,4,2]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,9,11,4,12,10]=>[2,3,4,2,1]=>[1,2,4,3,2]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,9,4,10,12,11]=>[2,3,3,3,1]=>[1,3,3,3,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,6,8,9,1,10,2,4,11,5,7,12]=>[4,2,3,3]=>[3,3,2,4]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,8,1,9,10,2,11,4,5,7,12]=>[3,3,2,4]=>[4,2,3,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,6,8,1,9,2,4,10,11,5,12,7]=>[3,2,4,2,1]=>[1,2,4,2,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,8,9,10,2,11,4,5,12,7]=>[2,4,2,3,1]=>[1,3,2,4,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,6,1,8,9,2,10,11,4,12,5,7]=>[2,3,3,2,2]=>[2,2,3,3,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,7,9,1,10,2,3,11,5,8,12]=>[4,2,3,3]=>[3,3,2,4]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,9,10,2,11,3,5,8,12]=>[3,3,2,4]=>[4,2,3,3]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,6,7,1,9,2,3,10,11,5,12,8]=>[3,2,4,2,1]=>[1,2,4,2,3]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,7,9,10,2,11,3,5,12,8]=>[2,4,2,3,1]=>[1,3,2,4,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,6,1,7,9,2,10,11,3,12,5,8]=>[2,3,3,2,2]=>[2,2,3,3,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,6,9,1,11,2,4,12,5,7,8,10]=>[3,2,3,4]=>[4,3,2,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,6,1,9,11,2,12,4,5,7,8,10]=>[2,3,2,5]=>[5,2,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,7,9,1,10,2,4,12,5,6,8,11]=>[3,2,3,4]=>[4,3,2,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,7,1,9,10,2,12,4,5,6,8,11]=>[2,3,2,5]=>[5,2,3,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,6,7,1,10,2,3,12,5,8,9,11]=>[3,2,3,4]=>[4,3,2,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,6,1,7,10,2,12,3,5,8,9,11]=>[2,3,2,5]=>[5,2,3,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,7,9,1,10,2,3,11,5,6,8,12]=>[3,2,3,4]=>[4,3,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,7,1,9,10,2,11,3,5,6,8,12]=>[2,3,2,5]=>[5,2,3,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,7,8,1,10,2,3,11,4,6,9,12]=>[3,2,3,4]=>[4,3,2,3]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,7,1,8,10,2,11,3,4,6,9,12]=>[2,3,2,5]=>[5,2,3,2]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,6,1,10,2,4,5,7,8,12,9,11]=>[2,2,6,2]=>[2,6,2,2]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,7,1,9,2,4,5,6,10,11,8,12]=>[2,2,6,2]=>[2,6,2,2]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[3,7,1,10,2,4,5,6,12,8,9,11]=>[2,2,5,3]=>[3,5,2,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[3,8,1,10,2,4,5,6,11,7,9,12]=>[2,2,5,3]=>[3,5,2,2]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8,10,11,9,12]=>[2,2,6,2]=>[2,6,2,2]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8,11,9,10,12]=>[2,2,5,3]=>[3,5,2,2]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,7,1,10,2,3,5,12,6,8,9,11]=>[2,2,4,4]=>[4,4,2,2]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,8,1,10,2,3,5,11,6,7,9,12]=>[2,2,4,4]=>[4,4,2,2]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,7,1,8,2,3,4,11,6,9,10,12]=>[2,2,4,4]=>[4,4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,8,1,10,2,3,4,11,6,7,12,9]=>[2,2,4,3,1]=>[1,3,4,2,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,8,1,9,2,3,4,11,5,7,12,10]=>[2,2,4,3,1]=>[1,3,4,2,2]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8,10,11,9,12]=>[1,5,4,2]=>[2,4,5,1]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8,11,9,10,12]=>[1,5,3,3]=>[3,3,5,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,7,10,5,12,6,8,9,11]=>[1,5,2,4]=>[4,2,5,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,8,10,5,11,6,7,9,12]=>[1,5,2,4]=>[4,2,5,1]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8,10,11,9,12]=>[1,4,5,2]=>[2,5,4,1]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8,11,9,10,12]=>[1,4,4,3]=>[3,4,4,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,10,11,7,12,9]=>[1,4,4,2,1]=>[1,2,4,4,1]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,11,7,9,10,12]=>[1,4,3,4]=>[4,3,4,1]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,9,5,6,11,7,8,12,10]=>[1,4,3,3,1]=>[1,3,3,4,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,6,7,8,3,11,5,9,10,12]=>[1,5,2,4]=>[4,2,5,1]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,9,11,5,12,10]=>[1,4,4,2,1]=>[1,2,4,4,1]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,9,5,10,12,11]=>[1,4,3,3,1]=>[1,3,3,4,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,7,9,3,10,11,5,12,6,8]=>[1,4,3,2,2]=>[2,2,3,4,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,7,8,3,10,11,4,12,6,9]=>[1,4,3,2,2]=>[2,2,3,4,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,8,10,3,11,4,6,7,12,9]=>[1,4,2,4,1]=>[1,4,2,4,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,1,2,8,9,3,11,4,5,7,12,10]=>[1,4,2,4,1]=>[1,4,2,4,1]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6,8,11,9,10,12]=>[1,3,