Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]=>[1]
[1,0,1,0]=>[2,1]=>[2,1]=>[2,1]=>[1,1]
[1,1,0,0]=>[1,2]=>[1,2]=>[1,2]=>[2]
[1,0,1,0,1,0]=>[3,2,1]=>[3,2,1]=>[3,2,1]=>[1,1,1]
[1,0,1,1,0,0]=>[2,3,1]=>[1,3,2]=>[1,3,2]=>[2,1]
[1,1,0,0,1,0]=>[3,1,2]=>[2,3,1]=>[3,1,2]=>[1,2]
[1,1,0,1,0,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>[1,2]
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>[3]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[1,4,3,2]=>[1,4,3,2]=>[2,1,1]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[2,4,3,1]=>[4,1,3,2]=>[1,2,1]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[2,1,4,3]=>[2,1,4,3]=>[1,2,1]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[1,2,4,3]=>[1,2,4,3]=>[3,1]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[3,4,2,1]=>[4,3,1,2]=>[1,1,2]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[3,1,4,2]=>[2,4,1,3]=>[2,2]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,2,4,1]=>[4,2,1,3]=>[1,1,2]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[3,2,1,4]=>[3,2,1,4]=>[1,1,2]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[1,3,2,4]=>[1,3,2,4]=>[2,2]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[2,3,4,1]=>[4,1,2,3]=>[1,3]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[2,3,1,4]=>[3,1,2,4]=>[1,3]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[1,3]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[4]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[2,1,1,1]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[2,5,4,3,1]=>[5,1,4,3,2]=>[1,2,1,1]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[1,2,1,1]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[3,1,1]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[3,5,4,2,1]=>[5,4,1,3,2]=>[1,1,2,1]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[3,1,5,4,2]=>[2,5,1,4,3]=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[3,2,5,4,1]=>[5,2,1,4,3]=>[1,1,2,1]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[1,1,2,1]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[2,2,1]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[2,3,5,4,1]=>[5,1,2,4,3]=>[1,3,1]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[2,3,1,5,4]=>[3,1,2,5,4]=>[1,3,1]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[1,3,1]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[4,1]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,2]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[4,1,5,3,2]=>[2,5,4,1,3]=>[2,1,2]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[4,2,5,3,1]=>[5,2,4,1,3]=>[1,2,2]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[4,2,1,5,3]=>[3,2,5,1,4]=>[1,2,2]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[1,4,2,5,3]=>[1,3,5,2,4]=>[3,2]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,2]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[4,3,1,5,2]=>[3,5,2,1,4]=>[2,1,2]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,2]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[1,1,1,2]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[2,1,2]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[2,4,3,5,1]=>[5,1,3,2,4]=>[1,2,2]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[2,4,3,1,5]=>[4,1,3,2,5]=>[1,2,2]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[1,2,2]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[3,2]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[1,1,3]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[3,4,1,5,2]=>[3,5,1,2,4]=>[2,3]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,1,3]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[1,1,3]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[3,1,4,2,5]=>[2,4,1,3,5]=>[2,3]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[1,1,3]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[1,1,3]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[1,1,3]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[2,3]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,4]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[1,4]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[1,4]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[1,4]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[2,6,5,4,3,1]=>[6,1,5,4,3,2]=>[1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[1,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[3,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>[6,5,1,4,3,2]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[3,1,6,5,4,2]=>[2,6,1,5,4,3]=>[2,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[3,2,6,5,4,1]=>[6,2,1,5,4,3]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[2,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[2,3,6,5,4,1]=>[6,1,2,5,4,3]=>[1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[2,3,1,6,5,4]=>[3,1,2,6,5,4]=>[1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[1,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[4,6,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[4,1,6,5,3,2]=>[2,6,5,1,4,3]=>[2,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[4,2,6,5,3,1]=>[6,2,5,1,4,3]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[4,2,1,6,5,3]=>[3,2,6,1,5,4]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[1,4,2,6,5,3]=>[1,3,6,2,5,4]=>[3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[4,3,1,6,5,2]=>[3,6,2,1,5,4]=>[2,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[1,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[2,1,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[2,4,3,6,5,1]=>[6,1,3,2,5,4]=>[1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[2,4,3,1,6,5]=>[4,1,3,2,6,5]=>[1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[1,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[3,4,6,5,2,1]=>[6,5,1,2,4,3]=>[1,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[3,4,1,6,5,2]=>[3,6,1,2,5,4]=>[2,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[3,4,2,6,5,1]=>[6,3,1,2,5,4]=>[1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[3,4,2,1,6,5]=>[4,3,1,2,6,5]=>[1,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[3,1,4,2,6,5]=>[2,4,1,3,6,5]=>[2,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[3,2,4,6,5,1]=>[6,2,1,3,5,4]=>[1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[3,2,4,1,6,5]=>[4,2,1,3,6,5]=>[1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[1,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[2,3,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[2,3,4,6,5,1]=>[6,1,2,3,5,4]=>[1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>[1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>[1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[1,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[5,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[5,1,6,4,3,2]=>[2,6,5,4,1,3]=>[2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[5,2,6,4,3,1]=>[6,2,5,4,1,3]=>[1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[5,2,1,6,4,3]=>[3,2,6,5,1,4]=>[1,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[1,5,2,6,4,3]=>[1,3,6,5,2,4]=>[3,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[5,3,1,6,4,2]=>[3,6,2,5,1,4]=>[2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[5,3,2,1,6,4]=>[4,3,2,6,1,5]=>[1,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[1,5,3,2,6,4]=>[1,4,3,6,2,5]=>[2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[2,5,3,6,4,1]=>[6,1,3,5,2,4]=>[1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,5,3,1,6,4]=>[4,1,3,6,2,5]=>[1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[2,1,5,3,6,4]=>[2,1,4,6,3,5]=>[1,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[1,2,5,3,6,4]=>[1,2,4,6,3,5]=>[4,2]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[5,4,1,6,3,2]=>[3,6,5,2,1,4]=>[2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[5,4,2,1,6,3]=>[4,3,6,2,1,5]=>[1,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[1,5,4,2,6,3]=>[1,4,6,3,2,5]=>[3,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[5,4,3,1,6,2]=>[4,6,3,2,1,5]=>[2,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[2,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[2,5,4,3,6,1]=>[6,1,4,3,2,5]=>[1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[2,5,4,3,1,6]=>[5,1,4,3,2,6]=>[1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[1,2,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[3,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[3,5,4,6,2,1]=>[6,5,1,3,2,4]=>[1,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[3,5,4,1,6,2]=>[4,6,1,3,2,5]=>[2,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[3,5,4,2,6,1]=>[6,4,1,3,2,5]=>[1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[3,5,4,2,1,6]=>[5,4,1,3,2,6]=>[1,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[3,1,5,4,2,6]=>[2,5,1,4,3,6]=>[2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[3,2,5,4,6,1]=>[6,2,1,4,3,5]=>[1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[3,2,5,4,1,6]=>[5,2,1,4,3,6]=>[1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[1,1,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[2,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[2,3,5,4,6,1]=>[6,1,2,4,3,5]=>[1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[2,3,5,4,1,6]=>[5,1,2,4,3,6]=>[1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>[1,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[1,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[4,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[4,5,1,6,3,2]=>[3,6,5,1,2,4]=>[2,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[4,5,2,6,3,1]=>[6,3,5,1,2,4]=>[1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[4,5,2,1,6,3]=>[4,3,6,1,2,5]=>[1,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>[2,4,6,1,3,5]=>[3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[4,5,3,1,6,2]=>[4,6,3,1,2,5]=>[2,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[1,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[4,1,5,3,2,6]=>[2,5,4,1,3,6]=>[2,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[4,2,5,3,6,1]=>[6,2,4,1,3,5]=>[1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[4,2,5,3,1,6]=>[5,2,4,1,3,6]=>[1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[4,2,1,5,3,6]=>[3,2,5,1,4,6]=>[1,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[1,4,2,5,3,6]=>[1,3,5,2,4,6]=>[3,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[1,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,3,5,1,6,2]=>[4,6,2,1,3,5]=>[2,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[1,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[4,3,1,5,2,6]=>[3,5,2,1,4,6]=>[2,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[2,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[2,4,3,5,6,1]=>[6,1,3,2,4,5]=>[1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