Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]=>[1]
[1,0,1,0]=>[1,2]=>[1,2]=>[2,1]=>[1,1]
[1,1,0,0]=>[2,1]=>[2,1]=>[1,2]=>[2]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[3,2,1]=>[1,1,1]
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[3,1,2]=>[1,2]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[2,3,1]=>[2,1]
[1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[1,3,2]=>[2,1]
[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[1,2,3]=>[3]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1]=>[1,1,1,1]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[4,3,1,2]=>[1,1,2]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[4,2,3,1]=>[1,2,1]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,2,3]=>[4,1,3,2]=>[1,2,1]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,4,3,2]=>[4,1,2,3]=>[1,3]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[3,4,2,1]=>[2,1,1]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[3,4,1,2]=>[2,2]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[2,4,3,1]=>[2,1,1]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[1,4,3,2]=>[2,1,1]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,3,1,2]=>[1,2,4,3]=>[3,1]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,4,1]=>[3,1]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,1,3,2]=>[1,4,2,3]=>[2,2]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,2,1,3]=>[1,3,4,2]=>[3,1]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]=>[4]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[1,1,1,2]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[1,1,2,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[1,1,2,1]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[1,1,3]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[1,2,1,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[5,3,4,1,2]=>[1,2,2]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[1,2,1,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[1,2,1,1]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,5,4,2,3]=>[5,1,2,4,3]=>[1,3,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[1,3,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,5,2,4,3]=>[5,1,4,2,3]=>[1,2,2]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[1,5,3,2,4]=>[5,1,3,4,2]=>[1,3,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[5,1,2,3,4]=>[1,4]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[2,1,1,1]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[2,1,2]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[2,2,1]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[2,2,1]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[4,5,1,2,3]=>[2,3]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[2,1,1,1]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,1,2,5,4]=>[3,5,4,1,2]=>[2,1,2]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[2,1,1,1]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[2,1,1,1]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[3,1,1]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[3,1,1]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,1,2,4,3]=>[1,5,4,2,3]=>[2,1,2]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[3,1,1]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[4,1]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[3,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[3,4,5,1,2]=>[3,2]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,1,3,2,5]=>[2,5,3,4,1]=>[2,2,1]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,1,3,2,4]=>[1,5,3,4,2]=>[2,2,1]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,4,1,3,2]=>[1,2,5,3,4]=>[3,2]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[3,1,1]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,1,4,2,3]=>[1,5,2,4,3]=>[2,2,1]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[3,1,1]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[4,1]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[4,1]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,1,4,3,2]=>[1,5,2,3,4]=>[2,3]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,2,1,4,3]=>[1,4,5,2,3]=>[3,2]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[4,1]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[1,1,1,1,2]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[1,1,1,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[1,1,1,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[1,1,1,3]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[1,1,2,2]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[1,1,3,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[1,1,3,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[1,1,2,2]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[1,1,3,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>[1,1,4]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[1,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[1,2,1,2]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>[1,2,3]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[1,2,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[1,2,1,2]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[1,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[1,3,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[1,3,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[1,2,1,2]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[1,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>[1,4,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[1,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>[1,3,2]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[1,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>[1,3,2]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[1,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[1,2,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>[1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>[1,2,3]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>[1,3,2]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>[1,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>[1,5]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[2,1,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[2,1,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[2,1,3]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[2,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>[2,3,1]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[2,3,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>[2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[2,3,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>[2,4]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[2,1,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>[2,1,3]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>[2,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[3,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[3,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,1,2,3,5,4]=>[1,6,5,4,2,3]=>[2,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[4,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[3,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>[3,1,2]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,1,2,4,3,6]=>[2,6,5,3,4,1]=>[2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>[2,1,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,5,1,2,4,3]=>[1,2,6,5,3,4]=>[3,1,2]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[3,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>[2,1,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[3,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[4,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[4,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,1,2,5,4,3]=>[1,6,5,2,3,4]=>[2,1,3]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,3,1,2,5,4]=>[1,4,6,5,2,3]=>[3,1,2]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[4,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[5,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[3,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[3,1,2]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>[2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>[2,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,1,3,2,4,6]=>[2,6,4,5,3,1]=>[2,2,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,1,3,2,4,5]=>[1,6,4,5,3,2]=>[2,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,5,1,3,2,4]=>[1,2,6,4,5,3]=>[3,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,4,1,3,2,6]=>[2,3,6,4,5,1]=>[3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>[2,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,4,1,3,2,5]=>[1,3,6,4,5,2]=>[3,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,5,4,1,3,2]=>[1,2,3,6,4,5]=>[4,2]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[3,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