5,3]=>[3,5,3,1]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,11,7,9,10,12]=>[1,3,4,4]=>[4,4,3,1]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,9,3,5,6,11,7,8,12,10]=>[1,3,4,3,1]=>[1,3,4,3,1]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,9,6,10,12,11]=>[1,3,4,3,1]=>[1,3,4,3,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,10,11,6,12,7,9]=>[1,3,4,2,2]=>[2,2,4,3,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,9,11,5,12,7,10]=>[1,3,4,2,2]=>[2,2,4,3,1]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,9,3,4,11,6,7,8,12,10]=>[1,3,3,4,1]=>[1,4,3,3,1]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,9,5,7,10,12,11]=>[1,3,3,4,1]=>[1,4,3,3,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,9,3,4,11,5,7,12,8,10]=>[1,3,3,3,2]=>[2,3,3,3,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1,2,9,3,4,10,5,6,12,8,11]=>[1,3,3,3,2]=>[2,3,3,3,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11]=>[11]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[9,2]=>[2,9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7,10,9]=>[1,4,2,2,1]=>[1,2,2,4,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7,10,9]=>[1,6,2,1]=>[1,2,6,1]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,7,10]=>[8,2]=>[2,8]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,2,10]=>[8,2]=>[2,8]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,10,11,2]=>[10,1]=>[1,10]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[2,10]=>[10,2]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[1,9,2,3,4,5,6,7,10,8]=>[2,7,1]=>[1,7,2]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7,9,10]=>[2,8]=>[8,2]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,2,9,10]=>[7,3]=>[3,7]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,10,2,9]=>[8,2]=>[2,8]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[11,1]=>[1,11]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,6,1,7,2,8,3,9,4]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6,9,8]=>[2,6,1]=>[1,6,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,9]=>[9,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7,10,9]=>[5,2,2,1]=>[1,2,2,5]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,9,7,10]=>[6,2,2]=>[2,2,6]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,9,3]=>[4,2,2,1]=>[1,2,2,4]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,5,6,7,8,1,9,2,10,3]=>[5,2,2,1]=>[1,2,2,5]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,6,7,1,8,2,9,3,10,4]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,6,1,7,3,8,4,9,5]=>[2,2,2,2,1]=>[1,2,2,2,2]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,8,10]=>[7,3]=>[3,7]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,1,10,3]=>[7,2,1]=>[1,2,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,8,9,10,2,3,4,5,6,7]=>[4,6]=>[6,4]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,6,7,8,9,1,4,5]=>[6,3]=>[3,6]
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4,9,10]=>[7,3]=>[3,7]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[8,2]=>[2,8]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[9,2]=>[2,9]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,8,9,10]=>[2,2,2,4]=>[4,2,2,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,9,8,10]=>[6,2,2]=>[2,2,6]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>[7,2,1]=>[1,2,7]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[1,10]=>[10,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2,9]=>[1,6,2]=>[2,6,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1,5,6,7,8,9,2]=>[2,6,1]=>[1,6,2]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,7,9,4,6,8,10]=>[6,4]=>[4,6]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[3,7]=>[7,3]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,6,7,8,9,10,2,3,4,5]=>[6,4]=>[4,6]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,5,6,7,8,9,10,2,3,4]=>[7,3]=>[3,7]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,4,5,6,7,8,9,10,2,3]=>[8,2]=>[2,8]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7,8,9,10]=>[5,5]=>[5,5]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[4,6]=>[6,4]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8,9,10]=>[3,7]=>[7,3]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,8,7,10,9]=>[5,2,2,1]=>[1,2,2,5]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,9,6,7,10,8]=>[6,3,1]=>[1,3,6]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,10,5,7,9]=>[1,2,2,2,3]=>[3,2,2,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,9,5,10,7]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,8,1,2,9,3,4,6,7]=>[2,3,4]=>[4,3,2]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,6,7,8,1,9,3,4]=>[5,2,2]=>[2,2,5]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[4,5,1,6,7,8,9,2,3]=>[2,5,2]=>[2,5,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,1,11,2,3,4,5,6,7,8,9]=>[1,2,8]=>[8,2,