[2,4,3,5,1,6]=>[5,1,3,2,4,6]=>[1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[2,4,3,1,5,6]=>[4,1,3,2,5,6]=>[1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[1,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[3,3]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[1,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[3,4,5,1,6,2]=>[4,6,1,2,3,5]=>[2,4]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[1,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[3,4,1,5,2,6]=>[3,5,1,2,4,6]=>[2,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[1,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[1,1,4]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[1,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[3,1,4,2,5,6]=>[2,4,1,3,5,6]=>[2,4]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[2,4]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,5]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[1,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[1,5]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[1,5]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[1,5]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[2,7,6,5,4,3,1]=>[7,1,6,5,4,3,2]=>[1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[3,7,6,5,4,2,1]=>[7,6,1,5,4,3,2]=>[1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[3,1,7,6,5,4,2]=>[2,7,1,6,5,4,3]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[3,2,7,6,5,4,1]=>[7,2,1,6,5,4,3]=>[1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[2,3,7,6,5,4,1]=>[7,1,2,6,5,4,3]=>[1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[2,3,1,7,6,5,4]=>[3,1,2,7,6,5,4]=>[1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4]=>[4,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[4,7,6,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[4,1,7,6,5,3,2]=>[2,7,6,1,5,4,3]=>[2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[4,2,7,6,5,3,1]=>[7,2,6,1,5,4,3]=>[1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[4,2,1,7,6,5,3]=>[3,2,7,1,6,5,4]=>[1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[1,4,2,7,6,5,3]=>[1,3,7,2,6,5,4]=>[3,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[4,3,1,7,6,5,2]=>[3,7,2,1,6,5,4]=>[2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5]=>[2,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[2,4,3,7,6,5,1]=>[7,1,3,2,6,5,4]=>[1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[2,4,3,1,7,6,5]=>[4,1,3,2,7,6,5]=>[1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>[1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5]=>[3,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>[7,6,1,2,5,4,3]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[3,4,1,7,6,5,2]=>[3,7,1,2,6,5,4]=>[2,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[3,4,2,7,6,5,1]=>[7,3,1,2,6,5,4]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[3,4,2,1,7,6,5]=>[4,3,1,2,7,6,5]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[3,1,4,2,7,6,5]=>[2,4,1,3,7,6,5]=>[2,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[3,2,4,7,6,5,1]=>[7,2,1,3,6,5,4]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[3,2,4,1,7,6,5]=>[4,2,1,3,7,6,5]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5]=>[2,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[2,3,4,7,6,5,1]=>[7,1,2,3,6,5,4]=>[1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[2,3,4,1,7,6,5]=>[4,1,2,3,7,6,5]=>[1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[2,3,1,4,7,6,5]=>[3,1,2,4,7,6,5]=>[1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>[1,4,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5]=>[5,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[5,1,7,6,4,3,2]=>[2,7,6,5,1,4,3]=>[2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[5,2,7,6,4,3,1]=>[7,2,6,5,1,4,3]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[5,2,1,7,6,4,3]=>[3,2,7,6,1,5,4]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[1,5,2,7,6,4,3]=>[1,3,7,6,2,5,4]=>[3,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[5,3,1,7,6,4,2]=>[3,7,2,6,1,5,4]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[5,3,2,1,7,6,4]=>[4,3,2,7,1,6,5]=>[1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[1,5,3,2,7,6,4]=>[1,4,3,7,2,6,5]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[2,5,3,7,6,4,1]=>[7,1,3,6,2,5,4]=>[1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[2,5,3,1,7,6,4]=>[4,1,3,7,2,6,5]=>[1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[2,1,5,3,7,6,4]=>[2,1,4,7,3,6,5]=>[1,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[1,2,5,3,7,6,4]=>[1,2,4,7,3,6,5]=>[4,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[5,4,1,7,6,3,2]=>[3,7,6,2,1,5,4]=>[2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[5,4,2,1,7,6,3]=>[4,3,7,2,1,6,5]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[1,5,4,2,7,6,3]=>[1,4,7,3,2,6,5]=>[3,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[5,4,3,1,7,6,2]=>[4,7,3,2,1,6,5]=>[2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>[2,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[2,5,4,3,7,6,1]=>[7,1,4,3,2,6,5]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[2,5,4,3,1,7,6]=>[5,1,4,3,2,7,6]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6]=>[3,1,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[3,5,4,7,6,2,1]=>[7,6,1,3,2,5,4]=>[1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[3,5,4,1,7,6,2]=>[4,7,1,3,2,6,5]=>[2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>[7,4,1,3,2,6,5]=>[1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[3,5,4,2,1,7,6]=>[5,4,1,3,2,7,6]=>[1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[3,1,5,4,2,7,6]=>[2,5,1,4,3,7,6]=>[2,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[3,2,5,4,7,6,1]=>[7,2,1,4,3,6,5]=>[1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[3,2,5,4,1,7,6]=>[5,2,1,4,3,7,6]=>[1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[2,3,5,4,7,6,1]=>[7,1,2,4,3,6,5]=>[1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[2,3,5,4,1,7,6]=>[5,1,2,4,3,7,6]=>[1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[2,3,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[1,3,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[4,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[4,5,7,6,3,2,1]=>[7,6,5,1,2,4,3]=>[1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[4,5,1,7,6,3,2]=>[3,7,6,1,2,5,4]=>[2,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[4,5,2,7,6,3,1]=>[7,3,6,1,2,5,4]=>[1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[4,5,2,1,7,6,3]=>[4,3,7,1,2,6,5]=>[1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[4,1,5,2,7,6,3]=>[2,4,7,1,3,6,5]=>[3,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[4,5,3,1,7,6,2]=>[4,7,3,1,2,6,5]=>[2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[4,5,3,2,1,7,6]=>[5,4,3,1,2,7,6]=>[1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[4,1,5,3,2,7,6]=>[2,5,4,1,3,7,6]=>[2,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[4,2,5,3,7,6,1]=>[7,2,4,1,3,6,5]=>[1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[4,2,5,3,1,7,6]=>[5,2,4,1,3,7,6]=>[1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[4,2,1,5,3,7,6]=>[3,2,5,1,4,7,6]=>[1,2,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[1,4,2,5,3,7,6]=>[1,3,5,2,4,7,6]=>[3,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[4,3,5,7,6,2,1]=>[7,6,2,1,3,5,4]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[4,3,5,1,7,6,2]=>[4,7,2,1,3,6,5]=>[2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[4,3,5,2,1,7,6]=>[5,4,2,1,3,7,6]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[4,3,1,5,2,7,6]=>[3,5,2,1,4,7,6]=>[2,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>[7,3,2,1,4,6,5]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[4,3,2,5,1,7,6]=>[5,3,2,1,4,7,6]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6]=>[2,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[2,4,3,5,7,6,1]=>[7,1,3,2,4,6,5]=>[1,2,3,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[2,4,3,5,1,7,6]=>[5,1,3,2,4,7,6]=>[1,2,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[2,4,3,1,5,7,6]=>[4,1,3,2,5,7,6]=>[1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[1,2,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[3,3,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[3,4,5,7,6,2,1]=>[7,6,1,2,3,5,4]=>[1,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[3,4,5,1,7,6,2]=>[4,7,1,2,3,6,5]=>[2,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[3,4,5,2,7,6,1]=>[7,4,1,2,3,6,5]=>[1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[3,4,5,2,1,7,6]=>[5,4,1,2,3,7,6]=>[1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[3,4,1,5,2,7,6]=>[3,5,1,2,4,7,6]=>[2,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[3,4,2,5,7,6,1]=>[7,3,1,2,4,6,5]=>[1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[3,4,2,5,1,7,6]=>[5,3,1,2,4,7,6]=>[1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[3,4,2,1,5,7,6]=>[4,3,1,2,5,7,6]=>[1,1,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[3,1,4,2,5,7,6]=>[2,4,1,3,5,7,6]=>[2,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[3,2,4,5,7,6,1]=>[7,2,1,3,4,6,5]=>[1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[3,2,4,5,1,7,6]=>[5,2,1,3,4,7,6]=>[1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[3,2,4,1,5,7,6]=>[4,2,1,3,5,7,6]=>[1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[1,1,4,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[2,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[2,3,4,5,7,6,1]=>[7,1,2,3,4,6,5]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[1,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[6,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[6,1,7,5,4,3,2]=>[2,7,6,5,4,1,3]=>[2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[6,2,7,5,4,3,1]=>[7,2,6,5,4,1,3]=>[1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[6,2,1,7,5,4,3]=>[3,2,7,6,5,1,4]=>[1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[1,6,2,7,5,4,3]=>[1,3,7,6,5,2,4]=>[3,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[6,3,1,7,5,4,2]=>[3,7,2,6,5,1,4]=>[2,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[6,3,2,1,7,5,4]=>[4,3,2,7,6,1,5]=>[1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[1,6,3,2,7,5,4]=>[1,4,3,7,6,2,5]=>[2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[2,6,3,7,5,4,1]=>[7,1,3,6,5,2,4]=>[1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[2,6,3,1,7,5,4]=>[4,1,3,7,6,2,5]=>[1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[2,1,6,3,7,5,4]=>[2,1,4,7,6,3,5]=>[1,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[1,2,6,3,7,5,4]=>[1,2,4,7,6,3,5]=>[4,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[6,4,1,7,5,3,2]=>[3,7,6,2,5,1,4]=>[2,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[6,4,2