>[3,1,2]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,1,4,2,3,6]=>[2,6,3,5,4,1]=>[2,2,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>[2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,5,1,4,2,3]=>[1,2,6,3,5,4]=>[3,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[3,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>[2,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[3,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[4,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[4,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,1,5,4,2,3]=>[1,6,2,3,5,4]=>[2,3,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,2,1,3,5,4]=>[1,5,6,4,2,3]=>[3,1,2]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[4,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[5,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[4,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>[4,2]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,1,4,3,2,6]=>[2,6,3,4,5,1]=>[2,3,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,1,4,3,2,5]=>[1,6,3,4,5,2]=>[2,3,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,5,1,4,3,2]=>[1,2,6,3,4,5]=>[3,3]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,2,1,4,3,6]=>[2,5,6,3,4,1]=>[3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>[2,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,2,1,4,3,5]=>[1,5,6,3,4,2]=>[3,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>[4,2]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[4,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,1,5,3,2,4]=>[1,6,2,4,5,3]=>[2,3,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,2,1,5,3,4]=>[1,5,6,2,4,3]=>[3,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[4,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[5,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[5,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>[2,4]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,2,1,5,4,3]=>[1,5,6,2,3,4]=>[3,3]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,3,2,1,5,4]=>[1,4,5,6,2,3]=>[4,2]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[5,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[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]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[1,1,1,2,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[1,1,1,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[1,1,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[1,1,2,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[1,1,2,1,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[1,1,2,1,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[1,1,4,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[1,1,3,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[1,1,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[1,1,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[1,1,3,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[1,1,2,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[1,1,4,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[1,1,4,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[1,1,2,3]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[1,1,3,2]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[1,1,4,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>[1,1,5]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[1,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[1,2,1,3]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[1,2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[1,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[1,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[1,2,2,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[1,2,3,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>[1,2,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[1,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[1,2,1,1,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[1,2,1,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[1,2,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[1,3,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[1,3,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[1,2,1,1,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[1,3,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[1,4,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[1,3,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[1,3,1,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[1,2,1,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[1,2,1,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[1,3,1,2]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[1,3,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[1,2,1,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[1,3,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[1,4,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[1,4,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[1,2,1,3]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[1,3,1,2]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[1,4,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>[1,5,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[1,3,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[1,3,1,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[1,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[1,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>[1,3,3]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[1,2,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[1,2,2,2]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[1,2,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[1,2,2,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[1,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[1,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[1,2,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[1,3,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>[1,4,2]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[1,3,1,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[1,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[1,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[1,3,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[1,2,2,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[1,4,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[1,4,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[1,2,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[1,3,1,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[1,4,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>[1,5,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[1,4,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>[1,4,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[1,2,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[1,2,3,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>[1,3,3]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[1,3,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[1,2,2,2]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[1,3,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>[1,4,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[1,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[1,2,3,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[1,3,2,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[1,4,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>[1,2,4]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>[1,3,3]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>[1,4,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>[1,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>[1,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>[6,7,5,4,1,3,2]=>[2,1,1,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>[6,7,5,4,1,2,3]=>[2,1,1,3]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[6,7,5,3,4,1,2]=>[2,1,2,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,4,5,7]=>[6,7,5,2,4,3,1]=>[2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>[6,7,5,1,4,3,2]=>[2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,7,6,4,5]=>[6,7,5,1,2,4,3]=>[2,1,3,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>[6,7,5,2,3,4,1]=>[2,1,3,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,7,4,6,5]=>[6,7,5,1,4,2,3]=>[2,1,2,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[2,1,3,7,5,4,6]=>[6,7,5,1,3,4,2]=>[2,1,3,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[6,7,5,1,2,3,4]=>[2,1,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[6,7,4,5,3,1,2]=>[2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[6,7,4,5,2,3,1]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,5,6]=>[6,7,4,5,1,3,2]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>[6,7,4,5,1,2,3]=>[2,2,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,3