Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00064: Permutations —reverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0002;cc-rep-4
[1,0]=>[1]=>[1]=>[1]=>[1]
[1,0,1,0]=>[2,1]=>[1,2]=>[2]=>[2]
[1,1,0,0]=>[1,2]=>[2,1]=>[1,1]=>[1,1]
[1,0,1,0,1,0]=>[2,3,1]=>[1,3,2]=>[2,1]=>[2,1]
[1,0,1,1,0,0]=>[2,1,3]=>[3,1,2]=>[1,2]=>[2,1]
[1,1,0,0,1,0]=>[1,3,2]=>[2,3,1]=>[2,1]=>[2,1]
[1,1,0,1,0,0]=>[3,1,2]=>[2,1,3]=>[1,2]=>[2,1]
[1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>[1,1,1]=>[1,1,1]
[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>[1,4,3,2]=>[2,1,1]=>[2,1,1]
[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[4,1,3,2]=>[1,2,1]=>[2,1,1]
[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[3,4,1,2]=>[2,2]=>[2,2]
[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>[3,1,4,2]=>[1,2,1]=>[2,1,1]
[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[4,3,1,2]=>[1,1,2]=>[2,1,1]
[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>[2,4,3,1]=>[2,1,1]=>[2,1,1]
[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[4,2,3,1]=>[1,2,1]=>[2,1,1]
[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>[2,4,1,3]=>[2,2]=>[2,2]
[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>[2,1,4,3]=>[1,2,1]=>[2,1,1]
[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>[4,2,1,3]=>[1,1,2]=>[2,1,1]
[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>[3,4,2,1]=>[2,1,1]=>[2,1,1]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[3,2,4,1]=>[1,2,1]=>[2,1,1]
[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>[3,2,1,4]=>[1,1,2]=>[2,1,1]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>[1,1,1,1]=>[1,1,1,1]
[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[2,1,1,1]=>[2,1,1,1]
[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[1,2,1,1]=>[2,1,1,1]
[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>[4,5,1,3,2]=>[2,2,1]=>[2,2,1]
[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>[4,1,5,3,2]=>[1,2,1,1]=>[2,1,1,1]
[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[1,1,2,1]=>[2,1,1,1]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>[3,5,4,1,2]=>[2,1,2]=>[2,2,1]
[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[5,3,4,1,2]=>[1,2,2]=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>[3,5,1,4,2]=>[2,2,1]=>[2,2,1]
[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>[3,1,5,4,2]=>[1,2,1,1]=>[2,1,1,1]
[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>[5,3,1,4,2]=>[1,1,2,1]=>[2,1,1,1]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[2,1,2]=>[2,2,1]
[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>[4,3,5,1,2]=>[1,2,2]=>[2,2,1]
[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>[4,3,1,5,2]=>[1,1,2,1]=>[2,1,1,1]
[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[1,1,1,2]=>[2,1,1,1]
[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[2,1,1,1]=>[2,1,1,1]
[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[1,2,1,1]=>[2,1,1,1]
[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[2,2,1]=>[2,2,1]
[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>[4,2,5,3,1]=>[1,2,1,1]=>[2,1,1,1]
[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[1,1,2,1]=>[2,1,1,1]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>[2,5,4,1,3]=>[2,1,2]=>[2,2,1]
[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>[5,2,4,1,3]=>[1,2,2]=>[2,2,1]
[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>[2,5,1,4,3]=>[2,2,1]=>[2,2,1]
[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>[2,1,5,4,3]=>[1,2,1,1]=>[2,1,1,1]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>[5,2,1,4,3]=>[1,1,2,1]=>[2,1,1,1]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>[4,5,2,1,3]=>[2,1,2]=>[2,2,1]
[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>[4,2,5,1,3]=>[1,2,2]=>[2,2,1]
[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>[4,2,1,5,3]=>[1,1,2,1]=>[2,1,1,1]
[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>[5,4,2,1,3]=>[1,1,1,2]=>[2,1,1,1]
[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[2,1,1,1]=>[2,1,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[1,2,1,1]=>[2,1,1,1]
[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[2,2,1]=>[2,2,1]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>[3,2,5,4,1]=>[1,2,1,1]=>[2,1,1,1]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[1,1,2,1]=>[2,1,1,1]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>[3,5,2,1,4]=>[2,1,2]=>[2,2,1]
[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>[3,2,5,1,4]=>[1,2,2]=>[2,2,1]
[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[1,1,2,1]=>[2,1,1,1]
[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>[5,3,2,1,4]=>[1,1,1,2]=>[2,1,1,1]
[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[2,1,1,1]=>[2,1,1,1]
[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[1,2,1,1]=>[2,1,1,1]
[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[1,1,2,1]=>[2,1,1,1]
[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[1,1,1,2]=>[2,1,1,1]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[2,1,1,1,1]=>[2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>[2,2,1,1]=>[2,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>[5,1,6,4,3,2]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>[2,1,2,1]=>[2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>[1,2,2,1]=>[2,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>[4,6,1,5,3,2]=>[2,2,1,1]=>[2,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>[4,1,6,5,3,2]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[6,4,1,5,3,2]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[2,1,2,1]=>[2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,2,2,1]=>[2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>[2,1,1,2]=>[2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>[1,2,1,2]=>[2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,2,2]=>[2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>[5,3,6,4,1,2]=>[1,2,1,2]=>[2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[1,1,2,2]=>[2,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>[3,6,5,1,4,2]=>[2,1,2,1]=>[2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>[6,3,5,1,4,2]=>[1,2,2,1]=>[2,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>[3,6,1,5,4,2]=>[2,2,1,1]=>[2,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>[3,1,6,5,4,2]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[6,3,1,5,4,2]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>[5,6,3,1,4,2]=>[2,1,2,1]=>[2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,2,2,1]=>[2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>[6,5,3,1,4,2]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>[2,1,1,2]=>[2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[1,2,1,2]=>[2,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>[4,6,3,5,1,2]=>[2,2,2]=>[2,2,2]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>[4,3,6,5,1,2]=>[1,2,1,2]=>[2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>[6,4,3,5,1,2]=>[1,1,2,2]=>[2,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>[4,6,3,1,5,2]=>[2,1,2,1]=>[2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>[4,3,6,1,5,2]=>[1,2,2,1]=>[2,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>[4,3,1,6,5,2]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>[6,4,3,1,5,2]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[2,1,1,2]=>[2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>[5,4,6,3,1,2]=>[1,2,1,2]=>[2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>[5,4,3,6,1,2]=>[1,1,2,2]=>[2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>[5,4,3,1,6,2]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[2,1,1,1,1]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[2,2,1,1]=>[2,2,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[2,1,2,1]=>[2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[2,2,1,1]=>[2,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[2,1,2,1]=>[2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>[2,6,5,4,1,3]=>[2,1,1,2]=>[2,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>[6,2,5,4,1,3]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>[5,6,2,4,1,3]=>[2,2,2]=>[2,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>[5,2,6,4,1,3]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>[6,5,2,4,1,3]=>[1,1,2,2]=>[2,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>[2,6,5,1,4,3]=>[2,1,2,1]=>[2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>[6,2,5,1,4,3]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>[2,6,1,5,4,3]=>[2,2,1,1]=>[2,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>[5,6,2,1,4,3]=>[2,1,2,1]=>[2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>[5,2,6,1,4,3]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>[5,2,1,6,4,3]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>[2,1,1,2]=>[2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>[6,4,5,2,1,3]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[2,2,2]=>[2,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>[4,2,6,5,1,3]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>[6,4,2,5,1,3]=>[1,1,2,2]=>[2,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>[4,6,2,1,5,3]=>[2,1,2,1]=>[2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[1,2,2,1]=>[2,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>[6,4,2,1,5,3]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>[5,6,4,2,1,3]=>[2,1,1,2]=>[2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>[5,4,6,2,1,3]=>[1,2,1,2]=>[2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>[5,4,2,6,1,3]=>[1,1,2,2]=>[2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>[5,4,2,1,6,3]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[2,1,1,1,1]=>[2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[2,2,1,1]=>[2,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[2,1,2,1]=>[2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[1,2,2,1]=>[2,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[2,2,1,1]=>[2,2,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[2,1,2,1]=>[2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[1,2,2,1]=>[2,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>[2,1,1,2]=>[2,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>[6,3,5,2,1,4]=>[1,2,1,2]=>[2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>[2,2,2]=>[2,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>[3,2,6,5,1,4]=>[1,2,1,2]=>[2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>[6,3,2,5,1,4]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>[3,6,2,1,5,4]=>[2,1,2,1]=>[2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>[1,2,2,1]=>[2,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>[5,6,3,2,1,4]=>[2,1,1,2]=>[2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>[5,3,6,2,1,4]=>[1,2,1,2]=>[2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>[5,3,2,6,1,4]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>[5,3,2,1,6,4]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[2,1,1,1,1]=>[2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[2,2,1,1]=>[2,2,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[2,1,2,1]=>[2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[1,2,2,1]=>[2,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>[4,6,3,2,1,5]=>[2,1,1,2]=>[2,2,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>[4,3,6,2,1,5]=>[1,2,1,2]=>[2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>[4,3,2,6,1,5]=>[1,1,2,2]=>[2,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[2,1,1,1,1]=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>[6,1,7,5,4,3,2]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>[5,7,1,6,4,3,2]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>[5,1,7,6,4,3,2]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]=>[7,5,1,6,4,3,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]=>[6,5,7,1,4,3,2]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>[6,5,1,7,4,3,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>[4,7,6,5,1,3,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>[7,4,6,5,1,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]=>[6,4,7,5,1,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]=>[4,7,6,1,5,3,2]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]=>[7,4,6,1,5,3,2]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]=>[4,7,1,6,5,3,2]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>[4,1,7,6,5,3,2]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]=>[7,4,1,6,5,3,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]=>[6,7,4,1,5,3,2]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]=>[6,4,7,1,5,3,2]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]=>[6,4,1,7,5,3,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]=>[7,6,4,1,5,3,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[5,7,6,4,1,3,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]=>[5,7,4,6,1,3,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]=>[5,4,7,6,1,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]=>[7,5,4,6,1,3,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]=>[5,7,4,1,6,3,2]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]=>[5,4,7,1,6,3,2]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]=>[5,4,1,7,6,3,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]=>[7,5,4,1,6,3,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[6,5,7,4,1,3,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]=>[6,5,4,7,1,3,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]=>[6,5,4,1,7,3,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>[3,7,6,5,4,1,2]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[7,3,6,5,4,1,2]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[6,7,3,5,4,1,2]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]=>[6,3,7,5,4,1,2]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>[7,6,3,5,4,1,2]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[5,7,6,3,4,1,2]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[5,7,3,6,4,1,2]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]=>[5,3,7,6,4,1,2]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]=>[7,5,3,6,4,1,2]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]=>[6,5,7,3,4,1,2]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]=>[6,5,3,7,4,1,2]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]=>[3,7,6,5,1,4,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]=>[7,3,6,5,1,4,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]=>[6,7,3,5,1,4,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]=>[6,3,7,5,1,4,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]=>[7,6,3,5,1,4,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]=>[3,7,6,1,5,4,2]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]=>[7,3,6,1,5,4,2]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]=>[3,7,1,6,5,4,2]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]=>[3,1,7,6,5,4,2]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]=>[7,3,1,6,5,4,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]=>[6,7,3,1,5,4,2]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]=>[6,3,7,1,5,4,2]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]=>[6,3,1,7,5,4,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]=>[7,6,3,1,5,4,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]=>[5,7,6,3,1,4,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[7,5,6,3,1,4,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]=>[5,7,3,6,1,4,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]=>[5,3,7,6,1,4,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]=>[7,5,3,6,1,4,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]=>[5,7,3,1,6,4,2]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]=>[5,3,7,1,6,4,2]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]=>[5,3,1,7,6,4,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5,7]=>[7,5,3,1,6,4,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]=>[6,7,5,3,1,4,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]=>[6,5,7,3,1,4,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]=>[6,5,3,7,1,4,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]=>[6,5,3,1,7,4,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>[7,6,5,3,1,4,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>[4,7,6,5,3,1,2]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[7,4,6,5,3,1,2]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]=>[6,4,7,5,3,1,2]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[4,7,6,3,5,1,2]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]=>[7,4,6,3,5,1,2]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[4,7,3,6,5,1,2]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]=>[4,3,7,6,5,1,2]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]=>[7,4,3,6,5,1,2]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]=>[6,7,4,3,5,1,2]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]=>[6,4,7,3,5,1,2]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]=>[6,4,3,7,5,1,2]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]=>[7,6,4,3,5,1,2]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]=>[4,7,6,3,1,5,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[7,4,6,3,1,5,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]=>[4,7,3,6,1,5,2]=>[2,2,2,1]=>[2,2,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]=>[4,3,7,6,1,5,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]=>[7,4,3,6,1,5,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]=>[4,7,3,1,6,5,2]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]=>[4,3,7,1,6,5,2]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]=>[4,3,1,7,6,5,2]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]=>[7,4,3,1,6,5,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]=>[6,7,4,3,1,5,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]=>[6,4,7,3,1,5,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]=>[6,4,3,7,1,5,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>[6,4,3,1,7,5,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>[7,6,4,3,1,5,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[5,7,6,4,3,1,2]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[5,7,4,6,3,1,2]=>[2,2,1,2]=>[2,2,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]=>[5,4,7,6,3,1,2]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]=>[7,5,4,6,3,1,2]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]=>[5,7,4,3,6,1,2]=>[2,1,2,2]=>[2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]=>[5,4,7,3,6,1,2]=>[1,2,2,2]=>[2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]=>[5,4,3,7,6,1,2]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>[7,5,4,3,6,1,2]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]=>[5,7,4,3,1,6,2]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]=>[5,4,7,3,1,6,2]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>[5,4,3,7,1,6,2]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>[5,4,3,1,7,6,2]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>[7,5,4,3,1,6,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>[6,5,7,4,3,1,2]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>[6,5,4,7,3,1,2]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>[6,5,4,3,7,1,2]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[6,5,4,3,1,7,2]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]=>[6,2,7,5,4,3,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]=>[5,7,2,6,4,3,1]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]=>[5,2,7,6,4,3,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[2,2,2,1]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]=>[4,7,6,2,5,3,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]=>[4,7,2,6,5,3,1]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]=>[4,2,7,6,5,3,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[2,2,2,1]=>[2,2,2,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]=>[2,7,6,5,4,1,3]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]=>[7,2,6,5,4,1,3]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[6,7,2,5,4,1,3]=>[2,2,1,2]=>[2,2,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]=>[6,2,7,5,4,1,3]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]=>[7,6,2,5,4,1,3]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[5,7,6,2,4,1,3]=>[2,1,2,2]=>[2,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