,1,7,5,3]=>[4,3,7,2,6,1,5]=>[1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[1,6,4,2,7,5,3]=>[1,4,7,3,6,2,5]=>[3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[6,4,3,1,7,5,2]=>[4,7,3,2,6,1,5]=>[2,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[6,4,3,2,1,7,5]=>[5,4,3,2,7,1,6]=>[1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[1,6,4,3,2,7,5]=>[1,5,4,3,7,2,6]=>[2,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[2,6,4,3,7,5,1]=>[7,1,4,3,6,2,5]=>[1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[2,6,4,3,1,7,5]=>[5,1,4,3,7,2,6]=>[1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[2,1,6,4,3,7,5]=>[2,1,5,4,7,3,6]=>[1,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[1,2,6,4,3,7,5]=>[1,2,5,4,7,3,6]=>[3,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[3,6,4,7,5,2,1]=>[7,6,1,3,5,2,4]=>[1,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[3,6,4,1,7,5,2]=>[4,7,1,3,6,2,5]=>[2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[3,6,4,2,7,5,1]=>[7,4,1,3,6,2,5]=>[1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[3,6,4,2,1,7,5]=>[5,4,1,3,7,2,6]=>[1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[3,1,6,4,2,7,5]=>[2,5,1,4,7,3,6]=>[2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[3,2,6,4,7,5,1]=>[7,2,1,4,6,3,5]=>[1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[3,2,6,4,1,7,5]=>[5,2,1,4,7,3,6]=>[1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[3,2,1,6,4,7,5]=>[3,2,1,5,7,4,6]=>[1,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[1,3,2,6,4,7,5]=>[1,3,2,5,7,4,6]=>[2,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[2,3,6,4,7,5,1]=>[7,1,2,4,6,3,5]=>[1,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[2,3,6,4,1,7,5]=>[5,1,2,4,7,3,6]=>[1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[2,3,1,6,4,7,5]=>[3,1,2,5,7,4,6]=>[1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[2,1,3,6,4,7,5]=>[2,1,3,5,7,4,6]=>[1,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[1,2,3,6,4,7,5]=>[1,2,3,5,7,4,6]=>[5,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[6,5,1,7,4,3,2]=>[3,7,6,5,2,1,4]=>[2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[6,5,2,1,7,4,3]=>[4,3,7,6,2,1,5]=>[1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[1,6,5,2,7,4,3]=>[1,4,7,6,3,2,5]=>[3,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[6,5,3,1,7,4,2]=>[4,7,3,6,2,1,5]=>[2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[6,5,3,2,1,7,4]=>[5,4,3,7,2,1,6]=>[1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[1,6,5,3,2,7,4]=>[1,5,4,7,3,2,6]=>[2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[2,6,5,3,7,4,1]=>[7,1,4,6,3,2,5]=>[1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[2,6,5,3,1,7,4]=>[5,1,4,7,3,2,6]=>[1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[2,1,6,5,3,7,4]=>[2,1,5,7,4,3,6]=>[1,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[1,2,6,5,3,7,4]=>[1,2,5,7,4,3,6]=>[4,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[6,5,4,1,7,3,2]=>[4,7,6,3,2,1,5]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[6,5,4,2,1,7,3]=>[5,4,7,3,2,1,6]=>[1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[1,6,5,4,2,7,3]=>[1,5,7,4,3,2,6]=>[3,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[6,5,4,3,1,7,2]=>[5,7,4,3,2,1,6]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[2,6,5,4,3,7,1]=>[7,1,5,4,3,2,6]=>[1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[2,6,5,4,3,1,7]=>[6,1,5,4,3,2,7]=>[1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7]=>[3,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[3,6,5,4,7,2,1]=>[7,6,1,4,3,2,5]=>[1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[3,6,5,4,1,7,2]=>[5,7,1,4,3,2,6]=>[2,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[3,6,5,4,2,7,1]=>[7,5,1,4,3,2,6]=>[1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>[6,5,1,4,3,2,7]=>[1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[3,1,6,5,4,2,7]=>[2,6,1,5,4,3,7]=>[2,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[3,2,6,5,4,7,1]=>[7,2,1,5,4,3,6]=>[1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[3,2,6,5,4,1,7]=>[6,2,1,5,4,3,7]=>[1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7]=>[2,2,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[2,3,6,5,4,7,1]=>[7,1,2,5,4,3,6]=>[1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[2,3,6,5,4,1,7]=>[6,1,2,5,4,3,7]=>[1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[2,3,1,6,5,4,7]=>[3,1,2,6,5,4,7]=>[1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>[1,3,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>[4,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[4,6,5,7,3,2,1]=>[7,6,5,1,3,2,4]=>[1,1,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[4,6,5,1,7,3,2]=>[4,7,6,1,3,2,5]=>[2,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[4,6,5,2,7,3,1]=>[7,4,6,1,3,2,5]=>[1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[4,6,5,2,1,7,3]=>[5,4,7,1,3,2,6]=>[1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[4,1,6,5,2,7,3]=>[2,5,7,1,4,3,6]=>[3,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[4,6,5,3,1,7,2]=>[5,7,4,1,3,2,6]=>[2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[4,6,5,3,2,1,7]=>[6,5,4,1,3,2,7]=>[1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[4,1,6,5,3,2,7]=>[2,6,5,1,4,3,7]=>[2,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[4,2,6,5,3,7,1]=>[7,2,5,1,4,3,6]=>[1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[4,2,6,5,3,1,7]=>[6,2,5,1,4,3,7]=>[1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[4,2,1,6,5,3,7]=>[3,2,6,1,5,4,7]=>[1,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[1,4,2,6,5,3,7]=>[1,3,6,2,5,4,7]=>[3,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[4,3,6,5,7,2,1]=>[7,6,2,1,4,3,5]=>[1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[4,3,6,5,1,7,2]=>[5,7,2,1,4,3,6]=>[2,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[4,3,6,5,2,1,7]=>[6,5,2,1,4,3,7]=>[1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[4,3,1,6,5,2,7]=>[3,6,2,1,5,4,7]=>[2,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[4,3,2,6,5,7,1]=>[7,3,2,1,5,4,6]=>[1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>[6,3,2,1,5,4,7]=>[1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7]=>[2,1,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[2,4,3,6,5,7,1]=>[7,1,3,2,5,4,6]=>[1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[2,4,3,6,5,1,7]=>[6,1,3,2,5,4,7]=>[1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[2,4,3,1,6,5,7]=>[4,1,3,2,6,5,7]=>[1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[1,2,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[3,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[3,4,6,5,7,2,1]=>[7,6,1,2,4,3,5]=>[1,1,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[3,4,6,5,1,7,2]=>[5,7,1,2,4,3,6]=>[2,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[3,4,6,5,2,7,1]=>[7,5,1,2,4,3,6]=>[1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[3,4,6,5,2,1,7]=>[6,5,1,2,4,3,7]=>[1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[3,4,1,6,5,2,7]=>[3,6,1,2,5,4,7]=>[2,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[3,4,2,6,5,7,1]=>[7,3,1,2,5,4,6]=>[1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[3,4,2,6,5,1,7]=>[6,3,1,2,5,4,7]=>[1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[3,4,2,1,6,5,7]=>[4,3,1,2,6,5,7]=>[1,1,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[3,1,4,2,6,5,7]=>[2,4,1,3,6,5,7]=>[2,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[3,2,4,6,5,7,1]=>[7,2,1,3,5,4,6]=>[1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[3,2,4,6,5,1,7]=>[6,2,1,3,5,4,7]=>[1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[3,2,4,1,6,5,7]=>[4,2,1,3,6,5,7]=>[1,1,3,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[1,1,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[2,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[2,3,4,6,5,7,1]=>[7,1,2,3,5,4,6]=>[1,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[2,3,4,6,5,1,7]=>[6,1,2,3,5,4,7]=>[1,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>[1,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[1,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[1,4,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[5,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[5,6,1,7,4,3,2]=>[3,7,6,5,1,2,4]=>[2,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[5,6,2,7,4,3,1]=>[7,3,6,5,1,2,4]=>[1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[5,6,2,1,7,4,3]=>[4,3,7,6,1,2,5]=>[1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[5,1,6,2,7,4,3]=>[2,4,7,6,1,3,5]=>[3,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[5,6,3,1,7,4,2]=>[4,7,3,6,1,2,5]=>[2,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[5,6,3,2,1,7,4]=>[5,4,3,7,1,2,6]=>[1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[5,1,6,3,2,7,4]=>[2,5,4,7,1,3,6]=>[2,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[5,2,6,3,7,4,1]=>[7,2,4,6,1,3,5]=>[1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[5,2,6,3,1,7,4]=>[5,2,4,7,1,3,6]=>[1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[5,2,1,6,3,7,4]=>[3,2,5,7,1,4,6]=>[1,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[1,5,2,6,3,7,4]=>[1,3,5,7,2,4,6]=>[4,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[5,6,4,1,7,3,2]=>[4,7,6,3,1,2,5]=>[2,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[5,6,4,2,1,7,3]=>[5,4,7,3,1,2,6]=>[1,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[5,1,6,4,2,7,3]=>[2,5,7,4,1,3,6]=>[3,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[5,6,4,3,1,7,2]=>[5,7,4,3,1,2,6]=>[2,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[5,1,6,4,3,2,7]=>[2,6,5,4,1,3,7]=>[2,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[5,2,6,4,3,7,1]=>[7,2,5,4,1,3,6]=>[1,2,1,3]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[5,2,6,4,3,1,7]=>[6,2,5,4,1,3,7]=>[1,2,1,3]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[5,2,1,6,4,3,7]=>[3,2,6,5,1,4,7]=>[1,2,1,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[1,5,2,6,4,3,7]=>[1,3,6,5,2,4,7]=>[3,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[5,3,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[5,3,6,4,1,7,2]=>[5,7,2,4,1,3,6]=>[2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[5,3,6,4,2,1,7]=>[6,5,2,4,1,3,7]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[5,3,1,6,4,2,7]=>[3,6,2,5,1,4,7]=>[2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[5,3,2,6,4,7,1]=>[7,3,2,5,1,4,6]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[5,3,2,6,4,1,7]=>[6,3,2,5,1,4,7]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[5,3,2,1,6,4,7]=>[4,3,2,6,1,5,7]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[1,5,3,2,6,4,7]=>[1,4,3,6,2,5,7]=>[2,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[2,5,3,6,4,7,1]=>[7,1,3,5,2,4,6]=>[1,3,