,4,6,7]=>[6,7,3,5,4,2,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>[2,2,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>[6,7,2,5,4,3,1]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>[6,7,1,5,4,3,2]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,7,6,3,4,5]=>[6,7,1,2,5,4,3]=>[2,3,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,6,5,3,4,7]=>[6,7,2,3,5,4,1]=>[2,3,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,7,3,4,6,5]=>[6,7,1,5,4,2,3]=>[2,2,1,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[2,1,7,5,3,4,6]=>[6,7,1,3,5,4,2]=>[2,3,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,7,6,5,3,4]=>[6,7,1,2,3,5,4]=>[2,4,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>[6,7,3,4,5,2,1]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,6,3,5,4,7]=>[6,7,2,5,3,4,1]=>[2,2,2,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,7,3,5,4,6]=>[6,7,1,5,3,4,2]=>[2,2,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,7,6,3,5,4]=>[6,7,1,2,5,3,4]=>[2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[2,1,6,4,3,5,7]=>[6,7,2,4,5,3,1]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[2,1,7,3,6,4,5]=>[6,7,1,5,2,4,3]=>[2,2,2,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[2,1,7,4,3,5,6]=>[6,7,1,4,5,3,2]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[2,1,7,6,4,3,5]=>[6,7,1,2,4,5,3]=>[2,4,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[6,7,2,3,4,5,1]=>[2,4,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,7,3,6,5,4]=>[6,7,1,5,2,3,4]=>[2,2,3]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[2,1,7,4,3,6,5]=>[6,7,1,4,5,2,3]=>[2,3,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[2,1,7,5,4,3,6]=>[6,7,1,3,4,5,2]=>[2,4,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[6,7,1,2,3,4,5]=>[2,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[5,7,6,4,3,1,2]=>[2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[5,7,6,4,2,3,1]=>[2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>[2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,1,2,4,7,6,5]=>[5,7,6,4,1,2,3]=>[2,1,1,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[5,7,6,3,4,2,1]=>[2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[5,7,6,3,4,1,2]=>[2,1,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,1,2,6,4,5,7]=>[5,7,6,2,4,3,1]=>[2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,1,2,7,4,5,6]=>[5,7,6,1,4,3,2]=>[2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,1,2,7,6,4,5]=>[5,7,6,1,2,4,3]=>[2,1,3,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,1,2,6,5,4,7]=>[5,7,6,2,3,4,1]=>[2,1,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,1,2,7,4,6,5]=>[5,7,6,1,4,2,3]=>[2,1,2,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[3,1,2,7,5,4,6]=>[5,7,6,1,3,4,2]=>[2,1,3,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,1,2,7,6,5,4]=>[5,7,6,1,2,3,4]=>[2,1,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>[4,7,6,5,3,1,2]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>[4,7,6,5,2,3,1]=>[2,1,1,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,1,2,3,7,5,6]=>[4,7,6,5,1,3,2]=>[2,1,1,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[4,1,2,3,7,6,5]=>[4,7,6,5,1,2,3]=>[2,1,1,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>[3,7,6,5,4,1,2]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[3,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,1,2,3,4,6,5]=>[1,7,6,5,4,2,3]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[3,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[4,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[3,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[5,4,1,2,3,7,6]=>[3,4,7,6,5,1,2]=>[3,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,1,2,3,5,4,7]=>[2,7,6,5,3,4,1]=>[2,1,1,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,1,2,3,5,4,6]=>[1,7,6,5,3,4,2]=>[2,1,1,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,6,1,2,3,5,4]=>[1,2,7,6,5,3,4]=>[3,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[3,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>[2,1,1,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[3,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[4,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[4,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,1,2,3,6,5,4]=>[1,7,6,5,2,3,4]=>[2,1,1,3]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[7,4,1,2,3,6,5]=>[1,4,7,6,5,2,3]=>[3,1,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[4,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[5,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[3,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[4,3,1,2,5,7,6]=>[4,5,7,6,3,1,2]=>[3,1,1,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[4,3,1,2,6,5,7]=>[4,5,7,6,2,3,1]=>[3,1,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[4,3,1,2,7,5,6]=>[4,5,7,6,1,3,2]=>[3,1,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[4,3,1,2,7,6,5]=>[4,5,7,6,1,2,3]=>[3,1,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,1,2,4,3,6,7]=>[3,7,6,4,5,2,1]=>[2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[5,1,2,4,3,7,6]=>[3,7,6,4,5,1,2]=>[2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,1,2,4,3,5,7]=>[2,7,6,4,5,3,1]=>[2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,1,2,4,3,5,6]=>[1,7,6,4,5,3,2]=>[2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,6,1,2,4,3,5]=>[1,2,7,6,4,5,3]=>[3,1,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,5,1,2,4,3,7]=>[2,3,7,6,4,5,1]=>[3,1,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,1,2,4,3,6,5]=>[1,7,6,4,5,2,3]=>[2,1,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[7,5,1,2,4,3,6]=>[1,3,7,6,4,5,2]=>[3,1,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,6,5,1,2,4,3]=>[1,2,3,7,6,4,5]=>[4,1,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[3,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[5,3,1,2,4,7,6]=>[3,5,7,6,4,1,2]=>[3,1,1,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,1,2,5,3,4,7]=>[2,7,6,3,5,4,1]=>[2,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>[2,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,6,1,2,5,3,4]=>[1,2,7,6,3,5,4]=>[3,1,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[3,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>[2,1,2,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[3,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[4,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[4,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,1,2,6,5,3,4]=>[1,7,6,2,3,5,4]=>[2,1,3,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[7,3,1,2,4,6,5]=>[1,5,7,6,4,2,3]=>[3,1,1,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[4,1,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[5,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[4,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[5,4,3,1,2,7,6]=>[3,4,5,7,6,1,2]=>[4,1,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,1,2,5,4,3,7]=>[2,7,6,3,4,5,1]=>[2,1,3,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>[2,1,3,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,6,1,2,5,4,3]=>[1,2,7,6,3,4,5]=>[3,1,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[6,3,1,2,5,4,7]=>[2,5,7,6,3,4,1]=>[3,1,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,1,2,6,3,5,4]=>[1,7,6,2,5,3,4]=>[2,1,2,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[7,3,1,2,5,4,6]=>[1,5,7,6,3,4,2]=>[3,1,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,6,3,1,2,5,4]=>[1,2,5,7,6,3,4]=>[4,1,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[4,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[7,1,2,6,4,3,5]=>[1,7,6,2,4,5,3]=>[2,1,3,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>[3,1,2,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[4,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[5,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[5,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,1,2,6,5,4,3]=>[1,7,6,2,3,4,5]=>[2,1,4]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[7,3,1,2,6,5,4]=>[1,5,7,6,2,3,4]=>[3,1,3]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,4,3,1,2,6,5]=>[1,4,5,7,6,2,3]=>[4,1,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[5,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[6,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[5,6,7,4,3,1,2]=>[3,1,1,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[5,6,7,4,2,3,1]=>[3,1,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[3,2,1,4,7,5,6]=>[5,6,7,4,1,3,2]=>[3,1,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[3,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[5,6,7,3,4,2,1]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[5,6,7,3,4,1,2]=>[3,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[3,2,1,6,4,5,7]=>[5,6,7,2,4,3,1]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[3,2,1,7,4,5,6]=>[5,6,7,1,4,3,2]