]=>[7,5,6,2,4,1,3]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[5,7,2,6,4,1,3]=>[2,2,1,2]=>[2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]=>[5,2,7,6,4,1,3]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]=>[7,5,2,6,4,1,3]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]=>[6,7,5,2,4,1,3]=>[2,1,2,2]=>[2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]=>[6,5,7,2,4,1,3]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]=>[6,5,2,7,4,1,3]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]=>[7,6,5,2,4,1,3]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]=>[2,7,6,5,1,4,3]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]=>[7,2,6,5,1,4,3]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]=>[6,7,2,5,1,4,3]=>[2,2,2,1]=>[2,2,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]=>[6,2,7,5,1,4,3]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]=>[7,6,2,5,1,4,3]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]=>[2,7,6,1,5,4,3]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]=>[7,2,6,1,5,4,3]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]=>[2,7,1,6,5,4,3]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]=>[6,7,2,1,5,4,3]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]=>[6,2,7,1,5,4,3]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]=>[6,2,1,7,5,4,3]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]=>[5,7,6,2,1,4,3]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[7,5,6,2,1,4,3]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]=>[5,7,2,6,1,4,3]=>[2,2,2,1]=>[2,2,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]=>[5,2,7,6,1,4,3]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]=>[7,5,2,6,1,4,3]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]=>[5,7,2,1,6,4,3]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]=>[5,2,7,1,6,4,3]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]=>[5,2,1,7,6,4,3]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]=>[7,5,2,1,6,4,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]=>[6,7,5,2,1,4,3]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]=>[6,5,7,2,1,4,3]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]=>[6,5,2,7,1,4,3]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,7,1,2,5,6]=>[6,5,2,1,7,4,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]=>[4,7,6,5,2,1,3]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]=>[7,4,6,5,2,1,3]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[6,7,4,5,2,1,3]=>[2,2,1,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]=>[6,4,7,5,2,1,3]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]=>[7,6,4,5,2,1,3]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[4,7,6,2,5,1,3]=>[2,1,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]=>[7,4,6,2,5,1,3]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[4,7,2,6,5,1,3]=>[2,2,1,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]=>[4,2,7,6,5,1,3]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]=>[7,4,2,6,5,1,3]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]=>[6,7,4,2,5,1,3]=>[2,1,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]=>[6,4,7,2,5,1,3]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]=>[6,4,2,7,5,1,3]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]=>[7,6,4,2,5,1,3]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]=>[4,7,6,2,1,5,3]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[7,4,6,2,1,5,3]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]=>[4,7,2,6,1,5,3]=>[2,2,2,1]=>[2,2,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]=>[4,2,7,6,1,5,3]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]=>[7,4,2,6,1,5,3]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]=>[4,7,2,1,6,5,3]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]=>[4,2,7,1,6,5,3]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]=>[4,2,1,7,6,5,3]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>[7,4,2,1,6,5,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]=>[6,7,4,2,1,5,3]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]=>[6,4,7,2,1,5,3]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]=>[6,4,2,7,1,5,3]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]=>[7,6,4,2,1,5,3]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]=>[5,7,6,4,2,1,3]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]=>[7,5,6,4,2,1,3]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[5,7,4,6,2,1,3]=>[2,2,1,2]=>[2,2,2,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]=>[5,4,7,6,2,1,3]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]=>[7,5,4,6,2,1,3]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]=>[5,7,4,2,6,1,3]=>[2,1,2,2]=>[2,2,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]=>[5,4,7,2,6,1,3]=>[1,2,2,2]=>[2,2,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]=>[5,4,2,7,6,1,3]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]=>[7,5,4,2,6,1,3]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]=>[5,7,4,2,1,6,3]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]=>[5,4,7,2,1,6,3]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]=>[5,4,2,7,1,6,3]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]=>[5,4,2,1,7,6,3]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>[7,5,4,2,1,6,3]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[6,7,5,4,2,1,3]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]=>[6,5,7,4,2,1,3]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]=>[6,5,4,7,2,1,3]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]=>[6,5,4,2,7,1,3]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[6,5,4,2,1,7,3]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[2,2,2,1]=>[2,2,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]=>[3,7,6,2,5,4,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]=>[3,7,2,6,5,4,1]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[2,2,2,1]=>[2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]=>[3,7,6,5,2,1,4]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]=>[7,3,6,5,2,1,4]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[6,7,3,5,2,1,4]=>[2,2,1,2]=>[2,2,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]=>[6,3,7,5,2,1,4]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]=>[7,6,3,5,2,1,4]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[3,7,6,2,5,1,4]=>[2,1,2,2]=>[2,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]=>[7,3,6,2,5,1,4]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[3,7,2,6,5,1,4]=>[2,2,1,2]=>[2,2,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]=>[3,2,7,6,5,1,4]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]=>[7,3,2,6,5,1,4]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]=>[6,7,3,2,5,1,4]=>[2,1,2,2]=>[2,2,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]=>[6,3,7,2,5,1,4]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]=>[6,3,2,7,5,1,4]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]=>[7,6,3,2,5,1,4]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]=>[3,7,6,2,1,5,4]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[7,3,6,2,1,5,4]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]=>[3,7,2,6,1,5,4]=>[2,2,2,1]=>[2,2,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]=>[3,2,7,6,1,5,4]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>[7,3,2,6,1,5,4]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]=>[3,7,2,1,6,5,4]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]=>[3,2,7,1,6,5,4]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]=>[6,7,3,2,1,5,4]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]=>[6,3,7,2,1,5,4]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]=>[6,3,2,7,1,5,4]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]=>[6,3,2,1,7,5,4]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]=>[5,7,6,3,2,1,4]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]=>[7,5,6,3,2,1,4]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[5,7,3,6,2,1,4]=>[2,2,1,2]=>[2,2,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,6,7,3,5]=>[5,3,7,6,2,1,4]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]=>[7,5,3,6,2,1,4]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]=>[5,7,3,2,6,1,4]=>[2,1,2,2]=>[2,2,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,5]=>[5,3,7,2,6,1,4]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]=>[5,3,2,7,6,1,4]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>[7,5,3,2,6,1,4]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>[5,7,3,2,1,6,4]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]=>[5,3,7,2,1,6,4]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]=>[5,3,2,7,1,6,4]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]=>[5,3,2,1,7,6,4]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>[7,5,3,2,1,6,4]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[6,7,5,3,2,1,4]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]=>[6,5,7,3,2,1,4]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]=>[6,5,3,7,2,1,4]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]=>[6,5,3,2,7,1,4]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[6,5,3,2,1,7,4]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[2,2,2,1]=>[2,2,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>[4,7,6,3,2,1,5]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>[7,4,6,3,2,1,5]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[4,7,3,6,2,1,5]=>[2,2,1,2]=>[2,2,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,2,6,7,3,4]=>[4,3,7,6,2,1,5]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>[7,4,3,6,2,1,5]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>[4,7,3,2,6,1,5]=>[2,1,2,2]=>[2,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,4]=>[4,3,7,2,6,1,5]=>[1,2,2,2]=>[2,2,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]=>[4,3,2,7,6,1,5]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>[7,4,3,2,6,1,5]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>[4,7,3,2,1,6,5]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]=>[4,3,7,2,1,6,5]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,3,4]=>[4,3,2,7,1,6,5]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[6,7,4,3,2,1,5]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>[6,4,7,3,2,1,5]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]=>[6,4,3,7,2,1,5]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]=>[6,4,3,2,7,1,5]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[2,2,1,1,1]=>[2,2,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[2,1,2,1,1]=>[2,2,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[2,1,1,2,1]=>[2,2,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[5,7,4,3,2,1,6]=>[2,1,1,1,2]=>[2,2,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>[5,4,7,3,2,1,6]=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>[5,4,3,7,2,1,6]=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]=>[5,4,3,2,7,1,6]=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>[7,8,1,6,5,4,3,2]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,8,1,7]=>[7,1,8,6,5,4,3,2]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,8,6]=>[6,8,7,1,5,4,3,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[8,6,7,1,5,4,3,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,7,1,8,6]=>[6,8,1,7,5,4,3,2]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,1,6]=>[6,1,8,7,5,4,3,2]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6,8]=>[8,6,1,7,5,4,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]=>[7,8,6,1,5,4,3,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,1,8,6,7]=>[7,6,8,1,5,4,3,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,8,1,6,7]=>[7,6,1,8,5,4,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>[8,5,7,6,1,4,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[7,8,5,6,1,4,3,2]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,8,5,7]=>[7,5,8,6,1,4,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[8,7,5,6,1,4,3,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,4,6,1,7,8,5]=>[5,8,7,1,6,4,3,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,4,6,1,7,5,8]=>[8,5,7,1,6,4,3,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,4,6,7,1,8,5]=>[5,8,1,7,6,4,3,2]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,1,5]=>[5,1,8,7,6,4,3,2]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,7,1,5,8]=>[8,5,1,7,6,4,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,8,7]=>[7,8,5,1,6,4,3,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,8,5,7]=>[7,5,8,1,6,4,3,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,8,1,5,7]=>[7,5,1,8,6,4,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]=>[8,7,5,1,6,4,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,1,5,7,8,6]=>[6,8,7,5,1,4,3,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[8,6,7,5,1,4,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,4,1,7,5,8,6]=>[6,8,5,7,1,4,3,2]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,1,7,8,5,6]=>[6,5,8,7,1,4,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,4,1,7,5,6,8]=>[8,6,5,7,1,4,3,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,4,7,1,5,8,6]=>[6,8,5,1,7,4,3,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,4,7,1,8,5,6]=>[6,5,8,1,7,4,3,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,7,8,1,5,6]=>[6,5,1,8,7,4,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>[8,6,5,1,7,4,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,1,5,6,8,7]=>[7,8,6,5,1,4,3,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,4,1,5,8,6,7]=>[7,6,8,5,1,4,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>[7,6,5,8,1,4,3,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]=>[4,8,7,6,5,1,3,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]=>[8,4,7,6,5,1,3,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,6,4,8,7]=>[7,8,4,6,5,1,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,5,6,8,4,7]=>[7,4,8,6,5,1,3,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[8,7,4,6,5,1,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,7,8,6]=>[6,8,7,4,5,1,3,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[8,6,7,4,5,1,3,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,7,4,8,6]=>[6,8,4,7,5,1,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,7,8,4,6]=>[6,4,8,7,5,1,3,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,4,6,8]=>[8,6,4,7,5,1,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,5,8,4,6,7]=>[7,6,4,8,5,1,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[8,7,6,4,5,1,3,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,4]=>[4,8,7,6,1,5,3,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,5,1,6,7,4,8]=>[8,4,7,6,1,5,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,5,1,6,4,8,7]=>[7,8,4,6,1,5,3,2]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,5,1,6,8,4,7]=>[7,4,8,6,1,5,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,4,7,8]=>[8,7,4,6,1,5,3,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,1,7,8,4]=>[4,8,7,1,6,5,3,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,5,6,1,7,4,8]=>[8,4,7,1,6,5,3,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,7,1,8,4]=>[4,8,1,7,6,5,3,2]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,1,4]=>[4,1,8,7,6,5,3,2]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,7,1,4,8]=>[8,4,1,7,6,5,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,6,1,4,8,7]=>[7,8,4,1,6,5,3,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,6,1,8,4,7]=>[7,4,8,1,6,5,3,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,8,1,4,7]=>[7,4,1,8,6,5,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]=>[8,7,4,1,6,5,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,7,8,6]=>[6,8,7,4,1,5,3,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6,8]=>[8,6,7,4,1,5,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,7,4,8,6]=>[6,8,4,7,1,5,3,2]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,1,7,8,4,6]=>[6,4,8,7,1,5,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,7,4,6,8]=>[8,6,4,7,1,5,3,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,7,1,4,8,6]=>[6,8,4,1,7,5,3,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,7,1,8,4,6]=>[6,4,8,1,7,5,3,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,7,8,1,4,6]=>[6,4,1,8,7,5,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6,8]=>[8,6,4,1,7,5,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,4,6,8,7]=>[7,8,6,4,1,5,3,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,5,1,4,8,6,7]=>[7,6,8,4,1,5,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]=>[7,6,4,8,1,5,3,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,8,1,4,6,7]=>[7,6,4,1,8,5,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,4,6,7,8]=>[8,7,6,4,1,5,3,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>[5,8,7,6,4,1,3,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[8,5,7,6,4,1,3,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,8,7]=>[7,8,5,6,4,1,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,1,4,6,8,5,7]=>[7,5,8,6,4,1,3,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,1,4,6,5,7,8]=>[8,7,5,6,4,1,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,6,4,7,8,5]=>[5,8,7,4,6,1,3,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,6,4,7,5,8]=>[8,5,7,4,6,1,3,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,6,7,4,8,5]=>[5,8,4,7,6,1,3,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>[5,4,8,7,6,1,3,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>[7,5,8,4,6,1,3,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,6,8,4,5,7]=>[7,5,4,8,6,1,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,1,6,4,5,7,8]=>[8,7,5,4,6,1,3,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,7,8,5]=>[5,8,7,4,1,6,3,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,6,1,4,7,5,8]=>[8,5,7,4,1,6,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,6,1,7,4,8,5]=>[5,8,4,7,1,6,3,2]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,1,7,8,4,5]=>[5,4,8,7,1,6,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,7,4,5,8]=>[8,5,4,7,1,6,3,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,6,7,1,4,8,5]=>[5,8,4,1,7,6,3,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,6,7,1,8,4,5]=>[5,4,8,1,7,6,3,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,7,8,1,4,5]=>[5,4,1,8,7,6,3,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,6,7,1,4,5,8]=>[8,5,4,1,7,6,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,8,7]=>[7,8,5,4,1,6,3,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,8,5,7]=>[7,5,8,4,1,6,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]=>[7,5,4,8,1,6,3,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,6,8,1,4,5,7]=>[7,5,4,1,8,6,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,6,1,4,5,7,8]=>[8,7,5,4,1,6,3,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[8,6,7,5,4,1,3,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>[6,5,8,7,4,1,3,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,1,4,7,5,6,8]=>[8,6,5,7,4,1,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,7,4,5,8,6]=>[6,8,5,4,7,1,3,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>[6,5,8,4,7,1,3,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,7,8,4,5,6]=>[6,5,4,8,7,1,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,1,7,4,5,6,8]=>[8,6,5,4,7,1,3,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,7,1,4,5,8,6]=>[6,8,5,4,1,7,3,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,7,1,4,8,5,6]=>[6,5,8,4,1,7,3,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[6,5,4,1,8,7,3,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6,8]=>[8,6,5,4,1,7,3,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[7,8,6,5,4,1,3,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]=>[7,6,8,5,4,1,3,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,1,4,8,5,6,7]=>[7,6,5,8,4,1,3,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>[7,6,5,4,8,1,3,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>[7,6,5,4,1,8,3,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,3]=>[3,8,7,6,5,4,1,2]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,7,3,8]=>[8,3,7,6,5,4,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[7,8,3,6,5,4,1,2]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,6,8,3,7]=>[7,3,8,6,5,4,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,6,3,7,8]=>[8,7,3,6,5,4,