Identifier
Mp00090:
Permutations
—cycle-as-one-line notation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00069: Permutations —complement⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Images
=>
Cc0005;cc-rep-4
[1]=>[1]=>[1]=>[1]=>[1,0]
[1,2]=>[1,2]=>[2,1]=>[2,1]=>[1,1,0,0]
[2,1]=>[1,2]=>[2,1]=>[2,1]=>[1,1,0,0]
[1,2,3]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0]
[1,3,2]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0]
[2,1,3]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0]
[2,3,1]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0]
[3,1,2]=>[1,3,2]=>[3,1,2]=>[3,2,1]=>[1,1,1,0,0,0]
[3,2,1]=>[1,3,2]=>[3,1,2]=>[3,2,1]=>[1,1,1,0,0,0]
[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[1,2,4,3]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[1,3,2,4]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[1,3,4,2]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[1,4,2,3]=>[1,2,4,3]=>[4,3,1,2]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[1,4,3,2]=>[1,2,4,3]=>[4,3,1,2]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[2,1,3,4]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[2,1,4,3]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[2,3,1,4]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[2,3,4,1]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[2,4,1,3]=>[1,2,4,3]=>[4,3,1,2]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[2,4,3,1]=>[1,2,4,3]=>[4,3,1,2]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[3,1,2,4]=>[1,3,2,4]=>[4,2,3,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[3,1,4,2]=>[1,3,4,2]=>[4,2,1,3]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[3,2,1,4]=>[1,3,2,4]=>[4,2,3,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[3,2,4,1]=>[1,3,4,2]=>[4,2,1,3]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[3,4,1,2]=>[1,3,2,4]=>[4,2,3,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[3,4,2,1]=>[1,3,2,4]=>[4,2,3,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[4,1,2,3]=>[1,4,3,2]=>[4,1,2,3]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[4,1,3,2]=>[1,4,2,3]=>[4,1,3,2]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[4,2,1,3]=>[1,4,3,2]=>[4,1,2,3]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[4,2,3,1]=>[1,4,2,3]=>[4,1,3,2]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[4,3,1,2]=>[1,4,2,3]=>[4,1,3,2]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[4,3,2,1]=>[1,4,2,3]=>[4,1,3,2]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[1,2,3,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,3,5,4]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,4,3,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,4,5,3]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,5,3,4]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,5,4,3]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,2,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,2,5,4]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,4,2,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,4,5,2]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,5,2,4]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,5,4,2]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,2,3,5]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,2,5,3]=>[1,2,4,5,3]=>[5,4,2,1,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,3,2,5]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,3,5,2]=>[1,2,4,5,3]=>[5,4,2,1,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,5,2,3]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,5,3,2]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,2,3,4]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,2,4,3]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,3,2,4]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,3,4,2]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,4,2,3]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,4,3,2]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,3,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,3,5,4]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,4,3,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,4,5,3]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,5,3,4]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,5,4,3]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,1,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,1,5,4]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,4,1,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,4,5,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,5,1,4]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,5,4,1]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,1,3,5]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,1,5,3]=>[1,2,4,5,3]=>[5,4,2,1,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,3,1,5]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,3,5,1]=>[1,2,4,5,3]=>[5,4,2,1,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,5,1,3]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,5,3,1]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,1,3,4]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,1,4,3]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,3,1,4]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,3,4,1]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,4,1,3]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,4,3,1]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,2,4,5]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,2,5,4]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,4,2,5]=>[1,3,4,2,5]=>[5,3,2,4,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,4,5,2]=>[1,3,4,5,2]=>[5,3,2,1,4]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,5,2,4]=>[1,3,5,4,2]=>[5,3,1,2,4]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,5,4,2]=>[1,3,5,2,4]=>[5,3,1,4,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,1,4,5]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,1,5,4]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,4,1,5]=>[1,3,4,2,5]=>[5,3,2,4,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,4,5,1]=>[1,3,4,5,2]=>[5,3,2,1,4]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,5,1,4]=>[1,3,5,4,2]=>[5,3,1,2,4]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,5,4,1]=>[1,3,5,2,4]=>[5,3,1,4,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,1,2,5]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,1,5,2]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,2,1,5]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,2,5,1]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,5,1,2]=>[1,3,5,2,4]=>[5,3,1,4,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,5,2,1]=>[1,3,5,2,4]=>[5,3,1,4,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,1,2,4]=>[1,3,2,5,4]=>[5,3,4,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,1,4,2]=>[1,3,2,5,4]=>[5,3,4,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,2,1,4]=>[1,3,2,5,4]=>[5,3,4,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,2,4,1]=>[1,3,2,5,4]=>[5,3,4,1,2]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,4,1,2]=>[1,3,4,2,5]=>[5,3,2,4,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,4,2,1]=>[1,3,4,2,5]=>[5,3,2,4,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,2,3,5]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,2,5,3]=>[1,4,5,3,2]=>[5,2,1,3,4]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,3,2,5]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,3,5,2]=>[1,4,5,2,3]=>[5,2,1,4,3]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,5,2,3]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,5,3,2]=>[1,4,3,5,2]=>[5,2,3,1,4]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,1,3,5]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,1,5,3]=>[1,4,5,3,2]=>[5,2,1,3,4]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,3,1,5]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,3,5,1]=>[1,4,5,2,3]=>[5,2,1,4,3]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,5,1,3]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,5,3,1]=>[1,4,3,5,2]=>[5,2,3,1,4]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,1,2,5]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,1,5,2]=>[1,4,5,2,3]=>[5,2,1,4,3]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,2,1,5]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,2,5,1]=>[1,4,5,2,3]=>[5,2,1,4,3]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,5,1,2]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,5,2,1]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,1,2,3]=>[1,4,2,5,3]=>[5,2,4,1,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,1,3,2]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,2,1,3]=>[1,4,2,5,3]=>[5,2,4,1,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,2,3,1]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,3,1,2]=>[1,4,2,5,3]=>[5,2,4,1,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,3,2,1]=>[1,4,2,5,3]=>[5,2,4,1,3]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,2,3,4]=>[1,5,4,3,2]=>[5,1,2,3,4]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,2,4,3]=>[1,5,3,2,4]=>[5,1,3,4,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,3,2,4]=>[1,5,4,2,3]=>[5,1,2,4,3]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,3,4,2]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,4,2,3]=>[1,5,3,4,2]=>[5,1,3,2,4]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,4,3,2]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,1,3,4]=>[1,5,4,3,2]=>[5,1,2,3,4]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,1,4,3]=>[1,5,3,2,4]=>[5,1,3,4,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,3,1,4]=>[1,5,4,2,3]=>[5,1,2,4,3]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,3,4,1]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,4,1,3]=>[1,5,3,4,2]=>[5,1,3,2,4]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,4,3,1]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,1,2,4]=>[1,5,4,2,3]=>[5,1,2,4,3]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,1,4,2]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,2,1,4]=>[1,5,4,2,3]=>[5,1,2,4,3]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,2,4,1]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,4,1,2]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,4,2,1]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,1,2,3]=>[1,5,3,2,4]=>[5,1,3,4,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,1,3,2]=>[1,5,2,4,3]=>[5,1,4,2,3]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,2,1,3]=>[1,5,3,2,4]=>[5,1,3,4,2]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,2,3,1]=>[1,5,2,4,3]=>[5,1,4,2,3]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,3,1,2]=>[1,5,2,4,3]=>[5,1,4,2,3]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,3,2,1]=>[1,5,2,4,3]=>[5,1,4,2,3]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,4,6,5]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,5,4,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,5,6,4]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,6,4,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,6,5,4]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,3,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,3,6,5]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,5,3,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,5,6,3]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,6,3,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,6,5,3]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,3,4,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,3,6,4]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,4,3,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,4,6,3]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,6,3,4]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,6,4,3]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,3,4,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,3,5,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,4,3,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,4,5,3]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,5,3,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,5,4,3]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,4,6,5]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,5,4,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,5,6,4]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,6,4,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,6,5,4]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,2,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,2,6,5]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,5,2,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,5,6,2]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,6,2,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,6,5,2]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,2,4,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,2,6,4]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,4,2,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,4,6,2]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,6,2,4]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,6,4,2]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,2,4,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,2,5,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,4,2,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,4,5,2]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,5,2,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,5,4,2]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,3,5,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,3,6,5]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,5,3,6]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,5,6,3]=>[1,2,4,5,6,3]=>[6,5,3,2,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,6,3,5]=>[1,2,4,6,5,3]=>[6,5,3,1,2,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,6,5,3]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,2,5,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,2,6,5]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,5,2,6]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,5,6,2]=>[1,2,4,5,6,3]=>[6,5,3,2,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,6,2,5]=>[1,2,4,6,5,3]=>[6,5,3,1,2,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,6,5,2]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,2,3,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,2,6,3]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,3,2,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,3,6,2]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,6,2,3]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,6,3,2]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,2,3,5]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,2,5,3]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,3,2,5]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,3,5,2]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,5,2,3]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,5,3,2]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,3,4,6]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,3,6,4]=>[1,2,5,6,4,3]=>[6,5,2,1,3,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,4,3,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,4,6,3]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,6,3,4]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,6,4,3]=>[1,2,5,4,6,3]=>[6,5,2,3,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,2,4,6]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,2,6,4]=>[1,2,5,6,4,3]=>[6,5,2,1,3,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,4,2,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,4,6,2]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,6,2,4]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,6,4,2]=>[1,2,5,4,6,3]=>[6,5,2,3,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,2,3,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,2,6,3]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,3,2,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,3,6,2]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,6,2,3]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,6,3,2]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,2,3,4]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,2,4,3]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,3,2,4]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,3,4,2]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,4,2,3]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,4,3,2]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,3,4,5]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,3,5,4]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,4,3,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,4,5,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,5,3,4]=>[1,2,6,4,5,3]=>[6,5,1,3,2,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,5,4,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,2,4,5]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,2,5,4]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,4,2,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,4,5,2]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,5,2,4]=>[1,2,6,4,5,3]=>[6,5,1,3,2,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,5,4,2]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,2,3,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,2,5,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,3,2,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,3,5,2]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,5,2,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,5,3,2]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,2,3,4]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,2,4,3]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,3,2,4]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,3,4,2]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,4,2,3]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,4,3,2]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,4,6,5]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,5,4,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,5,6,4]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,6,4,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,6,5,4]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,6,5]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,5,3,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,5,6,3]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,6,3,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,6,5,3]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,3,4,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,3,6,4]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,4,3,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,4,6,3]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,6,3,4]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,6,4,3]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,3,4,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,3,5,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,4,3,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,4,5,3]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,5,3,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,5,4,3]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,4,6,5]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,5,4,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,5,6,4]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,6,4,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,6,5,4]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,1,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,1,6,5]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,1,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,6,1,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,6,5,1]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,1,4,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,1,6,4]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,4,1,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,4,6,1]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,6,1,4]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,6,4,1]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,1,4,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,1,5,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,4,1,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,4,5,1]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,5,1,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,5,4,1]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,3,5,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,3,6,5]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,5,3,6]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,5,6,3]=>[1,2,4,5,6,3]=>[6,5,3,2,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,6,3,5]=>[1,2,4,6,5,3]=>[6,5,3,1,2,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,6,5,3]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,1,5,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,1,6,5]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,5,1,6]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,5,6,1]=>[1,2,4,5,6,3]=>[6,5,3,2,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,6,1,5]=>[1,2,4,6,5,3]=>[6,5,3,1,2,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,6,5,1]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,1,3,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,1,6,3]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,3,1,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,3,6,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,6,1,3]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,6,3,1]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,1,3,5]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,1,5,3]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,3,1,5]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,3,5,1]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,5,1,3]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,5,3,1]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,3,4,6]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,3,6,4]=>[1,2,5,6,4,3]=>[6,5,2,1,3,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,4,3,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,4,6,3]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,6,3,4]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,6,4,3]=>[1,2,5,4,6,3]=>[6,5,2,3,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,1,4,6]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,1,6,4]=>[1,2,5,6,4,3]=>[6,5,2,1,3,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,4,1,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,4,6,1]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,6,1,4]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,6,4,1]=>[1,2,5,4,6,3]=>[6,5,2,3,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,1,3,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,1,6,3]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,3,1,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,3,6,1]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,6,1,3]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,6,3,1]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,1,3,4]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,1,4,3]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,3,1,4]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,3,4,1]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,4,1,3]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,4,3,1]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,3,4,5]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,3,5,4]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,4,3,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,4,5,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,5,3,4]=>[1,2,6,4,5,3]=>[6,5,1,3,2,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,5,4,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,1,4,5]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,1,5,4]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,4,1,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,4,5,1]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,5,1,4]=>[1,2,6,4,5,3]=>[6,5,1,3,2,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,5,4,1]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,1,3,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,1,5,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,3,1,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,3,5,1]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,5,1,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,5,3,1]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,1,3,4]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,1,4,3]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,3,1,4]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,3,4,1]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,4,1,3]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,4,3,1]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,4,6,5]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,5,4,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,5,6,4]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,6,4,5]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,6,5,4]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,2,5,6]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,2,6,5]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,5,2,6]=>[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,5,6,2]=>[1,3,4,5,6,2]=>[6,4,3,2,1,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,6,2,5]=>[1,3,4,6,5,2]=>[6,4,3,1,2,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,6,5,2]=>[1,3,4,6,2,5]=>[6,4,3,1,5,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,2,4,6]=>[1,3,5,4,2,6]=>[6,4,2,3,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,2,6,4]=>[1,3,5,6,4,2]=>[6,4,2,1,3,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,4,2,6]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,4,6,2]=>[1,3,5,6,2,4]=>[6,4,2,1,5,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,6,2,4]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,6,4,2]=>[1,3,5,4,6,2]=>[6,4,2,3,1,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,2,4,5]=>[1,3,6,5,4,2]=>[6,4,1,2,3,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,2,5,4]=>[1,3,6,4,2,5]=>[6,4,1,3,5,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,4,2,5]=>[1,3,6,5,2,4]=>[6,4,1,2,5,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,4,5,2]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,5,2,4]=>[1,3,6,4,5,2]=>[6,4,1,3,2,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,5,4,2]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,4,5,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,4,6,5]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,5,4,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,5,6,4]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,6,4,5]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,6,5,4]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,1,5,6]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,1,6,5]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,5,1,6]=>[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,5,6,1]=>[1,3,4,5,6,2]=>[6,4,3,2,1,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,6,1,5]=>[1,3,4,6,5,2]=>[6,4,3,1,2,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,6,5,1]=>[1,3,4,6,2,5]=>[6,4,3,1,5,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,1,4,6]=>[1,3,5,4,2,6]=>[6,4,2,3,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,1,6,4]=>[1,3,5,6,4,2]=>[6,4,2,1,3,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,4,1,6]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,4,6,1]=>[1,3,5,6,2,4]=>[6,4,2,1,5,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,6,1,4]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,6,4,1]=>[1,3,5,4,6,2]=>[6,4,2,3,1,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,1,4,5]=>[1,3,6,5,4,2]=>[6,4,1,2,3,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,1,5,4]=>[1,3,6,4,2,5]=>[6,4,1,3,5,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,4,1,5]=>[1,3,6,5,2,4]=>[6,4,1,2,5,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,4,5,1]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,5,1,4]=>[1,3,6,4,5,2]=>[6,4,1,3,2,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,5,4,1]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,2,5,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,2,6,5]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,5,2,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,5,6,2]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,6,2,5]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,6,5,2]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,1,5,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,1,6,5]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,5,1,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,5,6,1]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,6,1,5]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,6,5,1]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,1,2,6]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,1,6,2]=>[1,3,5,6,2,4]=>[6,4,2,1,5,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,2,1,6]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,2,6,1]=>[1,3,5,6,2,4]=>[6,4,2,1,5,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,6,1,2]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,6,2,1]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,1,2,5]=>[1,3,6,5,2,4]=>[6,4,1,2,5,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,1,5,2]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,2,1,5]=>[1,3,6,5,2,4]=>[6,4,1,2,5,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,2,5,1]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,5,1,2]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,5,2,1]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,2,4,6]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,2,6,4]=>[1,3,2,5,6,4]=>[6,4,5,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,4,2,6]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,4,6,2]=>[1,3,2,5,6,4]=>[6,4,5,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,6,2,4]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,6,4,2]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,1,4,6]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,1,6,4]=>[1,3,2,5,6,4]=>[6,4,5,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,4,1,6]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,4,6,1]=>[1,3,2,5,6,4]=>[6,4,5,2,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,6,1,4]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,6,4,1]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,1,2,6]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,1,6,2]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,2,1,6]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,2,6,1]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,6,1,2]=>[1,3,4,6,2,5]=>[6,4,3,1,5,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,6,2,1]=>[1,3,4,6,2,5]=>[6,4,3,1,5,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,1,2,4]=>[1,3,6,4,2,5]=>[6,4,1,3,5,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,1,4,2]=>[1,3,6,2,5,4]=>[6,4,1,5,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,2,1,4]=>[1,3,6,4,2,5]=>[6,4,1,3,5,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,2,4,1]=>[1,3,6,2,5,4]=>[6,4,1,5,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,4,1,2]=>[1,3,6,2,5,4]=>[6,4,1,5,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,4,2,1]=>[1,3,6,2,5,4]=>[6,4,1,5,2,3]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,2,4,5]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,2,5,4]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,4,2,5]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,4,5,2]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,5,2,4]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,5,4,2]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,1,4,5]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,1,5,4]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,4,1,5]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,4,5,1]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,5,1,4]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,5,4,1]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,1,2,5]=>[1,3,4,2,6,5]=>[6,4,3,5,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,1,5,2]=>[1,3,4,2,6,5]=>[6,4,3,5,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,2,1,5]=>[1,3,4,2,6,5]=>[6,4,3,5,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,2,5,1]=>[1,3,4,2,6,5]=>[6,4,3,5,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,5,1,2]=>[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,5,2,1]=>[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,1,2,4]=>[1,3,5,2,6,4]=>[6,4,2,5,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,1,4,2]=>[1,3,5,4,2,6]=>[6,4,2,3,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,2,1,4]=>[1,3,5,2,6,4]=>[6,4,2,5,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,2,4,1]=>[1,3,5,4,2,6]=>[6,4,2,3,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,4,1,2]=>[1,3,5,2,6,4]=>[6,4,2,5,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,4,2,1]=>[1,3,5,2,6,4]=>[6,4,2,5,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,3,5,6]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,3,6,5]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,5,3,6]=>[1,4,5,3,2,6]=>[6,3,2,4,5,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,5,6,3]=>[1,4,5,6,3,2]=>[6,3,2,1,4,5]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,6,3,5]=>[1,4,6,5,3,2]=>[6,3,1,2,4,5]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,6,5,3]=>[1,4,6,3,2,5]=>[6,3,1,4,5,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,5,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,6,5]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,5,2,6]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,5,6,2]=>[1,4,5,6,2,3]=>[6,3,2,1,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,6,2,5]=>[1,4,6,5,2,3]=>[6,3,1,2,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,6,5,2]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,2,3,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,2,6,3]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,3,2,6]=>[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,3,6,2]=>[1,4,3,5,6,2]=>[6,3,4,2,1,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,6,2,3]=>[1,4,6,3,5,2]=>[6,3,1,4,2,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,6,3,2]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,2,3,5]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,2,5,3]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,3,2,5]=>[1,4,3,6,5,2]=>[6,3,4,1,2,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,3,5,2]=>[1,4,3,6,2,5]=>[6,3,4,1,5,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,5,2,3]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,5,3,2]=>[1,4,5,3,6,2]=>[6,3,2,4,1,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,3,5,6]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,3,6,5]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,5,3,6]=>[1,4,5,3,2,6]=>[6,3,2,4,5,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,5,6,3]=>[1,4,5,6,3,2]=>[6,3,2,1,4,5]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,6,3,5]=>[1,4,6,5,3,2]=>[6,3,1,2,4,5]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,6,5,3]=>[1,4,6,3,2,5]=>[6,3,1,4,5,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,1,5,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,1,6,5]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,5,1,6]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,5,6,1]=>[1,4,5,6,2,3]=>[6,3,2,1,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,6,1,5]=>[1,4,6,5,2,3]=>[6,3,1,2,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,6,5,1]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,1,3,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,1,6,3]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,3,1,6]=>[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,3,6,1]=>[1,4,3,5,6,2]=>[6,3,4,2,1,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,6,1,3]=>[1,4,6,3,5,2]=>[6,3,1,4,2,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,6,3,1]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,1,3,5]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,1,5,3]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,3,1,5]=>[1,4,3,6,5,2]=>[6,3,4,1,2,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,3,5,1]=>[1,4,3,6,2,5]=>[6,3,4,1,5,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,5,1,3]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,5,3,1]=>[1,4,5,3,6,2]=>[6,3,2,4,1,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,2,5,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,2,6,5]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,5,2,6]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,5,6,2]=>[1,4,5,6,2,3]=>[6,3,2,1,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,6,2,5]=>[1,4,6,5,2,3]=>[6,3,1,2,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,6,5,2]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,1,5,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,1,6,5]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,5,1,6]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,5,6,1]=>[1,4,5,6,2,3]=>[6,3,2,1,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,6,1,5]=>[1,4,6,5,2,3]=>[6,3,1,2,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,6,5,1]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,1,2,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,1,6,2]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,2,1,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,2,6,1]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,6,1,2]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,6,2,1]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,1,2,5]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,1,5,2]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,2,1,5]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,2,5,1]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,5,1,2]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,5,2,1]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,2,3,6]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,2,6,3]=>[1,4,2,5,6,3]=>[6,3,5,2,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,3,2,6]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,3,6,2]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,6,2,3]=>[1,4,6,3,2,5]=>[6,3,1,4,5,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,6,3,2]=>[1,4,6,2,5,3]=>[6,3,1,5,2,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,1,3,6]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,1,6,3]=>[1,4,2,5,6,3]=>[6,3,5,2,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,3,1,6]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,3,6,1]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,6,1,3]=>[1,4,6,3,2,5]=>[6,3,1,4,5,2]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,6,3,1]=>[1,4,6,2,5,3]=>[6,3,1,5,2,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,1,2,6]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,1,6,2]=>[1,4,2,5,6,3]=>[6,3,5,2,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,2,1,6]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,2,6,1]=>[1,4,2,5,6,3]=>[6,3,5,2,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,6,1,2]=>[1,4,6,2,5,3]=>[6,3,1,5,2,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,6,2,1]=>[1,4,6,2,5,3]=>[6,3,1,5,2,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,1,2,3]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,1,3,2]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,2,1,3]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,2,3,1]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,3,1,2]=>[1,4,3,6,2,5]=>[6,3,4,1,5,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,3,2,1]=>[1,4,3,6,2,5]=>[6,3,4,1,5,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,2,3,5]=>[1,4,2,6,5,3]=>[6,3,5,1,2,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,2,5,3]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,3,2,5]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,3,5,2]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,5,2,3]=>[1,4,5,2,6,3]=>[6,3,2,5,1,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,5,3,2]=>[1,4,5,3,2,6]=>[6,3,2,4,5,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,1,3,5]=>[1,4,2,6,5,3]=>[6,3,5,1,2,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,1,5,3]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,3,1,5]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,3,5,1]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,5,1,3]=>[1,4,5,2,6,3]=>[6,3,2,5,1,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,5,3,1]=>[1,4,5,3,2,6]=>[6,3,2,4,5,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,1,2,5]=>[1,4,2,6,5,3]=>[6,3,5,1,2,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,1,5,2]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,2,1,5]=>[1,4,2,6,5,3]=>[6,3,5,1,2,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,2,5,1]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,5,1,2]=>[1,4,5,2,6,3]=>[6,3,2,5,1,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,5,2,1]=>[1,4,5,2,6,3]=>[6,3,2,5,1,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,1,2,3]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,1,3,2]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,2,1,3]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,2,3,1]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,3,1,2]=>[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,3,2,1]=>[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,3,4,6]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,3,6,4]=>[1,5,6,4,3,2]=>[6,2,1,3,4,5]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,4,3,6]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,4,6,3]=>[1,5,6,3,2,4]=>[6,2,1,4,5,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,6,3,4]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,6,4,3]=>[1,5,4,6,3,2]=>[6,2,3,1,4,5]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,2,4,6]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,2,6,4]=>[1,5,6,4,2,3]=>[6,2,1,3,5,4]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,4,2,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,4,6,2]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,6,2,4]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,6,4,2]=>[1,5,4,6,2,3]=>[6,2,3,1,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,2,3,6]=>[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,2,6,3]=>[1,5,6,3,4,2]=>[6,2,1,4,3,5]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,3,2,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,3,6,2]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,6,2,3]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,6,3,2]=>[1,5,3,4,6,2]=>[6,2,4,3,1,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,2,3,4]=>[1,5,3,6,4,2]=>[6,2,4,1,3,5]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,2,4,3]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,3,2,4]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,3,4,2]=>[1,5,4,3,6,2]=>[6,2,3,4,1,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,4,2,3]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,4,3,2]=>[1,5,3,6,2,4]=>[6,2,4,1,5,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,3,4,6]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,3,6,4]=>[1,5,6,4,3,2]=>[6,2,1,3,4,5]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,4,3,6]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,4,6,3]=>[1,5,6,3,2,4]=>[6,2,1,4,5,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,6,3,4]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,6,4,3]=>[1,5,4,6,3,2]=>[6,2,3,1,4,5]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,1,4,6]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,1,6,4]=>[1,5,6,4,2,3]=>[6,2,1,3,5,4]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,4,1,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,4,6,1]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,6,1,4]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,6,4,1]=>[1,5,4,6,2,3]=>[6,2,3,1,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,1,3,6]=>[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,1,6,3]=>[1,5,6,3,4,2]=>[6,2,1,4,3,5]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,3,1,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,3,6,1]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,6,1,3]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,6,3,1]=>[1,5,3,4,6,2]=>[6,2,4,3,1,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,1,3,4]=>[1,5,3,6,4,2]=>[6,2,4,1,3,5]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,1,4,3]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,3,1,4]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,3,4,1]=>[1,5,4,3,6,2]=>[6,2,3,4,1,5]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,4,1,3]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,4,3,1]=>[1,5,3,6,2,4]=>[6,2,4,1,5,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,2,4,6]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,2,6,4]=>[1,5,6,4,2,3]=>[6,2,1,3,5,4]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,4,2,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,4,6,2]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,6,2,4]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,6,4,2]=>[1,5,4,6,2,3]=>[6,2,3,1,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,1,4,6]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,1,6,4]=>[1,5,6,4,2,3]=>[6,2,1,3,5,4]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,4,1,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,4,6,1]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,6,1,4]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,6,4,1]=>[1,5,4,6,2,3]=>[6,2,3,1,5,4]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,1,2,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,1,6,2]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,2,1,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,2,6,1]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,6,1,2]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,6,2,1]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,1,2,4]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,1,4,2]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,2,1,4]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,2,4,1]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,4,1,2]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,4,2,1]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,2,3,6]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,2,6,3]=>[1,5,6,3,2,4]=>[6,2,1,4,5,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,3,2,6]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,3,6,2]=>[1,5,6,2,4,3]=>[6,2,1,5,3,4]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,6,2,3]=>[1,5,2,4,6,3]=>[6,2,5,3,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,6,3,2]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,1,3,6]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,1,6,3]=>[1,5,6,3,2,4]=>[6,2,1,4,5,3]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,3,1,6]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,3,6,1]=>[1,5,6,2,4,3]=>[6,2,1,5,3,4]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,6,1,3]=>[1,5,2,4,6,3]=>[6,2,5,3,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,6,3,1]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,1,2,6]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,1,6,2]=>[1,5,6,2,4,3]=>[6,2,1,5,3,4]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,2,1,6]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,2,6,1]=>[1,5,6,2,4,3]=>[6,2,1,5,3,4]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,6,1,2]=>[1,5,2,4,6,3]=>[6,2,5,3,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,6,2,1]=>[1,5,2,4,6,3]=>[6,2,5,3,1,4]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,1,2,3]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,1,3,2]=>[1,5,3,6,2,4]=>[6,2,4,1,5,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,2,1,3]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,2,3,1]=>[1,5,3,6,2,4]=>[6,2,4,1,5,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,3,1,2]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,3,2,1]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,2,3,4]=>[1,5,3,2,6,4]=>[6,2,4,5,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,2,4,3]=>[1,5,4,2,6,3]=>[6,2,3,5,1,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,3,2,4]=>[1,5,2,6,4,3]=>[6,2,5,1,3,4]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,3,4,2]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,4,2,3]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,4,3,2]=>[1,5,3,2,6,4]=>[6,2,4,5,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,1,3,4]=>[1,5,3,2,6,4]=>[6,2,4,5,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,1,4,3]=>[1,5,4,2,6,3]=>[6,2,3,5,1,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,3,1,4]=>[1,5,2,6,4,3]=>[6,2,5,1,3,4]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,3,4,1]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,4,1,3]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,4,3,1]=>[1,5,3,2,6,4]=>[6,2,4,5,1,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,1,2,4]=>[1,5,2,6,4,3]=>[6,2,5,1,3,4]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,1,4,2]=>[1,5,4,2,6,3]=>[6,2,3,5,1,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,2,1,4]=>[1,5,2,6,4,3]=>[6,2,5,1,3,4]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,2,4,1]=>[1,5,4,2,6,3]=>[6,2,3,5,1,4]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,4,1,2]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,4,2,1]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,1,2,3]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,1,3,2]=>[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,2,1,3]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,2,3,1]=>[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,3,1,2]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,3,2,1]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,3,5,4]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,4,3,5]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,4,5,3]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,5,3,4]=>[1,6,4,5,3,2]=>[6,1,3,2,4,5]=>[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,5,4,3]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,4,5]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,5,4]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,4,2,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,4,5,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,5,2,4]=>[1,6,4,5,2,3]=>[6,1,3,2,5,4]=>[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,5,4,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,2,3,5]=>[1,6,5,3,4,2]=>[6,1,2,4,3,5]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,2,5,3]=>[1,6,3,4,2,5]=>[6,1,4,3,5,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,3,2,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,3,5,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,5,2,3]=>[1,6,3,4,5,2]=>[6,1,4,3,2,5]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,5,3,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,2,3,4]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,2,4,3]=>[1,6,3,5,4,2]=>[6,1,4,2,3,5]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,3,2,4]=>[1,6,4,3,5,2]=>[6,1,3,4,2,5]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,3,4,2]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,4,2,3]=>[1,6,3,5,2,4]=>[6,1,4,2,5,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,4,3,2]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,3,4,5]=>[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,3,5,4]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,4,3,5]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,4,5,3]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,5,3,4]=>[1,6,4,5,3,2]=>[6,1,3,2,4,5]=>[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,5,4,3]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,1,4,5]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,1,5,4]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,4,1,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,4,5,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,5,1,4]=>[1,6,4,5,2,3]=>[6,1,3,2,5,4]=>[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,5,4,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,1,3,5]=>[1,6,5,3,4,2]=>[6,1,2,4,3,5]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,1,5,3]=>[1,6,3,4,2,5]=>[6,1,4,3,5,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,3,1,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,3,5,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,5,1,3]=>[1,6,3,4,5,2]=>[6,1,4,3,2,5]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,5,3,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,1,3,4]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,1,4,3]=>[1,6,3,5,4,2]=>[6,1,4,2,3,5]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,3,1,4]=>[1,6,4,3,5,2]=>[6,1,3,4,2,5]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,3,4,1]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,4,1,3]=>[1,6,3,5,2,4]=>[6,1,4,2,5,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,4,3,1]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,2,4,5]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,2,5,4]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,4,2,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,4,5,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,5,2,4]=>[1,6,4,5,2,3]=>[6,1,3,2,5,4]=>[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,5,4,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,1,4,5]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,1,5,4]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,4,1,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,4,5,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,5,1,4]=>[1,6,4,5,2,3]=>[6,1,3,2,5,4]=>[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,5,4,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,1,2,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,1,5,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,2,1,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,2,5,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,5,1,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,5,2,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,1,2,4]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,1,4,2]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,2,1,4]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,2,4,1]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,4,1,2]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,4,2,1]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,2,3,5]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,2,5,3]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,3,2,5]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,3,5,2]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,5,2,3]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,5,3,2]=>[1,6,2,4,5,3]=>[6,1,5,3,2,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,1,3,5]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,1,5,3]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,3,1,5]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,3,5,1]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,5,1,3]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,5,3,1]=>[1,6,2,4,5,3]=>[6,1,5,3,2,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,1,2,5]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,1,5,2]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,2,1,5]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,2,5,1]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,5,1,2]=>[1,6,2,4,5,3]=>[6,1,5,3,2,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,5,2,1]=>[1,6,2,4,5,3]=>[6,1,5,3,2,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,1,2,3]=>[1,6,3,5,2,4]=>[6,1,4,2,5,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,1,3,2]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,2,1,3]=>[1,6,3,5,2,4]=>[6,1,4,2,5,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,2,3,1]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,3,1,2]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,3,2,1]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,2,3,4]=>[1,6,4,2,5,3]=>[6,1,3,5,2,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,2,4,3]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,3,2,4]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,3,4,2]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,4,2,3]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,4,3,2]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,1,3,4]=>[1,6,4,2,5,3]=>[6,1,3,5,2,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,1,4,3]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,3,1,4]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,3,4,1]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,4,1,3]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,4,3,1]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,1,2,4]=>[1,6,4,2,5,3]=>[6,1,3,5,2,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,1,4,2]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,2,1,4]=>[1,6,4,2,5,3]=>[6,1,3,5,2,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,2,4,1]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,4,1,2]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,4,2,1]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,1,2,3]=>[1,6,3,4,2,5]=>[6,1,4,3,5,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,1,3,2]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,2,1,3]=>[1,6,3,4,2,5]=>[6,1,4,3,5,2]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,2,3,1]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,3,1,2]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,3,2,1]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,5,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,6,5,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,6,7,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,7,5,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,7,6,5]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,4,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,4,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,6,4,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,6,7,4]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,7,4,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,7,6,4]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,4,5,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,4,7,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,5,4,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,5,7,4]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,7,4,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,7,5,4]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,4,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,4,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,5,4,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,5,6,4]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,6,4,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,6,5,4]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,5,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,6,5,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,6,7,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,7,5,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,7,6,5]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,3,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,3,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,6,3,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,6,7,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,7,3,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,7,6,3]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,3,5,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,3,7,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,5,3,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,5,7,3]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,7,3,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,7,5,3]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,3,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,3,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,5,3,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,5,6,3]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,6,3,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,6,5,3]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,4,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,4,7,6]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,6,4,7]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,6,7,4]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,7,4,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,7,6,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,3,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,3,7,6]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,6,3,7]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,6,7,3]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,7,3,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,7,6,3]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,3,4,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,3,7,4]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,4,3,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,4,7,3]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,7,3,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,7,4,3]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,3,4,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,3,6,4]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,4,3,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,4,6,3]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,6,3,4]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,6,4,3]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,4,5,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,4,7,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,5,4,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,5,7,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,7,4,5]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,7,5,4]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,3,5,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,3,7,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,5,3,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,5,7,3]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,7,3,5]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,7,5,3]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,3,4,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,3,7,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,4,3,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,4,7,3]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,7,3,4]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,7,4,3]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,3,4,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,3,5,4]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,4,3,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,4,5,3]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,5,3,4]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,5,4,3]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,4,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,4,6,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,5,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,5,6,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,6,4,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,6,5,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,3,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,3,6,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,5,3,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,5,6,3]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,6,3,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,6,5,3]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,3,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,3,6,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,4,3,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,4,6,3]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,6,3,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,6,4,3]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,3,4,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,3,5,4]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,4,3,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,4,5,3]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,5,3,4]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,5,4,3]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,5,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,6,5,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,6,7,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,7,5,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,7,6,5]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,4,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,6,4,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,6,7,4]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,7,4,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,7,6,4]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,4,5,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,4,7,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,5,4,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,5,7,4]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,7,4,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,7,5,4]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,4,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,4,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,5,4,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,5,6,4]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,6,4,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,6,5,4]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,5,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,6,5,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,6,7,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,7,5,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,7,6,5]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,2,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,2,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,6,2,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,6,7,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,7,2,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,7,6,2]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,2,5,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,2,7,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,5,2,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,5,7,2]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,7,2,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,7,5,2]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,2,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,2,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,5,2,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,5,6,2]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,6,2,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,6,5,2]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,4,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,4,7,6]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,6,4,7]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,6,7,4]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,7,4,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,7,6,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,2,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,2,7,6]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,6,2,7]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,6,7,2]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,7,2,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,7,6,2]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,2,4,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,2,7,4]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,4,2,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,4,7,2]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,7,2,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,7,4,2]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,2,4,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,2,6,4]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,4,2,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,4,6,2]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,6,2,4]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,6,4,2]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,4,5,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,4,7,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,5,4,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,5,7,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,7,4,5]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,7,5,4]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,2,5,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,2,7,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,5,2,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,5,7,2]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,7,2,5]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,7,5,2]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,2,4,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,2,7,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,4,2,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,4,7,2]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,7,2,4]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,7,4,2]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,2,4,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,2,5,4]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,4,2,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,4,5,2]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,5,2,4]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,5,4,2]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,4,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,4,6,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,5,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,5,6,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,6,4,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,6,5,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,2,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,2,6,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,5,2,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,5,6,2]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,6,2,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,6,5,2]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,2,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,2,6,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,4,2,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,4,6,2]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,6,2,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,6,4,2]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,2,4,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,2,5,4]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,4,2,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,4,5,2]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,5,2,4]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,5,4,2]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,5,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,5,7,6]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,6,5,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,6,7,5]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,7,5,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,7,6,5]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,3,6,7]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,3,7,6]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,6,3,7]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,6,7,3]=>[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,7,3,6]=>[1,2,4,5,7,6,3]=>[7,6,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,7,6,3]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,3,5,7]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,3,7,5]=>[1,2,4,6,7,5,3]=>[7,6,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,5,3,7]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,5,7,3]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,7,3,5]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,7,5,3]=>[1,2,4,6,5,7,3]=>[7,6,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,3,5,6]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,3,6,5]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,5,3,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,5,6,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,6,3,5]=>[1,2,4,7,5,6,3]=>[7,6,4,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,6,5,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,5,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,5,7,6]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,6,5,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,6,7,5]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,7,5,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,7,6,5]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,2,6,7]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,2,7,6]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,6,2,7]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,6,7,2]=>[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,7,2,6]=>[1,2,4,5,7,6,3]=>[7,6,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,7,6,2]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,2,5,7]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,2,7,5]=>[1,2,4,6,7,5,3]=>[7,6,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,5,2,7]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,5,7,2]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,7,2,5]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,7,5,2]=>[1,2,4,6,5,7,3]=>[7,6,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,2,5,6]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,2,6,5]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,5,2,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,5,6,2]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,6,2,5]=>[1,2,4,7,5,6,3]=>[7,6,4,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,6,5,2]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,3,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,3,7,6]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,6,3,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,6,7,3]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,7,3,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,7,6,3]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,2,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,2,7,6]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,6,2,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,6,7,2]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,7,2,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,7,6,2]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,2,3,7]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,2,7,3]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,3,2,7]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,3,7,2]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,7,2,3]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,7,3,2]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,2,3,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,2,6,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,3,2,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,3,6,2]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,6,2,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,6,3,2]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,3,5,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,3,7,5]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,5,3,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,5,7,3]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,7,3,5]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,7,5,3]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,2,5,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,2,7,5]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,5,2,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,5,7,2]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,7,2,5]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,7,5,2]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,2,3,7]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,2,7,3]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,3,2,7]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,3,7,2]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,7,2,3]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,7,3,2]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,2,3,5]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,2,5,3]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,3,2,5]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,3,5,2]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,5,2,3]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,5,3,2]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,3,5,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,3,6,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,5,3,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,5,6,3]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,6,3,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,6,5,3]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,2,5,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,2,6,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,5,2,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,5,6,2]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,6,2,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,6,5,2]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,2,3,6]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,2,6,3]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,3,2,6]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,3,6,2]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,6,2,3]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,6,3,2]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,2,3,5]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,2,5,3]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,3,2,5]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,3,5,2]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,5,2,3]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,5,3,2]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,4,6,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,4,7,6]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,6,4,7]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,6,7,4]=>[1,2,5,6,7,4,3]=>[7,6,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,7,4,6]=>[1,2,5,7,6,4,3]=>[7,6,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,7,6,4]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,3,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,3,7,6]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,6,3,7]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,6,7,3]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,7,3,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,7,6,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,3,4,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,3,7,4]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,4,3,7]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,4,7,3]=>[1,2,5,4,6,7,3]=>[7,6,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,7,3,4]=>[1,2,5,7,4,6,3]=>[7,6,3,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,7,4,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,3,4,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,3,6,4]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,4,3,6]=>[1,2,5,4,7,6,3]=>[7,6,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,4,6,3]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,6,3,4]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,6,4,3]=>[1,2,5,6,4,7,3]=>[7,6,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,4,6,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,4,7,6]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,6,4,7]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,6,7,4]=>[1,2,5,6,7,4,3]=>[7,6,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,7,4,6]=>[1,2,5,7,6,4,3]=>[7,6,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,7,6,4]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,2,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,2,7,6]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,6,2,7]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,6,7,2]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,7,2,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,7,6,2]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,2,4,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,2,7,4]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,4,2,7]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,4,7,2]=>[1,2,5,4,6,7,3]=>[7,6,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,7,2,4]=>[1,2,5,7,4,6,3]=>[7,6,3,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,7,4,2]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,2,4,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,2,6,4]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,4,2,6]=>[1,2,5,4,7,6,3]=>[7,6,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,4,6,2]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,6,2,4]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,6,4,2]=>[1,2,5,6,4,7,3]=>[7,6,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,3,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,3,7,6]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,6,3,7]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,6,7,3]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,7,3,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,7,6,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,2,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,2,7,6]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,6,2,7]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,6,7,2]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,7,2,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,7,6,2]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,2,3,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,2,7,3]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,3,2,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,3,7,2]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,7,2,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,7,3,2]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,2,3,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,2,6,3]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,3,2,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,3,6,2]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,6,2,3]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,6,3,2]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,3,4,7]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,3,7,4]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,4,3,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,4,7,3]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,7,3,4]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,7,4,3]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,2,4,7]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,2,7,4]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,4,2,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,4,7,2]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,7,2,4]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,7,4,2]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,2,3,7]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,2,7,3]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,3,2,7]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,3,7,2]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,7,2,3]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,7,3,2]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,2,3,4]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,2,4,3]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,3,2,4]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,3,4,2]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,4,2,3]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,4,3,2]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,3,4,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,3,6,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,4,3,6]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,4,6,3]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,6,3,4]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,6,4,3]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,2,4,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,2,6,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,4,2,6]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,4,6,2]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,6,2,4]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,6,4,2]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,2,3,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,2,6,3]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,3,2,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,3,6,2]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,6,2,3]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,6,3,2]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,2,3,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,2,4,3]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,3,2,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,3,4,2]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,4,2,3]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,4,3,2]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,4,5,7]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,4,7,5]=>[1,2,6,7,5,4,3]=>[7,6,2,1,3,4,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,5,4,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,5,7,4]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,7,4,5]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,7,5,4]=>[1,2,6,5,7,4,3]=>[7,6,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,3,5,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,3,7,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,5,3,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,5,7,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,7,3,5]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,7,5,3]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,3,4,7]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,3,7,4]=>[1,2,6,7,4,5,3]=>[7,6,2,1,4,3,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,4,3,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,4,7,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,7,3,4]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,7,4,3]=>[1,2,6,4,5,7,3]=>[7,6,2,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,3,4,5]=>[1,2,6,4,7,5,3]=>[7,6,2,4,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,3,5,4]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,4,3,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,4,5,3]=>[1,2,6,5,4,7,3]=>[7,6,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,5,3,4]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,5,4,3]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,4,5,7]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,4,7,5]=>[1,2,6,7,5,4,3]=>[7,6,2,1,3,4,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,5,4,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,5,7,4]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,7,4,5]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,7,5,4]=>[1,2,6,5,7,4,3]=>[7,6,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,2,5,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,2,7,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,5,2,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,5,7,2]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,7,2,5]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,7,5,2]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,2,4,7]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,2,7,4]=>[1,2,6,7,4,5,3]=>[7,6,2,1,4,3,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,4,2,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,4,7,2]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,7,2,4]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,7,4,2]=>[1,2,6,4,5,7,3]=>[7,6,2,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,2,4,5]=>[1,2,6,4,7,5,3]=>[7,6,2,4,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,2,5,4]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,4,2,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,4,5,2]=>[1,2,6,5,4,7,3]=>[7,6,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,5,2,4]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,5,4,2]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,3,5,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,3,7,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,5,3,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,5,7,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,7,3,5]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,7,5,3]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,2,5,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,2,7,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,5,2,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,5,7,2]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,7,2,5]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,7,5,2]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,2,3,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,2,7,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,3,2,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,3,7,2]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,7,2,3]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,7,3,2]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,2,3,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,2,5,3]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,3,2,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,3,5,2]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,5,2,3]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,5,3,2]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,3,4,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,3,7,4]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,4,3,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,4,7,3]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,7,3,4]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,7,4,3]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,2,4,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,2,7,4]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,4,2,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,4,7,2]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,7,2,4]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,7,4,2]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,2,3,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,2,7,3]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,3,2,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,3,7,2]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,7,2,3]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,7,3,2]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,2,3,4]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,2,4,3]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,3,2,4]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,3,4,2]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,4,2,3]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,4,3,2]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,3,4,5]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,3,5,4]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,4,3,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,4,5,3]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,5,3,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,5,4,3]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,2,4,5]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,2,5,4]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,4,2,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,4,5,2]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,5,2,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,5,4,2]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,2,3,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,2,5,3]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,3,2,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,3,5,2]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,5,2,3]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,5,3,2]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,2,3,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,2,4,3]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,3,2,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,3,4,2]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,4,2,3]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,4,3,2]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,4,5,6]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,4,6,5]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,5,4,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,5,6,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,6,4,5]=>[1,2,7,5,6,4,3]=>[7,6,1,3,2,4,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,6,5,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,3,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,3,6,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,5,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,5,6,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,6,3,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,6,5,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,3,4,6]=>[1,2,7,6,4,5,3]=>[7,6,1,2,4,3,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,3,6,4]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,4,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,4,6,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,6,3,4]=>[1,2,7,4,5,6,3]=>[7,6,1,4,3,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,6,4,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,3,4,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,3,5,4]=>[1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,4,3,5]=>[1,2,7,5,4,6,3]=>[7,6,1,3,4,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,4,5,3]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,5,3,4]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,5,4,3]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,4,5,6]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,4,6,5]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,5,4,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,5,6,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,6,4,5]=>[1,2,7,5,6,4,3]=>[7,6,1,3,2,4,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,6,5,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,2,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,2,6,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,5,2,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,5,6,2]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,6,2,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,6,5,2]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,2,4,6]=>[1,2,7,6,4,5,3]=>[7,6,1,2,4,3,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,2,6,4]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,4,2,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,4,6,2]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,6,2,4]=>[1,2,7,4,5,6,3]=>[7,6,1,4,3,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,6,4,2]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,2,4,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,2,5,4]=>[1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,4,2,5]=>[1,2,7,5,4,6,3]=>[7,6,1,3,4,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,4,5,2]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,5,2,4]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,5,4,2]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,3,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,3,6,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,5,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,5,6,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,6,3,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,6,5,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,2,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,2,6,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,5,2,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,5,6,2]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,6,2,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,6,5,2]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,2,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,2,6,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,3,2,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,3,6,2]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,6,2,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,6,3,2]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,2,3,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,2,5,3]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,3,2,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,3,5,2]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,5,2,3]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,5,3,2]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,3,4,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,3,6,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,4,3,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,4,6,3]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,6,3,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,6,4,3]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,2,4,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,2,6,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,4,2,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,4,6,2]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,6,2,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,6,4,2]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,2,3,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,2,6,3]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,3,2,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,3,6,2]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,6,2,3]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,6,3,2]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,2,3,4]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,2,4,3]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,3,2,4]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,3,4,2]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,4,2,3]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,4,3,2]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,3,4,5]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,3,5,4]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,4,3,5]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,4,5,3]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,5,3,4]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,5,4,3]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,2,4,5]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,2,5,4]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,4,2,5]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,4,5,2]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,5,2,4]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,5,4,2]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,2,3,5]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,2,5,3]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,3,2,5]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,3,5,2]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,5,2,3]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,5,3,2]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,2,3,4]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,2,4,3]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,3,2,4]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,3,4,2]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,4,2,3]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,4,3,2]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,5,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,6,5,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,6,7,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,7,5,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,7,6,5]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,4,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,4,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,6,4,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,6,7,4]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,7,4,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,7,6,4]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,4,5,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,4,7,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,5,4,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,5,7,4]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,7,4,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,7,5,4]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,4,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,4,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,5,4,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,5,6,4]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,6,4,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,6,5,4]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,5,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,6,5,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,6,7,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,7,5,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,7,6,5]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,3,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,3,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,6,3,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,6,7,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,7,3,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,7,6,3]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,3,5,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,3,7,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,5,3,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,5,7,3]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,7,3,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,7,5,3]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,3,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,3,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,5,3,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,5,6,3]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,6,3,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,6,5,3]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,4,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,4,7,6]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,6,4,7]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,6,7,4]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,7,4,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,7,6,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,3,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,3,7,6]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,6,3,7]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,6,7,3]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,7,3,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,7,6,3]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,3,4,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,3,7,4]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,4,3,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,4,7,3]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,7,3,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,7,4,3]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,3,4,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,3,6,4]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,4,3,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,4,6,3]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,6,3,4]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,6,4,3]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,4,5,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,4,7,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,5,4,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,5,7,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,7,4,5]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,7,5,4]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,3,5,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,3,7,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,5,3,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,5,7,3]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,7,3,5]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,7,5,3]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,3,4,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,3,7,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,4,3,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,4,7,3]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,7,3,4]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,7,4,3]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,3,4,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,3,5,4]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,4,3,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,4,5,3]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,5,3,4]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,5,4,3]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,4,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,4,6,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,5,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,5,6,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,6,4,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,6,5,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,3,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,3,6,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,5,3,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,5,6,3]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,6,3,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,6,5,3]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,3,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,3,6,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,4,3,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,4,6,3]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,6,3,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,6,4,3]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,3,4,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,3,5,4]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,4,3,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,4,5,3]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,5,3,4]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,5,4,3]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,5,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,6,5,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,6,7,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,7,5,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,7,6,5]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,4,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,4,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,6,4,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,6,7,4]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,7,4,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,7,6,4]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,4,5,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,4,7,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,5,4,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,5,7,4]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,7,4,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,7,5,4]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,4,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,4,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,5,4,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,5,6,4]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,6,4,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,6,5,4]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,5,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,6,5,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,6,7,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,7,5,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,7,6,5]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,1,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,1,7,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,6,1,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,7,1,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,7,6,1]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,1,5,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,1,7,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,5,1,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,5,7,1]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,7,1,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,7,5,1]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,1,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,1,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,5,1,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,5,6,1]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,6,1,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,6,5,1]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,4,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,4,7,6]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,6,4,7]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,6,7,4]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,7,4,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,7,6,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,1,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,1,7,6]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,6,1,7]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,6,7,1]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,7,1,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,7,6,1]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,1,4,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,1,7,4]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,4,1,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,4,7,1]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,7,1,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,7,4,1]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,1,4,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,1,6,4]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,4,1,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,4,6,1]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,6,1,4]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,6,4,1]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,4,5,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,4,7,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,5,4,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,5,7,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,7,4,5]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,7,5,4]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,1,5,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,1,7,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,5,1,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,5,7,1]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,7,1,5]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,7,5,1]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,1,4,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,1,7,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,4,1,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,4,7,1]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,7,1,4]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,7,4,1]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,1,4,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,1,5,4]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,4,1,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,4,5,1]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,5,1,4]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,5,4,1]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,4,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,4,6,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,5,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,5,6,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,6,4,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,6,5,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,1,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,1,6,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,5,1,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,5,6,1]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,6,1,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,6,5,1]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,1,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,1,6,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,4,1,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,4,6,1]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,6,1,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,6,4,1]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,1,4,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,1,5,4]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,4,1,5]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,4,5,1]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,5,1,4]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,5,4,1]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,5,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,5,7,6]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,6,5,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,6,7,5]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,7,5,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,7,6,5]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,3,6,7]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,3,7,6]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,6,3,7]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,6,7,3]=>[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,7,3,6]=>[1,2,4,5,7,6,3]=>[7,6,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,7,6,3]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,3,5,7]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,3,7,5]=>[1,2,4,6,7,5,3]=>[7,6,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,5,3,7]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,5,7,3]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,7,3,5]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,7,5,3]=>[1,2,4,6,5,7,3]=>[7,6,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,3,5,6]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,3,6,5]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,5,3,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,5,6,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,6,3,5]=>[1,2,4,7,5,6,3]=>[7,6,4,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,6,5,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,5,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,5,7,6]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,6,5,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,6,7,5]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,7,5,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,7,6,5]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,1,6,7]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,1,7,6]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,6,1,7]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,6,7,1]=>[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,7,1,6]=>[1,2,4,5,7,6,3]=>[7,6,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,7,6,1]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,1,5,7]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,1,7,5]=>[1,2,4,6,7,5,3]=>[7,6,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,5,1,7]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,5,7,1]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,7,1,5]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,7,5,1]=>[1,2,4,6,5,7,3]=>[7,6,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,1,5,6]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,1,6,5]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,5,1,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,5,6,1]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,6,1,5]=>[1,2,4,7,5,6,3]=>[7,6,4,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,6,5,1]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,3,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,3,7,6]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,6,3,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,6,7,3]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,7,3,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,7,6,3]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,1,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,1,7,6]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,6,1,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,6,7,1]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,7,1,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,7,6,1]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,1,3,7]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,1,7,3]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,3,1,7]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,3,7,1]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,7,1,3]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,7,3,1]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,1,3,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,1,6,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,3,1,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,3,6,1]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,6,1,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,6,3,1]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,3,5,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,3,7,5]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,5,3,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,5,7,3]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,7,3,5]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,7,5,3]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,1,5,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,1,7,5]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,5,1,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,5,7,1]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,7,1,5]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,7,5,1]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,1,3,7]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,1,7,3]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,3,1,7]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,3,7,1]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,7,1,3]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,7,3,1]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,1,3,5]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,1,5,3]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,3,1,5]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,3,5,1]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,5,1,3]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,5,3,1]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,3,5,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,3,6,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,5,3,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,5,6,3]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,6,3,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,6,5,3]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,1,5,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,1,6,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,5,1,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,5,6,1]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,6,1,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,6,5,1]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,1,3,6]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,1,6,3]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,3,1,6]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,3,6,1]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,6,1,3]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,6,3,1]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,1,3,5]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,1,5,3]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,3,1,5]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,3,5,1]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,5,1,3]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,5,3,1]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,4,6,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,4,7,6]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,6,4,7]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,6,7,4]=>[1,2,5,6,7,4,3]=>[7,6,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,7,4,6]=>[1,2,5,7,6,4,3]=>[7,6,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,7,6,4]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,3,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,3,7,6]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,6,3,7]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,6,7,3]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,7,3,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,7,6,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,3,4,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,3,7,4]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,4,3,7]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,4,7,3]=>[1,2,5,4,6,7,3]=>[7,6,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,7,3,4]=>[1,2,5,7,4,6,3]=>[7,6,3,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,7,4,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,3,4,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,3,6,4]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,4,3,6]=>[1,2,5,4,7,6,3]=>[7,6,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,4,6,3]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,6,3,4]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,6,4,3]=>[1,2,5,6,4,7,3]=>[7,6,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,4,6,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,4,7,6]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,6,4,7]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,6,7,4]=>[1,2,5,6,7,4,3]=>[7,6,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,7,4,6]=>[1,2,5,7,6,4,3]=>[7,6,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,7,6,4]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,1,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,1,7,6]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,6,1,7]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,6,7,1]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,7,1,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,7,6,1]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,1,4,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,1,7,4]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,4,1,7]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,4,7,1]=>[1,2,5,4,6,7,3]=>[7,6,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,7,1,4]=>[1,2,5,7,4,6,3]=>[7,6,3,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,7,4,1]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,1,4,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,1,6,4]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,4,1,6]=>[1,2,5,4,7,6,3]=>[7,6,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,4,6,1]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,6,1,4]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,6,4,1]=>[1,2,5,6,4,7,3]=>[7,6,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,3,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,3,7,6]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,6,3,7]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,6,7,3]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,7,3,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,7,6,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,1,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,1,7,6]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,6,1,7]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,6,7,1]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,7,1,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,7,6,1]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,1,3,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,1,7,3]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,3,1,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,3,7,1]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,7,1,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,7,3,1]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,1,3,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,1,6,3]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,3,1,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,3,6,1]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,6,1,3]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,6,3,1]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,3,4,7]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,3,7,4]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,4,3,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,4,7,3]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,7,3,4]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,7,4,3]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,1,4,7]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,1,7,4]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,4,1,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,4,7,1]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,7,1,4]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,7,4,1]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,1,3,7]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,1,7,3]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,3,1,7]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,3,7,1]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,7,1,3]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,7,3,1]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,1,3,4]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,1,4,3]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,3,1,4]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,3,4,1]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,4,1,3]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,4,3,1]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,3,4,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,3,6,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,4,3,6]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,4,6,3]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,6,3,4]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,6,4,3]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,1,4,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,1,6,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,4,1,6]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,4,6,1]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,6,1,4]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,6,4,1]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,1,3,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,1,6,3]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,3,1,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,3,6,1]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,6,1,3]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,6,3,1]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,1,3,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,1,4,3]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,3,1,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,3,4,1]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,4,1,3]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,4,3,1]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,4,5,7]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,4,7,5]=>[1,2,6,7,5,4,3]=>[7,6,2,1,3,4,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,5,4,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,5,7,4]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,7,4,5]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,7,5,4]=>[1,2,6,5,7,4,3]=>[7,6,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,3,5,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,3,7,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,5,3,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,5,7,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,7,3,5]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,7,5,3]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,3,4,7]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,3,7,4]=>[1,2,6,7,4,5,3]=>[7,6,2,1,4,3,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,4,3,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,4,7,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,7,3,4]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,7,4,3]=>[1,2,6,4,5,7,3]=>[7,6,2,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,3,4,5]=>[1,2,6,4,7,5,3]=>[7,6,2,4,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,3,5,4]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,4,3,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,4,5,3]=>[1,2,6,5,4,7,3]=>[7,6,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,5,3,4]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,5,4,3]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,4,5,7]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,4,7,5]=>[1,2,6,7,5,4,3]=>[7,6,2,1,3,4,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,5,4,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,5,7,4]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,7,4,5]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,7,5,4]=>[1,2,6,5,7,4,3]=>[7,6,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,1,5,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,1,7,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,5,1,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,5,7,1]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,7,1,5]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,7,5,1]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,1,4,7]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,1,7,4]=>[1,2,6,7,4,5,3]=>[7,6,2,1,4,3,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,4,1,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,4,7,1]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,7,1,4]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,7,4,1]=>[1,2,6,4,5,7,3]=>[7,6,2,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,1,4,5]=>[1,2,6,4,7,5,3]=>[7,6,2,4,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,1,5,4]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,4,1,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,4,5,1]=>[1,2,6,5,4,7,3]=>[7,6,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,5,1,4]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,5,4,1]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,3,5,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,3,7,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