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[3,2,1,7,6,4,5]=>[5,6,7,1,2,4,3]=>[3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[5,6,7,2,3,4,1]=>[3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[3,2,1,7,4,6,5]=>[5,6,7,1,4,2,3]=>[3,2,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[3,2,1,7,5,4,6]=>[5,6,7,1,3,4,2]=>[3,3,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[5,6,7,1,2,3,4]=>[3,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,1,3,2,5,6,7]=>[4,7,5,6,3,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[4,1,3,2,5,7,6]=>[4,7,5,6,3,1,2]=>[2,2,1,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[4,1,3,2,6,5,7]=>[4,7,5,6,2,3,1]=>[2,2,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[4,1,3,2,7,5,6]=>[4,7,5,6,1,3,2]=>[2,2,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[4,1,3,2,7,6,5]=>[4,7,5,6,1,2,3]=>[2,2,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,1,3,2,4,6,7]=>[3,7,5,6,4,2,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[5,1,3,2,4,7,6]=>[3,7,5,6,4,1,2]=>[2,2,1,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,1,3,2,4,5,7]=>[2,7,5,6,4,3,1]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,1,3,2,4,5,6]=>[1,7,5,6,4,3,2]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,6,1,3,2,4,5]=>[1,2,7,5,6,4,3]=>[3,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,5,1,3,2,4,7]=>[2,3,7,5,6,4,1]=>[3,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>[2,2,1,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[7,5,1,3,2,4,6]=>[1,3,7,5,6,4,2]=>[3,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,6,5,1,3,2,4]=>[1,2,3,7,5,6,4]=>[4,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,4,1,3,2,6,7]=>[3,4,7,5,6,2,1]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[5,4,1,3,2,7,6]=>[3,4,7,5,6,1,2]=>[3,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,1,3,2,5,4,7]=>[2,7,5,6,3,4,1]=>[2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,1,3,2,5,4,6]=>[1,7,5,6,3,4,2]=>[2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,6,1,3,2,5,4]=>[1,2,7,5,6,3,4]=>[3,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[6,4,1,3,2,5,7]=>[2,4,7,5,6,3,1]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[7,1,3,2,6,4,5]=>[1,7,5,6,2,4,3]=>[2,2,2,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[7,4,1,3,2,5,6]=>[1,4,7,5,6,3,2]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,6,4,1,3,2,5]=>[1,2,4,7,5,6,3]=>[4,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,5,4,1,3,2,7]=>[2,3,4,7,5,6,1]=>[4,2,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,1,3,2,6,5,4]=>[1,7,5,6,2,3,4]=>[2,2,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>[3,2,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[7,5,4,1,3,2,6]=>[1,3,4,7,5,6,2]=>[4,2,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,6,5,4,1,3,2]=>[1,2,3,4,7,5,6]=>[5,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[3,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[4,2,1,3,5,7,6]=>[4,6,7,5,3,1,2]=>[3,1,1,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[4,2,1,3,6,5,7]=>[4,6,7,5,2,3,1]=>[3,1,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[4,2,1,3,7,5,6]=>[4,6,7,5,1,3,2]=>[3,1,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[4,2,1,3,7,6,5]=>[4,6,7,5,1,2,3]=>[3,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,1,4,2,3,6,7]=>[3,7,4,6,5,2,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[5,1,4,2,3,7,6]=>[3,7,4,6,5,1,2]=>[2,2,1,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,1,4,2,3,5,7]=>[2,7,4,6,5,3,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,6,1,4,2,3,5]=>[1,2,7,4,6,5,3]=>[3,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,5,1,4,2,3,7]=>[2,3,7,4,6,5,1]=>[3,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[7,1,4,2,3,6,5]=>[1,7,4,6,5,2,3]=>[2,2,1,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,5,1,4,2,3,6]=>[1,3,7,4,6,5,2]=>[3,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,6,5,1,4,2,3]=>[1,2,3,7,4,6,5]=>[4,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[5,2,1,3,4,7,6]=>[3,6,7,5,4,1,2]=>[3,1,1,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[6,1,5,2,3,4,7]=>[2,7,3,6,5,4,1]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,6,1,5,2,3,4]=>[1,2,7,3,6,5,4]=>[3,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[4,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[4,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>[2,3,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,2,1,3,4,6,5]=>[1,6,7,5,4,2,3]=>[3,1,1,2]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[4,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[5,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[4,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[5,4,2,1,3,7,6]=>[3,4,6,7,5,1,2]=>[4,1,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,1,5,4,2,3,7]=>[2,7,3,4,6,5,1]=>[2,3,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,1,5,4,2,3,6]=>[1,7,3,4,6,5,2]=>[2,3,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,6,1,5,4,2,3]=>[1,2,7,3,4,6,5]=>[3,3,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[6,2,1,3,5,4,7]=>[2,6,7,5,3,4,1]=>[3,1,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,1,6,2,3,5,4]=>[1,7,2,6,5,3,4]=>[2,2,1,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,2,1,3,5,4,6]=>[1,6,7,5,3,4,2]=>[3,1,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,6,2,1,3,5,4]=>[1,2,6,7,5,3,4]=>[4,1,2]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[4,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>[2,3,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[7,2,1,3,6,4,5]=>[1,6,7,5,2,4,3]=>[3,1,2,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[4,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[5,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[5,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[7,1,6,5,4,2,3]=>[1,7,2,3,4,6,5]=>[2,4,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[7,2,1,3,6,5,4]=>[1,6,7,5,2,3,4]=>[3,1,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[7,4,2,1,3,6,5]=>[1,4,6,7,5,2,3]=>[4,1,2]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[5,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[6,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[4,5,6,7,3,1,2]=>[4,1,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[4,5,6,7,2,3,1]=>[4,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[4,3,2,1,7,5,6]=>[4,5,6,7,1,3,2]=>[4,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[4,5,6,7,1,2,3]=>[4,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,1,4,3,2,6,7]=>[3,7,4,5,6,2,1]=>[2,3,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[5,1,4,3,2,7,6]=>[3,7,4,5,6,1,2]=>[2,3,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,1,4,3,2,5,7]=>[2,7,4,5,6,3,1]=>[2,3,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,1,4,3,2,5,6]=>[1,7,4,5,6,3,2]=>[2,3,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,6,1,4,3,2,5]=>[1,2,7,4,5,6,3]=>[3,3,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,5,1,4,3,2,7]=>[2,3,7,4,5,6,1]=>[3,3,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,1,4,3,2,6,5]=>[1,7,4,5,6,2,3]=>[2,3,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[7,5,1,4,3,2,6]=>[1,3,7,4,5,6,2]=>[3,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,6,5,1,4,3,2]=>[1,2,3,7,4,5,6]=>[4,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,2,1,4,3,6,7]=>[3,6,7,4,5,2,1]=>[3,2,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[5,2,1,4,3,7,6]=>[3,6,7,4,5,1,2]=>[3,2,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,1,5,2,4,3,7]=>[2,7,3,6,4,5,1]=>[2,2,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,1,5,2,4,3,6]=>[1,7,3,6,4,5,2]=>[2,2,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,6,1,5,2,4,3]=>[1,2,7,3,6,4,5]=>[3,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[6,2,1,4,3,5,7]=>[2,6,7,4,5,3,1]=>[3,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,1,6,2,4,3,5]=>[1,7,2,6,4,5,3]=>[2,2,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,2,1,4,3,5,6]=>[1,6,7,4,5,3,2]=>[3,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,6,2,1,4,3,5]=>[1,2,6,7,4,5,3]=>[4,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,5,2,1,4,3,7]=>[2,3,6,7,4,5,1]=>[4,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,1,6,5,2,4,3]=>[1,7,2,3,6,4,5]=>[2,3,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[7,2,1,4,3,6,5]=>[1,6,7,4,5,2,3]=>[3,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[7,5,2,1,4,3,6]=>[1,3,6,7,4,5,2]=>[4,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,5,2,1,4,3]=>[1,2,3,6,7,4,5]=>[5,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[5,3,2,1,4,7,6]=>[3,5,6,7,4,1,2]=>[4,1,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[6,1,5,3,2,4,7]=>[2,7,3,5,6,4,1]=>[2,3,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,1,5,3,2,4,6]=>[1,7,3,5,6,4,2]=>[2,3,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,6,1,5,3,2,