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3,7,8,6]=>[6,8,7,3,5,4,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>[6,8,3,7,5,4,1,2]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,7,8,3,6]=>[6,3,8,7,5,4,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,4,5,3,8,6,7]=>[7,6,8,3,5,4,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4,5,8,3,6,7]=>[7,6,3,8,5,4,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[8,7,6,3,5,4,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[5,8,7,6,3,4,1,2]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[8,5,7,6,3,4,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,8,5,7]=>[7,5,8,6,3,4,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[8,7,5,6,3,4,1,2]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,6,3,7,8,5]=>[5,8,7,3,6,4,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,6,7,3,8,5]=>[5,8,3,7,6,4,1,2]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,6,7,8,3,5]=>[5,3,8,7,6,4,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,6,7,3,5,8]=>[8,5,3,7,6,4,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>[7,8,5,3,6,4,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,8,5,7]=>[7,5,8,3,6,4,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,8,3,5,7]=>[7,5,3,8,6,4,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,6,3,5,7,8]=>[8,7,5,3,6,4,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[6,8,7,5,3,4,1,2]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,3,7,5,8,6]=>[6,8,5,7,3,4,1,2]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>[6,5,8,7,3,4,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,4,3,7,5,6,8]=>[8,6,5,7,3,4,1,2]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,7,3,5,8,6]=>[6,8,5,3,7,4,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,4,7,3,8,5,6]=>[6,5,8,3,7,4,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,4,7,8,3,5,6]=>[6,5,3,8,7,4,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[7,8,6,5,3,4,1,2]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,3,5,8,6,7]=>[7,6,8,5,3,4,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,3,8,5,6,7]=>[7,6,5,8,3,4,1,2]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>[7,6,5,3,8,4,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,3]=>[3,8,7,6,5,1,4,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,5,6,7,3,8]=>[8,3,7,6,5,1,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,6,8,3,7]=>[7,3,8,6,5,1,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,5,6,3,7,8]=>[8,7,3,6,5,1,4,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,5,3,7,8,6]=>[6,8,7,3,5,1,4,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,8]=>[8,6,7,3,5,1,4,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,7,3,8,6]=>[6,8,3,7,5,1,4,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,7,8,3,6]=>[6,3,8,7,5,1,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,4,1,5,7,3,6,8]=>[8,6,3,7,5,1,4,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,3,6,8,7]=>[7,8,6,3,5,1,4,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>[7,6,8,3,5,1,4,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,5,8,3,6,7]=>[7,6,3,8,5,1,4,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,3,6,7,8]=>[8,7,6,3,5,1,4,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,5,1,6,7,8,3]=>[3,8,7,6,1,5,4,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,5,1,6,7,3,8]=>[8,3,7,6,1,5,4,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,5,1,6,3,8,7]=>[7,8,3,6,1,5,4,2]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,5,1,6,8,3,7]=>[7,3,8,6,1,5,4,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>[8,7,3,6,1,5,4,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,6,1,7,8,3]=>[3,8,7,1,6,5,4,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,6,1,7,3,8]=>[8,3,7,1,6,5,4,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,1,8,3]=>[3,8,1,7,6,5,4,2]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,1,3]=>[3,1,8,7,6,5,4,2]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,1,3,8]=>[8,3,1,7,6,5,4,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,6,1,3,8,7]=>[7,8,3,1,6,5,4,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,6,1,8,3,7]=>[7,3,8,1,6,5,4,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,6,8,1,3,7]=>[7,3,1,8,6,5,4,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>[8,7,3,1,6,5,4,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,7,8,6]=>[6,8,7,3,1,5,4,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,5,1,7,3,8,6]=>[6,8,3,7,1,5,4,2]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,5,1,7,8,3,6]=>[6,3,8,7,1,5,4,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>[8,6,3,7,1,5,4,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,7,1,3,8,6]=>[6,8,3,1,7,5,4,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,7,1,8,3,6]=>[6,3,8,1,7,5,4,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,7,8,1,3,6]=>[6,3,1,8,7,5,4,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,6,8]=>[8,6,3,1,7,5,4,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,5,1,3,6,8,7]=>[7,8,6,3,1,5,4,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,5,1,3,8,6,7]=>[7,6,8,3,1,5,4,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]=>[7,6,3,8,1,5,4,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,1,3,6,7,8]=>[8,7,6,3,1,5,4,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,6,7,8,5]=>[5,8,7,6,3,1,4,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,7,5,8]=>[8,5,7,6,3,1,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7]=>[7,8,5,6,3,1,4,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,8,5,7]=>[7,5,8,6,3,1,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,6,5,7,8]=>[8,7,5,6,3,1,4,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,6,3,7,8,5]=>[5,8,7,3,6,1,4,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5,8]=>[8,5,7,3,6,1,4,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,6,7,3,8,5]=>[5,8,3,7,6,1,4,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>[5,3,8,7,6,1,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,1,6,7,3,5,8]=>[8,5,3,7,6,1,4,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,8,7]=>[7,8,5,3,6,1,4,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>[7,5,8,3,6,1,4,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,8,3,5,7]=>[7,5,3,8,6,1,4,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,6,3,5,7,8]=>[8,7,5,3,6,1,4,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,6,1,3,7,8,5]=>[5,8,7,3,1,6,4,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,6,1,3,7,5,8]=>[8,5,7,3,1,6,4,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,6,1,7,3,8,5]=>[5,8,3,7,1,6,4,2]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,6,1,7,8,3,5]=>[5,3,8,7,1,6,4,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,6,1,7,3,5,8]=>[8,5,3,7,1,6,4,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,6,7,1,3,8,5]=>[5,8,3,1,7,6,4,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,6,7,1,8,3,5]=>[5,3,8,1,7,6,4,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,1,3,5]=>[5,3,1,8,7,6,4,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>[8,5,3,1,7,6,4,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,8,7]=>[7,8,5,3,1,6,4,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,8,5,7]=>[7,5,8,3,1,6,4,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>[7,5,3,8,1,6,4,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,6,1,3,5,7,8]=>[8,7,5,3,1,6,4,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,3,5,7,8,6]=>[6,8,7,5,3,1,4,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,6,8]=>[8,6,7,5,3,1,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,3,7,5,8,6]=>[6,8,5,7,3,1,4,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,3,7,8,5,6]=>[6,5,8,7,3,1,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,1,3,7,5,6,8]=>[8,6,5,7,3,1,4,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,7,3,5,8,6]=>[6,8,5,3,7,1,4,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>[6,5,8,3,7,1,4,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,7,8,3,5,6]=>[6,5,3,8,7,1,4,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,1,7,3,5,6,8]=>[8,6,5,3,7,1,4,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,7,1,3,5,8,6]=>[6,8,5,3,1,7,4,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,7,1,3,8,5,6]=>[6,5,8,3,1,7,4,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]=>[6,5,3,8,1,7,4,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[6,5,3,1,8,7,4,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,7,1,3,5,6,8]=>[8,6,5,3,1,7,4,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,3,5,8,6,7]=>[7,6,8,5,3,1,4,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,3,8,5,6,7]=>[7,6,5,8,3,1,4,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>[7,6,5,3,8,1,4,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,8,1,3,5,6,7]=>[7,6,5,3,1,8,4,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]=>[4,8,7,6,5,3,1,2]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,5,6,7,4,8]=>[8,4,7,6,5,3,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[7,8,4,6,5,3,1,2]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,8,4,7]=>[7,4,8,6,5,3,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[8,7,4,6,5,3,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[6,8,7,4,5,3,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6,8]=>[8,6,7,4,5,3,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,7,4,8,6]=>[6,8,4,7,5,3,1,2]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,7,8,4,6]=>[6,4,8,7,5,3,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,4,6,8]=>[8,6,4,7,5,3,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,5,4,8,6,7]=>[7,6,8,4,5,3,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,5,8,4,6,7]=>[7,6,4,8,5,3,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[8,7,6,4,5,3,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,1,5,3,6,7,4,8]=>[8,4,7,6,3,5,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7]=>[7,8,4,6,3,5,1,2]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,1,5,3,6,8,4,7]=>[7,4,8,6,3,5,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,6,4,7,8]=>[8,7,4,6,3,5,1,2]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,6,3,7,8,4]=>[4,8,7,3,6,5,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,1,5,6,3,7,4,8]=>[8,4,7,3,6,5,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,5,6,7,3,8,4]=>[4,8,3,7,6,5,1,2]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,3,4]=>[4,3,8,7,6,5,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,1,5,6,7,3,4,8]=>[8,4,3,7,6,5,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,1,5,6,3,8,4,7]=>[7,4,8,3,6,5,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,1,5,6,8,3,4,7]=>[7,4,3,8,6,5,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,1,5,6,3,4,7,8]=>[8,7,4,3,6,5,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,7,8,6]=>[6,8,7,4,3,5,1,2]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,1,5,3,4,7,6,8]=>[8,6,7,4,3,5,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,7,4,8,6]=>[6,8,4,7,3,5,1,2]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,7,8,4,6]=>[6,4,8,7,3,5,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6,8]=>[8,6,4,7,3,5,1,2]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,5,7,3,4,8,6]=>[6,8,4,3,7,5,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>[6,4,8,3,7,5,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,5,7,8,3,4,6]=>[6,4,3,8,7,5,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,5,3,4,6,8,7]=>[7,8,6,4,3,5,1,2]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,1,5,3,4,8,6,7]=>[7,6,8,4,3,5,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,1,5,3,8,4,6,7]=>[7,6,4,8,3,5,1,2]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,1,5,8,3,4,6,7]=>[7,6,4,3,8,5,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,1,5,3,4,6,7,8]=>[8,7,6,4,3,5,1,2]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,4]=>[4,8,7,6,3,1,5,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,7,4,8]=>[8,4,7,6,3,1,5,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,5,1,3,6,4,8,7]=>[7,8,4,6,3,1,5,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,6,8,4,7]=>[7,4,8,6,3,1,5,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,1,3,6,4,7,8]=>[8,7,4,6,3,1,5,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,5,1,6,3,7,8,4]=>[4,8,7,3,6,1,5,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,6,3,7,4,8]=>[8,4,7,3,6,1,5,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,1,6,7,3,8,4]=>[4,8,3,7,6,1,5,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>[4,3,8,7,6,1,5,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,5,1,6,7,3,4,8]=>[8,4,3,7,6,1,5,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,5,1,6,3,4,8,7]=>[7,8,4,3,6,1,5,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,5,1,6,3,8,4,7]=>[7,4,8,3,6,1,5,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,5,1,6,8,3,4,7]=>[7,4,3,8,6,1,5,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,5,1,6,3,4,7,8]=>[8,7,4,3,6,1,5,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,5,6,1,3,7,8,4]=>[4,8,7,3,1,6,5,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,5,6,1,3,7,4,8]=>[8,4,7,3,1,6,5,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,5,6,1,7,3,8,4]=>[4,8,3,7,1,6,5,2]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,5,6,1,7,8,3,4]=>[4,3,8,7,1,6,5,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,5,6,1,7,3,4,8]=>[8,4,3,7,1,6,5,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,7,1,3,8,4]=>[4,8,3,1,7,6,5,2]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,7,1,8,3,4]=>[4,3,8,1,7,6,5,2]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,1,3,4]=>[4,3,1,8,7,6,5,2]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,7,1,3,4,8]=>[8,4,3,1,7,6,5,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,8,7]=>[7,8,4,3,1,6,5,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,5,6,1,3,8,4,7]=>[7,4,8,3,1,6,5,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,5,6,1,8,3,4,7]=>[7,4,3,8,1,6,5,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,7,8,6]=>[6,8,7,4,3,1,5,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,6,8]=>[8,6,7,4,3,1,5,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,7,4,8,6]=>[6,8,4,7,3,1,5,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,7,8,4,6]=>[6,4,8,7,3,1,5,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,5,1,3,7,4,6,8]=>[8,6,4,7,3,1,5,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]=>[6,8,4,3,7,1,5,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,5,1,7,3,8,4,6]=>[6,4,8,3,7,1,5,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,7,8,3,4,6]=>[6,4,3,8,7,1,5,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,5,1,7,3,4,6,8]=>[8,6,4,3,7,1,5,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,5,7,1,3,4,8,6]=>[6,8,4,3,1,7,5,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,5,7,1,3,8,4,6]=>[6,4,8,3,1,7,5,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,5,7,1,8,3,4,6]=>[6,4,3,8,1,7,5,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>[6,4,3,1,8,7,5,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,5,1,3,4,6,8,7]=>[7,8,6,4,3,1,5,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,5,1,3,4,8,6,7]=>[7,6,8,4,3,1,5,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,5,1,3,8,4,6,7]=>[7,6,4,8,3,1,5,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,5,1,8,3,4,6,7]=>[7,6,4,3,8,1,5,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,5,8,1,3,4,6,7]=>[7,6,4,3,1,8,5,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,4,6,7,8]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[5,8,7,6,4,3,1,2]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,1,3,4,6,7,5,8]=>[8,5,7,6,4,3,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[7,8,5,6,4,3,1,2]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[8,7,5,6,4,3,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,1,3,6,4,7,8,5]=>[5,8,7,4,6,3,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>[5,8,4,7,6,3,1,2]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,6,7,8,4,5]=>[5,4,8,7,6,3,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,1,3,6,7,4,5,8]=>[8,5,4,7,6,3,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,1,3,6,4,8,5,7]=>[7,5,8,4,6,3,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,1,3,6,8,4,5,7]=>[7,5,4,8,6,3,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,1,3,6,4,5,7,8]=>[8,7,5,4,6,3,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>[5,8,7,4,3,6,1,2]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,1,6,3,4,7,5,8]=>[8,5,7,4,3,6,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,6,3,7,4,8,5]=>[5,8,4,7,3,6,1,2]=>[2,2,2,2]=>[2,2,2,2]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,6,3,7,8,4,5]=>[5,4,8,7,3,6,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,1,6,3,7,4,5,8]=>[8,5,4,7,3,6,1,2]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,6,7,3,4,8,5]=>[5,8,4,3,7,6,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,1,6,7,3,8,4,5]=>[5,4,8,3,7,6,1,2]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>[5,4,3,8,7,6,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,1,6,7,3,4,5,8]=>[8,5,4,3,7,6,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,8,7]=>[7,8,5,4,3,6,1,2]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,8,5,7]=>[7,5,8,4,3,6,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,1,6,3,8,4,5,7]=>[7,5,4,8,3,6,1,2]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,1,6,8,3,4,5,7]=>[7,5,4,3,8,6,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,1,6,3,4,5,7,8]=>[8,7,5,4,3,6,1,2]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,6,1,3,4,7,8,5]=>[5,8,7,4,3,1,6,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,7,5,8]=>[8,5,7,4,3,1,6,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,6,1,3,7,4,8,5]=>[5,8,4,7,3,1,6,2]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,6,1,3,7,4,5,8]=>[8,5,4,7,3,1,6,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,6,1,7,3,4,8,5]=>[5,8,4,3,7,1,6,2]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,6,1,7,3,8,4,5]=>[5,4,8,3,7,1,6,2]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,6,1,7,8,3,4,5]=>[5,4,3,8,7,1,6,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,6,1,7,3,4,5,8]=>[8,5,4,3,7,1,6,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,6,7,1,3,4,8,5]=>[5,8,4,3,1,7,6,2]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,6,7,1,3,8,4,5]=>[5,4,8,3,1,7,6,2]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,6,7,1,8,3,4,5]=>[5,4,3,8,1,7,6,2]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>[5,4,3,1,8,7,6,2]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,6,7,1,3,4,5,8]=>[8,5,4,3,1,7,6,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,8,7]=>[7,8,5,4,3,1,6,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,8,5,7]=>[7,5,8,4,3,1,6,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,8,4,5,7]=>[7,5,4,8,3,1,6,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,6,1,8,3,4,5,7]=>[7,5,4,3,8,1,6,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,6,8,1,3,4,5,7]=>[7,5,4,3,1,8,6,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,6,1,3,4,5,7,8]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[6,8,7,5,4,3,1,2]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[8,6,7,5,4,3,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,1,3,4,7,8,5,6]=>[6,5,8,7,4,3,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,1,3,4,7,5,6,8]=>[8,6,5,7,4,3,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,7,4,5,8,6]=>[6,8,5,4,7,3,1,2]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,1,3,7,8,4,5,6]=>[6,5,4,8,7,3,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,7,3,4,5,8,6]=>[6,8,5,4,3,7,1,2]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,1,7,3,4,8,5,6]=>[6,5,8,4,3,7,1,2]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,1,7,3,8,4,5,6]=>[6,5,4,8,3,7,1,2]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,7,8,3,4,5,6]=>[6,5,4,3,8,7,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6,8]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,7,1,3,4,5,8,6]=>[6,8,5,4,3,1,7,2]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,7,1,3,4,8,5,6]=>[6,5,8,4,3,1,7,2]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,7,1,3,8,4,5,6]=>[6,5,4,8,3,1,7,2]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,7,1,8,3,4,5,6]=>[6,5,4,3,8,1,7,2]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>[