,5,3,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,5,7,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,7,3,5]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,7,5,3]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,1,5,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,1,7,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,5,1,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,5,7,1]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,7,1,5]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,7,5,1]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,1,3,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,1,7,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,3,1,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,3,7,1]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,7,1,3]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,7,3,1]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,1,3,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,1,5,3]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,3,1,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,3,5,1]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,5,1,3]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,5,3,1]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,3,4,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,3,7,4]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,4,3,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,4,7,3]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,7,3,4]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,7,4,3]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,1,4,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,1,7,4]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,4,1,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,4,7,1]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,7,1,4]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,7,4,1]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,1,3,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,1,7,3]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,3,1,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,3,7,1]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,7,1,3]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,7,3,1]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,1,3,4]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,1,4,3]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,3,1,4]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,3,4,1]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,4,1,3]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,4,3,1]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,3,4,5]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,3,5,4]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,4,3,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,4,5,3]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,5,3,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,5,4,3]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,1,4,5]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,1,5,4]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,4,1,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,4,5,1]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,5,1,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,5,4,1]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,1,3,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,1,5,3]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,3,1,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,3,5,1]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,5,1,3]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,5,3,1]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,1,3,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,1,4,3]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,3,1,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,3,4,1]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,4,1,3]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,4,3,1]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,4,5,6]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,4,6,5]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,5,4,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,5,6,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,6,4,5]=>[1,2,7,5,6,4,3]=>[7,6,1,3,2,4,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,6,5,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,3,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,3,6,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,5,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,5,6,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,6,3,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,6,5,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,3,4,6]=>[1,2,7,6,4,5,3]=>[7,6,1,2,4,3,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,3,6,4]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,4,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,4,6,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,6,3,4]=>[1,2,7,4,5,6,3]=>[7,6,1,4,3,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,6,4,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,3,4,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,3,5,4]=>[1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,4,3,5]=>[1,2,7,5,4,6,3]=>[7,6,1,3,4,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,4,5,3]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,5,3,4]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,5,4,3]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,4,5,6]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,4,6,5]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,5,4,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,5,6,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,6,4,5]=>[1,2,7,5,6,4,3]=>[7,6,1,3,2,4,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,6,5,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,1,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,1,6,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,5,1,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,5,6,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,6,1,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,6,5,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,1,4,6]=>[1,2,7,6,4,5,3]=>[7,6,1,2,4,3,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,1,6,4]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,4,1,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,4,6,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,6,1,4]=>[1,2,7,4,5,6,3]=>[7,6,1,4,3,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,6,4,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,1,4,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,1,5,4]=>[1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,4,1,5]=>[1,2,7,5,4,6,3]=>[7,6,1,3,4,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,4,5,1]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,5,1,4]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,5,4,1]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,3,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,3,6,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,5,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,5,6,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,6,3,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,6,5,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,1,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,1,6,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,5,1,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,5,6,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,6,1,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,6,5,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,1,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,1,6,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,3,1,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,3,6,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,6,1,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,6,3,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,1,3,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,1,5,3]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,3,1,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,3,5,1]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,5,1,3]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,5,3,1]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,3,4,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,3,6,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,4,3,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,4,6,3]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,6,3,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,6,4,3]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,1,4,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,1,6,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,4,1,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,4,6,1]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,6,1,4]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,6,4,1]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,1,3,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,1,6,3]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,3,1,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,3,6,1]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,6,1,3]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,6,3,1]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,1,3,4]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,1,4,3]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,3,1,4]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,3,4,1]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,4,1,3]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,4,3,1]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,3,4,5]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,3,5,4]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,4,3,5]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,4,5,3]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,5,3,4]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,5,4,3]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,1,4,5]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,1,5,4]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,4,1,5]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,4,5,1]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,5,1,4]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,5,4,1]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,1,3,5]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,1,5,3]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,3,1,5]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,3,5,1]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,5,1,3]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,5,3,1]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,1,3,4]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,1,4,3]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,3,1,4]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,3,4,1]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,4,1,3]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,4,3,1]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,5,7,6]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,6,5,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,6,7,5]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,7,5,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,7,6,5]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,4,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,4,7,6]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,6,4,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,6,7,4]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,7,4,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,7,6,4]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,4,5,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,4,7,5]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,5,4,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,5,7,4]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,7,4,5]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,7,5,4]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,4,5,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,4,6,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,5,4,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,5,6,4]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,6,4,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,6,5,4]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,5,6,7]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,5,7,6]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,6,5,7]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,6,7,5]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,7,5,6]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,7,6,5]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,2,6,7]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,2,7,6]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,6,2,7]=>[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,6,7,2]=>[1,3,4,5,6,7,2]=>[7,5,4,3,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,7,2,6]=>[1,3,4,5,7,6,2]=>[7,5,4,3,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,7,6,2]=>[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,2,5,7]=>[1,3,4,6,5,2,7]=>[7,5,4,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,2,7,5]=>[1,3,4,6,7,5,2]=>[7,5,4,2,1,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,5,2,7]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,5,7,2]=>[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,7,2,5]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,7,5,2]=>[1,3,4,6,5,7,2]=>[7,5,4,2,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,2,5,6]=>[1,3,4,7,6,5,2]=>[7,5,4,1,2,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,2,6,5]=>[1,3,4,7,5,2,6]=>[7,5,4,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,5,2,6]=>[1,3,4,7,6,2,5]=>[7,5,4,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,5,6,2]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,6,2,5]=>[1,3,4,7,5,6,2]=>[7,5,4,1,3,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,6,5,2]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,4,6,7]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,4,7,6]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,6,4,7]=>[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,6,7,4]=>[1,3,5,6,7,4,2]=>[7,5,3,2,1,4,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,7,4,6]=>[1,3,5,7,6,4,2]=>[7,5,3,1,2,4,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,7,6,4]=>[1,3,5,7,4,2,6]=>[7,5,3,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,2,6,7]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,2,7,6]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,6,2,7]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,6,7,2]=>[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,7,2,6]=>[1,3,5,7,6,2,4]=>[7,5,3,1,2,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,7,6,2]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,2,4,7]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,2,7,4]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,4,2,7]=>[1,3,5,4,6,2,7]=>[7,5,3,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,4,7,2]=>[1,3,5,4,6,7,2]=>[7,5,3,4,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,7,2,4]=>[1,3,5,7,4,6,2]=>[7,5,3,1,4,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,7,4,2]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,2,4,6]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,2,6,4]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,4,2,6]=>[1,3,5,4,7,6,2]=>[7,5,3,4,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,4,6,2]=>[1,3,5,4,7,2,6]=>[7,5,3,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,6,2,4]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,6,4,2]=>[1,3,5,6,4,7,2]=>[7,5,3,2,4,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,4,5,7]=>[1,3,6,5,4,2,7]=>[7,5,2,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,4,7,5]=>[1,3,6,7,5,4,2]=>[7,5,2,1,3,4,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,5,4,7]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,5,7,4]=>[1,3,6,7,4,2,5]=>[7,5,2,1,4,6,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,7,4,5]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,7,5,4]=>[1,3,6,5,7,4,2]=>[7,5,2,3,1,4,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,2,5,7]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,2,7,5]=>[1,3,6,7,5,2,4]=>[7,5,2,1,3,6,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,5,2,7]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,5,7,2]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,7,2,5]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,7,5,2]=>[1,3,6,5,7,2,4]=>[7,5,2,3,1,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,2,4,7]=>[1,3,6,4,5,2,7]=>[7,5,2,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,2,7,4]=>[1,3,6,7,4,5,2]=>[7,5,2,1,4,3,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,4,2,7]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,4,7,2]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,7,2,4]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,7,4,2]=>[1,3,6,4,5,7,2]=>[7,5,2,4,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,2,4,5]=>[1,3,6,4,7,5,2]=>[7,5,2,4,1,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,2,5,4]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,4,2,5]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,4,5,2]=>[1,3,6,5,4,7,2]=>[7,5,2,3,4,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,5,2,4]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,5,4,2]=>[1,3,6,4,7,2,5]=>[7,5,2,4,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,4,5,6]=>[1,3,7,6,5,4,2]=>[7,5,1,2,3,4,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,4,6,5]=>[1,3,7,5,4,2,6]=>[7,5,1,3,4,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,5,4,6]=>[1,3,7,6,4,2,5]=>[7,5,1,2,4,6,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,5,6,4]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,6,4,5]=>[1,3,7,5,6,4,2]=>[7,5,1,3,2,4,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,6,5,4]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,2,5,6]=>[1,3,7,6,5,2,4]=>[7,5,1,2,3,6,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,2,6,5]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,5,2,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,5,6,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,6,2,5]=>[1,3,7,5,6,2,4]=>[7,5,1,3,2,6,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,6,5,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,2,4,6]=>[1,3,7,6,4,5,2]=>[7,5,1,2,4,3,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,2,6,4]=>[1,3,7,4,5,2,6]=>[7,5,1,4,3,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,4,2,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,4,6,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,6,2,4]=>[1,3,7,4,5,6,2]=>[7,5,1,4,3,2,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,6,4,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,2,4,5]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,2,5,4]=>[1,3,7,4,6,5,2]=>[7,5,1,4,2,3,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,4,2,5]=>[1,3,7,5,4,6,2]=>[7,5,1,3,4,2,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,4,5,2]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,5,2,4]=>[1,3,7,4,6,2,5]=>[7,5,1,4,2,6,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,5,4,2]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,5,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,5,7,6]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,6,5,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,6,7,5]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,7,5,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,7,6,5]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,4,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,4,7,6]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,6,4,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,6,7,4]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,7,4,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,7,6,4]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,4,5,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,4,7,5]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,5,4,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,5,7,4]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,7,4,5]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,7,5,4]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,4,5,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,4,6,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,5,4,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,5,6,4]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,6,4,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,6,5,4]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,5,6,7]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,5,7,6]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,6,5,7]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,6,7,5]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,7,5,6]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,7,6,5]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,1,6,7]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,1,7,6]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,6,1,7]=>[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,6,7,1]=>[1,3,4,5,6,7,2]=>[7,5,4,3,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,7,1,6]=>[1,3,4,5,7,6,2]=>[7,5,4,3,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,7,6,1]=>[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,1,5,7]=>[1,3,4,6,5,2,7]=>[7,5,4,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,1,7,5]=>[1,3,4,6,7,5,2]=>[7,5,4,2,1,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,5,1,7]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,5,7,1]=>[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,7,1,5]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,7,5,1]=>[1,3,4,6,5,7,2]=>[7,5,4,2,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,1,5,6]=>[1,3,4,7,6,5,2]=>[7,5,4,1,2,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,1,6,5]=>[1,3,4,7,5,2,6]=>[7,5,4,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,5,1,6]=>[1,3,4,7,6,2,5]=>[7,5,4,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,5,6,1]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,6,1,5]=>[1,3,4,7,5,6,2]=>[7,5,4,1,3,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,6,5,1]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,4,6,7]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,4,7,6]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,6,4,7]=>[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,6,7,4]=>[1,3,5,6,7,4,2]=>[7,5,3,2,1,4,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,7,4,6]=>[1,3,5,7,6,4,2]=>[7,5,3,1,2,4,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,7,6,4]=>[1,3,5,7,4,2,6]=>[7,5,3,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,1,6,7]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,1,7,6]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,6,1,7]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,6,7,1]=>[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,7,1,6]=>[1,3,5,7,6,2,4]=>[7,5,3,1,2,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,7,6,1]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,1,4,7]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,1,7,4]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,4,1,7]=>[1,3,5,4,6,2,7]=>[7,5,3,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,4,7,1]=>[1,3,5,4,6,7,2]=>[7,5,3,4,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,7,1,4]=>[1,3,5,7,4,6,2]=>[7,5,3,1,4,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,7,4,1]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,1,4,6]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,1,6,4]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,4,1,6]=>[1,3,5,4,7,6,2]=>[7,5,3,4,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,4,6,1]=>[1,3,5,4,7,2,6]=>[7,5,3,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,6,1,4]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,6,4,1]=>[1,3,5,6,4,7,2]=>[7,5,3,2,4,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,4,5,7]=>[1,3,6,5,4,2,7]=>[7,5,2,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,4,7,5]=>[1,3,6,7,5,4,2]=>[7,5,2,1,3,4,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,5,4,7]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,5,7,4]=>[1,3,6,7,4,2,5]=>[7,5,2,1,4,6,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,7,4,5]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,7,5,4]=>[1,3,6,5,7,4,2]=>[7,5,2,3,1,4,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,1,5,7]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,1,7,5]=>[1,3,6,7,5,2,4]=>[7,5,2,1,3,6,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,5,1,7]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,5,7,1]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,7,1,5]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,7,5,1]=>[1,3,6,5,7,2,4]=>[7,5,2,3,1,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,1,4,7]=>[1,3,6,4,5,2,7]=>[7,5,2,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,1,7,4]=>[1,3,6,7,4,5,2]=>[7,5,2,1,4,3,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,4,1,7]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,4,7,1]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,7,1,4]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,7,4,1]=>[1,3,6,4,5,7,2]=>[7,5,2,4,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,1,4,5]=>[1,3,6,4,7,5,2]=>[7,5,2,4,1,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,1,5,4]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,4,1,5]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,4,5,1]=>[1,3,6,5,4,7,2]=>[7,5,2,3,4,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,5,1,4]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,5,4,1]=>[1,3,6,4,7,2,5]=>[7,5,2,4,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,4,5,6]=>[1,3,7,6,5,4,2]=>[7,5,1,2,3,4,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,4,6,5]=>[1,3,7,5,4,2,6]=>[7,5,1,3,4,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,5,4,6]=>[1,3,7,6,4,2,5]=>[7,5,1,2,4,6,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,5,6,4]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,6,4,5]=>[1,3,7,5,6,4,2]=>[7,5,1,3,2,4,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,6,5,4]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,1,5,6]=>[1,3,7,6,5,2,4]=>[7,5,1,2,3,6,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,1,6,5]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,5,1,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,5,6,1]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,6,1,5]=>[1,3,7,5,6,2,4]=>[7,5,1,3,2,6,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,6,5,1]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,1,4,6]=>[1,3,7,6,4,5,2]=>[7,5,1,2,4,3,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,1,6,4]=>[1,3,7,4,5,2,6]=>[7,5,1,4,3,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,4,1,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,4,6,1]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,6,1,4]=>[1,3,7,4,5,6,2]=>[7,5,1,4,3,2,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,6,4,1]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,1,4,5]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,1,5,4]=>[1,3,7,4,6,5,2]=>[7,5,1,4,2,3,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,4,1,5]=>[1,3,7,5,4,6,2]=>[7,5,1,3,4,2,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,4,5,1]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,5,1,4]=>[1,3,7,4,6,2,5]=>[7,5,1,4,2,6,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,5,4,1]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,5,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,5,7,6]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,6,5,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,6,7,5]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,7,5,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,7,6,5]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,2,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,2,7,6]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,6,2,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,6,7,2]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,7,2,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,7,6,2]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,2,5,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,2,7,5]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,5,2,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,5,7,2]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,7,2,5]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,7,5,2]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,2,5,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,2,6,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,5,2,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,5,6,2]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,6,2,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,6,5,2]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,5,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,5,7,6]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,6,5,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,6,7,5]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,7,5,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,7,6,5]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,1,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,1,7,6]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,6,1,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,6,7,1]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,7,1,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,7,6,1]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,1,5,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,1,7,5]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,5,1,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,5,7,1]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,7,1,5]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,7,5,1]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,1,5,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,1,6,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,5,1,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,5,6,1]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,6,1,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,6,5,1]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,2,6,7]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,2,7,6]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,6,2,7]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,6,7,2]=>[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,7,2,6]=>[1,3,5,7,6,2,4]=>[7,5,3,1,2,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,7,6,2]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,1,6,7]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,1,7,6]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,6,1,7]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,6,7,1]=>[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,7,1,6]=>[1,3,5,7,6,2,4]=>[7,5,3,1,2,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,7,6,1]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,1,2,7]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,1,7,2]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,2,1,7]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,2,7,1]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,7,1,2]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,7,2,1]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,1,2,6]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,1,6,2]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,2,1,6]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,2,6,1]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,6,1,2]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,6,2,1]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,2,5,7]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,2,7,5]=>[1,3,6,7,5,2,4]=>[7,5,2,1,3,6,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,5,2,7]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,5,7,2]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,7,2,5]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,7,5,2]=>[1,3,6,5,7,2,4]=>[7,5,2,3,1,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,1,5,7]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,1,7,5]=>[1,3,6,7,5,2,4]=>[7,5,2,1,3,6,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,5,1,7]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,5,7,1]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,7,1,5]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,7,5,1]=>[1,3,6,5,7,2,4]=>[7,5,2,3,1,6,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,1,2,7]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,1,7,2]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,2,1,7]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,2,7,1]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,7,1,2]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,7,2,1]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,1,2,5]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,1,5,2]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,2,1,5]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,2,5,1]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,5,1,2]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,5,2,1]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,2,5,6]=>[1,3,7,6,5,2,4]=>[7,5,1,2,3,6,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,2,6,5]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,5,2,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,5,6,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,6,2,5]=>[1,3,7,5,6,2,4]=>[7,5,1,3,2,6,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,6,5,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,1,5,6]=>[1,3,7,6,5,2,4]=>[7,5,1,2,3,6,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,1,6,5]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,5,1,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,5,6,1]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,6,1,5]=>[1,3,7,5,6,2,4]=>[7,5,1,3,2,6,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,6,5,1]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,1,2,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,1,6,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,2,1,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,2,6,1]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,6,1,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,6,2,1]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,1,2,5]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,1,5,2]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,2,1,5]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,2,5,1]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,5,1,2]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,5,2,1]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,4,6,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,4,7,6]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,6,4,7]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,6,7,4]=>[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,7,4,6]=>[1,3,2,5,7,6,4]=>[7,5,6,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,7,6,4]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,2,6,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,2,7,6]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,6,2,7]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,6,7,2]=>[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,7,2,6]=>[1,3,2,5,7,6,4]=>[7,5,6,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,7,6,2]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,2,4,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,2,7,4]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,4,2,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,4,7,2]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,7,2,4]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,7,4,2]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,2,4,6]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,2,6,4]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,4,2,6]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,4,6,2]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,6,2,4]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,6,4,2]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,4,6,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,4,7,6]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,6,4,7]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,6,7,4]=>[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,7,4,6]=>[1,3,2,5,7,6,4]=>[7,5,6,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,7,6,4]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,1,6,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,1,7,6]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,6,1,7]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,6,7,1]=>[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,7,1,6]=>[1,3,2,5,7,6,4]=>[7,5,6,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,7,6,1]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,1,4,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,1,7,4]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,4,1,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,4,7,1]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,7,1,4]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,7,4,1]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,1,4,6]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,1,6,4]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,4,1,6]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,4,6,1]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,6,1,4]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,6,4,1]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,2,6,7]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,2,7,6]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,6,2,7]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,6,7,2]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,7,2,6]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,7,6,2]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,1,6,7]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,1,7,6]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,6,1,7]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,6,7,1]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,7,1,6]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,7,6,1]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,1,2,7]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,1,7,2]=>[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,2,1,7]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,2,7,1]=>[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,7,1,2]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,7,2,1]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,1,2,6]=>[1,3,4,7,6,2,5]=>[7,5,4,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,1,6,2]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,2,1,6]=>[1,3,4,7,6,2,5]=>[7,5,4,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,2,6,1]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,6,1,2]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,6,2,1]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,2,4,7]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,2,7,4]=>[1,3,6,7,4,2,5]=>[7,5,2,1,4,6,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,4,2,7]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,4,7,2]=>[1,3,6,7,2,5,4]=>[7,5,2,1,6,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,7,2,4]=>[1,3,6,2,5,7,4]=>[7,5,2,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,7,4,2]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,1,4,7]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,1,7,4]=>[1,3,6,7,4,2,5]=>[7,5,2,1,4,6,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,4,1,7]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,4,7,1]=>[1,3,6,7,2,5,4]=>[7,5,2,1,6,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,7,1,4]=>[1,3,6,2,5,7,4]=>[7,5,2,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,7,4,1]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,1,2,7]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,1,7,2]=>[1,3,6,7,2,5,4]=>[7,5,2,1,6,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,2,1,7]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,2,7,1]=>[1,3,6,7,2,5,4]=>[7,5,2,1,6,3,4]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,7,1,2]=>[1,3,6,2,5,7,4]=>[7,5,2,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,7,2,1]=>[1,3,6,2,5,7,4]=>[7,5,2,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,1,2,4]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,1,4,2]=>[1,3,6,4,7,2,5]=>[7,5,2,4,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,2,1,4]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,2,4,1]=>[1,3,6,4,7,2,5]=>[7,5,2,4,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,4,1,2]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,4,2,1]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,2,4,6]=>[1,3,7,6,4,2,5]=>[7,5,1,2,4,6,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,2,6,4]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,4,2,6]=>[1,3,7,6,2,5,4]=>[7,5,1,2,6,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,4,6,2]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,6,2,4]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,6,4,2]=>[1,3,7,2,5,6,4]=>[7,5,1,6,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,1,4,6]=>[1,3,7,6,4,2,5]=>[7,5,1,2,4,6,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,1,6,4]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,4,1,6]=>[1,3,7,6,2,5,4]=>[7,5,1,2,6,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,4,6,1]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,6,1,4]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,6,4,1]=>[1,3,7,2,5,6,4]=>[7,5,1,6,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,1,2,6]=>[1,3,7,6,2,5,4]=>[7,5,1,2,6,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,1,6,2]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,2,1,6]=>[1,3,7,6,2,5,4]=>[7,5,1,2,6,3,4]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,2,6,1]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,6,1,2]=>[1,3,7,2,5,6,4]=>[7,5,1,6,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,6,2,1]=>[1,3,7,2,5,6,4]=>[7,5,1,6,3,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,1,2,4]=>[1,3,7,4,6,2,5]=>[7,5,1,4,2,6,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,1,4,2]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,2,1,4]=>[1,3,7,4,6,2,5]=>[7,5,1,4,2,6,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,2,4,1]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,4,1,2]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,4,2,1]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,4,5,7]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,4,7,5]=>[1,3,2,6,7,5,4]=>[7,5,6,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,5,4,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,5,7,4]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,7,4,5]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,7,5,4]=>[1,3,2,6,5,7,4]=>[7,5,6,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,2,5,7]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,2,7,5]=>[1,3,2,6,7,5,4]=>[7,5,6,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,5,2,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,5,7,2]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,7,2,5]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,7,5,2]=>[1,3,2,6,5,7,4]=>[7,5,6,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,2,4,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,2,7,4]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,4,2,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,4,7,2]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,7,2,4]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,7,4,2]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,2,4,5]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,2,5,4]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,4,2,5]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,4,5,2]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,5,2,4]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,5,4,2]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,4,5,7]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,4,7,5]=>[1,3,2,6,7,5,4]=>[7,5,6,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,5,4,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,5,7,4]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,7,4,5]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,7,5,4]=>[1,3,2,6,5,7,4]=>[7,5,6,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,1,5,7]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,1,7,5]=>[1,3,2,6,7,5,4]=>[7,5,6,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,5,1,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,5,7,1]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,7,1,5]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,7,5,1]=>[1,3,2,6,5,7,4]=>[7,5,6,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,1,4,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,1,7,4]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,4,1,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,4,7,1]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,7,1,4]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,7,4,1]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,1,4,5]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,1,5,4]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,4,1,5]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,4,5,1]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,5,1,4]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,5,4,1]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,2,5,7]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,2,7,5]=>[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,5,2,7]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,5,7,2]=>[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,7,2,5]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,7,5,2]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,1,5,7]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,1,7,5]=>[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,5,1,7]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,5,7,1]=>[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,7,1,5]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,7,5,1]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,1,2,7]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,1,7,2]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,2,1,7]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,2,7,1]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,7,1,2]=>[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,7,2,1]=>[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,1,2,5]=>[1,3,4,7,5,2,6]=>[7,5,4,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,1,5,2]=>[1,3,4,7,2,6,5]=>[7,5,4,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,2,1,5]=>[1,3,4,7,5,2,6]=>[7,5,4,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,2,5,1]=>[1,3,4,7,2,6,5]=>[7,5,4,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,5,1,2]=>[1,3,4,7,2,6,5]=>[7,5,4,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,5,2,1]=>[1,3,4,7,2,6,5]=>[7,5,4,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,2,4,7]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,2,7,4]=>[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,4,2,7]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,4,7,2]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,7,2,4]=>[1,3,5,7,4,2,6]=>[7,5,3,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,7,4,2]=>[1,3,5,7,2,6,4]=>[7,5,3,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,1,4,7]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,1,7,4]=>[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,4,1,7]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,4,7,1]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,7,1,4]=>[1,3,5,7,4,2,6]=>[7,5,3,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,7,4,1]=>[1,3,5,7,2,6,4]=>[7,5,3,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,1,2,7]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,1,7,2]=>[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,2,1,7]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,2,7,1]=>[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,7,1,2]=>[1,3,5,7,2,6,4]=>[7,5,3,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,7,2,1]=>[1,3,5,7,2,6,4]=>[7,5,3,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,1,2,4]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,1,4,2]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,2,1,4]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,2,4,1]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,4,1,2]=>[1,3,5,4,7,2,6]=>[7,5,3,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,4,2,1]=>[1,3,5,4,7,2,6]=>[7,5,3,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,2,4,5]=>[1,3,7,5,2,6,4]=>[7,5,1,3,6,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,2,5,4]=>[1,3,7,4,2,6,5]=>[7,5,1,4,6,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,4,2,5]=>[1,3,7,5,4,2,6]=>[7,5,1,3,4,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,4,5,2]=>[1,3,7,2,6,5,4]=>[7,5,1,6,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,5,2,4]=>[1,3,7,4,2,6,5]=>[7,5,1,4,6,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,5,4,2]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,1,4,5]=>[1,3,7,5,2,6,4]=>[7,5,1,3,6,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,1,5,4]=>[1,3,7,4,2,6,5]=>[7,5,1,4,6,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,4,1,5]=>[1,3,7,5,4,2,6]=>[7,5,1,3,4,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,4,5,1]=>[1,3,7,2,6,5,4]=>[7,5,1,6,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,5,1,4]=>[1,3,7,4,2,6,5]=>[7,5,1,4,6,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,5,4,1]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,1,2,5]=>[1,3,7,5,2,6,4]=>[7,5,1,3,6,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,1,5,2]=>[1,3,7,2,6,5,4]=>[7,5,1,6,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,2,1,5]=>[1,3,7,5,2,6,4]=>[7,5,1,3,6,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,2,5,1]=>[1,3,7,2,6,5,4]=>[7,5,1,6,2,3,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,5,1,2]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,5,2,1]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,1,2,4]=>[1,3,7,4,5,2,6]=>[7,5,1,4,3,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,1,4,2]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,2,1,4]=>[1,3,7,4,5,2,6]=>[7,5,1,4,3,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,2,4,1]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,4,1,2]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,4,2,1]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,4,5,6]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,4,6,5]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,5,4,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,5,6,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,6,4,5]=>[1,3,2,7,5,6,4]=>[7,5,6,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,6,5,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,2,5,6]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,2,6,5]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,5,2,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,5,6,2]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,6,2,5]=>[1,3,2,7,5,6,4]=>[7,5,6,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,6,5,2]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,2,4,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,2,6,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,4,2,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,4,6,2]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,6,2,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,6,4,2]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,2,4,5]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,2,5,4]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,4,2,5]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,4,5,2]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,5,2,4]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,5,4,2]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,4,5,6]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,4,6,5]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,5,4,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,5,6,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,6,4,5]=>[1,3,2,7,5,6,4]=>[7,5,6,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,6,5,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,1,5,6]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,1,6,5]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,5,1,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,5,6,1]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,6,1,5]=>[1,3,2,7,5,6,4]=>[7,5,6,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,6,5,1]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,1,4,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,1,6,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,4,1,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,4,6,1]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,6,1,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,6,4,1]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,1,4,5]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,1,5,4]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,4,1,5]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,4,5,1]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,5,1,4]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,5,4,1]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,2,5,6]=>[1,3,4,2,7,6,5]=>[7,5,4,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,2,6,5]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,5,2,6]=>[1,3,4,2,7,6,5]=>[7,5,4,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,5,6,2]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,6,2,5]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,6,5,2]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,1,5,6]=>[1,3,4,2,7,6,5]=>[7,5,4,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,1,6,5]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,5,1,6]=>[1,3,4,2,7,6,5]=>[7,5,4,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,5,6,1]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,6,1,5]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,6,5,1]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,1,2,6]=>[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,1,6,2]=>[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,2,1,6]=>[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,2,6,1]=>[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,6,1,2]=>[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,6,2,1]=>[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,1,2,5]=>[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,1,5,2]=>[1,3,4,6,5,2,7]=>[7,5,4,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,2,1,5]=>[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,2,5,1]=>[1,3,4,6,5,2,7]=>[7,5,4,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,5,1,2]=>[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,5,2,1]=>[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,2,4,6]=>[1,3,5,2,7,6,4]=>[7,5,3,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,2,6,4]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,4,2,6]=>[1,3,5,4,2,7,6]=>[7,5,3,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,4,6,2]=>[1,3,5,4,2,7,6]=>[7,5,3,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,6,2,4]=>[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,6,4,2]=>[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,1,4,6]=>[1,3,5,2,7,6,4]=>[7,5,3,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,1,6,4]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,4,1,6]=>[1,3,5,4,2,7,6]=>[7,5,3,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,4,6,1]=>[1,3,5,4,2,7,6]=>[7,5,3,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,6,1,4]=>[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,6,4,1]=>[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,1,2,6]=>[1,3,5,2,7,6,4]=>[7,5,3,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,1,6,2]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,2,1,6]=>[1,3,5,2,7,6,4]=>[7,5,3,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,2,6,1]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,6,1,2]=>[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,6,2,1]=>[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,1,2,4]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,1,4,2]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,2,1,4]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,2,4,1]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,4,1,2]=>[1,3,5,4,6,2,7]=>[7,5,3,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,4,2,1]=>[1,3,5,4,6,2,7]=>[7,5,3,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,2,4,5]=>[1,3,6,4,2,7,5]=>[7,5,2,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,2,5,4]=>[1,3,6,5,2,7,4]=>[7,5,2,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,4,2,5]=>[1,3,6,2,7,5,4]=>[7,5,2,6,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,4,5,2]=>[1,3,6,5,4,2,7]=>[7,5,2,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,5,2,4]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,5,4,2]=>[1,3,6,4,2,7,5]=>[7,5,2,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,1,4,5]=>[1,3,6,4,2,7,5]=>[7,5,2,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,1,5,4]=>[1,3,6,5,2,7,4]=>[7,5,2,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,4,1,5]=>[1,3,6,2,7,5,4]=>[7,5,2,6,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,4,5,1]=>[1,3,6,5,4,2,7]=>[7,5,2,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,5,1,4]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,5,4,1]=>[1,3,6,4,2,7,5]=>[7,5,2,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,1,2,5]=>[1,3,6,2,7,5,4]=>[7,5,2,6,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,1,5,2]=>[1,3,6,5,2,7,4]=>[7,5,2,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,2,1,5]=>[1,3,6,2,7,5,4]=>[7,5,2,6,1,3,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,2,5,1]=>[1,3,6,5,2,7,4]=>[7,5,2,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,5,1,2]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,5,2,1]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,1,2,4]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,1,4,2]=>[1,3,6,4,5,2,7]=>[7,5,2,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,2,1,4]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,2,4,1]=>[1,3,6,4,5,2,7]=>[7,5,2,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,4,1,2]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,4,2,1]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,5,6,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,5,7,6]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,6,5,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,6,7,5]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,7,5,6]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,7,6,5]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,3,6,7]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,3,7,6]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,6,3,7]=>[1,4,5,6,3,2,7]=>[7,4,3,2,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,6,7,3]=>[1,4,5,6,7,3,2]=>[7,4,3,2,1,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,7,3,6]=>[1,4,5,7,6,3,2]=>[7,4,3,1,2,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,7,6,3]=>[1,4,5,7,3,2,6]=>[7,4,3,1,5,6,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,3,5,7]=>[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,3,7,5]=>[1,4,6,7,5,3,2]=>[7,4,2,1,3,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,5,3,7]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,5,7,3]=>[1,4,6,7,3,2,5]=>[7,4,2,1,5,6,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,7,3,5]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,7,5,3]=>[1,4,6,5,7,3,2]=>[7,4,2,3,1,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,3,5,6]=>[1,4,7,6,5,3,2]=>[7,4,1,2,3,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,3,6,5]=>[1,4,7,5,3,2,6]=>[7,4,1,3,5,6,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,5,3,6]=>[1,4,7,6,3,2,5]=>[7,4,1,2,5,6,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,5,6,3]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,6,3,5]=>[1,4,7,5,6,3,2]=>[7,4,1,3,2,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,6,5,3]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,5,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,5,7,6]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,6,5,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,6,7,5]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,7,5,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,7,6,5]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,2,6,7]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,2,7,6]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,6,2,7]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,6,7,2]=>[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,7,2,6]=>[1,4,5,7,6,2,3]=>[7,4,3,1,2,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,7,6,2]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,2,5,7]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,2,7,5]=>[1,4,6,7,5,2,3]=>[7,4,2,1,3,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,5,2,7]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,5,7,2]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,7,2,5]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,7,5,2]=>[1,4,6,5,7,2,3]=>[7,4,2,3,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,2,5,6]=>[1,4,7,6,5,2,3]=>[7,4,1,2,3,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,2,6,5]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,5,2,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,5,6,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,6,2,5]=>[1,4,7,5,6,2,3]=>[7,4,1,3,2,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,6,5,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,3,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,3,7,6]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,6,3,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,6,7,3]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,7,3,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,7,6,3]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,2,6,7]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,2,7,6]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,6,2,7]=>[1,4,3,5,6,2,7]=>[7,4,5,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,6,7,2]=>[1,4,3,5,6,7,2]=>[7,4,5,3,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,7,2,6]=>[1,4,3,5,7,6,2]=>[7,4,5,3,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,7,6,2]=>[1,4,3,5,7,2,6]=>[7,4,5,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,2,3,7]=>[1,4,6,3,5,2,7]=>[7,4,2,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,2,7,3]=>[1,4,6,7,3,5,2]=>[7,4,2,1,5,3,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,3,2,7]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,3,7,2]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,7,2,3]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,7,3,2]=>[1,4,6,3,5,7,2]=>[7,4,2,5,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,2,3,6]=>[1,4,7,6,3,5,2]=>[7,4,1,2,5,3,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,2,6,3]=>[1,4,7,3,5,2,6]=>[7,4,1,5,3,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,3,2,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,3,6,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,6,2,3]=>[1,4,7,3,5,6,2]=>[7,4,1,5,3,2,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,6,3,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,3,5,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,3,7,5]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,5,3,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,5,7,3]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,7,3,5]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,7,5,3]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,2,5,7]=>[1,4,3,6,5,2,7]=>[7,4,5,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,2,7,5]=>[1,4,3,6,7,5,2]=>[7,4,5,2,1,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,5,2,7]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,5,7,2]=>[1,4,3,6,7,2,5]=>[7,4,5,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,7,2,5]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,7,5,2]=>[1,4,3,6,5,7,2]=>[7,4,5,2,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,2,3,7]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,2,7,3]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,3,2,7]=>[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,3,7,2]=>[1,4,5,3,6,7,2]=>[7,4,3,5,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,7,2,3]=>[1,4,5,7,3,6,2]=>[7,4,3,1,5,2,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,7,3,2]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,2,3,5]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,2,5,3]=>[1,4,7,3,6,5,2]=>[7,4,1,5,2,3,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,3,2,5]=>[1,4,7,5,3,6,2]=>[7,4,1,3,5,2,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,3,5,2]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,5,2,3]=>[1,4,7,3,6,2,5]=>[7,4,1,5,2,6,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,5,3,2]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,3,5,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,3,6,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,5,3,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,5,6,3]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,6,3,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,6,5,3]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,2,5,6]=>[1,4,3,7,6,5,2]=>[7,4,5,1,2,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,2,6,5]=>[1,4,3,7,5,2,6]=>[7,4,5,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,5,2,6]=>[1,4,3,7,6,2,5]=>[7,4,5,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,5,6,2]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,6,2,5]=>[1,4,3,7,5,6,2]=>[7,4,5,1,3,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,6,5,2]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,2,3,6]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,2,6,3]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,3,2,6]=>[1,4,5,3,7,6,2]=>[7,4,3,5,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,3,6,2]=>[1,4,5,3,7,2,6]=>[7,4,3,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,6,2,3]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,6,3,2]=>[1,4,5,6,3,7,2]=>[7,4,3,2,5,1,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,2,3,5]=>[1,4,6,3,7,5,2]=>[7,4,2,5,1,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,2,5,3]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,3,2,5]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,3,5,2]=>[1,4,6,5,3,7,2]=>[7,4,2,3,5,1,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,5,2,3]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,5,3,2]=>[1,4,6,3,7,2,5]=>[7,4,2,5,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,5,6,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,5,7,6]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,6,5,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,6,7,5]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,7,5,6]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,7,6,5]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,3,6,7]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,3,7,6]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,6,3,7]=>[1,4,5,6,3,2,7]=>[7,4,3,2,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,6,7,3]=>[1,4,5,6,7,3,2]=>[7,4,3,2,1,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,7,3,6]=>[1,4,5,7,6,3,2]=>[7,4,3,1,2,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,7,6,3]=>[1,4,5,7,3,2,6]=>[7,4,3,1,5,6,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,3,5,7]=>[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,3,7,5]=>[1,4,6,7,5,3,2]=>[7,4,2,1,3,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,5,3,7]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,5,7,3]=>[1,4,6,7,3,2,5]=>[7,4,2,1,5,6,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,7,3,5]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,7,5,3]=>[1,4,6,5,7,3,2]=>[7,4,2,3,1,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,3,5,6]=>[1,4,7,6,5,3,2]=>[7,4,1,2,3,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,3,6,5]=>[1,4,7,5,3,2,6]=>[7,4,1,3,5,6,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,5,3,6]=>[1,4,7,6,3,2,5]=>[7,4,1,2,5,6,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,5,6,3]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,6,3,5]=>[1,4,7,5,6,3,2]=>[7,4,1,3,2,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,6,5,3]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,5,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,5,7,6]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,6,5,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,6,7,5]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,7,5,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,7,6,5]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,1,6,7]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,1,7,6]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,6,1,7]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,6,7,1]=>[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,7,1,6]=>[1,4,5,7,6,2,3]=>[7,4,3,1,2,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,7,6,1]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,1,5,7]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,1,7,5]=>[1,4,6,7,5,2,3]=>[7,4,2,1,3,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,5,1,7]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,5,7,1]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,7,1,5]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,7,5,1]=>[1,4,6,5,7,2,3]=>[7,4,2,3,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,1,5,6]=>[1,4,7,6,5,2,3]=>[7,4,1,2,3,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,1,6,5]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,5,1,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,5,6,1]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,6,1,5]=>[1,4,7,5,6,2,3]=>[7,4,1,3,2,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,6,5,1]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,3,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,3,7,6]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,6,3,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,6,7,3]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,7,3,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,7,6,3]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,1,6,7]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,1,7,6]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,6,1,7]=>[1,4,3,5,6,2,7]=>[7,4,5,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,6,7,1]=>[1,4,3,5,6,7,2]=>[7,4,5,3,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,7,1,6]=>[1,4,3,5,7,6,2]=>[7,4,5,3,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,7,6,1]=>[1,4,3,5,7,2,6]=>[7,4,5,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,1,3,7]=>[1,4,6,3,5,2,7]=>[7,4,2,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,1,7,3]=>[1,4,6,7,3,5,2]=>[7,4,2,1,5,3,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,3,1,7]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,3,7,1]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,7,1,3]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,7,3,1]=>[1,4,6,3,5,7,2]=>[7,4,2,5,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,1,3,6]=>[1,4,7,6,3,5,2]=>[7,4,1,2,5,3,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,1,6,3]=>[1,4,7,3,5,2,6]=>[7,4,1,5,3,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,3,1,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,3,6,1]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,6,1,3]=>[1,4,7,3,5,6,2]=>[7,4,1,5,3,2,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,6,3,1]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,3,5,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,3,7,5]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,5,3,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,5,7,3]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,7,3,5]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,7,5,3]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,1,5,7]=>[1,4,3,6,5,2,7]=>[7,4,5,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,1,7,5]=>[1,4,3,6,7,5,2]=>[7,4,5,2,1,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,5,1,7]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,5,7,1]=>[1,4,3,6,7,2,5]=>[7,4,5,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,7,1,5]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,7,5,1]=>[1,4,3,6,5,7,2]=>[7,4,5,2,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,1,3,7]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,1,7,3]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,3,1,7]=>[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,3,7,1]=>[1,4,5,3,6,7,2]=>[7,4,3,5,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,7,1,3]=>[1,4,5,7,3,6,2]=>[7,4,3,1,5,2,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,7,3,1]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,1,3,5]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,1,5,3]=>[1,4,7,3,6,5,2]=>[7,4,1,5,2,3,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,3,1,5]=>[1,4,7,5,3,6,2]=>[7,4,1,3,5,2,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,3,5,1]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,5,1,3]=>[1,4,7,3,6,2,5]=>[7,4,1,5,2,6,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,5,3,1]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,3,5,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,3,6,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,5,3,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,5,6,3]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,6,3,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,6,5,3]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,1,5,6]=>[1,4,3,7,6,5,2]=>[7,4,5,1,2,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,1,6,5]=>[1,4,3,7,5,2,6]=>[7,4,5,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,5,1,6]=>[1,4,3,7,6,2,5]=>[7,4,5,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,5,6,1]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,6,1,5]=>[1,4,3,7,5,6,2]=>[7,4,5,1,3,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,6,5,1]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,1,3,6]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,1,6,3]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,3,1,6]=>[1,4,5,3,7,6,2]=>[7,4,3,5,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,3,6,1]=>[1,4,5,3,7,2,6]=>[7,4,3,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,6,1,3]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,6,3,1]=>[1,4,5,6,3,7,2]=>[7,4,3,2,5,1,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,1,3,5]=>[1,4,6,3,7,5,2]=>[7,4,2,5,1,3,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,1,5,3]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,3,1,5]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,3,5,1]=>[1,4,6,5,3,7,2]=>[7,4,2,3,5,1,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,5,1,3]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,5,3,1]=>[1,4,6,3,7,2,5]=>[7,4,2,5,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,5,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,5,7,6]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,6,5,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,6,7,5]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,7,5,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,7,6,5]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,2,6,7]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,2,7,6]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,6,2,7]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,6,7,2]=>[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,7,2,6]=>[1,4,5,7,6,2,3]=>[7,4,3,1,2,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,7,6,2]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,2,5,7]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,2,7,5]=>[1,4,6,7,5,2,3]=>[7,4,2,1,3,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,5,2,7]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,5,7,2]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,7,2,5]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,7,5,2]=>[1,4,6,5,7,2,3]=>[7,4,2,3,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,2,5,6]=>[1,4,7,6,5,2,3]=>[7,4,1,2,3,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,2,6,5]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,5,2,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,5,6,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,6,2,5]=>[1,4,7,5,6,2,3]=>[7,4,1,3,2,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,6,5,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,5,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,5,7,6]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,6,5,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,6,7,5]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,7,5,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,7,6,5]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,1,6,7]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,1,7,6]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,6,1,7]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,6,7,1]=>[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,7,1,6]=>[1,4,5,7,6,2,3]=>[7,4,3,1,2,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,7,6,1]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,1,5,7]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,1,7,5]=>[1,4,6,7,5,2,3]=>[7,4,2,1,3,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,5,1,7]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,5,7,1]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,7,1,5]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,7,5,1]=>[1,4,6,5,7,2,3]=>[7,4,2,3,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,1,5,6]=>[1,4,7,6,5,2,3]=>[7,4,1,2,3,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,1,6,5]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,5,1,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,5,6,1]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,6,1,5]=>[1,4,7,5,6,2,3]=>[7,4,1,3,2,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,6,5,1]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,2,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,2,7,6]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,6,2,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,6,7,2]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,7,2,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,7,6,2]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,1,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,1,7,6]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,6,1,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,6,7,1]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,7,1,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,7,6,1]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,1,2,7]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,1,7,2]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,2,1,7]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,2,7,1]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,7,1,2]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,7,2,1]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,1,2,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,1,6,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,2,1,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,2,6,1]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,6,1,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,6,2,1]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,2,5,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,2,7,5]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,5,2,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,5,7,2]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,7,2,5]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,7,5,2]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,1,5,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,1,7,5]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,5,1,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,5,7,1]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,7,1,5]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,7,5,1]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,1,2,7]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,1,7,2]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,2,1,7]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,2,7,1]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,7,1,2]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,7,2,1]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,1,2,5]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,1,5,2]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,2,1,5]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,2,5,1]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,5,1,2]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,5,2,1]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,2,5,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,2,6,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,5,2,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,5,6,2]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,6,2,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,6,5,2]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,1,5,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,1,6,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,5,1,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,5,6,1]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,6,1,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,6,5,1]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,1,2,6]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,1,6,2]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,2,1,6]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,2,6,1]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,6,1,2]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,6,2,1]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,1,2,5]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,1,5,2]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,2,1,5]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,2,5,1]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,5,1,2]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,5,2,1]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,3,6,7]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,3,7,6]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,6,3,7]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,6,7,3]=>[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,7,3,6]=>[1,4,2,5,7,6,3]=>[7,4,6,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,7,6,3]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,2,6,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,2,7,6]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,6,2,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,6,7,2]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,7,2,6]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,7,6,2]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,2,3,7]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,2,7,3]=>[1,4,6,7,3,2,5]=>[7,4,2,1,5,6,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,3,2,7]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,3,7,2]=>[1,4,6,7,2,5,3]=>[7,4,2,1,6,3,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,7,2,3]=>[1,4,6,2,5,7,3]=>[7,4,2,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,7,3,2]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,2,3,6]=>[1,4,7,6,3,2,5]=>[7,4,1,2,5,6,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,2,6,3]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,3,2,6]=>[1,4,7,6,2,5,3]=>[7,4,1,2,6,3,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,3,6,2]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,6,2,3]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,6,3,2]=>[1,4,7,2,5,6,3]=>[7,4,1,6,3,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,3,6,7]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,3,7,6]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,6,3,7]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,6,7,3]=>[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,7,3,6]=>[1,4,2,5,7,6,3]=>[7,4,6,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,7,6,3]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,1,6,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,1,7,6]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,6,1,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,6,7,1]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,7,1,6]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,7,6,1]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,1,3,7]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,1,7,3]=>[1,4,6,7,3,2,5]=>[7,4,2,1,5,6,3]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,3,1,7]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,3,7,1]=>[1,4,6,7,2,5,3]=>[7,4,2,1,6,3,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,7,1,3]=>[1,4,6,2,5,7,3]=>[7,4,2,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,7,3,1]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,1,3,6]=>[1,4,7,6,3,2,5]=>[7,4,1,2,5,6,3]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,1,6,3]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,3,1,6]=>[1,4,7,6,2,5,3]=>[7,4,1,2,6,3,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,3,6,1]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,6,1,3]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,6,3,1]=>[1,4,7,2,5,6,3]=>[7,4,1,6,3,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,2,6,7]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,2,7,6]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,6,2,7]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,6,7,2]=>[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,7,2,6]=>[1,4,2,5,7,6,3]=>[7,4,6,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,7,6,2]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,1,6,7]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,1,7,6]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,6,1,7]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,6,7,1]=>[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,7,1,6]=>[1,4,2,5,7,6,3]=>[7,4,6,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,7,6,1]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,1,2,7]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,1,7,2]=>[1,4,6,7,2,5,3]=>[7,4,2,1,6,3,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,2,1,7]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,2,7,1]=>[1,4,6,7,2,5,3]=>[7,4,2,1,6,3,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,7,1,2]=>[1,4,6,2,5,7,3]=>[7,4,2,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,7,2,1]=>[1,4,6,2,5,7,3]=>[7,4,2,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,1,2,6]=>[1,4,7,6,2,5,3]=>[7,4,1,2,6,3,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,1,6,2]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,2,1,6]=>[1,4,7,6,2,5,3]=>[7,4,1,2,6,3,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,2,6,1]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,6,1,2]=>[1,4,7,2,5,6,3]=>[7,4,1,6,3,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,6,2,1]=>[1,4,7,2,5,6,3]=>[7,4,1,6,3,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,2,3,7]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,2,7,3]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,3,2,7]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,3,7,2]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,7,2,3]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,7,3,2]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,1,3,7]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,1,7,3]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,3,1,7]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,3,7,1]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,7,1,3]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,7,3,1]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,1,2,7]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,1,7,2]=>[1,4,3,6,7,2,5]=>[7,4,5,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,2,1,7]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,2,7,1]=>[1,4,3,6,7,2,5]=>[7,4,5,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,7,1,2]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,7,2,1]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,1,2,3]=>[1,4,7,3,6,2,5]=>[7,4,1,5,2,6,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,1,3,2]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,2,1,3]=>[1,4,7,3,6,2,5]=>[7,4,1,5,2,6,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,2,3,1]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,3,1,2]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,3,2,1]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,2,3,6]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,2,6,3]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,3,2,6]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,3,6,2]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,6,2,3]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,6,3,2]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,1,3,6]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,1,6,3]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,3,1,6]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,3,6,1]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,6,1,3]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,6,3,1]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,1,2,6]=>[1,4,3,7,6,2,5]=>[7,4,5,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,1,6,2]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,2,1,6]=>[1,4,3,7,6,2,5]=>[7,4,5,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,2,6,1]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,6,1,2]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,6,2,1]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,1,2,3]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,1,3,2]=>[1,4,6,3,7,2,5]=>[7,4,2,5,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,2,1,3]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,2,3,1]=>[1,4,6,3,7,2,5]=>[7,4,2,5,1,6,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,3,1,2]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,3,2,1]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,3,5,7]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,3,7,5]=>[1,4,2,6,7,5,3]=>[7,4,6,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,5,3,7]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,5,7,3]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,7,3,5]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,7,5,3]=>[1,4,2,6,5,7,3]=>[7,4,6,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,2,5,7]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,2,7,5]=>[1,4,3,2,6,7,5]=>[7,4,5,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,5,2,7]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,5,7,2]=>[1,4,3,2,6,7,5]=>[7,4,5,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,7,2,5]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,7,5,2]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,2,3,7]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,2,7,3]=>[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,3,2,7]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,3,7,2]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,7,2,3]=>[1,4,5,7,3,2,6]=>[7,4,3,1,5,6,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,7,3,2]=>[1,4,5,7,2,6,3]=>[7,4,3,1,6,2,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,2,3,5]=>[1,4,7,5,2,6,3]=>[7,4,1,3,6,2,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,2,5,3]=>[1,4,7,3,2,6,5]=>[7,4,1,5,6,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,3,2,5]=>[1,4,7,5,3,2,6]=>[7,4,1,3,5,6,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,3,5,2]=>[1,4,7,2,6,5,3]=>[7,4,1,6,2,3,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,5,2,3]=>[1,4,7,3,2,6,5]=>[7,4,1,5,6,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,5,3,2]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,3,5,7]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,3,7,5]=>[1,4,2,6,7,5,3]=>[7,4,6,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,5,3,7]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,5,7,3]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,7,3,5]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,7,5,3]=>[1,4,2,6,5,7,3]=>[7,4,6,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,1,5,7]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,1,7,5]=>[1,4,3,2,6,7,5]=>[7,4,5,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,5,1,7]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,5,7,1]=>[1,4,3,2,6,7,5]=>[7,4,5,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,7,1,5]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,7,5,1]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,1,3,7]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,1,7,3]=>[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,3,1,7]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,3,7,1]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,7,1,3]=>[1,4,5,7,3,2,6]=>[7,4,3,1,5,6,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,7,3,1]=>[1,4,5,7,2,6,3]=>[7,4,3,1,6,2,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,1,3,5]=>[1,4,7,5,2,6,3]=>[7,4,1,3,6,2,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,1,5,3]=>[1,4,7,3,2,6,5]=>[7,4,1,5,6,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,3,1,5]=>[1,4,7,5,3,2,6]=>[7,4,1,3,5,6,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,3,5,1]=>[1,4,7,2,6,5,3]=>[7,4,1,6,2,3,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,5,1,3]=>[1,4,7,3,2,6,5]=>[7,4,1,5,6,2,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,5,3,1]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,2,5,7]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,2,7,5]=>[1,4,2,6,7,5,3]=>[7,4,6,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,5,2,7]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,5,7,2]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,7,2,5]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,7,5,2]=>[1,4,2,6,5,7,3]=>[7,4,6,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,1,5,7]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,1,7,5]=>[1,4,2,6,7,5,3]=>[7,4,6,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,5,1,7]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,5,7,1]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,7,1,5]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,7,5,1]=>[1,4,2,6,5,7,3]=>[7,4,6,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,1,2,7]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,1,7,2]=>[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,2,1,7]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,2,7,1]=>[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,7,1,2]=>[1,4,5,7,2,6,3]=>[7,4,3,1,6,2,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,7,2,1]=>[1,4,5,7,2,6,3]=>[7,4,3,1,6,2,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,1,2,5]=>[1,4,7,5,2,6,3]=>[7,4,1,3,6,2,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,1,5,2]=>[1,4,7,2,6,5,3]=>[7,4,1,6,2,3,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,2,1,5]=>[1,4,7,5,2,6,3]=>[7,4,1,3,6,2,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,2,5,1]=>[1,4,7,2,6,5,3]=>[7,4,1,6,2,3,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,5,1,2]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,5,2,1]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,2,3,7]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,2,7,3]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,3,2,7]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,3,7,2]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,7,2,3]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,7,3,2]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,1,3,7]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,1,7,3]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,3,1,7]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,3,7,1]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,7,1,3]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,7,3,1]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,1,2,7]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,1,7,2]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,2,1,7]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,2,7,1]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,7,1,2]=>[1,4,3,5,7,2,6]=>[7,4,5,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,7,2,1]=>[1,4,3,5,7,2,6]=>[7,4,5,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,1,2,3]=>[1,4,7,3,5,2,6]=>[7,4,1,5,3,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,1,3,2]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,2,1,3]=>[1,4,7,3,5,2,6]=>[7,4,1,5,3,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,2,3,1]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,3,1,2]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,3,2,1]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,2,3,5]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,2,5,3]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,3,2,5]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,3,5,2]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,5,2,3]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,5,3,2]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,1,3,5]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,1,5,3]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,3,1,5]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,3,5,1]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,5,1,3]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,5,3,1]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,1,2,5]=>[1,4,3,7,5,2,6]=>[7,4,5,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,1,5,2]=>[1,4,3,7,2,6,5]=>[7,4,5,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,2,1,5]=>[1,4,3,7,5,2,6]=>[7,4,5,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,2,5,1]=>[1,4,3,7,2,6,5]=>[7,4,5,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,5,1,2]=>[1,4,3,7,2,6,5]=>[7,4,5,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,5,2,1]=>[1,4,3,7,2,6,5]=>[7,4,5,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,1,2,3]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,1,3,2]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,2,1,3]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,2,3,1]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,3,1,2]=>[1,4,5,3,7,2,6]=>[7,4,3,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,3,2,1]=>[1,4,5,3,7,2,6]=>[7,4,3,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,3,5,6]=>[1,4,2,7,6,5,3]=>[7,4,6,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,3,6,5]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,5,3,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,5,6,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,6,3,5]=>[1,4,2,7,5,6,3]=>[7,4,6,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,6,5,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,2,5,6]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,2,6,5]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,5,2,6]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,5,6,2]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,6,2,5]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,6,5,2]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,2,3,6]=>[1,4,5,2,7,6,3]=>[7,4,3,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,2,6,3]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,3,2,6]=>[1,4,5,3,2,7,6]=>[7,4,3,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,3,6,2]=>[1,4,5,3,2,7,6]=>[7,4,3,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,6,2,3]=>[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,6,3,2]=>[1,4,5,6,3,2,7]=>[7,4,3,2,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,2,3,5]=>[1,4,6,3,2,7,5]=>[7,4,2,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,2,5,3]=>[1,4,6,5,2,7,3]=>[7,4,2,3,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,3,2,5]=>[1,4,6,2,7,5,3]=>[7,4,2,6,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,3,5,2]=>[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,5,2,3]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,5,3,2]=>[1,4,6,3,2,7,5]=>[7,4,2,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,3,5,6]=>[1,4,2,7,6,5,3]=>[7,4,6,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,3,6,5]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,5,3,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,5,6,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,6,3,5]=>[1,4,2,7,5,6,3]=>[7,4,6,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,6,5,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,1,5,6]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,1,6,5]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,5,1,6]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,5,6,1]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,6,1,5]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,6,5,1]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,1,3,6]=>[1,4,5,2,7,6,3]=>[7,4,3,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,1,6,3]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,3,1,6]=>[1,4,5,3,2,7,6]=>[7,4,3,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,3,6,1]=>[1,4,5,3,2,7,6]=>[7,4,3,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,6,1,3]=>[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,6,3,1]=>[1,4,5,6,3,2,7]=>[7,4,3,2,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,1,3,5]=>[1,4,6,3,2,7,5]=>[7,4,2,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,1,5,3]=>[1,4,6,5,2,7,3]=>[7,4,2,3,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,3,1,5]=>[1,4,6,2,7,5,3]=>[7,4,2,6,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,3,5,1]=>[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,5,1,3]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,5,3,1]=>[1,4,6,3,2,7,5]=>[7,4,2,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,2,5,6]=>[1,4,2,7,6,5,3]=>[7,4,6,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,2,6,5]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,5,2,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,5,6,2]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,6,2,5]=>[1,4,2,7,5,6,3]=>[7,4,6,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,6,5,2]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,1,5,6]=>[1,4,2,7,6,5,3]=>[7,4,6,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,1,6,5]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,5,1,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,5,6,1]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,6,1,5]=>[1,4,2,7,5,6,3]=>[7,4,6,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,6,5,1]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,1,2,6]=>[1,4,5,2,7,6,3]=>[7,4,3,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,1,6,2]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,2,1,6]=>[1,4,5,2,7,6,3]=>[7,4,3,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,2,6,1]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,6,1,2]=>[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,6,2,1]=>[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,1,2,5]=>[1,4,6,2,7,5,3]=>[7,4,2,6,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,1,5,2]=>[1,4,6,5,2,7,3]=>[7,4,2,3,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,2,1,5]=>[1,4,6,2,7,5,3]=>[7,4,2,6,1,3,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,2,5,1]=>[1,4,6,5,2,7,3]=>[7,4,2,3,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,5,1,2]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,5,2,1]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,2,3,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,2,6,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,3,2,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,3,6,2]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,6,2,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,6,3,2]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,1,3,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,1,6,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,3,1,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,3,6,1]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,6,1,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,6,3,1]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,1,2,6]=>[1,4,3,5,2,7,6]=>[7,4,5,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,1,6,2]=>[1,4,3,5,2,7,6]=>[7,4,5,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,2,1,6]=>[1,4,3,5,2,7,6]=>[7,4,5,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,2,6,1]=>[1,4,3,5,2,7,6]=>[7,4,5,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,6,1,2]=>[1,4,3,5,6,2,7]=>[7,4,5,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,6,2,1]=>[1,4,3,5,6,2,7]=>[7,4,5,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,1,2,3]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,1,3,2]=>[1,4,6,3,5,2,7]=>[7,4,2,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,2,1,3]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,2,3,1]=>[1,4,6,3,5,2,7]=>[7,4,2,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,3,1,2]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,3,2,1]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,2,3,5]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,2,5,3]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,3,2,5]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,3,5,2]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,5,2,3]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,5,3,2]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,1,3,5]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,1,5,3]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,3,1,5]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,3,5,1]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,5,1,3]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,5,3,1]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,1,2,5]=>[1,4,3,6,2,7,5]=>[7,4,5,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,1,5,2]=>[1,4,3,6,5,2,7]=>[7,4,5,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,2,1,5]=>[1,4,3,6,2,7,5]=>[7,4,5,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,2,5,1]=>[1,4,3,6,5,2,7]=>[7,4,5,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,5,1,2]=>[1,4,3,6,2,7,5]=>[7,4,5,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,5,2,1]=>[1,4,3,6,2,7,5]=>[7,4,5,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,1,2,3]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,1,3,2]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,2,1,3]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,2,3,1]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,3,1,2]=>[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,3,2,1]=>[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,4,6,7]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,4,7,6]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,6,4,7]=>[1,5,6,4,3,2,7]=>[7,3,2,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,6,7,4]=>[1,5,6,7,4,3,2]=>[7,3,2,1,4,5,6]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,7,4,6]=>[1,5,7,6,4,3,2]=>[7,3,1,2,4,5,6]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,7,6,4]=>[1,5,7,4,3,2,6]=>[7,3,1,4,5,6,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,3,6,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,3,7,6]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,6,3,7]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,6,7,3]=>[1,5,6,7,3,2,4]=>[7,3,2,1,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,7,3,6]=>[1,5,7,6,3,2,4]=>[7,3,1,2,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,7,6,3]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,3,4,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,3,7,4]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,4,3,7]=>[1,5,4,6,3,2,7]=>[7,3,4,2,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,4,7,3]=>[1,5,4,6,7,3,2]=>[7,3,4,2,1,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,7,3,4]=>[1,5,7,4,6,3,2]=>[7,3,1,4,2,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,7,4,3]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,3,4,6]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,3,6,4]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,4,3,6]=>[1,5,4,7,6,3,2]=>[7,3,4,1,2,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,4,6,3]=>[1,5,4,7,3,2,6]=>[7,3,4,1,5,6,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,6,3,4]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,6,4,3]=>[1,5,6,4,7,3,2]=>[7,3,2,4,1,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,4,6,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,4,7,6]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,6,4,7]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,6,7,4]=>[1,5,6,7,4,2,3]=>[7,3,2,1,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,7,4,6]=>[1,5,7,6,4,2,3]=>[7,3,1,2,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,7,6,4]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,2,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,2,7,6]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,6,2,7]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,6,7,2]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,7,2,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,7,6,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,2,4,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,2,7,4]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,4,2,7]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,4,7,2]=>[1,5,4,6,7,2,3]=>[7,3,4,2,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,7,2,4]=>[1,5,7,4,6,2,3]=>[7,3,1,4,2,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,7,4,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,2,4,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,2,6,4]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,4,2,6]=>[1,5,4,7,6,2,3]=>[7,3,4,1,2,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,4,6,2]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,6,2,4]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,6,4,2]=>[1,5,6,4,7,2,3]=>[7,3,2,4,1,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,3,6,7]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,3,7,6]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,6,3,7]=>[1,5,6,3,4,2,7]=>[7,3,2,5,4,6,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,6,7,3]=>[1,5,6,7,3,4,2]=>[7,3,2,1,5,4,6]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,7,3,6]=>[1,5,7,6,3,4,2]=>[7,3,1,2,5,4,6]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,7,6,3]=>[1,5,7,3,4,2,6]=>[7,3,1,5,4,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,2,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,2,7,6]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,6,2,7]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,6,7,2]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,7,2,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,7,6,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,2,3,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,2,7,3]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,3,2,7]=>[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,3,7,2]=>[1,5,3,4,6,7,2]=>[7,3,5,4,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,7,2,3]=>[1,5,7,3,4,6,2]=>[7,3,1,5,4,2,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,7,3,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,2,3,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,2,6,3]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,3,2,6]=>[1,5,3,4,7,6,2]=>[7,3,5,4,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,3,6,2]=>[1,5,3,4,7,2,6]=>[7,3,5,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,6,2,3]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,6,3,2]=>[1,5,6,3,4,7,2]=>[7,3,2,5,4,1,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,3,4,7]=>[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,3,7,4]=>[1,5,3,6,7,4,2]=>[7,3,5,2,1,4,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,4,3,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,4,7,3]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,7,3,4]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,7,4,3]=>[1,5,7,3,6,4,2]=>[7,3,1,5,2,4,6]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,2,4,7]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,2,7,4]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,4,2,7]=>[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,4,7,2]=>[1,5,4,3,6,7,2]=>[7,3,4,5,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,7,2,4]=>[1,5,7,4,3,6,2]=>[7,3,1,4,5,2,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,7,4,2]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,2,3,7]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,2,7,3]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,3,2,7]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,3,7,2]=>[1,5,3,6,7,2,4]=>[7,3,5,2,1,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,7,2,3]=>[1,5,7,3,6,2,4]=>[7,3,1,5,2,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,7,3,2]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,2,3,4]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,2,4,3]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,3,2,4]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,3,4,2]=>[1,5,3,6,4,7,2]=>[7,3,5,2,4,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,4,2,3]=>[1,5,4,7,3,6,2]=>[7,3,4,1,5,2,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,4,3,2]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,3,4,6]=>[1,5,3,7,6,4,2]=>[7,3,5,1,2,4,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,3,6,4]=>[1,5,3,7,4,2,6]=>[7,3,5,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,4,3,6]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,4,6,3]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,6,3,4]=>[1,5,6,3,7,4,2]=>[7,3,2,5,1,4,6]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,6,4,3]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,2,4,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,2,6,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,4,2,6]=>[1,5,4,3,7,6,2]=>[7,3,4,5,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,4,6,2]=>[1,5,4,3,7,2,6]=>[7,3,4,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,6,2,4]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,6,4,2]=>[1,5,6,4,3,7,2]=>[7,3,2,4,5,1,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,2,3,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,2,6,3]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,3,2,6]=>[1,5,3,7,6,2,4]=>[7,3,5,1,2,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,3,6,2]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,6,2,3]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,6,3,2]=>[1,5,6,3,7,2,4]=>[7,3,2,5,1,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,2,3,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,2,4,3]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,3,2,4]=>[1,5,3,7,4,6,2]=>[7,3,5,1,4,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,3,4,2]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,4,2,3]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,4,3,2]=>[1,5,4,6,3,7,2]=>[7,3,4,2,5,1,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,4,6,7]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,4,7,6]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,6,4,7]=>[1,5,6,4,3,2,7]=>[7,3,2,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,6,7,4]=>[1,5,6,7,4,3,2]=>[7,3,2,1,4,5,6]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,7,4,6]=>[1,5,7,6,4,3,2]=>[7,3,1,2,4,5,6]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,7,6,4]=>[1,5,7,4,3,2,6]=>[7,3,1,4,5,6,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,3,6,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,3,7,6]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,6,3,7]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,6,7,3]=>[1,5,6,7,3,2,4]=>[7,3,2,1,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,7,3,6]=>[1,5,7,6,3,2,4]=>[7,3,1,2,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,7,6,3]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,3,4,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,3,7,4]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,4,3,7]=>[1,5,4,6,3,2,7]=>[7,3,4,2,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,4,7,3]=>[1,5,4,6,7,3,2]=>[7,3,4,2,1,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,7,3,4]=>[1,5,7,4,6,3,2]=>[7,3,1,4,2,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,7,4,3]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,3,4,6]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,3,6,4]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,4,3,6]=>[1,5,4,7,6,3,2]=>[7,3,4,1,2,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,4,6,3]=>[1,5,4,7,3,2,6]=>[7,3,4,1,5,6,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,6,3,4]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,6,4,3]=>[1,5,6,4,7,3,2]=>[7,3,2,4,1,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,4,6,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,4,7,6]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,6,4,7]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,6,7,4]=>[1,5,6,7,4,2,3]=>[7,3,2,1,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,7,4,6]=>[1,5,7,6,4,2,3]=>[7,3,1,2,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,7,6,4]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,1,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,1,7,6]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,6,1,7]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,6,7,1]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,7,1,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,7,6,1]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,1,4,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,1,7,4]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,4,1,7]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,4,7,1]=>[1,5,4,6,7,2,3]=>[7,3,4,2,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,7,1,4]=>[1,5,7,4,6,2,3]=>[7,3,1,4,2,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,7,4,1]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,1,4,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,1,6,4]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,4,1,6]=>[1,5,4,7,6,2,3]=>[7,3,4,1,2,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,4,6,1]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,6,1,4]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,6,4,1]=>[1,5,6,4,7,2,3]=>[7,3,2,4,1,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,3,6,7]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,3,7,6]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,6,3,7]=>[1,5,6,3,4,2,7]=>[7,3,2,5,4,6,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,6,7,3]=>[1,5,6,7,3,4,2]=>[7,3,2,1,5,4,6]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,7,3,6]=>[1,5,7,6,3,4,2]=>[7,3,1,2,5,4,6]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,7,6,3]=>[1,5,7,3,4,2,6]=>[7,3,1,5,4,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,1,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,1,7,6]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,6,1,7]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,6,7,1]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,7,1,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,7,6,1]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,1,3,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,1,7,3]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,3,1,7]=>[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,3,7,1]=>[1,5,3,4,6,7,2]=>[7,3,5,4,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,7,1,3]=>[1,5,7,3,4,6,2]=>[7,3,1,5,4,2,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,7,3,1]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,1,3,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,1,6,3]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,3,1,6]=>[1,5,3,4,7,6,2]=>[7,3,5,4,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,3,6,1]=>[1,5,3,4,7,2,6]=>[7,3,5,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,6,1,3]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,6,3,1]=>[1,5,6,3,4,7,2]=>[7,3,2,5,4,1,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,3,4,7]=>[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,3,7,4]=>[1,5,3,6,7,4,2]=>[7,3,5,2,1,4,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,4,3,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,4,7,3]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,7,3,4]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,7,4,3]=>[1,5,7,3,6,4,2]=>[7,3,1,5,2,4,6]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,1,4,7]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,1,7,4]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,4,1,7]=>[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,4,7,1]=>[1,5,4,3,6,7,2]=>[7,3,4,5,2,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,7,1,4]=>[1,5,7,4,3,6,2]=>[7,3,1,4,5,2,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,7,4,1]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,1,3,7]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,1,7,3]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,3,1,7]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,3,7,1]=>[1,5,3,6,7,2,4]=>[7,3,5,2,1,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,7,1,3]=>[1,5,7,3,6,2,4]=>[7,3,1,5,2,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,7,3,1]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,1,3,4]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,1,4,3]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,3,1,4]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,3,4,1]=>[1,5,3,6,4,7,2]=>[7,3,5,2,4,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,4,1,3]=>[1,5,4,7,3,6,2]=>[7,3,4,1,5,2,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,4,3,1]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,3,4,6]=>[1,5,3,7,6,4,2]=>[7,3,5,1,2,4,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,3,6,4]=>[1,5,3,7,4,2,6]=>[7,3,5,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,4,3,6]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,4,6,3]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,6,3,4]=>[1,5,6,3,7,4,2]=>[7,3,2,5,1,4,6]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,6,4,3]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,1,4,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,1,6,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,4,1,6]=>[1,5,4,3,7,6,2]=>[7,3,4,5,1,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,4,6,1]=>[1,5,4,3,7,2,6]=>[7,3,4,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,6,1,4]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,6,4,1]=>[1,5,6,4,3,7,2]=>[7,3,2,4,5,1,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,1,3,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,1,6,3]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,3,1,6]=>[1,5,3,7,6,2,4]=>[7,3,5,1,2,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,3,6,1]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,6,1,3]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,6,3,1]=>[1,5,6,3,7,2,4]=>[7,3,2,5,1,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,1,3,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,1,4,3]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,3,1,4]=>[1,5,3,7,4,6,2]=>[7,3,5,1,4,2,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,3,4,1]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,4,1,3]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,4,3,1]=>[1,5,4,6,3,7,2]=>[7,3,4,2,5,1,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,4,6,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,4,7,6]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,6,4,7]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,6,7,4]=>[1,5,6,7,4,2,3]=>[7,3,2,1,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,7,4,6]=>[1,5,7,6,4,2,3]=>[7,3,1,2,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,7,6,4]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,2,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,2,7,6]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,6,2,7]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,6,7,2]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,7,2,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,7,6,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,2,4,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,2,7,4]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,4,2,7]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,4,7,2]=>[1,5,4,6,7,2,3]=>[7,3,4,2,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,7,2,4]=>[1,5,7,4,6,2,3]=>[7,3,1,4,2,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,7,4,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,2,4,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,2,6,4]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,4,2,6]=>[1,5,4,7,6,2,3]=>[7,3,4,1,2,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,4,6,2]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,6,2,4]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,6,4,2]=>[1,5,6,4,7,2,3]=>[7,3,2,4,1,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,4,6,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,4,7,6]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,6,4,7]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,6,7,4]=>[1,5,6,7,4,2,3]=>[7,3,2,1,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,7,4,6]=>[1,5,7,6,4,2,3]=>[7,3,1,2,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,7,6,4]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,1,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,1,7,6]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,6,1,7]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,6,7,1]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,7,1,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,7,6,1]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,1,4,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,1,7,4]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,4,1,7]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,4,7,1]=>[1,5,4,6,7,2,3]=>[7,3,4,2,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,7,1,4]=>[1,5,7,4,6,2,3]=>[7,3,1,4,2,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,7,4,1]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,1,4,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,1,6,4]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,4,1,6]=>[1,5,4,7,6,2,3]=>[7,3,4,1,2,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,4,6,1]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,6,1,4]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,6,4,1]=>[1,5,6,4,7,2,3]=>[7,3,2,4,1,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,2,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,2,7,6]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,6,2,7]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,6,7,2]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,7,2,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,7,6,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,1,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,1,7,6]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,6,1,7]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,6,7,1]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,7,1,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,7,6,1]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,1,2,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,1,7,2]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,2,1,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,2,7,1]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,7,1,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,7,2,1]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,1,2,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,1,6,2]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,2,1,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,2,6,1]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,6,1,2]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,6,2,1]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,2,4,7]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,2,7,4]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,4,2,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,4,7,2]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,7,2,4]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,7,4,2]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,1,4,7]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,1,7,4]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,4,1,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,4,7,1]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,7,1,4]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,7,4,1]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,1,2,7]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,1,7,2]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,2,1,7]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,2,7,1]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,7,1,2]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,7,2,1]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,1,2,4]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,1,4,2]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,2,1,4]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,2,4,1]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,4,1,2]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,4,2,1]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,2,4,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,2,6,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,4,2,6]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,4,6,2]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,6,2,4]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,6,4,2]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,1,4,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,1,6,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,4,1,6]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,4,6,1]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,6,1,4]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,6,4,1]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,1,2,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,1,6,2]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,2,1,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,2,6,1]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,6,1,2]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,6,2,1]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,1,2,