4]=>[1,2,7,3,5,6,4]=>[3,3,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[6,2,1,5,3,4,7]=>[2,6,7,3,5,4,1]=>[3,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>[2,2,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[7,2,1,5,3,4,6]=>[1,6,7,3,5,4,2]=>[3,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>[4,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,1,6,3,2,4,5]=>[1,7,2,5,6,4,3]=>[2,3,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,2,1,6,3,4,5]=>[1,6,7,2,5,4,3]=>[3,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[5,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[5,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>[2,4,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[7,2,1,6,5,3,4]=>[1,6,7,2,3,5,4]=>[3,3,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[7,3,2,1,4,6,5]=>[1,5,6,7,4,2,3]=>[4,1,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[5,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[6,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[5,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[3,4,5,6,7,1,2]=>[5,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,1,5,4,3,2,7]=>[2,7,3,4,5,6,1]=>[2,4,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,1,5,4,3,2,6]=>[1,7,3,4,5,6,2]=>[2,4,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,6,1,5,4,3,2]=>[1,2,7,3,4,5,6]=>[3,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[6,2,1,5,4,3,7]=>[2,6,7,3,4,5,1]=>[3,3,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>[2,2,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,2,1,5,4,3,6]=>[1,6,7,3,4,5,2]=>[3,3,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>[4,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,3,2,1,5,4,7]=>[2,5,6,7,3,4,1]=>[4,2,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,1,6,3,2,5,4]=>[1,7,2,5,6,3,4]=>[2,3,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,2,1,6,3,5,4]=>[1,6,7,2,5,3,4]=>[3,2,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,3,2,1,5,4,6]=>[1,5,6,7,3,4,2]=>[4,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,6,3,2,1,5,4]=>[1,2,5,6,7,3,4]=>[5,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[5,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,1,6,4,3,2,5]=>[1,7,2,4,5,6,3]=>[2,4,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,2,1,6,4,3,5]=>[1,6,7,2,4,5,3]=>[3,3,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[7,3,2,1,6,4,5]=>[1,5,6,7,2,4,3]=>[4,2,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[5,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[2,5]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,2,1,6,5,4,3]=>[1,6,7,2,3,4,5]=>[3,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,3,2,1,6,5,4]=>[1,5,6,7,2,3,4]=>[4,3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,4,3,2,1,6,5]=>[1,4,5,6,7,2,3]=>[5,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,4]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[1,1,1,2,1,2]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[1,2,3,8,7,4,6,5]=>[8,7,6,1,2,5,3,4]=>[1,1,1,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[1,1,1,2,3]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[1,1,1,3,2]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[1,1,1,5]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[1,1,2,2,2]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[8,7,5,6,1,2,3,4]=>[1,1,2,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,5,3,7,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>[1,2,8,6,5,3,4,7]=>[8,7,1,3,4,6,5,2]=>[1,1,4,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[1,2,8,7,6,5,3,4]=>[8,7,1,2,3,4,6,5]=>[1,1,5,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,4,7,8,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[1,2,8,3,6,5,4,7]=>[8,7,1,6,3,4,5,2]=>[1,1,2,3,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[1,1,4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[1,2,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[1,2,1,2,2]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>[1,2,1,4]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[1,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,7,6,5,4]=>[8,6,7,1,2,3,4,5]=>[1,2,5]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[1,2,1,2,2]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>[1,2,1,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[1,3,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,5,7,6,2,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[1,3,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,6,2]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[1,3,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,4,6,7,5,2,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[1,3,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,7,6,8,5,2]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[1,3,1,1,2]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[1,8,7,6,5,2,3,4]=>[8,1,2,3,4,7,6,5]=>[1,5,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[1,3,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[1,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>[1,4,3,2,8,5,7,6]=>[8,5,6,7,1,4,2,3]=>[1,3,2,2]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[8,5,6,7,1,2,3,4]=>[1,3,4]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[1,2,2,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[1,8,7,2,4,3,6,5]=>[8,1,2,7,5,6,3,4]=>[1,3,2,2]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,7,6,8,5,2]=>[1,8,5,2,4,3,7,6]=>[8,1,4,7,5,6,2,3]=>[1,3,2,2]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>[1,8,6,5,2,4,3,7]=>[8,1,3,4,7,5,6,2]=>[1,4,2,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,8,7,6,5,2,4,3]=>[8,1,2,3,4,7,5,6]=>[1,5,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[1,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,4,7,8,6,5,3,2]=>[1,8,6,5,3,2,4,7]=>[8,1,3,4,6,7,5,2]=>[1,5,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[1,8,7,6,5,3,2,4]=>[8,1,2,3,4,6,7,5]=>[1,6,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[1,8,2,5,4,3,6,7]=>[8,1,7,4,5,6,3,2]=>[1,2,3,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,6,4,3,2,8,7]=>[1,6,4,3,2,5,8,7]=>[8,3,5,6,7,4,1,2]=>[1,4,1,2]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,4,3,8,7,2]=>[1,8,7,2,6,4,3,5]=>[8,1,2,7,3,5,6,4]=>[1,3,3,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>[1,8,7,6,4,3,2,5]=>[8,1,2,3,5,6,7,4]=>[1,6,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[1,8,7,2,6,5,4,3]=>[8,1,2,7,3,4,5,6]=>[1,3,4]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[1,8,5,4,3,2,6,7]=>[8,1,4,5,6,7,3,2]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>[1,8,7,5,4,3,2,6]=>[8,1,2,4,5,6,7,3]=>[1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[1,8,4,3,2,7,6,5]=>[8,1,5,6,7,2,3,4]=>[1,4,3]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>[1,8,5,4,3,2,7,6]=>[8,1,4,5,6,7,2,3]=>[1,5,2]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>[1,8,6,5,4,3,2,7]=>[8,1,3,4,5,6,7,2]=>[1,6,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[8,1,2,3,4,5,6,7]=>[1,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,5,6,7]=>[7,8,6,5,1,4,3,2]=>[2,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,5,7,6]=>[7,8,6,5,1,4,2,3]=>[2,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,6,5,7]=>[7,8,6,5,1,3,4,2]=>[2,1,1,3,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[7,8,6,5,1,2,3,4]=>[2,1,1,4]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,7,6,5,4]=>[7,8,6,1,2,3,4,5]=>[2,1,5]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>[7,8,5,6,1,4,3,2]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,8,7,5,6]=>[7,8,5,6,1,2,4,3]=>[2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,5,7,6]=>[7,8,5,6,1,4,2,3]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,6,5,7]=>[7,8,5,6,1,3,4,2]=>[2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[7,8,5,6,1,2,3,4]=>[2,2,4]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>[7,8,3,6,5,4,1,2]=>[2,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>[7,8,1,6,5,4,3,2]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>[2,1,8,6,3,4,5,7]=>[7,8,1,3,6,5,4,2]=>[2,3,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[2,1,8,7,6,3,4,5]=>[7,8,1,2,3,6,5,4]=>[2,4,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[2,1,6,5,3,4,8,7]=>[7,8,3,4,6,5,1,2]=>[2,3,1,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[2,1,8,7,3,4,6,5]=>[7,8,1,2,6,5,3,4]=>[2,3,1,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>[2,1,8,6,5,3,4,7]=>[7,8,1,3,4,6,5,2]=>[2,4,1,1]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[2,1,8,7,6,5,3,4]=>[7,8,1,2,3,4,6,5]=>[2,5,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[7,8,4,5,6,3,1,2]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[2,1,6,3,5,4,8,7]=>[7,8,3,6,4,5,1,2]=>[2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[2,1,8,3,5,4,7,6]=>[7,8,1,6,4,5,2,3]