6,5,4,3,1,8,7,2]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6,8]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,8,6,7]=>[7,6,8,5,4,3,1,2]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,1,3,4,8,5,6,7]=>[7,6,5,8,4,3,1,2]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>[7,6,5,4,8,3,1,2]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>[7,6,5,4,3,8,1,2]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]=>[7,6,5,4,3,1,8,2]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,2]=>[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]=>[8,2,7,6,5,4,3,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,6,2,8,7]=>[7,8,2,6,5,4,3,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,8,2,7]=>[7,2,8,6,5,4,3,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]=>[8,7,2,6,5,4,3,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,2,7,8,6]=>[6,8,7,2,5,4,3,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[8,6,7,2,5,4,3,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,5,7,2,8,6]=>[6,8,2,7,5,4,3,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,7,8,2,6]=>[6,2,8,7,5,4,3,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6,8]=>[8,6,2,7,5,4,3,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,5,2,6,8,7]=>[7,8,6,2,5,4,3,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,5,2,8,6,7]=>[7,6,8,2,5,4,3,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,5,8,2,6,7]=>[7,6,2,8,5,4,3,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[8,7,6,2,5,4,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,5]=>[5,8,7,6,2,4,3,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[7,8,5,6,2,4,3,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,6,5,7,8]=>[8,7,5,6,2,4,3,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,6,2,7,8,5]=>[5,8,7,2,6,4,3,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,6,2,7,5,8]=>[8,5,7,2,6,4,3,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,6,7,2,8,5]=>[5,8,2,7,6,4,3,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,6,7,8,2,5]=>[5,2,8,7,6,4,3,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,8,7]=>[7,8,5,2,6,4,3,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,8,5,7]=>[7,5,8,2,6,4,3,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,8,2,5,7]=>[7,5,2,8,6,4,3,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>[6,8,7,5,2,4,3,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[8,6,7,5,2,4,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,4,2,7,5,8,6]=>[6,8,5,7,2,4,3,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,4,2,7,8,5,6]=>[6,5,8,7,2,4,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,4,7,2,5,8,6]=>[6,8,5,2,7,4,3,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,4,7,2,8,5,6]=>[6,5,8,2,7,4,3,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,4,7,8,2,5,6]=>[6,5,2,8,7,4,3,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[7,8,6,5,2,4,3,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,4,2,5,8,6,7]=>[7,6,8,5,2,4,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>[7,6,5,8,2,4,3,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[7,6,5,2,8,4,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,4]=>[4,8,7,6,5,2,3,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[8,4,7,6,5,2,3,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,5,6,8,4,7]=>[7,4,8,6,5,2,3,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[8,7,4,6,5,2,3,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[6,8,7,4,5,2,3,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,7,4,8,6]=>[6,8,4,7,5,2,3,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>[6,4,8,7,5,2,3,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6,8]=>[8,6,4,7,5,2,3,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,5,4,6,8,7]=>[7,8,6,4,5,2,3,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>[7,6,8,4,5,2,3,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,5,8,4,6,7]=>[7,6,4,8,5,2,3,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,5,2,6,7,8,4]=>[4,8,7,6,2,5,3,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,5,2,6,7,4,8]=>[8,4,7,6,2,5,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,6,8,4,7]=>[7,4,8,6,2,5,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,5,2,6,4,7,8]=>[8,7,4,6,2,5,3,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,5,6,2,7,8,4]=>[4,8,7,2,6,5,3,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,5,6,2,7,4,8]=>[8,4,7,2,6,5,3,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,7,2,8,4]=>[4,8,2,7,6,5,3,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,2,4]=>[4,2,8,7,6,5,3,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,7,2,4,8]=>[8,4,2,7,6,5,3,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,5,6,2,4,8,7]=>[7,8,4,2,6,5,3,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,5,6,2,8,4,7]=>[7,4,8,2,6,5,3,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,8,2,4,7]=>[7,4,2,8,6,5,3,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>[8,7,4,2,6,5,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,7,8,6]=>[6,8,7,4,2,5,3,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6,8]=>[8,6,7,4,2,5,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,7,4,8,6]=>[6,8,4,7,2,5,3,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,7,8,4,6]=>[6,4,8,7,2,5,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,7,2,4,8,6]=>[6,8,4,2,7,5,3,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,7,2,8,4,6]=>[6,4,8,2,7,5,3,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,7,8,2,4,6]=>[6,4,2,8,7,5,3,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,5,2,4,6,8,7]=>[7,8,6,4,2,5,3,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,5,2,4,8,6,7]=>[7,6,8,4,2,5,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>[7,6,4,8,2,5,3,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[7,6,4,2,8,5,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[5,8,7,6,4,2,3,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[8,5,7,6,4,2,3,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[8,7,5,6,4,2,3,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,2,6,4,7,8,5]=>[5,8,7,4,6,2,3,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,6,4,7,5,8]=>[8,5,7,4,6,2,3,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,2,6,7,4,8,5]=>[5,8,4,7,6,2,3,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,7,8,4,5]=>[5,4,8,7,6,2,3,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>[7,5,8,4,6,2,3,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,6,2,4,7,8,5]=>[5,8,7,4,2,6,3,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,6,2,4,7,5,8]=>[8,5,7,4,2,6,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,2,7,4,8,5]=>[5,8,4,7,2,6,3,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,6,2,7,8,4,5]=>[5,4,8,7,2,6,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,7,4,5,8]=>[8,5,4,7,2,6,3,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,6,7,2,4,8,5]=>[5,8,4,2,7,6,3,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,6,7,2,8,4,5]=>[5,4,8,2,7,6,3,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,6,7,8,2,4,5]=>[5,4,2,8,7,6,3,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,6,7,2,4,5,8]=>[8,5,4,2,7,6,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,8,7]=>[7,8,5,4,2,6,3,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,8,5,7]=>[7,5,8,4,2,6,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,6,2,8,4,5,7]=>[7,5,4,8,2,6,3,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,6,8,2,4,5,7]=>[7,5,4,2,8,6,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[6,8,7,5,4,2,3,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,4,7,5,8,6]=>[6,8,5,7,4,2,3,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>[6,5,8,7,4,2,3,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,4,7,5,6,8]=>[8,6,5,7,4,2,3,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,7,4,5,8,6]=>[6,8,5,4,7,2,3,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>[6,5,8,4,7,2,3,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,7,8,4,5,6]=>[6,5,4,8,7,2,3,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,7,2,4,5,8,6]=>[6,8,5,4,2,7,3,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,7,2,4,8,5,6]=>[6,5,8,4,2,7,3,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,7,8,2,4,5,6]=>[6,5,4,2,8,7,3,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[7,8,6,5,4,2,3,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>[7,6,8,5,4,2,3,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,2]=>[2,8,7,6,5,4,1,3]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,2,8]=>[8,2,7,6,5,4,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>[7,8,2,6,5,4,1,3]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,6,8,2,7]=>[7,2,8,6,5,4,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,6,2,7,8]=>[8,7,2,6,5,4,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,5,2,7,8,6]=>[6,8,7,2,5,4,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6,8]=>[8,6,7,2,5,4,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,7,2,8,6]=>[6,8,2,7,5,4,1,3]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4,5,7,8,2,6]=>[6,2,8,7,5,4,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,4,5,7,2,6,8]=>[8,6,2,7,5,4,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,4,5,2,8,6,7]=>[7,6,8,2,5,4,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4,5,8,2,6,7]=>[7,6,2,8,5,4,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,2,6,7,8]=>[8,7,6,2,5,4,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>[5,8,7,6,2,4,1,3]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,6,7,5,8]=>[8,5,7,6,2,4,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7]=>[7,8,5,6,2,4,1,3]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,8,5,7]=>[7,5,8,6,2,4,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,6,5,7,8]=>[8,7,5,6,2,4,1,3]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,6,2,7,8,5]=>[5,8,7,2,6,4,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,1,4,6,2,7,5,8]=>[8,5,7,2,6,4,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,6,7,2,8,5]=>[5,8,2,7,6,4,1,3]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,4,6,7,8,2,5]=>[5,2,8,7,6,4,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,1,4,6,7,2,5,8]=>[8,5,2,7,6,4,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,8,7]=>[7,8,5,2,6,4,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,8,5,7]=>[7,5,8,2,6,4,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,8,2,5,7]=>[7,5,2,8,6,4,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,4,6,2,5,7,8]=>[8,7,5,2,6,4,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>[6,8,7,5,2,4,1,3]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,7,5,8,6]=>[6,8,5,7,2,4,1,3]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,4,2,7,8,5,6]=>[6,5,8,7,2,4,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,4,2,7,5,6,8]=>[8,6,5,7,2,4,1,3]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,7,2,5,8,6]=>[6,8,5,2,7,4,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,4,7,2,8,5,6]=>[6,5,8,2,7,4,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,1,4,7,8,2,5,6]=>[6,5,2,8,7,4,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,1,4,7,2,5,6,8]=>[8,6,5,2,7,4,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,2,5,8,6,7]=>[7,6,8,5,2,4,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,4,2,8,5,6,7]=>[7,6,5,8,2,4,1,3]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,4,8,2,5,6,7]=>[7,6,5,2,8,4,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,2,5,6,7,8]=>[8,7,6,5,2,4,1,3]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,2]=>[2,8,7,6,5,1,4,3]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,5,6,7,2,8]=>[8,2,7,6,5,1,4,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,5,6,2,8,7]=>[7,8,2,6,5,1,4,3]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,5,6,8,2,7]=>[7,2,8,6,5,1,4,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,1,5,6,2,7,8]=>[8,7,2,6,5,1,4,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,4,1,5,2,7,8,6]=>[6,8,7,2,5,1,4,3]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6,8]=>[8,6,7,2,5,1,4,3]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,4,1,5,7,2,8,6]=>[6,8,2,7,5,1,4,3]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>[6,2,8,7,5,1,4,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6,8]=>[8,6,2,7,5,1,4,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,4,1,5,2,6,8,7]=>[7,8,6,2,5,1,4,3]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,2,8,6,7]=>[7,6,8,2,5,1,4,3]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,5,8,2,6,7]=>[7,6,2,8,5,1,4,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,1,5,2,6,7,8]=>[8,7,6,2,5,1,4,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,2]=>[2,8,7,6,1,5,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,5,1,6,7,2,8]=>[8,2,7,6,1,5,4,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,5,1,6,2,8,7]=>[7,8,2,6,1,5,4,3]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,5,1,6,8,2,7]=>[7,2,8,6,1,5,4,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>[8,7,2,6,1,5,4,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,1,7,8,2]=>[2,8,7,1,6,5,4,3]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,6,1,7,2,8]=>[8,2,7,1,6,5,4,3]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,1,8,2]=>[2,8,1,7,6,5,4,3]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,6,1,2,8,7]=>[7,8,2,1,6,5,4,3]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,6,1,8,2,7]=>[7,2,8,1,6,5,4,3]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,6,8,1,2,7]=>[7,2,1,8,6,5,4,3]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[8,7,2,1,6,5,4,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,7,8,6]=>[6,8,7,2,1,5,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,5,1,7,2,8,6]=>[6,8,2,7,1,5,4,3]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,5,1,7,8,2,6]=>[6,2,8,7,1,5,4,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6,8]=>[8,6,2,7,1,5,4,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,5,7,1,2,8,6]=>[6,8,2,1,7,5,4,3]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,5,7,1,8,2,6]=>[6,2,8,1,7,5,4,3]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,7,8,1,2,6]=>[6,2,1,8,7,5,4,3]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6,8]=>[8,6,2,1,7,5,4,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,5,1,2,6,8,7]=>[7,8,6,2,1,5,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[7,6,2,1,8,5,4,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,5]=>[5,8,7,6,2,1,4,3]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,7,5,8]=>[8,5,7,6,2,1,4,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>[7,8,5,6,2,1,4,3]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,8,5,7]=>[7,5,8,6,2,1,4,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,6,5,7,8]=>[8,7,5,6,2,1,4,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,6,2,7,8,5]=>[5,8,7,2,6,1,4,3]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,6,2,7,5,8]=>[8,5,7,2,6,1,4,3]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,6,7,2,8,5]=>[5,8,2,7,6,1,4,3]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,6,7,8,2,5]=>[5,2,8,7,6,1,4,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,6,7,2,5,8]=>[8,5,2,7,6,1,4,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,8,7]=>[7,8,5,2,6,1,4,3]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,8,5,7]=>[7,5,8,2,6,1,4,3]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,8,2,5,7]=>[7,5,2,8,6,1,4,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,1,6,2,5,7,8]=>[8,7,5,2,6,1,4,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,6,1,2,7,8,5]=>[5,8,7,2,1,6,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,6,1,2,7,5,8]=>[8,5,7,2,1,6,4,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,6,1,7,2,8,5]=>[5,8,2,7,1,6,4,3]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,6,1,7,8,2,5]=>[5,2,8,7,1,6,4,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,6,1,7,2,5,8]=>[8,5,2,7,1,6,4,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,6,7,1,2,8,5]=>[5,8,2,1,7,6,4,3]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,6,7,1,8,2,5]=>[5,2,8,1,7,6,4,3]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,6,7,8,1,2,5]=>[5,2,1,8,7,6,4,3]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,7,1,2,5,8]=>[8,5,2,1,7,6,4,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,8,7]=>[7,8,5,2,1,6,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,1,2,8,5,7]=>[7,5,8,2,1,6,4,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,1,8,2,5,7]=>[7,5,2,8,1,6,4,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[7,5,2,1,8,6,4,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,6,1,2,5,7,8]=>[8,7,5,2,1,6,4,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,4,1,2,5,7,8,6]=>[6,8,7,5,2,1,4,3]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]=>[8,6,7,5,2,1,4,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,4,1,2,7,5,8,6]=>[6,8,5,7,2,1,4,3]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,4,1,2,7,5,6,8]=>[8,6,5,7,2,1,4,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,4,1,7,2,5,8,6]=>[6,8,5,2,7,1,4,3]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,7,2,8,5,6]=>[6,5,8,2,7,1,4,3]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,1,7,8,2,5,6]=>[6,5,2,8,7,1,4,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,7,2,5,6,8]=>[8,6,5,2,7,1,4,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,4,7,1,2,5,8,6]=>[6,8,5,2,1,7,4,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,4,7,1,2,8,5,6]=>[6,5,8,2,1,7,4,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>[6,5,2,8,1,7,4,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>[6,5,2,1,8,7,4,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6,8]=>[8,6,5,2,1,7,4,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1,2,5,6,8,7]=>[7,8,6,5,2,1,4,3]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1,2,5,8,6,7]=>[7,6,8,5,2,1,4,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1,2,8,5,6,7]=>[7,6,5,8,2,1,4,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>[7,6,5,2,8,1,4,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,8,1,2,5,6,7]=>[7,6,5,2,1,8,4,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,4]=>[4,8,7,6,5,2,1,3]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,5,6,7,4,8]=>[8,4,7,6,5,2,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,5,6,4,8,7]=>[7,8,4,6,5,2,1,3]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,5,6,8,4,7]=>[7,4,8,6,5,2,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,5,6,4,7,8]=>[8,7,4,6,5,2,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,5,4,7,8,6]=>[6,8,7,4,5,2,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,8]=>[8,6,7,4,5,2,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>[6,8,4,7,5,2,1,3]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,7,8,4,6]=>[6,4,8,7,5,2,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6,8]=>[8,6,4,7,5,2,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,5,4,6,8,7]=>[7,8,6,4,5,2,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,5,4,8,6,7]=>[7,6,8,4,5,2,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,5,8,4,6,7]=>[7,6,4,8,5,2,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,5,4,6,7,8]=>[8,7,6,4,5,2,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]=>[4,8,7,6,2,5,1,3]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,5,2,6,7,4,8]=>[8,4,7,6,2,5,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7]=>[7,8,4,6,2,5,1,3]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,5,2,6,8,4,7]=>[7,4,8,6,2,5,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,4,7,8]=>[8,7,4,6,2,5,1,3]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,6,2,7,8,4]=>[4,8,7,2,6,5,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,5,6,2,7,4,8]=>[8,4,7,2,6,5,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>[4,8,2,7,6,5,1,3]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,8,2,4]=>[4,2,8,7,6,5,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,5,6,7,2,4,8]=>[8,4,2,7,6,5,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,5,6,2,4,8,7]=>[7,8,4,2,6,5,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]=>[7,4,8,2,6,5,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,5,6,8,2,4,7]=>[7,4,2,8,6,5,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,5,6,2,4,7,8]=>[8,7,4,2,6,5,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,7,8,6]=>[6,8,7,4,2,5,1,3]