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,1,4,2]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,2,1,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,2,4,1]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,4,1,2]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,4,2,1]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,3,6,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,3,7,6]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,6,3,7]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,6,7,3]=>[1,5,6,7,3,2,4]=>[7,3,2,1,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,7,3,6]=>[1,5,7,6,3,2,4]=>[7,3,1,2,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,7,6,3]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,2,6,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,2,7,6]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,6,2,7]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,6,7,2]=>[1,5,6,7,2,4,3]=>[7,3,2,1,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,7,2,6]=>[1,5,7,6,2,4,3]=>[7,3,1,2,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,7,6,2]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,2,3,7]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,2,7,3]=>[1,5,2,4,6,7,3]=>[7,3,6,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,3,2,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,3,7,2]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,7,2,3]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,7,3,2]=>[1,5,7,2,4,6,3]=>[7,3,1,6,4,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,2,3,6]=>[1,5,2,4,7,6,3]=>[7,3,6,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,2,6,3]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,3,2,6]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,3,6,2]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,6,2,3]=>[1,5,6,2,4,7,3]=>[7,3,2,6,4,1,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,6,3,2]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,3,6,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,3,7,6]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,6,3,7]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,6,7,3]=>[1,5,6,7,3,2,4]=>[7,3,2,1,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,7,3,6]=>[1,5,7,6,3,2,4]=>[7,3,1,2,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,7,6,3]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,1,6,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,1,7,6]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,6,1,7]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,6,7,1]=>[1,5,6,7,2,4,3]=>[7,3,2,1,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,7,1,6]=>[1,5,7,6,2,4,3]=>[7,3,1,2,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,7,6,1]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,1,3,7]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,1,7,3]=>[1,5,2,4,6,7,3]=>[7,3,6,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,3,1,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,3,7,1]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,7,1,3]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,7,3,1]=>[1,5,7,2,4,6,3]=>[7,3,1,6,4,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,1,3,6]=>[1,5,2,4,7,6,3]=>[7,3,6,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,1,6,3]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,3,1,6]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,3,6,1]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,6,1,3]=>[1,5,6,2,4,7,3]=>[7,3,2,6,4,1,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,6,3,1]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,2,6,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,2,7,6]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,6,2,7]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,6,7,2]=>[1,5,6,7,2,4,3]=>[7,3,2,1,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,7,2,6]=>[1,5,7,6,2,4,3]=>[7,3,1,2,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,7,6,2]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,1,6,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,1,7,6]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,6,1,7]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,6,7,1]=>[1,5,6,7,2,4,3]=>[7,3,2,1,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,7,1,6]=>[1,5,7,6,2,4,3]=>[7,3,1,2,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,7,6,1]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,1,2,7]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,1,7,2]=>[1,5,2,4,6,7,3]=>[7,3,6,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,2,1,7]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,2,7,1]=>[1,5,2,4,6,7,3]=>[7,3,6,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,7,1,2]=>[1,5,7,2,4,6,3]=>[7,3,1,6,4,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,7,2,1]=>[1,5,7,2,4,6,3]=>[7,3,1,6,4,2,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,1,2,6]=>[1,5,2,4,7,6,3]=>[7,3,6,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,1,6,2]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,2,1,6]=>[1,5,2,4,7,6,3]=>[7,3,6,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,2,6,1]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,6,1,2]=>[1,5,6,2,4,7,3]=>[7,3,2,6,4,1,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,6,2,1]=>[1,5,6,2,4,7,3]=>[7,3,2,6,4,1,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,2,3,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,2,7,3]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,3,2,7]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,3,7,2]=>[1,5,3,6,7,2,4]=>[7,3,5,2,1,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,7,2,3]=>[1,5,7,3,6,2,4]=>[7,3,1,5,2,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,7,3,2]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,1,3,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,1,7,3]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,3,1,7]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,3,7,1]=>[1,5,3,6,7,2,4]=>[7,3,5,2,1,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,7,1,3]=>[1,5,7,3,6,2,4]=>[7,3,1,5,2,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,7,3,1]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,1,2,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,1,7,2]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,2,1,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,2,7,1]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,7,1,2]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,7,2,1]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,1,2,3]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,1,3,2]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,2,1,3]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,2,3,1]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,3,1,2]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,3,2,1]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,2,3,6]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,2,6,3]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,3,2,6]=>[1,5,3,7,6,2,4]=>[7,3,5,1,2,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,3,6,2]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,6,2,3]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,6,3,2]=>[1,5,6,3,7,2,4]=>[7,3,2,5,1,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,1,3,6]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,1,6,3]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,3,1,6]=>[1,5,3,7,6,2,4]=>[7,3,5,1,2,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,3,6,1]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,6,1,3]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,6,3,1]=>[1,5,6,3,7,2,4]=>[7,3,2,5,1,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,1,2,6]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,1,6,2]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,2,1,6]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,2,6,1]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,6,1,2]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,6,2,1]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,1,2,3]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,1,3,2]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,2,1,3]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,2,3,1]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,3,1,2]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,3,2,1]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,3,4,7]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,3,7,4]=>[1,5,3,2,6,7,4]=>[7,3,5,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,4,3,7]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,4,7,3]=>[1,5,4,2,6,7,3]=>[7,3,4,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,7,3,4]=>[1,5,7,4,2,6,3]=>[7,3,1,4,6,2,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,7,4,3]=>[1,5,7,3,2,6,4]=>[7,3,1,5,6,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,2,4,7]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,2,7,4]=>[1,5,2,6,7,4,3]=>[7,3,6,2,1,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,4,2,7]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,4,7,2]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,7,2,4]=>[1,5,7,4,3,2,6]=>[7,3,1,4,5,6,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,7,4,2]=>[1,5,7,2,6,4,3]=>[7,3,1,6,2,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,2,3,7]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,2,7,3]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,3,2,7]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,3,7,2]=>[1,5,3,2,6,7,4]=>[7,3,5,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,7,2,3]=>[1,5,7,3,2,6,4]=>[7,3,1,5,6,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,7,3,2]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,2,3,4]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,2,4,3]=>[1,5,2,6,4,7,3]=>[7,3,6,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,3,2,4]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,3,4,2]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,4,2,3]=>[1,5,4,7,3,2,6]=>[7,3,4,1,5,6,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,4,3,2]=>[1,5,4,7,2,6,3]=>[7,3,4,1,6,2,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,3,4,7]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,3,7,4]=>[1,5,3,2,6,7,4]=>[7,3,5,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,4,3,7]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,4,7,3]=>[1,5,4,2,6,7,3]=>[7,3,4,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,7,3,4]=>[1,5,7,4,2,6,3]=>[7,3,1,4,6,2,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,7,4,3]=>[1,5,7,3,2,6,4]=>[7,3,1,5,6,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,1,4,7]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,1,7,4]=>[1,5,2,6,7,4,3]=>[7,3,6,2,1,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,4,1,7]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,4,7,1]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,7,1,4]=>[1,5,7,4,3,2,6]=>[7,3,1,4,5,6,2]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,7,4,1]=>[1,5,7,2,6,4,3]=>[7,3,1,6,2,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,1,3,7]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,1,7,3]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,3,1,7]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,3,7,1]=>[1,5,3,2,6,7,4]=>[7,3,5,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,7,1,3]=>[1,5,7,3,2,6,4]=>[7,3,1,5,6,2,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,7,3,1]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,1,3,4]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,1,4,3]=>[1,5,2,6,4,7,3]=>[7,3,6,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,3,1,4]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,3,4,1]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,4,1,3]=>[1,5,4,7,3,2,6]=>[7,3,4,1,5,6,2]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,4,3,1]=>[1,5,4,7,2,6,3]=>[7,3,4,1,6,2,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,2,4,7]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,2,7,4]=>[1,5,2,6,7,4,3]=>[7,3,6,2,1,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,4,2,7]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,4,7,2]=>[1,5,4,2,6,7,3]=>[7,3,4,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,7,2,4]=>[1,5,7,4,2,6,3]=>[7,3,1,4,6,2,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,7,4,2]=>[1,5,7,2,6,4,3]=>[7,3,1,6,2,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,1,4,7]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,1,7,4]=>[1,5,2,6,7,4,3]=>[7,3,6,2,1,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,4,1,7]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,4,7,1]=>[1,5,4,2,6,7,3]=>[7,3,4,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,7,1,4]=>[1,5,7,4,2,6,3]=>[7,3,1,4,6,2,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,7,4,1]=>[1,5,7,2,6,4,3]=>[7,3,1,6,2,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,1,2,7]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,1,7,2]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,2,1,7]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,2,7,1]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,7,1,2]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,7,2,1]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,1,2,4]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,1,4,2]=>[1,5,2,6,4,7,3]=>[7,3,6,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,2,1,4]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,2,4,1]=>[1,5,2,6,4,7,3]=>[7,3,6,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,4,1,2]=>[1,5,4,7,2,6,3]=>[7,3,4,1,6,2,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,4,2,1]=>[1,5,4,7,2,6,3]=>[7,3,4,1,6,2,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,2,3,7]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,2,7,3]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,3,2,7]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,3,7,2]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,7,2,3]=>[1,5,7,3,4,2,6]=>[7,3,1,5,4,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,7,3,2]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,1,3,7]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,1,7,3]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,3,1,7]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,3,7,1]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,7,1,3]=>[1,5,7,3,4,2,6]=>[7,3,1,5,4,6,2]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,7,3,1]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,1,2,7]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,1,7,2]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,2,1,7]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,2,7,1]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,7,1,2]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,7,2,1]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,1,2,3]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,1,3,2]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,2,1,3]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,2,3,1]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,3,1,2]=>[1,5,3,4,7,2,6]=>[7,3,5,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,3,2,1]=>[1,5,3,4,7,2,6]=>[7,3,5,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,2,3,4]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,2,4,3]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,3,2,4]=>[1,5,3,7,4,2,6]=>[7,3,5,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,3,4,2]=>[1,5,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,4,2,3]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,4,3,2]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,1,3,4]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,1,4,3]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,3,1,4]=>[1,5,3,7,4,2,6]=>[7,3,5,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,3,4,1]=>[1,5,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,4,1,3]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,4,3,1]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,1,2,4]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,1,4,2]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,2,1,4]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,2,4,1]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,4,1,2]=>[1,5,4,3,7,2,6]=>[7,3,4,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,4,2,1]=>[1,5,4,3,7,2,6]=>[7,3,4,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,1,2,3]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,1,3,2]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,2,1,3]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,2,3,1]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,3,1,2]=>[1,5,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,3,2,1]=>[1,5,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,3,4,6]=>[1,5,3,2,7,6,4]=>[7,3,5,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,3,6,4]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,4,3,6]=>[1,5,4,2,7,6,3]=>[7,3,4,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,4,6,3]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,6,3,4]=>[1,5,6,3,2,7,4]=>[7,3,2,5,6,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,6,4,3]=>[1,5,6,4,2,7,3]=>[7,3,2,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,2,4,6]=>[1,5,2,7,6,4,3]=>[7,3,6,1,2,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,2,6,4]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,4,2,6]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,4,6,2]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,6,2,4]=>[1,5,6,2,7,4,3]=>[7,3,2,6,1,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,6,4,2]=>[1,5,6,4,3,2,7]=>[7,3,2,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,2,3,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,2,6,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,3,2,6]=>[1,5,3,2,7,6,4]=>[7,3,5,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,3,6,2]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,6,2,3]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,6,3,2]=>[1,5,6,3,2,7,4]=>[7,3,2,5,6,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,2,3,4]=>[1,5,2,7,4,6,3]=>[7,3,6,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,2,4,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,3,2,4]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,3,4,2]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,4,2,3]=>[1,5,4,6,2,7,3]=>[7,3,4,2,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,4,3,2]=>[1,5,4,6,3,2,7]=>[7,3,4,2,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,3,4,6]=>[1,5,3,2,7,6,4]=>[7,3,5,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,3,6,4]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,4,3,6]=>[1,5,4,2,7,6,3]=>[7,3,4,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,4,6,3]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,6,3,4]=>[1,5,6,3,2,7,4]=>[7,3,2,5,6,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,6,4,3]=>[1,5,6,4,2,7,3]=>[7,3,2,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,1,4,6]=>[1,5,2,7,6,4,3]=>[7,3,6,1,2,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,1,6,4]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,4,1,6]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,4,6,1]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,6,1,4]=>[1,5,6,2,7,4,3]=>[7,3,2,6,1,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,6,4,1]=>[1,5,6,4,3,2,7]=>[7,3,2,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,1,3,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,1,6,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,3,1,6]=>[1,5,3,2,7,6,4]=>[7,3,5,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,3,6,1]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,6,1,3]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,6,3,1]=>[1,5,6,3,2,7,4]=>[7,3,2,5,6,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,1,3,4]=>[1,5,2,7,4,6,3]=>[7,3,6,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,1,4,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,3,1,4]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,3,4,1]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,4,1,3]=>[1,5,4,6,2,7,3]=>[7,3,4,2,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,4,3,1]=>[1,5,4,6,3,2,7]=>[7,3,4,2,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,2,4,6]=>[1,5,2,7,6,4,3]=>[7,3,6,1,2,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,2,6,4]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,4,2,6]=>[1,5,4,2,7,6,3]=>[7,3,4,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,4,6,2]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,6,2,4]=>[1,5,6,2,7,4,3]=>[7,3,2,6,1,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,6,4,2]=>[1,5,6,4,2,7,3]=>[7,3,2,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,1,4,6]=>[1,5,2,7,6,4,3]=>[7,3,6,1,2,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,1,6,4]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,4,1,6]=>[1,5,4,2,7,6,3]=>[7,3,4,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,4,6,1]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,6,1,4]=>[1,5,6,2,7,4,3]=>[7,3,2,6,1,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,6,4,1]=>[1,5,6,4,2,7,3]=>[7,3,2,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,1,2,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,1,6,2]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,2,1,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,2,6,1]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,6,1,2]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,6,2,1]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,1,2,4]=>[1,5,2,7,4,6,3]=>[7,3,6,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,1,4,2]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,2,1,4]=>[1,5,2,7,4,6,3]=>[7,3,6,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,2,4,1]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,4,1,2]=>[1,5,4,6,2,7,3]=>[7,3,4,2,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,4,2,1]=>[1,5,4,6,2,7,3]=>[7,3,4,2,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,2,3,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,2,6,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,3,2,6]=>[1,5,3,4,2,7,6]=>[7,3,5,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,3,6,2]=>[1,5,3,4,2,7,6]=>[7,3,5,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,6,2,3]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,6,3,2]=>[1,5,6,3,4,2,7]=>[7,3,2,5,4,6,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,1,3,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,1,6,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,3,1,6]=>[1,5,3,4,2,7,6]=>[7,3,5,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,3,6,1]=>[1,5,3,4,2,7,6]=>[7,3,5,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,6,1,3]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,6,3,1]=>[1,5,6,3,4,2,7]=>[7,3,2,5,4,6,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,1,2,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,1,6,2]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,2,1,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,2,6,1]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,6,1,2]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,6,2,1]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,1,2,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,1,3,2]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,2,1,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,2,3,1]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,3,1,2]=>[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,3,2,1]=>[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,2,3,4]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,2,4,3]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,3,2,4]=>[1,5,3,6,2,7,4]=>[7,3,5,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,3,4,2]=>[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,4,2,3]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,4,3,2]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,1,3,4]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,1,4,3]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,3,1,4]=>[1,5,3,6,2,7,4]=>[7,3,5,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,3,4,1]=>[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,4,1,3]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,4,3,1]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,1,2,4]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,1,4,2]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,2,1,4]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,2,4,1]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,4,1,2]=>[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,4,2,1]=>[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,1,2,3]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,1,3,2]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,2,1,3]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,2,3,1]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,3,1,2]=>[1,5,3,6,2,7,4]=>[7,3,5,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,3,2,1]=>[1,5,3,6,2,7,4]=>[7,3,5,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,4,5,7]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,4,7,5]=>[1,6,7,5,4,3,2]=>[7,2,1,3,4,5,6]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,5,4,7]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,5,7,4]=>[1,6,7,4,3,2,5]=>[7,2,1,4,5,6,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,7,4,5]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,7,5,4]=>[1,6,5,7,4,3,2]=>[7,2,3,1,4,5,6]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,3,5,7]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,3,7,5]=>[1,6,7,5,3,2,4]=>[7,2,1,3,5,6,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,5,3,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,5,7,3]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,7,3,5]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,7,5,3]=>[1,6,5,7,3,2,4]=>[7,2,3,1,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,3,4,7]=>[1,6,4,5,3,2,7]=>[7,2,4,3,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,3,7,4]=>[1,6,7,4,5,3,2]=>[7,2,1,4,3,5,6]=>[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,4,3,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,4,7,3]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,7,3,4]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,7,4,3]=>[1,6,4,5,7,3,2]=>[7,2,4,3,1,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,3,4,5]=>[1,6,4,7,5,3,2]=>[7,2,4,1,3,5,6]=>[7,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,3,5,4]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,4,3,5]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,4,5,3]=>[1,6,5,4,7,3,2]=>[7,2,3,4,1,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,5,3,4]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,5,4,3]=>[1,6,4,7,3,2,5]=>[7,2,4,1,5,6,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,4,5,7]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,4,7,5]=>[1,6,7,5,4,2,3]=>[7,2,1,3,4,6,5]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,5,4,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,5,7,4]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,7,4,5]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,7,5,4]=>[1,6,5,7,4,2,3]=>[7,2,3,1,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,2,5,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,2,7,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,5,2,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,5,7,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,7,2,5]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,7,5,2]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,2,4,7]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,2,7,4]=>[1,6,7,4,5,2,3]=>[7,2,1,4,3,6,5]=>[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,4,2,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,4,7,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,7,2,4]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,7,4,2]=>[1,6,4,5,7,2,3]=>[7,2,4,3,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,2,4,5]=>[1,6,4,7,5,2,3]=>[7,2,4,1,3,6,5]=>[7,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,2,5,4]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,4,2,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,4,5,2]=>[1,6,5,4,7,2,3]=>[7,2,3,4,1,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,5,2,4]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,5,4,2]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,3,5,7]=>[1,6,5,3,4,2,7]=>[7,2,3,5,4,6,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,3,7,5]=>[1,6,7,5,3,4,2]=>[7,2,1,3,5,4,6]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,5,3,7]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,5,7,3]=>[1,6,7,3,4,2,5]=>[7,2,1,5,4,6,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,7,3,5]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,7,5,3]=>[1,6,5,7,3,4,2]=>[7,2,3,1,5,4,6]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,2,5,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,2,7,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,5,2,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,5,7,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,7,2,5]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,7,5,2]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,2,3,7]=>[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,2,7,3]=>[1,6,7,3,4,5,2]=>[7,2,1,5,4,3,6]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,3,2,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,3,7,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,7,2,3]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,7,3,2]=>[1,6,3,4,5,7,2]=>[7,2,5,4,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,2,3,5]=>[1,6,3,4,7,5,2]=>[7,2,5,4,1,3,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,2,5,3]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,3,2,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,3,5,2]=>[1,6,5,3,4,7,2]=>[7,2,3,5,4,1,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,5,2,3]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,5,3,2]=>[1,6,3,4,7,2,5]=>[7,2,5,4,1,6,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,3,4,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,3,7,4]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,4,3,7]=>[1,6,3,5,4,2,7]=>[7,2,5,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,4,7,3]=>[1,6,7,3,5,4,2]=>[7,2,1,5,3,4,6]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,7,3,4]=>[1,6,3,5,7,4,2]=>[7,2,5,3,1,4,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,7,4,3]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,2,4,7]=>[1,6,4,3,5,2,7]=>[7,2,4,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,2,7,4]=>[1,6,7,4,3,5,2]=>[7,2,1,4,5,3,6]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,4,2,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,4,7,2]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,7,2,4]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,7,4,2]=>[1,6,4,3,5,7,2]=>[7,2,4,5,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,2,3,7]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,2,7,3]=>[1,6,7,3,5,2,4]=>[7,2,1,5,3,6,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,3,2,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,3,7,2]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,7,2,3]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,7,3,2]=>[1,6,3,5,7,2,4]=>[7,2,5,3,1,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,2,3,4]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,2,4,3]=>[1,6,4,7,3,5,2]=>[7,2,4,1,5,3,6]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,3,2,4]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,3,4,2]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,4,2,3]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,4,3,2]=>[1,6,3,5,4,7,2]=>[7,2,5,3,4,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,3,4,5]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,3,5,4]=>[1,6,5,3,7,4,2]=>[7,2,3,5,1,4,6]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,4,3,5]=>[1,6,3,7,5,4,2]=>[7,2,5,1,3,4,6]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,4,5,3]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,5,3,4]=>[1,6,3,7,4,2,5]=>[7,2,5,1,4,6,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,5,4,3]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,2,4,5]=>[1,6,4,3,7,5,2]=>[7,2,4,5,1,3,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,2,5,4]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,4,2,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,4,5,2]=>[1,6,5,4,3,7,2]=>[7,2,3,4,5,1,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,5,2,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,5,4,2]=>[1,6,4,3,7,2,5]=>[7,2,4,5,1,6,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,2,3,5]=>[1,6,3,7,5,2,4]=>[7,2,5,1,3,6,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,2,5,3]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,3,2,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,3,5,2]=>[1,6,5,3,7,2,4]=>[7,2,3,5,1,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,5,2,3]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,5,3,2]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,2,3,4]=>[1,6,3,7,4,5,2]=>[7,2,5,1,4,3,6]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,2,4,3]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,3,2,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,3,4,2]=>[1,6,4,5,3,7,2]=>[7,2,4,3,5,1,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,4,2,3]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,4,3,2]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,4,5,7]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,4,7,5]=>[1,6,7,5,4,3,2]=>[7,2,1,3,4,5,6]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,5,4,7]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,5,7,4]=>[1,6,7,4,3,2,5]=>[7,2,1,4,5,6,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,7,4,5]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,7,5,4]=>[1,6,5,7,4,3,2]=>[7,2,3,1,4,5,6]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,3,5,7]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,3,7,5]=>[1,6,7,5,3,2,4]=>[7,2,1,3,5,6,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,5,3,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,5,7,3]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,7,3,5]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,7,5,3]=>[1,6,5,7,3,2,4]=>[7,2,3,1,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,3,4,7]=>[1,6,4,5,3,2,7]=>[7,2,4,3,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,3,7,4]=>[1,6,7,4,5,3,2]=>[7,2,1,4,3,5,6]=>[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,4,3,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,4,7,3]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,7,3,4]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,7,4,3]=>[1,6,4,5,7,3,2]=>[7,2,4,3,1,5,6]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,3,4,5]=>[1,6,4,7,5,3,2]=>[7,2,4,1,3,5,6]=>[7,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,3,5,4]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,4,3,5]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,4,5,3]=>[1,6,5,4,7,3,2]=>[7,2,3,4,1,5,6]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,5,3,4]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,5,4,3]=>[1,6,4,7,3,2,5]=>[7,2,4,1,5,6,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,4,5,7]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,4,7,5]=>[1,6,7,5,4,2,3]=>[7,2,1,3,4,6,5]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,5,4,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,5,7,4]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,7,4,5]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,7,5,4]=>[1,6,5,7,4,2,3]=>[7,2,3,1,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,1,5,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,1,7,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,5,1,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,5,7,1]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,7,1,5]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,7,5,1]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,1,4,7]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,1,7,4]=>[1,6,7,4,5,2,3]=>[7,2,1,4,3,6,5]=>[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,4,1,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,4,7,1]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,7,1,4]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,7,4,1]=>[1,6,4,5,7,2,3]=>[7,2,4,3,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,1,4,5]=>[1,6,4,7,5,2,3]=>[7,2,4,1,3,6,5]=>[7,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,1,5,4]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,4,1,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,4,5,1]=>[1,6,5,4,7,2,3]=>[7,2,3,4,1,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,5,1,4]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,5,4,1]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,3,5,7]=>[1,6,5,3,4,2,7]=>[7,2,3,5,4,6,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,3,7,5]=>[1,6,7,5,3,4,2]=>[7,2,1,3,5,4,6]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,5,3,7]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,5,7,3]=>[1,6,7,3,4,2,5]=>[7,2,1,5,4,6,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,7,3,5]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,7,5,3]=>[1,6,5,7,3,4,2]=>[7,2,3,1,5,4,6]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,1,5,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,1,7,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,5,1,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,5,7,1]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,7,1,5]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,7,5,1]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,1,3,7]=>[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,1,7,3]=>[1,6,7,3,4,5,2]=>[7,2,1,5,4,3,6]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,3,1,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,3,7,1]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,7,1,3]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,7,3,1]=>[1,6,3,4,5,7,2]=>[7,2,5,4,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,1,3,5]=>[1,6,3,4,7,5,2]=>[7,2,5,4,1,3,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,1,5,3]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,3,1,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,3,5,1]=>[1,6,5,3,4,7,2]=>[7,2,3,5,4,1,6]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,5,1,3]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,5,3,1]=>[1,6,3,4,7,2,5]=>[7,2,5,4,1,6,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,3,4,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,3,7,4]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,4,3,7]=>[1,6,3,5,4,2,7]=>[7,2,5,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,4,7,3]=>[1,6,7,3,5,4,2]=>[7,2,1,5,3,4,6]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,7,3,4]=>[1,6,3,5,7,4,2]=>[7,2,5,3,1,4,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,7,4,3]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,1,4,7]=>[1,6,4,3,5,2,7]=>[7,2,4,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,1,7,4]=>[1,6,7,4,3,5,2]=>[7,2,1,4,5,3,6]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,4,1,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,4,7,1]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,7,1,4]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,7,4,1]=>[1,6,4,3,5,7,2]=>[7,2,4,5,3,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,1,3,7]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,1,7,3]=>[1,6,7,3,5,2,4]=>[7,2,1,5,3,6,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,3,1,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,3,7,1]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,7,1,3]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,7,3,1]=>[1,6,3,5,7,2,4]=>[7,2,5,3,1,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,1,3,4]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,1,4,3]=>[1,6,4,7,3,5,2]=>[7,2,4,1,5,3,6]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,3,1,4]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,3,4,1]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,4,1,3]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,4,3,1]=>[1,6,3,5,4,7,2]=>[7,2,5,3,4,1,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,3,4,5]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,3,5,4]=>[1,6,5,3,7,4,2]=>[7,2,3,5,1,4,6]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,4,3,5]=>[1,6,3,7,5,4,2]=>[7,2,5,1,3,4,6]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,4,5,3]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,5,3,4]=>[1,6,3,7,4,2,5]=>[7,2,5,1,4,6,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,5,4,3]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,1,4,5]=>[1,6,4,3,7,5,2]=>[7,2,4,5,1,3,6]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,1,5,4]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,4,1,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,4,5,1]=>[1,6,5,4,3,7,2]=>[7,2,3,4,5,1,6]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,5,1,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,5,4,1]=>[1,6,4,3,7,2,5]=>[7,2,4,5,1,6,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,1,3,5]=>[1,6,3,7,5,2,4]=>[7,2,5,1,3,6,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,1,5,3]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,3,1,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,3,5,1]=>[1,6,5,3,7,2,4]=>[7,2,3,5,1,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,5,1,3]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,5,3,1]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,1,3,4]=>[1,6,3,7,4,5,2]=>[7,2,5,1,4,3,6]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,1,4,3]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,3,1,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,3,4,1]=>[1,6,4,5,3,7,2]=>[7,2,4,3,5,1,6]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,4,1,3]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,4,3,1]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,4,5,7]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,4,7,5]=>[1,6,7,5,4,2,3]=>[7,2,1,3,4,6,5]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,5,4,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,5,7,4]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,7,4,5]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,7,5,4]=>[1,6,5,7,4,2,3]=>[7,2,3,1,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,2,5,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,2,7,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,5,2,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,5,7,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,7,2,5]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,7,5,2]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,2,4,7]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,2,7,4]=>[1,6,7,4,5,2,3]=>[7,2,1,4,3,6,5]=>[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,4,2,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,4,7,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,7,2,4]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,7,4,2]=>[1,6,4,5,7,2,3]=>[7,2,4,3,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,2,4,5]=>[1,6,4,7,5,2,3]=>[7,2,4,1,3,6,5]=>[7,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,2,5,4]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,4,2,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,4,5,2]=>[1,6,5,4,7,2,3]=>[7,2,3,4,1,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,5,2,4]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,5,4,2]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,4,5,7]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,4,7,5]=>[1,6,7,5,4,2,3]=>[7,2,1,3,4,6,5]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,5,4,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,5,7,4]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,7,4,5]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,7,5,4]=>[1,6,5,7,4,2,3]=>[7,2,3,1,4,6,5]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,1,5,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,1,7,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,5,1,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,5,7,1]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,7,1,5]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,7,5,1]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,1,4,7]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,1,7,4]=>[1,6,7,4,5,2,3]=>[7,2,1,4,3,6,5]=>[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,4,1,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,4,7,1]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,7,1,4]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,7,4,1]=>[1,6,4,5,7,2,3]=>[7,2,4,3,1,6,5]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,1,4,5]=>[1,6,4,7,5,2,3]=>[7,2,4,1,3,6,5]=>[7,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,1,5,4]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,4,1,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,4,5,1]=>[1,6,5,4,7,2,3]=>[7,2,3,4,1,6,5]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,5,1,4]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,5,4,1]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,2,5,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,2,7,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,5,2,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,5,7,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,7,2,5]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,7,5,2]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,1,5,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,1,7,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,5,1,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,5,7,1]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,7,1,5]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,7,5,1]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,1,2,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,1,7,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,2,1,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,2,7,1]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,7,1,2]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,7,2,1]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,1,2,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,1,5,2]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,2,1,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,2,5,1]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,5,1,2]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,5,2,1]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,2,4,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,2,7,4]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,4,2,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,4,7,2]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,7,2,4]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,7,4,2]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,1,4,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,1,7,4]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,4,1,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,4,7,1]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,7,1,4]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,7,4,1]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,1,2,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,1,7,2]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,2,1,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,2,7,1]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,7,1,2]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,7,2,1]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,1,2,4]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,1,4,2]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,2,1,4]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,2,4,1]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,4,1,2]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,4,2,1]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,2,4,5]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,2,5,4]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,4,2,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,4,5,2]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,5,2,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,5,4,2]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,1,4,5]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,1,5,4]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,4,1,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,4,5,1]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,5,1,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,5,4,1]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,1,2,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,1,5,2]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,2,1,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,2,5,1]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,5,1,2]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,5,2,1]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,1,2,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,1,4,2]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,2,1,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,2,4,1]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,4,1,2]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,4,2,1]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,3,5,7]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,3,7,5]=>[1,6,7,5,3,2,4]=>[7,2,1,3,5,6,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,5,3,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,5,7,3]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,7,3,5]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,7,5,3]=>[1,6,5,7,3,2,4]=>[7,2,3,1,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,2,5,7]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,2,7,5]=>[1,6,7,5,2,4,3]=>[7,2,1,3,6,4,5]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,5,2,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,5,7,2]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,7,2,5]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,7,5,2]=>[1,6,5,7,2,4,3]=>[7,2,3,1,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,2,3,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,2,7,3]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,3,2,7]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,3,7,2]=>[1,6,7,2,4,5,3]=>[7,2,1,6,4,3,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,7,2,3]=>[1,6,2,4,5,7,3]=>[7,2,6,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,7,3,2]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,2,3,5]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,2,5,3]=>[1,6,5,2,4,7,3]=>[7,2,3,6,4,1,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,3,2,5]=>[1,6,2,4,7,5,3]=>[7,2,6,4,1,3,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,3,5,2]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,5,2,3]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,5,3,2]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,3,5,7]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,3,7,5]=>[1,6,7,5,3,2,4]=>[7,2,1,3,5,6,4]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,5,3,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,5,7,3]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,7,3,5]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,7,5,3]=>[1,6,5,7,3,2,4]=>[7,2,3,1,5,6,4]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,1,5,7]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,1,7,5]=>[1,6,7,5,2,4,3]=>[7,2,1,3,6,4,5]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,5,1,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,5,7,1]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,7,1,5]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,7,5,1]=>[1,6,5,7,2,4,3]=>[7,2,3,1,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,1,3,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,1,7,3]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,3,1,7]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,3,7,1]=>[1,6,7,2,4,5,3]=>[7,2,1,6,4,3,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,7,1,3]=>[1,6,2,4,5,7,3]=>[7,2,6,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,7,3,1]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,1,3,5]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,1,5,3]=>[1,6,5,2,4,7,3]=>[7,2,3,6,4,1,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,3,1,5]=>[1,6,2,4,7,5,3]=>[7,2,6,4,1,3,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,3,5,1]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,5,1,3]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,5,3,1]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,2,5,7]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,2,7,5]=>[1,6,7,5,2,4,3]=>[7,2,1,3,6,4,5]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,5,2,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,5,7,2]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,7,2,5]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,7,5,2]=>[1,6,5,7,2,4,3]=>[7,2,3,1,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,1,5,7]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,1,7,5]=>[1,6,7,5,2,4,3]=>[7,2,1,3,6,4,5]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,5,1,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,5,7,1]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,7,1,5]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,7,5,1]=>[1,6,5,7,2,4,3]=>[7,2,3,1,6,4,5]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,1,2,7]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,1,7,2]=>[1,6,7,2,4,5,3]=>[7,2,1,6,4,3,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,2,1,7]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,2,7,1]=>[1,6,7,2,4,5,3]=>[7,2,1,6,4,3,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,7,1,2]=>[1,6,2,4,5,7,3]=>[7,2,6,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,7,2,1]=>[1,6,2,4,5,7,3]=>[7,2,6,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,1,2,5]=>[1,6,2,4,7,5,3]=>[7,2,6,4,1,3,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,1,5,2]=>[1,6,5,2,4,7,3]=>[7,2,3,6,4,1,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,2,1,5]=>[1,6,2,4,7,5,3]=>[7,2,6,4,1,3,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,2,5,1]=>[1,6,5,2,4,7,3]=>[7,2,3,6,4,1,5]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,5,1,2]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,5,2,1]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,2,3,7]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,2,7,3]=>[1,6,7,3,5,2,4]=>[7,2,1,5,3,6,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,3,2,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,3,7,2]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,7,2,3]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,7,3,2]=>[1,6,3,5,7,2,4]=>[7,2,5,3,1,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,1,3,7]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,1,7,3]=>[1,6,7,3,5,2,4]=>[7,2,1,5,3,6,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,3,1,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,3,7,1]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,7,1,3]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,7,3,1]=>[1,6,3,5,7,2,4]=>[7,2,5,3,1,6,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,1,2,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,1,7,2]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,2,1,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,2,7,1]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,7,1,2]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,7,2,1]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,1,2,3]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,1,3,2]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,2,1,3]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,2,3,1]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,3,1,2]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,3,2,1]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,2,3,5]=>[1,6,3,7,5,2,4]=>[7,2,5,1,3,6,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,2,5,3]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,3,2,5]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,3,5,2]=>[1,6,5,3,7,2,4]=>[7,2,3,5,1,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,5,2,3]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,5,3,2]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,1,3,5]=>[1,6,3,7,5,2,4]=>[7,2,5,1,3,6,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,1,5,3]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,3,1,5]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,3,5,1]=>[1,6,5,3,7,2,4]=>[7,2,3,5,1,6,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,5,1,3]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,5,3,1]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,1,2,5]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,1,5,2]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,2,1,5]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,2,5,1]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,5,1,2]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,5,2,1]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,1,2,3]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,1,3,2]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,2,1,3]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,2,3,1]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,3,1,2]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,3,2,1]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,3,4,7]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,3,7,4]=>[1,6,7,4,2,5,3]=>[7,2,1,4,6,3,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,4,3,7]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,4,7,3]=>[1,6,7,3,2,5,4]=>[7,2,1,5,6,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,7,3,4]=>[1,6,3,2,5,7,4]=>[7,2,5,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,7,4,3]=>[1,6,4,2,5,7,3]=>[7,2,4,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,2,4,7]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,2,7,4]=>[1,6,7,4,3,2,5]=>[7,2,1,4,5,6,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,4,2,7]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,4,7,2]=>[1,6,7,2,5,4,3]=>[7,2,1,6,3,4,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,7,2,4]=>[1,6,2,5,7,4,3]=>[7,2,6,3,1,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,7,4,2]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,2,3,7]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,2,7,3]=>[1,6,7,3,2,5,4]=>[7,2,1,5,6,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,3,2,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,3,7,2]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,7,2,3]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,7,3,2]=>[1,6,3,2,5,7,4]=>[7,2,5,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,2,3,4]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,2,4,3]=>[1,6,4,7,3,2,5]=>[7,2,4,1,5,6,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,3,2,4]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,3,4,2]=>[1,6,4,7,2,5,3]=>[7,2,4,1,6,3,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,4,2,3]=>[1,6,2,5,4,7,3]=>[7,2,6,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,4,3,2]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,3,4,7]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,3,7,4]=>[1,6,7,4,2,5,3]=>[7,2,1,4,6,3,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,4,3,7]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,4,7,3]=>[1,6,7,3,2,5,4]=>[7,2,1,5,6,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,7,3,4]=>[1,6,3,2,5,7,4]=>[7,2,5,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,7,4,3]=>[1,6,4,2,5,7,3]=>[7,2,4,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,1,4,7]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,1,7,4]=>[1,6,7,4,3,2,5]=>[7,2,1,4,5,6,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,4,1,7]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,4,7,1]=>[1,6,7,2,5,4,3]=>[7,2,1,6,3,4,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,7,1,4]=>[1,6,2,5,7,4,3]=>[7,2,6,3,1,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,7,4,1]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,1,3,7]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,1,7,3]=>[1,6,7,3,2,5,4]=>[7,2,1,5,6,3,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,3,1,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,3,7,1]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,7,1,3]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,7,3,1]=>[1,6,3,2,5,7,4]=>[7,2,5,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,1,3,4]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,1,4,3]=>[1,6,4,7,3,2,5]=>[7,2,4,1,5,6,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,3,1,4]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,3,4,1]=>[1,6,4,7,2,5,3]=>[7,2,4,1,6,3,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,4,1,3]=>[1,6,2,5,4,7,3]=>[7,2,6,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,4,3,1]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,2,4,7]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,2,7,4]=>[1,6,7,4,2,5,3]=>[7,2,1,4,6,3,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,4,2,7]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,4,7,2]=>[1,6,7,2,5,4,3]=>[7,2,1,6,3,4,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,7,2,4]=>[1,6,2,5,7,4,3]=>[7,2,6,3,1,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,7,4,2]=>[1,6,4,2,5,7,3]=>[7,2,4,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,1,4,7]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,1,7,4]=>[1,6,7,4,2,5,3]=>[7,2,1,4,6,3,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,4,1,7]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,4,7,1]=>[1,6,7,2,5,4,3]=>[7,2,1,6,3,4,5]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,7,1,4]=>[1,6,2,5,7,4,3]=>[7,2,6,3,1,4,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,7,4,1]=>[1,6,4,2,5,7,3]=>[7,2,4,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,1,2,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,1,7,2]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,2,1,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,2,7,1]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,7,1,2]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,7,2,1]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,1,2,4]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,1,4,2]=>[1,6,4,7,2,5,3]=>[7,2,4,1,6,3,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,2,1,4]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,2,4,1]=>[1,6,4,7,2,5,3]=>[7,2,4,1,6,3,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,4,1,2]=>[1,6,2,5,4,7,3]=>[7,2,6,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,4,2,1]=>[1,6,2,5,4,7,3]=>[7,2,6,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,2,3,7]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,2,7,3]=>[1,6,7,3,4,2,5]=>[7,2,1,5,4,6,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,3,2,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,3,7,2]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,7,2,3]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,7,3,2]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,1,3,7]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,1,7,3]=>[1,6,7,3,4,2,5]=>[7,2,1,5,4,6,3]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,3,1,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,3,7,1]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,7,1,3]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,7,3,1]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,1,2,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,1,7,2]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,2,1,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,2,7,1]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,7,1,2]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,7,2,1]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,1,2,3]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,1,3,2]=>[1,6,3,4,7,2,5]=>[7,2,5,4,1,6,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,2,1,3]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,2,3,1]=>[1,6,3,4,7,2,5]=>[7,2,5,4,1,6,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,3,1,2]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,3,2,1]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,2,3,4]=>[1,6,3,7,4,2,5]=>[7,2,5,1,4,6,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,2,4,3]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,3,2,4]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,3,4,2]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,4,2,3]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,4,3,2]=>[1,6,3,7,2,5,4]=>[7,2,5,1,6,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,1,3,4]=>[1,6,3,7,4,2,5]=>[7,2,5,1,4,6,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,1,4,3]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,3,1,4]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,3,4,1]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,4,1,3]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,4,3,1]=>[1,6,3,7,2,5,4]=>[7,2,5,1,6,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,1,2,4]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,1,4,2]=>[1,6,4,3,7,2,5]=>[7,2,4,5,1,6,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,2,1,4]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,2,4,1]=>[1,6,4,3,7,2,5]=>[7,2,4,5,1,6,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,4,1,2]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,4,2,1]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,1,2,3]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,1,3,2]=>[1,6,3,7,2,5,4]=>[7,2,5,1,6,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,2,1,3]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,2,3,1]=>[1,6,3,7,2,5,4]=>[7,2,5,1,6,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,3,1,2]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,3,2,1]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,3,4,5]=>[1,6,4,2,7,5,3]=>[7,2,4,6,1,3,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,3,5,4]=>[1,6,5,3,2,7,4]=>[7,2,3,5,6,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,4,3,5]=>[1,6,3,2,7,5,4]=>[7,2,5,6,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,4,5,3]=>[1,6,5,4,2,7,3]=>[7,2,3,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,5,3,4]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,5,4,3]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,2,4,5]=>[1,6,4,3,2,7,5]=>[7,2,4,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,2,5,4]=>[1,6,5,2,7,4,3]=>[7,2,3,6,1,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,4,2,5]=>[1,6,2,7,5,4,3]=>[7,2,6,1,3,4,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,4,5,2]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,5,2,4]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,5,4,2]=>[1,6,4,3,2,7,5]=>[7,2,4,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,2,3,5]=>[1,6,3,2,7,5,4]=>[7,2,5,6,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,2,5,3]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,3,2,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,3,5,2]=>[1,6,5,3,2,7,4]=>[7,2,3,5,6,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,5,2,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,5,3,2]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,2,3,4]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,2,4,3]=>[1,6,4,5,2,7,3]=>[7,2,4,3,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,3,2,4]=>[1,6,2,7,4,5,3]=>[7,2,6,1,4,3,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,3,4,2]=>[1,6,4,5,3,2,7]=>[7,2,4,3,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,4,2,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,4,3,2]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,3,4,5]=>[1,6,4,2,7,5,3]=>[7,2,4,6,1,3,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,3,5,4]=>[1,6,5,3,2,7,4]=>[7,2,3,5,6,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,4,3,5]=>[1,6,3,2,7,5,4]=>[7,2,5,6,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,4,5,3]=>[1,6,5,4,2,7,3]=>[7,2,3,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,5,3,4]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,5,4,3]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,1,4,5]=>[1,6,4,3,2,7,5]=>[7,2,4,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,1,5,4]=>[1,6,5,2,7,4,3]=>[7,2,3,6,1,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,4,1,5]=>[1,6,2,7,5,4,3]=>[7,2,6,1,3,4,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,4,5,1]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,5,1,4]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,5,4,1]=>[1,6,4,3,2,7,5]=>[7,2,4,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,1,3,5]=>[1,6,3,2,7,5,4]=>[7,2,5,6,1,3,4]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,1,5,3]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,3,1,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,3,5,1]=>[1,6,5,3,2,7,4]=>[7,2,3,5,6,1,4]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,5,1,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,5,3,1]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,1,3,4]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,1,4,3]=>[1,6,4,5,2,7,3]=>[7,2,4,3,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,3,1,4]=>[1,6,2,7,4,5,3]=>[7,2,6,1,4,3,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,3,4,1]=>[1,6,4,5,3,2,7]=>[7,2,4,3,5,6,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,4,1,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,4,3,1]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,2,4,5]=>[1,6,4,2,7,5,3]=>[7,2,4,6,1,3,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,2,5,4]=>[1,6,5,2,7,4,3]=>[7,2,3,6,1,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,4,2,5]=>[1,6,2,7,5,4,3]=>[7,2,6,1,3,4,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,4,5,2]=>[1,6,5,4,2,7,3]=>[7,2,3,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,5,2,4]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,5,4,2]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,1,4,5]=>[1,6,4,2,7,5,3]=>[7,2,4,6,1,3,5]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,1,5,4]=>[1,6,5,2,7,4,3]=>[7,2,3,6,1,4,5]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,4,1,5]=>[1,6,2,7,5,4,3]=>[7,2,6,1,3,4,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,4,5,1]=>[1,6,5,4,2,7,3]=>[7,2,3,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,5,1,4]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,5,4,1]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,1,2,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,1,5,2]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,2,1,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,2,5,1]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,5,1,2]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,5,2,1]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,1,2,4]=>[1,6,2,7,4,5,3]=>[7,2,6,1,4,3,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,1,4,2]=>[1,6,4,5,2,7,3]=>[7,2,4,3,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,2,1,4]=>[1,6,2,7,4,5,3]=>[7,2,6,1,4,3,5]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,2,4,1]=>[1,6,4,5,2,7,3]=>[7,2,4,3,6,1,5]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,4,1,2]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,4,2,1]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,2,3,5]=>[1,6,3,4,2,7,5]=>[7,2,5,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,2,5,3]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,3,2,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,3,5,2]=>[1,6,5,3,4,2,7]=>[7,2,3,5,4,6,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,5,2,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,5,3,2]=>[1,6,3,4,2,7,5]=>[7,2,5,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,1,3,5]=>[1,6,3,4,2,7,5]=>[7,2,5,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,1,5,3]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,3,1,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,3,5,1]=>[1,6,5,3,4,2,7]=>[7,2,3,5,4,6,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,5,1,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,5,3,1]=>[1,6,3,4,2,7,5]=>[7,2,5,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,1,2,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,1,5,2]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,2,1,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,2,5,1]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,5,1,2]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,5,2,1]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,1,2,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,1,3,2]=>[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,2,1,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,2,3,1]=>[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,3,1,2]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,3,2,1]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,2,3,4]=>[1,6,3,5,2,7,4]=>[7,2,5,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,2,4,3]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,3,2,4]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,3,4,2]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,4,2,3]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,4,3,2]=>[1,6,3,5,4,2,7]=>[7,2,5,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,1,3,4]=>[1,6,3,5,2,7,4]=>[7,2,5,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,1,4,3]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,3,1,4]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,3,4,1]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,4,1,3]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,4,3,1]=>[1,6,3,5,4,2,7]=>[7,2,5,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,1,2,4]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,1,4,2]=>[1,6,4,3,5,2,7]=>[7,2,4,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,2,1,4]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,2,4,1]=>[1,6,4,3,5,2,7]=>[7,2,4,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,4,1,2]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,4,2,1]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,1,2,3]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,1,3,2]=>[1,6,3,5,2,7,4]=>[7,2,5,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,2,1,3]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,2,3,1]=>[1,6,3,5,2,7,4]=>[7,2,5,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,3,1,2]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,3,2,1]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,4,6,5]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,5,4,6]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,5,6,4]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,6,4,5]=>[1,7,5,6,4,3,2]=>[7,1,3,2,4,5,6]=>[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,6,5,4]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,3,5,6]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,3,6,5]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,5,3,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,5,6,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,6,3,5]=>[1,7,5,6,3,2,4]=>[7,1,3,2,5,6,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,6,5,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,3,4,6]=>[1,7,6,4,5,3,2]=>[7,1,2,4,3,5,6]=>[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,3,6,4]=>[1,7,4,5,3,2,6]=>[7,1,4,3,5,6,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,4,3,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,4,6,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,6,3,4]=>[1,7,4,5,6,3,2]=>[7,1,4,3,2,5,6]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,6,4,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,3,4,5]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,3,5,4]=>[1,7,4,6,5,3,2]=>[7,1,4,2,3,5,6]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,4,3,5]=>[1,7,5,4,6,3,2]=>[7,1,3,4,2,5,6]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,4,5,3]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,5,3,4]=>[1,7,4,6,3,2,5]=>[7,1,4,2,5,6,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,5,4,3]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,4,5,6]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,4,6,5]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,5,4,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,5,6,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,6,4,5]=>[1,7,5,6,4,2,3]=>[7,1,3,2,4,6,5]=>[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,6,5,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,2,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,2,6,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,5,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,6,2,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,6,5,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,2,4,6]=>[1,7,6,4,5,2,3]=>[7,1,2,4,3,6,5]=>[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,2,6,4]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,4,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,4,6,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,6,2,4]=>[1,7,4,5,6,2,3]=>[7,1,4,3,2,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,6,4,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,2,4,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,2,5,4]=>[1,7,4,6,5,2,3]=>[7,1,4,2,3,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,4,2,5]=>[1,7,5,4,6,2,3]=>[7,1,3,4,2,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,4,5,2]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,5,2,4]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,5,4,2]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,3,5,6]=>[1,7,6,5,3,4,2]=>[7,1,2,3,5,4,6]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,3,6,5]=>[1,7,5,3,4,2,6]=>[7,1,3,5,4,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,5,3,6]=>[1,7,6,3,4,2,5]=>[7,1,2,5,4,6,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,5,6,3]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,6,3,5]=>[1,7,5,6,3,4,2]=>[7,1,3,2,5,4,6]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,6,5,3]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,2,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,2,6,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,5,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,5,6,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,6,2,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,6,5,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,2,3,6]=>[1,7,6,3,4,5,2]=>[7,1,2,5,4,3,6]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,2,6,3]=>[1,7,3,4,5,2,6]=>[7,1,5,4,3,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,3,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,3,6,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,6,2,3]=>[1,7,3,4,5,6,2]=>[7,1,5,4,3,2,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,6,3,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,2,3,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,2,5,3]=>[1,7,3,4,6,5,2]=>[7,1,5,4,2,3,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,3,2,5]=>[1,7,5,3,4,6,2]=>[7,1,3,5,4,2,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,3,5,2]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,5,2,3]=>[1,7,3,4,6,2,5]=>[7,1,5,4,2,6,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,5,3,2]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,3,4,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,3,6,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,4,3,6]=>[1,7,6,3,5,4,2]=>[7,1,2,5,3,4,6]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,4,6,3]=>[1,7,3,5,4,2,6]=>[7,1,5,3,4,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,6,3,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,6,4,3]=>[1,7,3,5,6,4,2]=>[7,1,5,3,2,4,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,2,4,6]=>[1,7,6,4,3,5,2]=>[7,1,2,4,5,3,6]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,2,6,4]=>[1,7,4,3,5,2,6]=>[7,1,4,5,3,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,4,2,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,4,6,2]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,6,2,4]=>[1,7,4,3,5,6,2]=>[7,1,4,5,3,2,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,6,4,2]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,2,3,6]=>[1,7,6,3,5,2,4]=>[7,1,2,5,3,6,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,2,6,3]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,3,2,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,3,6,2]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,6,2,3]=>[1,7,3,5,6,2,4]=>[7,1,5,3,2,6,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,6,3,2]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,2,3,4]=>[1,7,4,6,3,5,2]=>[7,1,4,2,5,3,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,2,4,3]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,3,2,4]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,3,4,2]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,4,2,3]=>[1,7,3,5,4,6,2]=>[7,1,5,3,4,2,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,4,3,2]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,3,4,5]=>[1,7,5,3,6,4,2]=>[7,1,3,5,2,4,6]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,3,5,4]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,4,3,5]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,4,5,3]=>[1,7,3,6,5,4,2]=>[7,1,5,2,3,4,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,5,3,4]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,5,4,3]=>[1,7,3,6,4,2,5]=>[7,1,5,2,4,6,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,2,4,5]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,2,5,4]=>[1,7,4,3,6,5,2]=>[7,1,4,5,2,3,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,4,2,5]=>[1,7,5,4,3,6,2]=>[7,1,3,4,5,2,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,4,5,2]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,5,2,4]=>[1,7,4,3,6,2,5]=>[7,1,4,5,2,6,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,5,4,2]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,2,3,5]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,2,5,3]=>[1,7,3,6,5,2,4]=>[7,1,5,2,3,6,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,3,2,5]=>[1,7,5,3,6,2,4]=>[7,1,3,5,2,6,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,3,5,2]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,5,2,3]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,5,3,2]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,2,3,4]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,2,4,3]=>[1,7,3,6,4,5,2]=>[7,1,5,2,4,3,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,3,2,4]=>[1,7,4,5,3,6,2]=>[7,1,4,3,5,2,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,3,4,2]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,4,2,3]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,4,3,2]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,4,5,6]=>[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,4,6,5]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,5,4,6]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,5,6,4]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,6,4,5]=>[1,7,5,6,4,3,2]=>[7,1,3,2,4,5,6]=>[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,6,5,4]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,3,5,6]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,3,6,5]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,5,3,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,5,6,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,6,3,5]=>[1,7,5,6,3,2,4]=>[7,1,3,2,5,6,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,6,5,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,3,4,6]=>[1,7,6,4,5,3,2]=>[7,1,2,4,3,5,6]=>[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,3,6,4]=>[1,7,4,5,3,2,6]=>[7,1,4,3,5,6,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,4,3,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,4,6,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,6,3,4]=>[1,7,4,5,6,3,2]=>[7,1,4,3,2,5,6]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,6,4,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,3,4,5]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,3,5,4]=>[1,7,4,6,5,3,2]=>[7,1,4,2,3,5,6]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,4,3,5]=>[1,7,5,4,6,3,2]=>[7,1,3,4,2,5,6]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,4,5,3]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,5,3,4]=>[1,7,4,6,3,2,5]=>[7,1,4,2,5,6,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,5,4,3]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,4,5,6]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,4,6,5]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,5,4,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,5,6,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,6,4,5]=>[1,7,5,6,4,2,3]=>[7,1,3,2,4,6,5]=>[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,6,5,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,1,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,1,6,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,5,1,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,5,6,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,6,1,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,6,5,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,1,4,6]=>[1,7,6,4,5,2,3]=>[7,1,2,4,3,6,5]=>[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,1,6,4]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,4,1,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,4,6,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,6,1,4]=>[1,7,4,5,6,2,3]=>[7,1,4,3,2,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,6,4,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,1,4,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,1,5,4]=>[1,7,4,6,5,2,3]=>[7,1,4,2,3,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,4,1,5]=>[1,7,5,4,6,2,3]=>[7,1,3,4,2,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,4,5,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,5,1,4]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,5,4,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,3,5,6]=>[1,7,6,5,3,4,2]=>[7,1,2,3,5,4,6]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,3,6,5]=>[1,7,5,3,4,2,6]=>[7,1,3,5,4,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,5,3,6]=>[1,7,6,3,4,2,5]=>[7,1,2,5,4,6,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,5,6,3]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,6,3,5]=>[1,7,5,6,3,4,2]=>[7,1,3,2,5,4,6]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,6,5,3]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,1,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,1,6,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,5,1,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,5,6,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,6,1,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,6,5,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,1,3,6]=>[1,7,6,3,4,5,2]=>[7,1,2,5,4,3,6]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,1,6,3]=>[1,7,3,4,5,2,6]=>[7,1,5,4,3,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,3,1,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,3,6,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,6,1,3]=>[1,7,3,4,5,6,2]=>[7,1,5,4,3,2,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,6,3,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,1,3,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,1,5,3]=>[1,7,3,4,6,5,2]=>[7,1,5,4,2,3,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,3,1,5]=>[1,7,5,3,4,6,2]=>[7,1,3,5,4,2,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,3,5,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,5,1,3]=>[1,7,3,4,6,2,5]=>[7,1,5,4,2,6,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,5,3,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,3,4,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,3,6,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,4,3,6]=>[1,7,6,3,5,4,2]=>[7,1,2,5,3,4,6]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,4,6,3]=>[1,7,3,5,4,2,6]=>[7,1,5,3,4,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,6,3,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,6,4,3]=>[1,7,3,5,6,4,2]=>[7,1,5,3,2,4,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,1,4,6]=>[1,7,6,4,3,5,2]=>[7,1,2,4,5,3,6]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,1,6,4]=>[1,7,4,3,5,2,6]=>[7,1,4,5,3,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,4,1,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,4,6,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,6,1,4]=>[1,7,4,3,5,6,2]=>[7,1,4,5,3,2,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,6,4,1]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,1,3,6]=>[1,7,6,3,5,2,4]=>[7,1,2,5,3,6,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,1,6,3]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,3,1,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,3,6,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,6,1,3]=>[1,7,3,5,6,2,4]=>[7,1,5,3,2,6,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,6,3,1]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,1,3,4]=>[1,7,4,6,3,5,2]=>[7,1,4,2,5,3,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,1,4,3]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,3,1,4]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,3,4,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,4,1,3]=>[1,7,3,5,4,6,2]=>[7,1,5,3,4,2,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,4,3,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,3,4,5]=>[1,7,5,3,6,4,2]=>[7,1,3,5,2,4,6]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,3,5,4]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,4,3,5]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,4,5,3]=>[1,7,3,6,5,4,2]=>[7,1,5,2,3,4,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,5,3,4]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,5,4,3]=>[1,7,3,6,4,2,5]=>[7,1,5,2,4,6,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,1,4,5]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,1,5,4]=>[1,7,4,3,6,5,2]=>[7,1,4,5,2,3,6]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,4,1,5]=>[1,7,5,4,3,6,2]=>[7,1,3,4,5,2,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,4,5,1]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,5,1,4]=>[1,7,4,3,6,2,5]=>[7,1,4,5,2,6,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,5,4,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,1,3,5]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,1,5,3]=>[1,7,3,6,5,2,4]=>[7,1,5,2,3,6,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,3,1,5]=>[1,7,5,3,6,2,4]=>[7,1,3,5,2,6,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,3,5,1]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,5,1,3]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,5,3,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,1,3,4]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,1,4,3]=>[1,7,3,6,4,5,2]=>[7,1,5,2,4,3,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,3,1,4]=>[1,7,4,5,3,6,2]=>[7,1,4,3,5,2,6]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,3,4,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,4,1,3]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,4,3,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,4,5,6]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,4,6,5]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,5,4,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,5,6,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,6,4,5]=>[1,7,5,6,4,2,3]=>[7,1,3,2,4,6,5]=>[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,6,5,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,2,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,2,6,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,5,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,5,6,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,6,2,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,6,5,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,2,4,6]=>[1,7,6,4,5,2,3]=>[7,1,2,4,3,6,5]=>[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,2,6,4]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,4,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,4,6,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,6,2,4]=>[1,7,4,5,6,2,3]=>[7,1,4,3,2,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,6,4,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,2,4,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,2,5,4]=>[1,7,4,6,5,2,3]=>[7,1,4,2,3,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,4,2,5]=>[1,7,5,4,6,2,3]=>[7,1,3,4,2,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,4,5,2]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,5,2,4]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,5,4,2]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,4,5,6]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,4,6,5]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,5,4,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,5,6,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,6,4,5]=>[1,7,5,6,4,2,3]=>[7,1,3,2,4,6,5]=>[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,6,5,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,1,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,1,6,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,5,1,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,5,6,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,6,1,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,6,5,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,1,4,6]=>[1,7,6,4,5,2,3]=>[7,1,2,4,3,6,5]=>[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,1,6,4]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,4,1,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,4,6,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,6,1,4]=>[1,7,4,5,6,2,3]=>[7,1,4,3,2,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,6,4,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,1,4,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,1,5,4]=>[1,7,4,6,5,2,3]=>[7,1,4,2,3,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,4,1,5]=>[1,7,5,4,6,2,3]=>[7,1,3,4,2,6,5]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,4,5,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,5,1,4]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,5,4,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,2,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,2,6,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,5,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,5,6,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,6,2,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,6,5,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,1,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,1,6,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,5,1,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,5,6,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,6,1,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,6,5,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,1,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,1,6,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,2,1,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,2,6,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,6,1,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,6,2,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,1,2,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,1,5,2]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,2,1,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,2,5,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,5,1,2]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,5,2,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,2,4,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,2,6,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,4,2,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,4,6,2]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,6,2,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,6,4,2]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,1,4,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,1,6,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,4,1,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,4,6,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,6,1,4]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,6,4,1]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,1,2,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,1,6,2]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,2,1,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,2,6,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,6,1,2]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,6,2,1]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,1,2,4]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,1,4,2]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,2,1,4]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,2,4,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,4,1,2]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,4,2,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,2,4,5]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,2,5,4]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,4,2,5]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,4,5,2]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,5,2,4]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,5,4,2]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,1,4,5]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,1,5,4]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,4,1,5]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,4,5,1]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,5,1,4]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,5,4,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,1,2,5]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,1,5,2]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,2,1,5]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,2,5,1]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,5,1,2]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,5,2,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,1,2,4]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,1,4,2]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,2,1,4]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,2,4,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,4,1,2]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,4,2,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,3,5,6]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,3,6,5]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,5,3,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,5,6,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,6,3,5]=>[1,7,5,6,3,2,4]=>[7,1,3,2,5,6,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,6,5,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,2,5,6]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,2,6,5]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,5,2,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,5,6,2]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,6,2,5]=>[1,7,5,6,2,4,3]=>[7,1,3,2,6,4,5]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,6,5,2]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,2,3,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,2,6,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,3,2,6]=>[1,7,6,2,4,5,3]=>[7,1,2,6,4,3,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,3,6,2]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,6,2,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,6,3,2]=>[1,7,2,4,5,6,3]=>[7,1,6,4,3,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,2,3,5]=>[1,7,5,2,4,6,3]=>[7,1,3,6,4,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,2,5,3]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,3,2,5]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,3,5,2]=>[1,7,2,4,6,5,3]=>[7,1,6,4,2,3,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,5,2,3]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,5,3,2]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,3,5,6]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,3,6,5]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,5,3,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,5,6,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,6,3,5]=>[1,7,5,6,3,2,4]=>[7,1,3,2,5,6,4]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,6,5,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,1,5,6]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,1,6,5]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,5,1,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,5,6,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,6,1,5]=>[1,7,5,6,2,4,3]=>[7,1,3,2,6,4,5]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,6,5,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,1,3,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,1,6,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,3,1,6]=>[1,7,6,2,4,5,3]=>[7,1,2,6,4,3,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,3,6,1]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,6,1,3]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,6,3,1]=>[1,7,2,4,5,6,3]=>[7,1,6,4,3,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,1,3,5]=>[1,7,5,2,4,6,3]=>[7,1,3,6,4,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,1,5,3]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,3,1,5]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,3,5,1]=>[1,7,2,4,6,5,3]=>[7,1,6,4,2,3,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,5,1,3]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,5,3,1]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,2,5,6]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,2,6,5]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,5,2,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,5,6,2]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,6,2,5]=>[1,7,5,6,2,4,3]=>[7,1,3,2,6,4,5]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,6,5,2]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,1,5,6]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,1,6,5]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,5,1,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,5,6,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,6,1,5]=>[1,7,5,6,2,4,3]=>[7,1,3,2,6,4,5]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,6,5,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,1,2,6]=>[1,7,6,2,4,5,3]=>[7,1,2,6,4,3,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,1,6,2]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,2,1,6]=>[1,7,6,2,4,5,3]=>[7,1,2,6,4,3,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,2,6,1]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,6,1,2]=>[1,7,2,4,5,6,3]=>[7,1,6,4,3,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,6,2,1]=>[1,7,2,4,5,6,3]=>[7,1,6,4,3,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,1,2,5]=>[1,7,5,2,4,6,3]=>[7,1,3,6,4,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,1,5,2]=>[1,7,2,4,6,5,3]=>[7,1,6,4,2,3,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,2,1,5]=>[1,7,5,2,4,6,3]=>[7,1,3,6,4,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,2,5,1]=>[1,7,2,4,6,5,3]=>[7,1,6,4,2,3,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,5,1,2]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,5,2,1]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,2,3,6]=>[1,7,6,3,5,2,4]=>[7,1,2,5,3,6,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,2,6,3]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,3,2,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,3,6,2]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,6,2,3]=>[1,7,3,5,6,2,4]=>[7,1,5,3,2,6,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,6,3,2]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,1,3,6]=>[1,7,6,3,5,2,4]=>[7,1,2,5,3,6,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,1,6,3]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,3,1,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,3,6,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,6,1,3]=>[1,7,3,5,6,2,4]=>[7,1,5,3,2,6,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,6,3,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,1,2,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,1,6,2]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,2,1,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,2,6,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,6,1,2]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,6,2,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,1,2,3]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,1,3,2]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,2,1,3]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,2,3,1]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,3,1,2]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,3,2,1]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,2,3,5]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,2,5,3]=>[1,7,3,6,5,2,4]=>[7,1,5,2,3,6,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,3,2,5]=>[1,7,5,3,6,2,4]=>[7,1,3,5,2,6,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,3,5,2]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,5,2,3]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,5,3,2]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,1,3,5]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,1,5,3]=>[1,7,3,6,5,2,4]=>[7,1,5,2,3,6,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,3,1,5]=>[1,7,5,3,6,2,4]=>[7,1,3,5,2,6,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,3,5,1]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,5,1,3]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,5,3,1]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,1,2,5]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,1,5,2]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,2,1,5]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,2,5,1]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,5,1,2]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,5,2,1]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,1,2,3]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,1,3,2]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,2,1,3]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,2,3,1]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,3,1,2]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,3,2,1]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,3,4,6]=>[1,7,6,4,2,5,3]=>[7,1,2,4,6,3,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,3,6,4]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,4,3,6]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,4,6,3]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,6,3,4]=>[1,7,4,2,5,6,3]=>[7,1,4,6,3,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,6,4,3]=>[1,7,3,2,5,6,4]=>[7,1,5,6,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,2,4,6]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,2,6,4]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,4,2,6]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,4,6,2]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,6,2,4]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,6,4,2]=>[1,7,2,5,6,4,3]=>[7,1,6,3,2,4,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,2,3,6]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,2,6,3]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,3,2,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,3,6,2]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,6,2,3]=>[1,7,3,2,5,6,4]=>[7,1,5,6,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,6,3,2]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,2,3,4]=>[1,7,4,6,3,2,5]=>[7,1,4,2,5,6,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,2,4,3]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,3,2,4]=>[1,7,4,6,2,5,3]=>[7,1,4,2,6,3,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,3,4,2]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,4,2,3]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,4,3,2]=>[1,7,2,5,4,6,3]=>[7,1,6,3,4,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,3,4,6]=>[1,7,6,4,2,5,3]=>[7,1,2,4,6,3,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,3,6,4]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,4,3,6]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,4,6,3]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,6,3,4]=>[1,7,4,2,5,6,3]=>[7,1,4,6,3,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,6,4,3]=>[1,7,3,2,5,6,4]=>[7,1,5,6,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,1,4,6]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,1,6,4]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,4,1,6]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,4,6,1]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,6,1,4]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,6,4,1]=>[1,7,2,5,6,4,3]=>[7,1,6,3,2,4,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,1,3,6]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,1,6,3]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,3,1,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,3,6,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,6,1,3]=>[1,7,3,2,5,6,4]=>[7,1,5,6,3,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,6,3,1]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,1,3,4]=>[1,7,4,6,3,2,5]=>[7,1,4,2,5,6,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,1,4,3]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,3,1,4]=>[1,7,4,6,2,5,3]=>[7,1,4,2,6,3,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,3,4,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,4,1,3]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,4,3,1]=>[1,7,2,5,4,6,3]=>[7,1,6,3,4,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,2,4,6]=>[1,7,6,4,2,5,3]=>[7,1,2,4,6,3,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,2,6,4]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,4,2,6]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,4,6,2]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,6,2,4]=>[1,7,4,2,5,6,3]=>[7,1,4,6,3,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,6,4,2]=>[1,7,2,5,6,4,3]=>[7,1,6,3,2,4,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,1,4,6]=>[1,7,6,4,2,5,3]=>[7,1,2,4,6,3,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,1,6,4]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,4,1,6]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,4,6,1]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,6,1,4]=>[1,7,4,2,5,6,3]=>[7,1,4,6,3,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,6,4,1]=>[1,7,2,5,6,4,3]=>[7,1,6,3,2,4,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,1,2,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,1,6,2]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,2,1,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,2,6,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,6,1,2]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,6,2,1]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,1,2,4]=>[1,7,4,6,2,5,3]=>[7,1,4,2,6,3,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,1,4,2]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,2,1,4]=>[1,7,4,6,2,5,3]=>[7,1,4,2,6,3,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,2,4,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,4,1,2]=>[1,7,2,5,4,6,3]=>[7,1,6,3,4,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,4,2,1]=>[1,7,2,5,4,6,3]=>[7,1,6,3,4,2,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,2,3,6]=>[1,7,6,3,4,2,5]=>[7,1,2,5,4,6,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,2,6,3]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,3,2,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,3,6,2]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,6,2,3]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,6,3,2]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,1,3,6]=>[1,7,6,3,4,2,5]=>[7,1,2,5,4,6,3]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,1,6,3]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,3,1,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,3,6,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,6,1,3]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,6,3,1]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,1,2,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,1,6,2]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,2,1,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,2,6,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,6,1,2]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,6,2,1]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,1,2,3]=>[1,7,3,4,6,2,5]=>[7,1,5,4,2,6,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,1,3,2]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,2,1,3]=>[1,7,3,4,6,2,5]=>[7,1,5,4,2,6,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,2,3,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,3,1,2]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,3,2,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,2,3,4]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,2,4,3]=>[1,7,3,6,4,2,5]=>[7,1,5,2,4,6,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,3,2,4]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,3,4,2]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,4,2,3]=>[1,7,3,6,2,5,4]=>[7,1,5,2,6,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,4,3,2]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,1,3,4]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,1,4,3]=>[1,7,3,6,4,2,5]=>[7,1,5,2,4,6,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,3,1,4]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,3,4,1]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,4,1,3]=>[1,7,3,6,2,5,4]=>[7,1,5,2,6,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,4,3,1]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,1,2,4]=>[1,7,4,3,6,2,5]=>[7,1,4,5,2,6,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,1,4,2]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,2,1,4]=>[1,7,4,3,6,2,5]=>[7,1,4,5,2,6,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,2,4,1]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,4,1,2]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,4,2,1]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,1,2,3]=>[1,7,3,6,2,5,4]=>[7,1,5,2,6,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,1,3,2]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,2,1,3]=>[1,7,3,6,2,5,4]=>[7,1,5,2,6,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,2,3,1]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,3,1,2]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,3,2,1]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,3,4,5]=>[1,7,5,3,2,6,4]=>[7,1,3,5,6,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,3,5,4]=>[1,7,4,2,6,5,3]=>[7,1,4,6,2,3,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,4,3,5]=>[1,7,5,4,2,6,3]=>[7,1,3,4,6,2,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,4,5,3]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,5,3,4]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,5,4,3]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,2,4,5]=>[1,7,5,2,6,4,3]=>[7,1,3,6,2,4,5]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,2,5,4]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,4,2,5]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,4,5,2]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,5,2,4]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,5,4,2]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,2,3,5]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,2,5,3]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,3,2,5]=>[1,7,5,3,2,6,4]=>[7,1,3,5,6,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,3,5,2]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,5,2,3]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,5,3,2]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,2,3,4]=>[1,7,4,5,2,6,3]=>[7,1,4,3,6,2,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,2,4,3]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,3,2,4]=>[1,7,4,5,3,2,6]=>[7,1,4,3,5,6,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,3,4,2]=>[1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,4,2,3]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,4,3,2]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,3,4,5]=>[1,7,5,3,2,6,4]=>[7,1,3,5,6,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,3,5,4]=>[1,7,4,2,6,5,3]=>[7,1,4,6,2,3,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,4,3,5]=>[1,7,5,4,2,6,3]=>[7,1,3,4,6,2,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,4,5,3]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,5,3,4]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,5,4,3]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,1,4,5]=>[1,7,5,2,6,4,3]=>[7,1,3,6,2,4,5]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,1,5,4]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,4,1,5]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,4,5,1]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,5,1,4]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,5,4,1]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,1,3,5]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,1,5,3]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,3,1,5]=>[1,7,5,3,2,6,4]=>[7,1,3,5,6,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,3,5,1]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,5,1,3]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,5,3,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,1,3,4]=>[1,7,4,5,2,6,3]=>[7,1,4,3,6,2,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,1,4,3]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,3,1,4]=>[1,7,4,5,3,2,6]=>[7,1,4,3,5,6,2]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,3,4,1]=>[1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,4,1,3]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,4,3,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,2,4,5]=>[1,7,5,2,6,4,3]=>[7,1,3,6,2,4,5]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,2,5,4]=>[1,7,4,2,6,5,3]=>[7,1,4,6,2,3,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,4,2,5]=>[1,7,5,4,2,6,3]=>[7,1,3,4,6,2,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,4,5,2]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,5,2,4]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,5,4,2]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,1,4,5]=>[1,7,5,2,6,4,3]=>[7,1,3,6,2,4,5]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,1,5,4]=>[1,7,4,2,6,5,3]=>[7,1,4,6,2,3,5]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,4,1,5]=>[1,7,5,4,2,6,3]=>[7,1,3,4,6,2,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,4,5,1]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,5,1,4]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,5,4,1]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,1,2,5]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,1,5,2]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,2,1,5]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,2,5,1]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,5,1,2]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,5,2,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,1,2,4]=>[1,7,4,5,2,6,3]=>[7,1,4,3,6,2,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,1,4,2]=>[1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,2,1,4]=>[1,7,4,5,2,6,3]=>[7,1,4,3,6,2,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,2,4,1]=>[1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,4,1,2]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,4,2,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,2,3,5]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,2,5,3]=>[1,7,3,4,2,6,5]=>[7,1,5,4,6,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,3,2,5]=>[1,7,5,3,4,2,6]=>[7,1,3,5,4,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,3,5,2]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,5,2,3]=>[1,7,3,4,2,6,5]=>[7,1,5,4,6,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,5,3,2]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,1,3,5]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,1,5,3]=>[1,7,3,4,2,6,5]=>[7,1,5,4,6,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,3,1,5]=>[1,7,5,3,4,2,6]=>[7,1,3,5,4,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,3,5,1]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,5,1,3]=>[1,7,3,4,2,6,5]=>[7,1,5,4,6,2,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,5,3,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,1,2,5]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,1,5,2]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,2,1,5]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,2,5,1]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,5,1,2]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,5,2,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,1,2,3]=>[1,7,3,4,5,2,6]=>[7,1,5,4,3,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,1,3,2]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,2,1,3]=>[1,7,3,4,5,2,6]=>[7,1,5,4,3,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,2,3,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,3,1,2]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,3,2,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,2,3,4]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,2,4,3]=>[1,7,3,5,2,6,4]=>[7,1,5,3,6,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,3,2,4]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,3,4,2]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,4,2,3]=>[1,7,3,5,4,2,6]=>[7,1,5,3,4,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,4,3,2]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,1,3,4]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,1,4,3]=>[1,7,3,5,2,6,4]=>[7,1,5,3,6,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,3,1,4]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,3,4,1]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,4,1,3]=>[1,7,3,5,4,2,6]=>[7,1,5,3,4,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,4,3,1]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,1,2,4]=>[1,7,4,3,5,2,6]=>[7,1,4,5,3,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,1,4,2]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,2,1,4]=>[1,7,4,3,5,2,6]=>[7,1,4,5,3,6,2]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,2,4,1]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,4,1,2]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,4,2,1]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,1,2,3]=>[1,7,3,5,2,6,4]=>[7,1,5,3,6,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,1,3,2]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,2,1,3]=>[1,7,3,5,2,6,4]=>[7,1,5,3,6,2,4]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,2,3,1]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,3,1,2]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,3,2,1]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,1]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,3,2,1]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,4,3,2,1]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,3,2,1]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,4,3,2,1]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,4,3,2,1]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,4,3,2,1]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,4,3,2,1]=>[1,8,2,5,4,7,3,6]=>[8,1,7,4,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,3,2,1]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,4,3,2,1]=>[1,6,3,5,4,8,2,7]=>[8,3,6,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,4,3,2,1]=>[1,7,2,5,4,8,3,6]=>[8,2,7,4,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,4,3,2,1]=>[1,6,3,7,2,5,4,8]=>[8,3,6,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,3,2,1]=>[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,3,2,1]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,5,3,2,1]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,3,2,1]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,5,3,2,1]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,6,3,2,1]=>[1,8,2,7,3,5,6,4]=>[8,1,7,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,6,3,2,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,7,3,2,1]=>[1,8,2,6,3,5,7,4]=>[8,1,7,3,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,7,3,2,1]=>[1,8,2,5,7,3,6,4]=>[8,1,7,4,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,7,3,2,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,7,3,2,1]=>[1,8,2,5,7,3,4,6]=>[8,1,7,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,7,3,2,1]=>[1,8,2,4,6,3,5,7]=>[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,8,3,2,1]=>[1,6,3,5,8,2,7,4]=>[8,3,6,4,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,8,3,2,1]=>[1,5,8,2,6,3,7,4]=>[8,4,1,7,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,8,3,2,1]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,8,3,2,1]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,8,3,2,1]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,8,3,2,1]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,8,3,2,1]=>[1,6,3,5,8,2,4,7]=>[8,3,6,4,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,8,3,2,1]=>[1,5,8,2,4,7,3,6]=>[8,4,1,7,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,3,2,1]=>[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,4,2,1]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,4,2,1]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,3,4,2,1]=>[1,8,2,6,4,5,3,7]=>[8,1,7,3,5,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,3,4,2,1]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,4,2,1]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,3,4,2,1]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,3,4,2,1]=>[1,6,4,8,2,7,3,5]=>[8,3,5,1,7,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,3,4,2,1]=>[1,6,4,8,2,5,3,7]=>[8,3,5,1,7,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,4,2,1]=>[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,3,5,2,1]=>[1,8,2,7,3,6,5,4]=>[8,1,7,2,6,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,3,5,2,1]=>[1,7,2,8,3,6,5,4]=>[8,2,7,1,6,3,4,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,3,5,2,1]=>[1,8,2,6,5,3,7,4]=>[8,1,7,3,4,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,3,5,2,1]=>[1,7,2,6,5,3,8,4]=>[8,2,7,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,3,5,2,1]=>[1,6,5,3,8,2,7,4]=>[8,3,4,6,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,4,5,2,1]=>[1,8,2,7,3,6,5,4]=>[8,1,7,2,6,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,5,2,1]=>[1,7,2,8,3,6,5,4]=>[8,2,7,1,6,3,4,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,4,5,2,1]=>[1,8,2,6,5,4,3,7]=>[8,1,7,3,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,4,5,2,1]=>[1,7,2,6,5,4,3,8]=>[8,2,7,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,5,2,1]=>[1,6,5,4,3,8,2,7]=>[8,3,4,5,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,3,6,2,1]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,6,2,1]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,3,6,2,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,4,6,2,1]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,4,6,2,1]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,5,6,2,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,5,6,2,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,6,2,1]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,7,2,1]=>[1,8,2,6,7,3,5,4]=>[8,1,7,3,2,6,4,5]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,3,7,2,1]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,3,7,2,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,5,7,2,1]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,6,7,2,1]=>[1,8,2,5,6,7,3,4]=>[8,1,7,4,3,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,6,7,2,1]=>[1,8,2,5,6,7,3,4]=>[8,1,7,4,3,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,7,2,1]=>[1,8,2,4,5,6,7,3]=>[8,1,7,5,4,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,7,2,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,8,2,1]=>[1,7,2,6,8,3,5,4]=>[8,2,7,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,3,8,2,1]=>[1,6,8,2,7,3,5,4]=>[8,3,1,7,2,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,3,8,2,1]=>[1,6,8,2,5,3,7,4]=>[8,3,1,7,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,3,8,2,1]=>[1,5,3,7,2,6,8,4]=>[8,4,6,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,3,8,2,1]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,3,8,2,1]=>[1,6,8,2,7,3,4,5]=>[8,3,1,7,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,3,8,2,1]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,3,8,2,1]=>[1,7,2,4,6,8,3,5]=>[8,2,7,5,3,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,3,8,2,1]=>[1,5,3,6,8,2,4,7]=>[8,4,6,3,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,8,2,1]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,4,8,2,1]=>[1,7,2,6,8,3,5,4]=>[8,2,7,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,5,8,2,1]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,5,8,2,1]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,6,8,2,1]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,7,8,2,1]=>[1,6,8,2,5,7,3,4]=>[8,3,1,7,4,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,7,8,2,1]=>[1,4,3,6,8,2,5,7]=>[8,5,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,7,8,2,1]=>[1,6,8,2,5,7,3,4]=>[8,3,1,7,4,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,7,8,2,1]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,7,8,2,1]=>[1,5,7,2,4,6,8,3]=>[8,4,2,7,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,6,7,8,2,1]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,2,1]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,2,3,1]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,2,3,1]=>[1,7,3,6,2,8,4,5]=>[8,2,6,3,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,4,2,3,1]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,2,3,1]=>[1,7,3,8,2,6,4,5]=>[8,2,6,1,7,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,4,2,3,1]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,4,2,3,1]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,4,2,3,1]=>[1,8,2,5,4,7,3,6]=>[8,1,7,4,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,2,3,1]=>[1,7,3,5,4,8,2,6]=>[8,2,6,4,5,1,7,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,4,2,3,1]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,4,2,3,1]=>[1,7,3,6,2,5,4,8]=>[8,2,6,3,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,2,3,1]=>[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,2,3,1]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,2,3,1]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,5,2,3,1]=>[1,7,3,8,2,6,4,5]=>[8,2,6,1,7,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,5,2,3,1]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,6,2,3,1]=>[1,8,2,7,3,5,6,4]=>[8,1,7,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,6,2,3,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,6,2,3,1]=>[1,7,3,4,5,6,2,8]=>[8,2,6,5,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,7,2,3,1]=>[1,8,2,6,3,5,7,4]=>[8,1,7,3,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,7,2,3,1]=>[1,8,2,5,7,3,6,4]=>[8,1,7,4,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,7,2,3,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,7,2,3,1]=>[1,8,2,4,6,3,5,7]=>[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,8,2,3,1]=>[1,7,3,5,8,2,6,4]=>[8,2,6,4,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,8,2,3,1]=>[1,7,3,6,2,5,8,4]=>[8,2,6,3,7,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,8,2,3,1]=>[1,6,2,5,8,3,7,4]=>[8,3,7,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,8,2,3,1]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,2,3,1]=>[1,4,7,3,6,2,5,8]=>[8,5,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