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[2,5,3,6,4,1,7]=>[6,1,3,5,2,4,7]=>[1,3,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[2,5,3,1,6,4,7]=>[4,1,3,6,2,5,7]=>[1,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[2,1,5,3,6,4,7]=>[2,1,4,6,3,5,7]=>[1,3,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[1,2,5,3,6,4,7]=>[1,2,4,6,3,5,7]=>[4,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[5,4,6,1,7,3,2]=>[4,7,6,2,1,3,5]=>[2,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[5,4,6,2,1,7,3]=>[5,4,7,2,1,3,6]=>[1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[5,4,1,6,2,7,3]=>[3,5,7,2,1,4,6]=>[3,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[5,4,6,3,1,7,2]=>[5,7,4,2,1,3,6]=>[2,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[5,4,1,6,3,2,7]=>[3,6,5,2,1,4,7]=>[2,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[5,4,2,6,3,7,1]=>[7,3,5,2,1,4,6]=>[1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[5,4,2,6,3,1,7]=>[6,3,5,2,1,4,7]=>[1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[5,4,2,1,6,3,7]=>[4,3,6,2,1,5,7]=>[1,2,1,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[1,5,4,2,6,3,7]=>[1,4,6,3,2,5,7]=>[3,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[5,4,3,6,1,7,2]=>[5,7,3,2,1,4,6]=>[2,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[5,4,3,1,6,2,7]=>[4,6,3,2,1,5,7]=>[2,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7]=>[2,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[2,5,4,3,6,7,1]=>[7,1,4,3,2,5,6]=>[1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[2,5,4,3,6,1,7]=>[6,1,4,3,2,5,7]=>[1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[2,5,4,3,1,6,7]=>[5,1,4,3,2,6,7]=>[1,2,1,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>[1,2,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>[3,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[3,5,4,6,7,2,1]=>[7,6,1,3,2,4,5]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[3,5,4,6,1,7,2]=>[5,7,1,3,2,4,6]=>[2,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[3,5,4,6,2,7,1]=>[7,5,1,3,2,4,6]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[3,5,4,6,2,1,7]=>[6,5,1,3,2,4,7]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[3,5,4,1,6,2,7]=>[4,6,1,3,2,5,7]=>[2,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[3,5,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[3,5,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[3,5,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[3,1,5,4,2,6,7]=>[2,5,1,4,3,6,7]=>[2,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[3,2,5,4,6,7,1]=>[7,2,1,4,3,5,6]=>[1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[3,2,5,4,6,1,7]=>[6,2,1,4,3,5,7]=>[1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[3,2,5,4,1,6,7]=>[5,2,1,4,3,6,7]=>[1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[1,1,2,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[2,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[2,3,5,4,6,7,1]=>[7,1,2,4,3,5,6]=>[1,3,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[2,3,5,4,6,1,7]=>[6,1,2,4,3,5,7]=>[1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[2,3,5,4,1,6,7]=>[5,1,2,4,3,6,7]=>[1,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[1,3,3]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[1,3,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[4,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[4,5,6,1,7,3,2]=>[4,7,6,1,2,3,5]=>[2,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[4,5,6,2,7,3,1]=>[7,4,6,1,2,3,5]=>[1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[4,5,6,2,1,7,3]=>[5,4,7,1,2,3,6]=>[1,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[4,5,1,6,2,7,3]=>[3,5,7,1,2,4,6]=>[3,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[1,1,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[4,5,6,3,1,7,2]=>[5,7,4,1,2,3,6]=>[2,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[4,5,1,6,3,2,7]=>[3,6,5,1,2,4,7]=>[2,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[4,5,2,6,3,7,1]=>[7,3,5,1,2,4,6]=>[1,2,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[4,5,2,6,3,1,7]=>[6,3,5,1,2,4,7]=>[1,2,4]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[4,5,2,1,6,3,7]=>[4,3,6,1,2,5,7]=>[1,2,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[4,1,5,2,6,3,7]=>[2,4,6,1,3,5,7]=>[3,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[4,5,3,6,1,7,2]=>[5,7,3,1,2,4,6]=>[2,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[4,5,3,1,6,2,7]=>[4,6,3,1,2,5,7]=>[2,1,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[4,1,5,3,2,6,7]=>[2,5,4,1,3,6,7]=>[2,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[4,2,5,3,6,7,1]=>[7,2,4,1,3,5,6]=>[1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[4,2,5,3,6,1,7]=>[6,2,4,1,3,5,7]=>[1,2,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[4,2,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>[1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[4,2,1,5,3,6,7]=>[3,2,5,1,4,6,7]=>[1,2,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[1,4,2,5,3,6,7]=>[1,3,5,2,4,6,7]=>[3,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[4,3,5,6,1,7,2]=>[5,7,2,1,3,4,6]=>[2,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[4,3,5,1,6,2,7]=>[4,6,2,1,3,5,7]=>[2,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[4,3,1,5,2,6,7]=>[3,5,2,1,4,6,7]=>[2,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7]=>[2,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[2,4,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>[1,2,4]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[2,4,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>[1,2,4]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[2,4,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>[1,2,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[2,4,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>[1,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[1,2,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[3,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[3,4,5,6,1,7,2]=>[5,7,1,2,3,4,6]=>[2,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[1,1,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[3,4,5,1,6,2,7]=>[4,6,1,2,3,5,7]=>[2,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[1,1,5]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[1,1,5]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[1,1,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[3,4,1,5,2,6,7]=>[3,5,1,2,4,6,7]=>[2,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[1,1,5]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[1,1,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[1,1,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>[2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[1,1,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[1,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[2,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[1,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[1,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[2,8,7,6,5,4,3,1]=>[8,1,7,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[1,2,8,7,6,5,4,3]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[3,8,7,6,5,4,2,1]=>[8,7,1,6,5,4,3,2]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[3,1,8,7,6,5,4,2]=>[2,8,1,7,6,5,4,3]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[3,2,8,7,6,5,4,1]=>[8,2,1,7,6,5,4,3]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,7,6,5,4]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[2,3,8,7,6,5,4,1]=>[8,1,2,7,6,5,4,3]=>[1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[2,3,1,8,7,6,5,4]=>[3,1,2,8,7,6,5,4]=>[1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,7,6,5,4]=>[1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[4,2,8,7,6,5,3,1]=>[8,2,7,1,6,5,4,3]=>[1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[4,2,1,8,7,6,5,3]=>[3,2,8,1,7,6,5,4]=>[1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[4,3,8,7,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>[2,4,3,8,7,6,5,1]=>[8,1,3,2,7,6,5,4]=>[1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[2,4,3,1,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>[1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[3,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,2,1]=>[3,4,2,8,7,6,5,1]=>[8,3,1,2,7,6,5,4]=>[1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[3,4,2,1,8,7,6,5]=>[4,3,1,2,8,7,6,5]=>[1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[3,1,4,2,8,7,6,5]=>[2,4,1,3,8,7,6,5]=>[2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[3,2,4,1,8,7,6,5]=>[4,2,1,3,8,7,6,5]=>[1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[2,3,4,1,8,7,6,5]=>[4,1,2,3,8,7,6,5]=>[1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[2,3,1,4,8,7,6,5]=>[3,1,2,4,8,7,6,5]=>[1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[5,8,7,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[5,1,8,7,6,4,3,2]=>[2,8,7,6,1,5,4,3]=>[2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[5,2,1,8,7,6,4,3]=>[3,2,8,7,1,6,5,4]=>[1,2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[5,3,8,7,6,4,2,1]=>[8,7,2,6,1,5,4,3]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[5,3,1,8,7,6,4,2]=>[3,8,2,7,1,6,5,4]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[5,3,2,1,8,7,6,4]=>[4,3,2,8,1,7,6,5]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[1,2,5,3,8,7,6,4]=>[1,2,4,8,3,7,6,5]=>[4,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,2,1]=>[5,4,1,8,7,6,3,2]=>[3,8,7,2,1,6,5,4]=>[2,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[5,4,2,1,8,7,6,3]=>[4,3,8,2,1,7,6,5]=>[1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[5,4,3,8,7,6,2,1]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,2,1]=>[5,4,3,1,8,7,6,2]=>[4,8,3,2,1,7,6,5]=>[2,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,2,1]=>[2,5,4,3,1,8,7,6]=>[5,1,4,3,2,8,7,6]=>[1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,2,1]=>[2,3,5,4,1,8,7,6]=>[5,1,2,4,3,8,7,6]=>[1,3,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,8,7,6]=>[1,3,2,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,8,7,6]=>[4,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[4,5,8,7,6,3,2,1]=>[8,7,6,1,2,5,4,3]=>[1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>[4,5,2,1,8,7,6,3]=>[4,3,8,1,2,7,6,5]=>[1,2,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[4,1,5,2,8,7,6,3]=>[2,4,8,1,3,7,6,5]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>[4,5,3,1,8,7,6,2]=>[4,8,3,1,2,7,6,5]=>[2,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>[4,3,2,5,1,8,7,6]=>[5,3,2,1,4,8,7,6]=>[1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[1,1,1,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[3,4,5,2,1,8,7,6]=>[5,4,1,2,3,8,7,6]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