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6,8]=>[8,6,7,4,2,5,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,7,4,8,6]=>[6,8,4,7,2,5,1,3]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,7,8,4,6]=>[6,4,8,7,2,5,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6,8]=>[8,6,4,7,2,5,1,3]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>[6,8,4,2,7,5,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,7,2,8,4,6]=>[6,4,8,2,7,5,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,7,8,2,4,6]=>[6,4,2,8,7,5,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6,8]=>[8,6,4,2,7,5,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,5,2,4,6,8,7]=>[7,8,6,4,2,5,1,3]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,5,2,4,8,6,7]=>[7,6,8,4,2,5,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,5,2,8,4,6,7]=>[7,6,4,8,2,5,1,3]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,5,8,2,4,6,7]=>[7,6,4,2,8,5,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,5,2,4,6,7,8]=>[8,7,6,4,2,5,1,3]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,6,7,8,4]=>[4,8,7,6,2,1,5,3]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]=>[8,4,7,6,2,1,5,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,5,1,2,6,4,8,7]=>[7,8,4,6,2,1,5,3]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,6,8,4,7]=>[7,4,8,6,2,1,5,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,5,1,2,6,4,7,8]=>[8,7,4,6,2,1,5,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,5,1,6,2,7,8,4]=>[4,8,7,2,6,1,5,3]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,6,2,7,4,8]=>[8,4,7,2,6,1,5,3]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,5,1,6,7,2,8,4]=>[4,8,2,7,6,1,5,3]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>[4,2,8,7,6,1,5,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,5,1,6,7,2,4,8]=>[8,4,2,7,6,1,5,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>[7,8,4,2,6,1,5,3]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,5,1,6,2,8,4,7]=>[7,4,8,2,6,1,5,3]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,5,1,6,2,4,7,8]=>[8,7,4,2,6,1,5,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,5,6,1,2,7,8,4]=>[4,8,7,2,1,6,5,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,5,6,1,2,7,4,8]=>[8,4,7,2,1,6,5,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,5,6,1,7,2,8,4]=>[4,8,2,7,1,6,5,3]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,5,6,1,7,8,2,4]=>[4,2,8,7,1,6,5,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>[8,4,2,7,1,6,5,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,7,1,2,8,4]=>[4,8,2,1,7,6,5,3]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,7,1,8,2,4]=>[4,2,8,1,7,6,5,3]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,8,1,2,4]=>[4,2,1,8,7,6,5,3]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,7,1,2,4,8]=>[8,4,2,1,7,6,5,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,8,7]=>[7,8,4,2,1,6,5,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>[7,4,2,8,1,6,5,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[7,4,2,1,8,6,5,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,5,6,1,2,4,7,8]=>[8,7,4,2,1,6,5,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,7,8,6]=>[6,8,7,4,2,1,5,3]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>[8,6,7,4,2,1,5,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,7,4,8,6]=>[6,8,4,7,2,1,5,3]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,7,8,4,6]=>[6,4,8,7,2,1,5,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6,8]=>[8,6,4,7,2,1,5,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,7,2,4,8,6]=>[6,8,4,2,7,1,5,3]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,7,8,2,4,6]=>[6,4,2,8,7,1,5,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6,8]=>[8,6,4,2,7,1,5,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,7,1,2,4,8,6]=>[6,8,4,2,1,7,5,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,7,1,2,8,4,6]=>[6,4,8,2,1,7,5,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,7,1,8,2,4,6]=>[6,4,2,8,1,7,5,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6,8]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,5,1,2,4,8,6,7]=>[7,6,8,4,2,1,5,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,5,1,2,8,4,6,7]=>[7,6,4,8,2,1,5,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,5,1,8,2,4,6,7]=>[7,6,4,2,8,1,5,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,5,1,2,4,6,7,8]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,6,7,8,5]=>[5,8,7,6,4,2,1,3]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,7,5,8]=>[8,5,7,6,4,2,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,8,7]=>[7,8,5,6,4,2,1,3]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,1,2,4,6,8,5,7]=>[7,5,8,6,4,2,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,1,2,4,6,5,7,8]=>[8,7,5,6,4,2,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,2,6,4,7,8,5]=>[5,8,7,4,6,2,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,1,2,6,4,7,5,8]=>[8,5,7,4,6,2,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>[5,8,4,7,6,2,1,3]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,2,6,7,8,4,5]=>[5,4,8,7,6,2,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,1,2,6,7,4,5,8]=>[8,5,4,7,6,2,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,8,7]=>[7,8,5,4,6,2,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,1,2,6,4,8,5,7]=>[7,5,8,4,6,2,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,1,2,6,8,4,5,7]=>[7,5,4,8,6,2,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,1,2,6,4,5,7,8]=>[8,7,5,4,6,2,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]=>[5,8,7,4,2,6,1,3]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,1,6,2,4,7,5,8]=>[8,5,7,4,2,6,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,6,2,7,4,8,5]=>[5,8,4,7,2,6,1,3]=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,1,6,2,7,8,4,5]=>[5,4,8,7,2,6,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,1,6,2,7,4,5,8]=>[8,5,4,7,2,6,1,3]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,6,7,2,4,8,5]=>[5,8,4,2,7,6,1,3]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,1,6,7,2,8,4,5]=>[5,4,8,2,7,6,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,1,6,7,8,2,4,5]=>[5,4,2,8,7,6,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,1,6,7,2,4,5,8]=>[8,5,4,2,7,6,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,8,7]=>[7,8,5,4,2,6,1,3]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,8,5,7]=>[7,5,8,4,2,6,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,1,6,2,8,4,5,7]=>[7,5,4,8,2,6,1,3]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>[7,5,4,2,8,6,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,6,2,4,5,7,8]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,6,1,2,4,7,8,5]=>[5,8,7,4,2,1,6,3]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>[8,5,7,4,2,1,6,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,6,1,2,7,4,8,5]=>[5,8,4,7,2,1,6,3]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,6,1,2,7,8,4,5]=>[5,4,8,7,2,1,6,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,6,1,2,7,4,5,8]=>[8,5,4,7,2,1,6,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,6,1,7,2,4,8,5]=>[5,8,4,2,7,1,6,3]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>[5,4,8,2,7,1,6,3]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>[5,4,2,8,7,1,6,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,6,1,7,2,4,5,8]=>[8,5,4,2,7,1,6,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,6,7,1,2,4,8,5]=>[5,8,4,2,1,7,6,3]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]=>[5,4,8,2,1,7,6,3]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,6,7,1,8,2,4,5]=>[5,4,2,8,1,7,6,3]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[5,4,2,1,8,7,6,3]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,6,7,1,2,4,5,8]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,8,7]=>[7,8,5,4,2,1,6,3]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,8,5,7]=>[7,5,8,4,2,1,6,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,8,4,5,7]=>[7,5,4,8,2,1,6,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,6,1,8,2,4,5,7]=>[7,5,4,2,8,1,6,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]=>[7,5,4,2,1,8,6,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,6,1,2,4,5,7,8]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,2,4,5,7,8,6]=>[6,8,7,5,4,2,1,3]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,2,4,5,7,6,8]=>[8,6,7,5,4,2,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>[6,8,5,7,4,2,1,3]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,2,4,7,8,5,6]=>[6,5,8,7,4,2,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,1,2,4,7,5,6,8]=>[8,6,5,7,4,2,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,1,2,7,4,8,5,6]=>[6,5,8,4,7,2,1,3]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,2,7,8,4,5,6]=>[6,5,4,8,7,2,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,1,2,7,4,5,6,8]=>[8,6,5,4,7,2,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,7,2,4,5,8,6]=>[6,8,5,4,2,7,1,3]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,7,2,4,8,5,6]=>[6,5,8,4,2,7,1,3]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,1,7,2,8,4,5,6]=>[6,5,4,8,2,7,1,3]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,7,8,2,4,5,6]=>[6,5,4,2,8,7,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6,8]=>[8,6,5,4,2,7,1,3]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,8,6]=>[6,8,5,4,2,1,7,3]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,7,1,2,4,8,5,6]=>[6,5,8,4,2,1,7,3]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,7,1,2,8,4,5,6]=>[6,5,4,8,2,1,7,3]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,7,1,8,2,4,5,6]=>[6,5,4,2,8,1,7,3]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,1,2,4,5,6]=>[6,5,4,2,1,8,7,3]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6,8]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]=>[7,8,6,5,4,2,1,3]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,8,6,7]=>[7,6,8,5,4,2,1,3]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,2,4,8,5,6,7]=>[7,6,5,8,4,2,1,3]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>[7,6,5,4,8,2,1,3]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]=>[7,6,5,4,2,8,1,3]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,8,1,2,4,5,6,7]=>[7,6,5,4,2,1,8,3]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,3]=>[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,7,3,8]=>[8,3,7,6,5,4,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,6,8,3,7]=>[7,3,8,6,5,4,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,5,3,7,8,6]=>[6,8,7,3,5,4,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6,8]=>[8,6,7,3,5,4,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,7,8,3,6]=>[6,3,8,7,5,4,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6,8]=>[8,6,3,7,5,4,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,4,5,3,6,8,7]=>[7,8,6,3,5,4,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,4,5,3,8,6,7]=>[7,6,8,3,5,4,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,4,5,8,3,6,7]=>[7,6,3,8,5,4,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[8,7,6,3,5,4,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>[5,8,7,6,3,4,2,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[8,5,7,6,3,4,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,8,5,7]=>[7,5,8,6,3,4,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,6,3,7,8,5]=>[5,8,7,3,6,4,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,6,3,7,5,8]=>[8,5,7,3,6,4,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,6,7,3,8,5]=>[5,8,3,7,6,4,2,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,6,7,8,3,5]=>[5,3,8,7,6,4,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,8,7]=>[7,8,5,3,6,4,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,8,5,7]=>[7,5,8,3,6,4,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,8,3,5,7]=>[7,5,3,8,6,4,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[6,8,7,5,3,4,2,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[8,6,7,5,3,4,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,3,7,5,8,6]=>[6,8,5,7,3,4,2,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,4,3,7,8,5,6]=>[6,5,8,7,3,4,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,7,3,5,8,6]=>[6,8,5,3,7,4,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,4,7,3,8,5,6]=>[6,5,8,3,7,4,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]=>[8,6,5,3,7,4,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,3,5,8,6,7]=>[7,6,8,5,3,4,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,3]=>[3,8,7,6,5,2,4,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,5,6,7,3,8]=>[8,3,7,6,5,2,4,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,5,6,8,3,7]=>[7,3,8,6,5,2,4,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,5,6,3,7,8]=>[8,7,3,6,5,2,4,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,5,3,7,8,6]=>[6,8,7,3,5,2,4,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,8]=>[8,6,7,3,5,2,4,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,4,2,5,7,3,8,6]=>[6,8,3,7,5,2,4,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,4,2,5,7,8,3,6]=>[6,3,8,7,5,2,4,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6,8]=>[8,6,3,7,5,2,4,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,5,3,6,8,7]=>[7,8,6,3,5,2,4,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,4,2,5,8,3,6,7]=>[7,6,3,8,5,2,4,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,5,2,6,7,8,3]=>[3,8,7,6,2,5,4,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,4,5,2,6,7,3,8]=>[8,3,7,6,2,5,4,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,4,5,2,6,3,8,7]=>[7,8,3,6,2,5,4,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,5,2,6,8,3,7]=>[7,3,8,6,2,5,4,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>[8,7,3,6,2,5,4,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,6,2,7,8,3]=>[3,8,7,2,6,5,4,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,6,2,7,3,8]=>[8,3,7,2,6,5,4,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,2,8,3]=>[3,8,2,7,6,5,4,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,2,3]=>[3,2,8,7,6,5,4,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,2,3,8]=>[8,3,2,7,6,5,4,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,6,2,3,8,7]=>[7,8,3,2,6,5,4,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,6,2,8,3,7]=>[7,3,8,2,6,5,4,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,6,8,2,3,7]=>[7,3,2,8,6,5,4,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3,7,8]=>[8,7,3,2,6,5,4,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,7,8,6]=>[6,8,7,3,2,5,4,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,4,5,2,7,3,8,6]=>[6,8,3,7,2,5,4,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,7,8,3,6]=>[6,3,8,7,2,5,4,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6,8]=>[8,6,3,7,2,5,4,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,4,5,7,2,3,8,6]=>[6,8,3,2,7,5,4,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,7,8,2,3,6]=>[6,3,2,8,7,5,4,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>[8,6,3,2,7,5,4,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,4,5,2,3,6,8,7]=>[7,8,6,3,2,5,4,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,5,2,3,8,6,7]=>[7,6,8,3,2,5,4,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]=>[7,6,3,8,2,5,4,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,6,7,8,5]=>[5,8,7,6,3,2,4,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7]=>[7,8,5,6,3,2,4,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,8,5,7]=>[7,5,8,6,3,2,4,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,6,5,7,8]=>[8,7,5,6,3,2,4,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,6,3,7,8,5]=>[5,8,7,3,6,2,4,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,6,7,3,8,5]=>[5,8,3,7,6,2,4,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>[5,3,8,7,6,2,4,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,6,7,3,5,8]=>[8,5,3,7,6,2,4,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,8,7]=>[7,8,5,3,6,2,4,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,8,3,5,7]=>[7,5,3,8,6,2,4,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,6,3,5,7,8]=>[8,7,5,3,6,2,4,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,6,2,3,7,8,5]=>[5,8,7,3,2,6,4,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,6,2,3,7,5,8]=>[8,5,7,3,2,6,4,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,6,2,7,3,8,5]=>[5,8,3,7,2,6,4,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,6,2,7,8,3,5]=>[5,3,8,7,2,6,4,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,6,7,2,3,8,5]=>[5,8,3,2,7,6,4,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,6,7,2,8,3,5]=>[5,3,8,2,7,6,4,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,6,7,8,2,3,5]=>[5,3,2,8,7,6,4,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,8,7]=>[7,8,5,3,2,6,4,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,8,5,7]=>[7,5,8,3,2,6,4,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]=>[7,5,3,8,2,6,4,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[7,5,3,2,8,6,4,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,6,2,3,5,7,8]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,2,3,5,7,8,6]=>[6,8,7,5,3,2,4,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2,3,5,7,6,8]=>[8,6,7,5,3,2,4,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,2,3,7,5,8,6]=>[6,8,5,7,3,2,4,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>[6,5,8,3,7,2,4,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,7,2,3,5,8,6]=>[6,8,5,3,2,7,4,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,7,2,3,8,5,6]=>[6,5,8,3,2,7,4,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>[7,6,8,5,3,2,4,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>[7,6,5,3,8,2,4,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,3]=>[3,8,7,6,5,2,1,4]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,5,6,7,3,8]=>[8,3,7,6,5,2,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>[7,8,3,6,5,2,1,4]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,5,6,8,3,7]=>[7,3,8,6,5,2,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3,7,8]=>[8,7,3,6,5,2,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,5,3,7,8,6]=>[6,8,7,3,5,2,1,4]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6,8]=>[8,6,7,3,5,2,1,4]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,5,7,3,8,6]=>[6,8,3,7,5,2,1,4]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,5,7,8,3,6]=>[6,3,8,7,5,2,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6,8]=>[8,6,3,7,5,2,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,3,6,8,7]=>[7,8,6,3,5,2,1,4]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,5,3,8,6,7]=>[7,6,8,3,5,2,1,4]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,5,8,3,6,7]=>[7,6,3,8,5,2,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,3,6,7,8]=>[8,7,6,3,5,2,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>[3,8,7,6,2,5,1,4]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,5,2,6,7,3,8]=>[8,3,7,6,2,5,1,4]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,2,6,3,8,7]=>[7,8,3,6,2,5,1,4]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,5,2,6,8,3,7]=>[7,3,8,6,2,5,1,4]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,5,2,6,3,7,8]=>[8,7,3,6,2,5,1,4]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,6,2,7,8,3]=>[3,8,7,2,6,5,1,4]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,5,6,2,7,3,8]=>[8,3,7,2,6,5,1,4]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>[3,8,2,7,6,5,1,4]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,2,3]=>[3,2,8,7,6,5,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,5,6,7,2,3,8]=>[8,3,2,7,6,5,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,5,6,2,8,3,7]=>[7,3,8,2,6,5,1,4]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,5,6,8,2,3,7]=>[7,3,2,8,6,5,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,5,6,2,3,7,8]=>[8,7,3,2,6,5,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>[6,8,7,3,2,5,1,4]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,5,2,7,3,8,6]=>[6,8,3,7,2,5,1,4]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,5,2,7,8,3,6]=>[6,3,8,7,2,5,1,4]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6,8]=>[8,6,3,7,2,5,1,4]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,5,7,2,3,8,6]=>[6,8,3,2,7,5,1,4]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,5,7,2,8,3,6]=>[6,3,8,2,7,5,1,4]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,1,5,7,8,2,3,6]=>[6,3,2,8,7,5,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