,2,4,1]=>[1,8,2,7,4,5,3,6]=>[8,1,7,2,5,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,3,2,4,1]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,3,2,4,1]=>[1,8,2,7,4,6,3,5]=>[8,1,7,2,5,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,3,2,4,1]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,3,2,4,1]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,3,2,4,1]=>[1,6,2,7,4,8,3,5]=>[8,3,7,2,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,2,4,1]=>[1,5,3,7,4,8,2,6]=>[8,4,6,2,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,3,4,1]=>[1,8,2,7,4,5,3,6]=>[8,1,7,2,5,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,2,3,4,1]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,2,3,4,1]=>[1,7,4,5,2,6,3,8]=>[8,2,5,4,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,2,3,4,1]=>[1,8,2,7,4,6,3,5]=>[8,1,7,2,5,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,2,3,4,1]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,3,4,1]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,2,3,4,1]=>[1,6,3,5,2,7,4,8]=>[8,3,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,3,4,1]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,3,2,5,1]=>[1,8,2,7,5,3,6,4]=>[8,1,7,2,4,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,3,2,5,1]=>[1,7,5,3,6,2,8,4]=>[8,2,4,6,3,7,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,3,2,5,1]=>[1,8,2,6,3,7,5,4]=>[8,1,7,3,6,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,3,2,5,1]=>[1,7,5,3,8,2,6,4]=>[8,2,4,6,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,3,2,5,1]=>[1,6,2,7,5,3,8,4]=>[8,3,7,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,4,2,5,1]=>[1,8,2,7,5,4,3,6]=>[8,1,7,2,4,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,2,5,1]=>[1,7,5,4,3,6,2,8]=>[8,2,4,5,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,4,2,5,1]=>[1,8,2,6,3,7,5,4]=>[8,1,7,3,6,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,2,5,1]=>[1,6,2,7,5,4,3,8]=>[8,3,7,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,2,3,5,1]=>[1,8,2,7,5,3,6,4]=>[8,1,7,2,4,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,2,3,5,1]=>[1,8,2,6,3,7,5,4]=>[8,1,7,3,6,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,2,3,5,1]=>[1,7,5,2,6,3,8,4]=>[8,2,4,7,3,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,3,5,1]=>[1,6,3,8,2,7,5,4]=>[8,3,6,1,7,2,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,2,4,5,1]=>[1,8,2,7,5,3,6,4]=>[8,1,7,2,4,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,2,4,5,1]=>[1,8,2,6,4,3,7,5]=>[8,1,7,3,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,4,5,1]=>[1,6,4,3,8,2,7,5]=>[8,3,5,6,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,3,4,5,1]=>[1,8,2,7,5,3,6,4]=>[8,1,7,2,4,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,3,4,5,1]=>[1,8,2,6,4,3,7,5]=>[8,1,7,3,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,3,4,5,1]=>[1,7,5,3,8,2,6,4]=>[8,2,4,6,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,3,4,5,1]=>[1,6,4,2,7,5,3,8]=>[8,3,5,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,3,2,6,1]=>[1,8,2,7,6,3,5,4]=>[8,1,7,2,3,6,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,4,2,6,1]=>[1,8,2,7,6,3,5,4]=>[8,1,7,2,3,6,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,5,2,6,1]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,5,2,6,1]=>[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,2,3,6,1]=>[1,8,2,7,6,3,5,4]=>[8,1,7,2,3,6,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,2,4,6,1]=>[1,8,2,7,6,4,3,5]=>[8,1,7,2,3,5,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,2,5,6,1]=>[1,7,6,5,2,8,3,4]=>[8,2,3,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,2,5,6,1]=>[1,7,6,5,2,8,3,4]=>[8,2,3,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,4,5,6,1]=>[1,7,6,5,4,2,8,3]=>[8,2,3,4,5,7,1,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,4,5,6,1]=>[1,8,2,7,6,5,4,3]=>[8,1,7,2,3,4,5,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,4,5,6,1]=>[1,7,6,5,4,3,2,8]=>[8,2,3,4,5,6,7,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,2,7,1]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,3,2,7,1]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,3,2,7,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,3,2,7,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,4,2,7,1]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,5,2,7,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,5,2,7,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,6,2,7,1]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,6,2,7,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,2,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,3,7,1]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,2,3,7,1]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,2,3,7,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,2,4,7,1]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,4,5,7,1]=>[1,8,2,6,5,4,3,7]=>[8,1,7,3,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,6,7,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,2,6,7,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,2,6,7,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,2,6,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,3,6,7,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,6,7,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,5,6,7,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,5,6,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,5,6,7,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,5,6,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,6,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,3,2,8,1]=>[1,7,8,2,5,3,6,4]=>[8,2,1,7,4,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,3,2,8,1]=>[1,5,3,7,8,2,6,4]=>[8,4,6,2,1,7,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,3,2,8,1]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,3,2,8,1]=>[1,7,8,2,4,6,3,5]=>[8,2,1,7,5,3,6,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,3,2,8,1]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,3,2,8,1]=>[1,6,2,4,7,8,3,5]=>[8,3,7,5,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,2,8,1]=>[1,4,7,8,2,5,3,6]=>[8,5,2,1,7,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,4,2,8,1]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,6,2,8,1]=>[1,7,8,2,5,6,3,4]=>[8,2,1,7,4,3,6,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,6,2,8,1]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,6,2,8,1]=>[1,7,8,2,5,6,3,4]=>[8,2,1,7,4,3,6,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,6,2,8,1]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,7,2,8,1]=>[1,6,2,5,7,8,3,4]=>[8,3,7,4,2,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,7,2,8,1]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,7,2,8,1]=>[1,5,7,8,2,4,3,6]=>[8,4,2,1,7,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,7,2,8,1]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,7,2,8,1]=>[1,6,2,5,7,8,3,4]=>[8,3,7,4,2,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,7,2,8,1]=>[1,5,7,8,2,6,3,4]=>[8,4,2,1,7,3,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,7,2,8,1]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,7,2,8,1]=>[1,5,7,8,2,4,6,3]=>[8,4,2,1,7,5,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,7,2,8,1]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,2,8,1]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,2,3,8,1]=>[1,7,8,2,5,3,6,4]=>[8,2,1,7,4,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,2,3,8,1]=>[1,6,3,7,8,2,5,4]=>[8,3,6,2,1,7,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,2,3,8,1]=>[1,5,2,6,3,7,8,4]=>[8,4,7,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,2,3,8,1]=>[1,6,3,4,5,2,7,8]=>[8,3,6,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,2,3,8,1]=>[1,7,8,2,4,6,3,5]=>[8,2,1,7,5,3,6,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,2,3,8,1]=>[1,6,3,4,7,8,2,5]=>[8,3,6,5,2,1,7,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,2,3,8,1]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,2,3,8,1]=>[1,6,3,5,2,4,7,8]=>[8,3,6,4,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,2,3,8,1]=>[1,5,2,4,7,8,3,6]=>[8,4,7,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,3,8,1]=>[1,4,7,8,2,5,3,6]=>[8,5,2,1,7,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,2,4,8,1]=>[1,7,8,2,6,4,3,5]=>[8,2,1,7,3,5,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,3,2,4,8,1]=>[1,6,4,3,5,2,7,8]=>[8,3,5,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,3,4,8,1]=>[1,7,8,2,6,4,3,5]=>[8,2,1,7,3,5,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,2,3,4,8,1]=>[1,7,8,2,5,3,6,4]=>[8,2,1,7,4,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,3,4,8,1]=>[1,5,3,7,8,2,6,4]=>[8,4,6,2,1,7,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,4,5,8,1]=>[1,7,8,2,6,5,4,3]=>[8,2,1,7,3,4,5,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,4,5,8,1]=>[1,6,5,4,2,7,8,3]=>[8,3,4,5,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,4,5,8,1]=>[1,7,8,2,6,5,4,3]=>[8,2,1,7,3,4,5,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,4,5,8,1]=>[1,6,5,4,3,2,7,8]=>[8,3,4,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,3,6,8,1]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,5,6,8,1]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,5,6,8,1]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,5,6,8,1]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,5,6,8,1]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,7,8,1]=>[1,6,7,8,2,5,3,4]=>[8,3,2,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,2,7,8,1]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,2,7,8,1]=>[1,6,7,8,2,5,3,4]=>[8,3,2,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,2,7,8,1]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,2,7,8,1]=>[1,5,2,4,6,7,8,3]=>[8,4,7,5,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,2,7,8,1]=>[1,4,6,7,8,2,3,5]=>[8,5,3,2,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,2,7,8,1]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,3,7,8,1]=>[1,6,7,8,2,5,3,4]=>[8,3,2,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,3,7,8,1]=>[1,5,3,6,7,8,2,4]=>[8,4,6,3,2,1,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,3,7,8,1]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,4,7,8,1]=>[1,6,7,8,2,5,4,3]=>[8,3,2,1,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,3,4,7,8,1]=>[1,6,7,8,2,5,4,3]=>[8,3,2,1,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,4,7,8,1]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,5,7,8,1]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,6,7,8,1]=>[1,5,6,7,8,2,4,3]=>[8,4,3,2,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,6,7,8,1]=>[1,4,2,5,6,7,8,3]=>[8,5,7,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,6,7,8,1]=>[1,5,6,7,8,2,3,4]=>[8,4,3,2,1,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,6,7,8,1]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,6,7,8,1]=>[1,3,5,6,7,8,2,4]=>[8,6,4,3,2,1,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,6,7,8,1]=>[1,5,6,7,8,2,4,3]=>[8,4,3,2,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,6,7,8,1]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,6,7,8,1]=>[1,5,6,7,8,2,3,4]=>[8,4,3,2,1,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,6,7,8,1]=>[1,5,6,7,8,2,3,4]=>[8,4,3,2,1,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,6,7,8,1]=>[1,4,5,6,7,8,2,3]=>[8,5,4,3,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,6,7,8,1]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,6,7,8,1]=>[1,4,5,6,7,8,2,3]=>[8,5,4,3,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,1]=>[1,3,4,5,6,7,8,2]=>[8,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,1,2]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,3,1,2]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,4,3,1,2]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,3,1,2]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,4,3,1,2]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,4,3,1,2]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,4,3,1,2]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,3,1,2]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,4,3,1,2]=>[1,6,3,5,4,8,2,7]=>[8,3,6,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,4,3,1,2]=>[1,7,2,5,4,8,3,6]=>[8,2,7,4,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,4,3,1,2]=>[1,6,3,7,2,5,4,8]=>[8,3,6,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,3,1,2]=>[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,3,1,2]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,5,3,1,2]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,3,1,2]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,6,3,1,2]=>[1,8,2,7,3,5,6,4]=>[8,1,7,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,6,3,1,2]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,7,3,1,2]=>[1,8,2,5,7,3,6,4]=>[8,1,7,4,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,7,3,1,2]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,7,3,1,2]=>[1,8,2,5,7,3,4,6]=>[8,1,7,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,8,3,1,2]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,8,3,1,2]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,8,3,1,2]=>[1,5,8,2,4,7,3,6]=>[8,4,1,7,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,3,1,2]=>[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,4,1,2]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,4,1,2]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,3,4,1,2]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,4,1,2]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,3,4,1,2]=>[1,8,2,6,4,7,3,5]=>[8,1,7,3,5,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,3,4,1,2]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,3,4,1,2]=>[1,6,4,8,2,7,3,5]=>[8,3,5,1,7,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,3,4,1,2]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,3,4,1,2]=>[1,6,4,8,2,5,3,7]=>[8,3,5,1,7,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,4,1,2]=>[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,3,5,1,2]=>[1,6,5,3,8,2,7,4]=>[8,3,4,6,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,4,5,1,2]=>[1,8,2,7,3,6,5,4]=>[8,1,7,2,6,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,5,1,2]=>[1,7,2,8,3,6,5,4]=>[8,2,7,1,6,3,4,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,4,5,1,2]=>[1,8,2,6,5,4,3,7]=>[8,1,7,3,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,5,1,2]=>[1,6,5,4,3,8,2,7]=>[8,3,4,5,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,6,1,2]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,3,6,1,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,3,6,1,2]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,4,6,1,2]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,5,6,1,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,5,6,1,2]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,5,6,1,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,6,1,2]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,7,1,2]=>[1,8,2,6,7,3,5,4]=>[8,1,7,3,2,6,4,5]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,3,7,1,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,6,7,1,2]=>[1,8,2,5,6,7,3,4]=>[8,1,7,4,3,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,6,7,1,2]=>[1,8,2,5,6,7,3,4]=>[8,1,7,4,3,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,7,1,2]=>[1,8,2,4,5,6,7,3]=>[8,1,7,5,4,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,7,1,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,8,1,2]=>[1,7,2,6,8,3,5,4]=>[8,2,7,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,3,8,1,2]=>[1,6,8,2,5,3,7,4]=>[8,3,1,7,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,3,8,1,2]=>[1,5,3,7,2,6,8,4]=>[8,4,6,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,3,8,1,2]=>[1,6,8,2,7,3,4,5]=>[8,3,1,7,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,3,8,1,2]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,3,8,1,2]=>[1,5,3,4,7,2,6,8]=>[8,4,6,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,3,8,1,2]=>[1,5,3,6,8,2,4,7]=>[8,4,6,3,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,8,1,2]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,4,8,1,2]=>[1,7,2,6,8,3,5,4]=>[8,2,7,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,4,8,1,2]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,5,8,1,2]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,5,8,1,2]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,6,8,1,2]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,6,8,1,2]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,7,8,1,2]=>[1,6,8,2,5,7,3,4]=>[8,3,1,7,4,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,7,8,1,2]=>[1,4,3,6,8,2,5,7]=>[8,5,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,7,8,1,2]=>[1,6,8,2,5,7,3,4]=>[8,3,1,7,4,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,7,8,1,2]=>[1,6,8,2,4,5,7,3]=>[8,3,1,7,5,4,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,7,8,1,2]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,7,8,1,2]=>[1,5,7,2,4,6,8,3]=>[8,4,2,7,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,7,8,1,2]=>[1,4,6,8,2,5,7,3]=>[8,5,3,1,7,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,6,7,8,1,2]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,1,2]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,2,1,3]=>[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,2,1,3]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,4,2,1,3]=>[1,8,3,7,2,6,4,5]=>[8,1,6,2,7,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,2,1,3]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,4,2,1,3]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,4,2,1,3]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,4,2,1,3]=>[1,8,3,5,4,7,2,6]=>[8,1,6,4,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,2,1,3]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,4,2,1,3]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,4,2,1,3]=>[1,7,2,5,4,8,3,6]=>[8,2,7,4,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,4,2,1,3]=>[1,6,2,5,4,8,3,7]=>[8,3,7,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,2,1,3]=>[1,5,4,8,3,7,2,6]=>[8,4,5,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,2,1,3]=>[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,2,1,3]=>[1,8,3,7,2,6,4,5]=>[8,1,6,2,7,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,5,2,1,3]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,7,2,1,3]=>[1,8,3,5,7,2,6,4]=>[8,1,6,4,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,7,2,1,3]=>[1,8,3,5,7,2,4,6]=>[8,1,6,4,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,8,2,1,3]=>[1,6,2,7,3,5,8,4]=>[8,3,7,2,6,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,8,2,1,3]=>[1,6,2,5,8,3,7,4]=>[8,3,7,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,8,2,1,3]=>[1,5,8,3,7,2,6,4]=>[8,4,1,6,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,8,2,1,3]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,8,2,1,3]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,8,2,1,3]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,8,2,1,3]=>[1,5,8,3,6,2,4,7]=>[8,4,1,6,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,2,1,3]=>[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,1,2,3]=>[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,1,2,3]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,1,2,3]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,4,1,2,3]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,4,1,2,3]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,4,1,2,3]=>[1,8,3,5,4,7,2,6]=>[8,1,6,4,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,4,1,2,3]=>[1,8,3,6,2,5,4,7]=>[8,1,6,3,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,1,2,3]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,4,1,2,3]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,4,1,2,3]=>[1,7,2,5,4,8,3,6]=>[8,2,7,4,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,4,1,2,3]=>[1,6,2,5,4,8,3,7]=>[8,3,7,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,1,2,3]=>[1,5,4,8,3,7,2,6]=>[8,4,5,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,1,2,3]=>[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,1,2,3]=>[1,8,3,7,2,6,4,5]=>[8,1,6,2,7,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,5,1,2,3]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,6,1,2,3]=>[1,8,3,5,6,2,7,4]=>[8,1,6,4,3,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,6,1,2,3]=>[1,7,2,8,3,5,6,4]=>[8,2,7,1,6,4,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,6,1,2,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,7,1,2,3]=>[1,8,3,5,7,2,6,4]=>[8,1,6,4,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,7,1,2,3]=>[1,8,3,6,2,5,7,4]=>[8,1,6,3,7,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,7,1,2,3]=>[1,8,3,5,7,2,4,6]=>[8,1,6,4,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,8,1,2,3]=>[1,6,2,7,3,5,8,4]=>[8,3,7,2,6,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,8,1,2,3]=>[1,6,2,5,8,3,7,4]=>[8,3,7,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,8,1,2,3]=>[1,5,8,3,7,2,6,4]=>[8,4,1,6,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,8,1,2,3]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,8,1,2,3]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,8,1,2,3]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,8,1,2,3]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,8,1,2,3]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,8,1,2,3]=>[1,5,8,3,4,7,2,6]=>[8,4,1,6,5,2,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,8,1,2,3]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,8,1,2,3]=>[1,5,8,3,6,2,4,7]=>[8,4,1,6,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,1,2,3]=>[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,2,1,4]=>[1,8,4,5,3,6,2,7]=>[8,1,5,4,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,2,1,4]=>[1,7,2,8,4,5,3,6]=>[8,2,7,1,5,4,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,3,2,1,4]=>[1,8,4,5,3,7,2,6]=>[8,1,5,4,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,3,2,1,4]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,3,2,1,4]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,3,2,1,4]=>[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,2,1,4]=>[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,3,2,1,4]=>[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,3,2,1,4]=>[1,8,4,7,2,5,3,6]=>[8,1,5,2,7,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,3,2,1,4]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,3,2,1,4]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,3,2,1,4]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,3,2,1,4]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,2,1,4]=>[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,3,1,4]=>[1,8,4,5,2,7,3,6]=>[8,1,5,4,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,2,3,1,4]=>[1,7,2,8,4,5,3,6]=>[8,2,7,1,5,4,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,2,3,1,4]=>[1,8,4,5,2,6,3,7]=>[8,1,5,4,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,2,3,1,4]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,2,3,1,4]=>[1,8,4,6,3,5,2,7]=>[8,1,5,3,6,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,3,1,4]=>[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,2,3,1,4]=>[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,3,1,4]=>[1,8,4,7,2,5,3,6]=>[8,1,5,2,7,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,2,3,1,4]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,2,3,1,4]=>[1,6,3,5,2,7,4,8]=>[8,3,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,2,3,1,4]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,2,3,1,4]=>[1,6,3,7,2,5,4,8]=>[8,3,6,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,3,1,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,1,2,4]=>[1,8,4,5,3,6,2,7]=>[8,1,5,4,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,1,2,4]=>[1,7,2,8,4,5,3,6]=>[8,2,7,1,5,4,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,3,1,2,4]=>[1,8,4,5,3,7,2,6]=>[8,1,5,4,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,3,1,2,4]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,3,1,2,4]=>[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,1,2,4]=>[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,3,1,2,4]=>[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,3,1,2,4]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,3,1,2,4]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,3,1,2,4]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,3,1,2,4]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,1,2,4]=>[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,1,3,4]=>[1,8,4,5,2,7,3,6]=>[8,1,5,4,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,2,1,3,4]=>[1,7,3,6,2,8,4,5]=>[8,2,6,3,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,2,1,3,4]=>[1,7,3,8,4,5,2,6]=>[8,2,6,1,5,4,7,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,2,1,3,4]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,2,1,3,4]=>[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,1,3,4]=>[1,7,3,5,2,8,4,6]=>[8,2,6,4,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,2,1,3,4]=>[1,8,4,7,3,5,2,6]=>[8,1,5,2,6,4,7,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,1,3,4]=>[1,8,4,7,3,6,2,5]=>[8,1,5,2,6,3,7,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,2,1,3,4]=>[1,7,3,5,2,6,4,8]=>[8,2,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,2,1,3,4]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,2,1,3,4]=>[1,7,3,6,2,5,4,8]=>[8,2,6,3,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,2,1,3,4]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,1,3,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,2,3,4]=>[1,8,4,5,2,7,3,6]=>[8,1,5,4,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,1,2,3,4]=>[1,7,3,6,2,8,4,5]=>[8,2,6,3,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,1,2,3,4]=>[1,8,4,5,2,6,3,7]=>[8,1,5,4,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,1,2,3,4]=>[1,7,3,8,4,5,2,6]=>[8,2,6,1,5,4,7,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,1,2,3,4]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,1,2,3,4]=>[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,2,3,4]=>[1,7,3,5,2,8,4,6]=>[8,2,6,4,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,1,2,3,4]=>[1,8,4,7,3,5,2,6]=>[8,1,5,2,6,4,7,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,1,2,3,4]=>[1,8,4,7,3,6,2,5]=>[8,1,5,2,6,3,7,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,1,2,3,4]=>[1,7,3,5,2,6,4,8]=>[8,2,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,1,2,3,4]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,1,2,3,4]=>[1,7,3,6,2,5,4,8]=>[8,2,6,3,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,1,2,3,4]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,2,3,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,3,2,1,5]=>[1,8,5,3,6,2,7,4]=>[8,1,4,6,3,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,3,2,1,5]=>[1,7,2,8,5,3,6,4]=>[8,2,7,1,4,6,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,3,2,1,5]=>[1,8,5,3,7,2,6,4]=>[8,1,4,6,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,3,2,1,5]=>[1,7,2,6,3,8,5,4]=>[8,2,7,3,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,3,2,1,5]=>[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,4,2,1,5]=>[1,8,5,4,3,6,2,7]=>[8,1,4,5,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,2,1,5]=>[1,7,2,8,5,4,3,6]=>[8,2,7,1,4,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,2,1,5]=>[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,2,3,1,5]=>[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,2,3,1,5]=>[1,8,5,2,6,3,7,4]=>[8,1,4,7,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,2,3,1,5]=>[1,7,2,6,3,8,5,4]=>[8,2,7,3,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,3,1,5]=>[1,6,3,8,5,2,7,4]=>[8,3,6,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,2,4,1,5]=>[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,2,4,1,5]=>[1,8,5,2,6,4,3,7]=>[8,1,4,7,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,4,1,5]=>[1,6,4,3,8,5,2,7]=>[8,3,5,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,3,4,1,5]=>[1,8,5,3,6,4,2,7]=>[8,1,4,6,3,5,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,3,4,1,5]=>[1,8,5,3,7,2,6,4]=>[8,1,4,6,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,3,1,2,5]=>[1,8,5,3,6,2,7,4]=>[8,1,4,6,3,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,3,1,2,5]=>[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,4,1,2,5]=>[1,8,5,4,3,6,2,7]=>[8,1,4,5,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,1,2,5]=>[1,7,2,8,5,4,3,6]=>[8,2,7,1,4,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,4,1,2,5]=>[1,8,5,4,3,7,2,6]=>[8,1,4,5,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,1,2,5]=>[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,2,1,3,5]=>[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,2,1,3,5]=>[1,7,3,6,2,8,5,4]=>[8,2,6,3,7,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,2,1,3,5]=>[1,8,5,2,6,3,7,4]=>[8,1,4,7,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,1,3,5]=>[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,2,3,5]=>[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,1,2,3,5]=>[1,7,3,6,2,8,5,4]=>[8,2,6,3,7,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,1,2,3,5]=>[1,7,3,8,5,2,6,4]=>[8,2,6,1,4,7,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,1,2,3,5]=>[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,2,1,4,5]=>[1,8,5,2,7,4,3,6]=>[8,1,4,7,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,2,1,4,5]=>[1,7,4,3,6,2,8,5]=>[8,2,5,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,2,1,4,5]=>[1,8,5,2,6,3,7,4]=>[8,1,4,7,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,2,1,4,5]=>[1,7,4,3,8,5,2,6]=>[8,2,5,6,1,4,7,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,1,4,5]=>[1,6,2,7,4,3,8,5]=>[8,3,7,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,3,1,4,5]=>[1,8,5,3,6,2,7,4]=>[8,1,4,6,3,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,3,1,4,5]=>[1,7,4,2,8,5,3,6]=>[8,2,5,7,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,3,1,4,5]=>[1,8,5,3,7,4,2,6]=>[8,1,4,6,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,3,1,4,5]=>[1,7,4,2,6,3,8,5]=>[8,2,5,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,3,1,4,5]=>[1,6,2,7,4,3,8,5]=>[8,3,7,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,1,2,4,5]=>[1,8,5,2,7,4,3,6]=>[8,1,4,7,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,1,2,4,5]=>[1,7,4,3,6,2,8,5]=>[8,2,5,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,1,2,4,5]=>[1,8,5,2,6,3,7,4]=>[8,1,4,7,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,1,2,4,5]=>[1,7,4,3,8,5,2,6]=>[8,2,5,6,1,4,7,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,1,2,4,5]=>[1,6,2,7,4,3,8,5]=>[8,3,7,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,1,3,4,5]=>[1,8,5,2,7,4,3,6]=>[8,1,4,7,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,1,3,4,5]=>[1,7,4,2,8,5,3,6]=>[8,2,5,7,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,1,3,4,5]=>[1,8,5,2,6,3,7,4]=>[8,1,4,7,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,1,3,4,5]=>[1,6,3,8,5,2,7,4]=>[8,3,6,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,3,4,5]=>[1,8,5,2,7,4,3,6]=>[8,1,4,7,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,2,3,4,5]=>[1,7,4,2,8,5,3,6]=>[8,2,5,7,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,2,3,4,5]=>[1,8,5,2,6,3,7,4]=>[8,1,4,7,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,2,3,4,5]=>[1,7,4,2,6,3,8,5]=>[8,2,5,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,3,4,5]=>[1,6,3,8,5,2,7,4]=>[8,3,6,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,3,2,1,6]=>[1,8,6,2,7,3,5,4]=>[8,1,3,7,2,6,4,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,2,1,6]=>[1,7,2,8,6,3,5,4]=>[8,2,7,1,3,6,4,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,3,2,1,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,3,2,1,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,4,2,1,6]=>[1,8,6,2,7,3,5,4]=>[8,1,3,7,2,6,4,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,5,2,1,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,5,2,1,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,2,1,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,2,3,1,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,2,4,1,6]=>[1,8,6,4,3,5,2,7]=>[8,1,3,5,6,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,2,5,1,6]=>[1,8,6,5,2,7,3,4]=>[8,1,3,4,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,2,5,1,6]=>[1,7,2,8,6,5,3,4]=>[8,2,7,1,3,4,6,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,2,5,1,6]=>[1,8,6,5,2,7,3,4]=>[8,1,3,4,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,2,5,1,6]=>[1,7,2,8,6,5,3,4]=>[8,2,7,1,3,4,6,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,4,5,1,6]=>[1,8,6,5,4,3,2,7]=>[8,1,3,4,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,3,1,2,6]=>[1,8,6,2,7,3,5,4]=>[8,1,3,7,2,6,4,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,1,2,6]=>[1,7,2,8,6,3,5,4]=>[8,2,7,1,3,6,4,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,4,1,2,6]=>[1,8,6,2,7,3,5,4]=>[8,1,3,7,2,6,4,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,4,1,2,6]=>[1,7,2,8,6,3,5,4]=>[8,2,7,1,3,6,4,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,5,1,2,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,1,2,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,2,1,3,6]=>[1,7,3,5,2,8,6,4]=>[8,2,6,4,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,1,2,3,6]=>[1,8,6,2,7,3,5,4]=>[8,1,3,7,2,6,4,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,1,2,3,6]=>[1,7,3,5,2,8,6,4]=>[8,2,6,4,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,1,2,3,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,1,2,3,6]=>[1,7,3,4,5,2,8,6]=>[8,2,6,5,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,2,1,4,6]=>[1,8,6,2,7,4,3,5]=>[8,1,3,7,2,5,6,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,3,1,4,6]=>[1,8,6,2,7,4,3,5]=>[8,1,3,7,2,5,6,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,1,2,4,6]=>[1,8,6,2,7,4,3,5]=>[8,1,3,7,2,5,6,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,1,3,4,6]=>[1,8,6,3,5,2,7,4]=>[8,1,3,6,4,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,2,1,3,4,6]=>[1,7,4,2,8,6,3,5]=>[8,2,5,7,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,3,4,6]=>[1,8,6,3,5,2,7,4]=>[8,1,3,6,4,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,2,3,4,6]=>[1,7,4,2,8,6,3,5]=>[8,2,5,7,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,2,1,5,6]=>[1,8,6,2,7,5,3,4]=>[8,1,3,7,2,4,6,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,2,1,5,6]=>[1,7,5,2,8,6,3,4]=>[8,2,4,7,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,2,1,5,6]=>[1,8,6,2,7,5,3,4]=>[8,1,3,7,2,4,6,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,2,1,5,6]=>[1,7,5,2,8,6,3,4]=>[8,2,4,7,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,4,1,5,6]=>[1,8,6,2,7,5,4,3]=>[8,1,3,7,2,4,5,6]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,4,1,5,6]=>[1,8,6,2,7,5,4,3]=>[8,1,3,7,2,4,5,6]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,1,2,5,6]=>[1,7,5,2,8,6,3,4]=>[8,2,4,7,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,1,2,5,6]=>[1,8,6,2,7,5,3,4]=>[8,1,3,7,2,4,6,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,1,2,5,6]=>[1,7,5,2,8,6,3,4]=>[8,2,4,7,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,3,5,6]=>[1,7,5,2,8,6,3,4]=>[8,2,4,7,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,2,3,5,6]=>[1,7,5,2,8,6,3,4]=>[8,2,4,7,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,1,4,5,6]=>[1,8,6,4,2,7,5,3]=>[8,1,3,5,7,2,4,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,4,5,6]=>[1,7,5,2,8,6,4,3]=>[8,2,4,7,1,3,5,6]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,1,4,5,6]=>[1,8,6,4,3,2,7,5]=>[8,1,3,5,6,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,1,4,5,6]=>[1,7,5,2,8,6,4,3]=>[8,2,4,7,1,3,5,6]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,2,4,5,6]=>[1,7,5,2,8,6,4,3]=>[8,2,4,7,1,3,5,6]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,3,4,5,6]=>[1,8,6,4,2,7,5,3]=>[8,1,3,5,7,2,4,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,3,4,5,6]=>[1,7,5,3,2,8,6,4]=>[8,2,4,6,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,3,4,5,6]=>[1,8,6,4,2,7,5,3]=>[8,1,3,5,7,2,4,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,4,5,6]=>[1,7,5,3,2,8,6,4]=>[8,2,4,6,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,2,1,7]=>[1,8,7,2,6,3,5,4]=>[8,1,2,7,3,6,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,3,2,1,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,3,2,1,7]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,4,2,1,7]=>[1,8,7,2,6,3,5,4]=>[8,1,2,7,3,6,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,4,2,1,7]=>[1,8,7,2,5,4,3,6]=>[8,1,2,7,4,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,5,2,1,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,2,1,7]=>[1,8,7,2,4,5,6,3]=>[8,1,2,7,5,4,3,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,2,1,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,3,1,7]=>[1,8,7,2,6,3,5,4]=>[8,1,2,7,3,6,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,2,3,1,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,2,4,1,7]=>[1,8,7,2,6,4,3,5]=>[8,1,2,7,3,5,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,3,4,1,7]=>[1,8,7,2,6,4,3,5]=>[8,1,2,7,3,5,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,2,5,1,7]=>[1,8,7,2,6,5,3,4]=>[8,1,2,7,3,4,6,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,3,5,1,7]=>[1,8,7,2,6,5,3,4]=>[8,1,2,7,3,4,6,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,4,5,1,7]=>[1,8,7,2,6,5,4,3]=>[8,1,2,7,3,4,5,6]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,6,1,7]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,3,6,1,7]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,4,6,1,7]=>[1,8,7,2,5,4,3,6]=>[8,1,2,7,4,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,4,6,1,7]=>[1,8,7,2,5,4,3,6]=>[8,1,2,7,4,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,5,6,1,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,5,6,1,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,6,1,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,1,2,7]=>[1,8,7,2,6,3,5,4]=>[8,1,2,7,3,6,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,3,1,2,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,4,1,2,7]=>[1,8,7,2,6,3,5,4]=>[8,1,2,7,3,6,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,4,1,2,7]=>[1,8,7,2,5,4,3,6]=>[8,1,2,7,4,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,5,1,2,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,6,1,2,7]=>[1,8,7,2,5,6,3,4]=>[8,1,2,7,4,3,6,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,6,1,2,7]=>[1,8,7,2,5,6,3,4]=>[8,1,2,7,4,3,6,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,1,2,7]=>[1,8,7,2,4,5,6,3]=>[8,1,2,7,5,4,3,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,1,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,2,1,3,7]=>[1,8,7,3,6,2,5,4]=>[8,1,2,6,3,7,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,2,1,3,7]=>[1,8,7,3,5,2,4,6]=>[8,1,2,6,4,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,1,2,3,7]=>[1,8,7,3,6,2,5,4]=>[8,1,2,6,3,7,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,1,2,3,7]=>[1,8,7,3,5,2,4,6]=>[8,1,2,6,4,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,2,1,4,7]=>[1,8,7,4,3,6,2,5]=>[8,1,2,5,6,3,7,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,3,1,4,7]=>[1,8,7,4,2,6,3,5]=>[8,1,2,5,7,3,6,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,3,1,4,7]=>[1,8,7,4,2,5,3,6]=>[8,1,2,5,7,4,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,1,2,4,7]=>[1,8,7,4,3,6,2,5]=>[8,1,2,5,6,3,7,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,1,3,4,7]=>[1,8,7,4,2,6,3,5]=>[8,1,2,5,7,3,6,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,1,3,4,7]=>[1,8,7,4,2,5,3,6]=>[8,1,2,5,7,4,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,2,3,4,7]=>[1,8,7,4,2,6,3,5]=>[8,1,2,5,7,3,6,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,2,3,4,7]=>[1,8,7,4,2,5,3,6]=>[8,1,2,5,7,4,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,3,1,5,7]=>[1,8,7,5,3,4,2,6]=>[8,1,2,4,6,5,7,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,4,1,5,7]=>[1,8,7,5,4,3,2,6]=>[8,1,2,4,5,6,7,3]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,1,4,5,7]=>[1,8,7,5,2,6,4,3]=>[8,1,2,4,7,3,5,6]=>[8,2,3,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,3,4,5,7]=>[1,8,7,5,3,2,6,4]=>[8,1,2,4,6,7,3,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,2,1,6,7]=>[1,8,7,6,2,4,3,5]=>[8,1,2,3,7,5,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,2,1,6,7]=>[1,8,7,6,2,4,5,3]=>[8,1,2,3,7,5,4,6]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,2,1,6,7]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,1,6,7]=>[1,8,7,6,2,4,3,5]=>[8,1,2,3,7,5,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,4,1,6,7]=>[1,8,7,6,2,5,4,3]=>[8,1,2,3,7,4,5,6]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,5,1,6,7]=>[1,8,7,6,2,4,3,5]=>[8,1,2,3,7,5,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,1,6,7]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,1,2,6,7]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,3,6,7]=>[1,8,7,6,3,4,2,5]=>[8,1,2,3,6,5,7,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,2,3,6,7]=>[1,8,7,6,3,4,2,5]=>[8,1,2,3,6,5,7,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,2,3,6,7]=>[1,8,7,6,3,5,2,4]=>[8,1,2,3,6,4,7,5]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,1,4,6,7]=>[1,8,7,6,4,2,5,3]=>[8,1,2,3,5,7,4,6]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,2,4,6,7]=>[1,8,7,6,4,2,5,3]=>[8,1,2,3,5,7,4,6]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,3,4,6,7]=>[1,8,7,6,4,2,5,3]=>[8,1,2,3,5,7,4,6]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,3,4,6,7]=>[1,8,7,6,4,2,5,3]=>[8,1,2,3,5,7,4,6]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,5,6,7]=>[1,8,7,6,5,2,4,3]=>[8,1,2,3,4,7,5,6]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,1,5,6,7]=>[1,8,7,6,5,2,3,4]=>[8,1,2,3,4,7,6,5]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,1,5,6,7]=>[1,8,7,6,5,2,4,3]=>[8,1,2,3,4,7,5,6]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,1,5,6,7]=>[1,8,7,6,5,2,3,4]=>[8,1,2,3,4,7,6,5]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,2,5,6,7]=>[1,8,7,6,5,2,3,4]=>[8,1,2,3,4,7,6,5]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,3,5,6,7]=>[1,8,7,6,5,3,2,4]=>[8,1,2,3,4,6,7,5]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,3,5,6,7]=>[1,8,7,6,5,3,2,4]=>[8,1,2,3,4,6,7,5]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,4,5,6,7]=>[1,8,7,6,5,4,2,3]=>[8,1,2,3,4,5,7,6]=>[8,2,3,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,4,5,6,7]=>[1,8,7,6,5,4,2,3]=>[8,1,2,3,4,5,7,6]=>[8,2,3,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,4,5,6,7]=>[1,8,7,6,5,4,2,3]=>[8,1,2,3,4,5,7,6]=>[8,2,3,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>[8,1,2,3,4,5,6,7]=>[8,2,3,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>[8,1,2,3,4,5,6,7]=>[8,2,3,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,2,1,8]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,3,2,1,8]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,3,2,1,8]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,3,2,1,8]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,3,2,1,8]=>[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,3,2,1,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,3,2,1,8]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,3,2,1,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,3,2,1,8]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,3,2,1,8]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,3,2,1,8]=>[1,5,3,4,7,2,6,8]=>[8,4,6,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,3,2,1,8]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,2,1,8]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,4,2,1,8]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,3,4,2,1,8]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,4,2,1,8]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,4,2,1,8]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,5,2,1,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,5,2,1,8]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,5,2,1,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,6,2,1,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,6,2,1,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,7,2,1,8]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,2,1,8]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,2,3,1,8]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,2,3,1,8]=>[1,6,3,5,2,7,4,8]=>[8,3,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,2,3,1,8]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,2,3,1,8]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,2,3,1,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,2,3,1,8]=>[1,6,3,4,5,2,7,8]=>[8,3,6,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,2,3,1,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,2,3,1,8]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,2,3,1,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,2,3,1,8]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,3,1,8]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,2,4,1,8]=>[1,5,2,6,4,3,7,8]=>[8,4,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,2,3,4,1,8]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,2,3,4,1,8]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,3,4,1,8]=>[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,2,5,1,8]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,2,5,1,8]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,4,2,5,1,8]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,3,5,1,8]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,4,5,1,8]=>[1,7,2,6,5,4,3,8]=>[8,2,7,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,4,5,1,8]=>[1,7,2,6,5,4,3,8]=>[8,2,7,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,4,5,1,8]=>[1,6,5,4,3,2,7,8]=>[8,3,4,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,2,6,1,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,2,6,1,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,2,6,1,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,2,6,1,8]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,3,6,1,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,3,6,1,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,4,6,1,8]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,5,6,1,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,5,6,1,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,7,1,8]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,2,7,1,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,2,7,1,8]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,6,2,7,1,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,2,7,1,8]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,2,7,1,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,5,7,1,8]=>[1,6,7,2,4,3,5,8]=>[8,3,2,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,4,5,7,1,8]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,5,7,1,8]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,6,7,1,8]=>[1,5,6,7,2,4,3,8]=>[8,4,3,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,6,7,1,8]=>[1,3,5,6,7,2,4,8]=>[8,6,4,3,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,6,7,1,8]=>[1,5,6,7,2,4,3,8]=>[8,4,3,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,6,7,1,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,6,7,1,8]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,6,7,1,8]=>[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,6,7,1,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,6,7,1,8]=>[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,1,8]=>[1,3,4,5,6,7,2,8]=>[8,6,5,4,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,1,2,8]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,3,1,2,8]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,3,1,2,8]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,3,1,2,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,3,1,2,8]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,3,1,2,8]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,1,2,8]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,4,1,2,8]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,4,1,2,8]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,4,1,2,8]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,4,5,1,2,8]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,7,1,2,8]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,7,1,2,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,7,1,2,8]=>[1,6,2,4,5,7,3,8]=>[8,3,7,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,7,1,2,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,7,1,2,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,1,2,8]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,2,1,3,8]=>[1,7,3,5,2,6,4,8]=>[8,2,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,2,1,3,8]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,2,1,3,8]=>[1,7,3,4,5,2,6,8]=>[8,2,6,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,2,1,3,8]=>[1,7,3,5,2,4,6,8]=>[8,2,6,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,2,1,3,8]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,1,3,8]=>[1,4,7,3,6,2,5,8]=>[8,5,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,1,2,3,8]=>[1,7,3,5,2,6,4,8]=>[8,2,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,1,2,3,8]=>[1,7,3,6,2,5,4,8]=>[8,2,6,3,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,1,2,3,8]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,1,2,3,8]=>[1,7,3,4,5,2,6,8]=>[8,2,6,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,1,2,3,8]=>[1,7,3,5,2,4,6,8]=>[8,2,6,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,1,2,3,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,1,2,3,8]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,2,3,8]=>[1,4,7,3,6,2,5,8]=>[8,5,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,3,1,4,8]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,3,1,4,8]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,3,1,4,8]=>[1,5,3,7,4,2,6,8]=>[8,4,6,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,1,2,4,8]=>[1,7,4,3,6,2,5,8]=>[8,2,5,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,1,2,4,8]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,1,3,4,8]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,2,1,3,4,8]=>[1,6,3,5,2,7,4,8]=>[8,3,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,1,3,4,8]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,2,3,4,8]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,2,3,4,8]=>[1,6,3,5,2,7,4,8]=>[8,3,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,2,3,4,8]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,2,1,5,8]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,2,1,5,8]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,4,1,5,8]=>[1,7,5,4,2,6,3,8]=>[8,2,4,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,4,1,5,8]=>[1,6,2,7,5,4,3,8]=>[8,3,7,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,4,1,5,8]=>[1,7,5,4,3,2,6,8]=>[8,2,4,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,4,1,5,8]=>[1,6,2,7,5,4,3,8]=>[8,3,7,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,1,2,5,8]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,1,3,5,8]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,1,4,5,8]=>[1,7,5,2,6,4,3,8]=>[8,2,4,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,1,4,5,8]=>[1,6,4,2,7,5,3,8]=>[8,3,5,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,1,4,5,8]=>[1,7,5,2,6,4,3,8]=>[8,2,4,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,2,4,5,8]=>[1,6,4,2,7,5,3,8]=>[8,3,5,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,3,4,5,8]=>[1,6,4,2,7,5,3,8]=>[8,3,5,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,2,1,6,8]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,2,1,6,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,4,1,6,8]=>[1,7,6,2,5,4,3,8]=>[8,2,3,7,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,4,1,6,8]=>[1,7,6,2,5,4,3,8]=>[8,2,3,7,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,5,1,6,8]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,5,1,6,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,1,3,6,8]=>[1,7,6,3,5,2,4,8]=>[8,2,3,6,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,2,3,6,8]=>[1,7,6,3,5,2,4,8]=>[8,2,3,6,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,1,4,6,8]=>[1,7,6,4,3,2,5,8]=>[8,2,3,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,1,5,6,8]=>[1,7,6,5,2,3,4,8]=>[8,2,3,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,2,5,6,8]=>[1,7,6,5,2,3,4,8]=>[8,2,3,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,4,5,6,8]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,4,5,6,8]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,4,5,6,8]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,4,5,6,8]=>[1,7,6,5,4,3,2,8]=>[8,2,3,4,5,6,7,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,6,8]=>[1,7,6,5,4,3,2,8]=>[8,2,3,4,5,6,7,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,1,7,8]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,2,1,7,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,2,1,7,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,2,1,7,8]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,2,1,7,8]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,2,1,7,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,2,1,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,2,1,7,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,3,1,7,8]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,4,1,7,8]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,3,4,1,7,8]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,4,1,7,8]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,5,1,7,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,5,1,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,6,1,7,8]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,6,1,7,8]=>[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,6,1,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,6,1,7,8]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,6,1,7,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,6,1,7,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,6,1,7,8]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,6,1,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,6,1,7,8]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,6,1,7,8]=>[1,3,4,5,6,2,7,8]=>[8,6,5,4,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,1,2,7,8]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,1,2,7,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,1,2,7,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,1,2,7,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,1,2,7,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,1,2,7,8]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,1,2,7,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,1,2,7,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,1,3,7,8]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,1,3,7,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,1,3,7,8]=>[1,6,3,5,2,4,7,8]=>[8,3,6,4,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,1,3,7,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,1,3,7,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,2,3,7,8]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,2,3,7,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,1,4,7,8]=>[1,5,2,6,4,3,7,8]=>[8,4,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,3,4,7,8]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,3,4,7,8]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,2,1,5,7,8]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,4,5,7,8]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,4,5,7,8]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,4,5,7,8]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,3,4,5,7,8]=>[1,6,5,4,3,2,7,8]=>[8,3,4,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,5,7,8]=>[1,6,5,4,3,2,7,8]=>[8,3,4,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,6,7,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,1,6,7,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,1,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,1,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,1,6,7,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,1,6,7,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,1,6,7,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,1,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,1,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,1,6,7,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,1,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,1,6,7,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,1,6,7,8]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,2,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,2,6,7,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,3,6,7,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,3,6,7,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,4,6,7,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,4,6,7,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,4,6,7,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,4,6,7,8]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,4,6,7,8]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,4,3,2,1]=>[1,6,3,7,2,8,4,5]=>[8,3,6,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,4,3,2,1]=>[1,5,4,6,3,7,2,8]=>[8,4,5,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,4,3,2,1]=>[1,5,4,6,3,8,2,7]=>[8,4,5,3,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,4,3,2,1]=>[1,6,3,8,2,5,4,7]=>[8,3,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,4,3,2,1]=>[1,5,4,7,2,6,3,8]=>[8,4,5,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,4,3,2,1]=>[1,5,4,8,2,7,3,6]=>[8,4,5,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,5,3,2,1]=>[1,4,6,3,7,2,8,5]=>[8,5,3,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,5,3,2,1]=>[1,4,6,3,8,2,7,5]=>[8,5,3,6,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,6,3,2,1]=>[1,4,8,2,5,6,3,7]=>[8,5,1,7,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,7,3,2,1]=>[1,4,8,2,5,7,3,6]=>[8,5,1,7,4,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,8,3,2,1]=>[1,5,8,2,7,3,6,4]=>[8,4,1,7,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,8,3,2,1]=>[1,4,5,8,2,7,3,6]=>[8,5,4,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,8,3,2,1]=>[1,4,5,8,2,6,3,7]=>[8,5,4,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,8,3,2,1]=>[1,5,8,2,4,6,3,7]=>[8,4,1,7,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,8,3,2,1]=>[1,4,6,3,7,2,5,8]=>[8,5,3,6,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,8,3,2,1]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,5,4,2,1]=>[1,3,7,2,8,4,6,5]=>[8,6,2,7,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,5,4,2,1]=>[1,3,8,2,7,4,6,5]=>[8,6,1,7,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,5,4,2,1]=>[1,3,8,2,6,4,7,5]=>[8,6,1,7,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,5,4,2,1]=>[1,3,6,4,8,2,7,5]=>[8,6,3,5,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,4,2,1]=>[1,3,6,4,8,2,5,7]=>[8,6,3,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,5,8,4,2,1]=>[1,3,6,4,5,8,2,7]=>[8,6,3,5,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,8,4,2,1]=>[1,3,7,2,5,8,4,6]=>[8,6,2,7,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,4,2,1]=>[1,3,6,4,7,2,5,8]=>[8,6,3,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,6,5,2,1]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,6,5,2,1]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,7,6,2,1]=>[1,5,7,2,4,8,3,6]=>[8,4,2,7,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,8,6,2,1]=>[1,5,8,2,4,7,3,6]=>[8,4,1,7,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,8,6,2,1]=>[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,7,6,2,1]=>[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,8,6,2,1]=>[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,8,7,2,1]=>[1,5,8,2,6,7,3,4]=>[8,4,1,7,3,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,8,7,2,1]=>[1,3,5,8,2,6,7,4]=>[8,6,4,1,7,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,8,7,2,1]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,8,7,2,1]=>[1,5,8,2,4,6,7,3]=>[8,4,1,7,5,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,8,7,2,1]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,8,7,2,1]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,3,8,2,1]=>[1,5,3,6,8,2,7,4]=>[8,4,6,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,3,8,2,1]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,4,8,2,1]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,4,8,2,1]=>[1,3,6,8,2,5,4,7]=>[8,6,3,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,6,5,8,2,1]=>[1,3,7,2,4,6,8,5]=>[8,6,2,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,5,8,2,1]=>[1,3,6,8,2,4,7,5]=>[8,6,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,6,8,2,1]=>[1,4,7,2,5,6,8,3]=>[8,5,2,7,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,6,8,2,1]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,7,8,2,1]=>[1,3,5,7,2,6,8,4]=>[8,6,4,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,7,8,2,1]=>[1,3,6,8,2,5,7,4]=>[8,6,3,1,7,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,7,8,2,1]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,5,7,8,2,1]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,5,4,3,1]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,5,4,3,1]=>[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,5,4,3,1]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,5,4,3,1]=>[1,2,6,4,8,3,7,5]=>[8,7,3,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,6,4,3,1]=>[1,2,5,6,4,7,3,8]=>[8,7,4,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,8,4,3,1]=>[1,2,6,4,5,8,3,7]=>[8,7,3,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,4,3,1]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,8,5,3,1]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,7,6,3,1]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,8,6,3,1]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,8,7,3,1]=>[1,2,5,8,3,6,7,4]=>[8,7,4,1,6,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,8,7,3,1]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,8,7,3,1]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,4,8,3,1]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,5,8,3,1]=>[1,2,4,7,3,6,8,5]=>[8,7,5,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,7,8,3,1]=>[1,2,6,8,3,5,7,4]=>[8,7,3,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,7,8,3,1]=>[1,2,5,7,3,6,8,4]=>[8,7,4,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,7,8,3,1]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,7,8,3,1]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,6,5,4,1]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,6,5,4,1]=>[1,3,7,4,8,2,5,6]=>[8,6,2,5,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,8,6,4,1]=>[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,5,8,4,1]=>[1,3,6,8,2,4,7,5]=>[8,6,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,7,8,4,1]=>[1,3,5,7,4,6,8,2]=>[8,6,4,2,5,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,6,5,4,1]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,8,5,4,1]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,7,6,4,1]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,8,6,4,1]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,8,7,4,1]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,8,7,4,1]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,5,8,4,1]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,6,8,4,1]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,7,8,4,1]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,7,6,5,1]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,8,7,5,1]=>[1,4,6,7,5,8,2,3]=>[8,5,3,2,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,7,6,5,1]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,7,6,5,1]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,8,7,5,1]=>[1,2,4,6,7,5,8,3]=>[8,7,5,3,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,7,8,5,1]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,7,6,5,1]=>[1,3,4,8,2,5,7,6]=>[8,6,5,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,8,6,5,1]=>[1,3,4,7,5,8,2,6]=>[8,6,5,2,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,7,6,5,1]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,8,6,5,1]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,8,7,5,1]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,6,8,5,1]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,7,8,5,1]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,8,7,6,1]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,7,8,6,1]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,8,7,6,1]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,7,8,6,1]=>[1,3,5,7,6,8,2,4]=>[8,6,4,2,3,1,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,8,7,6,1]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,8,7,6,1]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,7,8,6,1]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,8,6,1]=>[1,3,5,7,6,8,2,4]=>[8,6,4,2,3,1,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,8,7,6,1]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,7,8,6,1]=>[1,2,3,5,7,6,8,4]=>[8,7,6,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,8,7,6,1]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,8,7,6,1]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,7,8,6,1]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,8,7,6,1]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,7,8,6,1]=>[1,3,4,5,7,6,8,2]=>[8,6,5,4,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,7,6,1]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,8,6,1]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,2,8,7,1]=>[1,4,3,5,2,6,8,7]=>[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,2,8,7,1]=>[1,4,3,6,8,2,5,7]=>[8,5,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,2,8,7,1]=>[1,3,5,2,6,8,4,7]=>[8,6,4,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,2,8,7,1]=>[1,3,6,8,2,5,4,7]=>[8,6,3,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,2,8,7,1]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,2,8,7,1]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,3,8,7,1]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,3,8,7,1]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,3,8,7,1]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,4,8,7,1]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,4,8,7,1]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,5,8,7,1]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,5,8,7,1]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,5,8,7,1]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,6,8,7,1]=>[1,5,6,8,2,4,3,7]=>[8,4,3,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,6,8,7,1]=>[1,4,2,5,6,8,3,7]=>[8,5,7,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,6,8,7,1]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,6,8,7,1]=>[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,6,8,7,1]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,6,8,7,1]=>[1,2,4,5,6,8,3,7]=>[8,7,5,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,6,8,7,1]=>[1,3,4,5,6,8,2,7]=>[8,6,5,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,7,1]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,3,2,8,1]=>[1,5,3,6,2,7,8,4]=>[8,4,6,3,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,3,2,8,1]=>[1,4,5,3,6,2,7,8]=>[8,5,4,6,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,5,2,8,1]=>[1,4,7,8,2,3,6,5]=>[8,5,2,1,7,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,5,2,8,1]=>[1,3,6,2,4,7,8,5]=>[8,6,3,7,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,6,2,8,1]=>[1,5,6,2,4,7,8,3]=>[8,4,3,7,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,6,2,8,1]=>[1,4,7,8,2,5,6,3]=>[8,5,2,1,7,4,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,6,2,8,1]=>[1,3,4,7,8,2,5,6]=>[8,6,5,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,6,2,8,1]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,7,2,8,1]=>[1,4,3,5,7,8,2,6]=>[8,5,6,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,7,2,8,1]=>[1,3,5,7,8,2,6,4]=>[8,6,4,2,1,7,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,7,2,8,1]=>[1,3,6,2,5,7,8,4]=>[8,6,3,7,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,7,2,8,1]=>[1,4,5,7,8,2,3,6]=>[8,5,4,2,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,6,7,2,8,1]=>[1,3,4,6,2,5,7,8]=>[8,6,5,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,4,3,8,1]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,4,3,8,1]=>[1,2,5,4,7,8,3,6]=>[8,7,4,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,6,3,8,1]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,7,3,8,1]=>[1,2,4,5,7,8,3,6]=>[8,7,5,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,7,3,8,1]=>[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,7,3,8,1]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,5,4,8,1]=>[1,3,6,4,7,8,2,5]=>[8,6,3,5,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,6,4,8,1]=>[1,3,5,6,4,7,8,2]=>[8,6,4,3,5,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,7,4,8,1]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,5,4,8,1]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,6,4,8,1]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,7,4,8,1]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,7,6,5,8,1]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,7,6,5,8,1]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,7,5,8,1]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,7,6,5,8,1]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,7,5,8,1]=>[1,2,4,6,5,7,8,3]=>[8,7,5,3,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,6,5,8,1]=>[1,3,4,7,8,2,5,6]=>[8,6,5,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,6,5,8,1]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,7,5,8,1]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,7,6,8,1]=>[1,5,7,8,2,4,3,6]=>[8,4,2,1,7,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,7,6,8,1]=>[1,3,4,2,5,7,8,6]=>[8,6,5,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,7,6,8,1]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,7,6,8,1]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,7,6,8,1]=>[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,6,8,1]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,7,6,8,1]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,7,6,8,1]=>[1,4,5,7,8,2,3,6]=>[8,5,4,2,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,7,6,8,1]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,7,6,8,1]=>[1,2,4,5,7,8,3,6]=>[8,7,5,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,7,6,8,1]=>[1,3,4,5,7,8,2,6]=>[8,6,5,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,6,8,1]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,2,7,8,1]=>[1,3,5,2,6,7,8,4]=>[8,6,4,7,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,2,7,8,1]=>[1,3,6,7,8,2,5,4]=>[8,6,3,2,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,5,2,7,8,1]=>[1,3,6,7,8,2,4,5]=>[8,6,3,2,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,6,2,7,8,1]=>[1,3,4,6,7,8,2,5]=>[8,6,5,3,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,3,7,8,1]=>[1,2,6,7,8,3,5,4]=>[8,7,3,2,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,3,7,8,1]=>[1,2,5,3,6,7,8,4]=>[8,7,4,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,3,7,8,1]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,3,7,8,1]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,3,7,8,1]=>[1,2,4,6,7,8,3,5]=>[8,7,5,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,4,7,8,1]=>[1,3,5,4,6,7,8,2]=>[8,6,4,5,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,4,7,8,1]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,4,7,8,1]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,5,7,8,1]=>[1,4,6,7,8,2,3,5]=>[8,5,3,2,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,5,7,8,1]=>[1,3,2,4,6,7,8,5]=>[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,5,7,8,1]=>[1,2,4,6,7,8,3,5]=>[8,7,5,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,5,7,8,1]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,6,7,8,1]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,6,7,8,1]=>[1,2,5,6,7,8,3,4]=>[8,7,4,3,2,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,6,7,8,1]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,6,7,8,1]=>[1,3,5,6,7,8,2,4]=>[8,6,4,3,2,1,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,6,7,8,1]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,6,7,8,1]=>[1,2,4,5,6,7,8,3]=>[8,7,5,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,5,4,3,2]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,5,4,3,2]=>[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,5,4,3,2]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,5,4,3,2]=>[1,2,6,4,8,3,7,5]=>[8,7,3,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,6,4,3,2]=>[1,2,5,6,4,7,3,8]=>[8,7,4,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,7,4,3,2]=>[1,2,6,4,8,3,5,7]=>[8,7,3,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,8,4,3,2]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,8,4,3,2]=>[1,2,6,4,5,8,3,7]=>[8,7,3,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,8,4,3,2]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,8,4,3,2]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,8,5,3,2]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,8,6,3,2]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,7,6,3,2]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,8,7,3,2]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,8,7,3,2]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,5,8,3,2]=>[1,2,4,7,3,6,8,5]=>[8,7,5,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,7,8,3,2]=>[1,2,6,8,3,5,7,4]=>[8,7,3,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,7,8,3,2]=>[1,2,5,7,3,6,8,4]=>[8,7,4,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,7,8,3,2]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,8,3,2]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,6,5,4,2]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,6,5,4,2]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,7,5,4,2]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,8,5,4,2]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,7,6,4,2]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,8,6,4,2]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,8,7,4,2]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,5,8,4,2]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,6,8,4,2]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,7,8,4,2]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,7,8,4,2]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,7,6,5,2]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,8,6,5,2]=>[1,2,4,7,5,8,3,6]=>[8,7,5,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,8,7,5,2]=>[1,2,4,6,7,5,8,3]=>[8,7,5,3,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,7,8,5,2]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,7,6,5,2]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,6,8,5,2]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,7,8,5,2]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,8,7,6,2]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,8,7,6,2]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,7,8,6,2]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,8,7,6,2]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,7,8,6,2]=>[1,2,3,5,7,6,8,4]=>[8,7,6,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,8,7,6,2]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,8,7,6,2]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,7,8,6,2]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,3,8,7,2]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,3,8,7,2]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,3,8,7,2]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,4,8,7,2]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,5,8,7,2]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,6,8,7,2]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,8,7,2]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,4,3,8,2]=>[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,4,3,8,2]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,4,3,8,2]=>[1,2,5,4,7,8,3,6]=>[8,7,4,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,7,3,8,2]=>[1,2,5,7,8,3,6,4]=>[8,7,4,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,7,3,8,2]=>[1,2,4,5,7,8,3,6]=>[8,7,5,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,7,3,8,2]=>[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,3,8,2]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,6,4,8,2]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,7,4,8,2]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,7,4,8,2]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,7,5,8,2]=>[1,2,4,6,5,7,8,3]=>[8,7,5,3,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,6,5,8,2]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,7,5,8,2]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,7,6,8,2]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,7,6,8,2]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,3,7,8,2]=>[1,2,6,7,8,3,5,4]=>[8,7,3,2,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,3,7,8,2]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,4,7,8,2]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,5,7,8,2]=>[1,2,4,6,7,8,3,5]=>[8,7,5,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,5,7,8,2]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,6,7,8,2]=>[1,2,5,6,7,8,3,4]=>[8,7,4,3,2,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,6,7,8,2]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,6,7,8,2]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,6,7,8,2]=>[1,2,4,5,6,7,8,3]=>[8,7,5,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,5,4,3]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,6,5,4,3]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,7,5,4,3]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,8,5,4,3]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,5,4,3]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,7,6,4,3]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,8,6,4,3]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,8,7,4,3]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,8,7,4,3]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,5,8,4,3]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,5,8,4,3]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,6,8,4,3]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,7,8,4,3]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,7,8,4,3]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,7,6,5,3]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,8,6,5,3]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,8,7,5,3]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,6,8,5,3]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,7,8,5,3]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,8,7,6,3]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,7,8,6,3]=>[1,2,3,5,7,6,8,4]=>[8,7,6,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,8,7,6,3]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,7,8,6,3]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,4,8,7,3]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,4,8,7,3]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,5,8,7,3]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,6,8,7,3]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,6,8,7,3]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,5,4,8,3]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,5,4,8,3]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,6,4,8,3]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,7,4,8,3]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,7,4,8,3]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,6,5,8,3]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,7,5,8,3]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,7,6,8,3]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,4,7,8,3]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,6,7,8,3]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,6,5,4,3]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,6,5,4,3]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,8,5,4,3]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,8,5,4,3]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,7,6,4,3]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,8,7,4,3]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,8,7,4,3]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,5,8,4,3]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,6,8,4,3]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,7,8,4,3]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,7,8,4,3]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,7,6,5,3]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,8,6,5,3]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,8,7,5,3]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,6,8,5,3]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,7,8,5,3]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,8,7,6,3]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,7,8,6,3]=>[1,2,3,5,7,6,8,4]=>[8,7,6,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,8,7,6,3]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,7,8,6,3]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,4,8,7,3]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,5,8,7,3]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,6,8,7,3]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,6,8,7,3]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,5,4,8,3]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,6,4,8,3]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,7,4,8,3]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,6,5,8,3]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,7,6,8,3]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,4,7,8,3]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,4,7,8,3]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,5,7,8,3]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,6,7,8,3]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,6,7,8,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,7,6,5,4]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,8,7,5,4]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,6,8,5,4]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,7,8,5,4]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,8,7,6,4]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,7,8,6,4]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,5,8,7,4]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,6,8,7,4]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,6,5,8,4]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,7,5,8,4]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,7,6,8,4]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,5,7,8,4]=>[1,3,2,4,6,7,8,5]=>[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,6,7,8,4]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,7,6,5,4]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,8,6,5,4]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,8,7,5,4]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,6,8,5,4]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,7,8,5,4]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,7,8,6,4]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,5,8,7,4]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,6,5,8,4]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,7,5,8,4]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,7,6,8,4]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,6,7,8,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,7,6,5,4]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,8,7,5,4]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,6,8,5,4]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,7,8,5,4]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,8,7,6,4]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,7,8,6,4]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,5,8,7,4]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,6,8,7,4]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,6,5,8,4]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,7,5,8,4]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,7,6,8,4]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,5,7,8,4]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,6,7,8,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,7,6,5,4]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,7,8,6,5,4]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,8,7,5,4]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,7,8,5,4]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,5,8,7,4]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,7,6,8,4]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,6,7,8,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,7,6,5,4]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,8,6,5,4]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,8,7,5,4]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,6,8,5,4]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,7,8,5,4]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,8,7,6,4]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,7,8,6,4]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,5,8,7,4]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,6,8,7,4]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,6,5,8,4]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,7,5,8,4]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,7,6,8,4]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,5,7,8,4]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,7,6,5]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,8,6,5]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,8,7,5]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,6,8,5]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,7,8,5]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,8,7,6,5]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,7,8,6,5]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,6,8,7,5]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,7,6,8,5]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,6,7,8,5]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,8,7,6,5]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,7,8,6,5]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,6,8,7,5]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,7,6,8,5]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,6,7,8,5]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,7,6,5]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,7,8,6,5]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,6,8,7,5]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,7,6,8,5]=>[1,3,4,2,5,7,8,6]=>[8,6,5,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,6,7,8,5]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,7,6,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,8,6,5]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,8,7,5]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,6,8,5]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,8,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,8,7,6,5]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,6,8,7,5]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,7,6,8,5]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,6,7,8,5]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,8,7,6,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,7,8,6,5]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,6,8,7,5]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,7,6,8,5]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,6,7,8,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,7,6,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,7,8,6,5]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,8,7,5]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,7,6,8,5]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,8,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,8,7,6,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,7,8,6,5]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,6,8,7,5]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,7,6,8,5]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,8,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,8,7,6,5]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,7,8,6,5]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,6,8,7,5]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,7,6,8,5]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,6,7,8,5]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,8,7,6,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,7,8,6,5]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,7,6,8,5]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,6,7,8,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,8,7,6,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,6,8,7,5]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,7,6,8,5]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,8,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,8,7,6,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,7,8,6,5]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,7,6,8,5]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,8,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,7,6,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,8,6,5]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,6,8,7,5]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,6,8,5]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,7,8,6]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,1,8,7,6]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,1,7,8,6]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,1,8,7,6]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,1,8,7,6]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,1,7,8,6]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,1,8,7,6]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,1,7,8,6]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,1,8,7,6]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,1,7,8,6]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,1,8,7,6]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,1,7,8,6]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,1,8,7,6]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,1,8,7,6]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,1,7,8,6]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,1,8,7,6]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,1,7,8,6]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,1,8,7,6]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,1,7,8,6]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,2,8,7,6]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,2,7,8,6]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,2,8,7,6]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,2,7,8,6]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,2,7,8,6]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,2,8,7,6]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,2,7,8,6]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,2,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,2,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,3,8,7,6]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,3,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,3,8,7,6]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,3,7,8,6]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,3,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,3,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,4,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,4,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,4,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,8,7,6]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,7,8,6]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,5,8,7,6]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,5,8,7,6]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,5,8,7,6]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,5,7,8,6]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,5,8,7,6]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,5,7,8,6]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,5,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,5,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,5,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,5,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,5,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,5,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,5,8,7,6]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,5,7,8,6]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,5,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,1,8,7]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,2,1,8,7]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,2,1,8,7]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,2,1,8,7]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,2,1,8,7]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,2,1,8,7]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,2,1,8,7]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,2,1,8,7]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,2,1,8,7]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,2,1,8,7]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,3,1,8,7]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,3,1,8,7]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,3,1,8,7]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,4,1,8,7]=>[1,3,5,4,6,2,7,8]=>[8,6,4,5,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,4,1,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,4,1,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,5,1,8,7]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,5,1,8,7]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,5,1,8,7]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,6,1,8,7]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,6,1,8,7]=>[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,6,1,8,7]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,6,1,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,6,1,8,7]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,6,1,8,7]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,6,1,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,6,1,8,7]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,6,1,8,7]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,6,1,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,6,1,8,7]=>[1,2,4,5,6,3,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,3,2,8,7]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,3,2,8,7]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,3,2,8,7]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,4,2,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,2,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,4,3,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,4,3,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,5,3,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,6,3,8,7]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,6,3,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,5,4,8,7]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,5,4,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,5,4,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,6,4,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,5,4,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,6,4,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,5,4,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,6,4,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,5,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,6,5,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,6,5,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,6,5,8,7]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,6,5,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,6,5,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,6,5,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,6,5,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,6,8,7]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,1,6,8,7]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,1,6,8,7]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,1,6,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,1,6,8,7]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,1,6,8,7]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,1,6,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,1,6,8,7]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,1,6,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,1,6,8,7]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,2,6,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,2,6,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,2,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,3,6,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,3,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,3,6,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,4,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,4,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,6,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,5,6,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,5,6,8,7]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,5,6,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,5,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,5,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,5,6,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,5,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,3,2,1,8]=>[1,5,3,6,2,7,4,8]=>[8,4,6,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,3,2,1,8]=>[1,4,5,3,6,2,7,8]=>[8,5,4,6,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,3,2,1,8]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,3,2,1,8]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,3,2,1,8]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,4,2,1,8]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,6,5,2,1,8]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,6,2,1,8]=>[1,5,6,2,4,7,3,8]=>[8,4,3,7,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,6,2,1,8]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,7,2,1,8]=>[1,3,5,7,2,6,4,8]=>[8,6,4,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,7,2,1,8]=>[1,3,6,2,5,7,4,8]=>[8,6,3,7,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,7,2,1,8]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,4,3,1,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,4,3,1,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,6,4,3,1,8]=>[1,2,5,4,6,3,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,5,3,1,8]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,6,3,1,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,7,3,1,8]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,7,3,1,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,7,3,1,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,5,4,1,8]=>[1,3,6,4,7,2,5,8]=>[8,6,3,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,6,4,1,8]=>[1,3,5,6,4,7,2,8]=>[8,6,4,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,7,4,1,8]=>[1,3,6,4,5,7,2,8]=>[8,6,3,5,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,7,4,1,8]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,5,4,1,8]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,5,4,1,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,6,4,1,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,7,4,1,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,7,4,1,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,7,5,1,8]=>[1,4,6,5,7,2,3,8]=>[8,5,3,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,7,6,5,1,8]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,7,5,1,8]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,6,7,5,1,8]=>[1,3,4,6,5,7,2,8]=>[8,6,5,3,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,6,5,1,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,7,5,1,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,7,6,1,8]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,7,6,1,8]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,7,6,1,8]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,7,6,1,8]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,6,1,8]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,7,6,1,8]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,7,6,1,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,6,1,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,2,7,1,8]=>[1,3,5,2,6,7,4,8]=>[8,6,4,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,2,7,1,8]=>[1,3,6,7,2,5,4,8]=>[8,6,3,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,5,2,7,1,8]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,3,7,1,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,3,7,1,8]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,4,7,1,8]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,4,7,1,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,5,7,1,8]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,5,7,1,8]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,5,7,1,8]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,5,7,1,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,6,7,1,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,6,7,1,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,6,7,1,8]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,6,7,1,8]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,4,3,2,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,4,3,2,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,4,3,2,8]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,5,3,2,8]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,5,3,2,8]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,6,3,2,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,7,3,2,8]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,7,3,2,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,3,2,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,5,4,2,8]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,5,4,2,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,6,4,2,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,7,4,2,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,7,4,2,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,7,5,2,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,7,6,2,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,7,6,2,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,3,7,2,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,3,7,2,8]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,4,7,2,8]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,4,7,2,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,5,7,2,8]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,5,7,2,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,6,7,2,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,6,7,2,8]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,6,7,2,8]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,2,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,5,4,3,8]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,5,4,3,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,7,4,3,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,7,5,3,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,6,7,3,8]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,3,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,5,4,3,8]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,5,4,3,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,6,4,3,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,7,4,3,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,7,5,3,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,4,7,3,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,5,7,3,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,6,7,3,8]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,6,7,3,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,6,5,4,8]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,7,5,4,8]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,7,6,4,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,5,7,4,8]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,6,7,4,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,7,5,4,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,5,7,4,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,6,7,4,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,6,5,4,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,7,5,4,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,7,6,4,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,5,7,4,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,6,7,4,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,7,5,4,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,6,5,4,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,7,5,4,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,7,6,4,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,5,7,4,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,4,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,6,5,8]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,7,5,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,7,6,5,8]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,6,7,5,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,6,5,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,5,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,7,6,5,8]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,6,7,5,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,6,7,5,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,5,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,5,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,7,6,5,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,6,7,5,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,7,6,5,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,5,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,5,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,6,5,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,5,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,7,6,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,1,7,6,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,1,7,6,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,1,7,6,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,1,7,6,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,1,7,6,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,1,7,6,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,1,7,6,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,1,7,6,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,1,7,6,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,2,7,6,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,2,7,6,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,2,7,6,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,2,7,6,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,2,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,3,7,6,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,3,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,4,7,6,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,4,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,7,6,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,5,7,6,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,5,7,6,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,5,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,5,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,5,7,6,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,5,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,2,1,7,8]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,2,1,7,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,3,1,7,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,3,1,7,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,4,1,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,4,1,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,5,1,7,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,5,1,7,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,5,1,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,6,1,7,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,6,1,7,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,3,2,7,8]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,3,2,7,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,3,2,7,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,3,2,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,3,2,7,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,4,2,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,5,2,7,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,6,2,7,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,6,2,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,6,2,7,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,6,2,7,8]=>[1,2,4,5,6,3,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,2,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,4,3,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,5,3,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,4,3,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,4,3,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,5,3,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,5,4,7,8]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,6,4,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,5,4,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,6,4,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,5,4,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,6,4,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,5,4,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,6,4,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,5,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,6,5,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,6,5,7,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,6,5,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,6,5,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,1,6,7,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,1,6,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,1,6,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,1,6,7,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,1,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,1,6,7,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,2,6,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,2,6,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,2,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,2,6,7,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,2,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,3,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,3,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,3,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,3,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,4,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,4,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,4,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,4,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,6,7,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,8,6,7,4]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,5,6,4,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,5,6,8,4]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,5,6,7,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,5,7,6,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,6,5,7,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,6,7,5,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,8,6,7,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,8,6,7,3]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,5,6,8,3]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,5,6,7,3]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,6,5,7,3]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,8,6,7,3]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,5,3,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,5,7,8,3]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,5,8,7,3]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,5,6,7,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,6,7,5,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,7,6,5,3]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,4,6,3,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,4,6,7,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,4,7,6,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,6,4,7,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,6,7,4,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,5,4,7,3]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,5,7,4,3]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,5,6,4,3]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,8,6,7,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,5,6,8,4]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,5,7,6,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,6,5,7,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,6,7,5,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,8,6,7,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,8,6,7,2]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,5,6,7,2]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,6,5,7,2]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,6,7,5,2]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,5,2,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,5,7,2,8]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,5,7,8,2]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,5,8,7,2]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,5,6,2,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,5,6,7,2]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,6,5,7,2]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,6,7,5,2]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,4,6,7,2]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,4,7,6,2]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,6,7,4,2]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,7,6,4,2]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,5,7,4,2]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,5,6,4,2]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,8,6,7,5]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,8,6,7,2]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,5,6,7,2]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,5,7,6,2]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,6,5,7,2]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,6,7,5,2]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,2,6,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,2,7,8,6]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,2,8,7,6]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,6,2,7,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,6,2,8,7]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,6,7,8,2]=>[1,2,5,6,7,8,3,4]=>[8,7,4,3,2,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,7,6,2,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,8,6,7,2]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,5,2,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,5,8,7,2]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,5,6,2,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,5,6,8,2]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,5,6,7,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,6,7,5,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,4,2,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,4,8,7,2]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,4,6,2,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,4,6,7,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,4,7,6,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,6,4,7,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,6,7,4,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,5,6,4,2]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,6,5,4,2]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,5,2,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,5,8,7,2]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,5,6,7,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,5,7,6,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,6,5,8,2]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,6,5,7,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,6,7,5,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,3,2,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,3,2,8,7]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,3,8,7,2]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,3,6,8,2]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,3,6,7,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,6,3,2,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,6,3,8,2]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,6,3,7,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,6,7,3,2]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,5,7,3,2]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,6,5,3,2]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,3,6,2,8]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,3,6,8,2]=>[1,2,7,8,3,5,4,6]=>[8,7,2,1,6,4,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,3,6,7,2]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,3,7,6,2]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,6,3,7,2]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,6,7,3,2]=>[1,2,8,3,5,6,7,4]=>[8,7,1,6,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,5,3,2,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,5,3,7,2]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,5,6,3,2]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,6,5,3,2]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,4,3,7,2]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,4,6,3,2]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,6,4,3,2]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,8,6,7,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,8,6,7,4]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,5,6,7,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,5,7,6,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,6,5,7,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,6,7,5,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,6,7,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,8,6,7,3]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,5,6,7,3]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,5,7,6,3]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,6,5,7,3]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,6,7,5,3]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,8,6,7,3]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,5,3,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,5,7,8,3]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,5,8,7,3]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,5,6,7,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,5,7,6,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,6,5,7,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,6,7,5,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,7,6,5,3]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,4,6,7,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,4,7,6,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,6,4,7,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,6,7,4,3]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,6,4,3]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,5,4,7,3]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,5,7,4,3]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,6,4,3]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,8,6,7,4]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,5,6,4,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,5,6,7,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,6,7,5,4]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,6,7,5]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,6,7,1]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,5,6,1,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,5,6,8,1]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,5,6,7,1]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,5,7,6,1]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,5,7,1]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,7,5,1]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,8,6,7,1]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,5,1,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,5,1,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,5,7,8,1]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,5,8,7,1]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,5,6,7,1]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,6,7,5,1]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,4,6,1,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,4,6,7,1]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,6,4,1,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,6,4,7,1]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,6,7,4,1]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,7,6,4,1]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,5,4,7,1]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,8,6,7,5]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,8,6,7,1]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,7,5,6,8,1]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,5,6,7,1]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,5,7,6,1]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,6,5,7,1]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,6,7,5,1]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,4,1,6,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,4,1,8,7,6]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,4,6,7,8,1]=>[1,2,5,6,7,8,3,4]=>[8,7,4,3,2,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,4,7,6,8,1]=>[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,4,8,6,7,1]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,4,8,7,6,1]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,4,5,1,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,4,5,7,8,1]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,4,5,8,7,1]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,4,5,6,1,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,5,6,7,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,5,7,6,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,5,4,1,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,5,4,1,8,7]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,5,4,7,8,1]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,5,4,8,7,1]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,5,4,6,8,1]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,4,7,6,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,5,6,4,8,1]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,6,7,4,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,5,6,4,1]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,6,5,4,1]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,8,6,7,1]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,5,1,8,7]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,5,7,8,1]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,5,8,7,1]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,5,6,8,1]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,5,6,7,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,5,7,6,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,6,5,8,1]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,6,5,7,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,6,7,5,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,3,1,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,3,1,8,7]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,3,7,8,1]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,3,8,7,1]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,3,6,7,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,6,3,1,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,6,3,8,1]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,6,3,7,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,6,7,3,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,6,5,3,1]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,3,6,8,1]=>[1,2,7,8,3,5,4,6]=>[8,7,2,1,6,4,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,3,6,7,1]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,3,7,6,1]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,6,7,3,1]=>[1,2,8,3,5,6,7,4]=>[8,7,1,6,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,5,6,3,1]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,6,5,3,1]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,4,6,3,1]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,6,4,3,1]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,8,6,7,5]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,8,6,7,4]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,5,6,4,8]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,5,6,8,4]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,5,6,7,4]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,5,7,6,4]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,6,5,7,4]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,6,7,5,4]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,6,7,5]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,5,6,8,1]=>[1,3,4,7,8,2,5,6]=>[8,6,5,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,5,6,7,1]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,6,7,5,1]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,8,6,7,1]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,5,7,1,8]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,5,6,1,8]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,5,6,7,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,6,5,1,8]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,6,5,7,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,4,6,1,8]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,4,6,7,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,4,7,6,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,6,4,1,8]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,6,4,7,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,7,6,4,1]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,5,7,4,1]=>[1,3,8,2,4,6,7,5]=>[8,6,1,7,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,5,6,4,1]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,5,7,6,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,5,7,8,6]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,5,8,7,6]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,6,5,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,6,5,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,6,7,8,5]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,6,8,7,5]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,7,6,5,8]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,7,6,8,5]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,6,7,5]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,7,6,5]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,1,6,8,7]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,1,7,8,6]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,1,8,7,6]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,6,1,8,7]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,6,8,7,1]=>[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,7,6,1,8]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,8,7,6,1]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,6,5,1,7,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,6,5,1,8,7]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,7,5,6,8,1]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,5,6,7,1]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,5,7,6,1]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,7,6,5,8,1]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,6,7,5,1]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,7,6,5,1]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,1,6,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,1,7,8,6]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,1,8,7,6]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,6,1,8,7]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,7,6,1,8]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,8,6,7,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,8,7,6,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,5,1,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,5,8,7,1]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,7,6,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,6,5,1,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,7,6,5,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,4,1,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,4,1,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,4,7,1,8]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,4,7,8,1]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,4,6,1,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,4,6,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,4,7,6,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,6,4,1,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,6,7,4,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,7,6,4,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,5,4,1,8]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,5,4,7,1]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,5,6,4,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,6,5,4,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,1,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,1,6,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,1,7,6,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,1,8,7,6]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,6,1,7,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,6,1,8,7]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,6,7,1,8]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,7,6,1,8]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,7,6,8,1]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,8,7,6,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,3,5,1,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,6,5,1,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,6,5,8,1]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,6,5,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,6,7,5,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,7,6,5,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,3,1,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,3,1,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,3,8,7,1]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,3,6,1,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,3,6,8,1]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,3,7,6,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,6,3,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,6,7,3,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,7,6,3,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,6,5,3,1,8]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,6,5,3,8,1]=>[1,7,8,2,3,4,6,5]=>[8,2,1,7,6,5,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,5,6,3,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,6,5,3,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,4,3,7,1,8]=>[1,6,7,2,3,5,4,8]=>[8,3,2,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,4,3,7,8,1]=>[1,6,7,8,2,3,5,4]=>[8,3,2,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,3,6,1,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,3,6,7,1]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,3,7,6,1]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,6,3,8,1]=>[1,7,8,2,3,5,6,4]=>[8,2,1,7,6,4,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,7,6,3,1]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,5,3,1,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,5,3,8,1]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,5,3,7,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,5,6,3,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,6,5,3,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,4,3,1,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,4,3,8,1]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,4,3,7,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,4,6,3,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,6,4,3,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,6,7,5]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,7,5,6,8,1]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,5,6,7,1]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,5,7,6,1]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,6,7,5,1]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