,2,1]=>[3,4,2,5,1,8,7,6]=>[5,3,1,2,4,8,7,6]=>[1,1,4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[6,2,8,7,5,4,3,1]=>[8,2,7,6,5,1,4,3]=>[1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[6,2,1,8,7,5,4,3]=>[3,2,8,7,6,1,5,4]=>[1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[6,3,2,1,8,7,5,4]=>[4,3,2,8,7,1,6,5]=>[1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[1,6,3,2,8,7,5,4]=>[1,4,3,8,7,2,6,5]=>[2,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[2,6,3,8,7,5,4,1]=>[8,1,3,7,6,2,5,4]=>[1,3,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,3,1]=>[2,6,3,1,8,7,5,4]=>[4,1,3,8,7,2,6,5]=>[1,3,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[1,2,6,3,8,7,5,4]=>[1,2,4,8,7,3,6,5]=>[4,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[6,4,8,7,5,3,2,1]=>[8,7,6,2,5,1,4,3]=>[1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[6,4,2,8,7,5,3,1]=>[8,3,7,2,6,1,5,4]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[6,4,2,1,8,7,5,3]=>[4,3,8,2,7,1,6,5]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[1,6,4,2,8,7,5,3]=>[1,4,8,3,7,2,6,5]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,3,1]=>[6,4,3,8,7,5,2,1]=>[8,7,3,2,6,1,5,4]=>[1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[2,6,4,3,8,7,5,1]=>[8,1,4,3,7,2,6,5]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[2,6,4,3,1,8,7,5]=>[5,1,4,3,8,2,7,6]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[3,6,4,8,7,5,2,1]=>[8,7,1,3,6,2,5,4]=>[1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[3,6,4,2,8,7,5,1]=>[8,4,1,3,7,2,6,5]=>[1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[1,2,3,6,4,8,7,5]=>[1,2,3,5,8,4,7,6]=>[5,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[6,5,1,8,7,4,3,2]=>[3,8,7,6,2,1,5,4]=>[2,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[6,5,2,1,8,7,4,3]=>[4,3,8,7,2,1,6,5]=>[1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[1,6,5,2,8,7,4,3]=>[1,4,8,7,3,2,6,5]=>[3,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[6,5,3,2,1,8,7,4]=>[5,4,3,8,2,1,7,6]=>[1,1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[1,2,6,5,3,8,7,4]=>[1,2,5,8,4,3,7,6]=>[4,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,5,1]=>[6,5,4,1,8,7,3,2]=>[4,8,7,3,2,1,6,5]=>[2,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[6,5,4,2,1,8,7,3]=>[5,4,8,3,2,1,7,6]=>[1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[2,3,6,5,4,1,8,7]=>[6,1,2,5,4,3,8,7]=>[1,3,1,2,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[1,2,3,6,5,4,8,7]=>[1,2,3,6,5,4,8,7]=>[4,1,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[4,6,5,8,7,3,2,1]=>[8,7,6,1,3,2,5,4]=>[1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[4,6,5,3,8,7,2,1]=>[8,7,4,1,3,2,6,5]=>[1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,6,1]=>[4,6,5,3,1,8,7,2]=>[5,8,4,1,3,2,7,6]=>[2,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[4,2,6,5,3,8,7,1]=>[8,2,5,1,4,3,7,6]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[4,2,6,5,3,1,8,7]=>[6,2,5,1,4,3,8,7]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[4,2,1,6,5,3,8,7]=>[3,2,6,1,5,4,8,7]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[4,3,6,5,1,8,7,2]=>[5,8,2,1,4,3,7,6]=>[2,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>[8,5,2,1,4,3,7,6]=>[1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[2,4,3,6,5,8,7,1]=>[8,1,3,2,5,4,7,6]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[2,4,3,6,5,1,8,7]=>[6,1,3,2,5,4,8,7]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[2,4,3,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[3,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[3,4,6,5,2,8,7,1]=>[8,5,1,2,4,3,7,6]=>[1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[3,4,2,1,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,8,1]=>[3,2,1,4,6,5,8,7]=>[3,2,1,4,6,5,8,7]=>[1,1,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[5,6,8,7,4,3,2,1]=>[8,7,6,5,1,2,4,3]=>[1,1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,4,1]=>[5,6,2,1,8,7,4,3]=>[4,3,8,7,1,2,6,5]=>[1,2,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[5,1,6,2,8,7,4,3]=>[2,4,8,7,1,3,6,5]=>[3,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[5,6,3,8,7,4,2,1]=>[8,7,3,6,1,2,5,4]=>[1,1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>[5,6,3,2,8,7,4,1]=>[8,4,3,7,1,2,6,5]=>[1,1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[5,6,3,2,1,8,7,4]=>[5,4,3,8,1,2,7,6]=>[1,1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[5,1,6,3,2,8,7,4]=>[2,5,4,8,1,3,7,6]=>[2,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[5,2,6,3,8,7,4,1]=>[8,2,4,7,1,3,6,5]=>[1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[1,5,2,6,3,8,7,4]=>[1,3,5,8,2,4,7,6]=>[4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,5,1]=>[5,6,4,2,1,8,7,3]=>[5,4,8,3,1,2,7,6]=>[1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[5,1,6,4,2,8,7,3]=>[2,5,8,4,1,3,7,6]=>[3,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>[5,1,6,4,3,2,8,7]=>[2,6,5,4,1,3,8,7]=>[2,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,7,1]=>[5,2,6,4,3,8,7,1]=>[8,2,5,4,1,3,7,6]=>[1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,8,1]=>[5,2,6,4,3,1,8,7]=>[6,2,5,4,1,3,8,7]=>[1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,8,1]=>[5,2,1,6,4,3,8,7]=>[3,2,6,5,1,4,8,7]=>[1,2,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[5,3,1,6,4,2,8,7]=>[3,6,2,5,1,4,8,7]=>[2,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>[5,3,2,1,6,4,8,7]=>[4,3,2,6,1,5,8,7]=>[1,1,2,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>[2,5,3,6,4,1,8,7]=>[6,1,3,5,2,4,8,7]=>[1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>[2,1,5,3,6,4,8,7]=>[2,1,4,6,3,5,8,7]=>[1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[1,2,5,3,6,4,8,7]=>[1,2,4,6,3,5,8,7]=>[4,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[5,4,6,2,8,7,3,1]=>[8,4,7,2,1,3,6,5]=>[1,2,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[5,4,1,6,2,8,7,3]=>[3,5,8,2,1,4,7,6]=>[3,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>[5,4,6,3,8,7,2,1]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>[5,4,1,6,3,2,8,7]=>[3,6,5,2,1,4,8,7]=>[2,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[5,4,3,6,1,8,7,2]=>[5,8,3,2,1,4,7,6]=>[2,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[5,4,3,1,6,2,8,7]=>[4,6,3,2,1,5,8,7]=>[2,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[1,2,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,6,1]=>[3,5,4,6,1,8,7,2]=>[5,8,1,3,2,4,7,6]=>[2,2,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[3,5,4,2,6,8,7,1]=>[8,4,1,3,2,5,7,6]=>[1,1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[3,2,1,5,4,6,8,7]=>[3,2,1,5,4,6,8,7]=>[1,1,2,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[4,3,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[4,5,6,8,7,3,2,1]=>[8,7,6,1,2,3,5,4]=>[1,1,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,5,1]=>[4,5,6,1,8,7,3,2]=>[4,8,7,1,2,3,6,5]=>[2,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[4,5,6,2,8,7,3,1]=>[8,4,7,1,2,3,6,5]=>[1,2,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>[4,5,6,2,1,8,7,3]=>[5,4,8,1,2,3,7,6]=>[1,2,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[4,5,1,6,2,8,7,3]=>[3,5,8,1,2,4,7,6]=>[3,4,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[4,5,6,3,2,1,8,7]=>[6,5,4,1,2,3,8,7]=>[1,1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[4,5,3,6,2,8,7,1]=>[8,5,3,1,2,4,7,6]=>[1,1,1,4,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,8,1]=>[4,2,1,5,3,6,8,7]=>[3,2,5,1,4,6,8,7]=>[1,2,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[4,3,5,6,1,8,7,2]=>[5,8,2,1,3,4,7,6]=>[2,1,4,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[1,1,1,4,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[1,2,4,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[3,4,5,1,6,2,8,7]=>[4,6,1,2,3,5,8,7]=>[2,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,8,1]=>[3,4,5,2,6,1,8,7]=>[6,4,1,2,3,5,8,7]=>[1,1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[3,4,2,1,5,6,8,7]=>[4,3,1,2,5,6,8,7]=>[1,1,5,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>[3,1,4,2,5,6,8,7]=>[2,4,1,3,5,6,8,7]=>[2,5,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[3,2,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[1,1,5,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[2,3,4,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[1,6,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[1,6,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[7,1,8,6,5,4,3,2]=>[2,8,7,6,5,4,1,3]=>[2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[7,3,8,6,5,4,2,1]=>[8,7,2,6,5,4,1,3]=>[1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[7,3,1,8,6,5,4,2]=>[3,8,2,7,6,5,1,4]=>[2,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[7,3,2,1,8,6,5,4]=>[4,3,2,8,7,6,1,5]=>[1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[1,7,3,2,8,6,5,4]=>[1,4,3,8,7,6,2,5]=>[2,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[1,2,7,3,8,6,5,4]=>[1,2,4,8,7,6,3,5]=>[4,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[7,4,1,8,6,5,3,2]=>[3,8,7,2,6,5,1,4]=>[2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>[7,4,2,8,6,5,3,1]=>[8,3,7,2,6,5,1,4]=>[1,2,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[7,4,3,8,6,5,2,1]=>[8,7,3,2,6,5,1,4]=>[1,1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[2,1,7,4,3,8,6,5]=>[2,1,5,4,8,7,3,6]=>[1,2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[3,7,4,1,8,6,5,2]=>[4,8,1,3,7,6,2,5]=>[2,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[3,1,7,4,2,8,6,5]=>[2,5,1,4,8,7,3,6]=>[2,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[1,3,2,7,4,8,6,5]=>[1,3,2,5,8,7,4,6]=>[2,3,1,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[1,2,3,7,4,8,6,5]=>[1,2,3,5,8,7,4,6]=>[5,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[7,5,8,6,4,3,2,1]=>[8,7,6,5,2,4,1,3]=>[1,1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[7,5,1,8,6,4,3,2]=>[3,8,7,6,2,5,1,4]=>[2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[1,7,5,2,8,6,4,3]=>[1,4,8,7,3,6,2,5]=>[3,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[7,5,3,8,6,4,2,1]=>[8,7,3,6,2,5,1,4]=>[1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[7,5,3,1,8,6,4,2]=>[4,8,3,7,2,6,1,5]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[7,5,3,2,1,8,6,4]=>[5,4,3,8,2,7,1,6]=>[1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[1,7,5,3,2,8,6,4]=>[1,5,4,8,3,7,2,6]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[2,7,5,3,8,6,4,1]=>[8,1,4,7,3,6,2,5]=>[1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[2,7,5,3,1,8,6,4]=>[5,1,4,8,3,7,2,6]=>[1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[2,1,7,5,3,8,6,4]=>[2,1,5,8,4,7,3,6]=>[1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[1,2,7,5,3,8,6,4]=>[1,2,5,8,4,7,3,6]=>[4,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