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[7,1,8,2,3,4,5,9,6]=>[1,2,5,1]=>[1,5,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,9,1,2,3,4,5,8]=>[3,6]=>[6,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,9,6,10,8]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[1,10]=>[10,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,7,1,4,8,9,5,6]=>[3,4,2]=>[2,4,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[3,6]=>[6,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,5,6,1,7,8,9,2,3]=>[3,4,2]=>[2,4,3]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,5,6,7,8,9,4]=>[1,7,1]=>[1,7,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,10,2,3,4,5,6,7,9]=>[1,2,7]=>[7,2,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,5,6,7,8,9,4]=>[1,7,1]=>[1,7,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[2,3,4,10,1,5,6,7,8,9]=>[4,6]=>[6,4]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,9,3]=>[1,7,1]=>[1,7,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,4,5,9,1,2,6,7,8]=>[4,5]=>[5,4]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,7,8,9,4,5,6]=>[1,5,3]=>[3,5,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,7,8,1,9,10,2,3,4,5]=>[3,3,4]=>[4,3,3]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[6,7,8,9,1,2,10,3,4,5]=>[4,3,3]=>[3,3,4]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,6,10]=>[8,2]=>[2,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,9,2,10,3,4,5,6,7,8]=>[2,2,6]=>[6,2,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,8,2,9,3,10,4,5,6,7]=>[2,2,2,4]=>[4,2,2,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,7,9,1,2,3,4,6,8]=>[3,6]=>[6,3]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,9,5,7,8]=>[2,2,2,3]=>[3,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4,8,9]=>[1,2,3,3]=>[3,3,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6,10,9]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,9,4]=>[2,6,1]=>[1,6,2]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,6,7,8,9,1,2,4,5]=>[5,4]=>[4,5]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,8,5,9,7]=>[1,3,2,2,1]=>[1,2,2,3,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7,8,9]=>[3,6]=>[6,3]
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8,9]=>[4,5]=>[5,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7,9]=>[2,7]=>[7,2]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,3,9]=>[1,6,2]=>[2,6,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7,9]=>[1,2,6]=>[6,2,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[3,8,1,2,4,5,6,7,9]=>[2,7]=>[7,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,5,6,1,3,8,9,4,7]=>[3,4,2]=>[2,4,3]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[2,8]=>[8,2]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,8,7,10,9]=>[1,4,2,2,1]=>[1,2,2,4,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7,10,9,12,11]=>[1,2,2,2,2,2,1]=>[1,2,2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6,11,12,9,10]=>[2,4,4,2]=>[2,4,4,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[2,10]=>[10,2]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,9,8,10]=>[4,4,2]=>[2,4,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,6,1,7,8,9,2,3,4]=>[2,4,3]=>[3,4,2]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,10,11,1,3]=>[9,2]=>[2,9]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[10,2]=>[2,10]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,12,11]=>[11,1]=>[1,11]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8,9,10]=>[2,8]=>[8,2]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[7,3]=>[3,7]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[6,4]=>[4,6]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[5,5]=>[5,5]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,9,10,11,3]=>[10,1]=>[1,10]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,3,10,2,4,5,6,7,8,9]=>[3,7]=>[7,3]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,5,6,7,8,9,2,4]=>[1,6,2]=>[2,6,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,6,7,8,9,2,3,5]=>[1,5,3]=>[3,5,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,1,8,9,2,3,4,5,7]=>[1,3,5]=>[5,3,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[1,9,1]=>[1,9,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,7,8,9,10,11,2,3,4,5]=>[1,6,4]=>[4,6,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,7,9,3,4,5,6,8]=>[1,3,5]=>[5,3,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,1,9,10,11,2,3,4,5,6,7]=>[1,4,6]=>[6,4,1]