,1,6,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,1,7,6,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,1,8,7,6]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,6,1,8,7]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,7,6,1,8]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,6,5,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,6,7,5,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,7,6,5,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,4,1,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,4,1,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,4,7,1,8]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,4,7,8,1]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,4,8,7,1]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,4,6,1,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,4,7,6,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,6,4,8,1]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,6,4,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,6,7,4,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,7,6,4,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,5,7,4,1]=>[1,8,2,3,4,6,7,5]=>[8,1,7,6,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,5,6,4,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,5,4,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,1,6,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,1,7,8,6]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,1,8,7,6]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,6,1,8,7]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,7,6,1,8]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,7,6,8,1]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,8,6,7,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,2,5,1,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,2,6,5,1,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,2,6,5,8,1]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,6,5,7,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,2,1,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,2,8,7,1]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,2,7,6,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,7,6,2,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,5,2,1,8]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,6,5,2,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,2,7,1,8]=>[1,6,7,2,3,5,4,8]=>[8,3,2,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,2,7,8,1]=>[1,6,7,8,2,3,5,4]=>[8,3,2,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,2,8,7,1]=>[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,2,6,1,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,2,6,7,1]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,2,7,6,1]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,6,2,8,1]=>[1,7,8,2,3,5,6,4]=>[8,2,1,7,6,4,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,6,7,2,1]=>[1,8,2,3,5,6,7,4]=>[8,1,7,6,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,7,6,2,1]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,5,2,1,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,5,2,8,1]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,5,2,7,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,5,6,2,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,5,2,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,4,2,1,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,4,2,8,1]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,4,2,7,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,4,6,2,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,4,2,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,5,1,8,7]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,5,8,7,1]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,5,7,6,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,6,5,1,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,6,5,8,1]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,6,5,7,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,6,7,5,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,7,6,5,1]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,2,1,8,7]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,7,6,2,1]=>[1,8,2,4,5,7,3,6]=>[8,1,7,5,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,5,2,1,8]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,5,2,8,1]=>[1,7,8,2,4,6,3,5]=>[8,2,1,7,5,3,6,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,2,1,8,7]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,2,7,6,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,7,6,2,1]=>[1,8,2,5,7,3,4,6]=>[8,1,7,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,6,5,2,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,4,2,1,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,4,2,7,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,4,7,2,1]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,4,6,2,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,6,4,2,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,7,6,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,7,6,2,1]=>[1,8,2,5,7,3,4,6]=>[8,1,7,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,5,2,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,6,5,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,3,5,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,3,5,8,7]=>[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,3,5,8,7]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,8,5,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,6,8,5,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,3,8,5,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,3,8,5,7]=>[1,2,4,6,8,7,5,3]=>[8,7,5,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,3,8,5,7]=>[1,2,4,3,6,8,7,5]=>[8,7,5,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,8,3,5,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,8,3,5,7]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,8,3,5,7]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,1,3,5,7]=>[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,6,5,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,3,5,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,3,5,7,8]=>[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,3,5,7,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,3,7,5,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,3,7,5,8]=>[1,2,4,6,7,5,3,8]=>[8,7,5,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,3,7,5,8]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,7,3,5,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,7,3,5,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,1,3,5,8]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,6,7,8,5]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,3,7,8,5]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,3,7,8,5]=>[1,2,4,6,7,8,5,3]=>[8,7,5,3,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,3,7,8,5]=>[1,2,4,3,6,7,8,5]=>[8,7,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,7,3,8,5]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,7,3,8,5]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,7,3,8,5]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,1,3,8,5]=>[1,2,4,7,8,5,3,6]=>[8,7,5,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,7,8,3,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,7,8,3,5]=>[1,2,4,6,8,5,7,3]=>[8,7,5,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,7,8,3,5]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,1,8,3,5]=>[1,2,4,7,3,6,8,5]=>[8,7,5,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,8,1,3,5]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,7,5,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,7,5,8,6]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,3,5,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,7,3,5,8,6]=>[1,2,4,7,8,6,5,3]=>[8,7,5,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,3,5,8,6]=>[1,2,4,3,7,8,6,5]=>[8,7,5,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,7,8,5,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,7,8,5,6]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,7,3,8,5,6]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,8,3,5,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,8,3,5,6]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,1,3,5,6]=>[1,2,4,8,6,3,7,5]=>[8,7,5,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,7,6,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,3,7,6,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,7,3,6,8]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,5,7,8,6]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,7,8,6]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,3,7,8,6]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,7,3,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,7,3,8,6]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,1,3,8,6]=>[1,2,4,7,8,6,3,5]=>[8,7,5,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,7,8,3,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,7,8,3,6]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,1,8,3,6]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,5,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,5,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,3,5,6,7]=>[1,2,4,8,7,6,5,3]=>[8,7,5,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,3,5,6,7]=>[1,2,4,3,8,7,6,5]=>[8,7,5,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,5,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,8,6,7]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,8,3,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,8,3,6,7]=>[1,2,4,5,8,7,6,3]=>[8,7,5,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,1,3,6,7]=>[1,2,4,8,7,6,3,5]=>[8,7,5,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,6,8,7]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,3,8,7]=>[1,2,4,5,6,3,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,6,3,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,1,3,8,7]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,6,8,3,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,8,3,7]=>[1,2,4,5,6,8,7,3]=>[8,7,5,4,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,6,8,3,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,1,8,3,7]=>[1,2,4,6,8,7,3,5]=>[8,7,5,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,8,1,3,7]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,6,7,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,3,6,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,3,7,8]=>[1,2,4,5,6,3,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,6,3,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,1,3,7,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,7,3,8]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,6,7,3,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,1,7,3,8]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,7,1,3,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,7,8,3]=>[1,2,4,5,6,7,8,3]=>[8,7,5,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,6,7,8,3]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,1,7,8,3]=>[1,2,4,6,7,8,3,5]=>[8,7,5,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,7,1,8,3]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,7,8,1,3]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,6,4,8,7]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,6,4,8,7]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,3,4,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,3,4,8,7]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,3,4,8,7]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,6,8,4,7]=>[1,2,3,5,6,8,7,4]=>[8,7,6,4,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,3,8,4,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,8,3,4,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,8,3,4,7]=>[1,2,5,8,7,4,6,3]=>[8,7,4,1,2,5,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,1,3,4,7]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,6,4,7,8]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,3,4,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,3,4,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,6,7,4,8]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,3,7,4,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,3,7,4,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,3,7,4,8]=>[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,7,3,4,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,7,3,4,8]=>[1,2,5,7,4,6,3,8]=>[8,7,4,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,6,7,8,4]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,6,7,8,4]=>[1,2,5,6,7,8,4,3]=>[8,7,4,3,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,3,7,8,4]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,3,7,8,4]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,3,7,8,4]=>[1,2,5,3,6,7,8,4]=>[8,7,4,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,7,3,8,4]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,7,3,8,4]=>[1,2,5,7,8,4,6,3]=>[8,7,4,2,1,5,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,1,3,8,4]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,7,8,3,4]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,7,8,3,4]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,7,8,3,4]=>[1,2,5,7,3,6,8,4]=>[8,7,4,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,1,3,4]=>[1,2,5,8,4,7,3,6]=>[8,7,4,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,7,4,8,6]=>[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,7,4,8,6]=>[1,2,5,7,8,6,4,3]=>[8,7,4,2,1,3,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,3,4,8,6]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,3,4,8,6]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,7,8,4,6]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,3,8,4,6]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,3,8,4,6]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,3,8,4,6]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,1,3,4,6]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,3,4,6,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,4,7,6,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,1,4,6,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,7,4,8,6]=>[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,1,4,8,6]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,7,8,4,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,1,8,4,6]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,8,4,6,7]=>[1,2,3,5,8,7,6,4]=>[8,7,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,8,4,6,7]=>[1,2,5,8,7,6,4,3]=>[8,7,4,1,2,3,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,3,4,6,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,3,4,6,7]=>[1,2,5,3,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,4,8,6,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,8,4,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,8,4,6,7]=>[1,2,3,5,8,7,6,4]=>[8,7,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,1,4,6,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,4,6,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,6,4,8,7]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,1,4,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,6,8,4,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,6,8,4,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,6,8,4,7]=>[1,2,3,5,6,8,7,4]=>[8,7,6,4,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,1,8,4,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,8,1,4,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,4,6,7,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,6,4,7,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,1,4,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,1,7,4,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,7,1,4,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,6,7,8,4]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,1,7,8,4]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,7,1,8,4]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,7,8,1,4]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,7,4,8,5]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,7,4,8,5]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,3,4,8,5]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,3,4,8,5]=>[1,2,6,4,7,8,5,3]=>[8,7,3,5,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,3,4,8,5]=>[1,2,6,4,3,7,8,5]=>[8,7,3,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,7,8,4,5]=>[1,2,3,6,8,5,7,4]=>[8,7,6,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,7,8,4,5]=>[1,2,6,8,5,7,4,3]=>[8,7,3,1,4,2,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,3,8,4,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,3,8,4,5]=>[1,2,6,8,5,3,7,4]=>[8,7,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,3,4,5]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,8,3,4,5]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,8,3,4,5]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,1,3,4,5]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,7,4,5,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,3,4,5,8]=>[1,2,6,4,7,5,3,8]=>[8,7,3,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,3,4,5,8]=>[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,4,7,5,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,4,7,5,8]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,1,4,5,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,4,7,8,5]=>[1,2,3,6,7,8,5,4]=>[8,7,6,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,4,7,8,5]=>[1,2,6,7,8,5,4,3]=>[8,7,3,2,1,4,5,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,4,7,8,5]=>[1,2,3,6,7,8,5,4]=>[8,7,6,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,7,4,8,5]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,1,4,8,5]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,7,8,4,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,7,8,4,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,7,8,4,5]=>[1,2,3,6,8,5,7,4]=>[8,7,6,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,8,1,4,5]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,8,4,5,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,3,4,5,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,3,4,5,7]=>[1,2,6,4,8,7,5,3]=>[8,7,3,5,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,3,4,5,7]=>[1,2,6,4,3,8,7,5]=>[8,7,3,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,4,8,5,7]=>[1,2,3,6,8,7,5,4]=>[8,7,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,4,8,5,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,4,8,5,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,4,8,5,7]=>[1,2,3,6,8,7,5,4]=>[8,7,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,8,4,5,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,8,4,5,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,1,4,5,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,4,5,8,7]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,4,5,8,7]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,4,5,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,4,5,8,7]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,8,5,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,1,8,5,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,8,1,5,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,4,5,7,8]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,4,5,7,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,1,5,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,1,7,5,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,7,1,5,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,1,7,8,5]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,7,8,1,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,8,4,5,6]=>[1,2,3,7,5,8,6,4]=>[8,7,6,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,8,4,5,6]=>[1,2,7,5,8,6,4,3]=>[8,7,2,4,1,3,5,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,3,4,5,6]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,3,4,5,6]=>[1,2,7,5,3,8,6,4]=>[8,7,2,4,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,4,8,5,6]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,4,8,5,6]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,7,4,8,5,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,4,8,5,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,4,8,5,6]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,7,8,4,5,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,8,4,5,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,1,4,5,6]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,4,5,8,6]=>[1,2,3,7,8,6,5,4]=>[8,7,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,4,5,8,6]=>[1,2,7,8,6,5,4,3]=>[8,7,2,1,3,4,5,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,4,5,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,4,5,8,6]=>[1,2,3,7,8,6,5,4]=>[8,7,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,7,5,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,5,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,1,5,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,7,8,5,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,7,8,5,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,8,5,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,1,8,5,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,8,1,5,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,4,5,6,8]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,4,5,6,8]=>[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,4,5,6,8]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,7,5,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,7,5,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,5,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,1,5,6,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,1,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,1,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,8,1,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,4,5,6,7]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]=>[8,7,1,2,3,4,5,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,4,5,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,4,5,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,4,5,6,7]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,8,5,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,8,5,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,5,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,1,5,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,5,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,1,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,1,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,6,5,8,7]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,6,5,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,2,5,8,7]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,6,8,5,7]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,6,8,5,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,2,8,5,7]=>[1,3,2,4,6,8,7,5]=>[8,6,7,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,1,2,5,7]=>[1,3,6,2,4,8,7,5]=>[8,6,3,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,6,5,7,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,6,5,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,6,7,5,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,6,7,5,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,2,7,5,8]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,2,7,5,8]=>[1,3,6,7,5,2,4,8]=>[8,6,3,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,7,2,5,8]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,1,2,5,8]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,6,7,8,5]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,6,7,8,5]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,2,7,8,5]=>[1,3,4,6,7,8,5,2]=>[8,6,5,3,2,1,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,2,7,8,5]=>[1,3,2,4,6,7,8,5]=>[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,2,7,8,5]=>[1,3,6,7,8,5,2,4]=>[8,6,3,2,1,4,7,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,7,2,8,5]=>[1,3,4,6,2,5,7,8]=>[8,6,5,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,7,2,8,5]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,1,2,8,5]=>[1,3,6,2,4,7,8,5]=>[8,6,3,7,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,7,8,2,5]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,7,8,2,5]=>[1,3,6,8,5,7,2,4]=>[8,6,3,1,4,2,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,1,8,2,5]=>[1,3,6,8,5,2,4,7]=>[8,6,3,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,8,1,2,5]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,7,5,8,6]=>[1,3,4,2,5,7,8,6]=>[8,6,5,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,7,5,8,6]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,2,5,8,6]=>[1,3,4,7,8,6,5,2]=>[8,6,5,2,1,3,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,7,8,5,6]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,7,8,5,6]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,8,2,5,6]=>[1,3,7,5,8,6,2,4]=>[8,6,2,4,1,3,7,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,1,2,5,6]=>[1,3,7,5,2,4,8,6]=>[8,6,2,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,7,5,6,8]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,7,5,6,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,5,7,6,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,2,7,6,8]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,2,7,6,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,7,2,6,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,7,2,6,8]=>[1,3,5,7,6,2,4,8]=>[8,6,4,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,1,2,6,8]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,5,7,8,6]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,5,7,8,6]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,2,7,8,6]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,2,7,8,6]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,7,2,8,6]=>[1,3,4,5,7,8,6,2]=>[8,6,5,4,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,7,2,8,6]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,1,2,8,6]=>[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,7,8,2,6]=>[1,3,4,5,7,2,6,8]=>[8,6,5,4,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,7,8,2,6]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,7,8,2,6]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,1,8,2,6]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,8,1,2,6]=>[1,3,5,8,6,2,4,7]=>[8,6,4,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,8,5,6,7]=>[1,3,4,2,5,8,7,6]=>[8,6,5,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,2,5,6,7]=>[1,3,4,8,7,6,5,2]=>[8,6,5,1,2,3,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,2,5,6,7]=>[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,2,5,6,7]=>[1,3,8,7,6,5,2,4]=>[8,6,1,2,3,4,7,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,5,8,6,7]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,5,8,6,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,2,8,6,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,2,8,6,7]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,8,2,6,7]=>[1,3,4,5,8,7,6,2]=>[8,6,5,4,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,1,2,6,7]=>[1,3,5,2,4,8,7,6]=>[8,6,4,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,5,6,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,2,6,8,7]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,6,2,8,7]=>[1,3,4,5,6,2,7,8]=>[8,6,5,4,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,2,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,6,2,8,7]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,1,2,8,7]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,6,8,2,7]=>[1,3,4,5,6,8,7,2]=>[8,6,5,4,3,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,8,2,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,1,8,2,7]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,8,1,2,7]=>[1,3,5,8,7,2,4,6]=>[8,6,4,1,2,7,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,2,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,6,2,7,8]=>[1,3,4,5,6,2,7,8]=>[8,6,5,4,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,2,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,6,2,7,8]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,2,8]=>[1,3,4,5,6,7,2,8]=>[8,6,5,4,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,7,2,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,6,7,2,8]=>[1,3,5,6,7,2,4,8]=>[8,6,4,3,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,1,7,2,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,2]=>[1,3,4,5,6,7,8,2]=>[8,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,7,8,2]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,6,7,8,2]=>[1,3,5,6,7,8,2,4]=>[8,6,4,3,2,1,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,1,7,8,2]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,1,8,2]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,6,4,8,7]=>[1,3,5,6,4,2,7,8]=>[8,6,4,3,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,6,4,8,7]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,2,4,8,7]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,2,4,8,7]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,2,4,8,7]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,6,8,4,7]=>[1,3,5,6,8,7,4,2]=>[8,6,4,3,1,2,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,2,8,4,7]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,2,8,4,7]=>[1,3,6,8,7,4,2,5]=>[8,6,3,1,2,5,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,8,2,4,7]=>[1,3,5,8,7,4,6,2]=>[8,6,4,1,2,5,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,8,2,4,7]=>[1,3,2,5,8,7,4,6]=>[8,6,7,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,8,2,4,7]=>[1,3,6,2,5,8,7,4]=>[8,6,3,7,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,2,4,7,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,2,4,7,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,2,4,7,8]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,6,7,4,8]=>[1,3,2,5,6,7,4,8]=>[8,6,7,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,2,7,4,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,2,7,4,8]=>[1,3,6,7,4,2,5,8]=>[8,6,3,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,7,2,4,8]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,2,4,8]=>[1,3,6,2,5,7,4,8]=>[8,6,3,7,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,6,7,8,4]=>[1,3,5,6,7,8,4,2]=>[8,6,4,3,2,1,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,6,7,8,4]=>[1,3,2,5,6,7,8,4]=>[8,6,7,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,2,7,8,4]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,2,7,8,4]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,7,2,8,4]=>[1,3,5,7,8,4,6,2]=>[8,6,4,2,1,5,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,7,2,8,4]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,2,8,4]=>[1,3,6,2,5,7,8,4]=>[8,6,3,7,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,7,8,2,4]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,7,8,2,4]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,8,2,4]=>[1,3,6,8,4,2,5,7]=>[8,6,3,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,1,2,4]=>[1,3,6,2,5,8,4,7]=>[8,6,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,7,4,8,6]=>[1,3,5,7,8,6,4,2]=>[8,6,4,2,1,3,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,7,4,8,6]=>[1,3,2,5,7,8,6,4]=>[8,6,7,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,2,4,8,6]=>[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,2,4,8,6]=>[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,2,4,8,6]=>[1,3,7,8,6,4,2,5]=>[8,6,2,1,3,5,7,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,7,8,4,6]=>[1,3,5,7,4,2,6,8]=>[8,6,4,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,7,8,4,6]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,2,8,4,6]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,2,8,4,6]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,2,8,4,6]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,8,2,4,6]=>[1,3,5,8,6,2,4,7]=>[8,6,4,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,8,2,4,6]=>[1,3,2,5,8,6,4,7]=>[8,6,7,4,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,1,2,4,6]=>[1,3,7,4,8,6,2,5]=>[8,6,2,5,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,7,4,6,8]=>[1,3,5,7,6,4,2,8]=>[8,6,4,2,3,5,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,7,4,6,8]=>[1,3,2,5,7,6,4,8]=>[8,6,7,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,2,4,6,8]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,2,4,6,8]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,2,4,6,8]=>[1,3,7,6,4,2,5,8]=>[8,6,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,4,7,6,8]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,4,7,6,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,4,7,6,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,4,7,6,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,7,4,6,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,7,4,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,7,4,6,8]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,2,4,6,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,4,7,8,6]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,4,7,8,6]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,4,7,8,6]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,7,4,8,6]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,7,4,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,7,4,8,6]=>[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,2,4,8,6]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,7,8,4,6]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,7,8,4,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,7,8,4,6]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,2,8,4,6]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,8,4,6,7]=>[1,3,5,8,7,6,4,2]=>[8,6,4,1,2,3,5,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,2,4,6,7]=>[1,3,5,2,4,8,7,6]=>[8,6,4,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,2,4,6,7]=>[1,3,2,5,4,8,7,6]=>[8,6,7,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,4,8,6,7]=>[1,3,5,4,2,6,8,7]=>[8,6,4,5,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,4,8,6,7]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,4,8,6,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,8,4,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,8,4,6,7]=>[1,2,3,5,8,7,6,4]=>[8,7,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,2,4,6,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,4,6,8,7]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,4,6,8,7]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,4,6,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,4,6,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,6,4,8,7]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,2,4,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,6,8,4,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,6,8,4,7]=>[1,2,3,5,6,8,7,4]=>[8,7,6,4,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,2,8,4,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,8,2,4,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,4,6,7,8]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,6,4,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,6,4,7,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,2,4,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,6,7,4,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,6,7,4,8]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,2,7,4,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,7,2,4,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,6,7,8,4]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,6,7,8,4]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,2,7,8,4]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,7,2,8,4]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,7,8,2,4]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,7,4,8,5]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,2,7,4,8,5]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,2,4,8,5]=>[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,2,8,4,5]=>[1,3,6,8,5,2,4,7]=>[8,6,3,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,2,8,4,5]=>[1,3,7,4,2,6,8,5]=>[8,6,2,5,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,8,2,4,5]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,7,4,5,8]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,2,4,5,8]=>[1,3,7,5,2,6,4,8]=>[8,6,2,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,2,4,7,5,8]=>[1,3,2,6,7,5,4,8]=>[8,6,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,4,7,5,8]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,4,7,5,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,4,7,5,8]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,7,4,5,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,7,4,5,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,4,7,8,5]=>[1,3,6,7,8,5,4,2]=>[8,6,3,2,1,4,5,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,2,4,7,8,5]=>[1,3,2,6,7,8,5,4]=>[8,6,7,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,4,7,8,5]=>[1,3,2,4,6,7,8,5]=>[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,4,7,8,5]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,4,7,8,5]=>[1,2,3,6,7,8,5,4]=>[8,7,6,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,7,4,8,5]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,7,4,8,5]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,7,4,8,5]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,2,4,8,5]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,7,8,4,5]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,7,8,4,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,7,8,4,5]=>[1,2,3,6,8,5,7,4]=>[8,7,6,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,8,2,4,5]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,8,4,5,7]=>[1,3,6,4,2,5,8,7]=>[8,6,3,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,2,4,5,7]=>[1,3,2,6,4,8,7,5]=>[8,6,7,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,2,4,5,7]=>[1,3,8,7,5,2,6,4]=>[8,6,1,2,4,7,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,2,4,8,5,7]=>[1,3,2,6,8,7,5,4]=>[8,6,7,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,4,8,5,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,4,8,5,7]=>[1,2,3,6,8,7,5,4]=>[8,7,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,8,4,5,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,2,4,5,8,7]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,4,5,8,7]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,4,5,8,7]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,6,5,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,2,5,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,6,8,5,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,6,8,5,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,8,2,5,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,2,4,5,7,8]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,4,5,7,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,2,5,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,6,7,5,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,2,7,5,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,7,2,5,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,6,7,8,5]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,7,2,8,5]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,7,8,2,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,8,4,5,6]=>[1,3,7,5,8,6,4,2]=>[8,6,2,4,1,3,5,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,8,4,5,6]=>[1,3,2,7,5,8,6,4]=>[8,6,7,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,2,4,5,6]=>[1,3,7,5,2,4,8,6]=>[8,6,2,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,2,4,5,6]=>[1,3,2,7,5,4,8,6]=>[8,6,7,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,2,4,5,6]=>[1,3,8,6,4,2,7,5]=>[8,6,1,3,5,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,4,8,5,6]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,4,8,5,6]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,4,8,5,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,4,8,5,6]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,8,4,5,6]=>[1,2,3,7,5,8,6,4]=>[8,7,6,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,2,4,5,6]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,4,5,8,6]=>[1,3,2,7,8,6,5,4]=>[8,6,7,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,4,5,8,6]=>[1,2,3,7,8,6,5,4]=>[8,7,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,7,5,8,6]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,7,5,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,7,5,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,2,5,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,7,8,5,6]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,7,8,5,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,7,8,5,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,8,2,5,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,4,5,6,8]=>[1,3,7,6,5,4,2,8]=>[8,6,2,3,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,4,5,6,8]=>[1,3,2,7,6,5,4,8]=>[8,6,7,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,4,5,6,8]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,4,5,6,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,4,5,6,8]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,7,5,6,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,2,5,6,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,7,6,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,7,2,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,7,8,6]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,7,2,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,7,8,2,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,4,5,6,7]=>[1,3,8,7,6,5,4,2]=>[8,6,1,2,3,4,5,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,4,5,6,7]=>[1,3,2,8,7,6,5,4]=>[8,6,7,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,4,5,6,7]=>[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,4,5,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,4,5,6,7]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,8,5,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,8,5,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,2,5,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,8,6,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,5,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,2,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,8,2,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,8,7]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,8,2,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,6,3,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,6,3,8,7]=>[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,2,3,8,7]=>[1,4,6,3,5,2,7,8]=>[8,5,3,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,2,3,8,7]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,6,8,3,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,2,8,3,7]=>[1,4,6,8,7,3,2,5]=>[8,5,3,1,2,6,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,8,2,3,7]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,8,2,3,7]=>[1,4,6,2,5,8,7,3]=>[8,5,3,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,8,2,3,7]=>[1,4,2,5,8,7,3,6]=>[8,5,7,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,1,2,3,7]=>[1,4,8,7,3,6,2,5]=>[8,5,1,2,6,3,7,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,6,3,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,2,3,7,8]=>[1,4,6,3,5,2,7,8]=>[8,5,3,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,6,7,3,8]=>[1,4,2,5,6,7,3,8]=>[8,5,7,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,2,7,3,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,7,2,3,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,7,2,3,8]=>[1,4,6,2,5,7,3,8]=>[8,5,3,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,7,2,3,8]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,6,7,8,3]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,6,7,8,3]=>[1,4,2,5,6,7,8,3]=>[8,5,7,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,2,7,8,3]=>[1,4,6,7,8,3,2,5]=>[8,5,3,2,1,6,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,2,7,8,3]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,7,2,8,3]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,7,2,8,3]=>[1,4,2,5,7,8,3,6]=>[8,5,7,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,2,8,3]=>[1,4,7,8,3,6,2,5]=>[8,5,2,1,6,3,7,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,7,8,2,3]=>[1,4,6,8,3,5,7,2]=>[8,5,3,1,6,4,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,7,8,2,3]=>[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,7,8,2,3]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,8,2,3]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,7,3,8,6]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,7,3,8,6]=>[1,4,2,5,7,8,6,3]=>[8,5,7,4,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,2,3,8,6]=>[1,4,2,5,3,7,8,6]=>[8,5,7,4,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,7,8,3,6]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,7,8,3,6]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,7,2,8,3,6]=>[1,4,7,3,5,2,6,8]=>[8,5,2,6,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,2,8,3,6]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,8,2,3,6]=>[1,4,7,3,2,5,8,6]=>[8,5,2,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,1,2,3,6]=>[1,4,8,6,2,5,3,7]=>[8,5,1,3,7,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,7,3,6,8]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,2,3,6,8]=>[1,4,7,6,3,2,5,8]=>[8,5,2,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,3,7,6,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,3,7,6,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,3,7,6,8]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,3,7,6,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,3,7,6,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,7,3,6,8]=>[1,4,5,7,6,3,2,8]=>[8,5,4,2,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,7,3,6,8]=>[1,2,4,5,7,6,3,8]=>[8,7,5,4,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,7,3,6,8]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,3,7,8,6]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,3,7,8,6]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,3,7,8,6]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,3,7,8,6]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,7,3,8,6]=>[1,4,5,7,8,6,3,2]=>[8,5,4,2,1,3,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,7,3,8,6]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,2,3,8,6]=>[1,2,4,7,8,6,3,5]=>[8,7,5,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,7,8,3,6]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,8,3,6,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,8,3,6,7]=>[1,4,2,5,8,7,6,3]=>[8,5,7,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,2,3,6,7]=>[1,4,8,7,6,3,2,5]=>[8,5,1,2,3,6,7,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,3,8,6,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,3,8,6,7]=>[1,4,5,3,2,6,8,7]=>[8,5,4,6,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,3,8,6,7]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,3,8,6,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,8,3,6,7]=>[1,4,5,8,7,6,3,2]=>[8,5,4,1,2,3,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,8,3,6,7]=>[1,2,4,5,8,7,6,3]=>[8,7,5,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,2,3,6,7]=>[1,2,4,8,7,6,3,5]=>[8,7,5,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,3,6,8,7]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,3,6,8,7]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,6,3,8,7]=>[1,4,5,6,3,2,7,8]=>[8,5,4,3,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,6,3,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,2,3,8,7]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,6,8,3,7]=>[1,2,4,5,6,8,7,3]=>[8,7,5,4,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,6,8,3,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,2,8,3,7]=>[1,2,4,6,8,7,3,5]=>[8,7,5,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,8,2,3,7]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,3,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,3,6,7,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,3,6,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,6,3,7,8]=>[1,4,5,6,3,2,7,8]=>[8,5,4,3,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,6,3,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,2,3,7,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,6,7,3,8]=>[1,4,5,6,7,3,2,8]=>[8,5,4,3,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,6,7,3,8]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,6,7,3,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,2,7,3,8]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,2,3,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,6,7,8,3]=>[1,4,5,6,7,8,3,2]=>[8,5,4,3,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,6,7,8,3]=>[1,2,4,5,6,7,8,3]=>[8,7,5,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,6,7,8,3]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,2,7,8,3]=>[1,2,4,6,7,8,3,5]=>[8,7,5,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,2,8,3]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,8,2,3]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,2,3,8,5]=>[1,4,7,8,5,2,3,6]=>[8,5,2,1,4,7,6,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,7,8,3,5]=>[1,4,2,6,8,5,7,3]=>[8,5,7,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,2,8,3,5]=>[1,4,7,3,2,6,8,5]=>[8,5,2,6,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,8,2,3,5]=>[1,4,7,3,6,2,5,8]=>[8,5,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,8,2,3,5]=>[1,4,7,3,2,6,5,8]=>[8,5,2,6,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,2,3,5]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,1,2,3,5]=>[1,4,8,5,2,6,3,7]=>[8,5,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,7,3,5,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,2,3,5,8]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,3,7,5,8]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,3,7,5,8]=>[1,4,2,6,7,5,3,8]=>[8,5,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,3,7,5,8]=>[1,2,4,6,7,5,3,8]=>[8,7,5,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,7,3,5,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,7,3,5,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,2,3,5,8]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,3,7,8,5]=>[1,4,2,3,6,7,8,5]=>[8,5,7,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,3,7,8,5]=>[1,4,6,7,8,5,3,2]=>[8,5,3,2,1,4,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,3,7,8,5]=>[1,2,4,3,6,7,8,5]=>[8,7,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,7,3,8,5]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,2,3,8,5]=>[1,2,4,7,8,5,3,6]=>[8,7,5,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,7,8,3,5]=>[1,2,4,6,8,5,7,3]=>[8,7,5,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,7,8,3,5]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,2,8,3,5]=>[1,2,4,7,3,6,8,5]=>[8,7,5,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,8,2,3,5]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,8,3,5,7]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,8,3,5,7]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,3,8,5,7]=>[1,4,2,6,8,7,5,3]=>[8,5,7,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,3,8,5,7]=>[1,4,6,8,7,5,3,2]=>[8,5,3,1,2,4,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,3,8,5,7]=>[1,2,4,6,8,7,5,3]=>[8,7,5,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,3,8,5,7]=>[1,2,4,3,6,8,7,5]=>[8,7,5,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,8,3,5,7]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,8,3,5,7]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,2,3,5,7]=>[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,3,5,8,7]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,3,5,8,7]=>[1,4,6,5,3,2,7,8]=>[8,5,3,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,3,5,8,7]=>[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,3,5,8,7]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,5,8,7]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,6,5,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,3,5,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,6,8,5,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,3,8,5,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,8,3,5,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,3,5,7,8]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,3,5,7,8]=>[1,4,6,5,3,2,7,8]=>[8,5,3,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,3,5,7,8]=>[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,3,5,7,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,5,7,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,6,5,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,3,5,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,7,5,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,6,7,5,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,3,7,5,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,7,3,5,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,7,8,5]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,6,7,8,5]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,3,7,8,5]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,7,3,8,5]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,7,8,3,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,8,3,5,6]=>[1,4,2,7,5,8,6,3]=>[8,5,7,2,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,8,2,3,5,6]=>[1,4,8,6,3,7,5,2]=>[8,5,1,3,6,2,4,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,2,3,5,6]=>[1,4,8,6,3,2,7,5]=>[8,5,1,3,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,3,8,5,6]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,3,8,5,6]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,3,8,5,6]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,8,3,5,6]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,8,2,3,5,6]=>[1,2,4,8,6,3,7,5]=>[8,7,5,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,3,5,8,6]=>[1,4,2,3,7,8,6,5]=>[8,5,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,3,5,8,6]=>[1,4,2,7,8,6,5,3]=>[8,5,7,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,3,5,8,6]=>[1,4,7,8,6,5,3,2]=>[8,5,2,1,3,4,6,7]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,3,5,8,6]=>[1,2,4,7,8,6,5,3]=>[8,7,5,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,3,5,8,6]=>[1,2,4,3,7,8,6,5]=>[8,7,5,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,7,5,8,6]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,7,5,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,3,5,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,8,5,6]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,7,8,5,6]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,7,8,5,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,3,8,5,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,8,3,5,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,3,5,6,8]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,3,5,6,8]=>[1,4,7,6,5,3,2,8]=>[8,5,2,3,4,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,3,5,6,8]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,5,6,8]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,7,5,6,8]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,7,5,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,3,5,6,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,7,6,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,5,7,6,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,7,3,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,7,8,6]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,5,7,8,6]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,7,3,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,7,8,3,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,3,5,6,7]=>[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,3,5,6,7]=>[1,4,2,8,7,6,5,3]=>[8,5,7,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,3,5,6,7]=>[1,4,8,7,6,5,3,2]=>[8,5,1,2,3,4,6,7]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,3,5,6,7]=>[1,2,4,8,7,6,5,3]=>[8,7,5,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,3,5,6,7]=>[1,2,4,3,8,7,6,5]=>[8,7,5,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,5,6,7]=>[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,8,5,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,3,5,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,5,8,6,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,5,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,3,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,8,3,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,6,8,7]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,5,6,8,7]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,6,8,3,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,2,3,8,4]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,2,3,8,4]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,2,3,8,4]=>[1,5,2,6,3,7,8,4]=>[8,4,7,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,7,8,3,4]=>[1,5,7,3,6,8,4,2]=>[8,4,2,6,3,1,5,7]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,7,8,3,4]=>[1,5,7,3,2,6,8,4]=>[8,4,2,6,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,2,8,3,4]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,2,8,3,4]=>[1,5,2,6,8,4,7,3]=>[8,4,7,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,2,8,3,4]=>[1,5,2,6,8,4,3,7]=>[8,4,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,8,2,3,4]=>[1,5,8,4,7,3,6,2]=>[8,4,1,5,2,6,3,7]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,8,2,3,4]=>[1,5,8,4,7,3,2,6]=>[8,4,1,5,2,6,7,3]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,8,2,3,4]=>[1,5,8,4,2,6,3,7]=>[8,4,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,7,3,4,8]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,7,3,4,8]=>[1,5,7,4,2,6,3,8]=>[8,4,2,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,2,3,4,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,3,7,4,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,7,4,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,7,3,4,8]=>[1,5,7,4,6,3,2,8]=>[8,4,2,5,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,7,3,4,8]=>[1,2,5,7,4,6,3,8]=>[8,7,4,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,2,3,4,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,3,7,8,4]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,7,8,4]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,3,7,8,4]=>[1,2,5,3,6,7,8,4]=>[8,7,4,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,7,3,8,4]=>[1,5,7,8,4,6,3,2]=>[8,4,2,1,5,3,6,7]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,2,3,8,4]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,7,8,3,4]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,7,8,3,4]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,7,8,3,4]=>[1,2,5,7,3,6,8,4]=>[8,7,4,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,8,2,3,4]=>[1,2,5,8,4,7,3,6]=>[8,7,4,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,8,3,4,7]=>[1,5,8,7,4,2,6,3]=>[8,4,1,2,5,7,3,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,2,3,4,7]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,2,3,4,7]=>[1,5,2,6,3,8,7,4]=>[8,4,7,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,3,8,4,7]=>[1,5,3,6,8,7,4,2]=>[8,4,6,3,1,2,5,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,3,8,4,7]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,8,4,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,8,3,4,7]=>[1,5,8,7,4,6,3,2]=>[8,4,1,2,5,3,6,7]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,8,3,4,7]=>[1,2,5,8,7,4,6,3]=>[8,7,4,1,2,5,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,8,3,4,7]=>[1,2,5,8,7,4,3,6]=>[8,7,4,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,2,3,4,7]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,3,4,8,7]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,3,4,8,7]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,4,8,7]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,3,4,8,7]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,6,4,8,7]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,6,4,8,7]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,3,4,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,3,8,4,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,8,3,4,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,3,4,7,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,4,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,3,4,7,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,6,4,7,8]=>[1,5,6,4,3,2,7,8]=>[8,4,3,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,6,4,7,8]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,6,4,7,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,3,4,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,6,7,4,8]=>[1,5,6,7,4,3,2,8]=>[8,4,3,2,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,6,7,4,8]=>[1,2,5,6,7,4,3,8]=>[8,7,4,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,6,7,4,8]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,3,7,4,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,6,7,8,4]=>[1,5,6,7,8,4,3,2]=>[8,4,3,2,1,5,6,7]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,6,7,8,4]=>[1,2,5,6,7,8,4,3]=>[8,7,4,3,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,6,7,8,4]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,3,7,8,4]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,7,3,8,4]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,7,8,3,4]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,8,3,4,6]=>[1,5,8,6,3,7,4,2]=>[8,4,1,3,6,2,5,7]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,8,3,4,6]=>[1,5,8,6,3,2,7,4]=>[8,4,1,3,6,7,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,2,3,4,6]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,2,3,4,6]=>[1,5,2,7,4,3,8,6]=>[8,4,7,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,3,8,4,6]=>[1,5,3,7,4,2,6,8]=>[8,4,6,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,3,8,4,6]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,3,8,4,6]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,3,8,4,6]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,3,8,4,6]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,8,3,4,6]=>[1,5,8,6,3,2,4,7]=>[8,4,1,3,6,7,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,2,3,4,6]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,3,4,8,6]=>[1,5,3,7,8,6,4,2]=>[8,4,6,2,1,3,5,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,3,4,8,6]=>[1,5,3,2,4,7,8,6]=>[8,4,6,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,3,4,8,6]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,7,4,8,6]=>[1,5,7,8,6,4,3,2]=>[8,4,2,1,3,5,6,7]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,7,4,8,6]=>[1,2,5,7,8,6,4,3]=>[8,7,4,2,1,3,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,7,4,8,6]=>[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,3,4,8,6]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,7,8,4,6]=>[1,5,7,4,3,2,6,8]=>[8,4,2,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,7,8,4,6]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,3,8,4,6]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,3,4,6,8]=>[1,5,3,2,7,6,4,8]=>[8,4,6,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,3,4,6,8]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,3,4,6,8]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,3,4,6,8]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,7,4,6,8]=>[1,5,7,6,4,3,2,8]=>[8,4,2,3,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,7,4,6,8]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,3,4,6,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,4,7,6,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,4,7,6,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,7,4,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,4,7,8,6]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,4,7,8,6]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,4,7,8,6]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,7,4,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,7,8,4,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,3,4,6,7]=>[1,5,3,2,8,7,6,4]=>[8,4,6,7,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,8,3,4,6,7]=>[1,5,3,2,4,8,7,6]=>[8,4,6,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,3,4,6,7]=>[1,2,5,3,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,8,4,6,7]=>[1,5,8,7,6,4,3,2]=>[8,4,1,2,3,5,6,7]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,8,4,6,7]=>[1,2,5,8,7,6,4,3]=>[8,7,4,1,2,3,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,8,4,6,7]=>[1,2,3,5,8,7,6,4]=>[8,7,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,3,4,6,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,4,8,6,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,4,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,8,4,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,4,6,8,7]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,4,6,8,7]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,4,6,8,7]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,6,8,4,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,4,6,7,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,2,3,4,5]=>[1,6,3,7,4,8,5,2]=>[8,3,6,2,5,1,4,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,3,8,4,5]=>[1,6,8,5,3,7,4,2]=>[8,3,1,4,6,2,5,7]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,3,8,4,5]=>[1,6,8,5,3,2,7,4]=>[8,3,1,4,6,7,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,3,8,4,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,3,8,4,5]=>[1,2,6,8,5,3,7,4]=>[8,7,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,8,3,4,5]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,8,3,4,5]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,8,3,4,5]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,2,3,4,5]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,3,4,8,5]=>[1,6,4,2,3,7,8,5]=>[8,3,5,7,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,3,4,8,5]=>[1,6,4,2,7,8,5,3]=>[8,3,5,7,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,3,4,8,5]=>[1,6,4,7,8,5,3,2]=>[8,3,5,2,1,4,6,7]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,3,4,8,5]=>[1,2,6,4,7,8,5,3]=>[8,7,3,5,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,3,4,8,5]=>[1,2,6,4,3,7,8,5]=>[8,7,3,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,7,4,8,5]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,7,4,8,5]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,3,4,8,5]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,7,8,4,5]=>[1,2,6,8,5,7,4,3]=>[8,7,3,1,4,2,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,7,8,4,5]=>[1,2,3,6,8,5,7,4]=>[8,7,6,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,8,3,4,5]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,3,4,5,8]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,3,4,5,8]=>[1,2,6,4,7,5,3,8]=>[8,7,3,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,3,4,5,8]=>[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,7,4,5,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,7,4,5,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,3,4,5,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,7,5,8]=>[1,6,7,5,4,3,2,8]=>[8,3,2,4,5,6,7,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,4,7,5,8]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,7,5,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,7,4,5,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,7,8,5]=>[1,6,7,8,5,4,3,2]=>[8,3,2,1,4,5,6,7]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,4,7,8,5]=>[1,2,6,7,8,5,4,3]=>[8,7,3,2,1,4,5,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,4,7,8,5]=>[1,2,3,6,7,8,5,4]=>[8,7,6,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,7,8,5]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,7,4,8,5]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,7,8,4,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,3,4,5,7]=>[1,6,4,2,3,8,7,5]=>[8,3,5,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,3,4,5,7]=>[1,6,4,2,8,7,5,3]=>[8,3,5,7,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,3,4,5,7]=>[1,6,4,8,7,5,3,2]=>[8,3,5,1,2,4,6,7]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,3,4,5,7]=>[1,2,6,4,8,7,5,3]=>[8,7,3,5,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,3,4,5,7]=>[1,2,6,4,3,8,7,5]=>[8,7,3,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,8,4,5,7]=>[1,6,4,3,2,5,8,7]=>[8,3,5,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,8,4,5,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,3,4,5,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,8,5,7]=>[1,6,8,7,5,4,3,2]=>[8,3,1,2,4,5,6,7]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,4,8,5,7]=>[1,2,3,6,8,7,5,4]=>[8,7,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,8,5,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,8,4,5,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,5,8,7]=>[1,6,5,4,3,2,7,8]=>[8,3,4,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,4,5,8,7]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,4,5,8,7]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,5,8,7]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,6,8,5,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,4,5,7,8]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,4,5,7,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,3,4,5,6]=>[1,7,5,3,8,6,4,2]=>[8,2,4,6,1,3,5,7]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,3,4,5,6]=>[1,2,7,5,3,8,6,4]=>[8,7,2,4,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,8,4,5,6]=>[1,7,5,8,6,4,3,2]=>[8,2,4,1,3,5,6,7]=>[8,4,5,2,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,8,4,5,6]=>[1,2,7,5,8,6,4,3]=>[8,7,2,4,1,3,5,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,8,4,5,6]=>[1,2,3,7,5,8,6,4]=>[8,7,6,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,3,4,5,6]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,8,5,6]=>[1,7,5,4,3,2,6,8]=>[8,2,4,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,8,5,6]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,4,8,5,6]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,4,8,5,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,8,4,5,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,8,6]=>[1,7,8,6,5,4,3,2]=>[8,2,1,3,4,5,6,7]=>[8,3,2,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,5,8,6]=>[1,2,7,8,6,5,4,3]=>[8,7,2,1,3,4,5,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,4,5,8,6]=>[1,2,3,7,8,6,5,4]=>[8,7,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,4,5,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,5,8,6]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,8,5,6]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,5,6,8]=>[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,4,5,6,8]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,4,5,6,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,5,6,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]=>[8,7,1,2,3,4,5,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,4,5,6,7]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,4,5,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,5,6,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,4,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,4,8,1,6]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,7,6,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,3,8,1,6]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,3,1,8,7]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,1,3,8,7]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,5,4,2,8,7]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,3,2,8,7]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,1,2,8,7]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,2,8,1,6]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,2,5,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,2,1,5]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,8,1,2,5]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,1,8,2,6]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,3,8,2,6]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,4,8,2,6]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,4,8,3,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,4,7,6,2]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,3,7,6,2]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,1,7,6,2]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,7,1,5,2]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,6,5,1,2]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,3,1,4,2]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,1,3,4,2]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,7,3,5,2]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,7,4,5,2]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,4,5,3]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,8,4,3,5]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,8,4,2,5]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,8,3,2,5]=>[1,4,2,7,3,6,5,8]=>[8,5,7,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,1,3,2,4]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,1,8,3,6]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,8,1,3,5]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,8,3,1,5]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,7,3,5,1]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,7,4,5,1]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,4,1,5]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,8,1,4,5]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,8,4,6]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,8,5,6]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,8,7,6,5]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,7,6,4]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,7,1,5,4]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,6,5,1,4]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,5,3,1]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,6,5,1,3]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,7,1,5,3]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,1,7,6,3]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,2,7,6,3]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,2,7,6,4]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,3,7,6,4]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,7,3,5,4]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,7,2,5,4]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,7,2,5,3]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,1,2,4,3]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,2,1,4,3]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,2,4,1,3]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,2,4,3,1]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,4,2,3]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,6,5,2,3]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,6,5,2,4]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,6,5,3,4]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,6,5,4,2]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,6,5,3,2]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,1,4,3,2]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,4,1,3,2]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,1,2,6,5,8,7,10,9]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,3,2,5,4,7,6,1,10,9]=>[1,8,2,3,4,5,6,7,9,10]=>[10,3,9,8,7,6,5,4,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,2,5,4,7,6,9,8,1]=>[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,5,6,3,4,8,7,10,9]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,6,5,4,3,8,7,10,9]=>[1,2,3,6,4,5,7,8,9,10]=>[10,9,8,5,7,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,5,4,7,6,9,8,3]=>[1,2,3,10,4,5,6,7,8,9]=>[10,9,8,1,7,6,5,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,10,7,6,9,8,5]=>[1,2,3,4,5,10,6,7,8,9]=>[10,9,8,7,6,1,5,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,1,2,3,4,5]=>[1,6,2,7,3,8,4,9,5,10]=>[10,5,9,4,8,3,7,2,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,8,9,10,5,6,7]=>[1,2,3,4,5,8,6,9,7,10]=>[10,9,8,7,6,3,5,2,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,5,1,7,2,9,4,10,6,8]=>[1,3,2,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,9,10,7,8]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,10,9,8,7]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,5,1,4,6,7,8]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,3,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,2,4,7,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,2,4,7,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,2,4,6,8]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,2,3,6,8]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,3,4,5,8]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,2,4,5,8]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,2,3,5,8]=>[1,6,3,7,5,2,4,8]=>[8,3,6,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,2,4,6,8]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,2,3,5,8]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,4,5,6,7]=>[1,3,8,7,6,5,4,2]=>[8,6,1,2,3,4,5,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,3,5,6,7]=>[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,3,4,5,7]=>[1,6,4,2,3,8,7,5]=>[8,3,5,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,2,4,5,7]=>[1,6,4,2,3,8,7,5]=>[8,3,5,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,2,3,5,7]=>[1,6,3,8,7,5,2,4]=>[8,3,6,1,2,4,7,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,2,3,4,7]=>[1,6,3,8,7,4,2,5]=>[8,3,6,1,2,5,7,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,1,3,4,5,6]=>[1,7,5,3,8,6,4,2]=>[8,2,4,6,1,3,5,7]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,2,3,4,6]=>[1,7,4,2,5,3,8,6]=>[8,2,5,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,3,5,6,7]=>[1,8,7,6,5,3,4,2]=>[8,1,2,3,4,6,5,7]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,2,4,6,7]=>[1,8,7,6,4,2,3,5]=>[8,1,2,3,5,7,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,2,4,5,6]=>[1,8,6,4,2,3,7,5]=>[8,1,3,5,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,2,3,5,6]=>[1,8,6,3,7,5,2,4]=>[8,1,3,6,2,4,7,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,3,4,6]=>[1,8,6,3,7,4,2,5]=>[8,1,3,6,2,5,7,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,1,4,6,8]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,7,1,3,6,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,1,2,6,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,1,3,4,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,1,2,4,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,7,1,3,4,8]=>[1,6,3,5,2,4,7,8]=>[8,3,6,4,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,6,1,3,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,1,2,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,1,2,4,8]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,1,4,6,7]=>[1,3,5,2,4,8,7,6]=>[8,6,4,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,1,3,6,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,1,3,4,7]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,1,3,5,7]=>[1,6,3,4,8,7,5,2]=>[8,3,6,5,1,2,4,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,1,2,4,7]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,1,2,3,7]=>[1,6,2,4,8,7,3,5]=>[8,3,7,5,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,4,5,6]=>[1,3,7,5,2,4,8,6]=>[8,6,2,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,1,2,5,6]=>[1,4,8,6,2,3,7,5]=>[8,5,1,3,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,1,2,4,6]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,1,3,4,5]=>[1,6,3,7,4,8,5,2]=>[8,3,6,2,5,1,4,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,1,2,4,5]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,1,2,3,5]=>[1,6,2,4,8,5,3,7]=>[8,3,7,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,1,3,5,6]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,1,2,5,6]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,1,2,4,6]=>[1,7,4,8,6,2,3,5]=>[8,2,5,1,3,7,6,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,1,2,3,5]=>[1,7,3,6,2,4,8,5]=>[8,2,6,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,1,3,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,1,2,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,1,2,4,7]=>[1,8,7,4,6,2,3,5]=>[8,1,2,5,3,7,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,1,3,5,6]=>[1,8,6,3,4,7,5,2]=>[8,1,3,6,5,2,4,7]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,1,2,4,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,1,2,3,5]=>[1,8,5,2,4,7,3,6]=>[8,1,4,7,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,5,1,4,7,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,1,3,7,8]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,1,2,7,8]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,1,3,7,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,1,4,6,8]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,1,3,6,8]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,1,2,6,8]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,1,4,5,8]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,1,2,5,8]=>[1,4,6,2,7,5,3,8]=>[8,5,3,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,1,3,4,8]=>[1,5,2,7,4,6,3,8]=>[8,4,7,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,1,2,4,8]=>[1,5,2,7,4,6,3,8]=>[8,4,7,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,1,3,6,7]=>[1,4,5,2,8,7,6,3]=>[8,5,4,7,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,1,3,6,7]=>[1,5,2,8,7,6,3,4]=>[8,4,7,1,2,3,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,1,2,6,7]=>[1,5,2,8,7,6,3,4]=>[8,4,7,1,2,3,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,1,3,5,7]=>[1,4,6,3,2,8,7,5]=>[8,5,3,6,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,1,2,4,7]=>[1,5,2,8,7,4,6,3]=>[8,4,7,1,2,5,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,1,2,3,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,1,2,5,7]=>[1,6,2,8,7,5,3,4]=>[8,3,7,1,2,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,1,3,5,6]=>[1,4,7,5,2,8,6,3]=>[8,5,2,4,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,1,2,5,6]=>[1,4,7,5,2,8,6,3]=>[8,5,2,4,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,1,3,4,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,1,2,4,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,1,2,3,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,1,2,4,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,1,2,3,4]=>[1,6,2,8,4,7,3,5]=>[8,3,7,1,5,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,1,3,5,6]=>[1,7,5,2,8,6,3,4]=>[8,2,4,7,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,1,5,7,8]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,4,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,1,4,7,8]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,4,6,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,1,2,6,8]=>[1,5,2,4,7,6,3,8]=>[8,4,7,5,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,1,3,5,8]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,1,2,5,8]=>[1,6,2,4,7,5,3,8]=>[8,3,7,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,1,2,4,8]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,1,4,6,8]=>[1,7,6,4,5,2,3,8]=>[8,2,3,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,1,4,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,1,3,4,8]=>[1,7,4,6,3,2,5,8]=>[8,2,5,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,1,2,4,8]=>[1,7,4,5,2,6,3,8]=>[8,2,5,4,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,4,6,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,1,2,6,7]=>[1,5,2,4,8,7,6,3]=>[8,4,7,5,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,1,4,5,7]=>[1,6,4,8,7,5,2,3]=>[8,3,5,1,2,4,7,6]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,1,3,5,7]=>[1,6,3,2,4,8,7,5]=>[8,3,6,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,1,2,5,7]=>[1,6,2,4,8,7,5,3]=>[8,3,7,5,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,1,2,4,7]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,1,2,3,7]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,1,4,5,6]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,1,2,4,6]=>[1,7,4,8,6,2,5,3]=>[8,2,5,1,3,7,4,6]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,1,2,3,6]=>[1,7,3,4,8,6,2,5]=>[8,2,6,5,1,3,7,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,1,3,6,7]=>[1,8,7,6,3,2,4,5]=>[8,1,2,3,6,7,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,1,4,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,1,2,4,7]=>[1,8,7,4,6,2,5,3]=>[8,1,2,5,3,7,4,6]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,1,3,4,6]=>[1,8,6,3,2,5,4,7]=>[8,1,3,6,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,1,2,4,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,1,2,3,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,1,2,4,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,1,3,5,6]=>[1,8,6,3,2,7,5,4]=>[8,1,3,6,7,2,4,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,1,3,4,5]=>[1,8,5,2,7,4,6,3]=>[8,1,4,7,2,5,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,1,2,4,5]=>[1,8,5,2,7,4,6,3]=>[8,1,4,7,2,5,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,1,2,3,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,8,1,2,7]=>[1,4,5,8,7,2,6,3]=>[8,5,4,1,2,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,8,1,3,7]=>[1,5,8,7,3,2,6,4]=>[8,4,1,2,6,7,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,8,1,3,6]=>[1,4,5,8,6,2,7,3]=>[8,5,4,1,3,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,8,1,2,6]=>[1,4,5,8,6,2,7,3]=>[8,5,4,1,3,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,8,1,3,6]=>[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,8,1,2,6]=>[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,8,1,4,5]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,8,1,2,5]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,8,1,3,4]=>[1,5,8,4,6,2,7,3]=>[8,4,1,5,3,7,2,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,4,8,1,2,5]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,8,1,2,4]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,7,1,3,6]=>[1,4,5,7,3,2,8,6]=>[8,5,4,2,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,7,1,3,6]=>[1,5,7,3,2,8,6,4]=>[8,4,2,6,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,7,1,4,5]=>[1,3,2,8,5,7,4,6]=>[8,6,7,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,7,1,2,5]=>[1,4,6,2,8,5,7,3]=>[8,5,3,7,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,7,1,3,4]=>[1,5,7,3,2,8,4,6]=>[8,4,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,7,1,2,3]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,7,1,2,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,6,1,2,5]=>[1,7,2,8,5,6,3,4]=>[8,2,7,1,4,3,6,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,6,1,2,4]=>[1,7,2,8,4,5,6,3]=>[8,2,7,1,5,4,3,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,8,1,5,7]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,8,1,4,7]=>[1,5,8,7,4,6,2,3]=>[8,4,1,2,5,3,7,6]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,8,1,3,7]=>[1,5,8,7,3,2,4,6]=>[8,4,1,2,6,7,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,8,1,2,7]=>[1,5,8,7,2,4,6,3]=>[8,4,1,2,7,5,3,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,8,1,2,7]=>[1,6,2,4,5,8,7,3]=>[8,3,7,5,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,7,8,1,5,6]=>[1,4,7,5,8,6,2,3]=>[8,5,2,4,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,8,1,4,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,8,1,3,6]=>[1,5,8,6,2,4,7,3]=>[8,4,1,3,7,5,2,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,8,1,2,6]=>[1,5,8,6,2,4,7,3]=>[8,4,1,3,7,5,2,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,8,1,3,5]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,8,1,2,5]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,8,1,3,4]=>[1,6,2,5,8,4,7,3]=>[8,3,7,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,8,1,3,6]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,8,1,2,6]=>[1,7,2,4,5,8,6,3]=>[8,2,7,5,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,8,1,2,6]=>[1,7,2,5,8,6,3,4]=>[8,2,7,4,1,3,6,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,1,4,5]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,8,1,3,4]=>[1,7,3,2,5,8,4,6]=>[8,2,6,7,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,8,1,2,4]=>[1,7,2,5,8,4,6,3]=>[8,2,7,4,1,5,3,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,8,1,2,4]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,7,1,4,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,7,1,3,6]=>[1,8,6,2,5,7,3,4]=>[8,1,3,7,4,2,6,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,7,1,4,5]=>[1,8,5,7,4,6,2,3]=>[8,1,4,2,5,3,7,6]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,7,1,3,5]=>[1,8,5,7,3,2,4,6]=>[8,1,4,2,6,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,7,1,3,4]=>[1,8,4,6,2,5,7,3]=>[8,1,5,3,7,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,7,1,2,4]=>[1,8,4,6,2,5,7,3]=>[8,1,5,3,7,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,1,3,5]=>[1,8,5,7,3,2,6,4]=>[8,1,4,2,6,7,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,7,1,2,4]=>[1,8,4,5,7,2,6,3]=>[8,1,5,4,2,7,3,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,6,1,3,5]=>[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,6,1,2,5]=>[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,6,1,3,4]=>[1,8,4,5,6,2,7,3]=>[8,1,5,4,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,6,1,2,4]=>[1,8,4,5,6,2,7,3]=>[8,1,5,4,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,1,5,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,6,1,3,8]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,5,1,4,8]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,5,1,3,8]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,5,1,2,8]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,6,1,5,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,5,1,4,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,5,1,3,7]=>[1,6,2,4,3,8,7,5]=>[8,3,7,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,5,1,2,7]=>[1,6,2,4,3,8,7,5]=>[8,3,7,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,4,1,3,7]=>[1,6,2,5,4,3,8,7]=>[8,3,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,4,1,2,7]=>[1,6,2,5,4,3,8,7]=>[8,3,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,7,1,2,6]=>[1,5,7,2,4,3,8,6]=>[8,4,2,7,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,7,1,3,5]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,7,1,2,5]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,7,1,3,4]=>[1,6,2,5,7,3,8,4]=>[8,3,7,4,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,5,1,2,6]=>[1,7,2,4,3,8,6,5]=>[8,2,7,5,6,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,4,1,2,6]=>[1,7,2,5,4,3,8,6]=>[8,2,7,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,6,1,3,5]=>[1,7,3,8,5,6,2,4]=>[8,2,6,1,4,3,7,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,5,1,3,4]=>[1,7,3,8,4,2,6,5]=>[8,2,6,1,5,7,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,5,1,2,4]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,5,1,3,7]=>[1,8,7,3,6,2,4,5]=>[8,1,2,6,3,7,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,4,1,3,7]=>[1,8,7,3,6,2,5,4]=>[8,1,2,6,3,7,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,5,1,2,6]=>[1,8,6,2,4,3,7,5]=>[8,1,3,7,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,4,1,3,6]=>[1,8,6,2,5,4,3,7]=>[8,1,3,7,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,1,3,5]=>[1,8,5,6,2,4,3,7]=>[8,1,4,3,7,5,6,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,1,2,5]=>[1,8,5,6,2,4,3,7]=>[8,1,4,3,7,5,6,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,4,1,3,5]=>[1,8,5,4,2,6,3,7]=>[8,1,4,5,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,1,3,4]=>[1,8,4,2,6,3,7,5]=>[8,1,5,7,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,7,1,6,8]=>[1,5,7,6,2,4,3,8]=>[8,4,2,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,7,1,5,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,7,1,4,8]=>[1,6,2,5,7,4,3,8]=>[8,3,7,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,7,1,3,8]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,6,1,4,8]=>[1,7,4,2,5,6,3,8]=>[8,2,5,7,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,6,1,3,8]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,5,1,4,8]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,8,1,6,7]=>[1,5,8,7,6,2,4,3]=>[8,4,1,2,3,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,8,1,4,7]=>[1,6,2,5,8,7,4,3]=>[8,3,7,4,1,2,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,8,1,4,6]=>[1,7,4,2,5,8,6,3]=>[8,2,5,7,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,8,1,3,6]=>[1,7,3,4,2,5,8,6]=>[8,2,6,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,8,1,4,5]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,1,2,5]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,8,1,3,4]=>[1,7,3,5,8,4,2,6]=>[8,2,6,4,1,5,7,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,6,1,3,7]=>[1,8,7,3,4,2,5,6]=>[8,1,2,6,5,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,5,1,4,7]=>[1,8,7,4,2,6,3,5]=>[8,1,2,5,7,3,6,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,5,1,3,7]=>[1,8,7,3,4,2,6,5]=>[8,1,2,6,5,7,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,4,1,3,7]=>[1,8,7,3,5,4,2,6]=>[8,1,2,6,4,5,7,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,7,1,4,6]=>[1,8,6,2,5,7,4,3]=>[8,1,3,7,4,2,5,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,7,1,4,5]=>[1,8,5,7,4,2,6,3]=>[8,1,4,2,5,7,3,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,7,1,3,5]=>[1,8,5,7,3,4,2,6]=>[8,1,4,2,6,5,7,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,1,2,5]=>[1,8,5,7,2,6,3,4]=>[8,1,4,2,7,3,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,5,1,4,6]=>[1,8,6,2,7,4,3,5]=>[8,1,3,7,2,5,6,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,6,1,4,5]=>[1,8,5,6,2,7,4,3]=>[8,1,4,3,7,2,5,6]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,1,3,5]=>[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,1,2,5]=>[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,6,1,3,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,2,6,1,4]=>[1,5,2,8,4,7,3,6]=>[8,4,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,2,5,1,3]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,2,4,1,3]=>[1,6,4,7,2,8,3,5]=>[8,3,5,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,3,4,1,2]=>[1,6,4,7,2,8,3,5]=>[8,3,5,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,2,5,1,4]=>[1,7,2,8,4,6,5,3]=>[8,2,7,1,5,3,4,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,4,1,3]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,2,7,1,6]=>[1,5,2,4,8,6,7,3]=>[8,4,7,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,2,7,1,4]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,2,7,1,3]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,3,7,1,2]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,2,6,1,5]=>[1,7,2,4,8,5,3,6]=>[8,2,7,5,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,2,6,1,4]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,2,6,1,3]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,2,5,1,4]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,8,2,5,1,3]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,2,6,1,5]=>[1,8,5,2,4,7,3,6]=>[8,1,4,7,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,2,6,1,4]=>[1,8,4,7,2,5,3,6]=>[8,1,5,2,7,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,2,6,1,3]=>[1,8,3,4,7,2,5,6]=>[8,1,6,5,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,2,5,1,4]=>[1,8,4,7,2,6,5,3]=>[8,1,5,2,7,3,4,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,2,5,1,3]=>[1,8,3,4,7,2,6,5]=>[8,1,6,5,2,7,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,2,4,1,3]=>[1,8,3,5,2,6,4,7]=>[8,1,6,4,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,2,5,1,4]=>[1,8,4,6,5,2,7,3]=>[8,1,5,3,4,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,2,5,1,3]=>[1,8,3,4,6,5,2,7]=>[8,1,6,5,3,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,2,4,1,3]=>[1,8,3,5,2,7,4,6]=>[8,1,6,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,2,8,1,3]=>[1,7,2,6,8,3,5,4]=>[8,2,7,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,7,1,6]=>[1,8,6,7,2,5,3,4]=>[8,1,3,2,7,4,6,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,2,7,1,4]=>[1,8,4,3,5,2,6,7]=>[8,1,5,6,4,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,7,1,3]=>[1,8,3,5,2,6,7,4]=>[8,1,6,4,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,2,6,1,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,2,6,1,4]=>[1,8,4,3,5,2,7,6]=>[8,1,5,6,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,2,6,1,3]=>[1,8,3,5,2,7,4,6]=>[8,1,6,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,2,5,1,3]=>[1,8,3,6,5,2,7,4]=>[8,1,6,3,4,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,4,1,3]=>[1,8,3,6,4,5,2,7]=>[8,1,6,3,5,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,4,5,7]=>[1,8,7,5,6,4,3,2]=>[8,1,2,4,3,5,6,7]=>[8,2,3,5,4,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,7,4,5,6]=>[1,8,6,4,3,2,5,7]=>[8,1,3,5,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,8,7,4,6]=>[1,5,8,6,7,4,3,2]=>[8,4,1,3,2,5,6,7]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,7,4,5]=>[1,8,5,6,7,4,3,2]=>[8,1,4,3,2,5,6,7]=>[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,3,7,5,6]=>[1,4,8,6,7,5,3,2]=>[8,5,1,3,2,4,6,7]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,3,4,5,7]=>[1,8,7,5,3,2,4,6]=>[8,1,2,4,6,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,3,8,4,7]=>[1,6,8,7,4,5,3,2]=>[8,3,1,2,5,4,6,7]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,3,7,4,6]=>[1,8,6,7,4,5,3,2]=>[8,1,3,2,5,4,6,7]=>[8,2,4,3,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,3,7,8,4]=>[1,6,7,8,4,5,3,2]=>[8,3,2,1,5,4,6,7]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,6,3,5,7]=>[1,4,8,7,5,6,3,2]=>[8,5,1,2,4,3,6,7]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,6,3,8,5]=>[1,4,7,8,5,6,3,2]=>[8,5,2,1,4,3,6,7]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,6,3,4,7]=>[1,8,7,4,5,6,3,2]=>[8,1,2,5,4,3,6,7]=>[8,2,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,7,3,4,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,8,7,3,6]=>[1,4,5,8,6,7,3,2]=>[8,5,4,1,3,2,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,6,7,3,4]=>[1,8,4,5,6,7,3,2]=>[8,1,5,4,3,2,6,7]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,4,7,5,6]=>[1,3,8,6,7,5,4,2]=>[8,6,1,3,2,4,5,7]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,6,4,5,7]=>[1,3,8,7,5,6,4,2]=>[8,6,1,2,4,3,5,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,7,4,5,6]=>[1,3,8,6,4,2,5,7]=>[8,6,1,3,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,6,4,8,5]=>[1,3,7,8,5,6,4,2]=>[8,6,2,1,4,3,5,7]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,8,7,4,6]=>[1,3,5,8,6,7,4,2]=>[8,6,4,1,3,2,5,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,6,7,4,5]=>[1,3,8,5,6,7,4,2]=>[8,6,1,4,3,2,5,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,3,5,6,7]=>[1,8,7,6,5,3,4,2]=>[8,1,2,3,4,6,5,7]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,3,8,5,7]=>[1,6,8,7,5,3,4,2]=>[8,3,1,2,4,6,5,7]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,3,7,8,5]=>[1,6,7,8,5,3,4,2]=>[8,3,2,1,4,6,5,7]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,3,4,6,7]=>[1,8,7,6,4,2,3,5]=>[8,1,2,3,5,7,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,3,4,5,6]=>[1,8,6,4,2,3,7,5]=>[8,1,3,5,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,3,8,4,7]=>[1,6,8,7,4,2,3,5]=>[8,3,1,2,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,3,7,4,5]=>[1,6,7,4,2,3,8,5]=>[8,3,2,5,7,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,3,7,8,4]=>[1,6,7,8,4,2,3,5]=>[8,3,2,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,7,3,8,6]=>[1,5,7,8,6,3,4,2]=>[8,4,2,1,3,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,3,5,7]=>[1,8,7,5,6,3,4,2]=>[8,1,2,4,3,6,5,7]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,7,3,5,6]=>[1,8,6,3,4,2,5,7]=>[8,1,3,6,5,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,6,3,8,5]=>[1,7,8,5,6,3,4,2]=>[8,2,1,4,3,6,5,7]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,6,3,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,6,8,3,7]=>[1,5,6,8,7,3,4,2]=>[8,4,3,1,2,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,8,7,3,6]=>[1,5,8,6,7,3,4,2]=>[8,4,1,3,2,6,5,7]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,7,3,5]=>[1,8,5,6,7,3,4,2]=>[8,1,4,3,2,6,5,7]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,6,7,3,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,6,7,8,3]=>[1,5,6,7,8,3,4,2]=>[8,4,3,2,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,2,7,5,6]=>[1,3,4,8,6,7,5,2]=>[8,6,5,1,3,2,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,2,4,6,7]=>[1,3,8,7,6,4,5,2]=>[8,6,1,2,3,5,4,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,2,4,8,6]=>[1,3,7,8,6,4,5,2]=>[8,6,2,1,3,5,4,7]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,2,8,4,7]=>[1,3,6,8,7,4,5,2]=>[8,6,3,1,2,5,4,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,2,7,8,4]=>[1,3,6,7,8,4,5,2]=>[8,6,3,2,1,5,4,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,2,3,6,7]=>[1,8,7,6,3,4,5,2]=>[8,1,2,3,6,5,4,7]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,2,3,8,6]=>[1,7,8,6,3,4,5,2]=>[8,2,1,3,6,5,4,7]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,2,3,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,2,3,5,6]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,2,3,4,6]=>[1,7,4,5,2,3,8,6]=>[8,2,5,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,2,3,4,5]=>[1,7,4,6,3,8,5,2]=>[8,2,5,3,6,1,4,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,2,8,3,7]=>[1,6,8,7,3,4,5,2]=>[8,3,1,2,6,5,4,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,2,7,3,6]=>[1,8,6,7,3,4,5,2]=>[8,1,3,2,6,5,4,7]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,2,7,3,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,2,7,3,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,2,7,8,3]=>[1,6,7,8,3,4,5,2]=>[8,3,2,1,6,5,4,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,6,2,5,7]=>[1,3,4,8,7,5,6,2]=>[8,6,5,1,2,4,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,7,2,5,6]=>[1,3,4,8,6,2,5,7]=>[8,6,5,1,3,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,6,2,8,5]=>[1,3,4,7,8,5,6,2]=>[8,6,5,2,1,4,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,6,2,4,7]=>[1,3,8,7,4,5,6,2]=>[8,6,1,2,5,4,3,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,6,2,4,5]=>[1,3,8,5,6,2,4,7]=>[8,6,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,6,2,8,4]=>[1,3,7,8,4,5,6,2]=>[8,6,2,1,5,4,3,7]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,6,2,3,7]=>[1,8,7,3,4,5,6,2]=>[8,1,2,6,5,4,3,7]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,7,2,3,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,6,2,3,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,2,3,4]=>[1,8,4,5,6,2,3,7]=>[8,1,5,4,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,8,7,2,6]=>[1,3,4,5,8,6,7,2]=>[8,6,5,4,1,3,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,6,7,2,5]=>[1,3,4,8,5,6,7,2]=>[8,6,5,1,4,3,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,6,7,2,4]=>[1,3,8,4,5,6,7,2]=>[8,6,1,5,4,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,6,7,2,3]=>[1,8,3,4,5,6,7,2]=>[8,1,6,5,4,3,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,7,5,6]=>[1,2,8,6,7,5,4,3]=>[8,7,1,3,2,4,5,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,6,4,5,7]=>[1,2,8,7,5,6,4,3]=>[8,7,1,2,4,3,5,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,6,4,8,5]=>[1,2,7,8,5,6,4,3]=>[8,7,2,1,4,3,5,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,6,7,4,5]=>[1,2,8,5,6,7,4,3]=>[8,7,1,4,3,2,5,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,3,4,8,6]=>[1,2,7,8,6,4,5,3]=>[8,7,2,1,3,5,4,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,3,4,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,3,7,4,6]=>[1,2,8,6,7,4,5,3]=>[8,7,1,3,2,5,4,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,3,7,4,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,3,7,8,4]=>[1,2,6,7,8,4,5,3]=>[8,7,3,2,1,5,4,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,6,3,5,7]=>[1,2,4,8,7,5,6,3]=>[8,7,5,1,2,4,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,6,3,4,7]=>[1,2,8,7,4,5,6,3]=>[8,7,1,2,5,4,3,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,7,3,4,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,6,3,4,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,6,3,8,4]=>[1,2,7,8,4,5,6,3]=>[8,7,2,1,5,4,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,8,7,3,6]=>[1,2,4,5,8,6,7,3]=>[8,7,5,4,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,6,7,3,5]=>[1,2,4,8,5,6,7,3]=>[8,7,5,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,4,5,8,6]=>[1,7,8,6,5,4,2,3]=>[8,2,1,3,4,5,7,6]=>[8,3,2,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,4,8,5,7]=>[1,6,8,7,5,4,2,3]=>[8,3,1,2,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,4,7,8,5]=>[1,6,7,8,5,4,2,3]=>[8,3,2,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,7,4,8,6]=>[1,5,7,8,6,4,2,3]=>[8,4,2,1,3,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,6,4,5,7]=>[1,8,7,5,6,4,2,3]=>[8,1,2,4,3,5,7,6]=>[8,2,3,5,4,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,7,4,5,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,6,8,4,7]=>[1,5,6,8,7,4,2,3]=>[8,4,3,1,2,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,8,7,4,6]=>[1,5,8,6,7,4,2,3]=>[8,4,1,3,2,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,6,7,4,5]=>[1,8,5,6,7,4,2,3]=>[8,1,4,3,2,5,7,6]=>[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,6,7,8,4]=>[1,5,6,7,8,4,2,3]=>[8,4,3,2,1,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,3,8,5,7]=>[1,6,8,7,5,3,2,4]=>[8,3,1,2,4,6,7,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,3,4,8,5]=>[1,7,8,5,3,2,6,4]=>[8,2,1,4,6,7,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,3,7,4,6]=>[1,5,3,2,8,6,7,4]=>[8,4,6,7,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,3,7,4,5]=>[1,8,5,3,2,6,7,4]=>[8,1,4,6,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,8,3,6,7]=>[1,5,8,7,6,3,2,4]=>[8,4,1,2,3,6,7,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,7,3,8,6]=>[1,5,7,8,6,3,2,4]=>[8,4,2,1,3,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,6,3,5,7]=>[1,8,7,5,6,3,2,4]=>[8,1,2,4,3,6,7,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,3,5,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,7,3,4,6]=>[1,5,7,4,2,8,6,3]=>[8,4,2,5,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,6,3,4,5]=>[1,8,5,6,3,2,7,4]=>[8,1,4,3,6,7,2,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,6,3,8,4]=>[1,5,6,3,2,7,8,4]=>[8,4,3,6,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,6,8,3,7]=>[1,5,6,8,7,3,2,4]=>[8,4,3,1,2,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,8,7,3,6]=>[1,5,8,6,7,3,2,4]=>[8,4,1,3,2,6,7,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,6,7,3,5]=>[1,8,5,6,7,3,2,4]=>[8,1,4,3,2,6,7,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,6,7,3,4]=>[1,5,6,7,3,2,8,4]=>[8,4,3,2,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,6,7,8,3]=>[1,5,6,7,8,3,2,4]=>[8,4,3,2,1,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,2,8,5,7]=>[1,4,6,8,7,5,2,3]=>[8,5,3,1,2,4,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,2,7,5,6]=>[1,4,8,6,7,5,2,3]=>[8,5,1,3,2,4,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,2,7,8,5]=>[1,4,6,7,8,5,2,3]=>[8,5,3,2,1,4,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,2,4,8,6]=>[1,7,8,6,4,5,2,3]=>[8,2,1,3,5,4,7,6]=>[8,3,2,4,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,4,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,2,4,5,6]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,2,8,4,7]=>[1,6,8,7,4,5,2,3]=>[8,3,1,2,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,2,7,4,6]=>[1,8,6,7,4,5,2,3]=>[8,1,3,2,5,4,7,6]=>[8,2,4,3,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,7,4,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,2,7,8,4]=>[1,6,7,8,4,5,2,3]=>[8,3,2,1,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,2,3,6,7]=>[1,8,7,6,3,2,4,5]=>[8,1,2,3,6,7,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,3,4,5]=>[1,8,5,2,7,4,6,3]=>[8,1,4,7,2,5,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,2,3,8,4]=>[1,6,3,2,7,8,4,5]=>[8,3,6,7,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,2,7,3,6]=>[1,8,6,7,3,2,4,5]=>[8,1,3,2,6,7,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,8,2,6,7]=>[1,4,5,8,7,6,2,3]=>[8,5,4,1,2,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,7,2,8,6]=>[1,4,5,7,8,6,2,3]=>[8,5,4,2,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,6,2,5,7]=>[1,4,8,7,5,6,2,3]=>[8,5,1,2,4,3,7,6]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,7,2,5,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,7,6,2,8,5]=>[1,4,7,8,5,6,2,3]=>[8,5,2,1,4,3,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,7,2,4,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,2,4,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,2,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,6,2,8,3]=>[1,7,8,3,2,4,5,6]=>[8,2,1,6,7,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,8,7,2,6]=>[1,4,5,8,6,7,2,3]=>[8,5,4,1,3,2,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,6,7,2,4]=>[1,8,4,5,6,7,2,3]=>[8,1,5,4,3,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,7,2,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,6,7,8,2]=>[1,4,5,6,7,8,2,3]=>[8,5,4,3,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,4,7,5,6]=>[1,2,3,8,6,7,5,4]=>[8,7,6,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,6,4,5,7]=>[1,2,3,8,7,5,6,4]=>[8,7,6,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,7,4,5,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,6,4,8,5]=>[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,8,7,4,6]=>[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,6,7,4,5]=>[1,2,3,8,5,6,7,4]=>[8,7,6,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,3,5,6,7]=>[1,2,8,7,6,5,3,4]=>[8,7,1,2,3,4,6,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,3,5,8,6]=>[1,2,7,8,6,5,3,4]=>[8,7,2,1,3,4,6,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,3,8,5,7]=>[1,2,6,8,7,5,3,4]=>[8,7,3,1,2,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,3,7,5,6]=>[1,2,8,6,7,5,3,4]=>[8,7,1,3,2,4,6,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,3,7,8,5]=>[1,2,6,7,8,5,3,4]=>[8,7,3,2,1,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,3,4,8,6]=>[1,2,7,8,6,4,3,5]=>[8,7,2,1,3,5,6,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,3,4,5,6]=>[1,2,8,6,4,3,7,5]=>[8,7,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,3,8,4,7]=>[1,2,6,8,7,4,3,5]=>[8,7,3,1,2,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,3,7,4,6]=>[1,2,8,6,7,4,3,5]=>[8,7,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,3,7,4,5]=>[1,2,6,7,4,3,8,5]=>[8,7,3,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,3,7,8,4]=>[1,2,6,7,8,4,3,5]=>[8,7,3,2,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,8,3,6,7]=>[1,2,5,8,7,6,3,4]=>[8,7,4,1,2,3,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,7,3,8,6]=>[1,2,5,7,8,6,3,4]=>[8,7,4,2,1,3,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,6,3,5,7]=>[1,2,8,7,5,6,3,4]=>[8,7,1,2,4,3,6,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,7,3,5,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,6,3,8,5]=>[1,2,7,8,5,6,3,4]=>[8,7,2,1,4,3,6,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,6,3,4,5]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,8,7,3,6]=>[1,2,5,8,6,7,3,4]=>[8,7,4,1,3,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,6,7,3,5]=>[1,2,8,5,6,7,3,4]=>[8,7,1,4,3,2,6,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,6,7,3,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,6,7,8,3]=>[1,2,5,6,7,8,3,4]=>[8,7,4,3,2,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,2,8,5,7]=>[1,6,8,7,5,2,3,4]=>[8,3,1,2,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,2,7,8,5]=>[1,6,7,8,5,2,3,4]=>[8,3,2,1,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,2,4,8,5]=>[1,6,4,2,3,7,8,5]=>[8,3,5,7,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,2,8,4,7]=>[1,6,8,7,4,2,3,5]=>[8,3,1,2,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,2,7,4,5]=>[1,6,7,4,2,3,8,5]=>[8,3,2,5,7,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,2,7,8,4]=>[1,6,7,8,4,2,3,5]=>[8,3,2,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,2,3,8,6]=>[1,7,8,6,3,4,2,5]=>[8,2,1,3,6,5,7,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,2,3,4,7]=>[1,6,3,5,2,8,7,4]=>[8,3,6,4,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,2,7,3,6]=>[1,8,6,7,3,4,2,5]=>[8,1,3,2,6,5,7,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,2,7,3,5]=>[1,6,7,3,4,2,8,5]=>[8,3,2,6,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,2,7,3,4]=>[1,6,7,3,5,2,8,4]=>[8,3,2,6,4,7,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,2,7,8,3]=>[1,6,7,8,3,4,2,5]=>[8,3,2,1,6,5,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,7,2,8,6]=>[1,5,7,8,6,2,3,4]=>[8,4,2,1,3,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,6,2,5,7]=>[1,8,7,5,6,2,3,4]=>[8,1,2,4,3,7,6,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,7,2,5,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,6,2,8,5]=>[1,7,8,5,6,2,3,4]=>[8,2,1,4,3,7,6,5]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,7,2,4,6]=>[1,8,6,2,3,5,7,4]=>[8,1,3,7,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,6,2,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,6,2,3,7]=>[1,8,7,3,4,2,5,6]=>[8,1,2,6,5,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,7,2,3,6]=>[1,8,6,2,5,7,3,4]=>[8,1,3,7,4,2,6,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,6,2,3,5]=>[1,7,3,4,2,8,5,6]=>[8,2,6,5,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,6,2,8,3]=>[1,7,8,3,4,2,5,6]=>[8,2,1,6,5,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,6,8,2,7]=>[1,5,6,8,7,2,3,4]=>[8,4,3,1,2,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,8,7,2,6]=>[1,5,8,6,7,2,3,4]=>[8,4,1,3,2,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,6,7,2,5]=>[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,6,7,2,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,6,7,2,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,6,7,8,2]=>[1,5,6,7,8,2,3,4]=>[8,4,3,2,1,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,1,7,5,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,1,4,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,1,4,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,1,7,4,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,1,7,4,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,1,7,8,4]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,1,3,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,1,3,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,1,3,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,1,3,4,7]=>[1,2,8,7,4,5,3,6]=>[8,7,1,2,5,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,1,3,4,6]=>[1,2,7,4,5,3,8,6]=>[8,7,2,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,1,3,4,5]=>[1,2,7,4,6,3,8,5]=>[8,7,2,5,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,1,3,8,4]=>[1,2,7,8,4,5,3,6]=>[8,7,2,1,5,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,1,7,3,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,1,7,3,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,1,7,8,3]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,1,2,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,1,2,4,6]=>[1,7,4,5,2,3,8,6]=>[8,2,5,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,1,2,8,3]=>[1,7,8,3,4,5,2,6]=>[8,2,1,6,5,4,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,1,8,2,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,1,7,2,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,1,7,2,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,1,7,2,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,1,7,8,2]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,1,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,7,1,5,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,6,1,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,6,1,4,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,7,1,4,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,6,1,4,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,6,1,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,7,1,3,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,6,1,3,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,6,1,8,3]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,7,1,2,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,6,1,2,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,1,2,4]=>[1,8,4,5,6,2,3,7]=>[8,1,5,4,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,6,1,8,2]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,7,1,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,7,1,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,6,7,1,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,6,7,1,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>[9,1,2,3,4,5,6,7,8]=>[9,2,3,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,9,7]=>[1,8,9,7,6,5,4,3,2]=>[9,2,1,3,4,5,6,7,8]=>[9,3,2,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,9,6,8]=>[1,7,9,8,6,5,4,3,2]=>[9,3,1,2,4,5,6,7,8]=>[9,4,3,2,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,2,5,6,7,8,9,3]=>[1,4,5,6,7,8,9,3,2]=>[9,6,5,4,3,2,1,7,8]=>[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,5,2,7,4,9,6,8]=>[1,3,5,7,9,8,6,4,2]=>[9,7,5,3,1,2,4,6,8]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,9,2,8]=>[1,3,4,5,6,7,9,8,2]=>[9,7,6,5,4,3,1,2,8]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,9,2]=>[1,3,4,5,6,7,8,9,2]=>[9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,1,5,9,3,6,7,8]=>[1,2,4,5,9,8,7,6,3]=>[9,8,6,5,1,2,3,4,7]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,1,5,6,7,8,9,3]=>[1,2,4,5,6,7,8,9,3]=>[9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,1,2,4,5,6,7,8]=>[1,9,8,7,6,5,4,2,3]=>[9,1,2,3,4,5,6,8,7]=>[9,2,3,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,1,5,6,7,8,2,3]=>[1,9,3,2,4,5,6,7,8]=>[9,1,7,8,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,3,1,5,6,7,8,9,2]=>[1,4,5,6,7,8,9,2,3]=>[9,6,5,4,3,2,1,8,7]=>[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,9,1,4,5,6,7,8]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,5,1,6,7,8,9,4]=>[1,2,3,5,6,7,8,9,4]=>[9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,9,5,1,6,7,8,3,4]=>[1,2,9,4,3,5,6,7,8]=>[9,8,1,6,7,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,9,1,5,6,7,8]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,6,1,7,8,9,5]=>[1,2,3,4,6,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,9,6,1,7,8,4,5]=>[1,2,3,9,5,4,6,7,8]=>[9,8,7,1,5,6,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,9,1,6,7,8]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,6,5,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,8,1,6,9,7]=>[1,2,3,4,5,8,9,7,6]=>[9,8,7,6,5,2,1,3,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,1,8,9,6]=>[1,2,3,4,5,7,8,9,6]=>[9,8,7,6,5,3,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,9,7,1,8,5,6]=>[1,2,3,4,9,6,5,7,8]=>[9,8,7,6,1,4,5,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,9,1,7,8]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,1,9,7]=>[1,2,3,4,5,6,8,9,7]=>[9,8,7,6,5,4,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,9,8,1,6,7]=>[1,2,3,4,5,9,7,6,8]=>[9,8,7,6,5,1,3,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,9,1,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,9,8,1,7]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,9,7,8,1,6]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,9,6,7,8,1,5]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,9,5,6,7,8,1,4]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,9,4,5,6,7,8,1,3]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,4,5,6,7,8,1,2]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,1]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[]=>[]=>[]=>[]=>[]