[7,5,4,3,2,1,8,6]=>[6,5,4,3,2,8,1,7]=>[1,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>[1,2,7,5,4,3,8,6]=>[1,2,6,5,4,8,3,7]=>[3,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[3,7,5,4,1,8,6,2]=>[5,8,1,4,3,7,2,6]=>[2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[3,1,7,5,4,2,8,6]=>[2,6,1,5,4,8,3,7]=>[2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[3,2,1,7,5,4,8,6]=>[3,2,1,6,5,8,4,7]=>[1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[1,3,2,7,5,4,8,6]=>[1,3,2,6,5,8,4,7]=>[2,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,1,2]=>[2,1,3,7,5,4,8,6]=>[2,1,3,6,5,8,4,7]=>[1,3,2,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[1,2,3,7,5,4,8,6]=>[1,2,3,6,5,8,4,7]=>[4,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[4,7,5,8,6,3,2,1]=>[8,7,6,1,3,5,2,4]=>[1,1,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[4,7,5,1,8,6,3,2]=>[4,8,7,1,3,6,2,5]=>[2,1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[4,7,5,3,1,8,6,2]=>[5,8,4,1,3,7,2,6]=>[2,1,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>[4,2,7,5,3,1,8,6]=>[6,2,5,1,4,8,3,7]=>[1,2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[4,3,7,5,1,8,6,2]=>[5,8,2,1,4,7,3,6]=>[2,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>[4,3,2,7,5,8,6,1]=>[8,3,2,1,5,7,4,6]=>[1,1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[4,3,2,1,7,5,8,6]=>[4,3,2,1,6,8,5,7]=>[1,1,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,6,8,5,7]=>[1,2,3,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,6,8,5,7]=>[3,3,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[3,4,7,5,2,1,8,6]=>[6,5,1,2,4,8,3,7]=>[1,1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[3,4,2,7,5,8,6,1]=>[8,3,1,2,5,7,4,6]=>[1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[3,2,4,7,5,8,6,1]=>[8,2,1,3,5,7,4,6]=>[1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[3,2,4,1,7,5,8,6]=>[4,2,1,3,6,8,5,7]=>[1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[3,2,1,4,7,5,8,6]=>[3,2,1,4,6,8,5,7]=>[1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,6,8,5,7]=>[2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[2,3,4,1,7,5,8,6]=>[4,1,2,3,6,8,5,7]=>[1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>[2,3,1,4,7,5,8,6]=>[3,1,2,4,6,8,5,7]=>[1,5,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[2,1,3,4,7,5,8,6]=>[2,1,3,4,6,8,5,7]=>[1,5,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,6,8,5,7]=>[6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[7,6,2,1,8,5,4,3]=>[4,3,8,7,6,2,1,5]=>[1,2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>[1,7,6,2,8,5,4,3]=>[1,4,8,7,6,3,2,5]=>[3,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[7,6,3,8,5,4,2,1]=>[8,7,3,6,5,2,1,4]=>[1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[7,6,3,1,8,5,4,2]=>[4,8,3,7,6,2,1,5]=>[2,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[2,7,6,3,1,8,5,4]=>[5,1,4,8,7,3,2,6]=>[1,3,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[2,1,7,6,3,8,5,4]=>[2,1,5,8,7,4,3,6]=>[1,3,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[1,2,7,6,3,8,5,4]=>[1,2,5,8,7,4,3,6]=>[4,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,1,3]=>[7,6,4,2,1,8,5,3]=>[5,4,8,3,7,2,1,6]=>[1,2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>[1,7,6,4,3,2,8,5]=>[1,6,5,4,8,3,2,7]=>[2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,1,3]=>[2,7,6,4,3,1,8,5]=>[6,1,5,4,8,3,2,7]=>[1,2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,1,3]=>[3,7,6,4,8,5,2,1]=>[8,7,1,4,6,3,2,5]=>[1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>[3,7,6,4,2,1,8,5]=>[6,5,1,4,8,3,2,7]=>[1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[1,2,3,7,6,4,8,5]=>[1,2,3,6,8,5,4,7]=>[5,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[7,6,5,1,8,4,3,2]=>[4,8,7,6,3,2,1,5]=>[2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[7,6,5,2,8,4,3,1]=>[8,4,7,6,3,2,1,5]=>[1,2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[7,6,5,2,1,8,4,3]=>[5,4,8,7,3,2,1,6]=>[1,2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[1,7,6,5,2,8,4,3]=>[1,5,8,7,4,3,2,6]=>[3,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[7,6,5,3,2,1,8,4]=>[6,5,4,8,3,2,1,7]=>[1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[1,7,6,5,3,2,8,4]=>[1,6,5,8,4,3,2,7]=>[2,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[2,7,6,5,3,8,4,1]=>[8,1,5,7,4,3,2,6]=>[1,3,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>[2,7,6,5,3,1,8,4]=>[6,1,5,8,4,3,2,7]=>[1,3,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[2,1,7,6,5,3,8,4]=>[2,1,6,8,5,4,3,7]=>[1,3,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[1,2,7,6,5,3,8,4]=>[1,2,6,8,5,4,3,7]=>[4,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[7,6,5,4,1,8,3,2]=>[5,8,7,4,3,2,1,6]=>[2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[7,6,5,4,2,1,8,3]=>[6,5,8,4,3,2,1,7]=>[1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[1,7,6,5,4,2,8,3]=>[1,6,8,5,4,3,2,7]=>[3,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,3,1,8,2]=>[6,8,5,4,3,2,1,7]=>[2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[2,7,6,5,4,3,8,1]=>[8,1,6,5,4,3,2,7]=>[1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[1,2,7,6,5,4,3,8]=>[1,2,7,6,5,4,3,8]=>[3,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[3,7,6,5,4,2,1,8]=>[7,6,1,5,4,3,2,8]=>[1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,7,6,5,4,8]=>[1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>[1,3,2,7,6,5,4,8]=>[1,3,2,7,6,5,4,8]=>[2,2,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[2,3,7,6,5,4,8,1]=>[8,1,2,6,5,4,3,7]=>[1,3,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[7,1,2,6,5,4,3,8]=>[1,3,1,1,2]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[1,2,3,7,6,5,4,8]=>[1,2,3,7,6,5,4,8]=>[4,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[4,7,6,5,8,3,2,1]=>[8,7,6,1,4,3,2,5]=>[1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>[4,7,6,5,1,8,3,2]=>[5,8,7,1,4,3,2,6]=>[2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>[4,1,7,6,5,2,8,3]=>[2,6,8,1,5,4,3,7]=>[3,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[4,7,6,5,3,8,2,1]=>[8,7,5,1,4,3,2,6]=>[1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[4,7,6,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>[1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,1,8]=>[4,7,6,5,3,2,1,8]=>[7,6,5,1,4,3,2,8]=>[1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,2,1,8]=>[4,1,7,6,5,3,2,8]=>[2,7,6,1,5,4,3,8]=>[2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[4,2,7,6,5,3,8,1]=>[8,2,6,1,5,4,3,7]=>[1,2,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[1,4,2,7,6,5,3,8]=>[1,3,7,2,6,5,4,8]=>[3,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[2,4,3,7,6,5,8,1]=>[8,1,3,2,6,5,4,7]=>[1,2,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,1,8]=>[2,4,3,7,6,5,1,8]=>[7,1,3,2,6,5,4,8]=>[1,2,2,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[3,4,7,6,5,8,2,1]=>[8,7,1,2,5,4,3,6]=>[1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[3,4,7,6,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>[1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[1,1,3,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[2,3,4,7,6,5,8,1]=>[8,1,2,3,6,5,4,7]=>[1,4,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>[2,3,4,7,6,5,1,8]=>[7,1,2,3,6,5,4,8]=>[1,4,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[5,7,6,8,4,3,2,1]=>[8,7,6,5,1,3,2,4]=>[1,1,1,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[5,7,6,1,8,4,3,2]=>[4,8,7,6,1,3,2,5]=>[2,1,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[5,7,6,2,1,8,4,3]=>[5,4,8,7,1,3,2,6]=>[1,2,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>[5,1,7,6,2,8,4,3]=>[2,5,8,7,1,4,3,6]=>[3,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[5,7,6,3,8,4,2,1]=>[8,7,4,6,1,3,2,5]=>[1,1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[5,7,6,3,1,8,4,2]=>[5,8,4,7,1,3,2,6]=>[2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>[5,7,6,3,2,8,4,1]=>[8,5,4,7,1,3,2,6]=>[1,1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[5,7,6,3,2,1,8,4]=>[6,5,4,8,1,3,2,7]=>[1,1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[5,1,7,6,3,2,8,4]=>[2,6,5,8,1,4,3,7]=>[2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[5,2,1,7,6,3,8,4]=>[3,2,6,8,1,5,4,7]=>[1,3,2,2]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[1,5,2,7,6,3,8,4]=>[1,3,6,8,2,5,4,7]=>[4,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[5,7,6,4,2,1,8,3]=>[6,5,8,4,1,3,2,7]=>[1,2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>[5,2,7,6,4,3,8,1]=>[8,2,6,5,1,4,3,7]=>[1,2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[5,2,7,6,4,3,1,8]=>[7,2,6,5,1,4,3,8]=>[1,2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>[1,5,2,7,6,4,3,8]=>[1,3,7,6,2,5,4,8]=>[3,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[5,3,7,6,4,8,2,1]=>[8,7,2,5,1,4,3,6]=>[1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[5,3,7,6,4,1,8,2]=>[6,8,2,5,1,4,3,7]=>[2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[5,3,7,6,4,2,1,8]=>[7,6,2,5,1,4,3,8]=>[1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[5,3,1,7,6,4,2,8]=>[3,7,2,6,1,5,4,8]=>[2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[5,3,2,1,7,6,4,8]=>[4,3,2,7,1,6,5,8]=>[1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[1,5,3,2,7,6,4,8]=>[1,4,3,7,2,6,5,8]=>[2,2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[5,4,7,6,8,3,2,1]=>[8,7,6,2,1,4,3,5]=>[1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>[5,4,7,6,2,8,3,1]=>[8,5,7,2,1,4,3,6]=>[1,2,1,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[5,4,1,7,6,2,8,3]=>[3,6,8,2,1,5,4,7]=>[3,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[5,4,7,6,3,8,2,1]=>[8,7,5,2,1,4,3,6]=>[1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[5,4,3,7,6,1,8,2]=>[6,8,3,2,1,5,4,7]=>[2,1,1,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[3,5,4,7,6,8,2,1]=>[8,7,1,3,2,5,4,6]=>[1,1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[3,5,4,7,6,1,8,2]=>[6,8,1,3,2,5,4,7]=>[2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>[3,5,4,1,7,6,2,8]=>[4,7,1,3,2,6,5,8]=>[2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[3,5,4,2,7,6,1,8]=>[7,4,1,3,2,6,5,8]=>[1,1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[3,1,5,4,2,7,6,8]=>[2,5,1,4,3,7,6,8]=>[2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[1,1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[2,2,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[2,3,5,4,1,7,6,8]=>[5,1,2,4,3,7,6,8]=>[1,3,2,2]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[4,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[4,5,7,6,8,3,2,1]=>[8,7,6,1,2,4,3,5]=>[1,1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[4,5,7,6,3,2,8,1]=>[8,6,5,1,2,4,3,7]=>[1,1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[4,5,7,6,3,2,1,8]=>[7,6,5,1,2,4,3,8]=>[1,1