6,8]=>[8,6,3,2,7,5,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,5,2,3,6,8,7]=>[7,8,6,3,2,5,1,4]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,1,5,2,3,8,6,7]=>[7,6,8,3,2,5,1,4]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,8,3,6,7]=>[7,6,3,8,2,5,1,4]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,5,8,2,3,6,7]=>[7,6,3,2,8,5,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,5,2,3,6,7,8]=>[8,7,6,3,2,5,1,4]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,6,7,8,3]=>[3,8,7,6,2,1,5,4]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]=>[8,3,7,6,2,1,5,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,6,3,8,7]=>[7,8,3,6,2,1,5,4]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,2,6,8,3,7]=>[7,3,8,6,2,1,5,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,5,1,2,6,3,7,8]=>[8,7,3,6,2,1,5,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,1,6,2,7,8,3]=>[3,8,7,2,6,1,5,4]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,6,2,7,3,8]=>[8,3,7,2,6,1,5,4]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,5,1,6,7,2,8,3]=>[3,8,2,7,6,1,5,4]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>[3,2,8,7,6,1,5,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,5,1,6,7,2,3,8]=>[8,3,2,7,6,1,5,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,5,1,6,2,3,8,7]=>[7,8,3,2,6,1,5,4]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>[7,3,8,2,6,1,5,4]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,5,1,6,8,2,3,7]=>[7,3,2,8,6,1,5,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,1,6,2,3,7,8]=>[8,7,3,2,6,1,5,4]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,6,1,2,7,8,3]=>[3,8,7,2,1,6,5,4]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,6,1,2,7,3,8]=>[8,3,7,2,1,6,5,4]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,1,7,2,8,3]=>[3,8,2,7,1,6,5,4]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,6,1,7,8,2,3]=>[3,2,8,7,1,6,5,4]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,6,1,7,2,3,8]=>[8,3,2,7,1,6,5,4]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,1,2,8,3]=>[3,8,2,1,7,6,5,4]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,1,8,2,3]=>[3,2,8,1,7,6,5,4]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>[7,8,3,2,1,6,5,4]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,6,1,2,8,3,7]=>[7,3,8,2,1,6,5,4]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]=>[7,3,2,8,1,6,5,4]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[7,3,2,1,8,6,5,4]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,7,8,6]=>[6,8,7,3,2,1,5,4]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]=>[8,6,7,3,2,1,5,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,7,3,8,6]=>[6,8,3,7,2,1,5,4]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,7,8,3,6]=>[6,3,8,7,2,1,5,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6,8]=>[8,6,3,7,2,1,5,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,5,1,7,2,3,8,6]=>[6,8,3,2,7,1,5,4]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>[6,3,8,2,7,1,5,4]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,5,1,7,8,2,3,6]=>[6,3,2,8,7,1,5,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6,8]=>[8,6,3,2,7,1,5,4]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>[6,3,8,2,1,7,5,4]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,5,7,1,8,2,3,6]=>[6,3,2,8,1,7,5,4]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[6,3,2,1,8,7,5,4]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,7,1,2,3,6,8]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,5,1,2,3,6,8,7]=>[7,8,6,3,2,1,5,4]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,5,1,2,3,8,6,7]=>[7,6,8,3,2,1,5,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,5,1,2,8,3,6,7]=>[7,6,3,8,2,1,5,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,5,1,8,2,3,6,7]=>[7,6,3,2,8,1,5,4]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>[7,6,3,2,1,8,5,4]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,6,7,8,5]=>[5,8,7,6,3,2,1,4]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,6,7,5,8]=>[8,5,7,6,3,2,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>[7,8,5,6,3,2,1,4]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,8,5,7]=>[7,5,8,6,3,2,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,6,5,7,8]=>[8,7,5,6,3,2,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,6,3,7,8,5]=>[5,8,7,3,6,2,1,4]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5,8]=>[8,5,7,3,6,2,1,4]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,7,3,8,5]=>[5,8,3,7,6,2,1,4]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,2,6,7,8,3,5]=>[5,3,8,7,6,2,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,6,7,3,5,8]=>[8,5,3,7,6,2,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>[7,8,5,3,6,2,1,4]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,8,5,7]=>[7,5,8,3,6,2,1,4]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,6,8,3,5,7]=>[7,5,3,8,6,2,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,6,3,5,7,8]=>[8,7,5,3,6,2,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>[5,8,7,3,2,6,1,4]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,6,2,3,7,5,8]=>[8,5,7,3,2,6,1,4]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,7,3,8,5]=>[5,8,3,7,2,6,1,4]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,6,2,7,8,3,5]=>[5,3,8,7,2,6,1,4]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,6,2,7,3,5,8]=>[8,5,3,7,2,6,1,4]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,6,7,2,3,8,5]=>[5,8,3,2,7,6,1,4]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,6,7,2,8,3,5]=>[5,3,8,2,7,6,1,4]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,6,7,2,3,5,8]=>[8,5,3,2,7,6,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,8,7]=>[7,8,5,3,2,6,1,4]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,8,5,7]=>[7,5,8,3,2,6,1,4]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,8,3,5,7]=>[7,5,3,8,2,6,1,4]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>[7,5,3,2,8,6,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,6,2,3,5,7,8]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,6,1,2,3,7,8,5]=>[5,8,7,3,2,1,6,4]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>[8,5,7,3,2,1,6,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,6,1,2,7,3,8,5]=>[5,8,3,7,2,1,6,4]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,6,1,2,7,8,3,5]=>[5,3,8,7,2,1,6,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,6,1,2,7,3,5,8]=>[8,5,3,7,2,1,6,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,6,1,7,2,3,8,5]=>[5,8,3,2,7,1,6,4]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,6,1,7,2,8,3,5]=>[5,3,8,2,7,1,6,4]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,6,1,7,8,2,3,5]=>[5,3,2,8,7,1,6,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,6,1,7,2,3,5,8]=>[8,5,3,2,7,1,6,4]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,6,7,1,2,3,8,5]=>[5,8,3,2,1,7,6,4]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,6,7,1,2,8,3,5]=>[5,3,8,2,1,7,6,4]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[5,3,2,8,1,7,6,4]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>[5,3,2,1,8,7,6,4]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,6,7,1,2,3,5,8]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,8,7]=>[7,8,5,3,2,1,6,4]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,8,5,7]=>[7,5,8,3,2,1,6,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,8,3,5,7]=>[7,5,3,8,2,1,6,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>[7,5,3,2,8,1,6,4]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>[7,5,3,2,1,8,6,4]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,6,1,2,3,5,7,8]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,7,8,6]=>[6,8,7,5,3,2,1,4]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,1,2,3,5,7,6,8]=>[8,6,7,5,3,2,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>[6,8,5,7,3,2,1,4]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,3,7,8,5,6]=>[6,5,8,7,3,2,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,3,7,5,6,8]=>[8,6,5,7,3,2,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>[6,8,5,3,7,2,1,4]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[4,1,2,7,3,8,5,6]=>[6,5,8,3,7,2,1,4]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,1,2,7,8,3,5,6]=>[6,5,3,8,7,2,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,1,2,7,3,5,6,8]=>[8,6,5,3,7,2,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,7,2,3,5,8,6]=>[6,8,5,3,2,7,1,4]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[4,1,7,2,3,8,5,6]=>[6,5,8,3,2,7,1,4]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,1,7,2,8,3,5,6]=>[6,5,3,8,2,7,1,4]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,1,7,8,2,3,5,6]=>[6,5,3,2,8,7,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6,8]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,7,1,2,3,5,8,6]=>[6,8,5,3,2,1,7,4]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[4,7,1,2,3,8,5,6]=>[6,5,8,3,2,1,7,4]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,7,1,2,8,3,5,6]=>[6,5,3,8,2,1,7,4]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>[6,5,3,2,8,1,7,4]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,7,8,1,2,3,5,6]=>[6,5,3,2,1,8,7,4]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6,8]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>[7,8,6,5,3,2,1,4]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,2,3,5,8,6,7]=>[7,6,8,5,3,2,1,4]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]=>[7,6,5,8,3,2,1,4]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>[7,6,5,3,8,2,1,4]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,1,8,2,3,5,6,7]=>[7,6,5,3,2,8,1,4]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>[7,6,5,3,2,1,8,4]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]=>[7,8,4,6,5,3,2,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>[8,7,4,6,5,3,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[6,8,7,4,5,3,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,7,4,8,6]=>[6,8,4,7,5,3,2,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,7,8,4,6]=>[6,4,8,7,5,3,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6,8]=>[8,6,4,7,5,3,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[7,8,6,4,5,3,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,5,4,8,6,7]=>[7,6,8,4,5,3,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,5,8,4,6,7]=>[7,6,4,8,5,3,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,4]=>[4,8,7,6,3,5,2,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,2,5,3,6,7,4,8]=>[8,4,7,6,3,5,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,5,3,6,4,8,7]=>[7,8,4,6,3,5,2,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,2,5,3,6,8,4,7]=>[7,4,8,6,3,5,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,2,5,6,3,7,8,4]=>[4,8,7,3,6,5,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,2,5,6,3,7,4,8]=>[8,4,7,3,6,5,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,2,5,6,7,3,8,4]=>[4,8,3,7,6,5,2,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,2,5,6,7,3,4,8]=>[8,4,3,7,6,5,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,2,5,6,3,4,8,7]=>[7,8,4,3,6,5,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,5,6,3,8,4,7]=>[7,4,8,3,6,5,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,7,8,6]=>[6,8,7,4,3,5,2,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6,8]=>[8,6,7,4,3,5,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,7,4,8,6]=>[6,8,4,7,3,5,2,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,7,8,4,6]=>[6,4,8,7,3,5,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,2,5,7,3,4,8,6]=>[6,8,4,3,7,5,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,2,5,7,3,8,4,6]=>[6,4,8,3,7,5,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,2,5,7,8,3,4,6]=>[6,4,3,8,7,5,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>[8,6,4,3,7,5,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,2,5,3,4,6,8,7]=>[7,8,6,4,3,5,2,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4,8,6,7]=>[7,6,8,4,3,5,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>[7,6,4,8,3,5,2,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,6,7,8,4]=>[4,8,7,6,3,2,5,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,6,4,8,7]=>[7,8,4,6,3,2,5,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,2,3,6,8,4,7]=>[7,4,8,6,3,2,5,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,6,4,7,8]=>[8,7,4,6,3,2,5,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,2,6,3,7,8,4]=>[4,8,7,3,6,2,5,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,5,2,6,7,3,8,4]=>[4,8,3,7,6,2,5,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,7,8,3,4]=>[4,3,8,7,6,2,5,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,2,6,7,3,4,8]=>[8,4,3,7,6,2,5,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,5,2,6,3,4,8,7]=>[7,8,4,3,6,2,5,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,2,6,8,3,4,7]=>[7,4,3,8,6,2,5,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,6,2,3,7,8,4]=>[4,8,7,3,2,6,5,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,5,6,2,7,3,8,4]=>[4,8,3,7,2,6,5,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,6,2,7,8,3,4]=>[4,3,8,7,2,6,5,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,5,6,7,2,3,8,4]=>[4,8,3,2,7,6,5,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,6,7,2,8,3,4]=>[4,3,8,2,7,6,5,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,8,7]=>[7,8,4,3,2,6,5,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]=>[7,4,3,8,2,6,5,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,7,8,6]=>[6,8,7,4,3,2,5,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,7,4,8,6]=>[6,8,4,7,3,2,5,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,7,8,4,6]=>[6,4,8,7,3,2,5,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,7,3,4,8,6]=>[6,8,4,3,7,2,5,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>[6,4,8,3,7,2,5,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,5,7,2,3,4,8,6]=>[6,8,4,3,2,7,5,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,7,2,3,8,4,6]=>[6,4,8,3,2,7,5,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>[6,4,3,2,8,7,5,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,2,3,4,6,8]=>[8,6,4,3,2,7,5,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,5,2,3,4,6,8,7]=>[7,8,6,4,3,2,5,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>[7,6,8,4,3,2,5,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,4]=>[4,8,7,6,3,2,1,5]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2,3,6,7,4,8]=>[8,4,7,6,3,2,1,5]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,3,6,4,8,7]=>[7,8,4,6,3,2,1,5]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,3,6,8,4,7]=>[7,4,8,6,3,2,1,5]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,6,4,7,8]=>[8,7,4,6,3,2,1,5]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,2,6,3,7,8,4]=>[4,8,7,3,6,2,1,5]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,1,2,6,3,7,4,8]=>[8,4,7,3,6,2,1,5]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>[4,8,3,7,6,2,1,5]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,1,2,6,7,8,3,4]=>[4,3,8,7,6,2,1,5]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,1,2,6,7,3,4,8]=>[8,4,3,7,6,2,1,5]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>[7,8,4,3,6,2,1,5]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,6,3,8,4,7]=>[7,4,8,3,6,2,1,5]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,1,2,6,8,3,4,7]=>[7,4,3,8,6,2,1,5]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,6,3,4,7,8]=>[8,7,4,3,6,2,1,5]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>[4,8,7,3,2,6,1,5]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,1,6,2,3,7,4,8]=>[8,4,7,3,2,6,1,5]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4]=>[4,8,3,7,2,6,1,5]=>[2,2,2,2]=>[2,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,1,6,2,7,8,3,4]=>[4,3,8,7,2,6,1,5]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,1,6,2,7,3,4,8]=>[8,4,3,7,2,6,1,5]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>[4,8,3,2,7,6,1,5]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[5,1,6,7,2,8,3,4]=>[4,3,8,2,7,6,1,5]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,2,3,4]=>[4,3,2,8,7,6,1,5]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,1,6,7,2,3,4,8]=>[8,4,3,2,7,6,1,5]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,8,7]=>[7,8,4,3,2,6,1,5]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[5,1,6,2,3,8,4,7]=>[7,4,8,3,2,6,1,5]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,1,6,2,8,3,4,7]=>[7,4,3,8,2,6,1,5]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,1,6,8,2,3,4,7]=>[7,4,3,2,8,6,1,5]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[5,1,6,2,3,4,7,8]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[5,6,1,2,3,7,8,4]=>[4,8,7,3,2,1,6,5]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,6,1,2,7,3,8,4]=>[4,8,3,7,2,1,6,5]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[5,6,1,2,7,8,3,4]=>[4,3,8,7,2,1,6,5]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,1,2,7,3,4,8]=>[8,4,3,7,2,1,6,5]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,6,1,7,2,3,8,4]=>[4,8,3,2,7,1,6,5]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[5,6,1,7,2,8,3,4]=>[4,3,8,2,7,1,6,5]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,6,1,7,8,2,3,4]=>[4,3,2,8,7,1,6,5]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,1,7,2,3,4,8]=>[8,4,3,2,7,1,6,5]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,7,1,2,3,8,4]=>[4,8,3,2,1,7,6,5]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,7,1,2,8,3,4]=>[4,3,8,2,1,7,6,5]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>[4,3,2,8,1,7,6,5]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,8,7]=>[7,8,4,3,2,1,6,5]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,8,4,7]=>[7,4,8,3,2,1,6,5]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,6,1,2,8,3,4,7]=>[7,4,3,8,2,1,6,5]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,6,1,8,2,3,4,7]=>[7,4,3,2,8,1,6,5]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>[7,4,3,2,1,8,6,5]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[5,6,1,2,3,4,7,8]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,7,8,6]=>[6,8,7,4,3,2,1,5]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6,8]=>[8,6,7,4,3,2,1,5]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>[6,8,4,7,3,2,1,5]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,7,8,4,6]=>[6,4,8,7,3,2,1,5]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,1,2,3,7,4,6,8]=>[8,6,4,7,3,2,1,5]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>[6,8,4,3,7,2,1,5]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,7,3,8,4,6]=>[6,4,8,3,7,2,1,5]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,7,8,3,4,6]=>[6,4,3,8,7,2,1,5]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6,8]=>[8,6,4,3,7,2,1,5]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,7,2,3,4,8,6]=>[6,8,4,3,2,7,1,5]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,7,2,3,8,4,6]=>[6,4,8,3,2,7,1,5]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,7,2,8,3,4,6]=>[6,4,3,8,2,7,1,5]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,7,8,2,3,4,6]=>[6,4,3,2,8,7,1,5]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,1,7,2,3,4,6,8]=>[8,6,4,3,2,7,1,5]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,8,6]=>[6,8,4,3,2,1,7,5]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[5,7,1,2,3,8,4,6]=>[6,4,8,3,2,1,7,5]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,7,1,2,8,3,4,6]=>[6,4,3,8,2,1,7,5]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,7,1,8,2,3,4,6]=>[6,4,3,2,8,1,7,5]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>[6,4,3,2,1,8,7,5]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6,8]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>[7,8,6,4,3,2,1,5]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[5,1,2,3,4,8,6,7]=>[7,6,8,4,3,2,1,5]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,8,4,6,7]=>[7,6,4,8,3,2,1,5]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>[7,6,4,3,8,2,1,5]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[5,1,8,2,3,4,6,7]=>[7,6,4,3,2,8,1,5]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,8,1,2,3,4,6,7]=>[7,6,4,3,2,1,8,5]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]=>[8,5,7,6,4,3,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,6,8,5,7]=>[7,5,8,6,4,3,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,6,4,7,8,5]=>[5,8,7,4,6,3,