[3,5,2,6,1,4,8,7]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,4,1,8,7]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,4,8,1,6]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,4,8,6,1]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,3,8,6,1]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,3,8,1,6]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,3,1,8,7]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,1,3,8,7]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,4,2,8,7]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,3,2,8,7]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,1,2,8,7]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,2,8,1,6]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,2,8,6,1]=>[1,4,3,7,6,8,2,5]=>[8,5,6,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,2,5,1]=>[1,4,3,7,5,8,2,6]=>[8,5,6,2,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,2,1,5]=>[1,4,3,7,2,6,5,8]=>[8,5,6,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,1,2,5]=>[1,4,3,7,2,6,5,8]=>[8,5,6,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,1,8,2,6]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,3,8,2,6]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,4,8,2,6]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,4,8,3,6]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,4,8,6,3]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,4,8,6,2]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,3,8,6,2]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,1,8,6,2]=>[1,4,3,7,6,8,2,5]=>[8,5,6,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,1,5,2]=>[1,4,3,7,5,8,2,6]=>[8,5,6,2,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,5,1,2]=>[1,4,3,7,2,6,5,8]=>[8,5,6,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,5,2,1]=>[1,4,3,7,2,6,5,8]=>[8,5,6,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,1,4,2]=>[1,5,3,7,4,8,2,6]=>[8,4,6,2,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,3,4,2]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,3,5,2]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,8,4,5,2]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,4,5,3]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,4,3,5]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,8,4,2,5]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,3,2,5]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,3,2,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,1,8,3,6]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,1,3,5]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,3,1,5]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,3,5,1]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,8,4,5,1]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,8,4,1,5]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,8,1,4,5]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,1,8,4,6]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,7,8,5,6]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,7,8,6,5]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,1,8,6,4]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,8,1,5,4]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,8,5,1,4]=>[1,3,2,6,5,8,4,7]=>[8,6,7,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,8,5,4,1]=>[1,3,2,6,5,8,4,7]=>[8,6,7,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,5,3,1]=>[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,5,1,3]=>[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,1,5,3]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,1,8,6,3]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,2,8,6,3]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,2,8,6,4]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,3,8,6,4]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,3,5,4]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,8,2,5,4]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,2,5,3]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,2,4,3]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,1,4,3]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,4,1,3]=>[1,5,2,6,4,8,3,7]=>[8,4,7,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,4,3,1]=>[1,5,2,6,4,8,3,7]=>[8,4,7,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,4,2,3]=>[1,5,2,6,4,8,3,7]=>[8,4,7,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,5,2,3]=>[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,8,5,2,4]=>[1,3,2,6,5,8,4,7]=>[8,6,7,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,5,3,4]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,8,5,4,2]=>[1,3,2,6,5,8,4,7]=>[8,6,7,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,5,3,2]=>[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,4,3,2]=>[1,5,2,6,4,8,3,7]=>[8,4,7,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,1,3,2]=>[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,6,5,8,7,10,9]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,5,2,7,4,9,6,10,8,1]=>[1,3,2,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,5,6,4,3,8,7,10,9]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,4,5,2,3,1]=>[1,6,4,9,3,8,2,7,5,10]=>[10,5,7,2,8,3,9,4,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,3,4,5,2,1]=>[1,6,3,8,5,10,2,7,4,9]=>[10,5,8,3,6,1,9,4,7,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,3,4,5,1,2]=>[1,6,3,8,5,10,2,7,4,9]=>[10,5,8,3,6,1,9,4,7,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,1,3,4,5,2]=>[1,6,2,7,3,8,4,9,5,10]=>[10,5,9,4,8,3,7,2,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,2,3,4,1,5]=>[1,6,2,7,3,8,4,9,5,10]=>[10,5,9,4,8,3,7,2,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,2,3,4,5,1]=>[1,6,2,7,3,8,4,9,5,10]=>[10,5,9,4,8,3,7,2,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,9,10,8,7]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,8,7,3,4,1,2]=>[1,6,4,7,2,5,3,8]=>[8,3,5,2,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,5,8,1,2]=>[1,3,7,2,6,8,4,5]=>[8,6,2,7,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,5,1,8,3]=>[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,5,2,3,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,6,2,3,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,6,1,8,3]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,6,8,1,2]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,8,6,1,2]=>[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,7,6,1,2]=>[1,5,7,2,4,8,3,6]=>[8,4,2,7,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,7,5,1,2]=>[1,6,5,7,2,4,3,8]=>[8,3,4,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,5,7,1,2]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,6,7,1,2]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,8,7,1,2]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,1,8,7,4]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,8,1,7,3]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,6,1,7,3]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,5,1,7,3]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,5,1,6,3]=>[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,5,2,3,6]=>[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,5,2,3,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,6,2,3,7]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,8,6,5,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,2,6,4,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,2,5,4,7]=>[1,6,5,2,3,8,7,4]=>[8,3,4,7,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,2,5,4,6]=>[1,7,4,3,2,8,6,5]=>[8,2,5,6,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,1,5,6,4]=>[1,7,6,5,2,8,4,3]=>[8,2,3,4,7,1,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,1,5,7,4]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,1,6,7,4]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,7,5,4]=>[1,6,7,5,2,3,8,4]=>[8,3,2,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,6,5,4]=>[1,7,5,2,8,4,3,6]=>[8,2,4,7,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,6,1,5,3]=>[1,7,5,6,2,8,3,4]=>[8,2,4,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,7,1,6,3]=>[1,5,7,6,2,4,8,3]=>[8,4,2,3,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,8,1,6,3]=>[1,4,7,6,2,5,8,3]=>[8,5,2,3,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,1,6,8,4]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,2,6,4,8]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,2,5,4,8]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,1,5,8,4]=>[1,2,6,5,3,7,8,4]=>[8,7,3,4,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,1,8,5,4]=>[1,3,7,5,2,6,8,4]=>[8,6,2,4,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,1,4,3]=>[1,7,4,6,2,8,3,5]=>[8,2,5,3,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,1,2,3,4]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,7,2,3,6]=>[1,5,7,3,2,4,8,6]=>[8,4,2,6,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,7,2,3,5]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,2,6,4,5]=>[1,7,4,2,8,5,3,6]=>[8,2,5,7,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,2,7,4,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,7,5,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,8,5,7,6]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,3,4,7,6]=>[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,3,4,7,5]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,3,4,6,5]=>[1,7,6,4,2,8,5,3]=>[8,2,3,5,7,1,4,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,6,5,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,2,4,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,2,4,8,7]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,2,8,4,6]=>[1,7,4,5,2,3,6,8]=>[8,2,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,2,7,3,6]=>[1,8,6,7,3,5,2,4]=>[8,1,3,2,6,4,7,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,2,8,3,6]=>[1,7,3,5,2,4,6,8]=>[8,2,6,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,2,3,8,7]=>[1,6,3,5,2,4,7,8]=>[8,3,6,4,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,2,3,8,7]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,3,4,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,5,2,4,8,7]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,2,3,8,7]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,1,2,3,8,7]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,2,3,8,7]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,2,8,3,6]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,7,2,3,5]=>[1,8,5,7,3,4,2,6]=>[8,1,4,2,6,5,7,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,8,2,3,5]=>[1,7,3,4,2,6,5,8]=>[8,2,6,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,8,2,3,5]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,2,8,3,6]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,2,8,3,6]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,2,8,4,6]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,3,8,4,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,3,7,4,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,2,7,4,6]=>[1,3,2,8,6,7,4,5]=>[8,6,7,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,2,7,3,6]=>[1,4,2,8,6,7,3,5]=>[8,5,7,1,3,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,2,7,3,6]=>[1,5,2,8,6,7,3,4]=>[8,4,7,1,3,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,7,2,3,5]=>[1,6,2,8,5,7,3,4]=>[8,3,7,1,4,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,2,3,5]=>[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,1,2,3,4]=>[1,5,2,8,4,7,3,6]=>[8,4,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,7,2,3,5]=>[1,4,2,8,5,7,3,6]=>[8,5,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,7,2,4,5]=>[1,3,2,8,5,7,4,6]=>[8,6,7,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,3,4,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,8,3,4,5]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,8,2,4,5]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,8,2,3,5]=>[1,4,2,7,3,6,5,8]=>[8,5,7,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,1,2,3,4]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,2,8,3,6]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,8,2,3,5]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,8,2,3,5]=>[1,7,3,6,2,4,5,8]=>[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,2,3,5]=>[1,8,5,7,3,6,2,4]=>[8,1,4,2,6,3,7,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,7,2,4,5]=>[1,8,5,7,4,6,2,3]=>[8,1,4,2,5,3,7,6]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,8,2,4,5]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,8,2,4,5]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,2,8,4,6]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,7,8,5,6]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,7,5,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,8,7,5,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,7,2,4,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,6,2,4,5]=>[1,7,4,8,5,6,2,3]=>[8,2,5,1,4,3,7,6]=>[8,4,6,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,6,2,3,5]=>[1,8,5,6,2,4,3,7]=>[8,1,4,3,7,5,6,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,6,2,3,5]=>[1,7,3,8,5,6,2,4]=>[8,2,6,1,4,3,7,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,2,7,3,6]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,2,7,3,6]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,2,7,4,6]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,3,7,4,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,7,3,4,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,7,2,4,5]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,7,2,3,5]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,1,2,3,4]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,1,2,3,4]=>[1,7,3,8,4,6,2,5]=>[8,2,6,1,5,3,7,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,1,2,3,4]=>[1,8,4,6,2,5,3,7]=>[8,1,5,3,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,2,3,4]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,6,2,3,5]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,6,2,4,5]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,6,3,4,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,3,4,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,6,2,4,5]=>[1,3,2,8,5,6,4,7]=>[8,6,7,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,6,2,3,5]=>[1,4,2,8,5,6,3,7]=>[8,5,7,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,1,2,3,4]=>[1,5,2,8,4,6,3,7]=>[8,4,7,1,5,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,1,2,3,4]=>[1,6,2,8,4,5,3,7]=>[8,3,7,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,8,5,1,2]=>[1,6,5,8,2,4,3,7]=>[8,3,4,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,5,8,1,2]=>[1,6,8,2,4,3,7,5]=>[8,3,1,7,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,5,1,8,3]=>[1,6,2,4,3,7,8,5]=>[8,3,7,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,6,1,3,8]=>[1,5,6,2,4,7,3,8]=>[8,4,3,7,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,6,1,8,3]=>[1,5,6,2,4,7,8,3]=>[8,4,3,7,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,6,8,1,2]=>[1,5,6,8,2,4,7,3]=>[8,4,3,1,7,5,2,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,8,6,1,2]=>[1,5,8,2,4,7,3,6]=>[8,4,1,7,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,5,7,1,2]=>[1,6,7,2,4,3,8,5]=>[8,3,2,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,6,7,1,2]=>[1,5,6,7,2,4,8,3]=>[8,4,3,2,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,8,7,1,2]=>[1,5,8,2,4,6,7,3]=>[8,4,1,7,5,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,7,1,8,3]=>[1,5,7,8,3,2,4,6]=>[8,4,2,1,6,7,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,7,1,3,8]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,7,4,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,7,8,4]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,8,7,4]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,8,1,7,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,6,1,7,3]=>[1,5,6,2,4,8,3,7]=>[8,4,3,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,5,1,7,3]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,5,1,6,3]=>[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,5,1,3,6]=>[1,7,3,4,2,8,6,5]=>[8,2,6,5,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,6,1,3,7]=>[1,5,6,2,4,8,7,3]=>[8,4,3,7,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,8,4,7]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,8,5,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,6,5,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,6,4,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,5,4,7]=>[1,6,5,2,3,8,7,4]=>[8,3,4,7,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,5,4,6]=>[1,7,4,2,8,6,5,3]=>[8,2,5,7,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,5,6,4]=>[1,7,6,5,2,8,4,3]=>[8,2,3,4,7,1,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,5,7,4]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,6,7,4]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,8,1,6,3]=>[1,5,8,3,2,4,7,6]=>[8,4,1,6,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,8,6,4]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,6,8,4]=>[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,6,4,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,1,5,4,8]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,1,5,8,4]=>[1,6,5,2,3,7,8,4]=>[8,3,4,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,1,8,5,4]=>[1,6,8,4,2,3,7,5]=>[8,3,1,5,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,8,1,5,3]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,2,1,4,3]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,2,1,3,4]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,1,8,4,5]=>[1,6,8,5,2,3,7,4]=>[8,3,1,4,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,1,4,8,5]=>[1,6,4,2,3,7,8,5]=>[8,3,5,7,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,1,4,5,8]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,4,8,6]=>[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,7,1,3,6]=>[1,5,7,3,2,4,8,6]=>[8,4,2,6,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,6,1,3,5]=>[1,7,3,4,2,8,5,6]=>[8,2,6,5,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,6,4,5]=>[1,7,4,2,8,5,3,6]=>[8,2,5,7,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,7,4,5]=>[1,6,7,4,2,3,8,5]=>[8,3,2,5,7,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,7,4,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,7,5,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,5,8,6]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,5,6,8]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,5,7,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,4,7,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,4,7,5]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,4,6,5]=>[1,7,6,4,2,8,5,3]=>[8,2,3,5,7,1,4,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,4,5,7]=>[1,6,4,2,3,8,7,5]=>[8,3,5,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,5,6,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,8,6,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,2,4,3]=>[1,7,4,6,2,8,3,5]=>[8,2,5,3,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,6,2,5,3]=>[1,7,5,6,2,8,3,4]=>[8,2,4,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,6,2,5,3]=>[1,7,5,6,2,8,3,4]=>[8,2,4,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,7,2,5,3]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,7,2,5,3]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,2,7,5,4]=>[1,2,6,7,5,3,8,4]=>[8,7,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,2,7,5,4]=>[1,6,7,5,2,3,8,4]=>[8,3,2,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,2,6,5,4]=>[1,7,5,2,8,4,3,6]=>[8,2,4,7,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,2,6,5,4]=>[1,7,5,2,8,4,3,6]=>[8,2,4,7,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,6,5,1,2]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,6,1,5,3]=>[1,7,5,6,2,8,3,4]=>[8,2,4,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,1,6,5,4]=>[1,7,5,2,8,4,3,6]=>[8,2,4,7,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,3,6,5,4]=>[1,7,5,3,2,8,4,6]=>[8,2,4,6,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,6,5,4]=>[1,7,5,3,2,8,4,6]=>[8,2,4,6,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,3,7,5,4]=>[1,6,7,5,3,8,4,2]=>[8,3,2,4,6,1,5,7]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,3,7,5,4]=>[1,2,6,7,5,3,8,4]=>[8,7,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,3,7,6,4]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,8,3,7,6,4]=>[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,3,7,6,4]=>[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,3,7,5,4]=>[1,6,7,5,3,8,4,2]=>[8,3,2,4,6,1,5,7]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,1,7,5,4]=>[1,6,7,5,2,3,8,4]=>[8,3,2,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,7,1,5,3]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,7,5,1,2]=>[1,6,5,7,2,3,8,4]=>[8,3,4,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,7,5,1,2]=>[1,3,8,2,6,5,7,4]=>[8,6,1,7,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,7,1,5,3]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,1,7,5,4]=>[1,2,6,7,5,3,8,4]=>[8,7,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,3,7,5,4]=>[1,2,6,7,5,3,8,4]=>[8,7,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,3,7,6,4]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,3,7,6,4]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,8,7,6,5]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,1,7,6,4]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,7,1,6,3]=>[1,2,5,7,6,3,4,8]=>[8,7,4,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,7,6,1,2]=>[1,3,4,8,2,5,7,6]=>[8,6,5,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,7,6,1,2]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,7,1,6,3]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,1,7,6,4]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,8,7,6,5]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,7,6,5]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,8,7,6,5]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,8,7,6,5]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,7,6,5]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,2,7,5,4]=>[1,6,7,5,2,3,8,4]=>[8,3,2,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,2,7,6,4]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,2,7,6,4]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,2,7,6,4]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,7,2,6,3]=>[1,2,5,7,6,3,4,8]=>[8,7,4,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,7,2,6,3]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,7,2,6,3]=>[1,5,7,6,2,4,8,3]=>[8,4,2,3,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,7,2,5,3]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,1,2,4,3]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,3,4,1,2]=>[1,5,3,8,2,6,4,7]=>[8,4,6,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,2,1,4,3]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,7,2,6,3]=>[1,4,8,3,2,5,7,6]=>[8,5,1,6,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,7,2,6,3]=>[1,4,8,3,5,7,6,2]=>[8,5,1,6,4,2,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,7,2,6,3]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,2,7,6,4]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,2,7,6,4]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,2,7,5,4]=>[1,3,8,4,2,6,7,5]=>[8,6,1,5,7,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,1,7,5,4]=>[1,3,8,4,2,6,7,5]=>[8,6,1,5,7,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,7,1,5,3]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,7,5,1,2]=>[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,7,6,1,2]=>[1,4,8,2,5,7,3,6]=>[8,5,1,7,4,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,8,7,1,6,3]=>[1,4,8,3,2,5,7,6]=>[8,5,1,6,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,1,7,6,4]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,8,7,6,5]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,8,7,6,5]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,1,7,6,4]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,7,1,6,3]=>[1,4,8,3,5,7,6,2]=>[8,5,1,6,4,2,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,7,6,1,2]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,7,6,1,2]=>[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,7,1,6,3]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,1,7,6,4]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,6,5,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,6,4,8,7]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,5,4,8,7]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,5,4,7,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,3,7,6]=>[1,8,6,3,4,2,5,7]=>[8,1,3,6,5,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,5,3,8,6]=>[1,7,8,6,3,4,2,5]=>[8,2,1,3,6,5,7,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,5,3,8,7]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,5,4,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,5,4,8,7]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,4,3,8,7]=>[1,6,3,5,4,2,7,8]=>[8,3,6,4,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,4,3,8,7]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,4,3,7,6]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,4,3,7,5]=>[1,6,3,8,5,4,2,7]=>[8,3,6,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,4,3,8,5]=>[1,6,3,7,8,5,4,2]=>[8,3,6,2,1,4,5,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,1,4,3,8,5]=>[1,7,8,5,4,2,3,6]=>[8,2,1,4,5,7,6,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,4,3,8,6]=>[1,7,8,6,3,5,4,2]=>[8,2,1,3,6,4,5,7]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,5,3,8,6]=>[1,4,2,3,7,8,6,5]=>[8,5,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,5,4,8,6]=>[1,3,7,8,6,4,2,5]=>[8,6,2,1,3,5,7,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,5,4,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,5,4,7,6]=>[1,3,8,6,4,2,5,7]=>[8,6,1,3,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,4,3,7,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,8,2,6,5]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,7,2,6,5]=>[1,8,5,7,6,2,3,4]=>[8,1,4,2,3,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,7,2,6,4]=>[1,8,4,3,5,7,6,2]=>[8,1,5,6,4,2,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,6,3,7,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,6,4,7,5]=>[1,3,8,5,6,4,2,7]=>[8,6,1,4,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,6,4,7,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,6,4,8,5]=>[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,6,3,8,5]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,6,3,8,4]=>[1,5,6,3,7,8,4,2]=>[8,4,3,6,2,1,5,7]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,1,5,3,8,4]=>[1,7,8,4,2,3,6,5]=>[8,2,1,5,7,6,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,5,3,7,4]=>[1,6,3,8,4,2,5,7]=>[8,3,6,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,6,3,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,7,3,8,4]=>[1,6,3,5,7,8,4,2]=>[8,3,6,4,2,1,5,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,7,3,8,5]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,3,7,5]=>[1,8,5,6,3,4,2,7]=>[8,1,4,3,6,5,7,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,6,4,7,5]=>[1,8,5,6,4,2,3,7]=>[8,1,4,3,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,7,4,8,5]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,7,4,8,6]=>[1,5,7,8,6,4,2,3]=>[8,4,2,1,3,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,7,5,8,6]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,5,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,8,5,7,6]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,8,5,7,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,3,2,6,5]=>[1,7,6,2,4,3,8,5]=>[8,2,3,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,4,2,6,5]=>[1,8,5,4,2,3,7,6]=>[8,1,4,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,8,3,7,6]=>[1,5,8,6,3,4,2,7]=>[8,4,1,3,6,5,7,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,8,3,7,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,8,4,7,6]=>[1,3,5,8,6,4,2,7]=>[8,6,4,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,8,4,7,5]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,8,4,7,5]=>[1,3,6,4,2,5,8,7]=>[8,6,3,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,8,3,7,5]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,8,3,7,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,8,3,7,4]=>[1,6,3,5,8,4,2,7]=>[8,3,6,4,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,5,2,6,4]=>[1,8,4,2,3,7,6,5]=>[8,1,5,7,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,7,1,5,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,1,5,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,7,2,6,4]=>[1,5,7,6,2,3,8,4]=>[8,4,2,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,7,2,6,5]=>[1,4,3,8,5,7,6,2]=>[8,5,6,1,4,2,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,7,2,6,5]=>[1,3,8,5,7,6,2,4]=>[8,6,1,4,2,3,7,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,7,3,6,5]=>[1,2,3,8,5,7,6,4]=>[8,7,6,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,8,3,6,5]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,8,2,6,5]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,8,2,6,5]=>[1,4,3,7,6,2,5,8]=>[8,5,6,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,8,2,6,4]=>[1,5,8,4,3,7,6,2]=>[8,4,1,5,6,2,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,6,1,5,4]=>[1,7,5,6,2,3,8,4]=>[8,2,4,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,2,4,1,6]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,8,3,1,6]=>[1,7,2,4,5,8,6,3]=>[8,2,7,5,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,8,2,4,7]=>[1,5,8,7,4,6,2,3]=>[8,4,1,2,5,3,7,6]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,1,3,4,7]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,2,8,1,7]=>[1,4,3,6,8,7,2,5]=>[8,5,6,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,8,2,1,6]=>[1,7,2,4,3,5,8,6]=>[8,2,7,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,8,2,6,1]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,3,2,1,5]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,1,8,2,6]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,8,3,2,6]=>[1,4,5,8,6,3,2,7]=>[8,5,4,1,3,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,1,4,2,6]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,4,6,1,3]=>[1,7,2,5,4,3,8,6]=>[8,2,7,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,1,4,6,2]=>[1,7,6,4,8,2,3,5]=>[8,2,3,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,8,3,6,2]=>[1,4,7,6,3,2,5,8]=>[8,5,2,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,8,1,5,2]=>[1,6,2,7,5,8,3,4]=>[8,3,7,2,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,3,5,2,1]=>[1,6,5,3,4,8,2,7]=>[8,3,4,6,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,8,4,2,1]=>[1,5,8,2,6,4,3,7]=>[8,4,1,7,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,1,8,4,2]=>[1,5,2,6,8,3,7,4]=>[8,4,7,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,3,8,4,2]=>[1,5,3,2,6,8,4,7]=>[8,4,6,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,3,8,4,2]=>[1,5,3,6,8,2,4,7]=>[8,4,6,3,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,8,3,5,2]=>[1,6,3,7,5,8,2,4]=>[8,3,6,2,4,1,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,1,4,5,2]=>[1,6,4,3,8,2,7,5]=>[8,3,5,6,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,4,5,1,3]=>[1,6,5,4,8,3,2,7]=>[8,3,4,5,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,4,1,3,5]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,8,3,2,5]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,3,2,8,4]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,3,2,8,4]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,2,1,8,4]=>[1,5,2,6,3,7,8,4]=>[8,4,7,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,2,8,4,1]=>[1,5,2,6,8,3,7,4]=>[8,4,7,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,8,4,1]=>[1,5,3,2,6,8,4,7]=>[8,4,6,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,1,8,4]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,2,8,3,5]=>[1,6,8,5,2,3,7,4]=>[8,3,1,4,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,1,3,4,6]=>[1,7,4,2,5,3,8,6]=>[8,2,5,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,8,2,4,6]=>[1,5,8,6,2,7,4,3]=>[8,4,1,3,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,2,8,3,6]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,1,8,3,6]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,1,8,3,5]=>[1,6,8,5,2,7,3,4]=>[8,3,1,4,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,1,8,4,5]=>[1,3,7,4,2,6,8,5]=>[8,6,2,5,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,2,1,5,6]=>[1,3,7,5,2,4,8,6]=>[8,6,2,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,4,6,2,5]=>[1,3,8,5,4,2,7,6]=>[8,6,1,4,5,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,2,6,1,5]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,2,6,1,4]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,8,5,1,4]=>[1,3,7,2,6,5,8,4]=>[8,6,2,7,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,5,2,1,4]=>[1,3,7,2,6,4,8,5]=>[8,6,2,7,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,2,5,3,1]=>[1,6,5,2,4,8,3,7]=>[8,3,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,2,1,5,3]=>[1,6,2,4,8,3,7,5]=>[8,3,7,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,1,6,2,4]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,5,1,3,4]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,7,8,4,3]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,7,8,4,3]=>[1,5,7,4,2,6,8,3]=>[8,4,2,5,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,1,8,4,3]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,8,4,3,1]=>[1,5,8,2,6,4,7,3]=>[8,4,1,7,3,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,8,4,3,1]=>[1,5,8,2,6,4,3,7]=>[8,4,1,7,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,1,8,4,3]=>[1,5,2,6,8,3,7,4]=>[8,4,7,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,2,8,4,3]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,2,8,4,3]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,8,2,5,3]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,8,5,2,4]=>[1,3,7,2,6,5,8,4]=>[8,6,2,7,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,5,1,4,2]=>[1,6,2,7,4,3,8,5]=>[8,3,7,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,1,5,3,2]=>[1,4,8,2,6,5,3,7]=>[8,5,1,7,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,8,4,3,2]=>[1,5,8,2,6,4,7,3]=>[8,4,1,7,3,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,8,4,3,2]=>[1,5,8,2,6,4,3,7]=>[8,4,1,7,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,4,2,5,7]=>[1,8,7,5,4,3,2,6]=>[8,1,2,4,5,6,7,3]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,2,4,1,7]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,7,1,8,6]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,6,3,1,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,6,1,3,7]=>[1,8,7,3,4,5,6,2]=>[8,1,2,6,5,4,3,7]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,5,6,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,1,4,3,7]=>[1,8,7,3,6,4,2,5]=>[8,1,2,6,3,5,7,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,4,1,2,7]=>[1,8,7,2,5,4,6,3]=>[8,1,2,7,4,5,3,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,3,2,7]=>[1,8,7,2,4,5,6,3]=>[8,1,2,7,5,4,3,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,6,3,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,3,2,6,1]=>[1,7,6,2,4,8,3,5]=>[8,2,3,7,5,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,2,8,1,5]=>[1,4,7,2,3,6,8,5]=>[8,5,2,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,7,2,8,5]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,1,8,2,6]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,7,2,8,6]=>[1,4,3,5,7,8,6,2]=>[8,5,6,4,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,1,2,8,6]=>[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,4,1,6,2]=>[1,7,6,2,5,4,8,3]=>[8,2,3,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,3,6,1,2]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,8,3,5,2]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,4,1,2]=>[1,3,6,4,7,2,5,8]=>[8,6,3,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,7,8,4,2]=>[1,3,5,7,4,6,8,2]=>[8,6,4,2,5,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,4,8,5,2]=>[1,3,7,5,4,2,6,8]=>[8,6,2,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,7,8,5,3]=>[1,6,8,3,4,2,5,7]=>[8,3,1,6,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,4,8,3,5]=>[1,2,6,8,5,4,3,7]=>[8,7,3,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,7,8,2,4]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,2,1,4]=>[1,3,6,2,5,8,4,7]=>[8,6,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,2,4,1]=>[1,3,6,2,5,8,4,7]=>[8,6,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,3,8,4,6]=>[1,5,3,7,4,2,6,8]=>[8,4,6,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,8,2,4,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,8,1,3,6]=>[1,4,7,3,2,5,8,6]=>[8,5,2,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,4,7,8,5]=>[1,3,2,4,6,7,8,5]=>[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,1,5,8,6]=>[1,3,4,2,7,8,6,5]=>[8,6,5,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,2,5,8,6]=>[1,2,7,8,6,5,3,4]=>[8,7,2,1,3,4,6,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,3,5,8,6]=>[1,4,2,7,8,6,5,3]=>[8,5,7,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,3,6,5]=>[1,7,6,3,4,2,8,5]=>[8,2,3,6,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,4,2,6,5]=>[1,7,6,2,8,5,4,3]=>[8,2,3,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,1,8,5,4]=>[1,6,8,4,7,5,2,3]=>[8,3,1,5,2,4,7,6]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,5,2,3,1]=>[1,6,2,4,8,3,7,5]=>[8,3,7,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,8,1,5,3]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,8,1,5,3]=>[1,4,7,5,8,3,2,6]=>[8,5,2,4,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,6,2,1,3]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,8,6,2,3]=>[1,7,2,4,5,8,3,6]=>[8,2,7,5,4,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,3,8,5,4]=>[1,6,8,4,2,3,7,5]=>[8,3,1,5,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,8,2,5,4]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,7,8,4,3]=>[1,5,7,4,6,8,3,2]=>[8,4,2,5,3,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,8,4,1,3]=>[1,5,8,3,6,4,7,2]=>[8,4,1,6,3,5,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,4,1,3]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,7,8,4,3]=>[1,2,5,7,4,6,8,3]=>[8,7,4,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,8,5,2,3]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,3,8,5,4]=>[1,2,6,8,4,3,7,5]=>[8,7,3,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,1,5,4,3]=>[1,6,5,2,7,4,3,8]=>[8,3,4,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,1,4,2]=>[1,6,2,7,4,8,3,5]=>[8,3,7,2,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,7,6,1,8]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,3,5,1,8]=>[1,4,7,2,6,5,3,8]=>[8,5,2,7,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,4,5,1,8]=>[1,3,6,5,4,7,2,8]=>[8,6,3,4,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,4,3,1,8]=>[1,5,4,2,7,3,6,8]=>[8,4,5,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,1,3,2,6]=>[1,8,6,3,5,2,7,4]=>[8,1,3,6,4,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,2,1,3,7]=>[1,6,2,8,7,3,5,4]=>[8,3,7,1,2,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,5,1,3,7]=>[1,4,6,2,8,7,3,5]=>[8,5,3,7,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,5,1,4,7]=>[1,3,8,7,4,6,2,5]=>[8,6,1,2,5,3,7,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,5,8,7,3]=>[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,7,6,2,3]=>[1,8,3,5,7,2,4,6]=>[8,1,6,4,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,4,5,2,3]=>[1,8,3,6,5,4,7,2]=>[8,1,6,3,4,5,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,4,2,5,3]=>[1,7,5,4,8,3,6,2]=>[8,2,4,5,1,6,3,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,2,4,5,3]=>[1,6,4,8,3,7,5,2]=>[8,3,5,1,6,2,4,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,8,4,6,3]=>[1,5,8,3,7,6,4,2]=>[8,4,1,6,2,3,5,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,8,5,6,3]=>[1,4,7,6,5,8,3,2]=>[8,5,2,3,4,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,8,5,6,4]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,1,5,3,6]=>[1,4,7,3,2,8,6,5]=>[8,5,2,6,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,4,2,3,5]=>[1,7,3,6,2,8,5,4]=>[8,2,6,3,7,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,4,3,5,2]=>[1,2,7,5,4,8,3,6]=>[8,7,2,4,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,3,4,5,2]=>[1,2,6,4,8,3,7,5]=>[8,7,3,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,3,4,2,5]=>[1,8,5,3,7,2,6,4]=>[8,1,4,6,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,3,2,4,5]=>[1,7,4,2,6,3,8,5]=>[8,2,5,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,3,4,6]=>[1,5,2,7,4,3,8,6]=>[8,4,7,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,1,3,5,6]=>[1,4,8,6,3,2,7,5]=>[8,5,1,3,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,4,1,5,7]=>[1,3,6,2,4,8,7,5]=>[8,6,3,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,3,1,5,7]=>[1,4,8,7,5,3,2,6]=>[8,5,1,2,4,6,7,3]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,3,1,4,7]=>[1,5,3,8,7,4,2,6]=>[8,4,6,1,2,5,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,2,1,4,7]=>[1,6,2,5,3,8,7,4]=>[8,3,7,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,1,4,2,6]=>[1,8,6,4,3,7,2,5]=>[8,1,3,5,6,2,7,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,8,4,6,2]=>[1,2,5,8,3,7,6,4]=>[8,7,4,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,2,1,5,7]=>[1,6,2,4,8,7,5,3]=>[8,3,7,5,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,8,1,6,7]=>[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,8,1,6,7]=>[1,3,5,8,7,6,2,4]=>[8,6,4,1,2,3,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,2,8,7,5]=>[1,6,8,5,2,4,3,7]=>[8,3,1,4,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,8,2,6,5]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,1,7,6,2,5]=>[1,8,5,7,2,4,3,6]=>[8,1,4,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,7,6,4,2]=>[1,2,5,7,4,3,8,6]=>[8,7,4,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,7,6,2,4]=>[1,8,4,3,2,5,7,6]=>[8,1,5,6,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,3,8,7,4]=>[1,5,3,2,6,8,4,7]=>[8,4,6,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,4,8,7,5]=>[1,3,6,8,5,4,2,7]=>[8,6,3,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,8,4,6,5]=>[1,3,7,6,4,2,5,8]=>[8,6,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,8,3,6,5]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,8,3,6,4]=>[1,5,8,4,2,7,6,3]=>[8,4,1,5,7,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,2,3,5,4]=>[1,6,3,2,7,5,4,8]=>[8,3,6,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,3,5,2,4]=>[1,8,4,7,2,6,5,3]=>[8,1,5,2,7,3,4,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,5,3,4,2]=>[1,2,7,4,6,3,8,5]=>[8,7,2,5,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,5,3,2,4]=>[1,8,4,6,3,2,7,5]=>[8,1,5,3,6,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,5,2,3,4]=>[1,7,3,2,8,4,6,5]=>[8,2,6,7,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,7,6,3,4]=>[1,5,7,3,2,8,4,6]=>[8,4,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,7,6,3,5]=>[1,4,2,8,5,7,3,6]=>[8,5,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,7,6,4,5]=>[1,3,8,5,7,4,2,6]=>[8,6,1,4,2,5,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,7,6,5,3]=>[1,4,8,3,2,5,7,6]=>[8,5,1,6,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,2,5,4,3]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,4,2,3]=>[1,8,3,7,2,4,6,5]=>[8,1,6,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,5,8,7,4]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,4,8,7,5]=>[1,3,6,8,5,4,2,7]=>[8,6,3,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,4,8,7,6]=>[1,3,5,4,2,6,8,7]=>[8,6,4,5,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,3,4,8,7,2]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,3,8,7,6]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,7,3,6,8]=>[1,5,7,6,3,2,4,8]=>[8,4,2,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,2,3,5,8]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,2,3,5,7]=>[1,6,3,2,4,8,7,5]=>[8,3,6,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,8,4,6,3]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,3,7,4,6,2]=>[1,2,8,3,5,7,6,4]=>[8,7,1,6,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,7,4,6,3]=>[1,8,3,5,7,6,4,2]=>[8,1,6,4,2,3,5,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,3,6,4]=>[1,8,4,2,5,7,6,3]=>[8,1,5,7,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,3,6,5]=>[1,8,5,7,6,3,2,4]=>[8,1,4,2,3,6,7,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,2,3,5,4]=>[1,8,4,7,5,2,6,3]=>[8,1,5,2,4,7,3,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,2,4,5,3]=>[1,8,3,6,4,7,5,2]=>[8,1,6,3,5,2,4,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,3,4,5,2]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,3,4,5,2]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,2,3,5,4]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,8,3,6,5]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,8,4,6,5]=>[1,3,7,6,4,2,5,8]=>[8,6,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,8,5,6,4]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,7,5,6,2]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,7,5,6,3]=>[1,4,8,3,2,5,7,6]=>[8,5,1,6,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,7,5,6,4]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,7,4,6,5]=>[1,3,8,5,7,6,4,2]=>[8,6,1,4,2,3,5,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,2,4,5,6]=>[1,3,8,6,4,7,5,2]=>[8,6,1,3,5,2,4,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,6,2,4,5,8]=>[1,3,7,5,2,4,6,8]=>[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,2,3,5,7]=>[1,4,6,3,2,8,7,5]=>[8,5,3,6,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,2,3,5,6]=>[1,4,7,5,2,8,6,3]=>[8,5,2,4,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,7,3,6,4]=>[1,5,7,6,3,2,8,4]=>[8,4,2,3,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,7,4,6,3]=>[1,5,7,6,4,2,3,8]=>[8,4,2,3,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,3,4,5,2]=>[1,2,6,4,7,5,3,8]=>[8,7,3,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,2,3,4,6]=>[1,5,2,8,6,3,7,4]=>[8,4,7,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,2,3,4,7]=>[1,5,2,8,7,4,3,6]=>[8,4,7,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,2,3,4,8]=>[1,5,2,7,4,3,6,8]=>[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,3,4,5,2]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,3,4,5,2]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,2,4,5,3]=>[1,8,3,7,5,2,4,6]=>[8,1,6,2,4,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,3,5,4]=>[1,8,4,6,3,2,7,5]=>[8,1,5,3,6,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,4,8,7]=>[1,3,5,6,4,2,7,8]=>[8,6,4,3,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,1,8,6]=>[1,3,5,7,8,6,2,4]=>[8,6,4,2,1,3,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,7,6,8,1]=>[1,4,3,5,7,8,2,6]=>[8,5,6,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,7,1,8,6]=>[1,4,3,5,7,8,6,2]=>[8,5,6,4,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,6,3,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,6,2,8,7]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,6,2,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,7,1,8,6]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,7,2,8,6]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,7,2,8,6]=>[1,3,5,7,8,6,2,4]=>[8,6,4,2,1,3,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,7,3,8,6]=>[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,7,6,8,2]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,7,6,8,2]=>[1,4,3,5,7,8,2,6]=>[8,5,6,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,7,6,8,2]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,7,1,8,2]=>[1,4,5,7,8,2,3,6]=>[8,5,4,2,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,7,2,8,1]=>[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,7,1,8,2]=>[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,7,4,8,2]=>[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,7,4,8,2]=>[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,7,5,8,2]=>[1,4,3,6,5,7,8,2]=>[8,5,6,3,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,7,5,8,3]=>[1,2,3,6,5,7,8,4]=>[8,7,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,7,3,8,5]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,7,2,8,5]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,7,2,8,4]=>[1,5,7,8,4,3,6,2]=>[8,4,2,1,5,6,3,7]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,7,4,8,1]=>[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,7,4,8,1]=>[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,7,1,8,4]=>[1,5,7,8,4,3,6,2]=>[8,4,2,1,5,6,3,7]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,7,3,8,6]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,7,1,8,5]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,7,5,8,1]=>[1,4,3,6,5,7,8,2]=>[8,5,6,3,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,7,4,8,5]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,4,8,6]=>[1,3,5,7,8,6,4,2]=>[8,6,4,2,1,3,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,7,5,8,6]=>[1,3,4,2,5,7,8,6]=>[8,6,5,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,7,6,8,5]=>[1,3,4,2,5,7,8,6]=>[8,6,5,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,6,8,4]=>[1,3,5,7,8,4,2,6]=>[8,6,4,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,7,5,8,4]=>[1,3,6,5,7,8,4,2]=>[8,6,3,4,2,1,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,7,3,8,1]=>[1,4,5,7,8,2,3,6]=>[8,5,4,2,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,7,1,8,3]=>[1,4,5,7,8,3,6,2]=>[8,5,4,2,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,7,6,8,3]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,7,6,8,3]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,7,6,8,4]=>[1,3,5,7,8,4,2,6]=>[8,6,4,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,7,6,8,4]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,7,5,8,4]=>[1,2,3,6,5,7,8,4]=>[8,7,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,7,5,8,4]=>[1,3,6,5,7,8,4,2]=>[8,6,3,4,2,1,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,7,4,8,3]=>[1,5,7,8,3,6,4,2]=>[8,4,2,1,6,3,5,7]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,7,4,8,3]=>[1,5,7,8,3,6,4,2]=>[8,4,2,1,6,3,5,7]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,7,3,8,1]=>[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,7,3,8,1]=>[1,5,7,8,2,4,3,6]=>[8,4,2,1,7,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,7,2,8,3]=>[1,4,5,7,8,3,6,2]=>[8,5,4,2,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,7,3,8,4]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,7,3,8,2]=>[1,4,5,7,8,2,3,6]=>[8,5,4,2,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,7,3,8,2]=>[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,7,3,8,2]=>[1,5,7,8,2,4,3,6]=>[8,4,2,1,7,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,7,1,8,2]=>[1,5,7,8,2,4,3,6]=>[8,4,2,1,7,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,2,4,1,7]=>[1,8,7,2,6,4,5,3]=>[8,1,2,7,3,5,4,6]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,4,1,8,6]=>[1,3,5,4,2,7,8,6]=>[8,6,4,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,7,3,6,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,3,1,8,6]=>[1,2,4,7,8,6,3,5]=>[8,7,5,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,6,1,3,7]=>[1,8,7,3,5,6,2,4]=>[8,1,2,6,4,3,7,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,1,4,2,7]=>[1,8,7,2,6,4,5,3]=>[8,1,2,7,3,5,4,6]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,5,3,2,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,4,3,2,7]=>[1,8,7,2,3,5,4,6]=>[8,1,2,7,6,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,2,1,8,6]=>[1,5,2,7,8,6,3,4]=>[8,4,7,2,1,3,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,3,2,6,1]=>[1,8,2,5,3,7,6,4]=>[8,1,7,4,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,2,7,5,1]=>[1,4,3,8,2,6,7,5]=>[8,5,6,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,3,2,8,5]=>[1,2,4,7,8,5,3,6]=>[8,7,5,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,1,8,2,6]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,3,2,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,4,2,8,6]=>[1,3,5,4,2,7,8,6]=>[8,6,4,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,1,3,8,6]=>[1,5,2,7,8,6,3,4]=>[8,4,7,2,1,3,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,2,1,6,3]=>[1,8,3,7,6,2,5,4]=>[8,1,6,2,3,7,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,6,3,5,2]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,7,4,1,2]=>[1,3,5,7,2,6,4,8]=>[8,6,4,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,6,7,4,2]=>[1,3,5,6,7,4,8,2]=>[8,6,4,3,2,5,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,8,7,5,2]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,4,7,5,3]=>[1,8,3,6,7,5,4,2]=>[8,1,6,3,2,4,5,7]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,1,4,3,5]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,4,8,2,5]=>[1,3,2,7,4,6,8,5]=>[8,6,7,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,6,8,2,4]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,5,8,2,4]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,7,2,4,1]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,6,8,1,4]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,7,8,3,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,8,3,1,5]=>[1,4,6,3,7,2,5,8]=>[8,5,3,6,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,7,3,5,1]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,6,7,5,1]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,4,8,1,5]=>[1,3,2,7,4,6,8,5]=>[8,6,7,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,4,7,8,5]=>[1,3,6,7,8,5,4,2]=>[8,6,3,2,1,4,5,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,1,8,4,6]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,1,5,8,6]=>[1,4,2,7,8,6,5,3]=>[8,5,7,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,4,2,5]=>[1,8,5,3,6,4,2,7]=>[8,1,4,6,3,5,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,2,1,6,4]=>[1,8,4,3,7,6,2,5]=>[8,1,5,6,2,3,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,2,1,5,4]=>[1,3,8,4,6,2,7,5]=>[8,6,1,5,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,5,2,4,1]=>[1,8,2,7,4,3,6,5]=>[8,1,7,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,1,7,5,3]=>[1,4,2,6,7,5,3,8]=>[8,5,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,7,2,6,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,1,6,2,4]=>[1,8,4,7,2,5,3,6]=>[8,1,5,2,7,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,3,6,4]=>[1,8,4,2,5,3,7,6]=>[8,1,5,7,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,6,7,4,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,5,6,4,3]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,6,4,3,1]=>[1,8,2,3,5,6,4,7]=>[8,1,7,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,5,4,1,3]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,1,3,5,4]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,5,1,4,2]=>[1,8,2,7,4,3,6,5]=>[8,1,7,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,1,3,2]=>[1,8,2,4,6,3,7,5]=>[8,1,7,5,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,6,4,3,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,1,2,8,7]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,2,1,4,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,5,1,3,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,5,1,8,7]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,5,3,8,7]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,1,4,8,7]=>[1,5,2,6,4,3,7,8]=>[8,4,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,5,2,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,2,6,3,1]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,2,6,3,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,5,1,2,6]=>[1,3,8,6,2,7,4,5]=>[8,6,1,3,7,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,3,4,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,5,7,3,4]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,5,8,3,2]=>[1,7,3,2,6,8,4,5]=>[8,2,6,7,3,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,1,6,3,2]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,7,6,2,3]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,7,6,1,3]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,5,6,7,1]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,5,6,7,1]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,5,6,7,2]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,3,6,1,2]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,4,1,7,2]=>[1,6,2,5,4,8,3,7]=>[8,3,7,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,4,6,7,3]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,6,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,2,1,7,5]=>[1,6,2,4,8,5,3,7]=>[8,3,7,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,2,6,1,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,5,6,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,5,6,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,5,6,7,1]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,5,6,7,1]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,5,6,7,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,5,6,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,5,6,7,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,3,6,1,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,4,1,7,5]=>[1,6,2,8,5,4,3,7]=>[8,3,7,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,4,6,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,5,4,3,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,1,4,2,6]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,3,6,2,5]=>[1,8,5,3,2,7,4,6]=>[8,1,4,6,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,2,6,1,5]=>[1,3,7,2,8,5,4,6]=>[8,6,2,7,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,3,6,2,1]=>[1,5,3,8,2,7,4,6]=>[8,4,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,4,2,7,1]=>[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,4,2,7,5]=>[1,8,5,4,2,6,3,7]=>[8,1,4,5,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,2,4,1,6]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,8,5,7,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,6,8,7,5]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,2,8,1,4]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,1,2,7,4]=>[1,8,4,5,2,6,3,7]=>[8,1,5,4,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,6,1,7,4]=>[1,5,6,2,8,4,3,7]=>[8,4,3,7,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,6,2,7,1]=>[1,4,8,2,5,6,3,7]=>[8,5,1,7,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,7,6,2,1]=>[1,3,8,2,5,7,4,6]=>[8,6,1,7,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,7,6,1,3]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,1,6,2,3]=>[1,8,3,5,2,7,4,6]=>[8,1,6,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,1,8,2,4]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,5,8,3,4]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,3,6,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,2,1,7,4]=>[1,6,2,8,4,5,3,7]=>[8,3,7,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,2,6,1,3]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,6,7,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,5,6,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,5,6,7,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,5,6,7,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,5,6,7,1]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,5,6,7,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,5,6,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,8,6,1,3]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,8,1,7,4]=>[1,6,2,5,8,4,3,7]=>[8,3,7,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,8,6,7,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,8,1,7,2]=>[1,6,2,4,5,8,3,7]=>[8,3,7,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,8,6,1,2]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,5,6,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,5,6,7,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,5,6,7,2]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,5,8,2,1]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,5,8,3,1]=>[1,6,8,2,7,3,4,5]=>[8,3,1,7,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,8,6,3,1]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,1,8,4,2]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,5,2,1,6]=>[1,3,7,2,8,6,4,5]=>[8,6,2,7,1,3,5,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,8,6,2,1]=>[1,3,5,8,2,7,4,6]=>[8,6,4,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,8,2,7,4]=>[1,5,8,4,2,6,3,7]=>[8,4,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,8,2,7,1]=>[1,4,5,8,2,6,3,7]=>[8,5,4,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,1,2,7,5]=>[1,4,8,5,2,6,3,7]=>[8,5,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,1,6,2,5]=>[1,3,8,5,2,7,4,6]=>[8,6,1,4,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,8,4,7]=>[1,3,5,6,8,7,4,2]=>[8,6,4,3,1,2,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,7,1,8,6]=>[1,3,2,5,7,8,6,4]=>[8,6,7,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,3,7,6,1]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,6,8,3,7]=>[1,5,6,8,7,3,2,4]=>[8,4,3,1,2,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,4,8,2,7]=>[1,6,8,7,2,3,5,4]=>[8,3,1,2,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,3,8,2,7]=>[1,4,5,3,2,6,8,7]=>[8,5,4,6,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,3,8,2,7]=>[1,5,3,6,8,7,2,4]=>[8,4,6,3,1,2,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,7,1,8,6]=>[1,5,7,8,6,2,4,3]=>[8,4,2,1,3,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,2,7,6,1]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,8,7,5,1]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,7,2,8,5]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,1,8,2,6]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,8,4,2,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,4,1,3,6]=>[1,7,3,5,4,8,6,2]=>[8,2,6,4,5,1,3,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,4,6,1,3]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,1,4,6,2]=>[1,3,8,2,5,4,7,6]=>[8,6,1,7,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,7,3,6,2]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,7,3,6,2]=>[1,2,5,7,6,3,4,8]=>[8,7,4,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,6,5,2,1]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,6,4,2,1]=>[1,5,6,4,7,2,3,8]=>[8,4,3,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,3,7,4,2]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,7,4,5,1,3]=>[1,6,5,4,7,2,3,8]=>[8,3,4,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,8,4,2,5]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,8,3,2,5]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,3,2,8,4]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,2,1,8,4]=>[1,7,8,4,3,5,2,6]=>[8,2,1,5,6,4,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,8,7,4,1]=>[1,6,7,4,2,5,8,3]=>[8,3,2,5,7,4,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,8,7,4,1]=>[1,5,8,2,3,6,7,4]=>[8,4,1,7,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,6,3,1,8,4]=>[1,5,3,7,8,4,6,2]=>[8,4,6,2,1,5,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,1,8,3,6]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,3,1,8,5]=>[1,4,6,2,7,8,5,3]=>[8,5,3,7,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,3,7,5,1]=>[1,2,4,6,7,5,3,8]=>[8,7,5,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,4,1,8,5]=>[1,7,8,5,4,2,3,6]=>[8,2,1,4,5,7,6,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,2,1,5,6]=>[1,4,8,6,2,3,7,5]=>[8,5,1,3,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,4,6,2,5]=>[1,8,5,4,2,3,7,6]=>[8,1,4,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,2,5,4,1]=>[1,8,2,7,4,6,5,3]=>[8,1,7,2,5,3,4,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,1,7,5,3]=>[1,4,8,3,6,7,5,2]=>[8,5,1,6,3,2,4,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,7,1,6,3]=>[1,5,7,6,2,4,3,8]=>[8,4,2,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,7,2,6,3]=>[1,4,5,7,6,2,8,3]=>[8,5,4,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,1,6,2,4]=>[1,5,2,8,4,7,3,6]=>[8,4,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,6,1,3,4]=>[1,5,6,2,8,4,3,7]=>[8,4,3,7,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,5,1,3,4]=>[1,8,4,7,3,2,6,5]=>[8,1,5,2,6,7,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,1,7,4,3]=>[1,6,7,4,8,3,2,5]=>[8,3,2,5,1,6,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,8,6,4,3]=>[1,5,8,3,7,4,2,6]=>[8,4,1,6,2,5,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,7,5,4,3,1]=>[1,6,4,7,3,8,2,5]=>[8,3,5,2,6,1,7,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,8,5,4,3]=>[1,6,5,8,3,7,4,2]=>[8,3,4,1,6,2,5,7]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,6,2,5,3]=>[1,4,8,3,2,7,5,6]=>[8,5,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,4,3,2]=>[1,8,2,5,6,4,3,7]=>[8,1,7,4,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,3,1,5,7]=>[1,8,7,5,3,2,4,6]=>[8,1,2,4,6,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,3,5,1,8]=>[1,4,6,5,3,2,7,8]=>[8,5,3,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,3,8,4,7]=>[1,2,6,8,7,4,3,5]=>[8,7,3,1,2,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,3,1,4,7]=>[1,6,2,8,7,4,3,5]=>[8,3,7,1,2,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,2,3,1,4,7]=>[1,5,3,6,2,8,7,4]=>[8,4,6,3,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,3,1,5,7]=>[1,4,6,2,8,7,5,3]=>[8,5,3,7,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,4,8,5,7]=>[1,3,2,4,6,8,7,5]=>[8,6,7,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,1,4,5,6]=>[1,3,8,6,4,7,5,2]=>[8,6,1,3,5,2,4,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,1,3,4,6]=>[1,5,2,8,6,3,7,4]=>[8,4,7,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,2,3,4,5]=>[1,2,7,4,8,5,3,6]=>[8,7,2,5,1,4,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,3,1,4,7]=>[1,6,2,5,3,8,7,4]=>[8,3,7,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,3,4,6]=>[1,8,6,3,7,4,2,5]=>[8,1,3,6,2,5,7,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,3,1,5,7]=>[1,6,2,4,8,7,5,3]=>[8,3,7,5,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,8,1,6,7]=>[1,5,8,7,6,2,4,3]=>[8,4,1,2,3,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,1,8,6,7]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,3,8,5,7]=>[1,6,8,7,5,3,2,4]=>[8,3,1,2,4,6,7,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,8,3,5,6]=>[1,7,5,8,6,3,2,4]=>[8,2,4,1,3,6,7,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,3,5,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,7,3,4,6]=>[1,2,5,7,4,3,8,6]=>[8,7,4,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,3,4,6]=>[1,8,6,3,2,5,7,4]=>[8,1,3,6,7,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,8,3,4,6]=>[1,7,4,2,5,8,6,3]=>[8,2,5,7,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,3,8,4,7]=>[1,6,8,7,4,2,5,3]=>[8,3,1,2,5,7,4,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,3,8,5,7]=>[1,4,2,6,8,7,5,3]=>[8,5,7,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,8,4,5,6]=>[1,3,7,5,8,6,4,2]=>[8,6,2,4,1,3,5,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,8,3,5,6]=>[1,4,2,7,5,8,6,3]=>[8,5,7,2,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,2,3,4,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,2,3,4,5]=>[1,2,7,4,6,3,8,5]=>[8,7,2,5,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,2,3,4,5]=>[1,7,4,6,3,2,8,5]=>[8,2,5,3,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,7,4,5,6]=>[1,3,8,6,4,2,5,7]=>[8,6,1,3,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,2,3,4,5]=>[1,6,3,8,5,2,4,7]=>[8,3,6,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,2,3,4,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,2,4,8,7]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,1,2,8,7]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,1,8,4,2]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,1,8,3,4]=>[1,6,8,4,7,3,2,5]=>[8,3,1,5,2,6,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,4,3,8,7]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,1,2,8,7]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,6,2,8,7]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,5,2,8,7]=>[1,3,4,6,2,5,7,8]=>[8,6,5,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,2,8,3,1]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,2,6,3,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,5,2,1,6]=>[1,3,7,2,4,8,6,5]=>[8,6,2,7,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,3,4,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,1,7,4,2]=>[1,8,2,6,7,4,5,3]=>[8,1,7,3,2,5,4,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,6,7,3,1]=>[1,5,6,7,3,2,8,4]=>[8,4,3,2,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,6,5,7,1,2]=>[1,3,8,2,4,6,7,5]=>[8,6,1,7,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,1,6,3,2]=>[1,7,3,4,8,2,5,6]=>[8,2,6,5,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,7,1,8,3]=>[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,7,5,8,1]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,8,5,7,2]=>[1,4,3,6,5,8,2,7]=>[8,5,6,3,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,8,6,5,1]=>[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,5,8,6,2]=>[1,7,6,8,2,4,3,5]=>[8,2,3,1,7,5,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,1,7,3,2]=>[1,6,7,3,8,2,5,4]=>[8,3,2,6,1,7,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,4,1,6,2]=>[1,8,2,5,4,7,6,3]=>[8,1,7,4,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,7,6,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,1,8,2,5]=>[1,6,8,5,2,3,7,4]=>[8,3,1,4,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,5,7,6,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,6,7,5,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,8,5,1]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,8,5,6,1]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,6,5,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,3,4,2,5]=>[1,8,5,3,2,7,4,6]=>[8,1,4,6,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,2,4,1,5]=>[1,3,6,4,7,2,8,5]=>[8,6,3,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,2,6,1]=>[1,5,4,7,6,2,3,8]=>[8,4,5,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,4,2,7,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,2,4,1,6]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,5,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,6,7,8,5]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,8,7,2,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,4,2,3]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,5,7,3,4]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,2,1,8,4]=>[1,6,2,7,8,4,5,3]=>[8,3,7,2,1,5,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,5,6,8,3]=>[1,7,8,3,4,2,5,6]=>[8,2,1,6,5,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,6,5,8,3]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,8,7,6,3]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,8,6,7,3]=>[1,4,5,8,3,2,6,7]=>[8,5,4,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,5,8,7,3]=>[1,6,8,3,2,4,5,7]=>[8,3,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,6,8,1,4]=>[1,7,2,5,6,8,4,3]=>[8,2,7,4,3,1,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,6,8,7,4]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,6,1,8,2]=>[1,7,8,2,3,5,6,4]=>[8,2,1,7,6,4,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,5,7,8,2]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,7,6,8,2]=>[1,4,5,7,8,2,3,6]=>[8,5,4,2,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,6,8,7,2]=>[1,3,4,5,6,8,2,7]=>[8,6,5,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,3,1,8,7]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,4,8,3,1]=>[1,6,8,2,5,4,7,3]=>[8,3,1,7,4,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,4,1,6,3]=>[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,2,1,6,4]=>[1,8,4,5,2,3,7,6]=>[8,1,5,4,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,8,4,1]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,4,1,8,7]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,1,5,8,7]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,5,4,8,7]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,4,8,5,1]=>[1,6,8,2,7,5,4,3]=>[8,3,1,7,2,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,4,1,6,5]=>[1,8,5,4,3,2,7,6]=>[8,1,4,5,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,8,4,6,2]=>[1,5,8,2,3,7,6,4]=>[8,4,1,7,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,8,6,4,1]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,1,8,5,2]=>[1,3,7,5,2,6,8,4]=>[8,6,2,4,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,4,8,5,3]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,4,3,6,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,4,2,6,1]=>[1,5,4,7,6,2,8,3]=>[8,4,5,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,1,2,6,5]=>[1,3,7,6,2,8,5,4]=>[8,6,2,3,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,5,2,6,4]=>[1,7,6,2,8,4,3,5]=>[8,2,3,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,2,6,1,4]=>[1,5,2,8,4,3,7,6]=>[8,4,7,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,2,5,4,7]=>[1,8,7,4,3,6,5,2]=>[8,1,2,5,6,3,4,7]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,6,3,7,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,7,6,3,5]=>[1,4,2,8,5,7,3,6]=>[8,5,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,5,7,1,6]=>[1,3,4,2,8,6,7,5]=>[8,6,5,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,2,7,4,1]=>[1,6,7,4,5,2,8,3]=>[8,3,2,5,4,7,1,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,8,7,6,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,8,7,1,4]=>[1,6,7,2,5,8,4,3]=>[8,3,2,7,4,1,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,8,1,6,3]=>[1,7,6,2,5,8,3,4]=>[8,2,3,7,4,1,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,5,7,6,1]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,7,6,5,3]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,5,3,6]=>[1,8,6,5,7,3,2,4]=>[8,1,3,4,2,6,7,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,6,7,5,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,6,5,7,2]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,8,4,2,1]=>[1,3,5,8,2,7,4,6]=>[8,6,4,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,1,7,4,3]=>[1,8,3,2,6,7,4,5]=>[8,1,6,7,3,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,8,7,3,4]=>[1,5,8,4,2,6,7,3]=>[8,4,1,5,7,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,8,3,7,1]=>[1,4,5,8,2,6,3,7]=>[8,5,4,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,3,8,1,4]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,4,3,1,7]=>[1,5,4,8,7,2,6,3]=>[8,4,5,1,2,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,4,5,6,3]=>[1,8,3,2,7,6,5,4]=>[8,1,6,7,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,1,5,4,2]=>[1,3,8,2,6,5,4,7]=>[8,6,1,7,3,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,3,4,1,2]=>[1,5,3,8,2,7,4,6]=>[8,4,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,5,3,6,1]=>[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,4,6,3,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,4,1,2,7]=>[1,6,2,5,4,8,7,3]=>[8,3,7,4,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,3,6,2,1]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,5,6,1,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,6,5,2,7]=>[1,4,3,8,7,2,5,6]=>[8,5,6,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,7,2,6,5]=>[1,8,5,7,6,2,4,3]=>[8,1,4,2,3,7,5,6]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,4,6,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,2,5,7,1]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,2,5,1,6]=>[1,7,2,4,8,6,5,3]=>[8,2,7,5,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,5,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,5,1,6,7]=>[1,4,3,2,8,7,6,5]=>[8,5,6,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,5,7,6]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,6,5,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,6,5,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,1,4,2,3]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,1,4,2,8]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,4,1,6,3]=>[1,7,6,2,5,4,3,8]=>[8,2,3,7,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,4,7,6,1]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,4,1,6,7]=>[1,2,8,7,6,3,5,4]=>[8,7,1,2,3,6,4,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,1,4,5,3]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,6,1,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,4,7,1,6]=>[1,2,8,6,7,3,5,4]=>[8,7,1,3,2,6,4,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,4,6,7,1]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,4,6,1,8]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,3,1,4,8]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,3,1,7,4]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,3,1,4,7]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,4,6,3,1]=>[1,7,3,8,2,5,4,6]=>[8,2,6,1,7,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,1,4,3,2]=>[1,7,3,8,2,5,4,6]=>[8,2,6,1,7,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,1,3,7,4]=>[1,6,3,8,4,2,5,7]=>[8,3,6,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,1,8,7,4]=>[1,3,6,8,4,2,5,7]=>[8,6,3,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,4,1,8,6]=>[1,3,7,8,6,2,5,4]=>[8,6,2,1,3,7,4,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,3,1,8,4]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,3,1,7,8]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,3,4,8,1]=>[1,6,4,7,8,2,5,3]=>[8,3,5,2,1,7,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,4,8,7,3]=>[1,5,4,6,8,3,2,7]=>[8,4,5,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,3,7,4,1]=>[1,6,7,4,8,2,5,3]=>[8,3,2,5,1,7,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,7,5,6]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,6,5,7]=>[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,6,7,5]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,6,5,8]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,5,7,6]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,4,5,7,3]=>[1,6,5,4,8,3,2,7]=>[8,3,4,5,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,3,1,7,4]=>[1,5,3,8,4,2,6,7]=>[8,4,6,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,4,3,1,7]=>[1,6,3,8,7,2,5,4]=>[8,3,6,1,2,7,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,4,3,7,1]=>[1,6,3,8,2,5,4,7]=>[8,3,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,8,3,4,1,6]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,3,7,1,4]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,3,4,1,8]=>[1,6,4,7,2,5,3,8]=>[8,3,5,2,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,4,3,2,8]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,3,4,2,1]=>[1,5,3,8,2,7,4,6]=>[8,4,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,6,2,7,5]=>[1,4,3,8,5,6,2,7]=>[8,5,6,1,4,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,6,2,7,5]=>[1,3,4,8,5,6,2,7]=>[8,6,5,1,4,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,6,5,2,7]=>[1,3,4,8,7,2,5,6]=>[8,6,5,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,8,3,2,4]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,7,3,2,8]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,3,8,1,6]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,4,8,7,1]=>[1,3,6,8,2,5,4,7]=>[8,6,3,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,8,4,1,2]=>[1,3,5,8,2,7,4,6]=>[8,6,4,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,8,1,7,4]=>[1,3,5,8,4,2,6,7]=>[8,6,4,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,8,4,7,3]=>[1,6,4,5,8,3,2,7]=>[8,3,5,4,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,8,3,4,2]=>[1,7,4,5,8,2,3,6]=>[8,2,5,4,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,3,8,4,1]=>[1,7,4,6,8,2,5,3]=>[8,2,5,3,1,7,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,8,6,5]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,8,5,7,3]=>[1,4,6,5,8,3,2,7]=>[8,5,3,4,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,6,8,7,3]=>[1,4,5,6,8,3,2,7]=>[8,5,4,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,4,3,2]=>[1,7,3,5,2,8,4,6]=>[8,2,6,4,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,5,3,6]=>[1,7,3,4,2,8,6,5]=>[8,2,6,5,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,5,7,3,8]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,7,2,5,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,1,6,2]=>[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,4,2,1,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,2,3,6,5]=>[1,7,6,3,4,2,8,5]=>[8,2,3,6,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,5,3,4,6]=>[1,7,4,2,8,6,3,5]=>[8,2,5,7,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,4,1,3,5]=>[1,7,3,2,8,5,4,6]=>[8,2,6,7,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,6,4,1,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,5,4,3,2]=>[1,7,3,2,8,4,6,5]=>[8,2,6,7,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,5,4,3,8]=>[1,6,4,7,3,2,5,8]=>[8,3,5,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,4,3,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,6,4,7,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,6,4,8,2]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,8,7,4,3]=>[1,6,7,4,5,8,3,2]=>[8,3,2,5,4,1,6,7]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,4,2,7,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,5,6,1,2]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,5,3,6,8]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,6,8,4,3]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,6,4,1,5]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,6,4,5,2]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,3,6,4,2]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,3,6,1,4]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,2,4,7,3]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,3,1,4,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,7,3,5,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,8,4,1,2]=>[1,5,8,2,6,4,3,7]=>[8,4,1,7,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,4,7,3,6]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,2,1,3,8]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,8,1,3]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,2,7,3,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,1,2,8,3]=>[1,4,7,8,3,5,2,6]=>[8,5,2,1,6,4,7,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,3,1,8,2]=>[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,2,3,8,6]=>[1,5,2,7,8,6,3,4]=>[8,4,7,2,1,3,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,3,8,1,2]=>[1,5,3,6,8,2,7,4]=>[8,4,6,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,8,7,1,2]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,4,8,1,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,5,8,7,2]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,7,8,3,5]=>[1,2,6,8,5,7,3,4]=>[8,7,3,1,4,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,1,6,3,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,1,4,3,2]=>[1,6,4,8,2,7,3,5]=>[8,3,5,1,7,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,2,3,1,4]=>[1,5,2,8,4,6,3,7]=>[8,4,7,1,5,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,6,5,3,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,5,6,3,7]=>[1,4,2,8,7,3,5,6]=>[8,5,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,5,3,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,6,3,8,5]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,6,8,1,2]=>[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,3,5,7,1,2]=>[1,4,3,6,7,2,8,5]=>[8,5,6,3,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,1,4,7,2]=>[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,2,1,6,4]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,1,6,4,3]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,5,2,4,3]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,5,2,1,4]=>[1,3,6,2,7,4,8,5]=>[8,6,3,7,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,1,2,4,6]=>[1,3,8,6,2,7,4,5]=>[8,6,1,3,7,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,4,2,5,8]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,2,3,5,7]=>[1,4,6,3,8,7,5,2]=>[8,5,3,6,1,2,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,5,4,1,2]=>[1,3,7,2,8,4,6,5]=>[8,6,2,7,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,5,3,4,8]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,4,5,3,7]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,1,4,3,6]=>[1,2,8,6,4,5,3,7]=>[8,7,1,3,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,5,1,3,4]=>[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,5,4,1,3]=>[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,7,4,8,5]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,1,8,2,4]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,1,7,2,4]=>[1,8,4,6,7,2,5,3]=>[8,1,5,3,2,7,4,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,4,7,1,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,4,8,1,5]=>[1,7,2,3,6,8,5,4]=>[8,2,7,6,3,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,2,5,8,6]=>[1,4,2,3,7,8,6,5]=>[8,5,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,1,4,8,5]=>[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,1,2,8,4]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,1,2,8,5]=>[1,6,2,3,7,8,5,4]=>[8,3,7,6,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,2,3,8,6]=>[1,4,5,2,7,8,6,3]=>[8,5,4,7,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,2,4,8,6]=>[1,3,5,2,7,8,6,4]=>[8,6,4,7,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,8,1,2,5]=>[1,4,3,6,2,7,5,8]=>[8,5,6,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,3,8,1,6]=>[1,5,3,4,2,7,6,8]=>[8,4,6,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,4,8,2,5]=>[1,3,6,8,5,4,2,7]=>[8,6,3,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,1,8,3,4]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,2,8,1,3]=>[1,6,8,3,7,2,4,5]=>[8,3,1,6,2,7,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,2,6,1,3]=>[1,7,2,4,5,3,8,6]=>[8,2,7,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,3,7,1,4]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,2,7,4,5]=>[1,3,6,7,4,2,8,5]=>[8,6,3,2,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,4,7,1,5]=>[1,3,6,7,2,8,5,4]=>[8,6,3,2,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,7,1,2,5]=>[1,6,2,8,5,7,3,4]=>[8,3,7,1,4,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,1,2,4,6]=>[1,3,5,2,8,6,4,7]=>[8,6,4,7,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,7,1,3,5]=>[1,4,2,8,5,7,3,6]=>[8,5,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,6,1,2,4]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,8,1,2,4]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,8,1,3,5]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,1,2,4,7]=>[1,3,5,2,6,4,8,7]=>[8,6,4,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,2,8,1,3]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,1,8,2,5]=>[1,4,7,2,6,8,5,3]=>[8,5,2,7,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,4,8,2,6]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,4,8,1,6]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,8,1,2,6]=>[1,5,8,6,2,4,3,7]=>[8,4,1,3,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,8,1,2,5]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,1,2,5]=>[1,8,5,7,2,4,3,6]=>[8,1,4,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,7,2,3,5]=>[1,8,5,7,3,2,4,6]=>[8,1,4,2,6,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,8,2,3,5]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,8,2,3,6]=>[1,5,8,6,2,4,7,3]=>[8,4,1,3,7,5,2,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,1,8,2,4]=>[1,6,8,4,7,2,5,3]=>[8,3,1,5,2,7,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,7,8,1,2]=>[1,5,7,2,3,6,8,4]=>[8,4,2,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,8,6,2,3]=>[1,4,5,8,3,2,7,6]=>[8,5,4,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,8,6,3,4]=>[1,7,3,2,5,8,4,6]=>[8,2,6,7,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,1,6,2,4]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,5,2,3,4]=>[1,8,4,7,3,2,6,5]=>[8,1,5,2,6,7,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,1,6,3,4]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,2,5,1,3]=>[1,6,5,2,4,8,3,7]=>[8,3,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,5,1,2,4]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,7,1,4,5]=>[1,3,8,5,7,4,2,6]=>[8,6,1,4,2,5,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,1,3,5,6]=>[1,2,4,7,5,3,8,6]=>[8,7,5,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,1,2,4,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,1,2,3,6]=>[1,5,2,4,7,3,8,6]=>[8,4,7,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,7,1,3,5]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,6,2,3,5]=>[1,4,8,5,6,2,7,3]=>[8,5,1,4,3,7,2,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,4,1,2,3]=>[1,7,2,5,4,6,3,8]=>[8,2,7,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,5,1,2,3]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,6,2,3,4]=>[1,5,6,2,8,4,3,7]=>[8,4,3,7,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,4,2,8,7]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,5,1,6,2]=>[1,3,7,6,2,8,4,5]=>[8,6,2,3,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,5,8,2,3]=>[1,6,8,3,2,7,4,5]=>[8,3,1,6,7,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,1,2,6,4]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,1,6,5,3]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,8,6,3,2]=>[1,7,3,2,5,8,4,6]=>[8,2,6,7,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,8,4,7,2]=>[1,6,4,2,5,8,3,7]=>[8,3,5,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,1,5,7,2]=>[1,6,5,2,4,8,3,7]=>[8,3,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,2,5,7,4]=>[1,8,4,2,6,5,3,7]=>[8,1,5,7,3,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,2,6,5,3]=>[1,8,3,2,7,5,4,6]=>[8,1,6,7,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,1,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,9,1,7]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,8,9,1,6]=>[1,2,3,4,5,7,9,6,8]=>[9,8,7,6,5,3,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,5,6,7,8,9,1,4]=>[1,2,3,5,7,9,4,6,8]=>[9,8,7,5,3,1,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,1,2]=>[1,3,5,7,9,2,4,6,8]=>[9,7,5,3,1,8,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,1]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,1,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,10,1,9]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,9,7,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,9,10,1,8]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,8,9,6,7]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,9,10,1,7]=>[1,2,3,4,5,6,8,10,7,9]=>[10,9,8,7,6,5,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,7,8,9,5,6]=>[1,2,3,4,5,7,9,6,8]=>[9,8,7,6,5,3,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,6,7,8,9,10,1,5]=>[1,2,3,4,6,8,10,5,7,9]=>[10,9,8,7,5,3,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,5,6,7,8,9,3,4]=>[1,2,3,5,7,9,4,6,8]=>[9,8,7,5,3,1,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,5,6,7,8,9,10,1,3]=>[1,2,4,6,8,10,3,5,7,9]=>[10,9,7,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,10,1,2]=>[1,3,5,7,9,2,4,6,8,10]=>[10,8,6,4,2,9,7,5,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,6,4,5,7,2,8,1]=>[1,3,4,5,7,8,2,6]=>[8,6,5,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,1,8,4,7]=>[1,6,8,7,4,5,2,3]=>[8,3,1,2,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,2,7,1,4]=>[1,8,4,6,7,2,5,3]=>[8,1,5,3,2,7,4,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,7,1,5]=>[1,8,5,4,3,6,7,2]=>[8,1,4,5,6,3,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,4,5,8,1]=>[1,7,8,2,3,6,5,4]=>[8,2,1,7,6,3,4,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,4,5,8,1]=>[1,6,5,4,3,7,8,2]=>[8,3,4,5,6,2,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,4,5,8,1]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,3,6,8,1]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,4,5,8,1]=>[1,2,7,8,3,6,5,4]=>[8,7,2,1,6,3,4,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,2,8,4,7]=>[1,6,8,7,4,2,5,3]=>[8,3,1,2,5,7,4,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,3,7,1,4]=>[1,8,4,2,6,7,3,5]=>[8,1,5,7,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,7,3,4,6]=>[1,8,6,3,2,5,7,4]=>[8,1,3,6,7,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,8,3,4,6]=>[1,7,4,2,5,8,6,3]=>[8,2,5,7,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,2,8,4,6]=>[1,5,2,7,4,3,6,8]=>[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,1,8,4,7]=>[1,5,2,6,8,7,4,3]=>[8,4,7,3,1,2,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,1,8,3,7]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,2,7,1,4]=>[1,6,7,2,8,4,5,3]=>[8,3,2,7,1,5,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,7,2,4,5]=>[1,2,8,5,7,4,3,6]=>[8,7,1,4,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,7,2,4,5]=>[1,3,6,2,8,5,7,4]=>[8,6,3,7,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,7,2,3,6]=>[1,4,5,7,3,2,8,6]=>[8,5,4,2,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,8,2,3,6]=>[1,4,5,8,6,2,3,7]=>[8,5,4,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,1,8,3,6]=>[1,4,7,3,5,2,6,8]=>[8,5,2,6,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,2,8,4,5]=>[1,6,8,5,2,3,7,4]=>[8,3,1,4,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,7,3,4,5]=>[1,8,5,7,4,2,3,6]=>[8,1,4,2,5,7,6,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,8,2,4,6]=>[1,7,4,5,8,6,2,3]=>[8,2,5,4,1,3,7,6]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,6,8,2,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,7,1,4,6]=>[1,5,7,4,8,6,2,3]=>[8,4,2,5,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,7,2,4,6]=>[1,5,7,4,8,6,2,3]=>[8,4,2,5,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,6,1,2,4]=>[1,8,4,7,2,5,6,3]=>[8,1,5,2,7,4,3,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,3,5,1,4]=>[1,7,2,6,5,3,8,4]=>[8,2,7,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,4,6,1,5]=>[1,3,8,5,4,2,7,6]=>[8,6,1,4,5,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,2,5,1,4]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,2,6,1,3]=>[1,5,2,4,8,3,7,6]=>[8,4,7,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,7,1,3,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,7,1,4,5]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,6,2,4,5]=>[1,3,8,5,6,2,7,4]=>[8,6,1,4,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,1,4,5,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,1,3,4,5]=>[1,7,4,6,3,8,5,2]=>[8,2,5,3,6,1,4,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,3,4,5,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,1,3,4,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,3,4,5,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,2,4,5,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,6,2,4,5]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,7,2,3,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,6,1,2,3]=>[1,5,6,2,4,7,3,8]=>[8,4,3,7,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,5,1,2,4]=>[1,6,2,8,4,7,3,5]=>[8,3,7,1,5,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,5,1,3,4]=>[1,7,3,6,2,8,4,5]=>[8,2,6,3,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,3,2,5,4]=>[1,8,4,7,5,3,6,2]=>[8,1,5,2,4,6,3,7]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,3,2,4,5]=>[1,8,5,3,6,2,4,7]=>[8,1,4,6,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,7,2,4,6]=>[1,8,6,2,3,5,7,4]=>[8,1,3,7,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,6,2,4,7]=>[1,8,7,4,3,5,6,2]=>[8,1,2,5,6,4,3,7]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,6,2,4,8]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,6,2,4,1]=>[1,7,4,3,8,2,5,6]=>[8,2,5,6,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,2,6,5,8]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,6,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,7,6,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,6,7,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,5,6,7]=>[1,8,7,6,5,2,3,4]=>[8,1,2,3,4,7,6,5]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,2,5,7,1]=>[1,6,5,2,4,8,3,7]=>[8,3,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,6,2,8,4]=>[1,7,8,4,3,2,5,6]=>[8,2,1,5,6,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,2,6,1,5]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,2,5,1,6]=>[1,7,2,4,3,8,6,5]=>[8,2,7,5,6,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,2,5,1,7]=>[1,6,5,2,4,8,7,3]=>[8,3,4,7,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,8,6,1,7]=>[1,5,8,7,2,4,3,6]=>[8,4,1,2,7,5,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,7,2,1,4]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,7,1,2,3]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,7,8,2,3]=>[1,6,8,3,4,2,5,7]=>[8,3,1,6,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,2,7,8,5]=>[1,6,7,8,5,2,4,3]=>[8,3,2,1,4,7,5,6]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,8,2,7,4]=>[1,6,2,5,8,4,3,7]=>[8,3,7,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,8,6,2,3]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,2,8,5,6]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,2,8,5,7]=>[1,6,8,7,5,2,4,3]=>[8,3,1,2,4,7,5,6]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,7,2,4,8]=>[1,6,2,5,7,4,3,8]=>[8,3,7,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,8,2,4,7]=>[1,6,2,5,8,7,4,3]=>[8,3,7,4,1,2,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,8,2,4,6]=>[1,7,4,3,2,5,8,6]=>[8,2,5,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,3,2,4,5]=>[1,7,4,8,5,3,2,6]=>[8,2,5,1,4,6,7,3]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,4,5,2,3]=>[1,7,2,6,5,4,8,3]=>[8,2,7,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,4,5,2,3]=>[1,7,2,6,5,4,3,8]=>[8,2,7,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,8,2,4,1]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,2,1,5,8]=>[1,6,2,4,7,5,3,8]=>[8,3,7,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,2,1,6,5]=>[1,7,6,2,4,3,8,5]=>[8,2,3,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,1,2,6,4]=>[1,7,6,2,5,3,8,4]=>[8,2,3,7,4,6,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,1,6,2,3]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,1,7,2,3]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,1,2,7,4]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,8,1,7,6]=>[1,5,8,6,2,4,3,7]=>[8,4,1,3,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,2,1,8,5]=>[1,6,2,4,7,8,5,3]=>[8,3,7,5,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,1,2,8,4]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,8,2,1,4]=>[1,6,2,5,8,4,7,3]=>[8,3,7,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,2,8,1,5]=>[1,6,8,5,2,4,7,3]=>[8,3,1,4,7,5,2,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,3,4,8,7]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,2,1,4,6]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,5,8,3,4]=>[1,7,3,2,6,8,4,5]=>[8,2,6,7,3,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,4,3,5,6]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,1,5,6,2]=>[1,8,2,3,7,6,5,4]=>[8,1,7,6,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,5,4,6,3]=>[1,7,6,4,2,8,3,5]=>[8,2,3,5,7,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,1,4,7,5]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,2,4,5,7]=>[1,6,4,3,8,7,5,2]=>[8,3,5,6,1,2,4,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,7,6,2,5]=>[1,8,5,7,2,4,3,6]=>[8,1,4,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,2,1,6,3]=>[1,5,2,8,3,7,6,4]=>[8,4,7,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,8,3,4,2]=>[1,7,4,6,3,2,5,8]=>[8,2,5,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,8,7,4,3]=>[1,6,7,4,2,5,8,3]=>[8,3,2,5,7,4,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,8,2,6,5]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,3,5,6,7]=>[1,2,8,7,6,5,3,4]=>[8,7,1,2,3,4,6,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,3,5,7,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,3,4,7,8]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,3,4,6,8]=>[1,2,7,6,4,5,3,8]=>[8,7,2,3,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,3,4,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,6,3,4,5,8]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,3,5,4,6]=>[1,2,7,4,8,6,5,3]=>[8,7,2,5,1,3,4,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,3,5,4,7]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,3,6,5,7]=>[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,4,6,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,4,6,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,4,6,5,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,4,6,5,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,3,6,5,8]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,3,6,4,8]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,3,5,4,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,3,5,4,7]=>[1,2,8,7,4,6,5,3]=>[8,7,1,2,5,3,4,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,3,6,4,7]=>[1,2,8,7,4,5,3,6]=>[8,7,1,2,5,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,3,7,4,8]=>[1,2,6,7,4,5,3,8]=>[8,7,3,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,3,7,6,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,3,7,5,8]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,3,6,5,8]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,3,6,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,6,5,7]=>[1,2,8,7,5,4,3,6]=>[8,7,1,2,4,5,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,6,5,8]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,7,5,6]=>[1,2,8,6,7,5,4,3]=>[8,7,1,3,2,4,5,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,3,7,5,6]=>[1,2,8,6,7,5,3,4]=>[8,7,1,3,2,4,6,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,3,8,5,6]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,3,8,5,7]=>[1,2,6,8,7,5,3,4]=>[8,7,3,1,2,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,3,8,6,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,3,7,4,6]=>[1,2,8,6,7,4,5,3]=>[8,7,1,3,2,5,4,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,3,7,4,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,6,3,8,4,5]=>[1,2,7,4,6,8,5,3]=>[8,7,2,5,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,4,7,5,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,4,7,5,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,3,7,4,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,3,7,4,5]=>[1,2,6,7,4,8,5,3]=>[8,7,3,2,5,1,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,3,6,4,5]=>[1,2,7,4,8,5,3,6]=>[8,7,2,5,1,4,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,3,6,4,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,2,5,1,8]=>[1,4,7,2,6,5,3,8]=>[8,5,2,7,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,5,2,1,8]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,5,1,2,7]=>[1,4,8,7,2,6,3,5]=>[8,5,1,2,7,3,6,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,5,3,1,8]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,4,3,1,8]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,3,1,7,2]=>[1,5,3,8,2,6,4,7]=>[8,4,6,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,6,2,3]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,6,3,2]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,3,6,2]=>[1,5,2,7,6,3,8,4]=>[8,4,7,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,2,1,7,3]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,4,1,7,3]=>[1,5,4,2,6,3,8,7]=>[8,4,5,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,5,1,7,4]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,5,1,4,7]=>[1,3,6,2,4,8,7,5]=>[8,6,3,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,5,1,3,7]=>[1,4,8,7,3,2,6,5]=>[8,5,1,2,6,7,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,4,1,3,7]=>[1,5,4,2,6,3,8,7]=>[8,4,5,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,2,1,3,7]=>[1,5,2,6,3,8,7,4]=>[8,4,7,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,3,2,6]=>[1,5,2,7,3,8,6,4]=>[8,4,7,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,2,6,3]=>[1,5,2,7,6,3,8,4]=>[8,4,7,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,2,3,6]=>[1,5,2,7,3,8,6,4]=>[8,4,7,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,5,2,3,4]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,5,2,4,3]=>[1,6,2,7,4,3,8,5]=>[8,3,7,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,5,3,2,4]=>[1,6,3,8,4,2,7,5]=>[8,3,6,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,6,3,4]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,1,6,3,5]=>[1,4,8,5,2,7,3,6]=>[8,5,1,4,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,6,5,4]=>[1,3,7,5,2,4,8,6]=>[8,6,2,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,1,6,5,3]=>[1,4,8,3,2,7,5,6]=>[8,5,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,6,4,3]=>[1,5,2,7,4,3,8,6]=>[8,4,7,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,5,4,2]=>[1,6,5,3,8,2,7,4]=>[8,3,4,6,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,3,5,2]=>[1,6,3,8,2,7,5,4]=>[8,3,6,1,7,2,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,4,5,2]=>[1,6,4,2,7,5,3,8]=>[8,3,5,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,4,6,3]=>[1,5,2,7,6,4,3,8]=>[8,4,7,2,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,1,5,6,3]=>[1,4,8,3,2,7,6,5]=>[8,5,1,6,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,4,1,7,5]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,3,1,7,5]=>[1,4,8,5,3,2,6,7]=>[8,5,1,4,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,2,1,7,4]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,4,6,2]=>[1,5,2,7,6,4,3,8]=>[8,4,7,2,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,6,4,2]=>[1,5,2,7,4,3,8,6]=>[8,4,7,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,6,2,4]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,1,6,2,5]=>[1,4,8,5,2,7,3,6]=>[8,5,1,4,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,1,6,5,2]=>[1,4,8,2,7,5,3,6]=>[8,5,1,7,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,1,5,6,2]=>[1,4,8,2,7,6,5,3]=>[8,5,1,7,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,2,1,7,5]=>[1,4,8,5,2,6,3,7]=>[8,5,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,8,1,7,6]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,8,1,7,6]=>[1,3,5,8,6,2,4,7]=>[8,6,4,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,8,1,6,7]=>[1,4,2,5,8,7,6,3]=>[8,5,7,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,1,2,5,6]=>[1,4,8,6,2,7,5,3]=>[8,5,1,3,7,2,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,2,4,6]=>[1,5,2,7,4,3,8,6]=>[8,4,7,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,2,6,4]=>[1,5,2,7,6,3,8,4]=>[8,4,7,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,4,2,6]=>[1,5,2,7,3,8,6,4]=>[8,4,7,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,2,1,4,7]=>[1,5,2,6,3,8,7,4]=>[8,4,7,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,5,4,6]=>[1,3,7,4,8,6,5,2]=>[8,6,2,5,1,3,4,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,4,3,6]=>[1,5,2,7,3,8,6,4]=>[8,4,7,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,3,2,5]=>[1,6,3,8,5,4,2,7]=>[8,3,6,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,2,5,3]=>[1,6,2,7,5,4,3,8]=>[8,3,7,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,2,3,5]=>[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,5,3,4]=>[1,6,5,2,7,3,8,4]=>[8,3,4,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,5,4,3]=>[1,6,5,2,7,4,3,8]=>[8,3,4,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,4,5,3]=>[1,6,4,2,7,5,3,8]=>[8,3,5,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,2,5,4]=>[1,6,2,7,5,3,8,4]=>[8,3,7,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,3,6,4]=>[1,5,2,7,6,3,8,4]=>[8,4,7,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,4,6,5]=>[1,3,7,6,4,8,5,2]=>[8,6,2,3,5,1,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,2,4,5]=>[1,6,2,7,4,3,8,5]=>[8,3,7,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,3,5,4]=>[1,6,3,8,4,2,7,5]=>[8,3,6,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,1,6,4,3]=>[1,7,4,5,2,3,8,6]=>[8,2,5,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,2,6,4,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,4,2,6,8]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,6,1,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,5,6,1,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,5,6,1,3]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,5,2,4,8]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,5,1,7,4]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,5,6,3,1]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,1,8,4]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,1,2,8,6]=>[1,4,5,2,3,7,8,6]=>[8,5,4,7,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,5,6,8,2]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,5,2,8,4]=>[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,7,6,8,5]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,7,5,8,6]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,7,1,4,8,2]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,4,1,8,3]=>[1,6,2,5,4,7,8,3]=>[8,3,7,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,4,8,7,1]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,7,2,4,3]=>[1,5,7,4,8,3,2,6]=>[8,4,2,5,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,2,7,4,1]=>[1,6,7,4,8,2,3,5]=>[8,3,2,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,2,3,7,1]=>[1,6,3,8,2,5,4,7]=>[8,3,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,3,7,1,4]=>[1,6,7,2,3,5,4,8]=>[8,3,2,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,7,6,3,4]=>[1,5,7,3,2,4,8,6]=>[8,4,2,6,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,4,6,2,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,1,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,5,1,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,5,8,6,1,4]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,2,7,3,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,7,1,8,3,6]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,1,8,7,2]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,8,4,2,1]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,8,4,7,3]=>[1,2,6,4,5,8,3,7]=>[8,7,3,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,3,8,4,2]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,7,8,5,6]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,7,8,6,5]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,2,8,6,3]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,8,2,5,1]=>[1,3,4,7,5,8,2,6]=>[8,6,5,2,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,7,1,8,2]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,1,7,8,3]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,3,6,5,8]=>[1,7,5,3,2,4,6,8]=>[8,2,4,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,2,6,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,6,5,8]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,5,4,8,1]=>[1,6,4,2,7,8,3,5]=>[8,3,5,7,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,2,3,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,6,2,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,5,6,3,4,8]=>[1,7,4,5,6,3,2,8]=>[8,2,5,4,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,5,4,3,8]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,1,5,4,2,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,1,3,2,8]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,3,7,2,5]=>[1,2,8,5,3,6,7,4]=>[8,7,1,4,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,1,3,8,2]=>[1,6,3,7,8,2,4,5]=>[8,3,6,2,1,7,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,5,4,8,2]=>[1,6,4,2,3,7,8,5]=>[8,3,5,7,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,5,4,8,3]=>[1,6,4,7,8,3,2,5]=>[8,3,5,2,1,6,7,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,5,4,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,1,3,7,6]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,3,7,1,5]=>[1,2,6,7,3,8,5,4]=>[8,7,3,2,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,3,6,5,1]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,3,6,5,2]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,6,3,4,2]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,6,3,4,1]=>[1,2,7,4,5,6,3,8]=>[8,7,2,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,7,3,1,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,1,3,4]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,1,7,3,5]=>[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,6,7,4,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,6,8,4,2]=>[1,5,6,8,2,3,7,4]=>[8,4,3,1,7,6,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,8,1,3,2]=>[1,4,6,2,5,8,3,7]=>[8,5,3,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,8,3,1,2]=>[1,4,5,8,2,6,3,7]=>[8,5,4,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,8,2,3,1]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,8,2,1,3]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,1,8,2,3]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,7,8,2,4]=>[1,5,7,2,3,6,8,4]=>[8,4,2,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,7,8,3,4]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,7,2,8,4]=>[1,6,2,3,5,7,8,4]=>[8,3,7,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,1,2,8,3]=>[1,6,2,4,7,8,3,5]=>[8,3,7,5,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,2,1,8,3]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,2,8,1,3]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,2,7,3,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,6,7,4,5]=>[1,2,8,5,6,7,4,3]=>[8,7,1,4,3,2,5,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,7,8,5]=>[1,6,7,8,5,2,4,3]=>[8,3,2,1,4,7,5,6]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,3,8,7,6]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,2,8,7,6]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,8,6,5,1]=>[1,4,2,7,5,8,3,6]=>[8,5,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,2,6,5,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,2,6,5,1]=>[1,3,4,8,2,7,5,6]=>[8,6,5,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,2,7,1,5]=>[1,3,4,8,5,2,6,7]=>[8,6,5,1,4,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,2,1,7,6]=>[1,3,4,8,6,2,5,7]=>[8,6,5,1,3,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,1,2,7,6]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,8,2,7,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,8,3,7,6]=>[1,4,5,8,6,3,2,7]=>[8,5,4,1,3,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,8,7,2,5]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,1,7,2,5]=>[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,1,2,4]=>[1,3,6,2,5,7,4,8]=>[8,6,3,7,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,7,2,1,4]=>[1,3,5,7,2,6,4,8]=>[8,6,4,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,6,2,4,1]=>[1,3,5,6,2,7,4,8]=>[8,6,4,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,6,2,4,3]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,5,4,2,3]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,5,4,1,2]=>[1,3,7,2,6,4,8,5]=>[8,6,2,7,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,6,1,4,2]=>[1,3,7,4,8,2,5,6]=>[8,6,2,5,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,1,6,5,2]=>[1,3,7,5,2,4,8,6]=>[8,6,2,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,8,6,5,3]=>[1,4,7,5,8,3,2,6]=>[8,5,2,4,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,7,6,5,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,1,6,5,3]=>[1,2,4,7,5,3,8,6]=>[8,7,5,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,6,1,4,3]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[7,4,6,1,8,3,5,2]=>[1,7,5,8,2,4,3,6]=>[8,2,4,1,7,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,7,4,6,2]=>[1,8,2,3,5,7,6,4]=>[8,1,7,6,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,7,5,6,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,7,5,6,2]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,7,5,8,3]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,6,8,4,3]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,1,7,5,2]=>[1,6,7,5,2,8,3,4]=>[8,3,2,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,1,7,5,2]=>[1,3,8,2,6,7,5,4]=>[8,6,1,7,3,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,1,8,4,2]=>[1,3,7,4,5,2,6,8]=>[8,6,2,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,1,8,3,2]=>[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,8,4,3,2]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,7,5,3,2]=>[1,6,5,7,3,4,2,8]=>[8,3,4,2,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,6,7,5,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,6,7,5,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,7,6,8,4]=>[1,2,5,7,8,4,3,6]=>[8,7,4,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,1,7,6,8,4]=>[1,2,5,7,8,4,3,6]=>[8,7,4,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,6,7,5,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,6,8,4,3]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,7,5,8,3]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,5,7,1,3]=>[1,4,6,7,2,8,3,5]=>[8,5,3,2,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,6,7,5,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,7,6,8,4]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,7,6,8,5]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,7,6,8,4]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,8,2,3,4]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,7,6,8,4]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,5,8,3,2,4]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,5,8,2,4]=>[1,3,7,2,6,8,4,5]=>[8,6,2,7,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,8,2,4,3]=>[1,7,4,5,8,3,6,2]=>[8,2,5,4,1,6,3,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,8,4,2,3]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,7,5,2,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,7,6,8,4]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,7,6,8,4]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,1,5,8,3,4]=>[1,7,3,2,6,8,4,5]=>[8,2,6,7,3,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,7,6,2,4]=>[1,8,4,5,7,2,3,6]=>[8,1,5,4,2,7,6,3]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,7,5,8,3]=>[1,6,5,7,8,3,4,2]=>[8,3,4,2,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,7,4,8,3]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,8,2,5,3]=>[1,7,5,8,3,6,2,4]=>[8,2,4,1,6,3,7,5]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,7,1,5,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,7,4,8,3]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,5,8,3,1,4]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,6,2,1,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,7,6,8,4]=>[1,2,5,7,8,4,3,6]=>[8,7,4,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,7,6,8,4]=>[1,5,7,8,4,3,2,6]=>[8,4,2,1,5,6,7,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,8,4,1,3]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,7,5,1,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,7,5,8,3]=>[1,6,5,7,8,3,4,2]=>[8,3,4,2,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,7,1,4,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,5,7,1,4]=>[1,3,8,4,2,6,7,5]=>[8,6,1,5,7,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,7,6,1,4]=>[1,8,4,5,7,2,3,6]=>[8,1,5,4,2,7,6,3]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,7,6,8,5]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,7,6,8,5]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,7,6,8,5]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,7,6,8,4]=>[1,2,5,7,8,4,3,6]=>[8,7,4,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,5,7,1,4]=>[1,6,7,2,8,4,3,5]=>[8,3,2,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,5,8,2,4]=>[1,6,8,4,3,2,7,5]=>[8,3,1,5,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,6,1,2,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,7,6,8,4]=>[1,5,7,8,4,3,2,6]=>[8,4,2,1,5,6,7,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,7,6,8,5]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,3,6,5,7]=>[1,8,7,5,3,2,4,6]=>[8,1,2,4,6,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,6,2,7,4]=>[1,8,4,5,6,2,3,7]=>[8,1,5,4,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,2,6,7,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,4,5,7,6]=>[1,8,6,5,4,2,3,7]=>[8,1,3,4,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,4,5,6,1]=>[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,4,5,7,1]=>[1,2,6,5,4,8,3,7]=>[8,7,3,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,4,5,8,7]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,5,6,1,2,3]=>[1,4,5,6,2,7,3,8]=>[8,5,4,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,2,6,1,5]=>[1,3,8,5,2,7,4,6]=>[8,6,1,4,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,4,5,1,6]=>[1,3,8,6,5,4,2,7]=>[8,6,1,3,4,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,4,5,1,7]=>[1,3,2,6,5,4,8,7]=>[8,6,7,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,4,5,8,1]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,8,6,1,7]=>[1,3,2,5,8,7,4,6]=>[8,6,7,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,8,7,1,6]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,8,7,1,2,3]=>[1,4,8,3,5,7,2,6]=>[8,5,1,6,4,2,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,3,8,5,6]=>[1,7,5,3,2,4,6,8]=>[8,2,4,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,3,7,5,8]=>[1,6,7,5,3,4,2,8]=>[8,3,2,4,6,5,7,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,7,5,1]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,8,7,3,4,1]=>[1,2,6,3,5,7,4,8]=>[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,3,4,1]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,3,8,5,1]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,2,1,6,5]=>[1,4,3,8,5,2,7,6]=>[8,5,6,1,4,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,1,2,7,4]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,7,1,6,8]=>[1,4,3,5,7,6,2,8]=>[8,5,6,4,2,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,2,1,8,5]=>[1,4,7,8,5,2,3,6]=>[8,5,2,1,4,7,6,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,2,8,1,5]=>[1,3,6,8,5,2,4,7]=>[8,6,3,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,7,8,1,6]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,6,8,1,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,8,6,4,3]=>[1,5,8,3,2,4,7,6]=>[8,4,1,6,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,6,5,2,3]=>[1,4,8,3,2,7,5,6]=>[8,5,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,8,6,5,3]=>[1,4,2,7,5,8,3,6]=>[8,5,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,2,7,5,3]=>[1,4,2,6,7,5,3,8]=>[8,5,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,5,3,2,4]=>[1,6,3,7,2,8,4,5]=>[8,3,6,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,5,1,2,4]=>[1,6,2,8,4,3,7,5]=>[8,3,7,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,3,5,2,4]=>[1,7,2,8,4,6,5,3]=>[8,2,7,1,5,3,4,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,5,2,1,4]=>[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,6,1,5,3]=>[1,4,8,3,2,7,5,6]=>[8,5,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,8,6,5,2]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,6,3,4]=>[1,8,4,2,5,3,7,6]=>[8,1,5,7,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,5,3,1,4]=>[1,6,3,7,2,8,4,5]=>[8,3,6,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,7,1,5,3]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,7,4,5,2]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,1,7,5,3]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,7,3,5,4]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,6,3,4]=>[1,8,4,2,5,3,7,6]=>[8,1,5,7,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,3,6,4]=>[1,8,4,2,5,3,7,6]=>[8,1,5,7,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,1,4,3,5]=>[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,3,1,6,4]=>[1,8,4,2,5,3,7,6]=>[8,1,5,7,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,7,1,6,3]=>[1,5,7,6,2,8,3,4]=>[8,4,2,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,3,4,6,2]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,5,4,6,2]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,7,1,6,3]=>[1,8,3,5,7,6,2,4]=>[8,1,6,4,2,3,7,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,3,1,6,4]=>[1,8,4,7,6,2,5,3]=>[8,1,5,2,3,7,4,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,4,3,5]=>[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,3,2,5]=>[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,4,3,6,2]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,3,7,5,2]=>[1,2,6,7,5,3,8,4]=>[8,7,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,3,2,5,4]=>[1,6,2,8,4,7,5,3]=>[8,3,7,1,5,2,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,3,2,6,4]=>[1,8,4,2,5,3,7,6]=>[8,1,5,7,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,1,2,6,4]=>[1,8,4,3,7,6,2,5]=>[8,1,5,6,2,3,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,7,2,6,3]=>[1,5,7,6,2,8,3,4]=>[8,4,2,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,5,7,4,3]=>[1,8,3,2,4,6,7,5]=>[8,1,6,7,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,7,4,1,3]=>[1,8,3,5,7,2,4,6]=>[8,1,6,4,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,1,6,2,3]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,1,2,6,3]=>[1,4,7,6,2,8,3,5]=>[8,5,2,3,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,7,2,6,3]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,7,2,6,4]=>[1,8,4,2,5,7,6,3]=>[8,1,5,7,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,1,2,6,4]=>[1,8,4,7,6,2,5,3]=>[8,1,5,2,3,7,4,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,3,7,5,2]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,5,3,6,2]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,2,1,6,3]=>[1,4,7,6,2,8,3,5]=>[8,5,2,3,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,2,1,6,4]=>[1,8,4,7,6,2,5,3]=>[8,1,5,2,3,7,4,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,1,4,2,5]=>[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,2,4,5]=>[1,8,5,3,6,2,7,4]=>[8,1,4,6,3,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,7,1,6,4]=>[1,8,4,2,5,7,6,3]=>[8,1,5,7,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,7,1,6,3]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,3,5,6,2]=>[1,2,8,3,7,6,5,4]=>[8,7,1,6,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,4,5,6,2]=>[1,2,8,3,7,6,5,4]=>[8,7,1,6,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,7,1,6,4]=>[1,8,4,3,2,5,7,6]=>[8,1,5,6,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,4,2,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,2,7,6,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,7,3,6]=>[1,8,6,7,3,4,2,5]=>[8,1,3,2,6,5,7,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,7,6,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,1,3,8,7]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,3,1,8,7]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,1,4,8,7]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,1,2,8,7]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,3,2,8,7]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,2,7,6,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,3,2,5]=>[1,8,5,6,3,4,2,7]=>[8,1,4,3,6,5,7,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,3,5,2]=>[1,8,2,7,5,6,3,4]=>[8,1,7,2,4,3,6,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,5,3,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,3,7,6,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,1,7,6,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,7,6,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,3,7,6,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,7,4,6]=>[1,8,6,7,4,5,2,3]=>[8,1,3,2,5,4,7,6]=>[8,2,4,3,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,1,7,2,6]=>[1,8,6,7,2,5,3,4]=>[8,1,3,2,7,4,6,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,3,7,2,6]=>[1,8,6,7,2,5,3,4]=>[8,1,3,2,7,4,6,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,5,2,3]=>[1,8,3,4,2,7,5,6]=>[8,1,6,5,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,2,5,3]=>[1,8,3,4,2,7,5,6]=>[8,1,6,5,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,1,4,3]=>[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,2,1,5]=>[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,4,1,5]=>[1,8,5,6,4,7,2,3]=>[8,1,4,3,5,2,7,6]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,4,3,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,4,5,3]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,4,5,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,2,5,1]=>[1,8,2,7,5,6,3,4]=>[8,1,7,2,4,3,6,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,4,3,1]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,3,7,6,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,5,3,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,3,5,1]=>[1,8,2,7,5,6,3,4]=>[8,1,7,2,4,3,6,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,3,1,5]=>[1,8,5,6,3,4,2,7]=>[8,1,4,3,6,5,7,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,4,2,5]=>[1,8,5,6,4,7,2,3]=>[8,1,4,3,5,2,7,6]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,4,5,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,5,4,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,4,7,6,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,4,7,2,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,5,2,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,2,5,4]=>[1,8,4,7,5,6,2,3]=>[8,1,5,2,4,3,7,6]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,1,5,3]=>[1,8,3,4,2,7,5,6]=>[8,1,6,5,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,5,1,3]=>[1,8,3,4,2,7,5,6]=>[8,1,6,5,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,3,7,1,6]=>[1,8,6,7,2,5,3,4]=>[8,1,3,2,7,4,6,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,4,7,1,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,4,7,3,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,5,1,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,5,1,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,1,4,2]=>[1,8,2,7,4,5,3,6]=>[8,1,7,2,5,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,3,2,4]=>[1,8,4,5,2,7,3,6]=>[8,1,5,4,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,3,4,2]=>[1,8,2,7,4,5,3,6]=>[8,1,7,2,5,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,4,3,2]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,1,3,2]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,1,5,2]=>[1,8,2,7,5,6,3,4]=>[8,1,7,2,4,3,6,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,1,5,4]=>[1,8,4,7,5,6,2,3]=>[8,1,5,2,4,3,7,6]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,3,5,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,1,4,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,4,2,3]=>[1,8,3,6,4,5,2,7]=>[8,1,6,3,5,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,2,4,3]=>[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,8,4,6,2]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,7,4,3,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,8,6,5,2]=>[1,7,5,8,2,4,3,6]=>[8,2,4,1,7,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,8,4,3,2]=>[1,7,3,5,8,2,6,4]=>[8,2,6,4,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,8,5,3,2]=>[1,7,3,4,2,6,5,8]=>[8,2,6,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,7,5,3,8]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,8,7,6,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,7,8,5,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,7,8,4,3]=>[1,2,6,8,3,5,7,4]=>[8,7,3,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,6,8,2,3]=>[1,4,2,5,6,8,3,7]=>[8,5,7,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,8,4,3,7]=>[1,6,4,2,5,8,7,3]=>[8,3,5,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,8,5,3,7]=>[1,6,5,8,7,3,2,4]=>[8,3,4,1,2,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,6,5,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,8,2,5,6]=>[1,7,5,8,6,2,3,4]=>[8,2,4,1,3,7,6,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,8,2,3,4]=>[1,7,3,5,8,4,6,2]=>[8,2,6,4,1,5,3,7]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,7,8,3,4]=>[1,2,6,8,4,5,7,3]=>[8,7,3,1,5,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,8,5,2,3]=>[1,7,2,4,6,5,8,3]=>[8,2,7,5,3,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,8,6,7,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,6,8,7,4]=>[1,3,2,5,6,8,4,7]=>[8,6,7,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,7,3,4,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,8,7,3,4]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,8,6,2,4]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,8,5,7,3]=>[1,6,5,8,3,4,2,7]=>[8,3,4,1,6,5,7,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,8,6,2,5]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,4,8,7,3,5]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,7,3,5,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,8,7,4,6]=>[1,5,8,6,7,4,3,2]=>[8,4,1,3,2,5,6,7]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,8,5,2,6]=>[1,7,2,4,3,5,8,6]=>[8,2,7,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,8,4,2,6]=>[1,7,2,5,8,6,4,3]=>[8,2,7,4,1,3,5,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,4,8,2,5]=>[1,3,7,2,6,8,5,4]=>[8,6,2,7,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,8,3,2,5]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,8,7,5,6]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,7,8,3,5]=>[1,2,6,8,5,7,3,4]=>[8,7,3,1,4,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,8,2,4,6]=>[1,7,4,5,8,6,2,3]=>[8,2,5,4,1,3,7,6]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,6,4,8,7]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,5,2,4,1]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,4,1,8,6]=>[1,7,8,6,2,3,5,4]=>[8,2,1,3,7,6,4,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,5,2,8,7]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,5,2,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,4,1,8,6]=>[1,5,4,3,7,8,6,2]=>[8,4,5,6,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,4,1,8,5]=>[1,6,2,3,7,8,5,4]=>[8,3,7,6,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,5,2,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,5,2,8,6]=>[1,4,3,7,8,6,2,5]=>[8,5,6,2,1,3,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,5,2,8,6]=>[1,3,7,8,6,2,4,5]=>[8,6,2,1,3,7,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,7,3,5,2]=>[1,4,6,3,8,2,5,7]=>[8,5,3,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,4,1,5,2]=>[1,8,2,6,3,7,5,4]=>[8,1,7,3,6,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,4,1,6,2]=>[1,8,2,5,4,3,7,6]=>[8,1,7,4,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,7,3,4,1]=>[1,8,2,5,7,4,3,6]=>[8,1,7,4,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,5,1,6,2]=>[1,8,2,4,3,7,6,5]=>[8,1,7,5,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,7,3,6,2]=>[1,4,5,7,6,3,8,2]=>[8,5,4,2,3,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,7,4,6,2]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,4,6,3]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,6,3,8,5]=>[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,6,2,8,5]=>[1,4,3,7,8,5,6,2]=>[8,5,6,2,1,4,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,6,2,8,4]=>[1,5,6,2,3,7,8,4]=>[8,4,3,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,5,1,8,4]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,2,5,1]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,5,1,8,4]=>[1,7,8,4,2,3,6,5]=>[8,2,1,5,7,6,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,7,3,8,4]=>[1,6,3,5,7,8,4,2]=>[8,3,6,4,2,1,5,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,1,7,3,8,6]=>[1,5,7,8,6,3,4,2]=>[8,4,2,1,3,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,7,3,8,5]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,6,2,4,1]=>[1,8,2,5,6,3,7,4]=>[8,1,7,4,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,6,2,3,1]=>[1,8,2,5,6,3,7,4]=>[8,1,7,4,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,3,1,8,5]=>[1,7,8,5,3,6,2,4]=>[8,2,1,4,6,3,7,5]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,7,4,8,5]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,7,4,8,6]=>[1,5,7,8,6,4,2,3]=>[8,4,2,1,3,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,7,5,8,6]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,8,6,7,5]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,8,5,7,4]=>[1,6,5,8,4,2,3,7]=>[8,3,4,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,3,1,7,4]=>[1,8,4,2,5,3,6,7]=>[8,1,5,7,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,6,2,3,1]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,6,2,4,1]=>[1,7,4,5,6,2,3,8]=>[8,2,5,4,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,4,1,7,3]=>[1,8,3,6,2,5,4,7]=>[8,1,6,3,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,1,8,6,7,3]=>[1,5,8,3,4,2,6,7]=>[8,4,1,6,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,8,6,7,3]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,8,6,7,4]=>[1,3,5,8,4,2,6,7]=>[8,6,4,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,8,5,7,4]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,8,5,7,3]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,8,4,7,3]=>[1,5,8,3,6,4,2,7]=>[8,4,1,6,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,5,1,7,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,6,2,5,1]=>[1,7,5,6,2,3,8,4]=>[8,2,4,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,8,4,5,1]=>[1,6,4,3,7,5,8,2]=>[8,3,5,6,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,6,2,7,3]=>[1,8,3,5,6,2,4,7]=>[8,1,6,4,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,6,2,7,3]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,6,2,7,3]=>[1,4,5,6,2,3,8,7]=>[8,5,4,3,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,6,3,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,8,5,6,3]=>[1,2,3,7,6,5,8,4]=>[8,7,6,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,8,5,6,2]=>[1,3,7,6,5,8,2,4]=>[8,6,2,3,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,8,5,6,2]=>[1,4,3,7,6,5,8,2]=>[8,5,6,2,3,4,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,7,3,6,2]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,8,4,5,1]=>[1,7,5,8,2,3,6,4]=>[8,2,4,1,7,6,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,7,2,5,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,7,2,5,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,5,6,1,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,6,4,1,2]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,2,3,6,5]=>[1,7,6,3,2,8,5,4]=>[8,2,3,6,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,3,1,6,2]=>[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,3,2,7,8]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,7,1,5]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,3,7,5,2]=>[1,2,4,8,3,6,7,5]=>[8,7,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,3,1,6,7]=>[1,2,4,5,3,8,7,6]=>[8,7,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,4,7,6,3]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,7,6,1,2]=>[1,3,8,2,5,7,4,6]=>[8,6,1,7,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,7,3,8,5]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,3,1,8,7]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,3,6,8,2]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,2,4,1,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,1,4,8,2]=>[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,2,1,8,4]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,2,4,8,3]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,4,5,8,7]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,5,3,8,6]=>[1,2,4,3,7,8,6,5]=>[8,7,5,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,3,5,1,2]=>[1,4,8,2,6,5,3,7]=>[8,5,1,7,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,4,2,5,7]=>[1,3,2,6,4,8,7,5]=>[8,6,7,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,8,2,4,3]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,1,4,2]=>[1,3,6,2,5,8,4,7]=>[8,6,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,7,8,2,1,4]=>[1,3,5,8,4,7,2,6]=>[8,6,4,1,5,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,6,1,4,3,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,8,4,1,3]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,4,5,3,7]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,5,3,4,6]=>[1,2,7,4,8,6,3,5]=>[8,7,2,5,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,5,4,1,2]=>[1,3,6,4,8,2,7,5]=>[8,6,3,5,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,6,7,1,2]=>[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,6,3,7,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,4,6,7,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,5,6,1,7]=>[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,6,1,7,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,5,2,6,8]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,6,2,5,7]=>[1,4,3,8,7,5,6,2]=>[8,5,6,1,2,4,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,3,4,2]=>[1,5,2,7,4,6,3,8]=>[8,4,7,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,8,2,6,5]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,1,2,7,8]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,7,8,6,3]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,8,3,5,6]=>[1,7,5,8,6,3,2,4]=>[8,2,4,1,3,6,7,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,6,3,8,1,4]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,1,4,8]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,2,8,1,3]=>[1,5,2,6,8,3,7,4]=>[8,4,7,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,1,8,3,2]=>[1,5,2,7,3,6,8,4]=>[8,4,7,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,2,8,3,4]=>[1,6,8,4,5,2,7,3]=>[8,3,1,5,4,7,2,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,4,8,3,6]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,2,3,8,7]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,4,2,8,6]=>[1,7,8,6,2,3,5,4]=>[8,2,1,3,7,6,4,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,2,5,3,8]=>[1,7,3,6,5,2,4,8]=>[8,2,6,3,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,2,5,7,3]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,7,5,4,2]=>[1,6,5,7,4,3,2,8]=>[8,3,4,2,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,6,4,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,4,5,2,8]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,6,5,1,3,8]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,1,5,2,8]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,4,1,6,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,3,8,6,4]=>[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,3,6,7,4]=>[1,5,3,8,4,2,6,7]=>[8,4,6,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,7,6,4,1]=>[1,5,7,4,3,2,8,6]=>[8,4,2,5,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,3,7,4,5]=>[1,6,7,4,2,3,8,5]=>[8,3,2,5,7,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,1,5,7,3]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,5,7,1,4,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,8,3,6,4]=>[1,2,5,8,4,7,6,3]=>[8,7,4,1,5,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,8,4,7,1]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,8,5,6,3]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,6,8,5,1,3]=>[1,2,4,6,5,8,3,7]=>[8,7,5,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,6,1,8,4]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,1,4,6,3]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,1,6,2,8]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,8,6,7,2]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,6,1,7,3]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,5,3,7,1]=>[1,4,6,3,8,2,5,7]=>[8,5,3,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,7,6,3,1]=>[1,4,5,7,3,8,2,6]=>[8,5,4,2,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,5,8,6,3]=>[1,2,4,7,6,8,3,5]=>[8,7,5,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,6,2,4,1]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,6,2,1,3]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,1,7,2,5]=>[1,6,7,2,4,3,8,5]=>[8,3,2,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,7,1,3,5]=>[1,6,2,4,8,5,7,3]=>[8,3,7,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,2,5,1,4]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,6,7,2,4]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,8,6,2,4]=>[1,2,5,8,4,7,3,6]=>[8,7,4,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,4,2,8,3]=>[1,2,5,4,6,3,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,1,6,2,3]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,2,7,3,5]=>[1,6,7,3,8,5,2,4]=>[8,3,2,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,7,6,3,8]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,6,8,7,3]=>[1,4,2,5,6,8,3,7]=>[8,5,7,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,8,4,7,2]=>[1,3,6,4,2,5,8,7]=>[8,6,3,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,2,8,6,4]=>[1,3,7,6,8,4,2,5]=>[8,6,2,3,1,5,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,5,1,4,8]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,2,7,5,8]=>[1,4,2,6,7,5,3,8]=>[8,5,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,7,6,2,8]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,1,6,3,8]=>[1,4,7,3,5,2,6,8]=>[8,5,2,6,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,5,6,2,8]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,5,8,7,1,2]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,5,2,7,1]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,8,4,7,1]=>[1,3,6,4,2,5,8,7]=>[8,6,3,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,1,8,7,3]=>[1,4,6,8,3,5,2,7]=>[8,5,3,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,6,8,7,2]=>[1,4,2,5,6,8,3,7]=>[8,5,7,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,8,6,4,3]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,5,2,3,8]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,5,2,4,8]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,5,4,8,6]=>[1,3,2,7,8,6,4,5]=>[8,6,7,2,1,3,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,4,8,6,5]=>[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,7,8,6,5,3]=>[1,2,4,7,5,8,3,6]=>[8,7,5,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,1,8,6,2]=>[1,3,7,6,8,2,4,5]=>[8,6,2,3,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,5,8,6,3]=>[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,3,7,4,6]=>[1,5,3,8,6,7,4,2]=>[8,4,6,1,3,2,5,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,3,4,7,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,5,1,8,2]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,5,8,1,4]=>[1,2,6,8,4,7,3,5]=>[8,7,3,1,5,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,8,3,4,6]=>[1,5,8,6,3,2,4,7]=>[8,4,1,3,6,7,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,6,8,1,5]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,2,8,1,3]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,6,1,8,2]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,6,1,7,2]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,1,6,7,3]=>[1,8,3,2,5,4,6,7]=>[8,1,6,7,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,1,6,7,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,6,7,1,5]=>[1,4,3,8,5,6,7,2]=>[8,5,6,1,4,3,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,7,3,5,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,7,1,6,3]=>[1,5,7,6,2,3,8,4]=>[8,4,2,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,1,7,5,2]=>[1,4,3,8,2,6,7,5]=>[8,5,6,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,7,1,5,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,2,6,4,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,2,6,3,7]=>[1,8,7,3,4,2,5,6]=>[8,1,2,6,5,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,5,3,7,4]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,1,7,4,2]=>[1,6,7,4,3,5,2,8]=>[8,3,2,5,6,4,7,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,2,6,3,7]=>[1,8,7,3,5,2,4,6]=>[8,1,2,6,4,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,1,2,4,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,2,8,4,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,8,5,1,4]=>[1,6,5,8,4,7,2,3]=>[8,3,4,1