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[4,5,1,7,6,3,2,8]=>[3,7,6,1,2,5,4,8]=>[2,1,3,2]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[4,1,5,2,7,6,3,8]=>[2,4,7,1,3,6,5,8]=>[3,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>[4,5,3,7,6,2,8,1]=>[8,6,3,1,2,5,4,7]=>[1,1,1,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[4,2,5,3,7,6,1,8]=>[7,2,4,1,3,6,5,8]=>[1,2,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[4,3,5,2,1,7,6,8]=>[5,4,2,1,3,7,6,8]=>[1,1,1,3,2]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[1,1,1,3,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[3,4,5,7,6,2,1,8]=>[7,6,1,2,3,5,4,8]=>[1,1,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,1,7]=>[3,4,5,2,7,6,8,1]=>[8,4,1,2,3,6,5,7]=>[1,1,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,1,8]=>[3,4,2,5,1,7,6,8]=>[5,3,1,2,4,7,6,8]=>[1,1,4,2]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,1,8]=>[3,1,4,2,5,7,6,8]=>[2,4,1,3,5,7,6,8]=>[2,4,2]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[2,3,4,5,1,7,6,8]=>[5,1,2,3,4,7,6,8]=>[1,5,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[6,1,7,2,8,5,4,3]=>[2,4,8,7,6,1,3,5]=>[3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[6,7,3,1,8,5,4,2]=>[4,8,3,7,6,1,2,5]=>[2,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[6,7,3,2,1,8,5,4]=>[5,4,3,8,7,1,2,6]=>[1,1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[6,1,7,3,2,8,5,4]=>[2,5,4,8,7,1,3,6]=>[2,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[6,2,7,3,8,5,4,1]=>[8,2,4,7,6,1,3,5]=>[1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[6,2,7,3,1,8,5,4]=>[5,2,4,8,7,1,3,6]=>[1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>[6,2,1,7,3,8,5,4]=>[3,2,5,8,7,1,4,6]=>[1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[1,6,2,7,3,8,5,4]=>[1,3,5,8,7,2,4,6]=>[4,1,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[6,7,4,2,8,5,3,1]=>[8,4,7,3,6,1,2,5]=>[1,2,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[6,7,4,3,8,5,2,1]=>[8,7,4,3,6,1,2,5]=>[1,1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[6,7,4,3,2,1,8,5]=>[6,5,4,3,8,1,2,7]=>[1,1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[6,2,7,4,3,1,8,5]=>[6,2,5,4,8,1,3,7]=>[1,2,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[6,2,1,7,4,3,8,5]=>[3,2,6,5,8,1,4,7]=>[1,2,2,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>[6,3,7,4,2,8,5,1]=>[8,5,2,4,7,1,3,6]=>[1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[6,3,7,4,2,1,8,5]=>[6,5,2,4,8,1,3,7]=>[1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[6,3,1,7,4,2,8,5]=>[3,6,2,5,8,1,4,7]=>[2,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[6,3,2,7,4,1,8,5]=>[6,3,2,5,8,1,4,7]=>[1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[6,3,2,1,7,4,8,5]=>[4,3,2,6,8,1,5,7]=>[1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[1,6,3,2,7,4,8,5]=>[1,4,3,6,8,2,5,7]=>[2,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[2,6,3,7,4,1,8,5]=>[6,1,3,5,8,2,4,7]=>[1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[2,6,3,1,7,4,8,5]=>[4,1,3,6,8,2,5,7]=>[1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[2,1,6,3,7,4,8,5]=>[2,1,4,6,8,3,5,7]=>[1,4,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[1,2,6,3,7,4,8,5]=>[1,2,4,6,8,3,5,7]=>[5,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>[6,7,5,1,8,4,3,2]=>[4,8,7,6,3,1,2,5]=>[2,1,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[6,7,5,3,1,8,4,2]=>[5,8,4,7,3,1,2,6]=>[2,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[6,7,5,3,2,1,8,4]=>[6,5,4,8,3,1,2,7]=>[1,1,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[6,2,7,5,3,1,8,4]=>[6,2,5,8,4,1,3,7]=>[1,3,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[6,2,1,7,5,3,8,4]=>[3,2,6,8,5,1,4,7]=>[1,3,1,3]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[1,6,2,7,5,3,8,4]=>[1,3,6,8,5,2,4,7]=>[4,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[6,1,7,5,4,2,8,3]=>[2,6,8,5,4,1,3,7]=>[3,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,1,2,6]=>[6,7,5,4,3,1,8,2]=>[6,8,5,4,3,1,2,7]=>[2,1,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,1,2,7]=>[6,3,7,5,4,2,8,1]=>[8,6,2,5,4,1,3,7]=>[1,1,2,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[6,4,7,5,8,3,2,1]=>[8,7,6,2,4,1,3,5]=>[1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[6,4,1,7,5,2,8,3]=>[3,6,8,2,5,1,4,7]=>[3,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[6,4,7,5,3,8,2,1]=>[8,7,5,2,4,1,3,6]=>[1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[6,4,2,7,5,3,8,1]=>[8,3,6,2,5,1,4,7]=>[1,2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,1,2,8]=>[6,4,2,7,5,3,1,8]=>[7,3,6,2,5,1,4,8]=>[1,2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>[6,4,2,1,7,5,3,8]=>[4,3,7,2,6,1,5,8]=>[1,2,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>[6,4,3,2,1,7,5,8]=>[5,4,3,2,7,1,6,8]=>[1,1,1,2,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>[3,6,4,7,5,2,8,1]=>[8,6,1,3,5,2,4,7]=>[1,1,3,3]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[3,6,4,1,7,5,2,8]=>[4,7,1,3,6,2,5,8]=>[2,3,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,1,2,8]=>[3,6,4,2,7,5,1,8]=>[7,4,1,3,6,2,5,8]=>[1,1,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>[3,2,6,4,7,5,8,1]=>[8,2,1,4,6,3,5,7]=>[1,1,3,3]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[1,2,3,6,4,7,5,8]=>[1,2,3,5,7,4,6,8]=>[5,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[6,5,1,7,2,8,4,3]=>[3,5,8,7,2,1,4,6]=>[3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[6,5,7,3,1,8,4,2]=>[5,8,4,7,2,1,3,6]=>[2,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[6,5,2,7,3,1,8,4]=>[6,3,5,8,2,1,4,7]=>[1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[6,5,2,1,7,3,8,4]=>[4,3,6,8,2,1,5,7]=>[1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[1,6,5,2,7,3,8,4]=>[1,4,6,8,3,2,5,7]=>[4,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>[6,5,7,4,1,8,3,2]=>[5,8,7,4,2,1,3,6]=>[2,1,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[6,5,7,4,2,8,3,1]=>[8,5,7,4,2,1,3,6]=>[1,2,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[6,5,1,7,4,2,8,3]=>[3,6,8,5,2,1,4,7]=>[3,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[6,5,7,4,3,1,8,2]=>[6,8,5,4,2,1,3,7]=>[2,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[6,5,2,7,4,3,8,1]=>[8,3,6,5,2,1,4,7]=>[1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>[1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[6,5,4,7,2,1,8,3]=>[6,5,8,3,2,1,4,7]=>[1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[6,5,4,1,7,2,8,3]=>[4,6,8,3,2,1,5,7]=>[3,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[6,5,4,7,3,1,8,2]=>[6,8,5,3,2,1,4,7]=>[2,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[6,5,4,2,7,3,8,1]=>[8,4,6,3,2,1,5,7]=>[1,2,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[6,5,4,3,7,1,8,2]=>[6,8,4,3,2,1,5,7]=>[2,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>[2,6,5,4,3,7,8,1]=>[8,1,5,4,3,2,6,7]=>[1,2,1,1,3]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[1,2,6,5,4,3,7,8]=>[1,2,6,5,4,3,7,8]=>[3,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[3,6,5,4,7,8,2,1]=>[8,7,1,4,3,2,5,6]=>[1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[3,6,5,4,7,1,8,2]=>[6,8,1,4,3,2,5,7]=>[2,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[3,6,5,4,7,2,8,1]=>[8,6,1,4,3,2,5,7]=>[1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,1,5,8]=>[3,6,5,4,1,7,2,8]=>[5,7,1,4,3,2,6,8]=>[2,2,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[2,3,6,5,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>[1,3,1,3]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[1,2,3,6,5,4,7,8]=>[1,2,3,6,5,4,7,8]=>[4,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[4,6,5,7,8,3,2,1]=>[8,7,6,1,3,2,4,5]=>[1,1,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[4,6,5,7,2,1,8,3]=>[6,5,8,1,3,2,4,7]=>[1,2,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[4,6,5,1,7,2,8,3]=>[4,6,8,1,3,2,5,7]=>[3,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[4,6,5,7,3,2,8,1]=>[8,6,5,1,3,2,4,7]=>[1,1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,1,4,8]=>[4,6,5,7,3,2,1,8]=>[7,6,5,1,3,2,4,8]=>[1,1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,1,4,8]=>[4,6,5,1,7,3,2,8]=>[4,7,6,1,3,2,5,8]=>[2,1,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[4,6,5,2,7,3,8,1]=>[8,4,6,1,3,2,5,7]=>[1,2,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,1,4,8]=>[4,6,5,2,7,3,1,8]=>[7,4,6,1,3,2,5,8]=>[1,2,2,3]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,1,4,8]=>[4,1,6,5,2,7,3,8]=>[2,5,7,1,4,3,6,8]=>[3,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>[4,6,5,3,7,1,8,2]=>[6,8,4,1,3,2,5,7]=>[2,1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[4,6,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>[1,1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[4,6,5,3,7,2,1,8]=>[7,6,4,1,3,2,5,8]=>[1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>[4,3,6,5,7,8,2,1]=>[8,7,2,1,4,3,5,6]=>[1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[4,3,6,5,7,1,8,2]=>[6,8,2,1,4,3,5,7]=>[2,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[4,3,6,5,7,2,8,1]=>[8,6,2,1,4,3,5,7]=>[1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[4,3,1,6,5,2,7,8]=>[3,6,2,1,5,4,7,8]=>[2,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[4,3,2,6,5,1,7,8]=>[6,3,2,1,5,4,7,8]=>[1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[1,4,3,2,6,5,7,8]=>[1,4,3,2,6,5,7,8]=>[2,1,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[3,4,6,5,7,1,8,2]=>[6,8,1,2,4,3,5,7]=>[2,3,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>[3,4,6,5,7,2,1,8]=>[7,6,1,2,4,3,5,8]=>[1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[3,4,6,5,2,7,8,1]=>[8,5,1,2,4,3,6,7]=>[1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,1,7,8]=>[3,4,6,5,2,1,7,8]=>[6,5,1,2,4,3,7,8]=>[1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>[3,4,1,6,5,2,7,8]=>[3,6,1,2,5,4,7,8]=>[2,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>[3,4,2,6,5,7,8,1]=>[8,3,1,2,5,4,6,7]=>[1,1,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,1,6,8]=>[3,4,2,6,5,7,1,8]=>[7,3,1,2,5,4,6,8]=>[1,1,3,3]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>[3,2,4,1,6,5,7,8]=>[4,2,1,3,6,5,7,8]=>[1,1,3,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[2,3,4,6,5,7,1,8]=>[7,1,2,3,5,4,6,8]=>[1,4,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[5,6,7,1,8,4,3,2]=>[4,8,7,6,1,2,3,5]=>[2,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[5,6,7,2,8,4,3,1]=>[8,4,7,6,1,2,3,5]=>[1,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[5,6,7,2,1,8,4,3]=>[5,4,8,7,1,2,3,6]=>[1,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[5,6,1,7,2,8,4,3]=>[3,5,8,7,1,2,4,6]=>[3,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[5,6,7,3,8,4,2,1]=>[8,7,4,6,1,2,3,5]=>[1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[5,6,7,3,1,8,4,2]=>[5,8,4,7,1,2,3,6]=>