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,6,4,7,5,8]=>[8,5,7,4,6,3,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,2,3,6,7,4,8,5]=>[5,8,4,7,6,3,2,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,7,8,4,5]=>[5,4,8,7,6,3,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,3,6,7,4,5,8]=>[8,5,4,7,6,3,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,8,7]=>[7,8,5,4,6,3,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,2,3,6,4,8,5,7]=>[7,5,8,4,6,3,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,2,3,6,8,4,5,7]=>[7,5,4,8,6,3,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,2,6,3,4,7,8,5]=>[5,8,7,4,3,6,2,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,2,6,3,4,7,5,8]=>[8,5,7,4,3,6,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,2,6,3,7,8,4,5]=>[5,4,8,7,3,6,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,2,6,7,3,4,8,5]=>[5,8,4,3,7,6,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,7,8,3,4,5]=>[5,4,3,8,7,6,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5,8]=>[8,5,4,3,7,6,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,8,7]=>[7,8,5,4,3,6,2,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,6,2,3,4,7,8,5]=>[5,8,7,4,3,2,6,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,6,2,3,7,4,8,5]=>[5,8,4,7,3,2,6,1]=>[2,2,1,2,1]=>[2,2,2,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,3,7,8,4,5]=>[5,4,8,7,3,2,6,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,6,2,7,3,4,8,5]=>[5,8,4,3,7,2,6,1]=>[2,1,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,6,2,7,3,4,5,8]=>[8,5,4,3,7,2,6,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,6,7,2,3,4,8,5]=>[5,8,4,3,2,7,6,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>[7,5,8,4,3,2,6,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>[7,5,4,3,8,2,6,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,7,8,5]=>[5,8,7,4,3,2,1,6]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,7,5,8]=>[8,5,7,4,3,2,1,6]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,3,7,4,8,5]=>[5,8,4,7,3,2,1,6]=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,1,2,3,7,8,4,5]=>[5,4,8,7,3,2,1,6]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[6,1,2,3,7,4,5,8]=>[8,5,4,7,3,2,1,6]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,7,3,4,8,5]=>[5,8,4,3,7,2,1,6]=>[2,1,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,1,2,7,3,8,4,5]=>[5,4,8,3,7,2,1,6]=>[1,2,2,1,2]=>[2,2,2,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[6,1,2,7,8,3,4,5]=>[5,4,3,8,7,2,1,6]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[6,1,2,7,3,4,5,8]=>[8,5,4,3,7,2,1,6]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,7,2,3,4,8,5]=>[5,8,4,3,2,7,1,6]=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,1,7,2,3,8,4,5]=>[5,4,8,3,2,7,1,6]=>[1,2,1,2,2]=>[2,2,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,7,2,8,3,4,5]=>[5,4,3,8,2,7,1,6]=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>[5,4,3,2,8,7,1,6]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,7,2,3,4,5,8]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,8,5]=>[5,8,4,3,2,1,7,6]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,7,1,2,3,8,4,5]=>[5,4,8,3,2,1,7,6]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,7,1,2,8,3,4,5]=>[5,4,3,8,2,1,7,6]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>[5,4,3,2,8,1,7,6]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>[7,8,5,4,3,2,1,6]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,8,5,7]=>[7,5,8,4,3,2,1,6]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,8,4,5,7]=>[7,5,4,8,3,2,1,6]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>[7,5,4,3,8,2,1,6]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>[7,5,4,3,2,8,1,6]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7]=>[7,5,4,3,2,1,8,6]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,7,5,8,6]=>[6,8,5,7,4,3,2,1]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>[6,8,5,4,3,2,1,7]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,8,5,6]=>[6,5,8,4,3,2,1,7]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[7,1,2,3,8,4,5,6]=>[6,5,4,8,3,2,1,7]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[7,1,2,8,3,4,5,6]=>[6,5,4,3,8,2,1,7]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[7,1,8,2,3,4,5,6]=>[6,5,4,3,2,8,1,7]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>[7,9,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,9,2]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>[8,10,7,6,5,4,3,2,1,9]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,8,2,3,4,5,6,9,7]=>[7,9,6,5,4,3,2,8,1]=>[2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>[8,9,6,5,4,3,2,1,7]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8]=>[8,7,6,5,4,3,9,1,2]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7,9]=>[9,7,6,5,4,3,1,8,2]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,10,2]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,10,9]=>[9,10,7,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,1,9,2]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,11,2]=>[1,1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,12,10]=>[10,12,9,8,7,6,5,4,3,2,1,11]=>[2,1,1,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,9,1,2,3,4,5,6,10,7]=>[7,10,6,5,4,3,2,1,9,8]=>[2,1,1,1,1,1,2,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,9,10,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,10,9,2]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,1,12,2]=>[1,1,1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,5,9,8]=>[8,9,5,4,3,2,1,7,6]=>[2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,1,8,9,3,4,5,6,7]=>[7,6,5,4,3,9,8,1,2]=>[1,1,1,1,2,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,8,6,9,7]=>[7,9,6,8,5,4,3,2,1]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[9,7,8,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,1,2]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9]=>[9,8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,7]=>[7,9,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,1,2,3,4,5,8,6,9]=>[9,6,8,5,4,3,2,1,7]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[8,7,6,5,4,2,9,3,1]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[10,8,9,7,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,2,3,4,5,8,9,6]=>[6,9,8,5,4,3,2,1,7]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,5,8,7,9]=>[9,7,8,5,4,3,2,1,6]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[8,7,6,5,4,1,9,3,2]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,9,10,8]=>[8,10,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,5,8,9,7]=>[7,9,8,5,4,3,2,1,6]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,1,9,4,5,6,7,8]=>[8,7,6,5,4,9,1,3,2]=>[1,1,1,1,2,2,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,1,2]=>[2,1,9,8,7,6,5,4,3]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[9,2,1,8,7,6,5,4,3]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,1,7,8,9,2,6]=>[6,2,9,8,7,1,5,4,3]=>[1,2,1,1,2,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,6,7,1,8,9,2,5]=>[5,2,9,8,1,7,6,4,3]=>[1,2,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,9,6,8]=>[8,6,9,4,7,2,5,1,3]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,7,4,6,8,9]=>[9,8,6,4,7,2,5,1,3]=>[1,1,1,2,2,2]=>[2,2,2,1,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,5,2,8,4,9,6,7]=>[7,6,9,4,8,2,5,1,3]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,7,8,1,9,2,4]=>[4,2,9,1,8,7,6,5,3]=>[1,2,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,9,1,2,4,6,8]=>[8,6,4,2,1,9,7,5,3]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[3,1,2,8,9,4,5,6,7]=>[7,6,5,4,9,8,2,1,3]=>[1,1,1,2,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,9,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,9,3]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,9,2,3]=>[3,2,9,8,7,6,5,4,1]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8,9]=>[9,8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[3,2,1,9,8,7,6,5,4]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,8,1,2,3,9]=>[9,3,2,1,8,7,6,5,4]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[9,8,7,3,2,1,6,5,4]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,5,1,2,3,9,6,7,8]=>[8,7,6,9,3,2,1,5,4]=>[1,1,2,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[4,1,2,3,8,9,5,6,7]=>[7,6,5,9,8,3,2,1,4]=>[1,1,2,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[4,9,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,9,4]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,9,6,8]=>[8,6,9,4,7,3,5,2,1]=>[1,2,2,2,1,1]=>[2,2,2,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[4,3,2,1,9,8,7,6,5]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[9,4,3,2,1,8,7,6,5]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[5,6,1,2,3,4,9,7,8]=>[8,7,9,4,3,2,1,6,5]=>[1,2,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,9,4,6,7,8]=>[8,7,6,4,9,3,2,1,5]=>[1,1,1,2,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[5,9,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,9,5]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,6,4,5,7,8,9]=>[9,8,7,5,4,6,3,2,1]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,9,2,3,4,5]=>[5,4,3,2,9,8,7,6,1]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,7,2,8,3,9,4,5]=>[5,4,9,3,8,2,7,1,6]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,8,1,2,3,4,5,9]=>[9,5,4,3,2,1,8,7,6]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,8,1,9,2,3,4,5,7]=>[7,5,4,3,2,9,1,8,6]=>[1,1,1,1,2,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7,9]=>[9,7,5,4,3,2,1,8,6]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[6,1,2,3,9,4,5,7,8]=>[8,7,5,4,9,3,2,1,6]=>[1,1,1,2,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[6,9,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,9,6]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,4,7,8,9,5,6]=>[6,5,9,8,7,4,3,2,1]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,4,7,5,6,8,9]=>[9,8,6,5,7,4,3,2,1]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,3,7,4,5,6,8,9]=>[9,8,6,5,4,7,3,2,1]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,7,3,4,5,6,8,9]=>[9,8,6,5,4,3,7,2,1]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,9,3,4,5,6,8]=>[8,6,5,4,3,9,2,7,1]=>[1,1,1,1,2,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[8,6,5,4,3,2,9,7,1]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[7,1,8,2,9,3,4,5,6]=>[6,5,4,3,9,2,8,1,7]=>[1,1,1,2,2,2]=>[2,2,2,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[7,1,8,2,3,4,5,6,9]=>[9,6,5,4,3,2,8,1,7]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[9,6,5,4,3,2,1,8,7]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[7,1,9,2,3,4,5,6,8]=>[8,6,5,4,3,2,9,1,7]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,9,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,9,7]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,8,9,6,7]=>[7,6,9,8,5,4,3,2,1]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7,9]=>[9,7,6,5,4,3,8,2,1]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,8,2,9,3,4,5,6,7]=>[7,6,5,4,3,9,2,8,1]=>[1,1,1,1,2,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[7,6,5,4,3,2,9,8,1]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,9,6,7]=>[7,6,9,5,4,3,2,1,8]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,9,5,6,7]=>[7,6,5,9,4,3,2,1,8]=>[1,1,2,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[8,1,2,3,9,4,5,6,7]=>[7,6,5,4,9,3,2,1,8]=>[1,1,1,2,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[8,1,2,9,3,4,5,6,7]=>[7,6,5,4,3,9,2,1,8]=>[1,1,1,1,2,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[8,1,9,2,3,4,5,6,7]=>[7,6,5,4,3,2,9,1,8]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>[8,7,6,9,5,4,3,2,1]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>[8,7,6,5,9,4,3,2,1]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>[8,7,6,5,4,9,3,2,1]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>[8,7,6,5,4,3,9,2,1]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]=>[9,1,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,9,1,8]=>[8,1,9,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,1,7]=>[7,1,9,8,6,5,4,3,2]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,1,6]=>[6,1,9,8,7,5,4,3,2]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,1,5]=>[5,1,9,8,7,6,4,3,2]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,1,4]=>[4,1,9,8,7,6,5,3,2]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,1,3]=>[3,1,9,8,7,6,5,4,2]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[10,1,9,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[9,8,1,7,6,5,4,3,2]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[9,1,10,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,6,1,9,7,8]=>[8,7,9,1,6,5,4,3,2]=>[1,2,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,9,10,1,8]=>[8,1,10,9,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,1,8,9,6,7]=>[7,6,9,8,1,5,4,3,2]=>[1,2,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,10,1,7]=>[7,1,10,9,8,6,5,4,3,2]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,1,7,8,9,5,6]=>[6,5,9,8,7,1,4,3,2]=>[1,2,1,1,2,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,10,1,6]=>[6,1,10,9,8,7,5,4,3,2]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,9,4,5]=>[5,4,9,8,7,6,1,3,2]=>[1,2,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,10,1,5]=>[5,1,10,9,8,7,6,4,3,2]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,9,3,4]=>[4,3,9,8,7,6,5,1,2]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,10,1,4]=>[4,1,10,9,8,7,6,5,3,2]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,10,1,3]=>[3,1,10,9,8,7,6,5,4,2]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[2,1,10,9,8,7,6,5,4,3]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[1,11,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[10,9,1,8,7,6,5,4,3,2]=>[1,1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,6,9,1,7,8]=>[8,7,1,9,6,5,4,3,2]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[9,8,7,1,6,5,4,3,2]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,6,1,7,8,9,4,5]=>[5,4,9,8,7,1,6,3,2]=>[1,2,1,1,2,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,9,10,2,3]=>[3,2,10,9,8,7,6,5,4,1]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,10,1,8,9]=>[9,8,1,10,7,6,5,4,3,2]=>[1,1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[10,9,8,1,7,6,5,4,3,2]=>[1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,9,1,6,7,8]=>[8,7,6,1,9,5,4,3,2]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,9,10,2,3]=>[3,2,10,9,8,7,6,5,1,4]=>[1,2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[9,8,7,6,1,5,4,3,2]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[10,9,8,7,1,6,5,4,3,2]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,9,1,5,6,7,8]=>[8,7,6,5,1,9,4,3,2]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[9,8,7,6,5,1,4,3,2]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[10,9,8,7,6,1,5,4,3,2]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8]=>[8,9,1,7,6,5,4,3,2]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,8,9,7]=>[7,9,8,1,6,5,4,3,2]=>[2,1,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,9]=>[9,7,8,1,6,5,4,3,2]=>[1,2,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,6]=>[6,9,8,7,1,5,4,3,2]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,7,8,6,9]=>[9,6,8,7,1,5,4,3,2]=>[1,2,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,9,8]=>[8,9,6,7,1,5,4,3,2]=>[2,2,2,1,1,1]=>[2,2,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,7,6,8,9]=>[9,8,6,7,1,5,4,3,2]=>[1,1,2,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,5,1,6,8,9,7]=>[7,9,8,6,1,5,4,3,2]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,7,5,9,8]=>[8,9,5,7,6,1,4,3,2]=>[2,2,1,2,1,1]=>[2,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7,9]=>[9,7,8,5,6,1,4,3,2]=>[1,2,2,2,1,1]=>[2,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,6,5,7,8,9]=>[9,8,7,5,6,1,4,3,2]=>[1,1,1,2,2,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,6,4,8,7,9]=>[9,7,8,4,6,5,1,3,2]=>[1,2,2,1,2,1]=>[2,2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[8,9,6,7,4,5,1,3,2]=>[2,2,2,2,1]=>[2,2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,7,6,8,9]=>[9,8,6,7,4,5,1,3,2]=>[1,1,2,2,2,1]=>[2,2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,5,4,6,7,8,9]=>[9,8,7,6,4,5,1,3,2]=>[1,1,1,1,2,2,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,6,8,7,9]=>[9,7,8,6,5,4,1,3,2]=>[1,2,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,7,9,8]=>[8,9,7,6,5,4,1,3,2]=>[2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[3,9,8,7,6,5,4,1,2]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,8,9,7]=>[7,9,8,5,6,3,4,1,2]=>[2,1,2,2,2]=>[2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[9,7,8,5,6,3,4,1,2]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[9,8,7,5,6,3,4,1,2]=>[1,1,1,2,2,2]=>[2,2,2,1,1,1]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[9,8,7,6,5,3,4,1,2]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,9,5]=>[5,9,8,7,6,4,3,1,2]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[9,7,8,6,5,4,3,1,2]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,2]=>[2,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,2,9]=>[9,2,8,7,6,5,4,3,1]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[9,8,7,6,5,2,4,3,1]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[8,9,6,7,4,5,2,3,1]=>[2,2,2,2,1]=>[2,2,2,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,3]=>[3,9,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,4]=>[4,9,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,6,4,7,8,9]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,7,8,9,6]=>[6,9,8,7,4,5,3,2,1]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[8,9,6,7,4,5,3,2,1]=>[2,2,2,1,1,1]=>[2,2,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,6,4,5,3,2,1]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,5]=>[5,9,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,6,7,5,8,9]=>[9,8,5,7,6,4,3,2,1]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,6]=>[6,9,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8]=>[8,9,6,7,5,4,3,2,1]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,10,9]=>[9,10,1,8,7,6,5,4,3,2]=>[2,2,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,9,10,8]=>[8,10,9,1,7,6,5,4,3,2]=>[2,1,2,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8,10]=>[10,8,9,1,7,6,5,4,3,2]=>[1,2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,8,9,10,7]=>[7,10,9,8,1,6,5,4,3,2]=>[2,1,1,2,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7,10,9]=>[9,10,7,8,1,6,5,4,3,2]=>[2,2,2,1,1,1,1]=>[2,2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,10,6]=>[6,10,9,8,7,1,5,4,3,2]=>[2,1,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,9,8,10]=>[10,8,9,6,7,1,5,4,3,2]=>[1,2,2,2,1,1,1]=>[2,2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7,10,9]=>[9,10,7,8,5,6,1,4,3,2]=>[2,2,2,2,1,1]=>[2,2,2,2,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[10,9,8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,1,3,2]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,1,3,2]=>[2,1,1,1,1,1,2,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,10,3]=>[3,10,9,8,7,6,5,4,1,2]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[10,9,7,8,5,6,3,4,1,2]=>[1,1,2,2,2,2]=>[2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,9,10,5]=>[5,10,9,8,7,6,4,3,1,2]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,7,8,9,10,6]=>[6,10,9,8,7,5,4,3,1,2]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,2]=>[2,10,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,9,2,10]=>[10,2,9,8,7,6,5,4,3,1]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,6,9,10,8]=>[8,10,9,6,7,4,5,2,3,1]=>[2,1,2,2,2,1]=>[2,2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,2,3,1]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7,9,8,10]=>[10,8,9,7,5,6,4,2,3,1]=>[1,2,1,2,1,2,1]=>[2,2,2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,10,3]=>[3,10,9,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,2,1]=>[2,2,2,2,1,1]=>[2,2,2,2,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,10,4]=>[4,10,9,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,10,5]=>[5,10,9,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,10,9]=>[9,10,7,8,5,6,4,3,2,1]=>[2,2,2,1,1,1,1]=>[2,2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,10,6]=>[6,10,9,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,10,7]=>[7,10,9,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