,5,2,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,3,1,6,2]=>[1,4,8,2,5,3,7,6]=>[8,5,1,7,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,8,1,6,3]=>[1,4,5,8,3,2,7,6]=>[8,5,4,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,6,2,5,7]=>[1,8,7,5,6,2,3,4]=>[8,1,2,4,3,7,6,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,6,7,1,5]=>[1,3,2,8,5,6,7,4]=>[8,6,7,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,2,7,1,4]=>[1,3,6,7,2,5,4,8]=>[8,6,3,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,8,1,7,3]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,4,1,2,5]=>[1,6,2,8,5,4,3,7]=>[8,3,7,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,1,5,3,2]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,2,5,3,1]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,2,6,3,1]=>[1,5,2,4,7,3,8,6]=>[8,4,7,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,1,6,3,2]=>[1,5,2,4,7,3,8,6]=>[8,4,7,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,6,1,2,4]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,6,1,2,5]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,5,1,2,6]=>[1,4,7,2,8,6,3,5]=>[8,5,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,6,1,2,5]=>[1,3,8,5,6,2,4,7]=>[8,6,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,6,1,2,4]=>[1,3,8,4,7,2,5,6]=>[8,6,1,5,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,7,6,4,1]=>[1,3,8,2,5,7,4,6]=>[8,6,1,7,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,1,7,6,4,2]=>[1,3,8,2,5,7,4,6]=>[8,6,1,7,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,7,6,4,3]=>[1,2,5,7,4,3,8,6]=>[8,7,4,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,1,6,3,4]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,1,5,3,7]=>[1,8,7,3,4,6,5,2]=>[8,1,2,6,5,3,4,7]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,2,5,3,7]=>[1,8,7,3,4,6,5,2]=>[8,1,2,6,5,3,4,7]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,2,6,3,4]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,7,6,4,3]=>[1,2,5,7,4,3,8,6]=>[8,7,4,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,3,7,6,4,1]=>[1,2,5,7,4,3,8,6]=>[8,7,4,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,7,6,5,3]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,7,6,4,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,7,6,4,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,7,6,5,2]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,7,6,5,2]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,7,6,5,3]=>[1,4,8,3,2,5,7,6]=>[8,5,1,6,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,7,5,4,6]=>[1,3,2,8,6,5,7,4]=>[8,6,7,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,1,5,3,7]=>[1,8,7,3,2,4,6,5]=>[8,1,2,6,7,5,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,1,6,3,5]=>[1,4,7,3,8,5,2,6]=>[8,5,2,6,1,4,7,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,1,6,3,4]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,2,4,3,7]=>[1,8,7,3,6,4,2,5]=>[8,1,2,6,3,5,7,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,7,5,4,1]=>[1,6,5,7,4,3,2,8]=>[8,3,4,2,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,7,6,4,1]=>[1,5,7,4,3,8,2,6]=>[8,4,2,5,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,7,6,4,2]=>[1,5,7,4,3,8,2,6]=>[8,4,2,5,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,2,6,3,4]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,2,6,3,5]=>[1,4,7,3,8,5,2,6]=>[8,5,2,6,1,4,7,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,2,5,3,6]=>[1,4,7,3,2,8,6,5]=>[8,5,2,6,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,2,5,3,7]=>[1,8,7,3,2,4,6,5]=>[8,1,2,6,7,5,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,7,5,4,6]=>[1,3,2,8,6,5,7,4]=>[8,6,7,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,7,6,4,5]=>[1,3,8,5,7,4,2,6]=>[8,6,1,4,2,5,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,7,6,5,4]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,7,6,5,2]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,7,6,5,2]=>[1,3,4,8,2,5,7,6]=>[8,6,5,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,6,4,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,6,5,4,7]=>[1,8,7,4,3,2,5,6]=>[8,1,2,5,6,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,5,4,7]=>[1,8,7,4,3,2,5,6]=>[8,1,2,5,6,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,7,6,4,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,8,2,5,7]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,5,8,4,7]=>[1,3,6,8,7,4,2,5]=>[8,6,3,1,2,5,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,2,4,7,6]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,8,3,7,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,5,8,3,7]=>[1,2,4,6,8,7,3,5]=>[8,7,5,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,7,3,8,6]=>[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,3,8,7,5]=>[1,4,6,8,5,3,2,7]=>[8,5,3,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,2,8,3,6]=>[1,7,3,5,2,4,6,8]=>[8,2,6,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,2,8,3,6]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,2,8,4,6]=>[1,7,4,5,2,3,6,8]=>[8,2,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,8,7,3,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,3,7,6,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,8,7,6,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,5,3,7,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,6,3,7,4]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,1,8,3,4,5]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,2,8,3,5]=>[1,2,7,3,6,8,5,4]=>[8,7,2,6,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,5,3,8,4]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,5,3,8,4]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,3,8,7,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,8,7,4]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,6,3,8,4]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,7,3,8,4]=>[1,2,6,3,5,7,8,4]=>[8,7,3,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,2,8,3,6]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,4,7,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,2,4,6,5]=>[1,7,6,4,3,8,5,2]=>[8,2,3,5,6,1,4,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,2,4,6,5]=>[1,2,8,5,3,7,6,4]=>[8,7,1,4,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,7,3,6,5]=>[1,2,4,8,5,7,6,3]=>[8,7,5,1,4,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,8,3,6,5]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,2,7,3,6]=>[1,8,6,7,3,5,2,4]=>[8,1,3,2,6,4,7,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,2,7,3,6]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,7,2,4,6]=>[1,8,6,2,5,7,4,3]=>[8,1,3,7,4,2,5,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,7,3,4,5]=>[1,8,5,7,4,2,6,3]=>[8,1,4,2,5,7,3,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,2,7,3,5]=>[1,2,8,5,3,6,7,4]=>[8,7,1,4,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,6,3,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,3,8,6,4]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,3,7,6,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,8,7,5,4]=>[1,2,3,6,7,5,8,4]=>[8,7,6,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,3,8,5,4]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,3,8,5,4]=>[1,2,6,8,4,7,5,3]=>[8,7,3,1,5,2,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,8,6,3,5]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,2,6,4,5]=>[1,7,4,3,8,5,2,6]=>[8,2,5,6,1,4,7,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,7,6,3,5]=>[1,2,4,8,5,7,3,6]=>[8,7,5,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,5,3,6,4]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,3,7,5,4]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,6,2,4,3]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,3,4,5,2]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,2,4,1,3]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,2,4,3,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,2,7,3,8]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,3,7,6,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,3,8,7,2]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,3,7,8,2]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,3,5,7,2]=>[1,6,5,3,4,8,2,7]=>[8,3,4,6,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,3,4,5,2]=>[1,7,5,3,8,2,4,6]=>[8,2,4,6,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,3,8,6,2]=>[1,7,6,8,2,3,4,5]=>[8,2,3,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,3,6,8,2]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,3,6,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,2,6,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,2,1,7,4]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,2,4,1,3]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,3,1,7,2]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,2,4,3,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,2,6,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,2,1,4,7]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,6,5,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,2,1,4,7]=>[1,8,7,4,6,2,3,5]=>[8,1,2,5,3,7,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,1,4,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,1,5,7,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,1,3,5,4]=>[1,2,8,4,7,5,3,6]=>[8,7,1,5,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,2,1,6,4]=>[1,8,4,7,6,2,3,5]=>[8,1,5,2,3,7,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,6,1,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,3,1,8,2]=>[1,7,8,2,4,6,3,5]=>[8,2,1,7,5,3,6,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,3,1,7,2]=>[1,8,2,4,6,3,5,7]=>[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,2,8,1,4]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,2,1,6,4]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,2,1,4,8]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,1,3,5,4]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,8,3,1,4]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,1,4,2,3]=>[1,8,3,5,2,7,4,6]=>[8,1,6,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,8,5,7,3]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,8,5,7,4]=>[1,2,6,5,8,4,3,7]=>[8,7,3,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,4,3,1,5]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,4,3,5,8]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,2,8,4,6]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,2,3,7,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,3,4,2,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,3,2,7,5]=>[1,6,2,4,8,5,3,7]=>[8,3,7,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,4,1,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,4,3,1,5]=>[1,2,8,5,4,7,3,6]=>[8,7,1,4,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,2,4,1,6]=>[1,8,6,4,7,2,3,5]=>[8,1,3,5,2,7,6,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,7,5,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,7,3,4,5]=>[1,2,8,5,7,4,3,6]=>[8,7,1,4,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,6,4,7,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,4,5,7,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,4,3,5,7]=>[1,2,8,7,5,4,3,6]=>[8,7,1,2,4,5,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,6,7,10,8]=>[1,9,10,8,7,6,5,4,3,2]=>[10,2,1,3,4,5,6,7,8,9]=>[10,3,2,4,5,6,7,8,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,6,9,8]=>[1,7,6,5,4,3,2,8,9]=>[9,3,4,5,6,7,8,2,1]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,9,3,4,5,6,7,8]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,8,1,3,4,5,6,7,9]=>[1,2,8,7,6,5,4,3,9]=>[9,8,2,3,4,5,6,7,1]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,4,3,6,5,1,7,2]=>[1,8,2,4,6,3,5,7]=>[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,1,7,2]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,4,2,3,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,2,7,3,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,1,6,3,2]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,2,1,7,3]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,2,4,1,7,3]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,5,1,7,3]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,6,4,5,8]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,3,2,4,8]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,2,3,7,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,3,4,5,8]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,7,4,5,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,3,5,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,6,4,3,5]=>[1,7,3,8,5,6,4,2]=>[8,2,6,1,4,3,5,7]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,4,7,3,5]=>[1,6,7,3,8,5,4,2]=>[8,3,2,6,1,4,5,7]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,2,7,5,6]=>[1,4,8,6,7,5,2,3]=>[8,5,1,3,2,4,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,4,7,5,6]=>[1,3,2,4,8,6,7,5]=>[8,6,7,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,1,6,5,4]=>[1,3,8,4,7,5,2,6]=>[8,6,1,5,2,4,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,1,6,5,3]=>[1,4,7,5,2,8,3,6]=>[8,5,2,4,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,1,6,4,3]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,5,3,4,2]=>[1,7,4,2,8,3,6,5]=>[8,2,5,7,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,5,4,3,2]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,6,5,3,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,5,6,3,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,4,5,3,2]=>[1,8,2,6,5,4,3,7]=>[8,1,7,3,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,4,3,5,2]=>[1,7,5,4,2,6,3,8]=>[8,2,4,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,2,1,7,4]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,1,6,4,2]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,2,7,3,5]=>[1,2,6,7,3,8,5,4]=>[8,7,3,2,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,2,7,3,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,1,6,5,2]=>[1,8,2,4,7,5,3,6]=>[8,1,7,5,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,1,5,6,2]=>[1,7,6,5,2,4,8,3]=>[8,2,3,4,7,5,1,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,5,2,7,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,2,6,5,8]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,2,3,7,6]=>[1,8,6,3,2,5,4,7]=>[8,1,3,6,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,2,6,3,8]=>[1,7,3,2,5,4,6,8]=>[8,2,6,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,4,3,2,7,8]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,4,2,7,8]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,5,3,7,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,5,4,7,8]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,4,6,5,8]=>[1,3,7,5,4,2,6,8]=>[8,6,2,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,3,6,5,8]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,2,6,4,8]=>[1,5,2,7,4,3,6,8]=>[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,5,3,7,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,6,4,5,8]=>[1,2,7,5,6,4,3,8]=>[8,7,2,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,3,6,5,4]=>[1,8,4,2,7,5,3,6]=>[8,1,5,7,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,5,6,4]=>[1,7,6,5,3,2,8,4]=>[8,2,3,4,6,7,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,3,5,7,6]=>[1,4,2,8,6,5,3,7]=>[8,5,7,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,4,5,7,6]=>[1,3,8,6,5,4,2,7]=>[8,6,1,3,4,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,3,6,7,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,6,5,8]=>[1,7,5,4,3,2,6,8]=>[8,2,4,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,7,6]=>[1,8,6,5,4,3,2,7]=>[8,1,3,4,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,1,2,4]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,1,8,3,2]=>[1,6,8,2,7,3,4,5]=>[8,3,1,7,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,8,1,2,3]=>[1,5,8,3,7,2,4,6]=>[8,4,1,6,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,7,1,2,6]=>[1,3,4,5,7,2,8,6]=>[8,6,5,4,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,6,7,1,2,5]=>[1,3,8,5,7,2,4,6]=>[8,6,1,4,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,8,3,2]=>[1,4,7,3,6,8,2,5]=>[8,5,2,6,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,4,8,1]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,8,4,2]=>[1,3,6,8,2,5,7,4]=>[8,6,3,1,7,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,8,7,4,3]=>[1,2,5,8,3,6,7,4]=>[8,7,4,1,6,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,1,7,3,4]=>[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,2,3,7,4]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,8,4,7,3]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,4,7,8,1]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,8,5,7,3]=>[1,2,4,6,5,8,3,7]=>[8,7,5,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,5,4,6,7]=>[1,8,7,6,4,2,3,5]=>[8,1,2,3,5,7,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,5,7,4,6]=>[1,2,8,6,7,4,3,5]=>[8,7,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,8,7,5,3]=>[1,2,4,6,7,5,8,3]=>[8,7,5,3,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,7,8,5,2]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,7,6,8,5,2]=>[1,4,7,5,6,8,2,3]=>[8,5,2,4,3,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,1,6,3,4]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,6,4,8,1]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,8,5,4,3]=>[1,6,5,8,3,2,7,4]=>[8,3,4,1,6,7,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,1,5,3,4]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,8,4,5,3]=>[1,6,4,2,7,5,8,3]=>[8,3,5,7,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,4,8,5,2]=>[1,6,8,2,7,5,4,3]=>[8,3,1,7,2,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,4,8,6,2]=>[1,5,4,3,7,6,8,2]=>[8,4,5,6,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,2,3,6,4]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,2,3,6,5]=>[1,4,7,6,3,8,5,2]=>[8,5,2,3,6,1,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,7,5,8,6,2]=>[1,4,7,6,8,2,3,5]=>[8,5,2,3,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,7,8,6,2]=>[1,3,4,5,7,6,8,2]=>[8,6,5,4,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,4,7,6,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,4,6,5,7]=>[1,8,7,5,4,3,2,6]=>[8,1,2,4,5,6,7,3]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,5,7,6]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,4,6,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,5,8,7,3]=>[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,1,8,7,3]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,8,1,6,3]=>[1,5,8,3,7,6,2,4]=>[8,4,1,6,2,3,7,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,8,6,1,3]=>[1,5,8,3,7,2,4,6]=>[8,4,1,6,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,8,6,1,4]=>[1,5,8,4,3,2,7,6]=>[8,4,1,5,6,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,8,1,6,4]=>[1,5,8,4,3,2,7,6]=>[8,4,1,5,6,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,1,8,7,4]=>[1,5,2,6,8,4,3,7]=>[8,4,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,3,8,7,4]=>[1,5,3,2,6,8,4,7]=>[8,4,6,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,2,8,7,3]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,2,8,7,4]=>[1,5,2,6,8,4,3,7]=>[8,4,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,2,8,7,4]=>[1,5,2,6,8,4,3,7]=>[8,4,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,1,8,7,4]=>[1,5,2,6,8,4,3,7]=>[8,4,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,8,1,6,4]=>[1,5,8,4,2,7,6,3]=>[8,4,1,5,7,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,8,6,1,4]=>[1,5,8,4,2,7,3,6]=>[8,4,1,5,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,8,2,6,4]=>[1,5,8,4,2,7,6,3]=>[8,4,1,5,7,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,8,2,6,4]=>[1,5,8,4,3,2,7,6]=>[8,4,1,5,6,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,8,2,6,3]=>[1,5,8,3,7,6,2,4]=>[8,4,1,6,2,3,7,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,8,3,6,2]=>[1,2,5,8,3,7,6,4]=>[8,7,4,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,8,6,3,2]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,8,6,2,3]=>[1,5,8,3,7,2,4,6]=>[8,4,1,6,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,8,6,2,4]=>[1,5,8,4,3,2,7,6]=>[8,4,1,5,6,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,8,6,2,4]=>[1,5,8,4,2,7,3,6]=>[8,4,1,5,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,1,5,2,4]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,2,1,4]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,1,4,2,5]=>[1,6,4,3,8,5,2,7]=>[8,3,5,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,4,5,3,2]=>[1,2,6,5,4,8,3,7]=>[8,7,3,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,4,2,5,3]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,1,8,3,6,4]=>[1,5,8,4,2,7,6,3]=>[8,4,1,5,7,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,1,3,5,4]=>[1,6,3,2,7,5,4,8]=>[8,3,6,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,4,1,5,3]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,1,4,5,3]=>[1,6,4,8,3,7,5,2]=>[8,3,5,1,6,2,4,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,8,4,6,3]=>[1,5,8,3,7,6,4,2]=>[8,4,1,6,2,3,5,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,8,5,6,3]=>[1,4,7,6,5,8,3,2]=>[8,5,2,3,4,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,8,6,5,3]=>[1,4,7,5,8,3,2,6]=>[8,5,2,4,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,1,5,4,3]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,5,1,4,3]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,1,8,6,3,4]=>[1,5,8,4,2,7,3,6]=>[8,4,1,5,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,8,6,3,4]=>[1,5,8,4,2,7,3,6]=>[8,4,1,5,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,8,6,4,3]=>[1,5,8,3,7,4,2,6]=>[8,4,1,6,2,5,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,8,6,4,2]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,3,5,4,2]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,2,5,4,3]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,2,5,3,4]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,4,1,3,5]=>[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,4,3,1,5]=>[1,6,3,8,5,4,2,7]=>[8,3,6,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,5,2,3,4]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,5,2,4,3]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,5,3,4,2]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,1,3,2,5]=>[1,6,3,8,5,2,7,4]=>[8,3,6,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,2,7,4,1]=>[1,6,7,4,5,2,3,8]=>[8,3,2,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,4,7,3,1]=>[1,6,7,3,2,5,4,8]=>[8,3,2,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,8,7,2,1]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,7,2,3,6]=>[1,5,7,3,2,8,6,4]=>[8,4,2,6,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,8,7,3,2]=>[1,5,8,2,6,7,3,4]=>[8,4,1,7,3,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,5,7,1,2]=>[1,3,4,8,2,6,7,5]=>[8,6,5,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,6,3,7,2]=>[1,5,6,3,4,8,2,7]=>[8,4,3,6,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,2,7,1,5]=>[1,6,7,2,3,8,5,4]=>[8,3,2,7,6,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,1,4,2,5]=>[1,3,8,5,2,6,4,7]=>[8,6,1,4,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,6,7,2,1]=>[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,6,2,4,3]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,7,8,5,3]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,8,7,5,1]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,8,1,4]=>[1,6,8,4,5,2,3,7]=>[8,3,1,5,4,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,8,3,2,6]=>[1,5,8,6,3,2,7,4]=>[8,4,1,3,6,7,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,1,4,6,2]=>[1,7,6,4,5,2,8,3]=>[8,2,3,5,4,7,1,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,6,7,2,3]=>[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,2,8,5,1]=>[1,6,8,2,3,7,5,4]=>[8,3,1,7,6,2,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,4,5,3]=>[1,8,3,2,7,5,4,6]=>[8,1,6,7,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,1,2,6]=>[1,5,4,7,2,3,8,6]=>[8,4,5,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,3,6,8,1]=>[1,5,3,2,4,7,8,6]=>[8,4,6,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,4,7,3,1]=>[1,8,2,5,4,6,7,3]=>[8,1,7,4,5,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,7,5,1]=>[1,8,2,3,6,7,5,4]=>[8,1,7,6,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,5,4,8,1]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,4,2,8,1]=>[1,5,4,6,2,7,8,3]=>[8,4,5,3,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,5,2,8,1]=>[1,3,6,2,7,8,4,5]=>[8,6,3,7,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,7,3,1]=>[1,8,2,6,7,3,5,4]=>[8,1,7,3,2,6,4,5]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,8,3,2,6]=>[1,7,2,5,8,6,3,4]=>[8,2,7,4,1,3,6,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,8,3,4,7]=>[1,2,6,3,5,8,7,4]=>[8,7,3,6,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,1,8,3,6]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,3,4,8,2,7]=>[1,2,6,8,7,3,5,4]=>[8,7,3,1,2,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,2,7,3,1]=>[1,6,7,3,8,2,5,4]=>[8,3,2,6,1,7,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,4,7,3,1]=>[1,5,4,6,7,3,2,8]=>[8,4,5,3,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,5,7,4,1]=>[1,3,6,7,4,2,8,5]=>[8,6,3,2,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,6,4,3,1]=>[1,8,2,7,3,5,6,4]=>[8,1,7,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,5,4,3]=>[1,8,3,2,7,4,6,5]=>[8,1,6,7,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,3,2,5,4]=>[1,7,5,3,2,8,4,6]=>[8,2,4,6,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,3,5,6,4]=>[1,2,8,4,7,6,5,3]=>[8,7,1,5,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,7,2,6,5]=>[1,4,3,2,8,5,7,6]=>[8,5,6,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,7,3,6,1]=>[1,4,5,7,6,3,8,2]=>[8,5,4,2,3,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,8,4,2,5]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,4,5,2,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,5,3,4,6]=>[1,2,7,4,8,6,3,5]=>[8,7,2,5,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,3,4,6,5]=>[1,8,5,3,2,4,7,6]=>[8,1,4,6,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,7,5,6,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,8,4,2,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,8,3,6,7]=>[1,4,5,8,7,6,3,2]=>[8,5,4,1,2,3,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,1,8,3,6]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,2,7,3,1]=>[1,6,7,3,4,8,2,5]=>[8,3,2,6,5,1,7,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,5,3,2,1]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,7,6,2,4]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,7,2,6,3]=>[1,5,7,6,2,4,3,8]=>[8,4,2,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,2,6,4,1]=>[1,7,4,3,8,2,5,6]=>[8,2,5,6,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,4,7,5,1]=>[1,3,8,2,6,7,5,4]=>[8,6,1,7,3,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,2,6,4,1]=>[1,5,2,7,4,8,3,6]=>[8,4,7,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,2,7,3,1]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,6,3,5,1]=>[1,4,8,2,7,5,6,3]=>[8,5,1,7,2,4,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,4,5,6,1]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,6,3,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,2,4,3]=>[1,8,3,7,4,6,2,5]=>[8,1,6,2,5,3,7,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,6,3,4,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,4,6,2,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,7,6,2,4]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,5,3,2,1]=>[1,6,3,4,7,2,8,5]=>[8,3,6,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,5,4,3,1]=>[1,6,4,2,8,3,7,5]=>[8,3,5,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,4,5,2,1]=>[1,3,7,2,8,4,6,5]=>[8,6,2,7,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,5,3,4,1]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,5,4,2,3]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,3,4,1,2]=>[1,5,3,6,4,7,2,8]=>[8,4,6,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,3,5,1,2]=>[1,4,7,2,8,3,6,5]=>[8,5,2,7,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,4,5,1,2]=>[1,3,6,5,4,7,2,8]=>[8,6,3,4,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,4,6,2,3]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,4,6,1,2]=>[1,3,5,4,7,2,8,6]=>[8,6,4,5,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,3,6,1,2]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,4,5,1,2]=>[1,6,5,4,7,2,8,3]=>[8,3,4,5,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,5,6,1,2]=>[1,3,4,8,2,7,5,6]=>[8,6,5,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,5,6,1,2]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,5,6,1,3]=>[1,4,8,3,2,7,5,6]=>[8,5,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,5,6,2,3]=>[1,4,8,3,2,7,5,6]=>[8,5,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,5,6,2,4]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,5,6,1,4]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,8,5,6,1,4]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,5,6,1,3]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,4,5,1,3]=>[1,6,5,4,7,2,8,3]=>[8,3,4,5,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,4,5,2,3]=>[1,6,5,4,7,2,8,3]=>[8,3,4,5,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,5,6,2,3]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,5,6,2,4]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,1,7,3,4]=>[1,2,8,4,6,7,3,5]=>[8,7,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,2,7,3,4]=>[1,2,8,4,6,7,3,5]=>[8,7,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,4,6,2,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,3,6,2,4]=>[1,5,3,2,8,4,7,6]=>[8,4,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,3,5,1,4]=>[1,7,2,8,4,6,5,3]=>[8,2,7,1,5,3,4,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,3,6,1,4]=>[1,5,3,2,8,4,7,6]=>[8,4,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,8,4,6,1,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,4,6,1,5]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,4,6,2,5]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,3,6,2,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,3,6,1,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,2,6,1,5]=>[1,3,4,7,2,8,5,6]=>[8,6,5,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,2,6,1,3]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,2,6,1,4]=>[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,3,5,2,4]=>[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,3,5,1,4]=>[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,2,5,1,3]=>[1,4,7,2,8,3,6,5]=>[8,5,2,7,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,2,4,1,3]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,1,4,2,3]=>[1,6,4,7,2,8,3,5]=>[8,3,5,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,1,4,2,3]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,1,5,2,3]=>[1,4,7,2,8,3,6,5]=>[8,5,2,7,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,5,7,3,4]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,5,7,3,4]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,1,6,2,4]=>[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,1,5,2,3]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,1,5,2,4]=>[1,7,2,8,4,6,5,3]=>[8,2,7,1,5,3,4,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,1,6,2,5]=>[1,3,4,7,2,8,5,6]=>[8,6,5,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,4,7,3,5]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,4,7,3,5]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,1,8,4,5]=>[1,3,2,7,4,6,8,5]=>[8,6,7,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,2,8,4,5]=>[1,3,2,7,4,6,8,5]=>[8,6,7,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,2,7,3,5]=>[1,4,6,7,3,2,8,5]=>[8,5,3,2,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,1,7,3,5]=>[1,4,6,7,3,2,8,5]=>[8,5,3,2,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,2,8,4,5]=>[1,2,7,4,6,8,5,3]=>[8,7,2,5,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,6,1,8,4,5]=>[1,2,7,4,6,8,5,3]=>[8,7,2,5,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,9,4]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,7,8,9,3]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,9,2]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,6,8,9,7]=>[9,8,7,6,5,4,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,5,7,8,9,6]=>[9,8,7,6,5,3,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,6,5,7,8,9,4]=>[1,2,3,4,6,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,5,4,6,7,8,9,3]=>[1,2,3,5,6,7,8,9,4]=>[9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,4,3,5,6,7,8,9,2]=>[1,2,4,5,6,7,8,9,3]=>[9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,7,8,9,10,3]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,9,1]=>[1,3,4,5,6,7,8,9,2]=>[9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,9,10,2]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,4,8,3,5,1,2]=>[1,6,5,3,4,8,2,7]=>[8,3,4,6,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,2,3,1,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,3,8,1,2]=>[1,5,3,4,6,8,2,7]=>[8,4,6,5,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,3,6,1,2]=>[1,5,3,4,8,2,7,6]=>[8,4,6,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,3,7,1,2]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,2,4,1,8]=>[1,5,2,6,4,7,3,8]=>[8,4,7,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,2,8,1,4]=>[1,5,2,6,8,4,7,3]=>[8,4,7,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,2,7,1,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,2,7,1,3]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,2,6,1,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,2,3,1,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,2,3,1,7]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,2,4,1,7]=>[1,5,2,6,4,8,7,3]=>[8,4,7,3,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,2,8,1,7]=>[1,5,2,6,8,7,3,4]=>[8,4,7,3,1,2,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,2,8,1,7]=>[1,4,5,2,6,8,7,3]=>[8,5,4,7,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,2,5,1,7]=>[1,4,8,7,2,6,5,3]=>[8,5,1,2,7,3,4,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,2,4,1,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,2,4,1,7]=>[1,6,4,5,2,8,7,3]=>[8,3,5,4,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,2,6,1,4]=>[1,7,2,8,4,5,3,6]=>[8,2,7,1,5,4,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,2,7,1,5]=>[1,4,6,7,2,8,5,3]=>[8,5,3,2,7,1,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,2,7,1,5]=>[1,4,8,5,2,6,7,3]=>[8,5,1,4,7,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,2,8,1,5]=>[1,4,7,2,6,8,5,3]=>[8,5,2,7,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,2,6,1,5]=>[1,4,8,5,2,7,3,6]=>[8,5,1,4,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,2,6,1,3]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,2,8,1,4]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,2,4,1,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,2,8,1,4]=>[1,6,8,4,5,2,7,3]=>[8,3,1,5,4,7,2,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,2,5,1,3]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,2,4,1,3]=>[1,6,4,8,3,5,2,7]=>[8,3,5,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,2,4,1,5]=>[1,6,4,8,5,2,7,3]=>[8,3,5,1,4,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,4,2,8,1,5]=>[1,6,8,5,2,7,3,4]=>[8,3,1,4,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,2,6,1,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,2,8,1,6]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,2,3,1,6]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,2,3,1,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,2,3,1,5]=>[1,6,3,4,7,2,8,5]=>[8,3,6,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,2,3,1,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,2,4,1,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,2,4,1,5]=>[1,6,4,7,2,8,5,3]=>[8,3,5,2,7,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,2,5,1,6]=>[1,4,7,2,8,6,5,3]=>[8,5,2,7,1,3,4,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,2,8,1,6]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,2,6,1,8]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,2,6,1,8]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,2,8,1,6]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,2,7,1,6]=>[1,4,5,2,8,6,7,3]=>[8,5,4,7,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,2,7,1,6]=>[1,5,2,8,6,7,3,4]=>[8,4,7,1,3,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,2,6,1,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,2,5,1,7]=>[1,6,5,2,8,7,3,4]=>[8,3,4,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,2,6,1,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,2,6,1,7]=>[1,4,5,2,8,7,3,6]=>[8,5,4,7,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,2,6,1,7]=>[1,4,8,7,2,5,3,6]=>[8,5,1,2,7,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,1,8,3,6]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,1,7,6,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,1,3,8,7]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,1,2,8,7]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,3,2,8,7]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,7,3,2,5]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,6,3,5,2]=>[1,4,2,7,5,6,3,8]=>[8,5,7,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,6,5,3,2]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,3,7,6,2]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,1,7,6,2]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,3,8,2,6]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,7,5,2,3]=>[1,6,5,7,2,4,3,8]=>[8,3,4,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,2,1,3,4]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,4,2,1,3]=>[1,8,3,7,2,5,4,6]=>[8,1,6,2,7,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,2,1,5]=>[1,8,5,7,2,4,3,6]=>[8,1,4,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,7,4,1,5]=>[1,6,4,8,5,7,2,3]=>[8,3,5,1,4,2,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,7,4,3,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,6,4,5,1]=>[1,7,5,6,4,8,2,3]=>[8,2,4,3,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,2,4,3,1]=>[1,7,3,8,2,6,4,5]=>[8,2,6,1,7,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,2,3,1,4]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,3,2,4,1]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,3,7,6,1]=>[1,5,3,4,2,8,6,7]=>[8,4,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,6,5,3,1]=>[1,7,3,4,2,8,5,6]=>[8,2,6,5,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,6,3,5,1]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,7,3,1,5]=>[1,4,2,8,5,7,3,6]=>[8,5,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,7,4,2,5]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,7,5,2,4]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,8,2,5,4]=>[1,3,2,7,5,8,4,6]=>[8,6,7,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,8,1,3,5]=>[1,4,2,7,3,6,5,8]=>[8,5,7,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,8,1,5,3]=>[1,6,2,7,5,8,3,4]=>[8,3,7,2,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,5,3,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,7,5,1,4]=>[1,8,4,6,5,7,2,3]=>[8,1,5,3,4,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,5,1,2]=>[1,8,2,6,5,7,3,4]=>[8,1,7,3,4,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,3,1,2,4]=>[1,5,3,6,2,8,4,7]=>[8,4,6,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,1,3,4,2]=>[1,6,3,5,2,7,4,8]=>[8,3,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,1,4,3,2]=>[1,7,3,5,2,6,4,8]=>[8,2,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,4,1,3,2]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,1,5,2]=>[1,7,5,8,2,6,3,4]=>[8,2,4,1,7,3,6,5]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,1,5,4]=>[1,7,5,8,4,6,2,3]=>[8,2,4,1,5,3,7,6]=>[8,4,6,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,1,4,2,3]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,1,2,4,3]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,4,6,5,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,4,6,1,3]=>[1,5,4,7,2,3,8,6]=>[8,4,5,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,4,8,3,1]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,4,7,6,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,4,3,8,7,2]=>[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,4,5,7,2]=>[1,6,5,4,3,8,2,7]=>[8,3,4,5,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,4,8,6,2]=>[1,7,6,8,2,3,5,4]=>[8,2,3,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,5,6,8,2]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,5,6,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,5,6,3,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,4,7,3,1]=>[1,6,7,3,8,2,5,4]=>[8,3,2,6,1,7,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,4,3,7,6]=>[1,8,6,3,2,5,4,7]=>[8,1,3,6,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,4,1,3,7]=>[1,6,2,5,4,8,7,3]=>[8,3,7,4,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,5,2,4,7]=>[1,3,2,6,4,8,7,5]=>[8,6,7,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,5,4,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,6,8,5,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,3,2,4,7]=>[1,5,3,2,8,7,4,6]=>[8,4,6,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,2,1,4,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,2,4,7,6]=>[1,8,6,4,5,2,3,7]=>[8,1,3,5,4,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,1,5,7,4]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,2,1,5,4]=>[1,3,6,2,8,4,7,5]=>[8,6,3,7,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,2,1,7,3]=>[1,8,3,6,2,5,4,7]=>[8,1,6,3,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,3,1,6,4]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,8,5,7,4]=>[1,6,5,8,4,3,2,7]=>[8,3,4,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,6,5,8,4]=>[1,7,8,4,3,2,5,6]=>[8,2,1,5,6,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,8,6,4,5]=>[1,7,4,3,2,5,8,6]=>[8,2,5,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,2,4,6,8]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,1,8,4,6]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,1,3,7,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,3,4,1,5]=>[1,8,5,3,2,7,4,6]=>[8,1,4,6,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,2,4,1,6]=>[1,3,8,6,4,7,2,5]=>[8,6,1,3,5,2,7,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,7,8,5,6]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,8,7,5,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,7,2,4,5]=>[1,8,5,7,4,3,2,6]=>[8,1,4,2,5,6,7,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,6,4,7,5]=>[1,2,8,5,6,4,3,7]=>[8,7,1,4,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,4,1,5,7]=>[1,6,2,8,7,5,4,3]=>[8,3,7,1,2,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,2,4,6,7]=>[1,5,2,3,8,7,6,4]=>[8,4,7,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,8,5,3,7]=>[1,2,6,5,8,7,3,4]=>[8,7,3,4,1,2,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,7,5,3,8]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,5,2,4,6]=>[1,2,7,4,8,6,3,5]=>[8,7,2,5,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,8,5,6,4]=>[1,7,6,5,8,4,2,3]=>[8,2,3,4,1,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,3,4,7,5]=>[1,6,4,8,5,3,2,7]=>[8,3,5,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,5,1,7,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,5,7,1,3]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,8,5,7,2]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,7,5,8,2]=>[1,2,3,6,5,7,8,4]=>[8,7,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,3,1,8,5]=>[1,7,8,5,3,4,2,6]=>[8,2,1,4,6,5,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,1,6,8,4]=>[1,5,2,7,8,4,3,6]=>[8,4,7,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,4,6,8,2]=>[1,2,7,8,3,5,4,6]=>[8,7,2,1,6,4,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,1,8,7,4]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,3,1,7,5]=>[1,8,5,3,6,2,4,7]=>[8,1,4,6,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,1,3,5,6]=>[1,8,6,3,7,5,2,4]=>[8,1,3,6,2,4,7,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,3,5,6,7]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,3,2,5,7]=>[1,6,2,8,7,5,3,4]=>[8,3,7,1,2,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,3,2,5,6]=>[1,2,8,6,3,7,5,4]=>[8,7,1,3,6,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,2,4,7,5]=>[1,2,6,4,8,5,3,7]=>[8,7,3,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,2,6,4,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,2,6,4,8]=>[1,5,2,7,4,3,6,8]=>[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,2,6,3,8]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,4,6,3,7]=>[1,2,5,4,3,8,7,6]=>[8,7,4,5,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,8,3,7,5]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,7,2,4,8]=>[1,5,7,4,6,2,3,8]=>[8,4,2,5,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,2,8,4,7]=>[1,5,2,3,6,8,7,4]=>[8,4,7,6,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,7,8,4,5]=>[1,2,6,8,5,7,4,3]=>[8,7,3,1,4,2,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,3,8,6,2]=>[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,2,5,8,7]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,2,7,5,8]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,4,5,6,7]=>[1,2,8,7,6,5,4,3]=>[8,7,1,2,3,4,5,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,4,1,7,5]=>[1,8,5,4,2,6,3,7]=>[8,1,4,5,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,8,1,7,3]=>[1,4,6,2,5,8,3,7]=>[8,5,3,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,7,8,1,3]=>[1,4,6,8,3,5,7,2]=>[8,5,3,1,6,4,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,7,1,8,4]=>[1,5,7,8,4,6,2,3]=>[8,4,2,1,5,3,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,1,7,8,5]=>[1,6,7,8,5,2,3,4]=>[8,3,2,1,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,4,5,8,6]=>[1,7,8,6,5,4,2,3]=>[8,2,1,3,4,5,7,6]=>[8,3,2,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,3,2,5,7]=>[1,8,7,5,3,2,6,4]=>[8,1,2,4,6,7,3,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,5,2,4,7]=>[1,8,7,4,6,2,3,5]=>[8,1,2,5,3,7,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,8,2,4,6]=>[1,3,5,8,6,2,7,4]=>[8,6,4,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,8,7,3,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,6,5,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,4,6,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,5,4,7]=>[1,8,7,4,6,5,2,3]=>[8,1,2,5,3,4,7,6]=>[8,2,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,4,5,3,7]=>[1,8,7,3,2,4,6,5]=>[8,1,2,6,7,5,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,6,4,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,5,4,3,7]=>[1,8,7,3,2,4,6,5]=>[8,1,2,6,7,5,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,2,8,3,6]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,2,7,3,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,2,7,3,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,2,8,3,5]=>[1,2,4,6,8,5,3,7]=>[8,7,5,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,2,8,3,6]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,2,8,3,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,2,8,4,6]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,8,7,3,5]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,6,7,3,5]=>[1,2,4,8,5,6,7,3]=>[8,7,5,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,4,8,7,5]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,4,6,8,5]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,8,5,7,4]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,7,8,3,6]=>[1,5,7,3,4,2,6,8]=>[8,4,2,6,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,6,8,3,5]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,8,7,3,5]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,4,6,7,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,6,4,8,5]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,8,2,4,6]=>[1,5,8,6,2,3,7,4]=>[8,4,1,3,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,2,5,8,6]=>[1,2,7,8,6,5,3,4]=>[8,7,2,1,3,4,6,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,4,2,5,6]=>[1,2,8,6,3,7,5,4]=>[8,7,1,3,6,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,3,4,7,6]=>[1,5,3,8,6,4,2,7]=>[8,4,6,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,3,4,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,8,3,7,5]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,8,5,6,4]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,5,8,6,4]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,3,8,6,5]=>[1,2,4,7,6,8,5,3]=>[8,7,5,2,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,8,6,4,5]=>[1,3,7,4,2,5,8,6]=>[8,6,2,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,7,5,6,4]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>[10,1,2,3,4,5,6,7,8,9]=>[10,2,3,4,5,6,7,8,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11,1,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,2,3,4,5,6,7,8,9,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[4,7,8,5,6,2,1,3]=>[1,4,5,6,2,7,3,8]=>[8,5,4,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,2,6,1,3]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,5,1,3]=>[1,6,5,2,7,3,8,4]=>[8,3,4,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,2,1,5,4]=>[1,8,4,7,5,2,6,3]=>[8,1,5,2,4,7,3,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,2,1,5,4]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,1,5,4]=>[1,6,2,7,5,3,8,4]=>[8,3,7,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,2,1,6,4]=>[1,5,2,7,6,3,8,4]=>[8,4,7,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,3,5,6,1]=>[1,2,7,6,5,3,8,4]=>[8,7,2,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,2,1,4,6]=>[1,5,2,7,4,3,8,6]=>[8,4,7,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,2,1,4,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,2,1,4,7]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,2,5,1,7]=>[1,3,4,8,7,2,6,5]=>[8,6,5,1,2,7,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,5,7,1]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,3,5,8,1]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,2,5,1,8]=>[1,3,4,7,2,6,5,8]=>[8,6,5,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,2,1,4,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,6,5,7]=>[1,8,7,5,2,4,3,6]=>[8,1,2,4,7,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,8,6,1,7]=>[1,3,4,2,5,8,7,6]=>[8,6,5,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,8,5,7]=>[1,6,8,7,5,2,4,3]=>[8,3,1,2,4,7,5,6]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,8,5,6]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,8,7,5]=>[1,6,8,5,2,4,3,7]=>[8,3,1,4,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,2,1,7,4]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,8,6,1,3]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,8,7,2,1,3]=>[1,4,8,3,5,7,2,6]=>[8,5,1,6,4,2,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,7,8,1,3]=>[1,6,8,3,4,2,5,7]=>[8,3,1,6,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,6,7,1,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,2,1,8,4]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,2,8,1,5]=>[1,3,4,7,2,6,8,5]=>[8,6,5,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,3,8,5,1]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,7,8,1,6]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,7,1,8,6]=>[1,4,2,5,7,8,6,3]=>[8,5,7,4,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,6,8,1,7]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,1,2,8,7]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,2,6,3,1]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,2,6,1,3]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,5,6,3,4]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,5,1,4,2]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,1,6,2,4]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,8,5,1,7]=>[1,3,6,5,8,7,2,4]=>[8,6,3,4,1,2,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,1,7,6,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,7,3,6,8]=>[1,4,5,7,6,3,2,8]=>[8,5,4,2,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,7,1,6,8]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,8,1,6,7]=>[1,4,3,5,8,7,6,2]=>[8,5,6,4,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,2,8,6,7]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,8,2,6,7]=>[1,4,3,5,8,7,6,2]=>[8,5,6,4,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,2,1,6,7]=>[1,4,5,2,3,8,7,6]=>[8,5,4,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,5,1,7,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,3,2,5,8]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,3,2,6,8]=>[1,4,7,6,2,5,3,8]=>[8,5,2,3,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,7,2,6,8]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,2,7,6,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,3,7,8,6]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,3,7,8,6]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,2,7,6,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,7,2,6,8]=>[1,4,5,7,6,2,3,8]=>[8,5,4,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,5,2,7,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,1,2,7,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,2,7,5,8]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,3,7,8,5]=>[1,6,7,8,5,3,4,2]=>[8,3,2,1,4,6,5,7]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,2,7,5,8]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,7,2,5,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,1,4,7,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,1,3,4,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,3,1,6,8]=>[1,4,7,6,2,5,3,8]=>[8,5,2,3,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,3,1,5,8]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,7,3,5,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,4,7,5,8]=>[1,3,2,6,7,5,4,8]=>[8,6,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,4,5,1,8]=>[1,3,7,2,6,5,4,8]=>[8,6,2,7,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,4,6,1,8]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,6,8,2,5]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,5,7,4,8]=>[1,3,6,7,4,2,5,8]=>[8,6,3,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,5,7,4,8]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,5,3,6,8]=>[1,4,7,6,3,2,5,8]=>[8,5,2,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,6,2,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,2,6,4,8]=>[1,7,4,5,2,3,6,8]=>[8,2,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,3,7,8,4]=>[1,6,7,8,4,2,3,5]=>[8,3,2,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,2,7,4,8]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,7,2,3,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,1,3,7,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,7,2,3,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,2,7,4,8]=>[1,3,5,2,6,7,4,8]=>[8,6,4,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,5,4,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,8,7,6]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,2,8,7,6]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,8,2,7,6]=>[1,3,5,8,6,2,4,7]=>[8,6,4,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,3,2,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,3,1,7,6]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,2,1,7,6]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,8,1,7,6]=>[1,3,5,8,6,2,4,7]=>[8,6,4,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,1,7,8,5]=>[1,3,6,7,8,5,2,4]=>[8,6,3,2,1,4,7,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,1,7,5,8]=>[1,3,6,7,5,2,4,8]=>[8,6,3,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,1,4,8]=>[1,3,6,2,5,7,4,8]=>[8,6,3,7,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,1,8,4]=>[1,3,6,2,5,7,8,4]=>[8,6,3,7,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,8,1,4]=>[1,3,6,8,4,2,5,7]=>[8,6,3,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,8,7,1,5]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,2,7,1,5]=>[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,3,7,1,5]=>[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,3,7,2,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,3,7,5,2]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,2,7,5,1]=>[1,3,6,7,5,2,4,8]=>[8,6,3,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,8,7,5,1]=>[1,3,6,7,5,8,2,4]=>[8,6,3,2,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,8,4,1]=>[1,3,6,8,2,5,7,4]=>[8,6,3,1,7,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,4,1,8]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,8,3,1]=>[1,4,7,3,6,8,2,5]=>[8,5,2,6,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,2,4,1]=>[1,3,6,2,5,7,4,8]=>[8,6,3,7,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,3,4,1]=>[1,2,5,7,4,6,3,8]=>[8,7,4,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,3,1,4]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,2,1,4]=>[1,3,6,2,5,7,4,8]=>[8,6,3,7,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,1,8,3]=>[1,4,7,8,3,6,2,5]=>[8,5,2,1,6,3,7,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,8,7,2,5]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,8,7,3,5]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,6,7,4,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,6,7,5,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,7,8,4,3]=>[1,2,5,7,4,6,8,3]=>[8,7,4,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,7,4,8,3]=>[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,7,4,3,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,4,2,8]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,4,8,2]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,8,7,5,2]=>[1,3,6,7,5,8,2,4]=>[8,6,3,2,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,1,7,5,2]=>[1,3,6,7,5,2,4,8]=>[8,6,3,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,1,7,5,3]=>[1,2,4,6,7,5,3,8]=>[8,7,5,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,2,7,5,3]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,1,4,3]=>[1,2,5,7,4,6,3,8]=>[8,7,4,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,1,4,2]=>[1,3,6,2,5,7,4,8]=>[8,6,3,7,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,1,3,2]=>[1,4,7,3,6,2,5,8]=>[8,5,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,3,8,2]=>[1,4,7,8,2,5,3,6]=>[8,5,2,1,7,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,3,2,8]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,1,8,2]=>[1,4,7,8,2,5,3,6]=>[8,5,2,1,7,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,4,1,2]=>[1,3,6,4,8,2,5,7]=>[8,6,3,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,4,1,3]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,4,3,1]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,7,1,6,4]=>[1,8,4,3,5,7,6,2]=>[8,1,5,6,4,2,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,7,1,6,5]=>[1,8,5,7,6,2,3,4]=>[8,1,4,2,3,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,3,7,1,6]=>[1,5,3,2,8,6,7,4]=>[8,4,6,7,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,1,7,3,8]=>[1,4,6,7,3,5,2,8]=>[8,5,3,2,6,4,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,3,2,4,7]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,7,1,8,2]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,6,8,2,4]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,6,1,5,7]=>[1,8,7,5,6,2,3,4]=>[8,1,2,4,3,7,6,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,6,1,5,8]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,4,6,8]=>[1,3,5,7,6,4,2,8]=>[8,6,4,2,3,5,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,4,6,7]=>[1,3,5,8,7,6,4,2]=>[8,6,4,1,2,3,5,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,8,4,6]=>[1,3,5,7,4,2,6,8]=>[8,6,4,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,4,6,1,5]=>[1,7,2,8,5,4,3,6]=>[8,2,7,1,4,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,7,8,3,2,4]=>[1,6,3,5,8,4,7,2]=>[8,3,6,4,1,5,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,1,7,8,3]=>[1,4,6,7,8,3,5,2]=>[8,5,3,2,1,6,4,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,7,3,4,2]=>[1,5,7,4,2,8,3,6]=>[8,4,2,5,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,7,4,6]=>[1,3,5,8,6,7,4,2]=>[8,6,4,1,3,2,5,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,4,7,8]=>[1,3,5,6,4,2,7,8]=>[8,6,4,3,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,7,5,6]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,8,7,4]=>[1,3,5,6,8,4,2,7]=>[8,6,4,3,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,1,7,4,2]=>[1,3,6,7,4,5,2,8]=>[8,6,3,2,5,4,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,8,4,2,3]=>[1,6,4,7,2,5,8,3]=>[8,3,5,2,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,7,8,4]=>[1,3,5,6,7,8,4,2]=>[8,6,4,3,2,1,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,5,6,7]=>[1,3,4,2,5,8,7,6]=>[8,6,5,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,7,5,6,8]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,6,8,5,7]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,5,7,6]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,4,7,6]=>[1,3,5,8,6,4,2,7]=>[8,6,4,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,7,4,8]=>[1,3,5,6,7,4,2,8]=>[8,6,4,3,2,5,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,4,2,3,8]=>[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,4,2,3,7]=>[1,6,2,5,4,8,7,3]=>[8,3,7,4,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,8,3,7,5]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,8,3,7,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,3,5,2]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,8,4,7,3]=>[1,5,8,3,6,4,2,7]=>[8,4,1,6,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,8,5,1,6]=>[1,7,2,4,3,5,8,6]=>[8,2,7,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,4,2,3,7]=>[1,8,7,3,2,5,4,6]=>[8,1,2,6,7,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,4,2,3,8]=>[1,7,3,2,5,4,6,8]=>[8,2,6,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,6,4,8]=>[1,3,5,7,4,2,6,8]=>[8,6,4,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,6,4,7]=>[1,3,5,8,7,4,2,6]=>[8,6,4,1,2,5,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,8,6,1,5]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,7,3,2,4]=>[1,8,4,5,7,2,6,3]=>[8,1,5,4,2,7,3,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,8,5,7,3]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,7,3,4,2]=>[1,8,2,5,7,4,3,6]=>[8,1,7,4,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,1,7,4,2]=>[1,3,8,2,6,7,4,5]=>[8,6,1,7,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,6,7,4]=>[1,3,5,8,4,2,6,7]=>[8,6,4,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,6,5,7]=>[1,3,4,2,5,8,7,6]=>[8,6,5,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,5,8,6,7]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,8,6,4]=>[1,3,5,7,6,8,4,2]=>[8,6,4,2,3,1,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,6,4,2,3]=>[1,7,2,8,3,5,6,4]=>[8,2,7,1,6,4,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,1,7,6,4,2]=>[1,3,5,7,4,2,8,6]=>[8,6,4,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,8,6,4,2]=>[1,3,5,8,2,7,4,6]=>[8,6,4,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,6,4,2,3]=>[1,8,3,5,6,4,2,7]=>[8,1,6,4,3,5,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,7,6,4]=>[1,3,5,8,4,2,6,7]=>[8,6,4,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,1,8,4,2]=>[1,6,8,2,5,3,7,4]=>[8,3,1,7,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,1,8,5,2]=>[1,4,7,5,2,6,8,3]=>[8,5,2,4,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,1,6,3,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,1,6,8,3]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,6,1,8,2]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,3,1,6,2]=>[1,5,3,7,6,2,4,8]=>[8,4,6,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,5,1,7,2]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,6,1,7,2]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,7,1,8,2]=>[1,5,7,8,2,4,6,3]=>[8,4,2,1,7,5,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,1,7,3,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,1,6,7,4]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,8,1,7,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,8,5,7,3]=>[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,7,5,8,6,3]=>[1,2,4,7,6,8,3,5]=>[8,7,5,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,7,5,3,8,6]=>[1,2,4,7,8,6,3,5]=>[8,7,5,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,8,5,3,7]=>[1,2,6,5,8,7,3,4]=>[8,7,3,4,1,2,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,1,6,3,7]=>[1,2,5,3,8,7,4,6]=>[8,7,4,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,1,8,4,7]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,1,6,4,7]=>[1,3,2,5,4,8,7,6]=>[8,6,7,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,5,4,8,6]=>[1,3,7,8,6,4,2,5]=>[8,6,2,1,3,5,7,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,5,8,6,4]=>[1,3,7,6,8,4,2,5]=>[8,6,2,3,1,5,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,1,6,7,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,6,7,1,5]=>[1,4,2,8,5,6,7,3]=>[8,5,7,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,6,7,1,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,7,1,5,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,8,1,5]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,8,1,6,3]=>[1,2,5,8,3,7,6,4]=>[8,7,4,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,8,1,6,4]=>[1,3,5,8,4,7,6,2]=>[8,6,4,1,5,2,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,1,6,8,4]=>[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,1,6,4,8]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,1,5,4,8]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,1,5,8,4]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,8,1,5,4]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,7,8,5,3]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,7,8,4,3]=>[1,6,8,3,2,5,7,4]=>[8,3,1,6,7,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,1,4,8,5]=>[1,6,4,7,8,5,2,3]=>[8,3,5,2,1,4,7,6]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,4,7,8,5]=>[1,6,7,8,5,4,2,3]=>[8,3,2,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,7,4,6,8]=>[1,3,2,5,7,6,4,8]=>[8,6,7,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,7,8,4,6]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,1,7,3,6]=>[1,5,2,8,6,7,3,4]=>[8,4,7,1,3,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,8,3,7,5]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,7,3,8,6,5]=>[1,2,4,7,6,8,5,3]=>[8,7,5,2,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,1,7,4,6]=>[1,3,8,6,7,4,2,5]=>[8,6,1,3,2,5,7,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,2,1,5,6]=>[1,4,7,5,2,8,6,3]=>[8,5,2,4,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,1,5,6,8]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,1,7,4,6]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,7,5,8,6]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,1,5,6,7]=>[1,4,2,8,7,6,5,3]=>[8,5,7,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,1,5,6,7]=>[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,5,4,8,7]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,1,7,6]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,3,4,1]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,4,1,7,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,4,3,8,7]=>[1,6,3,5,4,2,7,8]=>[8,3,6,4,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,3,2,8,7]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,4,1,7,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,2,4,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,4,1,6,5]=>[1,8,5,4,2,3,7,6]=>[8,1,4,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,4,2,7,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,4,2,7,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,3,2,7,6]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,5,3,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,1,3,2]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,3,4,2]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,5,1,4,2]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,1,4,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,6,1,4,2]=>[1,8,2,5,6,3,7,4]=>[8,1,7,4,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,2,5,1]=>[1,8,2,3,7,5,6,4]=>[8,1,7,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,1,5,2]=>[1,8,2,3,7,5,6,4]=>[8,1,7,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,6,4,5,2]=>[1,8,2,3,7,5,6,4]=>[8,1,7,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,6,4,5,2]=>[1,8,2,3,7,5,6,4]=>[8,1,7,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,3,4,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,7,5,6,3]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,4,2,6,5]=>[1,8,5,4,3,7,6,2]=>[8,1,4,5,6,2,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,6,2,5,4]=>[1,8,4,3,7,5,6,2]=>[8,1,5,6,2,4,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,6,2,5,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,4,5,1]=>[1,8,2,3,7,5,6,4]=>[8,1,7,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,6,4,5,1]=>[1,8,2,3,7,5,6,4]=>[8,1,7,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,6,1,5,4]=>[1,8,4,3,7,5,6,2]=>[8,1,5,6,2,4,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,3,5,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,4,3,6,5]=>[1,8,5,4,2,3,7,6]=>[8,1,4,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,7,4,6,5]=>[1,8,5,7,6,4,2,3]=>[8,1,4,2,3,5,7,6]=>[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,4,6,5]=>[1,2,3,8,5,7,6,4]=>[8,7,6,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,4,3,6,5]=>[1,8,5,4,2,3,7,6]=>[8,1,4,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,4,1,6,5]=>[1,8,5,4,3,7,6,2]=>[8,1,4,5,6,2,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,6,3,4,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,7,4,6,5]=>[1,8,5,7,6,4,2,3]=>[8,1,4,2,3,5,7,6]=>[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,5,4,7,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,5,7,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,8,6,7,5]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,3,1,5,4]=>[1,8,4,2,6,3,7,5]=>[8,1,5,7,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,6,3,4,1]=>[1,8,2,5,6,3,7,4]=>[8,1,7,4,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,6,1,4,3]=>[1,8,3,7,4,2,5,6]=>[8,1,6,2,5,7,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,1,4,3]=>[1,8,3,7,4,2,6,5]=>[8,1,6,2,5,7,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,2,4,3]=>[1,8,3,7,4,2,6,5]=>[8,1,6,2,5,7,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,3,2,5,4]=>[1,8,4,2,6,3,7,5]=>[8,1,5,7,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,3,5,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,5,6,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,4,5,3]=>[1,8,3,7,5,6,4,2]=>[8,1,6,2,4,3,5,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,4,5,3]=>[1,8,3,7,5,6,4,2]=>[8,1,6,2,4,3,5,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,6,1,5,3]=>[1,8,3,7,5,6,2,4]=>[8,1,6,2,4,3,7,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,6,3,5,1]=>[1,8,2,3,7,5,6,4]=>[8,1,7,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,3,5,1]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,1,5,3]=>[1,8,3,7,5,6,2,4]=>[8,1,6,2,4,3,7,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,6,2,5,3]=>[1,8,3,7,5,6,2,4]=>[8,1,6,2,4,3,7,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,2,5,3]=>[1,8,3,7,5,6,2,4]=>[8,1,6,2,4,3,7,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,2,4,3]=>[1,8,3,7,4,2,5,6]=>[8,1,6,2,5,7,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,3,6,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,6,1,3,2]=>[1,8,2,5,6,3,7,4]=>[8,1,7,4,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,3,4,2]=>[1,8,2,5,6,3,7,4]=>[8,1,7,4,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,3,5,2]=>[1,8,2,3,7,5,6,4]=>[8,1,7,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,6,3,5,2]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,1,5,2]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,6,1,7,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,3,2,7,4]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,3,1,2,4]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,3,6,2,4]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,4,6,5,3]=>[1,2,7,5,4,8,3,6]=>[8,7,2,4,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,4,5,7,1]=>[1,3,2,6,5,4,8,7]=>[8,6,7,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,4,5,7,3]=>[1,2,6,5,4,8,3,7]=>[8,7,3,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,4,5,7,2]=>[1,3,6,5,4,8,2,7]=>[8,6,3,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,4,5,7,1]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,4,1,5,2]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,4,6,5,2]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,2,4,6,3]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,2,4,6,3]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,4,2,5,1]=>[1,3,7,5,4,8,2,6]=>[8,6,2,4,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,4,2,5,3]=>[1,7,5,4,8,3,2,6]=>[8,2,4,5,1,6,7,3]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,1,6,5,4]=>[1,2,8,4,7,5,3,6]=>[8,7,1,5,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,8,4,6,5,3]=>[1,7,5,4,8,3,2,6]=>[8,2,4,5,1,6,7,3]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,4,6,5,1]=>[1,3,7,5,4,8,2,6]=>[8,6,2,4,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,1,4,6,3]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,8,5,6,7]=>[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,3,4,6,1]=>[1,7,6,4,8,2,3,5]=>[8,2,3,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,4,1,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,3,1,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,2,4,6,1]=>[1,7,6,4,8,2,3,5]=>[8,2,3,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,5,6,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,4,3,5,1]=>[1,2,7,5,4,8,3,6]=>[8,7,2,4,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,3,4,6,2]=>[1,5,3,2,7,6,4,8]=>[8,4,6,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,1,4,6,2]=>[1,3,5,2,7,6,4,8]=>[8,6,4,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,4,3,2,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,1,3,2,7]=>[1,4,5,2,6,3,8,7]=>[8,5,4,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,4,3,2,7]=>[1,5,4,2,6,3,8,7]=>[8,4,5,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,3,4,2,1]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,6,5,1,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,5,6,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,5,6,2,7]=>[1,4,3,8,7,2,5,6]=>[8,5,6,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,1,3,2,7]=>[1,5,2,6,3,8,7,4]=>[8,4,7,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,5,3,2,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,8,4,6,5,1]=>[1,2,7,5,4,8,3,6]=>[8,7,2,4,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,3,6,1,2]=>[1,5,3,8,2,7,4,6]=>[8,4,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,1,6,5,3]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,3,1,6,7]=>[1,2,8,7,6,3,5,4]=>[8,7,1,2,3,6,4,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,2,3,1,7]=>[1,6,3,8,7,2,5,4]=>[8,3,6,1,2,7,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,8,5,6,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,5,4,6,1]=>[1,7,6,4,8,2,3,5]=>[8,2,3,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,5,1,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,5,1,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,5,4,6,1]=>[1,7,6,4,8,2,3,5]=>[8,2,3,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,5,6,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,3,4,7,6]=>[1,2,8,6,4,5,3,7]=>[8,7,1,3,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,5,3,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,5,3,6,7]=>[1,2,4,8,7,6,3,5]=>[8,7,5,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,5,3,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,2,4,6,7]=>[1,8,7,6,4,3,5,2]=>[8,1,2,3,5,6,4,7]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,4,3,6,7]=>[1,2,5,4,8,7,6,3]=>[8,7,4,5,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,4,3,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,3,8,6,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,5,3,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,8,5,3,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,4,7,2,6]=>[1,8,6,7,2,3,5,4]=>[8,1,3,2,7,6,4,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,7,4,3,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,7,5,3,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,3,7,6,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,8,7,3,5]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,1,7,2,5]=>[1,3,4,8,5,2,6,7]=>[8,6,5,1,4,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,8,4,3,5]=>[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,2,8,3,5]=>[1,6,8,5,2,7,3,4]=>[8,3,1,4,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,4,8,2,5]=>[1,6,8,5,4,2,3,7]=>[8,3,1,4,5,7,6,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,5,2,4,6]=>[1,3,8,6,2,7,4,5]=>[8,6,1,3,7,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,4,5,3,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,2,4,8,5]=>[1,7,8,5,2,6,4,3]=>[8,2,1,4,7,3,5,6]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,5,8,4,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,8,3,4,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,7,2,4,6]=>[1,5,7,4,3,2,8,6]=>[8,4,2,5,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,7,3,4,6]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,3,7,4,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,2,4,7,5]=>[1,8,5,2,6,4,3,7]=>[8,1,4,7,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,7,3,6,5]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,4,3,6,5]=>[1,2,8,5,4,7,6,3]=>[8,7,1,4,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,4,3,6,5]=>[1,7,6,3,2,4,8,5]=>[8,2,3,6,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,7,5,3,6]=>[1,2,3,8,6,5,7,4]=>[8,7,6,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,4,5,3,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,5,3,4,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,4,7,2,5]=>[1,3,6,7,2,8,5,4]=>[8,6,3,2,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,7,4,3,5]=>[1,8,5,7,3,6,4,2]=>[8,1,4,2,6,3,5,7]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,8,6,3,5]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,1,6,2,5]=>[1,3,8,5,2,4,7,6]=>[8,6,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,7,6,3,5]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,6,4,3,5]=>[1,2,8,5,6,4,7,3]=>[8,7,1,4,3,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,1,5,2,6]=>[1,7,2,8,6,5,3,4]=>[8,2,7,1,3,4,6,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,1,6,2,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,4,1,8,2,5]=>[1,6,8,5,2,7,3,4]=>[8,3,1,4,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,1,8,2,6]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,1,7,2,6]=>[1,5,2,8,6,7,3,4]=>[8,4,7,1,3,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,1,6,2,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,1,5,2,7]=>[1,6,5,2,8,7,3,4]=>[8,3,4,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,4,1,5,2,8]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,1,6,2,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,4,1,8]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,3,5,1,7]=>[1,4,8,7,2,6,5,3]=>[8,5,1,2,7,3,4,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,1,6,2,8]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,1,6,2,7]=>[1,4,5,2,8,7,3,6]=>[8,5,4,7,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,1,7,2,6]=>[1,4,5,2,8,6,7,3]=>[8,5,4,7,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,1,8,2,6]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,1,7,4,8]=>[1,5,2,6,7,4,3,8]=>[8,4,7,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,1,8,3,7]=>[1,5,2,6,8,7,3,4]=>[8,4,7,3,1,2,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,1,8,3,7]=>[1,4,5,2,6,8,7,3]=>[8,5,4,7,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,3,8,2,6]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,3,8,1,5]=>[1,4,7,2,6,8,5,3]=>[8,5,2,7,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,8,1,4]=>[1,5,3,2,6,8,4,7]=>[8,4,6,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,3,7,1,4]=>[1,5,3,2,6,7,4,8]=>[8,4,6,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,3,7,1,5]=>[1,4,8,5,3,2,6,7]=>[8,5,1,4,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,3,6,2,8]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,3,6,2,7]=>[1,4,8,7,2,5,3,6]=>[8,5,1,2,7,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,2,1,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>[9,1,2,3,4,5,6,7,8]=>[9,2,3,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,2,1,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>[10,1,2,3,4,5,6,7,8,9]=>[10,2,3,4,5,6,7,8,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,2,3,1,4,5,6,7,8]=>[1,9,8,7,6,5,4,2,3]=>[9,1,2,3,4,5,6,8,7]=>[9,2,3,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,2,3,5,6,7,8,9,1]=>[1,4,5,6,7,8,9,2,3]=>[9,6,5,4,3,2,1,8,7]=>[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,2,5,6,7,8,9,1]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,9,10,1]=>[1,3,4,5,6,7,8,9,10,2]=>[10,8,7,6,5,4,3,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,11,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[4,6,3,5,2,1,8,7]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,2,4,1,6]=>[1,8,6,4,5,2,7,3]=>[8,1,3,5,4,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,5,2,8,7]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,5,7,2,1]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,3,6,2,5]=>[1,8,5,3,7,2,4,6]=>[8,1,4,6,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,4,2,6]=>[1,8,6,4,5,2,7,3]=>[8,1,3,5,4,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,5,7,4,3]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,1,7,4,2]=>[1,6,7,4,5,2,8,3]=>[8,3,2,5,4,7,1,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,7,6,3,1]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,5,6,7,2]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,5,6,7,2]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,1,6,3,2]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,1,4,7,2]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,1,6,2,5]=>[1,3,7,2,8,5,4,6]=>[8,6,2,7,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,5,6,7,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,2,6,3,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,2,4,7,5]=>[1,8,5,2,6,4,3,7]=>[8,1,4,7,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,5,1,3,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,1,6,3,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,2,4,7,1]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,1,4,7,5]=>[1,8,5,2,6,4,3,7]=>[8,1,4,7,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,2,1,7,4]=>[1,5,2,8,4,6,3,7]=>[8,4,7,1,5,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,2,6,1,3]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,5,7,1,3]=>[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,5,7,2,3]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,1,7,2,4]=>[1,6,7,2,8,4,5,3]=>[8,3,2,7,1,5,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,3,6,7,4]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,1,2,7,4]=>[1,5,2,8,4,6,3,7]=>[8,4,7,1,5,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,5,6,7,3]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,5,6,7,3]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,5,6,7,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,5,6,7,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,7,6,2,3]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,6,2,7,4]=>[1,5,6,2,8,4,3,7]=>[8,4,3,7,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,6,1,7,2]=>[1,4,8,2,5,6,3,7]=>[8,5,1,7,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,5,6,7,2]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,10,1,3,5,7,9]=>[1,2,4,8,5,10,9,7,3,6]=>[10,9,7,3,6,1,2,4,8,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,5,6,9,10,1,3,4,7,8]=>[1,2,5,10,8,4,9,7,3,6]=>[10,9,6,1,3,7,2,4,8,5]=>[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,5,8,9,10,1,3,4,6,7]=>[1,2,5,10,7,3,8,4,9,6]=>[10,9,6,1,4,8,3,7,2,5]=>[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,7,8,9,10,1,3,4,5,6]=>[1,2,7,3,8,4,9,5,10,6]=>[10,9,4,8,3,7,2,6,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,7,8,10,1,2,5,6,9]=>[1,3,7,2,4,8,5,10,9,6]=>[10,8,4,9,7,3,6,1,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,8,9,10,1,2,5,6,7]=>[1,3,8,5,10,7,2,4,9,6]=>[10,8,3,6,1,4,9,7,2,5]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,5,7,9,10,1,2,4,6,8]=>[1,3,7,2,5,10,8,4,9,6]=>[10,8,4,9,6,1,3,7,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,5,7,8,10,1,2,3,6,9]=>[1,4,8,3,7,2,5,10,9,6]=>[10,7,3,8,4,9,6,1,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,4,6,8,10,12,1,3,5,7,9,11]=>[1,2,4,8,3,6,12,11,9,5,10,7]=>[12,11,9,5,10,7,1,2,4,8,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,4,6,9,11,12,1,3,5,7,8,10]=>[1,2,4,9,5,11,8,3,6,12,10,7]=>[12,11,9,4,8,2,5,10,7,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,4,7,9,10,12,1,3,5,6,8,11]=>[1,2,4,9,5,10,6,12,11,8,3,7]=>[12,11,9,4,8,3,7,1,2,5,10,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,5,6,8,11,12,1,3,4,7,9,10]=>[1,2,5,11,9,4,8,3,6,12,10,7]=>[12,11,8,2,4,9,5,10,7,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,8,9,10,11,12,1,3,4,5,6,7]=>[1,2,8,3,9,4,10,5,11,6,12,7]=>[12,11,5,10,4,9,3,8,2,7,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[3,4,8,9,10,12,1,2,5,6,7,11]=>[1,3,8,2,4,9,5,10,6,12,11,7]=>[12,10,5,11,9,4,8,3,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[3,4,8,10,11,12,1,2,5,6,7,9]=>[1,3,8,2,4,10,6,12,9,5,11,7]=>[12,10,5,11,9,3,7,1,4,8,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,5,6,8,11,12,1,2,3,7,9,10]=>[1,4,8,2,5,11,9,3,6,12,10,7]=>[12,9,5,11,8,2,4,10,7,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,5,7,8,10,12,1,2,3,6,9,11]=>[1,4,8,2,5,10,6,12,11,9,3,7]=>[12,9,5,11,8,3,7,1,2,4,10,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,5,8,9,10,12,1,2,3,6,7,11]=>[1,4,9,3,8,2,5,10,6,12,11,7]=>[12,9,4,10,5,11,8,3,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,6,8,9,11,12,1,2,3,5,7,10]=>[1,4,9,3,8,2,6,12,10,5,11,7]=>[12,9,4,10,5,11,7,1,3,8,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[5,6,8,9,10,12,1,2,3,4,7,11]=>[1,5,10,4,9,3,8,2,6,12,11,7]=>[12,8,3,9,4,10,5,11,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,5,7,6,2,3,8,1]=>[1,4,6,3,7,8,2,5]=>[8,5,3,6,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,6,4,8,1]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,6,8,4,2]=>[1,2,5,6,8,3,7,4]=>[8,7,4,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,6,1,5,2]=>[1,8,2,4,7,5,6,3]=>[8,1,7,5,2,4,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,6,4,8,1]=>[1,5,6,4,3,7,8,2]=>[8,4,3,5,6,2,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,6,1,5,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,7,6,8,5,2]=>[1,4,7,5,6,8,2,3]=>[8,5,2,4,3,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,6,8,4,2]=>[1,5,6,8,2,3,7,4]=>[8,4,3,1,7,6,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,6,1,5,2]=>[1,4,7,5,6,2,8,3]=>[8,5,2,4,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,6,1,5,2]=>[1,3,4,7,5,6,2,8]=>[8,6,5,2,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,1,6,5,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,8,5,4,3]=>[1,6,5,8,3,2,7,4]=>[8,3,4,1,6,7,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,6,8,5,2]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,8,6,5,3]=>[1,2,4,7,5,8,3,6]=>[8,7,5,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,1,6,5,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,6,4,3]=>[1,8,3,7,4,2,5,6]=>[8,1,6,2,5,7,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,8,6,4,3]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,8,6,4,3]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,6,8,4,2]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,8,1,3,2]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,8,1,3,2]=>[1,5,8,2,4,6,3,7]=>[8,4,1,7,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,1,6,4,3]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,2,6,4,3]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,6,4,3]=>[1,8,3,7,4,2,5,6]=>[8,1,6,2,5,7,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,2,6,5,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,2,6,5,3]=>[1,2,4,7,5,3,8,6]=>[8,7,5,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,6,1,5,2]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,1,6,4,3]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,7,6,5,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,7,6,5,4]=>[1,8,4,3,2,5,7,6]=>[8,1,5,6,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,7,6,5,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,6,5,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,2,6,4,3]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,2,6,4,3]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,2,6,5,3]=>[1,4,7,5,2,8,3,6]=>[8,5,2,4,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,7,6,5,4]=>[1,8,4,3,2,5,7,6]=>[8,1,5,6,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,9,10,2]=>[1,3,4,5,6,7,8,9,10,2]=>[10,8,7,6,5,4,3,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,11,1,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,10,9,8,7,6,5,4,3,1,2]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,9,10,11,2]=>[1,3,4,5,6,7,8,9,10,11,2]=>[11,9,8,7,6,5,4,3,2,1,10]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,9,10,11,12,2]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,7,1,8,4,5,2,3]=>[1,6,5,4,8,3,2,7]=>[8,3,4,5,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,8,2,6,4]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,8,3,6,4]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,8,2,7,4]=>[1,3,5,8,4,2,6,7]=>[8,6,4,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,1,8,7,2,3]=>[1,5,8,3,4,2,6,7]=>[8,4,1,6,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,8,7,2,3]=>[1,6,7,2,4,3,5,8]=>[8,3,2,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,8,7,2,3]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,8,2,7,4]=>[1,3,6,2,5,8,4,7]=>[8,6,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,3,8,7,5]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,2,8,7,5]=>[1,3,6,8,5,2,4,7]=>[8,6,3,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,2,8,7,5]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,8,2,7,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,8,2,6,4]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,7,3,6,4]=>[1,8,4,5,7,6,3,2]=>[8,1,5,4,2,3,6,7]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,8,3,7,4]=>[1,6,3,5,8,4,2,7]=>[8,3,6,4,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,3,8,7,5]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,1,8,7,6]=>[1,4,3,5,2,6,8,7]=>[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,2,7,6,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,3,8,7,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,4,2,8,6,5]=>[1,3,2,7,6,8,5,4]=>[8,6,7,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,2,8,6,5]=>[1,4,3,2,7,6,8,5]=>[8,5,6,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,4,8,6,5]=>[1,3,2,7,6,8,5,4]=>[8,6,7,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,4,8,6,5]=>[1,2,7,6,8,5,4,3]=>[8,7,2,3,1,4,5,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,4,8,7,5]=>[1,2,6,8,5,4,3,7]=>[8,7,3,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,8,3,7,4]=>[1,5,8,4,2,6,3,7]=>[8,4,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,1,8,7,6]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,4,8,7,5]=>[1,6,8,5,4,2,3,7]=>[8,3,1,4,5,7,6,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,4,8,6,5]=>[1,7,6,8,5,4,2,3]=>[8,2,3,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,4,7,6,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,7,6,5]=>[1,8,5,4,3,2,6,7]=>[8,1,4,5,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,4,8,6,5]=>[1,7,6,8,5,4,3,2]=>[8,2,3,1,4,5,6,7]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,4,8,7,5]=>[1,6,8,5,4,2,3,7]=>[8,3,1,4,5,7,6,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,1,5,8,7]=>[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,5,8,1,7]=>[1,2,4,6,8,7,3,5]=>[8,7,5,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,5,8,7,1]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,5,8,1,7]=>[1,2,4,3,6,8,7,5]=>[8,7,5,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,5,1,8,7]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,1,5,8,7]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,5,3,8,7]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,5,3,8,7]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,3,1,8,7]=>[1,4,5,3,6,2,7,8]=>[8,5,4,6,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,1,3,8,7]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,1,8,7,3]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,8,1,7,3]=>[1,4,5,8,3,6,2,7]=>[8,5,4,1,6,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,8,1,3,7]=>[1,4,5,8,7,3,6,2]=>[8,5,4,1,2,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,8,3,1,7]=>[1,4,5,8,7,2,3,6]=>[8,5,4,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,5,8,3,7]=>[1,2,4,3,6,8,7,5]=>[8,7,5,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,5,8,3,7]=>[1,2,4,6,8,7,3,5]=>[8,7,5,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,5,8,3,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,5,8,7,3]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,5,8,7,3]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,8,3,7,1]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,8,7,5,1]=>[1,2,6,7,5,8,3,4]=>[8,7,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,5,3,7,1]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,8,5,7,3]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,8,5,7,3]=>[1,2,4,6,5,8,3,7]=>[8,7,5,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,8,5,7,3]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,8,5,3,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,8,5,3,7]=>[1,2,4,6,5,8,7,3]=>[8,7,5,3,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,8,5,3,7]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,1,5,3,7]=>[1,2,4,8,7,3,6,5]=>[8,7,5,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,5,3,1,7]=>[1,4,8,7,2,3,6,5]=>[8,5,1,2,7,6,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,5,1,3,7]=>[1,4,8,7,3,6,2,5]=>[8,5,1,2,6,3,7,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,3,5,1,7]=>[1,2,4,8,7,3,6,5]=>[8,7,5,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,3,1,5,7]=>[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,1,8,5,7]=>[1,2,4,3,6,8,7,5]=>[8,7,5,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,8,1,5,7]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,8,5,1,7]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,8,5,7,1]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,8,5,7,1]=>[1,2,4,6,5,8,3,7]=>[8,7,5,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,8,5,1,7]=>[1,2,4,6,5,8,7,3]=>[8,7,5,3,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,8,1,5,7]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,1,8,5,7]=>[1,2,4,6,8,7,5,3]=>[8,7,5,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,6,8,5,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,6,8,7,5]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,1,8,7,5]=>[1,2,4,6,8,5,3,7]=>[8,7,5,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,8,1,7,5]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,8,7,1,3]=>[1,4,5,8,3,2,6,7]=>[8,5,4,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,8,7,3,1]=>[1,4,5,8,2,6,7,3]=>[8,5,4,1,7,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,8,1,7,5]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,1,8,7,5]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,3,8,7,5]=>[1,2,4,6,8,5,3,7]=>[8,7,5,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,3,8,7,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,8,3,7,5]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,8,3,7,5]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,8,3,7,5]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,1,3,7,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,3,1,7,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,7,1,3,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,1,7,5,3]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,8,7,5,3]=>[1,2,6,7,5,8,3,4]=>[8,7,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,8,7,5,3]=>[1,2,6,7,5,8,3,4]=>[8,7,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,8,7,5,3]=>[1,2,3,6,7,5,8,4]=>[8,7,6,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,8,7,3,5]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,1,7,3,5]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,3,8,2,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,5,8,2,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,7,3,6,8,1]=>[1,5,3,4,7,8,2,6]=>[8,4,6,5,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,4,8,2,5]=>[1,2,7,3,6,8,5,4]=>[8,7,2,6,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,7,2,4,5]=>[1,8,5,7,4,3,6,2]=>[8,1,4,2,5,6,3,7]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,8,2,4,5]=>[1,7,4,3,6,2,5,8]=>[8,2,5,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,8,3,5,6]=>[1,2,3,7,5,8,6,4]=>[8,7,6,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,5,8,3,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,3,8,2,6]=>[1,5,3,4,7,2,6,8]=>[8,4,6,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,7,1,4,5]=>[1,2,8,5,7,4,3,6]=>[8,7,1,4,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,7,3,4,6]=>[1,5,7,4,2,8,6,3]=>[8,4,2,5,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,1,8,3,4,6]=>[1,5,8,6,3,2,7,4]=>[8,4,1,3,6,7,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,8,3,6,7]=>[1,5,8,7,6,3,2,4]=>[8,4,1,2,3,6,7,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,3,4,8,2,7]=>[1,6,8,7,2,5,4,3]=>[8,3,1,2,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,7,2,4,6]=>[1,8,6,2,5,7,4,3]=>[8,1,3,7,4,2,5,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,8,4,6,7]=>[1,2,5,8,7,6,4,3]=>[8,7,4,1,2,3,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,4,1,8,6,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,1,8,6,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,7,1,3,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,7,2,3,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,6,1,4,5]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,7,1,5,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,7,1,3,6]=>[1,5,7,3,4,8,6,2]=>[8,4,2,6,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,7,2,3,6]=>[1,5,7,3,4,8,6,2]=>[8,4,2,6,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,1,3,7,6]=>[1,4,5,2,8,6,3,7]=>[8,5,4,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,1,3,8,6]=>[1,4,5,2,7,8,6,3]=>[8,5,4,7,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,5,4,8,6]=>[1,3,2,7,8,6,4,5]=>[8,6,7,2,1,3,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,5,4,6,7]=>[1,8,7,6,4,2,3,5]=>[8,1,2,3,5,7,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,6,4,5,7]=>[1,8,7,5,6,4,2,3]=>[8,1,2,4,3,5,7,6]=>[8,2,3,5,4,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,1,6,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,4,5,7,6]=>[1,3,2,8,6,5,4,7]=>[8,6,7,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,4,5,8,6]=>[1,3,2,7,8,6,5,4]=>[8,6,7,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,5,7,4,6]=>[1,3,2,8,6,7,4,5]=>[8,6,7,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,1,7,3,6]=>[1,4,5,2,8,6,7,3]=>[8,5,4,7,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,1,8,3,6]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,5,8,4,6]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,4,8,5,6]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,5,8,6,4]=>[1,3,2,4,7,6,8,5]=>[8,6,7,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,6,8,4,5]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,6,8,1,2,5]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,7,1,2,5]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,1,7,3,5]=>[1,4,6,7,3,8,5,2]=>[8,5,3,2,6,1,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,6,7,4,5]=>[1,3,8,5,6,7,4,2]=>[8,6,1,4,3,2,5,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,7,5,6,4]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,7,4,6,5]=>[1,3,8,5,7,6,4,2]=>[8,6,1,4,2,3,5,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,6,4,7,5]=>[1,3,8,5,6,4,2,7]=>[8,6,1,4,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,6,4,8,5]=>[1,3,7,8,5,6,4,2]=>[8,6,2,1,4,3,5,7]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,1,3,7,5]=>[1,4,6,3,8,5,2,7]=>[8,5,3,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,1,3,6,5]=>[1,4,7,6,3,8,5,2]=>[8,5,2,3,6,1,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,4,1,2,6]=>[1,5,4,3,8,6,2,7]=>[8,4,5,6,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,1,3,7,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,1,3,8,5]=>[1,4,7,8,5,2,3,6]=>[8,5,2,1,4,7,6,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,8,4,7,5]=>[1,3,6,4,2,5,8,7]=>[8,6,3,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,8,4,5,6]=>[1,3,2,7,5,8,6,4]=>[8,6,7,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,5,1,2,6]=>[1,4,8,6,2,7,3,5]=>[8,5,1,3,7,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,6,1,2,5]=>[1,4,8,5,6,2,3,7]=>[8,5,1,4,3,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,8,6,4,5]=>[1,3,7,4,2,5,8,6]=>[8,6,2,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,8,7,4,5]=>[1,3,6,7,4,2,5,8]=>[8,6,3,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,1,7,3,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,7,8,4,5]=>[1,3,6,8,5,7,4,2]=>[8,6,3,1,4,2,5,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,8,7,1,2]=>[1,5,8,2,3,6,7,4]=>[8,4,1,7,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,7,8,5,3]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,4,8,1,2]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,4,6,1,2]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,4,6,1,2]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,4,7,1,2]=>[1,3,8,2,6,7,4,5]=>[8,6,1,7,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,4,7,1,2]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,4,8,1,2]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,4,8,7,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,7,3,6,4]=>[1,2,8,4,5,7,6,3]=>[8,7,1,5,4,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,4,8,7,3]=>[1,6,8,3,2,4,5,7]=>[8,3,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,8,7,5,3]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,4,6,5,3]=>[1,7,5,4,2,8,3,6]=>[8,2,4,5,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,4,2,6,5]=>[1,7,6,2,8,5,4,3]=>[8,2,3,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,8,2,7,5]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,4,1,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,2,3,7,6]=>[1,4,5,2,8,6,3,7]=>[8,5,4,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,4,3,2,8]=>[1,7,2,5,4,6,3,8]=>[8,2,7,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,7,4,3,2,8]=>[1,6,3,5,4,7,2,8]=>[8,3,6,4,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,4,3,2,7]=>[1,2,5,4,6,3,8,7]=>[8,7,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,5,3,2,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,7,3,8,4]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,4,3,2,8]=>[1,5,4,7,2,6,3,8]=>[8,4,5,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,4,3,2,8]=>[1,5,4,6,3,7,2,8]=>[8,4,5,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,4,3,2,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,4,3,2,5]=>[1,2,8,5,4,6,3,7]=>[8,7,1,4,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,5,3,2,4]=>[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,4,5,6,3]=>[1,7,6,5,4,2,8,3]=>[8,2,3,4,5,7,1,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,4,6,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,5,4,6,8,3]=>[1,7,8,3,2,4,5,6]=>[8,2,1,6,7,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,6,3,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,6,3,7,8]=>[1,4,5,6,3,2,7,8]=>[8,5,4,3,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,5,7,2,8]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,7,8,2,4]=>[1,5,7,2,3,6,8,4]=>[8,4,2,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,5,7,2,4]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,7,1,8,5]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,8,7,2,5]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,3,8,2,5]=>[1,4,7,2,3,6,8,5]=>[8,5,2,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,2,3,8,6]=>[1,4,5,2,3,7,8,6]=>[8,5,4,7,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,8,3,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,4,1,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,4,1,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,4,1,6,5]=>[1,7,6,2,8,5,4,3]=>[8,2,3,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,6,3,2,5]=>[1,7,2,8,5,6,3,4]=>[8,2,7,1,4,3,6,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,7,8,2,5]=>[1,3,6,8,5,7,2,4]=>[8,6,3,1,4,2,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,4,3,2,6]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,4,3,2,6]=>[1,5,4,7,2,3,8,6]=>[8,4,5,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,1,4,3,2,8]=>[1,6,3,7,2,5,4,8]=>[8,3,6,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,4,3,2,6]=>[1,7,2,5,4,3,8,6]=>[8,2,7,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,4,3,2,6]=>[1,5,4,2,8,6,3,7]=>[8,4,5,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,4,3,2,6]=>[1,2,5,4,8,6,3,7]=>[8,7,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,1,3,2,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,1,3,2,6]=>[1,7,2,8,6,3,5,4]=>[8,2,7,1,3,6,4,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,1,3,8,7]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,4,3,2,8]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,6,8,9,7]=>[9,8,7,6,5,4,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,7,5,8,9,6]=>[1,2,3,4,5,7,8,9,6]=>[9,8,7,6,5,3,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,6,4,7,8,9,5]=>[1,2,3,4,6,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,5,3,6,7,8,9,4]=>[1,2,3,5,6,7,8,9,4]=>[9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,2,5,6,7,8,9,3]=>[1,2,4,5,6,7,8,9,3]=>[9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,9,1,2,3,4,5]=>[1,6,2,7,3,8,4,9,5]=>[9,4,8,3,7,2,6,1,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,6,2,5,4,1,7,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,4,1,6,8]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,8,1,5,7]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,1,3,7,8]=>[1,6,3,4,5,2,7,8]=>[8,3,6,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,1,3,7,6]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,1,7,2,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,8,3,5,2]=>[1,2,6,3,7,5,8,4]=>[8,7,3,6,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,7,5,8,2]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,5,8,1,3]=>[1,4,2,6,8,3,7,5]=>[8,5,7,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,7,5,3,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,1,6,3,8]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,2,8,1,3]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,3,8,6,2]=>[1,2,7,6,8,3,5,4]=>[8,7,2,3,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,5,8,7,2]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,3,6,7,2]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,7,1,4,8]=>[1,5,7,4,2,6,3,8]=>[8,4,2,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,8,1,7,3]=>[1,5,8,3,6,2,4,7]=>[8,4,1,6,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,6,3,8,7]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,1,8,4,7]=>[1,5,2,6,8,7,4,3]=>[8,4,7,3,1,2,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,6,4,7,8]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,2,1,5,7]=>[1,6,2,8,7,5,3,4]=>[8,3,7,1,2,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,1,6,4,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,2,1,4,6]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,2,1,7,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,2,1,8,5]=>[1,7,8,5,2,6,3,4]=>[8,2,1,4,7,3,6,5]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,1,8,6,3]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,2,6,1,4]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,1,6,8,4]=>[1,5,2,7,8,4,3,6]=>[8,4,7,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,1,6,4,8]=>[1,5,2,7,4,3,6,8]=>[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,5,1,8,4]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,5,2,1,4]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,8,6,3,4]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,8,1,4,5]=>[1,3,7,4,2,6,5,8]=>[8,6,2,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,8,1,4,5]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,7,4,5,8]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,4,7,6,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,1,8,4,6]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,3,7,8,6]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,6,1,4,5]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,1,7,4,5]=>[1,3,8,5,2,6,7,4]=>[8,6,1,4,7,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,2,1,5,6]=>[1,4,3,7,5,2,8,6]=>[8,5,6,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,2,1,5,6]=>[1,8,6,2,4,3,7,5]=>[8,1,3,7,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,1,4,7,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,6,1,4,5]=>[1,7,4,8,5,6,2,3]=>[8,2,5,1,4,3,7,6]=>[8,4,6,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,4,6,8,7]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,4,6,1,2]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,5,2,4,1]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,3,2,8,7]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,2,8,3,4]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,2,8,4,3]=>[1,5,2,7,4,6,8,3]=>[8,4,7,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,1,4,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,1,5,8,7]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,5,4,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,4,8,5,3]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,4,8,3,5]=>[1,2,7,3,6,8,5,4]=>[8,7,2,6,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,8,4,2,6]=>[1,7,2,3,5,8,6,4]=>[8,2,7,6,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,5,8,4,3]=>[1,2,7,4,3,6,8,5]=>[8,7,2,5,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,1,8,5,3]=>[1,2,7,5,3,6,8,4]=>[8,7,2,4,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,3,8,5,4]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,3,8,4,5]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,2,8,4,1]=>[1,5,2,7,4,6,8,3]=>[8,4,7,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,1,8,3,5]=>[1,2,7,3,6,8,5,4]=>[8,7,2,6,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,8,6,2,4]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,7,6,1,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,5,7,1,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,8,1,2,6]=>[1,7,2,3,5,8,6,4]=>[8,2,7,6,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,8,7,3,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,7,5,6,1]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,7,5,1,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,8,4,1,2]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,8,1,4,2]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,8,1,2,4]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,8,7,3,2]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,3,8,2,4]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,8,2,3,6]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,8,2,6,3]=>[1,7,6,2,4,5,8,3]=>[8,2,3,7,5,4,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,1,8,4,2]=>[1,5,2,7,4,6,8,3]=>[8,4,7,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,8,6,3,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,8,6,2,1]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,5,6,1,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,7,1,6,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,1,7,6,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,1,6,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,5,1,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,8,2,1,6]=>[1,7,2,4,5,8,6,3]=>[8,2,7,5,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,8,3,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,8,2,6,1]=>[1,7,6,2,4,5,8,3]=>[8,2,3,7,5,4,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,5,1,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,1,6,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,1,5,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,1,5,3,4]=>[1,7,3,2,8,4,6,5]=>[8,2,6,7,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,2,5,3,4]=>[1,7,3,2,8,4,6,5]=>[8,2,6,7,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,2,5,3,4]=>[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,2,6,3,4]=>[1,5,2,8,4,7,3,6]=>[8,4,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,1,6,3,4]=>[1,5,2,8,4,7,3,6]=>[8,4,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,1,5,3,4]=>[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,4,6,3,5]=>[1,2,8,5,4,7,3,6]=>[8,7,1,4,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,4,6,3,5]=>[1,2,8,5,4,7,3,6]=>[8,7,1,4,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,1,6,3,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,1,6,3,5]=>[1,4,7,3,2,8,5,6]=>[8,5,2,6,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,2,6,3,5]=>[1,4,7,3,2,8,5,6]=>[8,5,2,6,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,2,6,3,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,5,6,2,3]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,5,6,2,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,5,6,2,4]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,4,6,2,5]=>[1,3,2,8,5,4,7,6]=>[8,6,7,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,4,6,2,5]=>[1,2,8,5,4,7,3,6]=>[8,7,1,4,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,2,6,4,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,2,6,4,5]=>[1,3,2,8,5,4,7,6]=>[8,6,7,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,1,6,4,5]=>[1,3,2,8,5,4,7,6]=>[8,6,7,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,4,6,1,5]=>[1,3,2,8,5,4,7,6]=>[8,6,7,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,5,6,1,4]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,5,6,1,3]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,5,6,1,2]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,5,6,1,2]=>[1,3,4,7,2,8,5,6]=>[8,6,5,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,5,6,1,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,4,6,1,5]=>[1,2,8,5,4,7,3,6]=>[8,7,1,4,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,1,6,4,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,3,6,4,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,4,2,5,3]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,2,8,5,3]=>[1,2,6,8,3,7,5,4]=>[8,7,3,1,6,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,8,5,2,4]=>[1,2,6,5,8,4,3,7]=>[8,7,3,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,5,6,2,4]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,4,2,5,6]=>[1,7,5,4,8,6,2,3]=>[8,2,4,5,1,3,7,6]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,3,4,6,1,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,2,6,3,4]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,5,7,4,1]=>[1,6,7,4,8,2,3,5]=>[8,3,2,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,8,5,4,1]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,8,4,5,1]=>[1,2,6,4,7,5,8,3]=>[8,7,3,5,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,5,6,8,1]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,8,1,6,4]=>[1,2,5,8,4,7,6,3]=>[8,7,4,1,5,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,7,8,2,6]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,6,1,3,7]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,6,1,7,5]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,5,7,1,6]=>[1,4,3,2,8,6,7,5]=>[8,5,6,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,8,3,6,2,5]=>[1,2,4,8,5,3,7,6]=>[8,7,5,1,4,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,6,7,2,5]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,4,7,1,6]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,5,1,7,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,4,7,2,5]=>[1,6,7,2,3,8,5,4]=>[8,3,2,7,6,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,6,2,7,4]=>[1,5,6,2,8,4,3,7]=>[8,4,3,7,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,2,6,8,3]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,2,6,3,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,2,7,6,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,8,7,3,4]=>[1,6,7,3,2,5,8,4]=>[8,3,2,6,7,4,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,4,2,8,7]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,4,2,7,8]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,2,8,7,4]=>[1,3,6,8,4,2,5,7]=>[8,6,3,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,8,6,2,4]=>[1,3,7,2,5,8,4,6]=>[8,6,2,7,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,5,1,8,4]=>[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,1,8,6,3]=>[1,4,7,6,8,3,5,2]=>[8,5,2,3,1,6,4,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,8,6,1,5]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,2,7,1,6]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,8,1,7,4]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,1,3,8,7]=>[1,4,6,3,5,2,7,8]=>[8,5,3,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,5,6,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,4,8,6,1]=>[1,3,2,7,6,8,4,5]=>[8,6,7,2,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,7,3,6,1]=>[1,8,2,4,5,7,6,3]=>[8,1,7,5,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,8,3,6,1]=>[1,4,5,8,2,7,6,3]=>[8,5,4,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,8,3,2,7]=>[1,4,5,8,7,2,3,6]=>[8,5,4,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,4,3,2,7]=>[1,5,4,8,7,2,3,6]=>[8,4,5,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,6,3,2,1]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,4,3,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,4,3,7,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,7,3,2,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,1,3,2,4]=>[1,8,4,7,2,5,3,6]=>[8,1,5,2,7,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,3,2,5]=>[1,8,5,7,2,4,3,6]=>[8,1,4,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,4,7,2,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,4,3,8,5]=>[1,2,7,8,5,4,3,6]=>[8,7,2,1,4,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,2,3,4,1]=>[1,5,2,7,4,8,3,6]=>[8,4,7,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,4,3,6,1]=>[1,5,4,8,2,7,6,3]=>[8,4,5,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,4,3,5,1]=>[1,6,3,8,2,7,5,4]=>[8,3,6,1,7,2,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,8,3,5,1]=>[1,4,2,7,5,8,3,6]=>[8,5,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,4,7,5,1]=>[1,8,2,3,6,7,5,4]=>[8,1,7,6,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,4,8,5,1]=>[1,3,6,8,2,7,5,4]=>[8,6,3,1,7,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,4,6,2,1]=>[1,5,4,8,2,7,3,6]=>[8,4,5,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,8,6,2,1]=>[1,4,5,8,2,7,3,6]=>[8,5,4,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,4,3,6,5]=>[1,8,5,4,2,7,6,3]=>[8,1,4,5,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,2,5,4,1]=>[1,8,2,7,4,3,6,5]=>[8,1,7,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,6,2,4]=>[1,8,4,5,2,7,3,6]=>[8,1,5,4,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,1,3,6,4]=>[1,8,4,5,2,7,6,3]=>[8,1,5,4,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,1,3,7,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,7,1,2,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,8,1,2,3]=>[1,4,5,8,3,6,2,7]=>[8,5,4,1,6,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,9,2,3,4,5,6,8]=>[1,2,7,5,3,9,8,6,4]=>[9,8,3,5,7,1,2,4,6]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,4,3,8,7,1,2]=>[1,5,8,2,6,7,3,4]=>[8,4,1,7,3,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,7,8,5,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,8,1,6,5]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,5,8,6,3]=>[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,5,6,1,2]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,8,7,1,2]=>[1,3,6,7,2,5,8,4]=>[8,6,3,2,7,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,3,7,1,2]=>[1,4,5,3,8,2,6,7]=>[8,5,4,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,4,7,1,2]=>[1,6,7,2,8,3,5,4]=>[8,3,2,7,1,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,2,8,7,3]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,2,6,5,3]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,8,2,5,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,3,4,2,8,7]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,2,8,1,6]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,1,4,2,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,4,1,3,7]=>[1,2,5,4,6,3,8,7]=>[8,7,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,5,8,3,7]=>[1,2,4,3,6,8,7,5]=>[8,7,5,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,3,4,2,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,5,6,8,3]=>[1,7,8,3,2,4,5,6]=>[8,2,1,6,7,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,6,5,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,5,7,2,4]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,3,2,1,4]=>[1,5,3,6,2,8,4,7]=>[8,4,6,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,7,2,8,5]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,5,2,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,4,2,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,6,3,1,5]=>[1,7,2,8,5,6,3,4]=>[8,2,7,1,4,3,6,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,7,8,1,5]=>[1,3,6,8,5,7,2,4]=>[8,6,3,1,4,2,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,3,4,1,6]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,1,2,6,4]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,2,1,7,4]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,1,3,2,6]=>[1,5,2,8,6,3,7,4]=>[8,4,7,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,4,1,2,6]=>[1,3,7,2,5,4,8,6]=>[8,6,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,3,8,2,6]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,3,1,8,5]=>[1,2,4,7,8,5,3,6]=>[8,7,5,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,3,1,2,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,2,3,1,7]=>[1,5,2,6,3,8,7,4]=>[8,4,7,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,3,1,2,7]=>[1,6,2,8,7,3,5,4]=>[8,3,7,1,2,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,8,5,7,3]=>[1,6,5,8,3,4,2,7]=>[8,3,4,1,6,5,7,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,3,2,7,1]=>[1,4,5,3,6,2,8,7]=>[8,5,4,6,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,2,4,7,3]=>[1,8,3,5,2,6,4,7]=>[8,1,6,4,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,2,1,4,3]=>[1,6,2,7,4,8,3,5]=>[8,3,7,2,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,2,6,4,3]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,7,6,2,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,7,1,2,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,6,2,7,4]=>[1,8,4,5,6,2,3,7]=>[8,1,5,4,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,1,4,7,3]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,6,1,7,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,6,3,7,4]=>[1,8,4,5,6,3,2,7]=>[8,1,5,4,3,6,7,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,1,7,3,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,7,1,2,4]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,8,4,2,3]=>[1,5,8,3,7,2,4,6]=>[8,4,1,6,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,8,6,2,4]=>[1,5,8,4,7,2,3,6]=>[8,4,1,5,2,7,6,3]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,7,6,1,4]=>[1,3,8,4,5,7,2,6]=>[8,6,1,5,4,2,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,5,7,3,4]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,6,7,8,5]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,4,1,8,3]=>[1,7,8,3,6,2,4,5]=>[8,2,1,6,3,7,5,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,5,4,7,8,2]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,3,4,7,8,2]=>[1,6,7,8,2,3,5,4]=>[8,3,2,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,3,7,1,4]=>[1,8,4,6,7,2,5,3]=>[8,1,5,3,2,7,4,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,6,7,8,5]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,7,3,2,4]=>[1,8,4,5,7,2,3,6]=>[8,1,5,4,2,7,6,3]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,3,7,2,4]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,3,7,2,4]=>[1,2,8,4,6,7,3,5]=>[8,7,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,6,5,8,3]=>[1,7,8,3,4,2,5,6]=>[8,2,1,6,5,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,5,6,8,3]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,1,2,8,3]=>[1,5,2,7,8,3,6,4]=>[8,4,7,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,5,2,8,3]=>[1,4,2,7,8,3,6,5]=>[8,5,7,2,1,6,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,5,7,2,4]=>[1,2,8,4,6,7,3,5]=>[8,7,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,5,7,2,4]=>[1,3,2,8,4,6,7,5]=>[8,6,7,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,7,6,2,4]=>[1,8,4,5,7,2,3,6]=>[8,1,5,4,2,7,6,3]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,1,6,2,3]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,4,3,7,8,2]=>[1,6,7,8,2,3,5,4]=>[8,3,2,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,5,1,8,3]=>[1,7,8,3,6,2,4,5]=>[8,2,1,6,3,7,5,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,5,7,8,2]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,5,7,8,2]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,5,1,8,3]=>[1,7,8,3,6,2,4,5]=>[8,2,1,6,3,7,5,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,6,8,1,2]=>[1,5,6,8,2,4,3,7]=>[8,4,3,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,5,6,1,2]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,5,1,6,8]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,7,1,5,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,5,7,1,2]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,5,8,1,2]=>[1,4,7,2,3,6,8,5]=>[8,5,2,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,5,8,3,4]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,4,1,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,5,1,4,6]=>[1,7,4,2,8,6,3,5]=>[8,2,5,7,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,5,7,3,8]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,8,7,3,4]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,4,7,3,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,8,4,2,5]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,3,6,2,4]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,2,3,6,4]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,1,8,3,6]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,1,4,2,3,8]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,3,2,4,7]=>[1,5,3,8,7,4,2,6]=>[8,4,6,1,2,5,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,3,4,2,7]=>[1,6,4,2,8,7,3,5]=>[8,3,5,7,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,5,1,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,3,1,5,7,8]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,1,7,5,6]=>[1,4,3,8,6,7,5,2]=>[8,5,6,1,3,2,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,8,2,5,6]=>[1,2,3,7,5,8,6,4]=>[8,7,6,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,1,6,2,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,6,1,8,5]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,1,4,3,2]=>[1,7,3,6,4,8,2,5]=>[8,2,6,3,5,1,7,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,5,4,3,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,6,5,8,7]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,5,6,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,5,4,6,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,8,5,3,7]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,4,5,3,6]=>[1,7,3,2,8,6,5,4]=>[8,2,6,7,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,5,3,6,2]=>[1,7,6,3,4,2,8,5]=>[8,2,3,6,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,5,8,7,2]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,3,4,7,2]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,2,7,4,3]=>[1,6,7,4,8,3,2,5]=>[8,3,2,5,1,6,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,5,2,3,4]=>[1,6,2,8,4,7,3,5]=>[8,3,7,1,5,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,5,7,4,2,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,7,4,8,3]=>[1,2,5,7,8,3,6,4]=>[8,7,4,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,4,8,3,2]=>[1,5,4,6,8,2,3,7]=>[8,4,5,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,3,4,8,1]=>[1,2,6,4,7,8,3,5]=>[8,7,3,5,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,5,8,2,3]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,2,7,4,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,6,8,2,5]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,3,2,8,1]=>[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,7,2,4,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,8,3,4,5]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,6,8,3,4]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,2,7,3,1]=>[1,4,6,7,3,5,2,8]=>[8,5,3,2,6,4,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,2,7,5,1]=>[1,3,6,7,5,2,8,4]=>[8,6,3,2,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,7,4,5,1]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,2,4,5,3]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,7,2,5,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,7,2,6,5]=>[1,3,4,2,8,5,7,6]=>[8,6,5,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,8,3,2,6]=>[1,5,8,6,3,7,2,4]=>[8,4,1,3,6,2,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,8,5,2,6]=>[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,4,5,3,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,4,3,5,7]=>[1,6,3,2,4,8,7,5]=>[8,3,6,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,7,2,6,4]=>[1,8,4,3,2,5,7,6]=>[8,1,5,6,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,3,6,5]=>[1,8,5,7,6,3,2,4]=>[8,1,4,2,3,6,7,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,8,5,3,6]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,8,3,6,7]=>[1,2,5,8,7,6,3,4]=>[8,7,4,1,2,3,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,4,5,2,1]=>[1,3,6,5,4,8,2,7]=>[8,6,3,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,5,3,4,1]=>[1,2,7,4,8,3,6,5]=>[8,7,2,5,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,5,4,2,3]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,7,5,2,3]=>[1,2,4,6,5,7,3,8]=>[8,7,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,4,6,2,1]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,6,7,2,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,4,7,2,1]=>[1,6,7,2,3,5,4,8]=>[8,3,2,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,6,7,2,1]=>[1,5,6,7,2,4,8,3]=>[8,4,3,2,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,7,3,6,1]=>[1,5,7,6,3,2,4,8]=>[8,4,2,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,7,4,6,1]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,5,6,2,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,4,6,3,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,7,6,2,4]=>[1,3,8,4,5,7,2,6]=>[8,6,1,5,4,2,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,7,4,2,3]=>[1,6,4,8,3,5,7,2]=>[8,3,5,1,6,4,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,7,6,2,3]=>[1,5,7,2,4,8,3,6]=>[8,4,2,7,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,6,3,2,1]=>[1,4,5,6,3,7,2,8]=>[8,5,4,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,3,5,8,7]=>[1,4,6,5,3,2,7,8]=>[8,5,3,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,4,3,8,5,7]=>[1,6,8,7,5,3,2,4]=>[8,3,1,2,4,6,7,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,3,6,5,7]=>[1,8,7,5,3,2,4,6]=>[8,1,2,4,6,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,3,6,5,7]=>[1,8,7,5,3,4,2,6]=>[8,1,2,4,6,5,7,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,3,8,5,7]=>[1,6,8,7,5,3,4,2]=>[8,3,1,2,4,6,5,7]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,3,5,8,7]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,3,5,8,7]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,3,5,8,7]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,3,5,8,7]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,3,6,5,7]=>[1,8,7,5,3,2,4,6]=>[8,1,2,4,6,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,6,3,5,7]=>[1,8,7,5,6,3,2,4]=>[8,1,2,4,3,6,7,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,8,3,5,7]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,3,8,5,7]=>[1,2,6,8,7,5,3,4]=>[8,7,3,1,2,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,3,8,5,7]=>[1,2,3,6,8,7,5,4]=>[8,7,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,3,6,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,3,6,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,3,6,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,3,6,5,7]=>[1,4,2,8,7,5,3,6]=>[8,5,7,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,6,3,5,7]=>[1,2,8,7,5,6,3,4]=>[8,7,1,2,4,3,6,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,6,3,5,7]=>[1,2,3,8,7,5,6,4]=>[8,7,6,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