[2,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[5,6,7,3,2,8,4,1]=>[8,5,4,7,1,2,3,6]=>[1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[5,6,7,3,2,1,8,4]=>[6,5,4,8,1,2,3,7]=>[1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[5,6,1,7,3,2,8,4]=>[3,6,5,8,1,2,4,7]=>[2,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[5,6,2,7,3,8,4,1]=>[8,3,5,7,1,2,4,6]=>[1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[5,6,2,7,3,1,8,4]=>[6,3,5,8,1,2,4,7]=>[1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[5,6,2,1,7,3,8,4]=>[4,3,6,8,1,2,5,7]=>[1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[5,1,6,2,7,3,8,4]=>[2,4,6,8,1,3,5,7]=>[4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>[1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>[5,6,7,4,1,8,3,2]=>[5,8,7,4,1,2,3,6]=>[2,1,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[5,6,7,4,2,1,8,3]=>[6,5,8,4,1,2,3,7]=>[1,2,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[5,6,1,7,4,2,8,3]=>[3,6,8,5,1,2,4,7]=>[3,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[5,6,7,4,3,1,8,2]=>[6,8,5,4,1,2,3,7]=>[2,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>[1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,1,2,3,8]=>[5,6,2,7,4,3,1,8]=>[7,3,6,5,1,2,4,8]=>[1,2,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>[5,6,3,7,4,8,2,1]=>[8,7,3,5,1,2,4,6]=>[1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,1,2,3,8]=>[5,6,3,7,4,2,1,8]=>[7,6,3,5,1,2,4,8]=>[1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,1,2,3,8]=>[5,6,3,2,7,4,1,8]=>[7,4,3,6,1,2,5,8]=>[1,1,2,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>[5,2,6,3,7,4,8,1]=>[8,2,4,6,1,3,5,7]=>[1,3,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>[5,2,6,3,7,4,1,8]=>[7,2,4,6,1,3,5,8]=>[1,3,4]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[5,2,1,6,3,7,4,8]=>[3,2,5,7,1,4,6,8]=>[1,3,4]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[1,5,2,6,3,7,4,8]=>[1,3,5,7,2,4,6,8]=>[4,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>[1,1,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[5,6,4,7,1,8,3,2]=>[5,8,7,3,1,2,4,6]=>[2,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[5,6,4,1,7,2,8,3]=>[4,6,8,3,1,2,5,7]=>[3,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[5,6,4,7,3,8,2,1]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[5,6,4,2,7,3,8,1]=>[8,4,6,3,1,2,5,7]=>[1,2,1,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,1,2,4,8]=>[5,6,4,2,7,3,1,8]=>[7,4,6,3,1,2,5,8]=>[1,2,1,4]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[5,1,6,4,2,7,3,8]=>[2,5,7,4,1,3,6,8]=>[3,1,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[5,6,4,3,7,1,8,2]=>[6,8,4,3,1,2,5,7]=>[2,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>[1,1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[5,1,6,4,3,2,7,8]=>[2,6,5,4,1,3,7,8]=>[2,1,1,4]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[5,2,1,6,4,3,7,8]=>[3,2,6,5,1,4,7,8]=>[1,2,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[5,3,6,4,7,8,2,1]=>[8,7,2,4,1,3,5,6]=>[1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[5,3,6,4,7,1,8,2]=>[6,8,2,4,1,3,5,7]=>[2,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>[5,3,6,4,7,2,8,1]=>[8,6,2,4,1,3,5,7]=>[1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>[5,3,6,4,2,7,8,1]=>[8,5,2,4,1,3,6,7]=>[1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,1,2,6,8]=>[5,3,6,4,2,7,1,8]=>[7,5,2,4,1,3,6,8]=>[1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[5,3,1,6,4,2,7,8]=>[3,6,2,5,1,4,7,8]=>[2,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,1,2,7,8]=>[5,3,2,6,4,1,7,8]=>[6,3,2,5,1,4,7,8]=>[1,1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[5,3,2,1,6,4,7,8]=>[4,3,2,6,1,5,7,8]=>[1,1,2,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[5,4,6,7,1,8,3,2]=>[5,8,7,2,1,3,4,6]=>[2,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[5,4,6,1,7,2,8,3]=>[4,6,8,2,1,3,5,7]=>[3,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,1,3,4,7]=>[5,4,6,7,3,2,8,1]=>[8,6,5,2,1,3,4,7]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1,3,4,8]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[5,4,6,2,7,3,8,1]=>[8,4,6,2,1,3,5,7]=>[1,2,1,4]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[5,4,1,6,2,7,3,8]=>[3,5,7,2,1,4,6,8]=>[3,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[5,4,6,3,7,1,8,2]=>[6,8,4,2,1,3,5,7]=>[2,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[5,4,1,6,3,2,7,8]=>[3,6,5,2,1,4,7,8]=>[2,1,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>[5,4,2,6,3,1,7,8]=>[6,3,5,2,1,4,7,8]=>[1,2,1,4]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[5,4,2,1,6,3,7,8]=>[4,3,6,2,1,5,7,8]=>[1,2,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[5,4,3,6,7,1,8,2]=>[6,8,3,2,1,4,5,7]=>[2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[5,4,3,1,6,2,7,8]=>[4,6,3,2,1,5,7,8]=>[2,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[1,5,4,3,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>[2,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>[1,2,1,4]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[2,1,5,4,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[1,2,1,4]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[1,2,5,4,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[3,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[3,5,4,6,7,1,8,2]=>[6,8,1,3,2,4,5,7]=>[2,2,4]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[3,5,4,2,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>[1,1,2,4]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>[5,2,1,4,3,6,7,8]=>[1,1,2,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[2,2,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[2,3,5,4,6,7,8,1]=>[8,1,2,4,3,5,6,7]=>[1,3,4]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>[1,3,4]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[4,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>[1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[4,5,6,7,1,8,3,2]=>[5,8,7,1,2,3,4,6]=>[2,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[4,5,6,7,2,8,3,1]=>[8,5,7,1,2,3,4,6]=>[1,2,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[4,5,6,7,2,1,8,3]=>[6,5,8,1,2,3,4,7]=>[1,2,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[4,5,6,1,7,2,8,3]=>[4,6,8,1,2,3,5,7]=>[3,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>[1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[4,5,6,7,3,1,8,2]=>[6,8,5,1,2,3,4,7]=>[2,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>[1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>[1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[4,5,6,1,7,3,2,8]=>[4,7,6,1,2,3,5,8]=>[2,1,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[4,5,6,2,7,3,8,1]=>[8,4,6,1,2,3,5,7]=>[1,2,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[4,5,6,2,7,3,1,8]=>[7,4,6,1,2,3,5,8]=>[1,2,5]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[4,5,6,2,1,7,3,8]=>[5,4,7,1,2,3,6,8]=>[1,2,5]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[4,5,1,6,2,7,3,8]=>[3,5,7,1,2,4,6,8]=>[3,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>[4,5,6,3,7,1,8,2]=>[6,8,4,1,2,3,5,7]=>[2,1,5]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>[1,1,1,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,1,2,3,6,8]=>[4,5,2,6,3,7,1,8]=>[7,3,5,1,2,4,6,8]=>[1,2,5]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>[4,5,3,6,1,7,2,8]=>[5,7,3,1,2,4,6,8]=>[2,1,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[4,5,3,6,2,7,8,1]=>[8,5,3,1,2,4,6,7]=>[1,1,1,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>[1,1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>[4,5,3,2,6,7,1,8]=>[7,4,3,1,2,5,6,8]=>[1,1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>[1,1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>[1,1,1,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[4,2,5,3,6,7,8,1]=>[8,2,4,1,3,5,6,7]=>[1,2,5]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>[4,2,5,3,1,6,7,8]=>[5,2,4,1,3,6,7,8]=>[1,2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>[1,1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[4,3,5,6,7,1,8,2]=>[6,8,2,1,3,4,5,7]=>[2,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>[1,1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>[1,1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>[1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>[1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>[1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[2,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[2,4,3,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>[1,2,5]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[2,4,3,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>[1,2,5]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[1,2,5]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[1,2,5]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[3,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[3,4,5,6,7,1,8,2]=>[6,8,1,2,3,4,5,7]=>[2,6]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[3,4,5,6,1,7,2,8]=>[5,7,1,2,3,4,6,8]=>[2,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>[1,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>[1,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,1,2,3,4,7,8]=>[3,4,5,6,2,1,7,8]=>[6,5,1,2,3,4,7,8]=>[1,1,6]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>[1,1,6]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[3,4,1,5,2,6,7,8]=>[3,5,1,2,4,6,7,8]=>[2,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>[1,1,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>[1,1,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[1,1,6]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[1,1,6]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[2,6]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>[1,1,6]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[1,1,6]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[2,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[1,7]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[1,7]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[1,7]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[1,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,10,9,8,7,6,5]=>[1,2,3,4,10,9,8,7,6,5]=>[5,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[1,1,1,1,6]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
Lehmer-code to major-code bijection
Description
Sends a permutation to the unique permutation such that the Lehmer code is sent to the major code.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
Map
inverse
Description
Sends a permutation to its inverse.
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 $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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