=>[2,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[2,1,6,4,3,5,8,7]=>[7,8,3,5,6,4,1,2]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[2,1,8,4,3,5,6,7]=>[7,8,1,5,6,4,3,2]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[2,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[2,1,8,3,7,4,6,5]=>[7,8,1,6,2,5,3,4]=>[2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>[2,1,8,4,3,6,5,7]=>[7,8,1,5,6,3,4,2]=>[2,3,2,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>[2,1,8,7,4,3,6,5]=>[7,8,1,2,5,6,3,4]=>[2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,6,7,5,4,3,8]=>[2,1,7,5,4,3,6,8]=>[7,8,2,4,5,6,3,1]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[2,1,8,4,3,7,5,6]=>[7,8,1,5,6,2,4,3]=>[2,3,2,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[2,1,8,5,4,3,6,7]=>[7,8,1,4,5,6,3,2]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[2,1,8,4,3,7,6,5]=>[7,8,1,5,6,2,3,4]=>[2,3,3]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[7,8,1,2,3,4,5,6]=>[2,6]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>[6,8,7,5,4,1,3,2]=>[2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,1,2,4,8,5,6,7]=>[6,8,7,5,1,4,3,2]=>[2,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[3,1,2,4,8,5,7,6]=>[6,8,7,5,1,4,2,3]=>[2,1,1,2,2]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[3,1,2,4,8,7,6,5]=>[6,8,7,5,1,2,3,4]=>[2,1,1,4]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[6,8,7,4,5,2,3,1]=>[2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[3,1,2,7,4,5,6,8]=>[6,8,7,2,5,4,3,1]=>[2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[3,1,2,8,7,6,5,4]=>[6,8,7,1,2,3,4,5]=>[2,1,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[5,8,7,6,4,3,1,2]=>[2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[5,8,7,6,4,2,3,1]=>[2,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[4,1,2,3,5,8,6,7]=>[5,8,7,6,4,1,3,2]=>[2,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[4,1,2,3,5,8,7,6]=>[5,8,7,6,4,1,2,3]=>[2,1,1,1,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[5,8,7,6,3,4,2,1]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[5,8,7,6,3,4,1,2]=>[2,1,1,2,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[4,1,2,3,7,5,6,8]=>[5,8,7,6,2,4,3,1]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>[5,8,7,6,1,4,3,2]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[4,1,2,3,8,7,5,6]=>[5,8,7,6,1,2,4,3]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[4,1,2,3,7,6,5,8]=>[5,8,7,6,2,3,4,1]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[4,1,2,3,8,5,7,6]=>[5,8,7,6,1,4,2,3]=>[2,1,1,2,2]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[4,1,2,3,8,6,5,7]=>[5,8,7,6,1,3,4,2]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[4,1,2,3,8,7,6,5]=>[5,8,7,6,1,2,3,4]=>[2,1,1,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[5,1,2,3,4,8,7,6]=>[4,8,7,6,5,1,2,3]=>[2,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>[3,8,7,6,5,4,1,2]=>[2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[8,7,1,2,3,4,5,6]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,6,1,8]=>[7,6,1,2,3,4,5,8]=>[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,6,5,1,7,8]=>[6,5,1,2,3,4,7,8]=>[3,4,8,7,6,5,2,1]=>[3,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[8,1,2,3,4,7,6,5]=>[1,8,7,6,5,2,3,4]=>[2,1,1,1,3]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[8,7,6,5,1,2,3,4]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[5,4,1,2,3,8,7,6]=>[4,5,8,7,6,1,2,3]=>[3,1,1,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[8,1,2,3,5,4,7,6]=>[1,8,7,6,4,5,2,3]=>[2,1,1,2,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[8,4,1,2,3,5,6,7]=>[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[8,7,4,1,2,3,5,6]=>[1,2,5,8,7,6,4,3]=>[4,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[6,5,4,1,2,3,8,7]=>[3,4,5,8,7,6,1,2]=>[4,1,1,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[5,6,8,7,3,4,1,2]=>[3,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[4,3,1,2,8,5,6,7]=>[5,6,8,7,1,4,3,2]=>[3,1,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[4,3,1,2,8,7,5,6]=>[5,6,8,7,1,2,4,3]=>[3,1,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[4,3,1,2,8,5,7,6]=>[5,6,8,7,1,4,2,3]=>[3,1,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,7,8,6,5]=>[4,3,1,2,8,6,5,7]=>[5,6,8,7,1,3,4,2]=>[3,1,3,1]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[4,3,1,2,8,7,6,5]=>[5,6,8,7,1,2,3,4]=>[3,1,4]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[8,7,1,2,4,3,5,6]=>[1,2,8,7,5,6,4,3]=>[3,1,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[6,5,1,2,4,3,8,7]=>[3,4,8,7,5,6,1,2]=>[3,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[8,1,2,4,3,6,5,7]=>[1,8,7,5,6,3,4,2]=>[2,1,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[8,7,1,2,4,3,6,5]=>[1,2,8,7,5,6,3,4]=>[3,1,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[8,1,2,4,3,7,6,5]=>[1,8,7,5,6,2,3,4]=>[2,1,2,3]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[8,7,6,5,1,2,4,3]=>[1,2,3,4,8,7,5,6]=>[5,1,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[5,3,1,2,4,8,7,6]=>[4,6,8,7,5,1,2,3]=>[3,1,1,3]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,7,8,6,1]=>[8,6,1,2,5,3,4,7]=>[1,3,8,7,4,6,5,2]=>[3,1,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>[8,7,5,3,1,2,4,6]=>[1,2,4,6,8,7,5,3]=>[5,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[8,7,6,5,3,1,2,4]=>[1,2,3,4,6,8,7,5]=>[6,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>[5,4,3,1,2,8,7,6]=>[4,5,6,8,7,1,2,3]=>[4,1,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[8,1,2,5,4,3,6,7]=>[1,8,7,4,5,6,3,2]=>[2,1,3,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[8,7,1,2,5,4,3,6]=>[1,2,8,7,4,5,6,3]=>[3,1,3,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>[8,1,2,5,4,3,7,6]=>[1,8,7,4,5,6,2,3]=>[2,1,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>[8,6,1,2,5,4,3,7]=>[1,3,8,7,4,5,6,2]=>[3,1,3,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[8,7,6,1,2,5,4,3]=>[1,2,3,8,7,4,5,6]=>[4,1,3]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>[8,1,2,7,3,5,4,6]=>[1,8,7,2,6,4,5,3]=>[2,1,2,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>[8,1,2,7,6,3,5,4]=>[1,8,7,2,3,6,4,5]=>[2,1,3,2]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[8,4,3,1,2,5,6,7]=>[1,5,6,8,7,4,3,2]=>[4,1,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[8,7,5,4,3,1,2,6]=>[1,2,4,5,6,8,7,3]=>[6,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[8,3,1,2,7,6,5,4]=>[1,6,8,7,2,3,4,5]=>[3,1,4]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[8,6,5,4,3,1,2,7]=>[1,3,4,5,6,8,7,2]=>[6,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>[3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[3,2,1,4,8,5,6,7]=>[6,7,8,5,1,4,3,2]=>[3,1,2,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[6,7,8,5,2,3,4,1]=>[3,1,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[3,2,1,4,8,5,7,6]=>[6,7,8,5,1,4,2,3]=>[3,1,2,2]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[6,7,8,5,1,2,3,4]=>[3,1,4]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[6,7,8,4,5,2,3,1]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[3,2,1,8,4,5,6,7]=>[6,7,8,1,5,4,3,2]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[3,2,1,8,7,4,5,6]=>[6,7,8,1,2,5,4,3]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[3,2,1,8,4,5,7,6]=>[6,7,8,1,5,4,2,3]=>[3,2,1,2]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[3,2,1,8,6,4,5,7]=>[6,7,8,1,3,5,4,2]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[3,2,1,8,7,6,4,5]=>[6,7,8,1,2,3,5,4]=>[3,4,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[3,2,1,8,4,6,5,7]=>[6,7,8,1,5,3,4,2]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[3,2,1,8,7,4,6,5]=>[6,7,8,1,2,5,3,4]=>[3,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[3,2,1,8,4,7,5,6]=>[6,7,8,1,5,2,4,3]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,6,7,8,5,4]=>[3,2,1,8,5,4,6,7]=>[6,7,8,1,4,5,3,2]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[3,2,1,8,7,5,4,6]=>[6,7,8,1,2,4,5,3]=>[3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[3,2,1,8,4,7,6,5]=>[6,7,8,1,5,2,3,4]=>[3,2,3]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[3,2,1,8,5,4,7,6]=>[6,7,8,1,4,5,2,3]=>[3,3,2]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[3,2,1,8,6,5,4,7]=>[6,7,8,1,3,4,5,2]=>[3,4,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[6,7,8,1,2,3,4,5]=>[3,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[5,8,6,7,4,3,2,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[4,1,3,2,5,6,8,7]=>[5,8,6,7,4,3,1,2]=>[2,2,1,1,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[5,8,6,7,4,2,3,1]=>[2,2,1,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>[4,1,3,2,5,8,6,7]=>[5,8,6,7,4,1,3,2]=>[2,2,1,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>[4,1,3,2,5,8,7,6]=>[5,8,6,7,4,1,2,3]=>[2,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>[4,1,3,2,6,5,7,8]=>[5,8,6,7,3,4,2,