,10,9]=>[9,10,7,8,6,5,4,3,2,1]=>[2,2,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,2]=>[2,9,8,7,6,5,4,1,3]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,9,2]=>[2,9,8,7,6,5,1,4,3]=>[2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,9,2]=>[2,9,8,7,6,1,5,4,3]=>[2,1,1,1,2,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,2]=>[2,9,8,7,1,6,5,4,3]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,2]=>[2,9,8,1,7,6,5,4,3]=>[2,1,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,1,9,2]=>[2,9,1,8,7,6,5,4,3]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]=>[2,10,9,8,7,6,5,4,1,3]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,9,4]=>[4,9,8,7,6,5,2,1,3]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,9,10,2]=>[2,10,9,8,7,6,5,1,4,3]=>[2,1,1,1,1,1,2,1]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,9,5]=>[5,9,8,7,6,2,1,4,3]=>[2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,9,10,2]=>[2,10,9,8,7,6,1,5,4,3]=>[2,1,1,1,1,2,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,1,2,7,8,9,6]=>[6,9,8,7,2,1,5,4,3]=>[2,1,1,1,2,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,10,2]=>[2,10,9,8,7,1,6,5,4,3]=>[2,1,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,5,6,1,2,8,9,7]=>[7,9,8,2,1,6,5,4,3]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,10,2]=>[2,10,9,8,1,7,6,5,4,3]=>[2,1,1,2,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,6,7,1,2,9,8]=>[8,9,2,1,7,6,5,4,3]=>[2,1,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,8,1,9,10,2]=>[2,10,9,1,8,7,6,5,4,3]=>[2,1,2,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,1,10,2]=>[2,10,1,9,8,7,6,5,4,3]=>[2,2,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5,10]=>[10,5,4,3,2,1,9,8,7,6]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4,10]=>[10,4,3,2,1,9,8,7,6,5]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,11,2]=>[2,11,10,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,7,9,2,8]=>[8,2,9,7,6,5,4,3,1]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]=>[10,2,1,9,8,7,6,5,4,3]=>[1,1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[11,9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[10,7,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,10,9,1]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,11,1]=>[1,1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,8,2,9]=>[9,2,8,7,6,5,4,1,3]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,9,3]=>[3,9,8,7,6,5,2,1,4]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[9,8,10,7,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,10,7,8]=>[8,7,10,6,5,4,3,2,1,9]=>[1,2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,4,7,5,8,9,6]=>[6,9,8,5,7,4,3,2,1]=>[2,1,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,3,6,4,7,8,9,5]=>[5,9,8,7,4,6,3,2,1]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,9,4]=>[4,9,8,7,6,3,5,2,1]=>[2,1,1,1,2,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,9,3]=>[3,9,8,7,6,5,2,4,1]=>[2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[10,9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[10,9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[10,9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[10,9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,2,5,6,7,8,9]=>[9,8,7,6,5,2,4,1,3]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,3,6,7,8,9]=>[9,8,7,6,3,5,2,1,4]=>[1,1,1,1,2,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,4,7,8,9]=>[9,8,7,4,6,3,2,1,5]=>[1,1,1,2,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,5,8,9]=>[9,8,5,7,4,3,2,1,6]=>[1,1,2,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,9,10,1,3,4,5,6]=>[6,5,4,3,1,10,9,8,7,2]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,8,2,9,3]=>[3,9,2,8,7,6,5,4,1]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,8,1,3,9]=>[9,3,1,8,7,6,5,4,2]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,6,7,1,8,2,9]=>[9,2,8,1,7,6,5,4,3]=>[1,2,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,9,2,4]=>[4,2,9,8,7,6,5,3,1]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,1,4,8,9,2,5,6,7]=>[7,6,5,2,9,8,4,1,3]=>[1,1,1,2,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[4,3,2,1,10,9,8,7,6,5]=>[1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]=>[8,7,6,4,9,5,3,2,1]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,9,6,8]=>[8,6,9,7,5,4,3,2,1]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[9,8,7,10,6,5,4,3,2,1]=>[1,1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,6,9,5,7,8]=>[8,7,5,9,6,4,3,2,1]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[9,8,7,6,10,5,4,3,2,1]=>[1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,10,5,6,7,8,9]=>[9,8,7,6,5,10,4,3,2,1]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,9,3,5,6,7,8]=>[8,7,6,5,3,9,4,2,1]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[9,8,7,6,5,4,10,3,2,1]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,10,2,1]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,7,8,1,9,6]=>[6,9,1,8,7,5,4,3,2]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8]=>[8,9,6,7,4,5,2,1,3]=>[2,2,2,1,2]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,2,4,7,6,9,8]=>[8,9,6,7,4,2,5,1,3]=>[2,2,1,2,2]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,7,4,6,9,8]=>[8,9,6,4,7,2,5,1,3]=>[2,1,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6,9]=>[9,6,8,4,7,2,5,1,3]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7,9]=>[9,7,8,4,6,2,5,1,3]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7,9]=>[9,7,8,5,6,2,4,1,3]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,2,1,3]=>[1,2,2,2,1,2]=>[2,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,4,7,6,9,8,10]=>[10,8,9,6,7,4,2,5,1,3]=>[1,2,2,1,2,2]=>[2,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,7,4,6,9,8,10]=>[10,8,9,6,4,7,2,5,1,3]=>[1,2,1,2,2,2]=>[2,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,9,6,8,10]=>[10,8,6,9,4,7,2,5,1,3]=>[1,1,2,2,2,2]=>[2,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,10,8]=>[8,10,6,9,4,7,2,5,1,3]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,8,6,10,9]=>[9,10,6,8,4,7,2,5,1,3]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7,10,9]=>[9,10,7,8,4,6,2,5,1,3]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7,10,9]=>[9,10,7,8,5,6,2,4,1,3]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[10,9,8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,6,7,8,10,1,2,9]=>[9,2,1,10,8,7,6,5,4,3]=>[1,1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[3,2,1,10,9,8,7,6,5,4]=>[1,1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,9,2,1]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7,9,10]=>[10,9,7,6,5,4,3,8,2,1]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,8,4,5,6,7,9,10]=>[10,9,7,6,5,4,8,3,2,1]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,7,4,5,6,8,9,10]=>[10,9,8,6,5,4,7,3,2,1]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,8,9,10]=>[10,9,8,6,5,7,4,3,2,1]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>[9,7,5,3,1,10,8,6,4,2]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,1,6,2,7,3,8,10,4,9]=>[9,4,10,8,3,7,2,6,1,5]=>[1,2,1,2,2,2]=>[2,2,2,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,7,2,8,3,9,4,10,5]=>[5,10,4,9,3,8,2,7,1,6]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[11,9,7,5,3,1,12,10,8,6,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,1,7,2,8,3,9,4,10,12,5,11]=>[11,5,12,10,4,9,3,8,2,7,1,6]=>[1,2,1,2,2,2,2]=>[2,2,2,2,2,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[6,12,5,11,4,10,3,9,2,8,1,7]=>[2,2,2,2,2,2]=>[2,2,2,2,2,2]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,8,9,1,2,10,3]=>[3,10,2,1,9,8,7,6,5,4]=>[2,1,2,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,8,9,1,2,3,4,10,5]=>[5,10,4,3,2,1,9,8,7,6]=>[2,1,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,10,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,10,8]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,10,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,10,3]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[11,10,12,9,8,7,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,1,4,6,7,8,9]=>[9,8,7,6,4,1,5,3,2]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,5,7,8,9]=>[9,8,7,5,1,6,4,3,2]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,6,8,9]=>[9,8,6,1,7,5,4,3,2]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,1,7,9]=>[9,7,1,8,6,5,4,3,2]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,2,3,7,9,4,8]=>[8,4,9,7,3,2,1,6,5]=>[1,2,1,1,1,2,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,10,1,9]=>[1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,9,10,1,2,4,5,6]=>[6,5,4,2,1,10,9,8,7,3]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,10,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,10,3,2]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,2,3,4,7,8,9,5]=>[5,9,8,7,4,3,2,1,6]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,9,4]=>[4,9,8,7,6,3,2,1,5]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[5,10,1,2,3,4,6,7,8,9]=>[9,8,7,6,4,3,2,1,10,5]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,10,9]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,11,10]=>[1,1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,8,9,1,2,3,10]=>[10,3,2,1,9,8,7,6,5,4]=>[1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,4,5,1,2,8,9,10,6,7]=>[7,6,10,9,8,2,1,5,4,3]=>[1,2,1,1,1,2,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,8,1,9,7]=>[7,9,1,8,6,5,4,3,2]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,9,1,10,8]=>[8,10,1,9,7,6,5,4,3,2]=>[2,2,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[6,5,4,3,2,1,10,9,8,7]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,10,9,8]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,8,1,9,3]=>[3,9,1,8,7,6,5,4,2]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[10,9,4,3,2,1,8,7,6,5]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[10,9,8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,6,4,5,7,8,9,10]=>[10,9,8,7,5,4,6,3,2,1]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,10,6,7,8,9]=>[9,8,7,6,10,4,3,2,1,5]=>[1,1,1,2,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,9,10,1,2,3,4,6]=>[6,4,3,2,1,10,9,8,7,5]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,7,8,9,10,1,2,3,5,6]=>[6,5,3,2,1,10,9,8,7,4]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,9,1,3,5]=>[5,3,1,9,8,7,6,4,2]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,9,10,3]=>[3,10,9,8,7,6,5,2,1,4]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,7,8,10,1,2,3,4,9]=>[9,4,3,2,1,10,8,7,6,5]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,9,6,8]=>[8,6,9,7,4,5,2,3,1]=>[1,2,1,2,2,1]=>[2,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,4,7,9,6,10,8]=>[8,10,6,9,7,4,5,2,3,1]=>[2,2,1,2,2,1]=>[2,2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,8,7,9]=>[9,7,8,3,6,2,5,1,4]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,8,9,1,10,2,3,4,5]=>[5,4,3,2,10,1,9,8,7,6]=>[1,1,1,2,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[9,11,10,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,6,1,7,8,9,5]=>[5,9,8,7,1,6,4,3,2]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,6,1,7,8,9,10,5]=>[5,10,9,8,7,1,6,4,3,2]=>[2,1,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,5,6,1,7,8,9,10,3]=>[3,10,9,8,7,1,6,5,4,2]=>[2,1,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,6,1,7,8,9,10,4]=>[4,10,9,8,7,1,6,5,3,2]=>[2,1,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,7,8,9,1,2,3,10,4,5]=>[5,4,10,3,2,1,9,8,7,6]=>[1,2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,7,8,9,1,2,10,3,4,5]=>[5,4,3,10,2,1,9,8,7,6]=>[1,1,2,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,7,1,8,9,4]=>[4,9,8,1,7,6,5,3,2]=>[2,1,2,1,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6,9,8]=>[8,9,6,7,3,5,2,4,1]=>[2,2,2,2,1]=>[2,2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,8,5,9,7]=>[7,9,5,8,3,6,2,4,1]=>[2,2,2,2,1]=>[2,2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,10,7,9]=>[9,7,10,5,8,3,6,2,4,1]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,5,8,7,9]=>[9,7,8,5,6,3,1,4,2]=>[1,2,2,1,2,1]=>[2,2,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,7,1,2,8,9,6]=>[6,9,8,2,1,7,5,4,3]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,8,9,2,10,3]=>[3,10,2,9,8,7,6,5,4,1]=>[2,2,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,2,3,4,5,6,9,10,7]=>[7,10,9,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7,9,10]=>[10,9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[9,1,2,3,4,5,10,6,7,8]=>[8,7,6,10,5,4,3,2,1,9]=>[1,1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[4,10,1,2,3,5,6,7,8,9]=>[9,8,7,6,5,3,2,1,10,4]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,6,9,10,7,8]=>[8,7,10,9,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,8,9,10,6,7]=>[7,6,10,9,8,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,9,7,8]=>[8,7,9,5,6,3,4,1,2]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,9,6,8]=>[8,6,9,5,7,3,4,1,2]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,9,6,8]=>[8,6,9,4,7,3,5,1,2]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,9,6,8]=>[8,6,9,4,7,2,5,3,1]=>[1,2,2,2,1,1]=>[2,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,9,6,8]=>[8,6,9,4,7,5,2,3,1]=>[1,2,2,1,2,1]=>[2,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,7,6,10,8,9]=>[9,8,10,6,7,4,5,2,3,1]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,10,7,9]=>[9,7,10,6,8,4,5,2,3,1]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,10,7,9]=>[9,7,10,5,8,4,6,2,3,1]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,10,7,9]=>[9,7,10,5,8,3,6,1,4,2]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,8,5,10,7,9]=>[9,7,10,5,8,3,6,4,1,2]=>[1,2,2,2,1,2]=>[2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,3,6,8,5,10,7,9]=>[9,7,10,5,8,6,3,4,1,2]=>[1,2,2,1,2,2]=>[2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,5,8,10,7,9]=>[9,7,10,8,5,6,3,4,1,2]=>[1,2,1,2,2,2]=>[2,2,2,2,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,7,8,9,10,3,4,5,6]=>[6,5,4,3,10,9,8,7,2,1]=>[1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,1,3,5,7,9]=>[9,7,5,3,1,8,6,4,2]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,7,9,2,4,6,8,10]=>[10,8,6,4,2,9,7,5,3,1]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,4,6,8,10,1,2,5,7,9]=>[9,7,5,2,1,10,8,6,4,3]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,6,8,10,1,2,3,5,7,9]=>[9,7,5,3,2,1,10,8,6,4]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[7,1,8,2,9,3,10,4,5,6]=>[6,5,4,10,3,9,2,8,1,7]=>[1,1,2,2,2,2]=>[2,2,2,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,10,11,12,1,2,3]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[1,1,2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,1,2,3,6,9,4,7,8]=>[8,7,4,9,6,3,2,1,5]=>[1,1,2,1,1,1,2]=>[2,2,1,1,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,7,5,8,6,9]=>[9,6,8,5,7,3,4,1,2]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,6,7,10,8,9]=>[9,8,10,7,6,5,4,2,1,3]=>[1,2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,6,2,7,3,8,4,9,5,10]=>[10,5,9,4,8,3,7,2,6,1]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,1,2,3,4,5,6,9,8,10]=>[10,8,9,6,5,4,3,2,1,7]=>[1,2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,7,8,9,1,10,2,3,4,6]=>[6,4,3,2,10,1,9,8,7,5]=>[1,1,1,2,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,7,1,8,2,9,3,10,4,5]=>[5,4,10,3,9,2,8,1,7,6]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,12,1]=>[1,1,1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1,10,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,10,1,8]=>[1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,9,8,10]=>[10,8,9,6,7,3,5,1,4,2]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,4,6,8,1,10,3,5,7,9]=>[9,7,5,3,10,1,8,6,4,2]=>[1,1,1,2,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,7,3,8,4,9,5,10,6]=>[6,10,5,9,4,8,3,7,1,2]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[2,4,6,8,10,1,12,3,5,7,9,11]=>[11,9,7,5,3,12,1,10,8,6,4,2]=>[1,1,1,1,2,2,1,1,1,1]=>[2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,10,7,9]=>[9,7,10,8,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[7,8,9,1,2,3,4,5,6,10]=>[10,6,5,4,3,2,1,9,8,7]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,2,4,7,6,9,8]=>[8,9,6,7,4,2,5,3,1]=>[2,2,1,2,1,1]=>[2,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,5,7,4,9,6,10,8]=>[8,10,6,9,4,7,5,2,3,1]=>[2,2,2,1,2,1]=>[2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,5,7,9]=>[9,7,5,8,6,3,4,1,2]=>[1,1,2,1,2,2]=>[2,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,8,5,7,9]=>[9,7,5,8,3,6,1,4,2]=>[1,1,2,2,2,1]=>[2,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,5,4,8,6,9,7]=>[7,9,6,8,4,5,2,3,1]=>[2,2,2,2,1]=>[2,2,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,3,5,7,9]=>[9,7,5,3,8,6,4,2,1]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7,10,9]=>[9,10,7,8,4,6,3,5,1,2]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[2,4,6,8,1,3,5,7,10,12,9,11]=>[11,9,12,10,7,5,3,1,8,6,4,2]=>[1,2,1,1,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,5,6,9,10,1,2,3,7,8]=>[8,7,3,2,1,10,9,6,5,4]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,5,8,9,10,1,2,3,6,7]=>[7,6,3,2,1,10,9,8,5,4]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,5,7,9,1,2,4,6,8,10]=>[10,8,6,4,2,1,9,7,5,3]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,6,3,5,8,7,9]=>[9,7,8,5,3,6,1,4,2]=>[1,2,1,2,2,1]=>[2,2,2,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,9,8]=>[8,9,6,7,3,5,1,4,2]=>[2,2,2,2,1]=>[2,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,1,4,2]=>[2,2,2,1,2,1]=>[2,2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,8,3,9,5,10,7]=>[7,10,5,9,3,8,2,6,1,4]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2,2]=>[2,2,2,2,2,2]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,1,2,3,4,5,6,7,8,9,10,12]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,8,9,10,11,1,2,3,4,5,12,6]=>[6,12,5,4,3,2,1,11,10,9,8,7]=>[2,1,1,1,1,2,1,1,1,1]=>[2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[6,7,8,1,9,2,3,4,10,5]=>[5,10,4,3,2,9,1,8,7,6]=>[2,1,1,2,2,1,1]=>[2,2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,6,8,9,10,1,3,4,5,7]=>[7,5,4,3,1,10,9,8,6,2]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,8,9,10,11,12,1,3,4,5,6,7]=>[7,6,5,4,3,1,12,11,10,9,8,2]=>[1,1,1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,1,6,2,7,3,8,4,9]=>[9,4,8,3,7,2,6,1,5]=>[1,2,2,2,2]=>[2,2,2,2,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[6,7,1,8,9,10,2,3,4,5]=>[5,4,3,2,10,9,8,1,7,6]=>[1,1,1,2,1,1,2,1]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,9,8]=>[8,9,6,4,7,5,2,1,3]=>[2,1,2,1,1,2]=>[2,2,2,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[6,7,8,1,9,10,2,3,4,5]=>[5,4,3,2,10,9,1,8,7,6]=>[1,1,1,2,1,2,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[8,1,9,2,10,3,4,5,6,7]=>[7,6,5,4,3,10,2,9,1,8]=>[1,1,1,1,2,2,2]=>[2,2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[2,12,11,10,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,4,6,8,1,3,5,7,10,9]=>[9,10,7,5,3,1,8,6,4,2]=>[2,1,1,1,2,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[2,4,6,8,10,1,3,5,7,9,12,11]=>[11,12,9,7,5,3,1,10,8,6,4,2]=>[2,1,1,1,1,2,1,1,1,1]=>[2,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,4,5,6,9,1,7,10,8]=>[8,10,7,1,9,6,5,4,3,2]=>[2,1,2,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,7,2,8,3,9,4,10,6]=>[6,10,4,9,3,8,2,7,1,5]=>[2,2,2,2,2]=>[2,2,2,2,2]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,9,10,1,3,5]=>[5,3,1,10,9,8,7,6,4,2]=>[1,1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[6,1,7,2,8,3,9,10,4,5]=>[5,4,10,9,3,8,2,7,1,6]=>[1,2,1,2,2,2]=>[2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,5,8,7,10,12,9,11]=>[11,9,12,10,7,8,5,6,3,4,1,2]=>[1,2,1,2,2,2,2]=>[2,2,2,2,2,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,1,8,2,9,3,10,4,11,12,5,6]=>[6,5,12,11,4,10,3,9,2,8,1,7]=>[1,2,1,2,2,2,2]=>[2,2,2,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,6,1,3,5,7,8,9]=>[9,8,7,5,3,1,6,4,2]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,6,1,3,5,7,8,9,10]=>[10,9,8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,4,6,8,1,3,5,7,9,10]=>[10,9,7,5,3,1,8,6,4,2]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,8,9,1,3,5,7]=>[7,5,3,1,9,8,6,4,2]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
searching the database
Sorry, this map was not found in the database.