[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,2,11,10]=>[8,2,1]=>[1,2,8]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5,9,10,8]=>[1,5,3,1]=>[1,3,5,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,8,1,9,2,10,3,4,5,6]=>[2,2,2,4]=>[4,2,2,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,7,1,8,2,9,3,10,4,5]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[5,6,1,7,2,8,3,9,4,10]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,9,6,8,10]=>[7,3]=>[3,7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7,10,9,12,11]=>[1,2,2,2,2,2,1]=>[1,2,2,2,2,2,1]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,10,9]=>[2,7,1]=>[1,7,2]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[1,8,1]=>[1,8,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[3,8,9,1,2,4,5,6,7]=>[3,6]=>[6,3]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5,9,8]=>[1,2,3,2,1]=>[1,2,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,9,7,8]=>[3,4,2]=>[2,4,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,8,4,6,9,7]=>[1,2,2,3,1]=>[1,3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7,9,10,8]=>[1,4,4,1]=>[1,4,4,1]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7,9,12,10,11]=>[2,4,4,2]=>[2,4,4,2]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,7,8,6,9,11,12,10]=>[3,4,4,1]=>[1,4,4,3]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7,8,9,10]=>[2,3,5]=>[5,3,2]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7,9,10]=>[2,4,4]=>[4,4,2]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,8,9,5,7]=>[3,4,2]=>[2,4,3]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,6,8,1,3,9,4,7]=>[4,3,2]=>[2,3,4]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,5,6,7,8,9,10,11,1,4]=>[9,2]=>[2,9]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,7,8,9,2,10,3,4,5,6]=>[4,2,4]=>[4,2,4]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,8,9,6,7]=>[2,5,2]=>[2,5,2]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,9,4,8]=>[3,4,2]=>[2,4,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,7,2,9,3,4,6,8]=>[1,2,2,4]=>[4,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,8,1,2,3,6,9,7]=>[3,5,1]=>[1,5,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7,10,9,12,11]=>[1,2,2,2,2,2,1]=>[1,2,2,2,2,2,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,9,7]=>[1,3,4,1]=>[1,4,3,1]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,11,12,10]=>[11,1]=>[1,11]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,9,10,11]=>[2,9]=>[9,2]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,10,7,9]=>[3,2,3,2]=>[2,3,2,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[3,1,2,9,4,5,6,7,8]=>[1,3,5]=>[5,3,1]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2,10,9]=>[5,2,2,1]=>[1,2,2,5]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,10,6,8,9]=>[2,5,3]=>[3,5,2]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,6,7,8,9,2,3,4,5,10]=>[5,5]=>[5,5]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,7,8,9,10,6]=>[4,5,1]=>[1,5,4]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7,8,9]=>[3,2,4]=>[4,2,3]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,9,10,5]=>[3,6,1]=>[1,6,3]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7,8,9]=>[2,2,5]=>[5,2,2]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,9,10,4]=>[2,7,1]=>[1,7,2]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,8,5,10,9]=>[3,2,2,2,1]=>[1,2,2,2,3]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,6,7,1,8,2,3,4,9]=>[3,2,4]=>[4,2,3]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[2,9]=>[9,2]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7,12,8,9,10,11]=>[2,3,3,4]=>[4,3,3,2]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,9,10,2]=>[6,3,1]=>[1,3,6]
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,9,2,10]=>[6,2,2]=>[2,2,6]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,8,9]=>[4,2,3]=>[3,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,6,7,9]=>[1,3,5]=>[5,3,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,9,10,5,8]=>[4,4,2]=>[2,4,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,6,9,1,10,3,4,11,5,12,7,8]=>[3,2,3,2,2]=>[2,2,3,2,3]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,5,2,7,8,9,6]=>[2,2,4,1]=>[1,4,2,2]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,10,6,7,8,9]=>[4,2,4]=>[4,2,4]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[1,2,9,3,4,5,6,7,10,8]=>[3,6,1]=>[1,6,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,10,9,12,11]=>[1,2,2,2,2,2,1]=>[1,2,2,2,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,7,2,8,3,9,5,10,6]=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,9,1,2,3,4,8]=>[4,5]=>[5,4]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,9,5]=>[3,5,1]=>[1,5,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,8,9,5]=>[2,6,1]=>[1,6,2]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8,9]=>[5,4]=>[4,5]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[3,7]=>[7,3]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,9,3,10,4,7,8]=>[2,3,2,3]=>[3,2,3,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,9,10,7,8]=>[2,2,4,2]=>[2,4,2,2]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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 $(i_k, i_{k-1}, \ldots, i_1)$.
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