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[5,8,6,7,3,4,1,2]=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>[4,1,3,2,7,5,6,8]=>[5,8,6,7,2,4,3,1]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[4,1,3,2,8,5,6,7]=>[5,8,6,7,1,4,3,2]=>[2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[4,1,3,2,8,7,5,6]=>[5,8,6,7,1,2,4,3]=>[2,2,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>[4,1,3,2,7,6,5,8]=>[5,8,6,7,2,3,4,1]=>[2,2,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[4,1,3,2,8,5,7,6]=>[5,8,6,7,1,4,2,3]=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[4,1,3,2,8,6,5,7]=>[5,8,6,7,1,3,4,2]=>[2,2,3,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>[5,8,6,7,1,2,3,4]=>[2,2,4]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>[5,1,3,2,4,8,7,6]=>[4,8,6,7,5,1,2,3]=>[2,2,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>[2,8,6,7,5,4,3,1]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>[1,8,6,7,5,4,3,2]=>[2,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>[8,1,3,2,4,5,7,6]=>[1,8,6,7,5,4,2,3]=>[2,2,1,1,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[8,1,3,2,4,7,6,5]=>[1,8,6,7,5,2,3,4]=>[2,2,1,3]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[8,7,6,5,1,3,2,4]=>[1,2,3,4,8,6,7,5]=>[5,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>[4,5,8,6,7,3,2,1]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[5,4,1,3,2,8,7,6]=>[4,5,8,6,7,1,2,3]=>[3,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>[6,1,3,2,5,4,8,7]=>[3,8,6,7,4,5,1,2]=>[2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[7,6,1,3,2,5,4,8]=>[2,3,8,6,7,4,5,1]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[8,1,3,2,5,4,7,6]=>[1,8,6,7,4,5,2,3]=>[2,2,2,2]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>[8,7,1,3,2,6,5,4]=>[1,2,8,6,7,3,4,5]=>[3,2,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[8,1,3,2,7,4,6,5]=>[1,8,6,7,2,5,3,4]=>[2,2,2,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[7,5,4,1,3,2,6,8]=>[2,4,5,8,6,7,3,1]=>[4,2,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[7,6,5,4,1,3,2,8]=>[2,3,4,5,8,6,7,1]=>[5,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[5,7,8,6,3,4,1,2]=>[3,1,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[4,2,1,3,8,5,6,7]=>[5,7,8,6,1,4,3,2]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>[4,2,1,3,8,7,5,6]=>[5,7,8,6,1,2,4,3]=>[3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[4,2,1,3,8,5,7,6]=>[5,7,8,6,1,4,2,3]=>[3,1,2,2]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[4,2,1,3,8,6,5,7]=>[5,7,8,6,1,3,4,2]=>[3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[4,2,1,3,8,7,6,5]=>[5,7,8,6,1,2,3,4]=>[3,1,4]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[5,1,4,2,3,8,7,6]=>[4,8,5,7,6,1,2,3]=>[2,2,1,3]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[8,6,1,4,2,3,5,7]=>[1,3,8,5,7,6,4,2]=>[3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[8,1,4,2,3,7,5,6]=>[1,8,5,7,6,2,4,3]=>[2,2,1,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,2,7,6,5,8,1]=>[8,1,4,2,3,7,6,5]=>[1,8,5,7,6,2,3,4]=>[2,2,1,3]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[8,7,6,5,1,4,2,3]=>[1,2,3,4,8,5,7,6]=>[5,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[5,2,1,3,4,8,7,6]=>[4,7,8,6,5,1,2,3]=>[3,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[8,1,5,2,3,4,6,7]=>[1,8,4,7,6,5,3,2]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[8,7,6,2,1,3,4,5]=>[1,2,3,7,8,6,5,4]=>[5,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>[7,6,5,2,1,3,4,8]=>[2,3,4,7,8,6,5,1]=>[5,1,1,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[8,7,6,5,2,1,3,4]=>[1,2,3,4,7,8,6,5]=>[6,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[5,4,2,1,3,8,7,6]=>[4,5,7,8,6,1,2,3]=>[4,1,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,4,2,7,6,1,8]=>[7,6,1,5,4,2,3,8]=>[2,3,8,4,5,7,6,1]=>[3,3,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[8,4,2,1,3,5,6,7]=>[1,5,7,8,6,4,3,2]=>[4,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]=>[8,7,4,2,1,3,5,6]=>[1,2,5,7,8,6,4,3]=>[5,1,1,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[8,7,6,4,2,1,3,5]=>[1,2,3,5,7,8,6,4]=>[6,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>[6,5,4,2,1,3,8,7]=>[3,4,5,7,8,6,1,2]=>[5,1,2]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>[8,5,4,2,1,3,7,6]=>[1,4,5,7,8,6,2,3]=>[5,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[5,6,7,8,4,3,1,2]=>[4,1,1,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[5,6,7,8,4,2,3,1]=>[4,1,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,8,6,7]=>[5,6,7,8,4,1,3,2]=>[4,1,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[5,6,7,8,4,1,2,3]=>[4,1,3]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[5,6,7,8,3,4,2,1]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[5,6,7,8,3,4,1,2]=>[4,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,7,5,6,8]=>[5,6,7,8,2,4,3,1]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,8,5,6,7]=>[5,6,7,8,1,4,3,2]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,8,7,5,6]=>[5,6,7,8,1,2,4,3]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[5,6,7,8,2,3,4,1]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,8,5,7,6]=>[5,6,7,8,1,4,2,3]=>[4,2,2]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,8,6,5,7]=>[5,6,7,8,1,3,4,2]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[4,4]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[5,1,4,3,2,8,7,6]=>[4,8,5,6,7,1,2,3]=>[2,3,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,3,2,5,6,1,8,7]=>[6,1,4,3,2,5,8,7]=>[3,8,5,6,7,4,1,2]=>[2,3,1,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>[1,8,5,6,7,4,3,2]=>[2,3,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[8,1,4,3,2,7,6,5]=>[1,8,5,6,7,2,3,4]=>[2,3,3]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[8,7,6,5,1,4,3,2]=>[1,2,3,4,8,5,6,7]=>[5,3]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>[5,2,1,4,3,8,7,6]=>[4,7,8,5,6,1,2,3]=>[3,2,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>[6,1,5,2,4,3,8,7]=>[3,8,4,7,5,6,1,2]=>[2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[8,1,5,2,4,3,7,6]=>[1,8,4,7,5,6,2,3]=>[2,2,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,3,5,6,2,1,8,7]=>[6,2,1,4,3,5,8,7]=>[3,7,8,5,6,4,1,2]=>[3,2,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]=>[8,2,1,4,3,5,6,7]=>[1,7,8,5,6,4,3,2]=>[3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>[6,5,2,1,4,3,8,7]=>[3,4,7,8,5,6,1,2]=>[4,2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>[8,7,1,6,5,2,4,3]=>[1,2,8,3,4,7,5,6]=>[3,3,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[8,1,7,2,4,3,6,5]=>[1,8,2,7,5,6,3,4]=>[2,2,2,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[8,7,2,1,4,3,6,5]=>[1,2,7,8,5,6,3,4]=>[4,2,2]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>[5,3,2,1,4,8,7,6]=>[4,6,7,8,5,1,2,3]=>[4,1,3]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>[7,6,1,5,3,2,4,8]=>[2,3,8,4,6,7,5,1]=>[3,3,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[6,2,1,5,3,4,8,7]=>[3,7,8,4,6,5,1,2]=>[3,2,1,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[7,1,6,2,5,3,4,8]=>[2,8,3,7,4,6,5,1]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[6,3,2,1,4,5,8,7]=>[3,6,7,8,5,4,1,2]=>[4,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>[7,3,2,1,4,5,6,8]=>[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[8,1,7,3,2,4,5,6]=>[1,8,2,6,7,5,4,3]=>[2,3,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[8,2,1,7,3,4,5,6]=>[1,7,8,2,6,5,4,3]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[8,3,2,1,4,5,6,7]=>[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[2,3,4,6,7,8,5,1]=>[6,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[8,3,2,1,4,7,6,5]=>[1,6,7,8,5,2,3,4]=>[4,1,3]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,2,3,4,6,7,8,5]=>[7,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[4,5,6,7,8,3,2,1]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[4,5,6,7,8,3,1,2]=>[5,1,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[4,5,6,7,8,2,3,1]=>[5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[5,4,3,2,1,8,6,7]=>[4,5,6,7,8,1,3,2]=>[5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[4,5,6,7,8,1,2,3]=>[5,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[6,1,5,4,3,2,7,8]=>[3,8,4,5,6,7,2,1]=>[2,4,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[6,1,5,4,3,2,8,7]=>[3,8,4,5,6,7,1,2]=>[2,4,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>[7,1,5,4,3,2,6,8]=>[2,8,4,5,6,7,3,1]=>[2,4,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[8,1,5,4,3,2,6,7]=>[1,8,4,5,6,7,3,2]=>[2,4,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>[8,7,1,5,4,3,2,6]=>[1,2,8,4,5,6,7,3]=>[3,4,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[7,6,1,5,4,3,2,8]=>[2,3,8,4,5,6,7,1]=>[3,4,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[8,1,5,4,3,2,7,6]=>[1,8,4,5,6,7,2,3]=>[2,4,2]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[8,6,1,5,4,3,2,7]=>[1,3,8,4,5,6,7,2]=>[3,4,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[8,7,6,1,5,4,3,2]=>[1,2,3,8,4,5,6,7]=>[4,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,4,3,6,2,1,8,7]=>[6,2,1,5,4,3,8,7]=>[3,7,8,4,5,6,1,2]=>[3,3,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[8,1,7,2,6,3,5,4]=>[1,8,2,7,3,6,4,5]=>[2,2,2,2]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[8,2,1,7,3,5,4,6]=>[1,7,8,2,6,4,5,3]=>[3,2,2,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,4,3,2,1,8,7]=>[6,4,3,2,1,5,8,7]=>[3,5,6,7,8,4,1,2]=>[5,1,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[7,4,3,2,1,5,6,8]=>[2,5,6,7,8,4,3,1]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[8,4,3,2,1,5,6,7]=>[1,5,6,7,8,4,3,2]=>[5,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[7,6,4,3,2,1,5,8]=>[2,3,5,6,7,8,4,1]=>[6,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>[8,2,1,7,6,4,3,5]=>[1,7,8,2,3,5,6,4]=>[3,4,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>[7,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[3,4,5,6,7,8,2,1]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[3,4,5,6,7,8,1,2]=>[6,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[8,1,7,2,6,5,4,3]=>[1,8,2,7,3,4,5,6]=>[2,2,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>[7,3,2,1,6,5,4,8]=>[2,6,7,8,3,4,5,1]=>[4,3,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[7,4,3,2,1,6,5,8]=>[2,5,6,7,8,3,4,1]=>[5,2,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[8,1,7,4,3,2,6,5]=>[1,8,2,5,6,7,3,4]=>[2,4,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[8,3,2,1,7,4,6,5]=>[1,6,7,8,2,5,3,4]=>[4,2,2]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[8,4,3,2,1,6,5,7]=>[1,5,6,7,8,3,4,2]=>[5,2,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[8,7,4,3,2,1,6,5]=>[1,2,5,6,7,8,3,4]=>[6,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[7,5,4,3,2,1,6,8]=>[2,4,5,6,7,8,3,1]=>[6,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>[8,1,7,5,4,3,2,6]=>[1,8,2,4,5,6,7,3]=>[2,5,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[8,5,4,3,2,1,6,7]=>[1,4,5,6,7,8,3,2]=>[6,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,8,1]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[8,1,7,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[2,6]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[8,2,1,7,6,5,4,3]=>[1,7,8,2,3,4,5,6]=>[3,5]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[8,3,2,1,7,6,5,4]=>[1,6,7,8,2,3,4,5]=>[4,4]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[8,4,3,2,1,7,6,5]=>[1,5,6,7,8,2,3,4]=>[5,3]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[8,5,4,3,2,1,7,6]=>[1,4,5,6,7,8,2,3]=>[6,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[8,6,5,4,3,2,1,7]=>[1,3,4,5,6,7,8,2]=>[7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,9,1]=>[8,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[9,1,2,3,4,5,6,7,8]=>[1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,10,1]=>[9,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,6,5,4,3,2,1,9]=>[8,6,5,4,3,2,1,7,9]=>[2,4,5,6,7,8,9,3,1]=>[7,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,7,6,5,4,3,2]=>[1,9,7,6,5,4,3,2,8]=>[9,1,3,4,5,6,7,8,2]=>[1,7,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[10,1,2,3,4,5,6,7,8,9]=>[1,9]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,11,1]=>[10,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,7,6,5,4,3,2,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>[2,4,5,6,7,8,9,10,3,1]=>[8,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,8,7,5,4,3,2,1,9]=>[8,7,5,4,3,2,1,6,9]=>[2,3,5,6,7,8,9,4,1]=>[7,1,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9,10,8,7,6,5,4,3,2]=>[1,10,8,7,6,5,4,3,2,9]=>[10,1,3,4,5,6,7,8,9,2]=>[1,8,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[3,4,5,6,7,8,9,2,1]=>[7,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[3,4,5,6,7,8,9,10,1,2]=>[8,2]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[9,10,1,2,3,4,5,6,7,8]=>[2,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[3,4,5,6,7,8,9,10,2,1]=>[8,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>[1,9,7,8,6,5,4,3,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[9,6,5,4,3,2,1,7,8]=>[1,4,5,6,7,8,9,3,2]=>[7,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[9,1,8,7,6,5,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>[2,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]=>[9,2,1,8,7,6,5,4,3]=>[1,8,9,2,3,4,5,6,7]=>[3,6]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,7,6,5,4,9,3,2,1]=>[9,3,2,1,8,7,6,5,4]=>[1,7,8,9,2,3,4,5,6]=>[4,5]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]=>[9,4,3,2,1,8,7,6,5]=>[1,6,7,8,9,2,3,4,5]=>[5,4]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,7,6,9,5,4,3,2,1]=>[9,5,4,3,2,1,8,7,6]=>[1,5,6,7,8,9,2,3,4]=>[6,3]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]=>[9,6,5,4,3,2,1,8,7]=>[1,4,5,6,7,8,9,2,3]=>[7,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]=>[9,7,6,5,4,3,2,1,8]=>[1,3,4,5,6,7,8,9,2]=>[8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[1,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,7,8,9]=>[10,9,8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,6,7,8,9]=>[10,9,8,7,6,1,5,4,3,2]=>[1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,5,6,7,8,9]=>[10,9,8,7,1,6,5,4,3,2]=>[1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,4,5,6,7,8,9]=>[10,9,8,1,7,6,5,4,3,2]=>[1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,3,4,5,6,7,8,9]=>[10,9,1,8,7,6,5,4,3,2]=>[1,1,2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[10,1,3,2,4,5,6,7,8,9]=>[1,10,8,9,7,6,5,4,3,2]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[9,7,8,5,6,3,4,1,2]=>[1,2,2,2,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[8,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[8,9,6,7,4,5,2,3,1]=>[2,2,2,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[7,8,9,6,5,4,3,2,1]=>[3,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[6,7,8,9,5,4,3,2,1]=>[4,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,6,7,8,9,4,3,2,1]=>[5,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[4,5,6,7,8,9,3,2,1]=>[6,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,2,3,1]=>[1,2,2,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[9,10,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,6,5,4,3,10,9,8,7]=>[9,10,5,6,7,8,1,2,3,4]=>[2,4,4]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[9,10,3,4,5,6,7,8,1,2]=>[2,6,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[8,9,10,7,6,5,4,3,2,1]=>[3,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[7,8,9,10,6,5,4,3,2,1]=>[4,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[7,8,9,10,5,6,3,4,1,2]=>[4,2,2,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,6,5,10,9,8,7]=>[4,3,2,1,6,5,10,9,8,7]=>[7,8,9,10,5,6,1,2,3,4]=>[4,2,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,8,7,6,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[7,8,9,10,3,4,5,6,1,2]=>[4,4,2]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[7,8,9,10,1,2,3,4,5,6]=>[4,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[6,7,8,9,10,5,4,3,2,1]=>[5,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[5,6,7,8,9,10,4,3,2,1]=>[6,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[5,6,7,8,9,10,1,2,3,4]=>[6,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[4,5,6,7,8,9,10,3,2,1]=>[7,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[3,9,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[2,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[2,10,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[10,7,6,5,4,3,2,1,9,8]=>[1,4,5,6,7,8,9,10,2,3]=>[8,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[10,1,9,8,7,6,5,4,3,2]=>[1,10,2,3,4,5,6,7,8,9]=>[2,8]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,3,4,5,6,7,8,9,10,2]=>[9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[10,2,1,9,8,7,6,5,4,3]=>[1,9,10,2,3,4,5,6,7,8]=>[3,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[10,3,2,1,9,8,7,6,5,4]=>[1,8,9,10,2,3,4,5,6,7]=>[4,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[10,4,3,2,1,9,8,7,6,5]=>[1,7,8,9,10,2,3,4,5,6]=>[5,5]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[10,5,4,3,2,1,9,8,7,6]=>[1,6,7,8,9,10,2,3,4,5]=>[6,4]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[10,6,5,4,3,2,1,9,8,7]=>[1,5,6,7,8,9,10,2,3,4]=>[7,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[3,1,2,5,4,7,6,9,8]=>[7,9,8,5,6,3,4,1,2]=>[2,1,2,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,1,2,5,4,7,6,9,8,10]=>[8,10,9,6,7,4,5,2,3,1]=>[2,1,2,2,2,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[10,5,4,3,2,1,6,7,8,9]=>[1,6,7,8,9,10,5,4,3,2]=>[6,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[3,4,5,6,7,8,9,10,11,12,1,2]=>[10,2]
Map
to 312-avoiding permutation
Description
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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