,8,3,5,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,1,3,5,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,8,3,5,7]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,6,3,5,7]=>[1,8,7,5,6,3,4,2]=>[8,1,2,4,3,6,5,7]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,6,3,5,7]=>[1,8,7,5,6,3,2,4]=>[8,1,2,4,3,6,7,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,3,8,5,7]=>[1,4,6,8,7,5,3,2]=>[8,5,3,1,2,4,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,6,5,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,8,6,5,7]=>[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,3,6,5,7]=>[1,4,8,7,5,3,2,6]=>[8,5,1,2,4,6,7,3]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,6,3,5,7]=>[1,4,8,7,5,6,3,2]=>[8,5,1,2,4,3,6,7]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,4,3,5,7]=>[1,6,3,2,4,8,7,5]=>[8,3,6,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,4,3,5,7]=>[1,8,7,5,4,6,3,2]=>[8,1,2,4,5,3,6,7]=>[8,2,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,4,3,5,7]=>[1,6,3,8,7,5,4,2]=>[8,3,6,1,2,4,5,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,6,3,5,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,3,6,5,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,3,6,5,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,3,6,5,7]=>[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,6,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,6,3,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,6,3,5,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,1,3,5,7]=>[1,2,4,6,3,8,7,5]=>[8,7,5,3,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,1,3,5,7]=>[1,4,6,3,8,7,5,2]=>[8,5,3,6,1,2,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,1,3,5,7]=>[1,6,3,8,7,5,2,4]=>[8,3,6,1,2,4,7,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,1,3,5,7]=>[1,8,7,5,2,4,3,6]=>[8,1,2,4,7,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,1,3,5,7]=>[1,6,3,8,7,5,2,4]=>[8,3,6,1,2,4,7,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,1,3,5,7]=>[1,2,6,3,8,7,5,4]=>[8,7,3,6,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,4,3,5,7]=>[1,2,6,3,8,7,5,4]=>[8,7,3,6,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,4,3,5,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,4,3,5,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,4,3,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,4,3,5,7]=>[1,2,8,7,5,4,6,3]=>[8,7,1,2,4,5,3,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,1,3,5,7]=>[1,2,8,7,5,3,6,4]=>[8,7,1,2,4,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,1,3,5,7]=>[1,4,2,8,7,5,3,6]=>[8,5,7,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,5,4,8,7]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,8,1,7,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,5,3,8,7]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,8,1,7,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,5,8,1]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,6,1,7,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,7,2,6,5]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,4,2,7,6]=>[1,5,4,3,8,6,2,7]=>[8,4,5,6,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,6,8,1,5,2]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,8,5,6,2]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,8,1,7,2]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,7,2,8,1]=>[1,6,2,3,5,7,8,4]=>[8,3,7,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,8,4,5,2]=>[1,7,5,8,2,3,6,4]=>[8,2,4,1,7,6,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,8,1,3,2]=>[1,7,3,6,2,4,5,8]=>[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,6,3,7,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,3,2,7,5]=>[1,8,5,3,6,2,4,7]=>[8,1,4,6,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,4,2,7,5]=>[1,8,5,4,3,6,2,7]=>[8,1,4,5,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,6,1,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,6,4,8,1]=>[1,7,8,2,3,5,6,4]=>[8,2,1,7,6,4,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,5,3,6,4]=>[1,8,4,2,3,7,6,5]=>[8,1,5,7,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,5,3,7,6]=>[1,8,6,3,4,2,5,7]=>[8,1,3,6,5,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,7,3,6,5]=>[1,8,5,7,6,3,4,2]=>[8,1,4,2,3,6,5,7]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,6,1,7,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,6,1,7,5]=>[1,3,8,5,6,2,4,7]=>[8,6,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,5,4,7,6]=>[1,3,8,6,4,2,5,7]=>[8,6,1,3,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,8,1,5,4]=>[1,3,7,5,8,4,6,2]=>[8,6,2,4,1,5,3,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,8,5,6,4]=>[1,3,7,6,5,8,4,2]=>[8,6,2,3,4,1,5,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,4,3,8,1]=>[1,6,3,7,8,2,5,4]=>[8,3,6,2,1,7,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,4,1,7,3]=>[1,6,2,5,4,3,8,7]=>[8,3,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,4,1,5,3]=>[1,7,5,4,2,6,3,8]=>[8,2,4,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,5,2,4,3]=>[1,7,4,2,6,3,8,5]=>[8,2,5,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,8,5,6,4]=>[1,2,3,7,6,5,8,4]=>[8,7,6,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,8,5,6,4]=>[1,7,6,5,8,4,2,3]=>[8,2,3,4,1,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,6,2,4,3]=>[1,7,4,5,6,2,3,8]=>[8,2,5,4,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,5,3,8,1]=>[1,6,3,7,8,2,4,5]=>[8,3,6,2,1,7,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,7,2,4,3]=>[1,6,2,5,7,4,3,8]=>[8,3,7,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,8,3,7,4]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,8,1,3,2]=>[1,6,2,5,8,3,7,4]=>[8,3,7,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,8,3,5,2]=>[1,6,3,7,5,8,2,4]=>[8,3,6,2,4,1,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,8,3,6,2]=>[1,5,8,2,4,3,7,6]=>[8,4,1,7,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,4,7,1,8,6]=>[1,2,5,7,8,6,3,4]=>[8,7,4,2,1,3,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,5,7,6,1]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,1,8,6,7]=>[1,4,3,5,2,6,8,7]=>[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,5,3,6,7]=>[1,4,8,7,6,3,2,5]=>[8,5,1,2,3,6,7,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,8,2,6,7]=>[1,5,8,7,6,2,4,3]=>[8,4,1,2,3,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,3,2,6,7]=>[1,2,5,3,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,3,2,6,7]=>[1,2,8,7,6,3,5,4]=>[8,7,1,2,3,6,4,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,8,5,2,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,8,3,2,6]=>[1,5,8,6,3,4,7,2]=>[8,4,1,3,6,5,2,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,7,3,6,2]=>[1,4,5,7,6,3,2,8]=>[8,5,4,2,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,7,4,6,2]=>[1,8,2,3,5,7,6,4]=>[8,1,7,6,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,6,5,2,1]=>[1,3,4,7,2,8,5,6]=>[8,6,5,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,3,7,4,2]=>[1,2,6,7,4,5,3,8]=>[8,7,3,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,3,2,8,4]=>[1,2,7,8,4,6,3,5]=>[8,7,2,1,5,3,6,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,8,5,3,6]=>[1,4,7,3,2,5,8,6]=>[8,5,2,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,3,7,5,1]=>[1,2,6,7,5,3,8,4]=>[8,7,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,3,7,5,1]=>[1,6,7,5,3,4,8,2]=>[8,3,2,4,6,5,1,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,1,4,8,5]=>[1,2,6,4,3,7,8,5]=>[8,7,3,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,3,5,4,6]=>[1,2,7,4,8,6,5,3]=>[8,7,2,5,1,3,4,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,5,8,4,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,6,2,4,5]=>[1,8,5,6,2,7,4,3]=>[8,1,4,3,7,2,5,6]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,3,5,6,4]=>[1,8,4,7,6,5,3,2]=>[8,1,5,2,3,4,6,7]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,3,1,5,4]=>[1,7,5,3,2,8,4,6]=>[8,2,4,6,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,3,5,4,1]=>[1,8,2,7,4,6,5,3]=>[8,1,7,2,5,3,4,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,4,5,6,3]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,5,6,2,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,6,7,4,3]=>[1,2,8,3,5,6,7,4]=>[8,7,1,6,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,6,4,3,1]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,2,6,4,3]=>[1,2,7,4,5,3,8,6]=>[8,7,2,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,5,3,4,2]=>[1,8,2,7,4,3,6,5]=>[8,1,7,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,4,3,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,5,4,3,2]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,1,4,8,7]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,7,2,8,4,1]=>[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,4,3,1,6]=>[1,8,6,3,2,5,4,7]=>[8,1,3,6,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,1,2,8,7]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,6,2,8,7]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,7,2,1,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,3,8,2,1]=>[1,5,3,4,6,8,2,7]=>[8,4,6,5,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,3,7,1,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,3,6,2,5]=>[1,8,5,3,4,7,2,6]=>[8,1,4,6,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,7,3,2,6]=>[1,8,6,3,2,5,7,4]=>[8,1,3,6,7,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,4,3,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,4,7,8,3,2]=>[1,6,8,2,5,7,3,4]=>[8,3,1,7,4,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,7,5,8,1,2]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,8,3,7,2]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,5,8,6,2]=>[1,4,3,2,7,6,8,5]=>[8,5,6,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,1,7,2,5]=>[1,3,6,7,2,8,5,4]=>[8,6,3,2,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,5,7,6,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,4,1,3,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,4,1,3,5]=>[1,8,5,4,6,2,7,3]=>[8,1,4,5,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,4,2,3,1]=>[1,5,4,8,2,7,3,6]=>[8,4,5,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,2,4,6,1]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,2,1,8,4]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,8,7,1,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,4,2,1,3]=>[1,5,4,6,2,7,3,8]=>[8,4,5,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,4,8,1,3]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,5,8,2,3]=>[1,6,8,3,7,2,4,5]=>[8,3,1,6,2,7,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,1,8,2,4]=>[1,6,8,4,5,2,7,3]=>[8,3,1,5,4,7,2,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,5,8,3,4]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,3,6,8,4]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,1,2,8,4]=>[1,5,2,7,8,4,6,3]=>[8,4,7,2,1,5,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,5,6,8,3]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,6,5,8,3]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,7,8,5,1]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,5,8,7,3]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,8,2,7,3]=>[1,5,8,3,2,6,4,7]=>[8,4,1,6,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,8,7,2,4]=>[1,5,8,4,2,6,7,3]=>[8,4,1,5,7,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,7,1,8,2]=>[1,3,6,2,5,7,8,4]=>[8,6,3,7,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,5,7,8,2]=>[1,3,6,7,8,2,4,5]=>[8,6,3,2,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,7,6,8,2]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,1,6,5,4]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,6,1,5,4]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,6,5,1,4]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,6,5,4,1]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,6,5,3,1]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,6,5,1,3]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,6,1,5,3]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,1,6,5,3]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,1,6,5,2]=>[1,4,3,7,5,2,8,6]=>[8,5,6,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,2,6,1,5]=>[1,4,3,7,2,8,5,6]=>[8,5,6,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,2,6,5,1]=>[1,4,3,7,5,2,8,6]=>[8,5,6,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,6,2,5,1]=>[1,4,3,7,5,6,2,8]=>[8,5,6,2,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,6,2,1,5]=>[1,4,3,7,2,8,5,6]=>[8,5,6,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,6,1,5,2]=>[1,4,3,7,5,6,2,8]=>[8,5,6,2,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,6,5,1,2]=>[1,4,3,7,2,8,5,6]=>[8,5,6,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,6,5,2,1]=>[1,4,3,7,2,8,5,6]=>[8,5,6,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,3,1,4,2]=>[1,5,3,7,4,6,2,8]=>[8,4,6,2,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,3,2,4,1]=>[1,5,3,7,4,6,2,8]=>[8,4,6,2,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,2,4,3,1]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,2,1,4,3]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,4,3,1,2]=>[1,5,4,6,3,7,2,8]=>[8,4,5,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,2,1,6,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,6,1,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,7,4,8,1]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,5,6,4,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,1,3,2,8]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,3,2,8,6]=>[1,2,4,7,8,6,3,5]=>[8,7,5,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,3,8,2,5]=>[1,2,4,7,3,6,8,5]=>[8,7,5,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,3,1,8,2]=>[1,6,2,4,7,8,3,5]=>[8,3,7,5,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,1,3,8,2]=>[1,6,3,5,2,4,7,8]=>[8,3,6,4,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,7,4,8,2]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,7,4,8,3]=>[1,6,4,5,7,8,3,2]=>[8,3,5,4,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,7,4,8,6]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,3,8,1,5]=>[1,2,4,7,3,6,8,5]=>[8,7,5,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,3,8,5,2]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,8,3,4,2]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,3,1,4]=>[1,2,5,8,4,7,3,6]=>[8,7,4,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,7,8,4,5]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,7,8,4,3]=>[1,5,7,4,6,8,3,2]=>[8,4,2,5,3,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,7,8,4,2]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,1,8,3,2]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,8,3,2,4]=>[1,2,5,8,4,7,3,6]=>[8,7,4,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,2,1,8,3]=>[1,6,2,4,7,8,3,5]=>[8,3,7,5,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,2,8,3,1]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,7,8,4,1]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,7,8,1,4]=>[1,5,7,2,3,6,8,4]=>[8,4,2,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,7,1,8,4]=>[1,6,2,3,5,7,8,4]=>[8,3,7,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,2,1,7,8,5]=>[1,6,7,8,5,2,3,4]=>[8,3,2,1,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,2,7,8,6]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,7,8,1,5]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,7,8,5,1]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,7,8,5,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,2,8,5,3]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,2,8,5,1]=>[1,3,6,8,2,4,7,5]=>[8,6,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,2,1,8,6]=>[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,7,3,8,6]=>[1,4,5,7,8,6,3,2]=>[8,5,4,2,1,3,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,7,8,2,5]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,8,2,4,3]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,8,4,2,3]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,1,8,5,2]=>[1,3,6,8,2,4,7,5]=>[8,6,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,7,8,5,2]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,7,8,5,3]=>[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,7,8,5,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,1,8,5,3]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,1,4,3]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,5,4,7,6,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,1,6,3,8,5,10,7,9]=>[1,2,4,6,8,10,9,7,5,3]=>[10,9,7,5,3,1,2,4,6,8]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,1,6,4,7,5,9,8]=>[1,2,3,4,6,7,5,8,9]=>[9,8,7,6,4,3,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,1,5,3,7,6,9,8,10]=>[1,2,4,5,3,6,7,8,9,10]=>[10,9,7,6,8,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,1,5,4,7,6,9,8,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,9,8,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,6,8,9]=>[1,7,6,5,4,3,2,8,9]=>[9,3,4,5,6,7,8,2,1]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,3,6,2,5,7,8]=>[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,6,8,2,5]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,5,8,2,6]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,2,6,5,8]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,5,8,4,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,3,7,2,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,5,8,4,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,5,7,1,3]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,5,2,6,1]=>[1,3,8,2,7,6,4,5]=>[8,6,1,7,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,5,3,6,2]=>[1,7,6,3,2,8,4,5]=>[8,2,3,6,7,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,1,6,5,2]=>[1,3,7,5,2,8,4,6]=>[8,6,2,4,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,6,4,7,2]=>[1,5,6,4,2,8,3,7]=>[8,4,3,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,7,6,3,2]=>[1,5,7,3,2,8,4,6]=>[8,4,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,2,6,3,5]=>[1,7,3,8,5,2,4,6]=>[8,2,6,1,4,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,5,2,4,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,6,2,5,4]=>[1,7,5,6,2,3,8,4]=>[8,2,4,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,3,6,5,1,4]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,3,6,1,5,4]=>[1,7,5,6,2,3,8,4]=>[8,2,4,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,3,5,4,7]=>[1,6,5,3,2,4,8,7]=>[8,3,4,6,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,8,4,7,6]=>[1,5,8,6,4,3,2,7]=>[8,4,1,3,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,1,4,7,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,3,5,4,7]=>[1,6,5,3,8,7,4,2]=>[8,3,4,6,1,2,5,7]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,8,7,3,5]=>[1,6,7,3,4,2,5,8]=>[8,3,2,6,5,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,2,8,5,7]=>[1,6,8,7,5,2,3,4]=>[8,3,1,2,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,2,8,5,7]=>[1,3,6,8,7,5,2,4]=>[8,6,3,1,2,4,7,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,7,1,5,4]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,5,1,4,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,3,4,7,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,3,7,6,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,3,7,6,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,7,1,6,5]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,7,6,1,5]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,1,7,4,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,3,8,7,6]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,8,2,7,6]=>[1,3,5,8,6,2,4,7]=>[8,6,4,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,8,2,7,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,4,7,1,6]=>[1,5,4,8,6,7,2,3]=>[8,4,5,1,3,2,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,7,6,1,5]=>[1,4,3,2,8,5,7,6]=>[8,5,6,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,7,1,6,5]=>[1,4,3,2,8,5,7,6]=>[8,5,6,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,3,7,6,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,3,7,6,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,7,2,6,5]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,5,2,4,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,2,4,7,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,2,4,7,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,2,7,6,3]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,2,7,6,3]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,2,7,6,3]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,8,7,4,3]=>[1,6,7,4,2,5,8,3]=>[8,3,2,5,7,4,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,4,2,8,7]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,8,7,4,3]=>[1,5,8,3,6,7,4,2]=>[8,4,1,6,3,2,5,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,8,7,6,3]=>[1,4,5,8,3,2,6,7]=>[8,5,4,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,8,7,6,3]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,8,7,4,6]=>[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,7,5,1,4]=>[1,3,2,6,5,7,4,8]=>[8,6,7,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,8,7,3,5]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,8,2,7,6]=>[1,4,5,8,6,2,3,7]=>[8,5,4,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,7,1,4,6]=>[1,3,2,5,7,4,8,6]=>[8,6,7,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,2,6,1,5]=>[1,3,8,5,2,4,7,6]=>[8,6,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,1,2,6,5]=>[1,3,8,5,2,4,7,6]=>[8,6,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,7,2,6,5]=>[1,3,8,5,7,6,2,4]=>[8,6,1,4,2,3,7,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,7,2,6,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,2,7,6,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,7,1,6,5]=>[1,3,8,5,7,6,2,4]=>[8,6,1,4,2,3,7,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,7,6,1,5]=>[1,3,8,5,7,2,4,6]=>[8,6,1,4,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,5,8,7,6]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,5,8,7,6]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,8,7,6,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,5,3,6,4]=>[1,7,6,3,2,8,4,5]=>[8,2,3,6,7,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,4,2,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,4,2,6,3]=>[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,4,1,6,2]=>[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,4,1,3,6]=>[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,4,6,1,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,4,7,3,8]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,4,7,8,2]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,4,7,1,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,8,6,1,2]=>[1,4,5,8,2,3,7,6]=>[8,5,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,8,3,6,5]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,4,8,5,2]=>[1,3,6,8,2,4,7,5]=>[8,6,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,8,3,5,6]=>[1,2,7,5,8,6,3,4]=>[8,7,2,4,1,3,6,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,8,4,1,2]=>[1,5,8,2,7,3,6,4]=>[8,4,1,7,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,2,1,3,8]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,2,8,1,3]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,1,8,3,2]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,3,2,8,4]=>[1,2,7,8,4,5,3,6]=>[8,7,2,1,5,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,3,1,8,2]=>[1,4,5,3,6,2,7,8]=>[8,5,4,6,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,5,4,8,7,2]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,4,7,8,3]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,8,3,6,5]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,6,3,5,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,5,3,6,8]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,2,3,8,5]=>[1,4,6,3,2,7,8,5]=>[8,5,3,6,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,6,8,3,5,4]=>[1,2,7,5,8,4,6,3]=>[8,7,2,4,1,5,3,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,4,8,5,3]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,4,2,8,5]=>[1,3,6,2,4,7,8,5]=>[8,6,3,7,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,4,6,1,7]=>[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,5,3,8,6]=>[1,4,2,7,8,6,3,5]=>[8,5,7,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,5,2,4,1,8]=>[1,3,6,4,5,2,7,8]=>[8,6,3,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,5,1,4,8,2]=>[1,3,6,4,5,2,7,8]=>[8,6,3,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,5,2,1,8,4]=>[1,3,6,2,7,8,4,5]=>[8,6,3,7,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,4,2,5,7]=>[1,3,6,2,4,8,7,5]=>[8,6,3,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,1,4,3,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,8,1,3,4]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,8,4,1,3]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,7,4,8,5]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,3,5,8,6]=>[1,4,7,8,6,5,3,2]=>[8,5,2,1,3,4,6,7]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,4,2,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,2,7,6,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,3,7,6,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,1,5,8,6]=>[1,4,2,3,7,8,6,5]=>[8,5,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,2,1,8,5]=>[1,6,2,3,7,8,5,4]=>[8,3,7,6,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,1,3,8,6]=>[1,2,7,8,6,3,5,4]=>[8,7,2,1,3,6,4,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,2,1,8,6]=>[1,7,8,6,2,5,3,4]=>[8,2,1,3,7,4,6,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,1,7,6,4]=>[1,8,4,2,5,3,6,7]=>[8,1,5,7,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,8,4,3,7]=>[1,6,4,2,5,8,7,3]=>[8,3,5,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,8,1,5,7]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,2,8,1,6]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,4,8,3,5]=>[1,2,7,3,6,8,5,4]=>[8,7,2,6,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,2,7,4,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,3,7,5,4]=>[1,2,8,4,3,6,7,5]=>[8,7,1,5,6,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,2,7,5,4]=>[1,2,8,4,3,6,7,5]=>[8,7,1,5,6,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,7,1,6,4]=>[1,5,7,6,2,8,4,3]=>[8,4,2,3,7,1,5,6]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,6,5,4,2]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,1,5,4,3]=>[1,8,3,2,7,4,6,5]=>[8,1,6,7,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,4,3,6,2]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,2,4,6,3]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,7,2,5,4]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,7,1,3,2]=>[1,5,7,3,4,6,2,8]=>[8,4,2,6,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,6,1,4,3]=>[1,7,4,5,6,2,3,8]=>[8,2,5,4,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,8,2,1,4]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,8,4,1,5]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,1,4,2,7]=>[1,3,5,2,6,4,8,7]=>[8,6,4,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,3,2,1,7]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,2,1,6,5]=>[1,8,5,2,4,7,6,3]=>[8,1,4,7,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,1,3,6,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,1,4,3,7]=>[1,6,4,8,7,3,5,2]=>[8,3,5,1,2,6,4,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,7,3,6,2]=>[1,8,2,4,5,7,6,3]=>[8,1,7,5,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,8,2,3,7]=>[1,5,8,7,3,2,4,6]=>[8,4,1,2,6,7,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,8,6,3,1]=>[1,4,5,8,2,7,3,6]=>[8,5,4,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,7,4,1,2]=>[1,6,4,8,2,5,7,3]=>[8,3,5,1,7,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,7,6,2,3]=>[1,5,7,2,4,3,8,6]=>[8,4,2,7,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,7,3,6,4]=>[1,5,7,6,3,8,4,2]=>[8,4,2,3,6,1,5,7]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,4,7,5,2]=>[1,3,8,2,6,7,5,4]=>[8,6,1,7,3,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,1,6,4,2]=>[1,5,2,7,4,8,3,6]=>[8,4,7,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,1,5,3,2]=>[1,6,5,2,4,8,3,7]=>[8,3,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,5,2,4,1]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,1,3,6,4]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,2,1,6,4]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,5,1,4,3]=>[1,8,3,7,4,6,2,5]=>[8,1,6,2,5,3,7,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,6,2,1,5]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,2,6,1,4]=>[1,3,8,4,7,2,5,6]=>[8,6,1,5,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,6,5,1,2]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,4,3,2,1]=>[1,7,2,5,4,6,3,8]=>[8,2,7,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,6,4,2,1]=>[1,5,6,4,3,7,2,8]=>[8,4,3,5,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,5,4,1,3]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,1,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,1,2,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,1,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,3,2,7,8,1,4,5,9,10]=>[1,6,2,3,4,7,5,8,9,10]=>[10,5,9,8,7,4,6,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,6,5,1,2,4,8,7]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,2,4,1,6]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,2,4,1,6]=>[1,3,5,2,8,6,4,7]=>[8,6,4,7,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,6,3,8,7]=>[1,5,6,3,2,4,7,8]=>[8,4,3,6,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,7,3,2,6]=>[1,4,8,6,3,5,7,2]=>[8,5,1,3,6,4,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,8,5,2,3,6]=>[1,4,8,6,2,3,7,5]=>[8,5,1,3,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,8,2,3,6]=>[1,5,8,6,2,3,7,4]=>[8,4,1,3,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,1,4,2,6]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,7,3,4,6]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,5,2,3,6]=>[1,4,7,3,8,6,2,5]=>[8,5,2,6,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,3,2,8,5]=>[1,4,6,2,7,8,5,3]=>[8,5,3,7,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,7,5,8,4]=>[1,6,5,7,8,4,3,2]=>[8,3,4,2,1,5,6,7]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,8,6,5,4]=>[1,7,5,8,4,3,2,6]=>[8,2,4,1,5,6,7,3]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,5,8,6,4]=>[1,7,6,8,4,3,2,5]=>[8,2,3,1,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,4,1,6,5]=>[1,8,5,4,2,7,6,3]=>[8,1,4,5,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,4,8,6,5]=>[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,4,1,6,5]=>[1,7,6,2,8,5,4,3]=>[8,2,3,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,3,8,2,5]=>[1,6,8,5,3,2,7,4]=>[8,3,1,4,6,7,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,5,7,6,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,7,5,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,8,5,6,4]=>[1,7,6,5,8,4,3,2]=>[8,2,3,4,1,5,6,7]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,7,5,6,4]=>[1,8,4,3,2,5,7,6]=>[8,1,5,6,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,5,7,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,3,4,1,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,3,4,1,5]=>[1,6,4,7,2,8,5,3]=>[8,3,5,2,7,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,3,4,1,5]=>[1,6,4,8,5,3,2,7]=>[8,3,5,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,4,2,6,5]=>[1,3,7,6,2,8,5,4]=>[8,6,2,3,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,4,2,6,5]=>[1,3,8,5,4,2,7,6]=>[8,6,1,4,5,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,2,4,1,6]=>[1,3,7,2,5,4,8,6]=>[8,6,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,8,3,1,4,5]=>[1,7,4,8,5,3,2,6]=>[8,2,5,1,4,6,7,3]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,3,1,4,5]=>[1,8,5,3,2,6,4,7]=>[8,1,4,6,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,4,3,2,6]=>[1,8,6,3,7,2,4,5]=>[8,1,3,6,2,7,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,5,3,2,6]=>[1,8,6,3,7,2,4,5]=>[8,1,3,6,2,7,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,4,1,8,5]=>[1,6,2,7,8,5,4,3]=>[8,3,7,2,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,3,6,1,5]=>[1,8,5,3,2,7,4,6]=>[8,1,4,6,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,5,6,8,4]=>[1,7,8,4,3,2,5,6]=>[8,2,1,5,6,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,8,7,4,5]=>[1,6,7,4,3,2,5,8]=>[8,3,2,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,7,8,6,4]=>[1,5,7,6,8,4,3,2]=>[8,4,2,3,1,5,6,7]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,8,7,6,4]=>[1,5,8,4,3,2,6,7]=>[8,4,1,5,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,8,6,7,4]=>[1,5,8,4,3,2,6,7]=>[8,4,1,5,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,3,1,7,5]=>[1,8,5,3,2,6,4,7]=>[8,1,4,6,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,4,8,1,5]=>[1,7,2,6,8,5,4,3]=>[8,2,7,3,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,4,7,1,5]=>[1,8,5,4,2,6,7,3]=>[8,1,4,5,7,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,3,1,8,5]=>[1,7,8,5,3,2,6,4]=>[8,2,1,4,6,7,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,5,7,8,4]=>[1,6,7,8,4,3,2,5]=>[8,3,2,1,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,6,8,7,4]=>[1,5,6,8,4,3,2,7]=>[8,4,3,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,6,3,5,4]=>[1,7,5,6,3,2,8,4]=>[8,2,4,3,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,7,3,5,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,4,7,3,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,4,2,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,4,7,1,5]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,4,7,5,2]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,7,3,6,5]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,7,6,1,2]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,4,5,7,3]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,4,3,6,8]=>[1,7,6,3,2,5,4,8]=>[8,2,3,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,5,2,3,8]=>[1,7,3,6,2,4,5,8]=>[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,6,3,5,8]=>[1,7,5,6,3,4,2,8]=>[8,2,4,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,7,2,3,5]=>[1,6,2,8,5,7,3,4]=>[8,3,7,1,4,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,5,4,2,7]=>[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,5,4,2,8]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,5,4,2,8]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,6,3,5,8]=>[1,7,5,6,3,2,4,8]=>[8,2,4,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,5,1,4,8]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,6,5,4,8]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,7,3,5,4]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,8,5,4,7]=>[1,2,6,5,8,7,4,3]=>[8,7,3,4,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,7,6,3,4]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,7,6,3,4]=>[1,5,7,3,8,4,2,6]=>[8,4,2,6,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,7,3,5,4]=>[1,6,3,8,4,2,5,7]=>[8,3,6,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,2,8,5,7]=>[1,3,4,2,6,8,7,5]=>[8,6,5,7,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,8,5,4,7]=>[1,2,3,6,5,8,7,4]=>[8,7,6,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,7,6,3,4]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,8,7,4,6]=>[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,7,1,6,4]=>[1,2,5,7,6,3,4,8]=>[8,7,4,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,1,7,6,3]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,1,4,2,6]=>[1,3,8,6,4,7,2,5]=>[8,6,1,3,5,2,7,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,6,3,5,1]=>[1,4,7,5,6,3,8,2]=>[8,5,2,4,3,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,6,5,1,2]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,7,2,5,4]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,6,1,4,2]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,7,6,2,4]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,7,6,2,4]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,7,2,6,3]=>[1,2,5,7,6,3,8,4]=>[8,7,4,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,7,2,6,3]=>[1,5,7,6,2,3,8,4]=>[8,4,2,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,2,4,7,3]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,2,4,8,7]=>[1,5,2,6,4,3,7,8]=>[8,4,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,3,1,8,7]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,4,3,8,7]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,7,2,3,6]=>[1,4,2,5,7,3,8,6]=>[8,5,7,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,8,7,4,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,7,4,6,2]=>[1,3,2,5,7,6,4,8]=>[8,6,7,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,7,2,6,4]=>[1,3,2,5,7,6,4,8]=>[8,6,7,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,3,1,7,2,6]=>[1,4,3,8,6,7,2,5]=>[8,5,6,1,3,2,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,8,7,1,3,6]=>[1,4,8,6,2,5,7,3]=>[8,5,1,3,7,4,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,7,1,6,4]=>[1,3,5,7,6,2,4,8]=>[8,6,4,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,6,2,1,5]=>[1,3,8,5,6,2,4,7]=>[8,6,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,6,5,1,2]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,7,6,2,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,6,2,5,1]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,7,4,6,1]=>[1,3,5,7,6,4,8,2]=>[8,6,4,2,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,8,7,4,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,8,6,4,3]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,2,6,5,3]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,2,6,5,4]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,1,6,5,4]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,3,6,5,4]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,7,5,3,4]=>[1,8,4,6,5,7,3,2]=>[8,1,5,3,4,2,6,7]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,7,1,5,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,7,1,5,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,1,7,5,2]=>[1,6,7,5,2,8,3,4]=>[8,3,2,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,4,1,5,2]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,1,6,3,4]=>[1,8,4,7,3,5,2,6]=>[8,1,5,2,6,4,7,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,3,6,1,5]=>[1,8,5,3,7,2,4,6]=>[8,1,4,6,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,2,6,1,3]=>[1,8,3,7,2,5,4,6]=>[8,1,6,2,7,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,4,1,6,2]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,7,1,6,3]=>[1,8,3,2,5,7,6,4]=>[8,1,6,7,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,3,6,1,5]=>[1,8,5,3,4,7,2,6]=>[8,1,4,6,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,4,6,3,5]=>[1,8,5,4,2,3,7,6]=>[8,1,4,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,6,2,3,5]=>[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,3,6,2,5]=>[1,8,5,3,7,2,4,6]=>[8,1,4,6,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,7,2,5,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,1,2,6,4]=>[1,8,4,7,6,2,3,5]=>[8,1,5,2,3,7,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,1,6,2,3]=>[1,8,3,4,7,2,5,6]=>[8,1,6,5,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,1,2,6,3]=>[1,8,3,4,7,6,2,5]=>[8,1,6,5,2,3,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,7,2,6,3]=>[1,8,3,2,5,7,6,4]=>[8,1,6,7,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,2,7,5,3]=>[1,2,4,8,3,6,7,5]=>[8,7,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,2,7,4,3]=>[1,2,6,7,4,8,3,5]=>[8,7,3,2,5,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,1,7,4,2]=>[1,8,2,5,3,6,7,4]=>[8,1,7,4,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,1,7,4,3]=>[1,5,2,6,7,4,8,3]=>[8,4,7,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,6,1,2,4]=>[1,5,6,2,8,4,3,7]=>[8,4,3,7,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,1,6,2,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,7,5,1,4]=>[1,6,5,7,2,3,8,4]=>[8,3,4,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,7,1,5,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,3,1,5,2]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,7,1,6,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,2,6,1,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,4,6,2,5]=>[1,8,5,4,3,2,7,6]=>[8,1,4,5,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,4,6,1,5]=>[1,8,5,4,2,3,7,6]=>[8,1,4,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,5,1,6,2]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,2,6,1,3]=>[1,8,3,4,5,2,7,6]=>[8,1,6,5,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,4,6,1,5]=>[1,8,5,4,3,2,7,6]=>[8,1,4,5,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,6,1,4,5]=>[1,8,5,6,2,7,4,3]=>[8,1,4,3,7,2,5,6]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,5,4,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,3,7,5,1]=>[1,6,7,5,3,8,2,4]=>[8,3,2,4,6,1,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,8,2,7,5,1]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,8,2,7,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,3,2,7,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,8,1,7,6]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,8,7,5,1]=>[1,6,7,5,8,2,4,3]=>[8,3,2,4,1,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,1,7,8,4]=>[1,6,7,8,4,2,5,3]=>[8,3,2,1,5,7,4,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,7,8,4,1]=>[1,5,7,4,2,6,8,3]=>[8,4,2,5,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,2,7,8,5]=>[1,4,3,6,7,8,5,2]=>[8,5,6,3,2,1,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,3,6,5,2]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,3,6,5,8]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,6,1,5,8]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,2,6,5,8]=>[1,4,3,7,5,2,6,8]=>[8,5,6,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,5,4,1,8]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,2,3,8,1]=>[1,4,6,3,5,2,7,8]=>[8,5,3,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,6,2,4,8]=>[1,3,7,4,5,6,2,8]=>[8,6,2,5,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,1,3,8,4]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,2,8,1,3]=>[1,4,7,2,6,8,3,5]=>[8,5,2,7,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,2,8,3,1]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,7,2,8,3]=>[1,6,2,5,7,8,3,4]=>[8,3,7,4,2,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,8,7,3,5]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,7,1,2,5]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,8,7,2,5]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,8,7,2,4]=>[1,6,7,2,3,5,8,4]=>[8,3,2,7,6,4,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,6,3,1,4]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,1,7,3,4]=>[1,6,7,3,8,4,5,2]=>[8,3,2,6,1,5,4,7]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,6,7,4,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,7,1,4,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,6,7,4,5]=>[1,8,5,6,7,4,2,3]=>[8,1,4,3,2,5,7,6]=>[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,1,6,5,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,6,4,1,3]=>[1,5,6,4,7,2,3,8]=>[8,4,3,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,5,4,2,1]=>[1,6,4,8,2,3,7,5]=>[8,3,5,1,7,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,6,1,5,2]=>[1,3,7,5,6,2,4,8]=>[8,6,2,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,6,2,4,3]=>[1,8,3,5,6,2,4,7]=>[8,1,6,4,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,8,3,1,2]=>[1,4,6,3,7,2,5,8]=>[8,5,3,6,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,6,8,3,2]=>[1,5,6,8,2,4,7,3]=>[8,4,3,1,7,5,2,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,8,3,2,1]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,3,1,8,2]=>[1,7,8,2,5,3,6,4]=>[8,2,1,7,4,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,1,4,8,2]=>[1,3,7,8,2,6,4,5]=>[8,6,2,1,7,3,5,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,5,4,2,3]=>[1,8,3,6,4,7,2,5]=>[8,1,6,3,5,2,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,5,4,3,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,5,1,4,2,8]=>[1,3,6,4,5,2,7,8]=>[8,6,3,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,3,1,2,8]=>[1,4,5,3,6,2,7,8]=>[8,5,4,6,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,5,2,7,3]=>[1,8,3,4,2,6,5,7]=>[8,1,6,5,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,3,2,7,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,7,2,4,5]=>[1,8,5,7,4,2,6,3]=>[8,1,4,2,5,7,3,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,5,2,4,6]=>[1,8,6,2,7,4,3,5]=>[8,1,3,7,2,5,6,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,2,4,6,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,4,7,3,5]=>[1,8,5,4,2,6,7,3]=>[8,1,4,5,7,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,4,2,7,3]=>[1,8,3,2,5,4,6,7]=>[8,1,6,7,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,6,4,7,2]=>[1,8,2,5,6,4,3,7]=>[8,1,7,4,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,3,4,7,2]=>[1,8,2,6,4,5,3,7]=>[8,1,7,3,5,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,2,4,7,3]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,5,7,3,4]=>[1,8,4,2,6,7,3,5]=>[8,1,5,7,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,7,4,3,5]=>[1,8,5,7,3,2,6,4]=>[8,1,4,2,6,7,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,5,4,3,6]=>[1,8,6,4,2,7,3,5]=>[8,1,3,5,7,2,6,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,7,3,6,8]=>[1,5,7,6,3,4,2,8]=>[8,4,2,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,2,4,6,3]=>[1,5,2,7,6,4,3,8]=>[8,4,7,2,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,3,4,6,2]=>[1,5,3,8,2,7,6,4]=>[8,4,6,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,3,4,6,2]=>[1,5,3,2,8,4,7,6]=>[8,4,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,2,4,6,3]=>[1,8,3,5,2,4,7,6]=>[8,1,6,4,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,6,3,5]=>[1,8,5,7,3,2,4,6]=>[8,1,4,2,6,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,8,7,5,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,6,3,5,8]=>[1,2,4,7,5,6,3,8]=>[8,7,5,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,6,7,5,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,6,4,8,5,2]=>[1,3,7,5,4,6,8,2]=>[8,6,2,4,5,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,8,5,3,4]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,4,8,5,3]=>[1,6,8,3,2,4,7,5]=>[8,3,1,6,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,7,8,5,2]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,8,4,6,2]=>[1,5,8,2,7,6,4,3]=>[8,4,1,7,2,3,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,4,2,6,3]=>[1,5,4,8,3,2,7,6]=>[8,4,5,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,2,8,6,4]=>[1,7,6,8,4,3,5,2]=>[8,2,3,1,5,6,4,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,2,8,6,3]=>[1,7,6,8,3,4,5,2]=>[8,2,3,1,6,5,4,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,1,5,8,6,2]=>[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,5,2,6,3]=>[1,8,3,7,6,2,4,5]=>[8,1,6,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,2,6,4,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,4,7,5,6]=>[1,3,2,4,8,6,7,5]=>[8,6,7,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,8,5,7,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,4,7,5,2]=>[1,3,8,2,4,6,7,5]=>[8,6,1,7,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,7,4,5,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,8,4,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,8,6,4,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,4,6,5,2]=>[1,3,7,5,4,8,2,6]=>[8,6,2,4,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,6,4,5,2]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,4,6,5,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,3,6,5,4]=>[1,8,4,7,5,3,2,6]=>[8,1,5,2,4,6,7,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,8,7,4,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,8,5,4,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,1,4,2]=>[1,7,4,6,2,8,3,5]=>[8,2,5,3,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,1,4,2,8]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,1,4,2,6]=>[1,7,2,5,3,8,6,4]=>[8,2,7,4,6,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,6,4,1,2]=>[1,7,2,8,3,5,6,4]=>[8,2,7,1,6,4,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,1,2,6,4]=>[1,7,6,2,8,4,3,5]=>[8,2,3,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,4,1,6,2]=>[1,7,6,2,5,4,3,8]=>[8,2,3,7,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,4,6,1,2]=>[1,7,2,5,4,3,8,6]=>[8,2,7,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,1,4,8,2]=>[1,7,8,2,5,3,6,4]=>[8,2,1,7,4,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,1,2,8,4]=>[1,7,8,4,3,6,2,5]=>[8,2,1,5,6,3,7,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,1,2,8,4]=>[1,7,8,4,6,2,5,3]=>[8,2,1,5,3,7,4,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,1,2,8,6]=>[1,7,8,6,2,5,3,4]=>[8,2,1,3,7,4,6,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,4,2,6,8]=>[1,7,6,2,5,4,3,8]=>[8,2,3,7,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,6,4,8,2]=>[1,7,8,2,5,6,4,3]=>[8,2,1,7,4,3,5,6]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,4,8,1,2]=>[1,7,2,5,4,6,8,3]=>[8,2,7,4,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,4,6,1,2]=>[1,7,2,5,4,8,3,6]=>[8,2,7,4,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,8,2,4,6]=>[1,7,4,2,5,8,6,3]=>[8,2,5,7,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,6,2,4,8]=>[1,7,4,2,5,6,3,8]=>[8,2,5,7,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,8,4,2,6]=>[1,7,2,5,8,6,4,3]=>[8,2,7,4,1,3,5,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,8,6,2,4]=>[1,7,2,5,8,4,3,6]=>[8,2,7,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,6,1,4,2]=>[1,7,4,3,8,2,5,6]=>[8,2,5,6,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,1,6,4,2]=>[1,7,4,3,8,2,5,6]=>[8,2,5,6,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,1,6,2,4]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,1,4,2,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,4,1,2,8]=>[1,7,2,5,4,6,3,8]=>[8,2,7,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,3,1,2,4]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,3,4,1,2]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,8,1,2,4]=>[1,7,2,5,8,4,3,6]=>[8,2,7,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,1,6,2,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,1,8,2,6]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,1,8,4,2]=>[1,7,4,3,6,8,2,5]=>[8,2,5,6,3,1,7,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,8,1,4,2]=>[1,7,4,3,6,2,5,8]=>[8,2,5,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,8,4,1,2]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,8,1,4,2]=>[1,7,4,6,2,5,8,3]=>[8,2,5,3,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,1,8,4,2]=>[1,7,4,6,8,2,5,3]=>[8,2,5,3,1,7,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,6,8,2,4]=>[1,7,2,5,6,8,4,3]=>[8,2,7,4,3,1,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,4,8,2,6]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,4,6,2,8]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,4,8,6,2]=>[1,7,6,8,2,5,4,3]=>[8,2,3,1,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,1,8,6,2]=>[1,7,6,8,2,5,3,4]=>[8,2,3,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,8,1,6,2]=>[1,7,6,2,5,8,3,4]=>[8,2,3,7,4,1,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,8,6,1,2]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,6,1,8,2]=>[1,7,8,2,5,6,3,4]=>[8,2,1,7,4,3,6,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,2,4,8,6]=>[1,7,8,6,4,2,5,3]=>[8,2,1,3,5,7,4,6]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,5,4,1,8,7]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,4,7,6,1]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,2,8,6,1]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,2,7,6,1]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,2,1,8,7]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,4,1,8,7]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,8,5,2,1]=>[1,4,3,6,5,8,2,7]=>[8,5,6,3,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,3,7,5,2,1]=>[1,4,3,6,5,7,2,8]=>[8,5,6,3,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,2,7,6,1]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,4,7,6,3]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,4,8,6,1]=>[1,5,4,7,6,8,2,3]=>[8,4,5,2,3,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,2,8,6,1]=>[1,5,2,7,6,8,3,4]=>[8,4,7,2,3,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,3,2,8,6,1]=>[1,4,3,5,2,7,6,8]=>[8,5,6,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,6,5,2,1]=>[1,4,3,8,2,7,5,6]=>[8,5,6,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,7,5,2,1]=>[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,5,2,1]=>[1,7,2,6,5,8,3,4]=>[8,2,7,3,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,5,4,1]=>[1,7,4,6,5,8,2,3]=>[8,2,5,3,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,5,4,3]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,7,5,4,1]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,5,2,1]=>[1,8,2,6,5,7,3,4]=>[8,1,7,3,4,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,2,7,6,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,5,2,1]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,5,2,1]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,8,5,2,1]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,8,5,4,1]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,7,5,4,1]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,4,7,6,1]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,6,5,4,1]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,7,5,4,1]=>[1,3,2,6,5,7,4,8]=>[8,6,7,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,8,5,2,1]=>[1,6,5,8,2,4,3,7]=>[8,3,4,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,7,5,2,1]=>[1,6,5,7,2,4,3,8]=>[8,3,4,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,6,5,2,1]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,2,8,6,1]=>[1,7,6,8,2,4,3,5]=>[8,2,3,1,7,5,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,2,8,6,1]=>[1,7,6,8,2,5,3,4]=>[8,2,3,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,4,8,6,1]=>[1,7,6,8,2,3,4,5]=>[8,2,3,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,6,5,4,1]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,6,5,2,1]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,4,3,2,1]=>[1,6,3,5,4,7,2,8]=>[8,3,6,4,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,1,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,5,4,1,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,6,5,1,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,6,1,8,9]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,7,1,9]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,1,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,9,8,1]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,6,8,3,5,7,1,2]=>[1,4,3,8,2,6,7,5]=>[8,5,6,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,4,5,7,3]=>[1,6,5,4,2,8,3,7]=>[8,3,4,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,4,7,1,6]=>[1,3,8,6,7,2,5,4]=>[8,6,1,3,2,7,4,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,8,3,1,6,7]=>[1,4,8,7,6,2,5,3]=>[8,5,1,2,3,7,4,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,3,7,1,6]=>[1,4,8,6,7,2,3,5]=>[8,5,1,3,2,7,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,4,7,3,5]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,3,6,7,4]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,2,4,7,3]=>[1,2,6,4,8,3,5,7]=>[8,7,3,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,2,6,7,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,2,6,1,8]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,1,8,5,7]=>[1,4,2,6,8,7,5,3]=>[8,5,7,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,2,5,8,6]=>[1,4,3,7,8,6,5,2]=>[8,5,6,2,1,3,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,7,8,6,4]=>[1,3,2,5,7,6,8,4]=>[8,6,7,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,8,2,6,3]=>[1,7,6,2,5,8,3,4]=>[8,2,3,7,4,1,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,8,6,1,2]=>[1,5,8,2,4,3,7,6]=>[8,4,1,7,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,2,7,6,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,5,2,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,5,2,8,7]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,5,2,1,8]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,4,2,1,8]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,2,8,7,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,4,2,5,3]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,5,3,1,2]=>[1,6,3,8,2,4,7,5]=>[8,3,6,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,5,1,2]=>[1,7,2,6,5,8,3,4]=>[8,2,7,3,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,8,4,5,3]=>[1,2,7,5,8,3,6,4]=>[8,7,2,4,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,7,4,8,6]=>[1,2,5,7,8,6,4,3]=>[8,7,4,2,1,3,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,8,5,4,7]=>[1,6,5,8,7,4,2,3]=>[8,3,4,1,2,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,7,4,1,8]=>[1,6,4,2,5,7,3,8]=>[8,3,5,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,8,5,4,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,8,4,5,3]=>[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,8,3,6,4]=>[1,5,8,4,7,6,3,2]=>[8,4,1,5,2,3,6,7]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,3,8,5,6]=>[1,4,7,5,3,2,6,8]=>[8,5,2,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,3,1,5,7]=>[1,6,2,3,8,7,5,4]=>[8,3,7,6,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,8,4,5,6]=>[1,7,5,8,6,4,2,3]=>[8,2,4,1,3,5,7,6]=>[8,4,5,2,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,4,5,6,3]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,4,5,3]=>[1,8,3,6,4,2,7,5]=>[8,1,6,3,5,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,2,1,4,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,5,1,4,6]=>[1,3,8,6,2,4,7,5]=>[8,6,1,3,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,5,3,1,8]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,6,5,3,7]=>[1,8,7,3,4,2,5,6]=>[8,1,2,6,5,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,7,6,3,5]=>[1,8,5,7,3,4,2,6]=>[8,1,4,2,6,5,7,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,6,2,4,3]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,6,4,1,2]=>[1,8,2,5,6,4,3,7]=>[8,1,7,4,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,5,4,1,2]=>[1,6,4,7,2,8,3,5]=>[8,3,5,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,4,3,7,5]=>[1,8,5,4,6,3,2,7]=>[8,1,4,5,3,6,7,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,5,4,3,6]=>[1,2,8,6,4,7,3,5]=>[8,7,1,3,5,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,4,3,1,8]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,5,4,3,7]=>[1,2,3,8,7,4,6,5]=>[8,7,6,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,5,2,4,3]=>[1,2,7,4,6,3,8,5]=>[8,7,2,5,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,5,2,4,3]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,2,6,5,4]=>[1,8,4,3,7,5,2,6]=>[8,1,5,6,2,4,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,2,8,7,6]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,2,1,7,4]=>[1,8,4,3,5,2,6,7]=>[8,1,5,6,4,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,1,7,4,5]=>[1,8,5,2,6,7,4,3]=>[8,1,4,7,3,2,5,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,1,7,2,3]=>[1,8,3,5,2,6,7,4]=>[8,1,6,4,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,7,3,2,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,4,3,2,5]=>[1,8,5,4,7,2,6,3]=>[8,1,4,5,2,7,3,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,7,5,1,8]=>[1,4,2,6,5,7,3,8]=>[8,5,7,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,2,5,8,6]=>[1,2,4,7,8,6,5,3]=>[8,7,5,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,1,6,2,5]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,3,2,6,4]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,1,8,6,2]=>[1,5,2,7,6,8,3,4]=>[8,4,7,2,3,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,5,4,6,3]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,5,2,1,8]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,8,4,2,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,7,1,2,6]=>[1,3,4,8,6,2,5,7]=>[8,6,5,1,3,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,7,2,5,4]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,8,7,5,3]=>[1,2,6,7,5,8,3,4]=>[8,7,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,6,8,4,5]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,8,1,4,7]=>[1,3,5,8,7,4,2,6]=>[8,6,4,1,2,5,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,7,2,4,1,8]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,7,5,1,8]=>[1,3,2,6,5,7,4,8]=>[8,6,7,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,1,8,5,7]=>[1,3,2,6,8,7,5,4]=>[8,6,7,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,1,8,6,4]=>[1,7,6,8,4,2,3,5]=>[8,2,3,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,3,1,5,2]=>[1,8,2,7,5,3,6,4]=>[8,1,7,2,4,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,5,2,3]=>[1,8,3,6,5,2,7,4]=>[8,1,6,3,4,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,1,4,6,5]=>[1,3,7,6,4,2,8,5]=>[8,6,2,3,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,1,5,4,6]=>[1,3,2,8,6,5,4,7]=>[8,6,7,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,1,5,4,7]=>[1,3,8,7,4,2,6,5]=>[8,6,1,2,5,7,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,6,5,3,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,5,7,3,6]=>[1,4,2,3,8,6,7,5]=>[8,5,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,1,4,2,3]=>[1,8,3,7,2,5,4,6]=>[8,1,6,2,7,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,7,3,5,4]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,6,7,3,5]=>[1,2,8,5,6,7,3,4]=>[8,7,1,4,3,2,6,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,6,4,3,1,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,8,6,3,5]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,3,6,5,4]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,6,3,2,5]=>[1,2,8,5,6,3,7,4]=>[8,7,1,4,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,3,4,6,2]=>[1,7,6,4,8,2,3,5]=>[8,2,3,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,3,5,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,5,7,3,1]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,5,8,3,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,5,2,3,8]=>[1,7,3,6,2,4,5,8]=>[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,6,8,2,3]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,8,5,4,6]=>[1,7,4,3,2,5,8,6]=>[8,2,5,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,3,8,2,6]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,4,3,2,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,4,3,7,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,8,6,2,7]=>[1,3,2,5,8,7,4,6]=>[8,6,7,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,4,7,1,5]=>[1,6,7,2,3,8,5,4]=>[8,3,2,7,6,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,5,8,1,6]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,2,7,5,6]=>[1,4,2,3,8,6,7,5]=>[8,5,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,5,4,2,6]=>[1,3,7,2,8,6,4,5]=>[8,6,2,7,1,3,5,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,5,6,8,2]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,7,6,2,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,6,2,8,5]=>[1,3,4,2,7,8,5,6]=>[8,6,5,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,5,3,6,1]=>[1,8,2,4,3,7,6,5]=>[8,1,7,5,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,3,8,2,4]=>[1,7,2,6,8,4,3,5]=>[8,2,7,3,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,3,4,8,2]=>[1,7,8,2,6,4,3,5]=>[8,2,1,7,3,5,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,1,3,8,5]=>[1,7,8,5,2,3,6,4]=>[8,2,1,4,7,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,7,2,6,1]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,8,1,6,3]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,1,5,7,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,1,5,2,6]=>[1,7,2,3,8,6,5,4]=>[8,2,7,6,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,1,6,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,6,1,5,7]=>[1,4,3,8,7,5,6,2]=>[8,5,6,1,2,4,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,2,1,3,4]=>[1,6,2,8,4,7,3,5]=>[8,3,7,1,5,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,1,7,4,8]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,2,8,1,7]=>[1,3,5,2,6,8,7,4]=>[8,6,4,7,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,2,5,3,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,2,5,3,7]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,2,4,3,7]=>[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,3,7,8,5]=>[1,2,6,7,8,5,3,4]=>[8,7,3,2,1,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,4,7,3,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,4,7,8,3]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,4,7,3,6]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,4,8,3,6]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,2,4,8,3]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,4,6,7,3]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,4,6,8,3]=>[1,2,5,4,3,7,8,6]=>[8,7,4,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,3,2,4,6]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,2,4,6,7]=>[1,2,5,3,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,3,8,7,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,5,8,7,6]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,8,6,5,3]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,2,3,8,4]=>[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,8,4,3,6]=>[1,2,7,3,5,8,6,4]=>[8,7,2,6,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,2,8,3,4]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,2,4,8,3]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,3,7,4,8]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,3,7,8,4]=>[1,2,6,7,8,4,3,5]=>[8,7,3,2,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,2,3,7,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,3,7,8,5]=>[1,2,6,7,8,5,3,4]=>[8,7,3,2,1,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,3,7,5,8]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,2,4,7,3]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,2,8,5,6]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,8,5,3,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,3,8,5,7]=>[1,2,6,8,7,5,3,4]=>[8,7,3,1,2,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,2,8,5,3]=>[1,2,7,5,3,6,8,4]=>[8,7,2,4,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,3,8,7,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,1,4,8,2]=>[1,3,5,2,7,8,4,6]=>[8,6,4,7,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,6,7,5,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,2,7,5,3]=>[1,8,3,2,6,7,5,4]=>[8,1,6,7,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,2,8,5,7]=>[1,3,2,6,8,7,5,4]=>[8,6,7,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,3,5,8,2]=>[1,2,6,5,3,7,8,4]=>[8,7,3,4,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,6,7,8,2]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,3,5,8,2]=>[1,4,6,5,3,2,7,8]=>[8,5,3,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,6,5,8,2]=>[1,3,4,7,8,2,5,6]=>[8,6,5,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,3,5,8,2]=>[1,7,8,2,3,6,5,4]=>[8,2,1,7,6,3,4,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,3,5,8,2]=>[1,2,7,8,3,6,5,4]=>[8,7,2,1,6,3,4,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,2,7,5,3]=>[1,8,3,6,7,5,2,4]=>[8,1,6,3,2,4,7,5]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,7,2,5,6]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,8,2,5,6]=>[1,7,5,8,6,2,4,3]=>[8,2,4,1,3,7,5,6]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,2,8,5,7]=>[1,2,3,6,8,7,5,4]=>[8,7,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,1,2,8,5,6]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,2,7,5,3]=>[1,6,7,5,2,8,3,4]=>[8,3,2,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,6,2,5,4]=>[1,8,4,3,2,7,5,6]=>[8,1,5,6,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,3,2,1,4]=>[1,6,2,8,4,7,3,5]=>[8,3,7,1,5,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,7,2,5,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,7,6,1,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,6,2,1,5]=>[1,3,8,5,6,2,7,4]=>[8,6,1,4,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,6,8,2,1,5]=>[1,3,4,6,2,7,5,8]=>[8,6,5,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,8,2,5,6]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,3,2,1,4]=>[1,5,3,6,2,7,4,8]=>[8,4,6,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,4,8,6,1,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,8,2,1,6]=>[1,3,5,8,6,2,7,4]=>[8,6,4,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,2,8,5,6]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,8,2,5,6]=>[1,4,3,7,5,8,6,2]=>[8,5,6,2,4,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,7,2,5,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,8,6,1,7]=>[1,5,8,7,2,3,4,6]=>[8,4,1,2,7,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,3,8,1,4]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,3,8,1,4]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,6,8,4,1,3]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,5,6,1,7]=>[1,4,8,7,2,3,5,6]=>[8,5,1,2,7,6,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,7,6,1,4]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,5,6,1,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,7,2,5,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,2,6,5,3]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,2,5,6,3]=>[1,4,8,3,2,7,6,5]=>[8,5,1,6,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,5,6,1,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,6,2,5,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,3,2,1,4]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,3,2,1,4]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,3,2,1,4]=>[1,8,4,6,2,5,3,7]=>[8,1,5,3,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,7,6,1,4]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,6,2,1,4]=>[1,3,5,6,2,7,4,8]=>[8,6,4,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,5,2,1,4]=>[1,3,8,4,6,2,7,5]=>[8,6,1,5,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,6,2,5,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,3,2,1,4]=>[1,6,2,8,4,5,3,7]=>[8,3,7,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,3,4,1,2]=>[1,5,3,6,4,8,2,7]=>[8,4,6,3,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,4,5,1,2]=>[1,3,6,5,4,8,2,7]=>[8,6,3,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,6,7,1,2]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,6,5,7,1,2]=>[1,3,4,6,7,2,8,5]=>[8,6,5,3,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,5,8,1,2]=>[1,3,4,7,2,6,8,5]=>[8,6,5,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,5,8,3,4]=>[1,2,6,8,4,7,3,5]=>[8,7,3,1,5,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,5,7,2,3]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,5,7,2,3]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,4,6,2,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,2,4,3,6]=>[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,5,7,3,4]=>[1,2,8,4,6,7,3,5]=>[8,7,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,5,6,3,4]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,6,8,3,4]=>[1,2,5,6,8,4,7,3]=>[8,7,4,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,1,4,2,3]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,3,2,4]=>[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,1,3,2,4]=>[1,5,2,8,4,7,3,6]=>[8,4,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,6,8,4,5]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,2,4,3,5]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,2,6,4,5]=>[1,7,4,3,2,8,5,6]=>[8,2,5,6,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,2,4,3,5]=>[1,7,3,2,8,5,4,6]=>[8,2,6,7,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,2,6,3,5]=>[1,7,3,2,8,5,4,6]=>[8,2,6,7,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,2,5,3,6]=>[1,7,3,2,8,6,5,4]=>[8,2,6,7,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,4,3,6,5]=>[1,7,6,3,2,8,5,4]=>[8,2,3,6,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,8,7,1,2]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,5,7,8,1,2]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,7,8,9,2]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,1,6,7,8,9,2]=>[1,3,5,6,7,8,9,2,4]=>[9,7,5,4,3,2,1,8,6]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,1,9,2]=>[1,3,5,7,2,4,6,8,9]=>[9,7,5,3,8,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,2,5,6,7,8,9,4]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,1,5,6,7,8,9,10,2]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,1,2,6,7,8,9,5]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,1,2,9,8]=>[1,3,5,7,2,4,6,8,9]=>[9,7,5,3,8,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,1,9,10,2]=>[1,3,5,7,2,4,6,8,9,10]=>[10,8,6,4,9,7,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,1,2,9]=>[1,3,5,7,2,4,6,8,9]=>[9,7,5,3,8,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,1,10,2]=>[1,3,5,7,9,10,2,4,6,8]=>[10,8,6,4,2,1,9,7,5,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,6,2,3,8,7,4,5]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,2,5,8,3]=>[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,3,7,4,8]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,3,7,8,4]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,3,7,8,5]=>[1,2,3,6,7,8,5,4]=>[8,7,6,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,3,7,5,8]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,2,5,8,6]=>[1,2,4,3,7,8,6,5]=>[8,7,5,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,5,8,6,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,2,8,6,4]=>[1,2,7,6,8,4,3,5]=>[8,7,2,3,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,3,2,1,7]=>[1,6,2,8,7,3,5,4]=>[8,3,7,1,2,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,3,8,6,2]=>[1,7,6,8,2,3,5,4]=>[8,2,3,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,3,2,7,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,3,7,1,6]=>[1,2,8,6,7,3,5,4]=>[8,7,1,3,2,6,4,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,3,7,6,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,4,7,2,1,6]=>[1,3,5,7,2,8,6,4]=>[8,6,4,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,8,7,5,2]=>[1,2,6,7,5,8,3,4]=>[8,7,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,3,7,6,2]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,1,2,7,3]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,3,7,6,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,3,2,1,6]=>[1,7,2,5,3,8,6,4]=>[8,2,7,4,6,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,3,2,1,6]=>[1,4,7,2,8,6,3,5]=>[8,5,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,2,1,7,3]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,1,2,7,3]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,2,1,8,3]=>[1,7,8,3,6,2,4,5]=>[8,2,1,6,3,7,5,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,2,1,7,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,8,4,3,6]=>[1,2,7,3,5,8,6,4]=>[8,7,2,6,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,4,2,3,6]=>[1,5,4,7,3,8,6,2]=>[8,4,5,2,6,1,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,4,3,5,1]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,4,1,8,7]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,4,1,8,7]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,3,2,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,4,6,5,2]=>[1,3,7,5,4,2,8,6]=>[8,6,2,4,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,6,8,2,5,1]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,5,7,1,4]=>[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,4,8,5,1]=>[1,6,8,2,3,7,5,4]=>[8,3,1,7,6,2,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,5,4,3,6]=>[1,7,3,8,6,4,2,5]=>[8,2,6,1,3,5,7,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,2,5,6,3]=>[1,8,3,7,6,5,2,4]=>[8,1,6,2,3,4,7,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,3,5,6,1]=>[1,4,7,6,5,3,8,2]=>[8,5,2,3,4,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,2,5,6,3]=>[1,8,3,7,6,5,2,4]=>[8,1,6,2,3,4,7,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,2,5,6,1]=>[1,7,6,5,2,4,8,3]=>[8,2,3,4,7,5,1,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,8,2,7,3]=>[1,6,2,4,5,8,3,7]=>[8,3,7,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,3,6,1,4]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,7,4,6,3]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,7,4,1,2]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,8,5,6,1]=>[1,7,6,5,8,2,4,3]=>[8,2,3,4,1,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,8,5,6,3]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,8,5,6,3]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,8,5,6,1]=>[1,3,7,6,5,8,2,4]=>[8,6,2,3,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,4,8,5,6,2]=>[1,3,2,7,6,5,8,4]=>[8,6,7,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,5,2,7,4,3]=>[1,6,7,4,5,2,3,8]=>[8,3,2,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,6,7,5,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,4,7,5,3]=>[1,8,3,2,4,6,7,5]=>[8,1,6,7,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,6,1,8,3]=>[1,4,7,8,3,2,5,6]=>[8,5,2,1,6,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,7,3,2,5]=>[1,8,5,7,2,3,6,4]=>[8,1,4,2,7,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,2,3,8,5]=>[1,7,8,5,2,6,3,4]=>[8,2,1,4,7,3,6,5]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,5,3,7,1]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,4,2,1,6]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,4,1,7,6]=>[1,3,5,4,8,6,2,7]=>[8,6,4,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,5,2,3,6]=>[1,8,6,2,4,3,7,5]=>[8,1,3,7,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,3,5,6,1]=>[1,7,6,5,3,8,2,4]=>[8,2,3,4,6,1,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,3,5,6,1]=>[1,4,7,6,5,3,2,8]=>[8,5,2,3,4,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,2,5,6,4]=>[1,3,8,4,7,6,5,2]=>[8,6,1,5,2,3,4,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,2,5,6,4]=>[1,3,2,8,4,7,6,5]=>[8,6,7,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,1,3,2,5]=>[1,6,3,8,5,2,4,7]=>[8,3,6,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,7,3,1,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,7,6,1,5]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,1,3,7,5]=>[1,6,3,4,2,8,5,7]=>[8,3,6,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,3,5,6,1]=>[1,7,6,5,3,2,8,4]=>[8,2,3,4,6,7,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,1,5,6,4]=>[1,2,8,4,7,6,5,3]=>[8,7,1,5,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,3,5,6,4]=>[1,8,4,7,6,5,3,2]=>[8,1,5,2,3,4,6,7]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,2,8,5,7]=>[1,6,8,7,5,2,4,3]=>[8,3,1,2,4,7,5,6]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,2,1,4,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,8,3,1,7]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,7,4,3,1]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,3,8,1,6]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,4,5,2,7]=>[1,3,8,7,2,6,5,4]=>[8,6,1,2,7,3,4,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,4,5,3,7]=>[1,6,5,4,2,8,7,3]=>[8,3,4,5,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,4,5,3,7]=>[1,8,7,3,6,5,4,2]=>[8,1,2,6,3,4,5,7]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,2,3,4,7]=>[1,5,2,8,7,4,6,3]=>[8,4,7,1,2,5,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,8,2,3,7]=>[1,4,5,8,7,3,6,2]=>[8,5,4,1,2,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,4,5,2,7]=>[1,8,7,2,3,6,5,4]=>[8,1,2,7,6,3,4,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,4,5,1,7]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,3,8,1,6]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,7,6,1,2]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,1,6,2,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,8,6,2,5]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,4,8,2,6]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,7,4,5,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,2,1,5,3]=>[1,4,8,3,6,2,7,5]=>[8,5,1,6,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,4,3,5,2]=>[1,6,3,8,2,4,7,5]=>[8,3,6,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,1,6,7,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,3,4,7,2]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,3,4,7,1]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,5,6,7,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,3,1,7,2]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,8,1,7,3]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,3,6,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,5,6,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,5,6,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,5,6,7,1]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,5,6,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,5,6,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,3,6,7,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,1,2,4,7,6]=>[1,3,8,6,4,2,5,7]=>[8,6,1,3,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,2,3,7,6]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,2,6,7,5]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,3,6,7,1]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,7,4,1,2]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,8,4,7,5]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,7,1,8,5,6]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,3,8,5,6]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,6,3,7,5]=>[1,2,4,8,5,6,3,7]=>[8,7,5,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,6,2,7,5]=>[1,8,5,6,2,4,3,7]=>[8,1,4,3,7,5,6,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,8,2,1,4]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,8,2,1,4]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,3,6,1,2]=>[1,4,7,2,5,3,8,6]=>[8,5,2,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,1,4,7,3]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,1,2,7,3]=>[1,8,3,5,2,6,4,7]=>[8,1,6,4,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,3,7,5,4]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,3,8,7,2,4]=>[1,6,7,2,3,5,8,4]=>[8,3,2,7,6,4,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,1,2,7,4]=>[1,3,8,4,5,2,6,7]=>[8,6,1,5,4,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,4,8,1,7,3]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,2,6,7,3]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,1,6,7,3]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,2,6,7,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,2,6,7,3]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,5,8,6,3,4]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,1,6,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,7,6,1,2]=>[1,5,7,2,4,3,8,6]=>[8,4,2,7,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,6,2,7,4]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,8,5,1,7,2]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,1,6,7,2]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,1,2,6,3]=>[1,7,6,2,5,3,8,4]=>[8,2,3,7,4,6,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,6,1,3,2]=>[1,7,3,8,2,5,6,4]=>[8,2,6,1,7,4,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,7,1,3,2]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,1,2,7,3]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,8,2,4,3]=>[1,7,4,6,2,5,8,3]=>[8,2,5,3,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,8,2,7,3]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,1,2,8,3]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,8,1,3,2]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,1,4,2,8]=>[1,6,4,7,2,5,3,8]=>[8,3,5,2,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,8,4,2,7]=>[1,6,4,2,5,8,7,3]=>[8,3,5,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,8,3,2,6]=>[1,7,2,5,8,6,3,4]=>[8,2,7,4,1,3,6,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,7,3,5,2]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,1,4,8,2]=>[1,6,4,7,8,2,5,3]=>[8,3,5,2,1,7,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,5,8,7,2]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,3,7,6,2]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,3,7,2,6]=>[1,8,6,7,2,3,5,4]=>[8,1,3,2,7,6,4,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,3,8,2,6]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,1,4,2,7]=>[1,6,4,8,7,2,5,3]=>[8,3,5,1,2,7,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,4,3,2,5]=>[1,7,2,6,3,8,5,4]=>[8,2,7,3,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,5,4,3,6]=>[1,8,6,4,2,3,7,5]=>[8,1,3,5,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,5,4,6,3]=>[1,8,3,7,6,4,2,5]=>[8,1,6,2,3,5,7,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,5,4,8,3]=>[1,7,8,3,2,6,4,5]=>[8,2,1,6,7,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,1,4,7,2]=>[1,6,4,8,2,5,3,7]=>[8,3,5,1,7,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,2,7,8,4]=>[1,6,7,8,4,2,5,3]=>[8,3,2,1,5,7,4,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,2,6,8,3]=>[1,7,8,3,2,5,4,6]=>[8,2,1,6,7,4,5,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,5,2,8,7]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,5,7,2,8]=>[1,6,7,2,4,3,5,8]=>[8,3,2,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,3,6,2,8]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,3,6,2,7]=>[1,8,7,2,3,5,4,6]=>[8,1,2,7,6,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,3,6,7,2]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,4,5,1,2]=>[1,6,5,4,8,2,7,3]=>[8,3,4,5,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,2,3,1,8]=>[1,4,6,3,5,2,7,8]=>[8,5,3,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,1,8,2,3]=>[1,4,6,8,3,5,2,7]=>[8,5,3,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,3,8,1,2]=>[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,4,6,1,2]=>[1,3,5,4,8,2,7,6]=>[8,6,4,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,5,7,1,2]=>[1,4,6,7,2,8,3,5]=>[8,5,3,2,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,1,8,2,3]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,3,8,2,4]=>[1,5,3,2,6,8,4,7]=>[8,4,6,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,5,7,2,3]=>[1,4,6,7,2,8,3,5]=>[8,5,3,2,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,1,6,2,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,1,4,3,7]=>[1,5,2,6,4,8,7,3]=>[8,4,7,3,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,1,8,2,7]=>[1,5,2,6,8,7,3,4]=>[8,4,7,3,1,2,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,5,2,7,1,8]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,1,5,3,7]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,1,5,4,7]=>[1,2,8,7,4,6,5,3]=>[8,7,1,2,5,3,4,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,1,6,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,3,6,2,4]=>[1,7,2,8,4,5,3,6]=>[8,2,7,1,5,4,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,2,7,4,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,2,7,3,5]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,3,5,1,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,4,6,3,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,4,6,2,3]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,2,6,3,4]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,3,8,2,4]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,3,4,1,8]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,5,3,4,1,8]=>[1,6,4,5,3,2,7,8]=>[8,3,5,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,3,8,2,4]=>[1,6,8,4,5,3,2,7]=>[8,3,1,5,4,6,7,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,1,4,2,3]=>[1,6,4,8,3,5,2,7]=>[8,3,5,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,2,3,1,4]=>[1,5,2,8,4,7,3,6]=>[8,4,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,1,8,4,5]=>[1,6,8,5,2,7,4,3]=>[8,3,1,4,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,1,4,3,5]=>[1,6,4,8,5,2,7,3]=>[8,3,5,1,4,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,7,5,6,1,8]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,5,8,2,6]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,1,4,3,6]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,5,8,4,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,4,7,5,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,1,6,4,5]=>[1,7,4,3,2,8,5,6]=>[8,2,5,6,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,1,4,3,5]=>[1,7,3,2,8,5,4,6]=>[8,2,6,7,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,3,7,5,6]=>[1,2,8,6,7,5,3,4]=>[8,7,1,3,2,4,6,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,4,6,1,8]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,3,6,1,8]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,2,7,3,6]=>[1,4,8,6,7,3,2,5]=>[8,5,1,3,2,6,7,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,2,7,5,6]=>[1,3,2,4,8,6,7,5]=>[8,6,7,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,6,7,2,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,1,8,6,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,4,6,2,3]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,5,1,2,4]=>[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,3,2,5,4]=>[1,8,4,7,5,3,2,6]=>[8,1,5,2,4,6,7,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,3,5,2,4]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,8,5,2,4]=>[1,7,2,6,5,8,4,3]=>[8,2,7,3,4,1,5,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,4,5,1,3]=>[1,7,2,6,5,4,3,8]=>[8,2,7,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,8,3,5,1,4]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,8,5,1,4]=>[1,7,2,6,5,8,4,3]=>[8,2,7,3,4,1,5,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,2,6,3,4]=>[1,8,4,5,2,7,3,6]=>[8,1,5,4,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,2,3,6,4]=>[1,8,4,5,2,7,6,3]=>[8,1,5,4,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,1,7,6,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,7,1,5,4]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,3,1,5,4]=>[1,8,4,7,5,3,2,6]=>[8,1,5,2,4,6,7,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,4,1,5,2]=>[1,6,2,8,3,7,5,4]=>[8,3,7,1,6,2,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,1,6,3,4]=>[1,8,4,5,2,7,3,6]=>[8,1,5,4,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,6,3,5]=>[1,8,5,7,3,2,4,6]=>[8,1,4,2,6,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,4,3,6]=>[1,8,6,4,2,5,3,7]=>[8,1,3,5,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,1,4,6,2]=>[1,5,2,8,3,7,6,4]=>[8,4,7,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,4,6,3]=>[1,8,3,7,6,4,2,5]=>[8,1,6,2,3,5,7,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,2,3,6,5]=>[1,8,5,2,7,6,3,4]=>[8,1,4,7,2,3,6,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,2,6,3,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,1,7,2,6,5]=>[1,8,5,7,6,2,4,3]=>[8,1,4,2,3,7,5,6]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,7,2,5,4]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,2,7,6,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,1,6,2,3]=>[1,8,3,7,2,5,4,6]=>[8,1,6,2,7,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,1,2,6,3]=>[1,8,3,7,6,2,5,4]=>[8,1,6,2,3,7,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,2,7,6,3]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,7,2,5,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,4,2,7,3]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,4,1,2,7]=>[1,5,4,6,2,8,7,3]=>[8,4,5,3,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,1,2,6,3]=>[1,8,3,7,6,2,4,5]=>[8,1,6,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,2,6,4]=>[1,8,4,5,2,7,6,3]=>[8,1,5,4,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,5,1,4,7]=>[1,8,7,4,6,2,3,5]=>[8,1,2,5,3,7,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,1,5,2,6]=>[1,4,3,7,2,8,6,5]=>[8,5,6,2,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,7,6,4,5]=>[1,8,5,7,4,2,3,6]=>[8,1,4,2,5,7,6,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,4,2,6,5]=>[1,8,5,4,2,7,6,3]=>[8,1,4,5,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,6,2,4,5]=>[1,8,5,6,2,7,4,3]=>[8,1,4,3,7,2,5,6]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,2,6,4,5]=>[1,8,5,2,7,4,3,6]=>[8,1,4,7,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,2,4,6,5]=>[1,8,5,2,7,6,4,3]=>[8,1,4,7,2,3,5,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,4,7,6,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,7,4,6,5]=>[1,8,5,7,6,4,2,3]=>[8,1,4,2,3,5,7,6]=>[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,1,5,6,3]=>[1,8,3,7,6,5,2,4]=>[8,1,6,2,3,4,7,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,1,2,5,6]=>[1,3,7,5,2,8,6,4]=>[8,6,2,4,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,6,3,4,5]=>[1,8,5,6,3,2,7,4]=>[8,1,4,3,6,7,2,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,3,6,4,5]=>[1,8,5,3,2,7,4,6]=>[8,1,4,6,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,1,2,8,7]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,7,4,1,2]=>[1,3,5,7,2,8,4,6]=>[8,6,4,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,6,2,1,3]=>[1,4,8,3,5,6,2,7]=>[8,5,1,6,4,3,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,6,3,4,1]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,6,3,1,2]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,1,5,8,7]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,3,4,8,7]=>[1,6,4,5,3,2,7,8]=>[8,3,5,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,7,6,4,2]=>[1,5,7,4,3,2,8,6]=>[8,4,2,5,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,6,1,8,5]=>[1,4,3,2,7,8,5,6]=>[8,5,6,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,8,1,5,6]=>[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,7,6,3,4]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,6,3,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,7,6,2,8,5]=>[1,4,7,8,5,6,2,3]=>[8,5,2,1,4,3,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,3,2,7,4]=>[1,8,4,6,2,5,3,7]=>[8,1,5,3,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,5,2,8,4]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,4,7,5,1]=>[1,3,6,7,5,4,8,2]=>[8,6,3,2,4,5,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,3,2,5,7]=>[1,8,7,5,3,6,2,4]=>[8,1,2,4,6,3,7,5]=>[8,2,3,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,1,6,3,2]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,6,7,8,3]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,7,1,3,6]=>[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,6,1,4,3]=>[1,7,4,5,6,2,8,3]=>[8,2,5,4,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,7,5,6,1]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,5,1,8,4]=>[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,2,5,3,1]=>[1,7,3,8,2,6,5,4]=>[8,2,6,1,7,3,4,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,8,4,3,1]=>[1,6,4,2,5,8,3,7]=>[8,3,5,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,6,5,2,1,7]=>[1,3,8,7,2,4,6,5]=>[8,6,1,2,7,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,4,5,8,3]=>[1,2,7,8,3,6,5,4]=>[8,7,2,1,6,3,4,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,1,7,3,4]=>[1,6,7,3,8,4,2,5]=>[8,3,2,6,1,5,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,5,8,7,2]=>[1,4,3,6,8,2,5,7]=>[8,5,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,4,3,7,1]=>[1,6,3,5,4,8,2,7]=>[8,3,6,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,4,3,2]=>[1,8,2,6,4,3,7,5]=>[8,1,7,3,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,8,4,7,3]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,5,4,3,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,6,2,3,7]=>[1,4,5,6,2,3,8,7]=>[8,5,4,3,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,7,3,5,1]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,6,1,3,5]=>[1,4,7,3,2,8,5,6]=>[8,5,2,6,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,7,5,4,6]=>[1,3,8,6,5,7,4,2]=>[8,6,1,3,4,2,5,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,6,7,4,5]=>[1,3,2,8,5,6,7,4]=>[8,6,7,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,2,7,1,6]=>[1,5,2,8,6,7,3,4]=>[8,4,7,1,3,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,6,3,2,5,1]=>[1,7,5,3,8,2,4,6]=>[8,2,4,6,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,2,1,3,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,3,7,5,6]=>[1,2,3,8,6,7,5,4]=>[8,7,6,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,4,5,7,1]=>[1,6,5,4,2,3,8,7]=>[8,3,4,5,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,3,6,1,7]=>[1,5,3,4,2,8,7,6]=>[8,4,6,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,3,1,6,7]=>[1,5,3,2,8,7,6,4]=>[8,4,6,7,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,6,4,5,7]=>[1,2,8,7,5,6,4,3]=>[8,7,1,2,4,3,5,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,6,3,5,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,4,5,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,4,5,7,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,6,4,5,7]=>[1,2,3,8,7,5,6,4]=>[8,7,6,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,3,6,4,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,5,4,8,6]=>[1,2,7,8,6,4,3,5]=>[8,7,2,1,3,5,6,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,4,5,7,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,4,6,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,3,6,4,5]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,5,3,6,4]=>[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,4,5,3,6]=>[1,2,7,3,8,6,5,4]=>[8,7,2,6,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,6,4,5,7]=>[1,2,3,8,7,5,6,4]=>[8,7,6,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,6,4,5,7]=>[1,2,8,7,5,6,4,3]=>[8,7,1,2,4,3,5,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,5,4,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,3,6,4,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,8,3,6,4]=>[1,2,5,8,4,7,6,3]=>[8,7,4,1,5,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,4,6,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,6,7,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,4,3,6,5]=>[1,2,7,6,3,8,5,4]=>[8,7,2,3,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,5,2,4,8]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,5,2,8,4]=>[1,6,2,7,8,4,3,5]=>[8,3,7,2,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,1,2,7,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,1,2,8,3]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,5,3,4,8]=>[1,7,4,6,3,2,5,8]=>[8,2,5,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,1,2,3,8]=>[1,7,3,6,2,4,5,8]=>[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,1,8,2,3]=>[1,5,2,7,3,6,8,4]=>[8,4,7,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,1,8,2,3]=>[1,5,2,6,8,3,7,4]=>[8,4,7,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,1,2,8,3]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,5,2,7,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,1,2,7,3]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,1,7,2,3]=>[1,5,2,6,7,3,8,4]=>[8,4,7,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,7,1,2,3]=>[1,4,5,7,2,6,3,8]=>[8,5,4,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,6,7,1,2,3]=>[1,4,6,2,5,7,3,8]=>[8,5,3,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,6,7,2,4]=>[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,6,7,3,4]=>[1,5,6,7,3,2,4,8]=>[8,4,3,2,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,8,1,2,3]=>[1,4,6,2,5,8,3,7]=>[8,5,3,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,8,1,2,3]=>[1,4,5,8,3,7,2,6]=>[8,5,4,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,7,1,2,3]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,8,1,2,3]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,8,1,2,3]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,1,8,2,3]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,1,7,2,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,7,6,2,4]=>[1,5,7,2,8,4,3,6]=>[8,4,2,7,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,1,6,2,3]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,8,7,3,4]=>[1,5,8,4,6,7,3,2]=>[8,4,1,5,3,2,6,7]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,1,7,2,3]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,6,1,2,3]=>[1,4,8,3,5,6,2,7]=>[8,5,1,6,4,3,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,6,1,2,3]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,5,1,2,3]=>[1,4,7,2,8,3,6,5]=>[8,5,2,7,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,5,1,2,3]=>[1,4,8,3,6,2,7,5]=>[8,5,1,6,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,5,1,2,3]=>[1,4,8,3,7,2,6,5]=>[8,5,1,6,2,7,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,1,6,2,3]=>[1,5,2,4,8,3,7,6]=>[8,4,7,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,8,6,2,4]=>[1,5,8,4,2,3,7,6]=>[8,4,1,5,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,8,6,3,4]=>[1,5,8,4,7,3,2,6]=>[8,4,1,5,2,6,7,3]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,7,6,2,4]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,1,6,2,3]=>[1,5,2,4,7,3,8,6]=>[8,4,7,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,5,1,2,3]=>[1,4,6,2,7,3,8,5]=>[8,5,3,7,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,5,1,2,3]=>[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,3,6,1,8]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,7,5,1,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,6,5,1,8]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,1,6,4,8,7]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,6,4,1,8]=>[1,2,5,6,4,7,3,8]=>[8,7,4,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,7,4,1,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,3,8,4,6]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,7,5,4,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,6,5,4,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,1,8,6,4,7]=>[1,2,5,8,7,4,3,6]=>[8,7,4,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,4,1,5,7]=>[1,8,7,5,4,6,2,3]=>[8,1,2,4,5,3,7,6]=>[8,2,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,1,4,5,7]=>[1,3,8,7,5,2,6,4]=>[8,6,1,2,4,7,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,3,4,7,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,8,7,4,5]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,6,4,7,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,7,5,4,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,6,4,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,4,8,6,5]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,3,8,4,5]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,8,7,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,6,4,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,8,5,4,7]=>[1,2,6,5,8,7,4,3]=>[8,7,3,4,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,5,4,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,3,5,7,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,1,8,5,7]=>[1,4,3,6,8,7,5,2]=>[8,5,6,3,1,2,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,3,1,6,7]=>[1,5,3,2,4,8,7,6]=>[8,4,6,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,4,1,6,7]=>[1,3,8,7,6,2,5,4]=>[8,6,1,2,3,7,4,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,3,5,7,6]=>[1,4,8,6,5,3,2,7]=>[8,5,1,3,4,6,7,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,2,3,5,6]=>[1,2,8,6,3,7,5,4]=>[8,7,1,3,6,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,6,4,8,5]=>[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,3,7,4,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,8,6,4,5]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,4,7,6,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,4,8,6,5]=>[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,8,4,7,5]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,3,7,5,6]=>[1,4,8,6,7,5,3,2]=>[8,5,1,3,2,4,6,7]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,7,4,5,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,7,3,5,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,3,4,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,8,4,6,5]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,7,4,6,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,7,6,4,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,1,5,3,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,1,2,6,4]=>[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,2,6,4,1]=>[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,4,8,6,3]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,5,7,6,3]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,1,6,5,7]=>[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,5,6,4,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,6,5,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,3,5,7,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,2,3,5,1]=>[1,4,7,5,2,8,3,6]=>[8,5,2,4,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,1,2,3,5]=>[1,4,7,3,6,2,8,5]=>[8,5,2,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,1,3,5,2]=>[1,4,7,5,2,8,3,6]=>[8,5,2,4,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,1,6,4,2]=>[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,2,1,6,4]=>[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,2,1,3,5]=>[1,4,7,3,6,2,8,5]=>[8,5,2,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,3,5,2,1]=>[1,4,7,2,8,3,6,5]=>[8,5,2,7,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,3,4,2,1]=>[1,5,3,6,4,7,2,8]=>[8,4,6,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,2,1,3,4]=>[1,5,2,8,4,7,3,6]=>[8,4,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,2,1,4,3]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,2,1,5,3]=>[1,4,7,5,2,8,3,6]=>[8,5,2,4,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,5,1,7,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,1,6,7,2]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,1,5,3,2]=>[1,4,7,3,6,5,2,8]=>[8,5,2,6,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,1,4,3,2]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,2,3,4,1]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,2,4,3,1]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,1,2,4,3]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,1,7,6,3]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,6,1,5,7]=>[1,3,4,8,7,5,6,2]=>[8,6,5,1,2,4,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,6,1,4,8]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,1,2,5,3]=>[1,4,7,5,2,8,3,6]=>[8,5,2,4,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,2,5,3,1]=>[1,4,7,3,6,5,2,8]=>[8,5,2,6,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,2,6,7,1]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,1,2,6,7]=>[1,4,5,2,3,8,7,6]=>[8,5,4,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,5,1,3,8]=>[1,4,7,3,6,2,5,8]=>[8,5,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,1,4,2,6]=>[1,3,5,2,8,6,4,7]=>[8,6,4,7,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,4,6,1,7]=>[1,3,2,5,4,8,7,6]=>[8,6,7,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,4,6,2,8]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,7,5,3,8]=>[1,4,6,5,7,3,2,8]=>[8,5,3,4,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,5,3,8,1]=>[1,4,7,8,2,3,6,5]=>[8,5,2,1,7,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,6,2,4,8]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,5,6,2,8]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,5,2,3,8]=>[1,4,7,3,6,2,5,8]=>[8,5,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,3,2,4,1]=>[1,5,3,6,2,8,4,7]=>[8,4,6,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,4,2,3,1]=>[1,5,4,7,3,6,2,8]=>[8,4,5,2,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,4,1,3,2]=>[1,5,4,7,3,6,2,8]=>[8,4,5,2,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,3,1,4,2]=>[1,5,3,6,2,8,4,7]=>[8,4,6,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,5,3,8,2]=>[1,4,7,8,2,3,6,5]=>[8,5,2,1,7,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,7,5,3,8]=>[1,4,6,5,7,3,2,8]=>[8,5,3,4,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,1,4,2,6]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,1,4,2,5]=>[1,3,7,2,8,5,4,6]=>[8,6,2,7,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,6,7,2,4]=>[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,5,8,6,2]=>[1,3,7,6,8,2,4,5]=>[8,6,2,3,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,5,7,2,4]=>[1,6,7,2,8,4,3,5]=>[8,3,2,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,5,4,2,7]=>[1,3,2,8,7,4,6,5]=>[8,6,7,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,6,5,8,4,2]=>[1,3,7,4,6,8,2,5]=>[8,6,2,5,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,7,5,3,2]=>[1,4,6,5,7,3,2,8]=>[8,5,3,4,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,8,2,5,3]=>[1,7,5,8,3,2,4,6]=>[8,2,4,1,6,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,2,7,5,4]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,7,8,4,5]=>[1,6,8,5,7,4,2,3]=>[8,3,1,4,2,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,8,1,5,3]=>[1,4,6,2,7,5,8,3]=>[8,5,3,7,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,2,1,4,3]=>[1,5,2,7,4,6,3,8]=>[8,4,7,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,6,8,3,5]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,5,1,6,8]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,5,1,3,7]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,5,2,6,8]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,3,1,4,2]=>[1,5,3,8,2,6,4,7]=>[8,4,6,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,4,6,2,1,7]=>[1,3,5,6,2,8,7,4]=>[8,6,4,3,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,5,1,6,2]=>[1,4,8,2,3,7,6,5]=>[8,5,1,7,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,7,6,1,3]=>[1,5,7,2,4,3,8,6]=>[8,4,2,7,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,3,4,1,7]=>[1,5,3,2,8,7,4,6]=>[8,4,6,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,8,6,2,3]=>[1,4,5,8,3,7,2,6]=>[8,5,4,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,4,3,6,2]=>[1,5,4,8,2,3,7,6]=>[8,4,5,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,6,1,2,7]=>[1,3,4,5,6,2,8,7]=>[8,6,5,4,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,1,3,4,2]=>[1,6,3,8,2,5,4,7]=>[8,3,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,4,8,1,5]=>[1,3,7,2,6,8,5,4]=>[8,6,2,7,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,8,5,6,3]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,8,6,2,4]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,5,7,2,4]=>[1,3,8,4,2,6,7,5]=>[8,6,1,5,7,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,5,8,6,3,4]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,8,6,3,4]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,2,3,5,4]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,2,3,5,4]=>[1,7,5,2,6,3,8,4]=>[8,2,4,7,3,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,8,6,3,4]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,8,5,6,3]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,1,3,5,4]=>[1,7,5,2,6,3,8,4]=>[8,2,4,7,3,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,2,1,5,4]=>[1,3,6,2,7,5,4,8]=>[8,6,3,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,6,8,5,3]=>[1,2,7,5,6,8,3,4]=>[8,7,2,4,3,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,6,8,5,1,3]=>[1,7,2,4,6,5,8,3]=>[8,2,7,5,3,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,8,6,1,4]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,6,8,2,5,4]=>[1,3,7,5,8,4,6,2]=>[8,6,2,4,1,5,3,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,1,2,5,4]=>[1,3,6,2,7,5,4,8]=>[8,6,3,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,6,8,5,3]=>[1,2,7,5,6,8,3,4]=>[8,7,2,4,3,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,6,1,5,2]=>[1,7,5,6,2,3,8,4]=>[8,2,4,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,3,2,5,4]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,1,2,5,4]=>[1,7,5,2,6,3,8,4]=>[8,2,4,7,3,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,8,5,4,2]=>[1,3,7,4,2,6,5,8]=>[8,6,2,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,3,1,5,4]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,8,5,4,2]=>[1,6,5,8,2,7,4,3]=>[8,3,4,1,7,2,5,6]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,5,4,3,2]=>[1,6,4,8,2,7,3,5]=>[8,3,5,1,7,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,2,1,5,4]=>[1,7,5,2,6,3,8,4]=>[8,2,4,7,3,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,5,6,1,3,2]=>[1,4,5,6,2,7,3,8]=>[8,5,4,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,1,2,7,3]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,7,2,4,3]=>[1,8,3,5,7,4,6,2]=>[8,1,6,4,2,5,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,1,2,8,3]=>[1,5,2,4,7,8,3,6]=>[8,4,7,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,1,4,2,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,7,4,5,2]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,8,4,5,3]=>[1,7,5,8,3,2,4,6]=>[8,2,4,1,6,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,1,4,8,3]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,5,8,7,3]=>[1,6,8,3,4,2,5,7]=>[8,3,1,6,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,3,7,2,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,4,8,2,6]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,5,8,2,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,1,8,6,7]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,7,1,6,8]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,1,4,2,7]=>[1,5,2,6,4,8,7,3]=>[8,4,7,3,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,4,5,6,3]=>[1,8,3,7,6,5,4,2]=>[8,1,6,2,3,4,5,7]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,4,5,8,3]=>[1,7,8,3,2,6,5,4]=>[8,2,1,6,7,3,4,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,1,4,7,3]=>[1,5,2,6,4,8,3,7]=>[8,4,7,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,3,7,8,4]=>[1,6,7,8,4,2,5,3]=>[8,3,2,1,5,7,4,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,2,6,8,4]=>[1,7,8,4,3,2,5,6]=>[8,2,1,5,6,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,1,6,8,7]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,5,6,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,5,6,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,5,7,8,4]=>[1,6,7,8,4,2,3,5]=>[8,3,2,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,6,5,3]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,5,6,3]=>[1,7,6,5,2,8,3,4]=>[8,2,3,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,8,7,1,5]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,6,2,1,5]=>[1,7,2,8,5,6,3,4]=>[8,2,7,1,4,3,6,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,6,2,1,4]=>[1,7,2,8,4,5,6,3]=>[8,2,7,1,5,4,3,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,8,5,1,4]=>[1,6,5,8,4,7,2,3]=>[8,3,4,1,5,2,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,8,7,1,4]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,4,7,1,5]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,7,3,5,8]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,6,1,8,4]=>[1,5,6,2,7,8,4,3]=>[8,4,3,7,2,1,5,6]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,6,1,7,4]=>[1,5,6,2,8,4,3,7]=>[8,4,3,7,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,3,2,1,6]=>[1,4,8,6,2,7,3,5]=>[8,5,1,3,7,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,3,2,1,7]=>[1,4,8,7,2,5,3,6]=>[8,5,1,2,7,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,3,2,1,7]=>[1,4,5,3,8,7,2,6]=>[8,5,4,6,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,2,3,7,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,3,7,1,2]=>[1,5,3,8,2,6,7,4]=>[8,4,6,1,7,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,2,3,8,7]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,4,1,7,6]=>[1,5,4,3,8,6,2,7]=>[8,4,5,6,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,8,3,2,1,7]=>[1,4,8,7,2,6,3,5]=>[8,5,1,2,7,3,6,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,3,2,1,8]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,5,8,1,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,6,2,8,7]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,7,2,8,6]=>[1,5,7,8,6,2,3,4]=>[8,4,2,1,3,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,8,2,7,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,1,8,7,3]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,1,8,6,3]=>[1,5,2,7,6,8,3,4]=>[8,4,7,2,3,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,7,8,5,3]=>[1,6,8,3,4,2,5,7]=>[8,3,1,6,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,1,7,6,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,1,6,8,3]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,7,2,6,8]=>[1,5,7,6,2,4,3,8]=>[8,4,2,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,6,2,7,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,2,3,7,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,3,2,1,7]=>[1,4,5,3,6,2,8,7]=>[8,5,4,6,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,3,2,1,7]=>[1,4,6,2,8,7,3,5]=>[8,5,3,7,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,4,2,6,8]=>[1,5,4,3,2,7,6,8]=>[8,4,5,6,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,2,3,6,7]=>[1,5,2,3,8,7,6,4]=>[8,4,7,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,2,3,6,8]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,4,2,6,7]=>[1,5,4,3,2,8,7,6]=>[8,4,5,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,3,2,1,6]=>[1,4,5,3,7,2,8,6]=>[8,5,4,6,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,3,2,1,5]=>[1,4,6,2,7,3,8,5]=>[8,5,3,7,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,6,7,5,1]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,6,7,5,2]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,6,2,5,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,3,5,2,6]=>[1,2,4,7,3,8,6,5]=>[8,7,5,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,2,5,1,6]=>[1,4,7,2,3,8,6,5]=>[8,5,2,7,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,7,1,6,2]=>[1,5,7,6,2,8,3,4]=>[8,4,2,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,7,2,6,3]=>[1,5,7,6,2,8,3,4]=>[8,4,2,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,3,4,2,6]=>[1,5,3,7,2,8,6,4]=>[8,4,6,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,7,5,6,1]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,7,5,6,2]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,2,6,5,7]=>[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,7,5,6,2]=>[1,4,3,8,2,5,7,6]=>[8,5,6,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,3,5,2,6]=>[1,4,7,2,3,8,6,5]=>[8,5,2,7,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,5,4,2,6]=>[1,3,8,6,4,2,7,5]=>[8,6,1,3,5,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,6,2,5,7]=>[1,3,8,7,5,6,2,4]=>[8,6,1,2,4,3,7,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,7,5,6,1]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,3,6,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,8,6,5,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,4,1,2,5]=>[1,3,7,2,6,4,8,5]=>[8,6,2,7,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,3,6,5,7]=>[1,4,8,7,5,3,2,6]=>[8,5,1,2,4,6,7,3]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,6,5,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,4,2,1,5]=>[1,3,6,2,7,4,8,5]=>[8,6,3,7,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,5,2,3,6]=>[1,4,8,6,2,7,3,5]=>[8,5,1,3,7,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,2,4,1,5]=>[1,3,8,5,2,7,4,6]=>[8,6,1,4,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,6,4,5,1]=>[1,3,8,2,7,5,6,4]=>[8,6,1,7,2,4,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,8,5,3,2,6]=>[1,2,4,8,6,3,7,5]=>[8,7,5,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,5,2,1,6]=>[1,4,8,6,2,3,7,5]=>[8,5,1,3,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,4,6,5,1]=>[1,3,2,7,5,4,8,6]=>[8,6,7,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,3,1,5,7]=>[1,4,6,2,3,8,7,5]=>[8,5,3,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,7,3,1,5]=>[1,2,6,3,8,5,7,4]=>[8,7,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,3,1,5,7]=>[1,2,4,6,3,8,7,5]=>[8,7,5,3,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,8,3,5,4,1]=>[1,7,4,8,2,6,5,3]=>[8,2,5,1,7,3,4,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,4,6,5,2]=>[1,2,7,5,4,8,3,6]=>[8,7,2,4,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,2,6,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,1,6,5,7]=>[1,3,4,8,7,5,2,6]=>[8,6,5,1,2,4,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,6,2,4,1,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,6,1,5,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,7,4,3,5,1]=>[1,6,3,8,2,4,7,5]=>[8,3,6,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,5,2,6,3]=>[1,7,6,2,4,8,3,5]=>[8,2,3,7,5,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,8,6,5,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,8,6,5,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,8,6,5,7]=>[1,3,4,2,5,8,7,6]=>[8,6,5,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,2,6,5,7]=>[1,3,4,8,7,5,2,6]=>[8,6,5,1,2,4,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,8,6,5,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,8,6,5,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,6,5,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,2,1,5,7]=>[1,4,6,2,8,7,5,3]=>[8,5,3,7,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,2,4,1,7]=>[1,3,5,2,6,4,8,7]=>[8,6,4,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,2,4,6,1]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,3,8,1,6]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,8,3,1,7]=>[1,6,3,4,5,8,7,2]=>[8,3,6,5,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,5,6,3,7]=>[1,4,2,8,7,3,5,6]=>[8,5,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,3,8,4,7]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,8,3,2,7]=>[1,6,3,4,5,8,7,2]=>[8,3,6,5,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,1,3,2,7]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,2,8,1,6]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,7,2,6,1]=>[1,5,7,6,2,8,3,4]=>[8,4,2,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,7,2,5,1]=>[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,2,7,8,5]=>[1,2,4,6,7,8,5,3]=>[8,7,5,3,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,7,2,8,6]=>[1,2,5,7,8,6,3,4]=>[8,7,4,2,1,3,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,1,2,8,6]=>[1,5,2,7,8,6,3,4]=>[8,4,7,2,1,3,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,6,2,1,3]=>[1,8,3,4,7,2,5,6]=>[8,1,6,5,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,3,6,1,2]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,6,7,5,2]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,6,1,5,2]=>[1,4,3,8,2,7,5,6]=>[8,5,6,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,7,4,1,2]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,4,7,5,2]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,4,2,8,5]=>[1,7,8,5,4,3,2,6]=>[8,2,1,4,5,6,7,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,2,6,8,4]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,2,5,8,4]=>[1,2,6,5,3,7,8,4]=>[8,7,3,4,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,6,7,4,1]=>[1,5,6,7,4,3,2,8]=>[8,4,3,2,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,1,6,8,4]=>[1,7,8,4,3,2,5,6]=>[8,2,1,5,6,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,2,3,8,5]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,2,8,4,6]=>[1,3,7,4,5,2,6,8]=>[8,6,2,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,1,8,3,6]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,7,8,3,5]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,2,3,5,1]=>[1,6,3,8,2,4,7,5]=>[8,3,6,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,7,4,5,1]=>[1,3,6,4,8,2,5,7]=>[8,6,3,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,7,8,4,5]=>[1,6,8,5,7,4,2,3]=>[8,3,1,4,2,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,4,2,5,6]=>[1,3,2,7,5,4,8,6]=>[8,6,7,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,4,2,6,5]=>[1,8,5,4,7,6,2,3]=>[8,1,4,5,2,3,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,7,1,5,4]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,1,6,5,4]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,6,5,4,1]=>[1,3,7,4,2,8,5,6]=>[8,6,2,5,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,7,1,5,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,7,3,6,4]=>[1,5,7,6,3,2,4,8]=>[8,4,2,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,3,7,5,4]=>[1,8,4,6,7,5,3,2]=>[8,1,5,3,2,4,6,7]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,5,7,4,3]=>[1,6,7,4,2,3,8,5]=>[8,3,2,5,7,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,6,1,4,3]=>[1,5,6,2,7,4,3,8]=>[8,4,3,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,6,4,3,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,2,4,3,1]=>[1,8,2,6,4,5,3,7]=>[8,1,7,3,5,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,5,6,4,3]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,6,2,5,3]=>[1,7,5,6,2,4,3,8]=>[8,2,4,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,2,6,5,4]=>[1,3,2,7,5,4,8,6]=>[8,6,7,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,6,5,4,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,6,5,3,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,1,4,3,2]=>[1,8,2,6,4,5,3,7]=>[8,1,7,3,5,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,1,3,2]=>[1,7,3,6,2,8,4,5]=>[8,2,6,3,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,2,1,6,7]=>[1,5,2,8,7,6,3,4]=>[8,4,7,1,2,3,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,2,1,8,5]=>[1,6,2,4,3,7,8,5]=>[8,3,7,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,2,1,6,8]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,2,1,4,8]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,2,1,4,7]=>[1,5,2,8,7,4,6,3]=>[8,4,7,1,2,5,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,2,1,4,5]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,2,1,4,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,6,1,3,7]=>[1,5,6,2,8,7,3,4]=>[8,4,3,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,6,1,4,7]=>[1,5,6,2,8,7,4,3]=>[8,4,3,7,1,2,5,6]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,5,1,8,6]=>[1,4,2,3,7,8,6,5]=>[8,5,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,5,1,4,6]=>[1,3,7,4,2,8,6,5]=>[8,6,2,5,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,5,1,3,8]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,5,1,4,8]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,7,1,4,8]=>[1,5,7,4,6,2,3,8]=>[8,4,2,5,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,5,1,4,7]=>[1,3,2,8,7,4,6,5]=>[8,6,7,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,5,1,3,4]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,5,1,3,8]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,5,1,3,4]=>[1,2,8,4,6,3,7,5]=>[8,7,1,5,3,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,1,7,8,2]=>[1,6,7,8,2,5,3,4]=>[8,3,2,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,1,8,6,2]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,1,4,5,2]=>[1,6,4,8,2,3,7,5]=>[8,3,5,1,7,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,1,4,8,2]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,6,1,5,8,2]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,1,4,5,2]=>[1,3,7,5,2,8,4,6]=>[8,6,2,4,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,1,7,3,8]=>[1,6,7,3,4,2,5,8]=>[8,3,2,6,5,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,1,5,3,6]=>[1,4,2,8,6,5,3,7]=>[8,5,7,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,1,5,7,6]=>[1,4,2,8,6,5,3,7]=>[8,5,7,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,1,4,8,6]=>[1,5,2,3,7,8,6,4]=>[8,4,7,6,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,1,4,5,6]=>[1,3,7,5,2,8,6,4]=>[8,6,2,4,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,1,4,3,8]=>[1,6,4,7,3,2,5,8]=>[8,3,5,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,1,4,3,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,1,5,8,7]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,1,5,3,8]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,1,4,5,8]=>[1,3,7,5,2,4,6,8]=>[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,8,7,3,2]=>[1,6,7,3,4,2,5,8]=>[8,3,2,6,5,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,6,7,3,2]=>[1,5,6,7,3,4,2,8]=>[8,4,3,2,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,5,8,3,2]=>[1,6,8,2,4,3,7,5]=>[8,3,1,7,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,6,8,3,2]=>[1,5,6,8,2,4,3,7]=>[8,4,3,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,5,6,3,2]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,6,8,7,2]=>[1,5,6,8,2,4,3,7]=>[8,4,3,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,5,6,7,2]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,5,4,6,2]=>[1,3,7,6,4,2,8,5]=>[8,6,2,3,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,5,4,8,7]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,6,4,8,7]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,5,4,3,8]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,6,4,3,8]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,5,6,3,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,5,4,6,8]=>[1,3,7,6,4,2,5,8]=>[8,6,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,5,4,3,6]=>[1,2,8,6,4,3,7,5]=>[8,7,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,8,4,3,2]=>[1,6,4,7,3,2,5,8]=>[8,3,5,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,7,4,3,2]=>[1,5,7,3,2,8,4,6]=>[8,4,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,7,8,3,2]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,5,7,3,2]=>[1,4,6,7,3,2,8,5]=>[8,5,3,2,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,7,4,8,2]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,5,7,8,2]=>[1,4,6,7,8,2,3,5]=>[8,5,3,2,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,5,4,7,2]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,7,4,3,8]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,5,4,3,7]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,5,4,3,2]=>[1,6,4,8,2,3,7,5]=>[8,3,5,1,7,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,2,6,3,8]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,6,2,4,8]=>[1,2,7,4,5,6,3,8]=>[8,7,2,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,7,2,4,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,7,2,4,5]=>[1,3,8,5,7,4,2,6]=>[8,6,1,4,2,5,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,8,1,7,2]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,6,7,1,3]=>[1,4,2,5,6,7,3,8]=>[8,5,7,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,6,7,1,4]=>[1,8,4,5,6,7,2,3]=>[8,1,5,4,3,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,5,4,6,7]=>[1,8,7,6,4,3,2,5]=>[8,1,2,3,5,6,7,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,3,5,4,6]=>[1,2,7,4,3,8,6,5]=>[8,7,2,5,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,5,6,1,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,7,6,3,2]=>[1,4,2,5,7,3,8,6]=>[8,5,7,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,2,1,6,3]=>[1,4,7,6,2,5,3,8]=>[8,5,2,3,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,6,2,1,4]=>[1,8,4,5,6,2,7,3]=>[8,1,5,4,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,3,5,4,6]=>[1,8,6,5,3,2,7,4]=>[8,1,3,4,6,7,2,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,2,1,5,4]=>[1,3,8,4,7,5,2,6]=>[8,6,1,5,2,4,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,7,5,3,2]=>[1,8,2,6,5,7,3,4]=>[8,1,7,3,4,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,1,8,5,2]=>[1,7,5,2,6,8,3,4]=>[8,2,4,7,3,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,8,1,5,4]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,2,5,4,7]=>[1,3,8,7,4,2,6,5]=>[8,6,1,2,5,7,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,2,5,4,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,5,2,3,6]=>[1,7,3,2,4,8,6,5]=>[8,2,6,7,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,2,5,4,7]=>[1,8,7,4,2,6,5,3]=>[8,1,2,5,7,3,4,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,3,2,4,5]=>[1,8,5,3,7,4,6,2]=>[8,1,4,6,2,5,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,6,3,1,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,7,5,4,2]=>[1,3,8,2,6,5,7,4]=>[8,6,1,7,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,5,4,1,3]=>[1,8,3,6,4,7,2,5]=>[8,1,6,3,5,2,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,3,1,5,4]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,6,5,4,3]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,6,5,4,2]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,6,5,4,3]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,3,7,4,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,2,7,4,3]=>[1,8,3,2,6,7,4,5]=>[8,1,6,7,3,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,4,2,6,3]=>[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,5,3,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,3,6,5,4]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,6,3,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,5,7,3,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,6,8,3,7]=>[1,2,3,5,6,8,7,4]=>[8,7,6,4,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,2,6,1,4]=>[1,8,4,5,2,3,7,6]=>[8,1,5,4,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,6,8,1,2]=>[1,5,6,8,2,3,7,4]=>[8,4,3,1,7,6,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,6,2,1,4]=>[1,5,6,2,8,4,7,3]=>[8,4,3,7,1,5,2,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,6,3,1,7]=>[1,5,6,3,4,8,7,2]=>[8,4,3,6,5,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,8,5,1,7]=>[1,4,3,6,5,8,7,2]=>[8,5,6,3,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,7,8,1,5]=>[1,4,2,6,8,5,7,3]=>[8,5,7,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,7,5,1,6]=>[1,3,2,8,6,5,7,4]=>[8,6,7,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,5,4,1,2]=>[1,3,8,2,6,4,7,5]=>[8,6,1,7,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,4,6,1,3]=>[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,7,6,4,3]=>[1,5,7,4,2,8,3,6]=>[8,4,2,5,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,5,7,4,2]=>[1,6,7,4,2,3,8,5]=>[8,3,2,5,7,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,5,4,6,2]=>[1,7,6,4,2,8,3,5]=>[8,2,3,5,7,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,4,5,8,7]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,3,2,8,7]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,3,6,2,4]=>[1,5,3,2,7,4,8,6]=>[8,4,6,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,4,3,8,2]=>[1,6,3,2,7,8,4,5]=>[8,3,6,7,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,3,4,2,6]=>[1,8,6,4,2,7,3,5]=>[8,1,3,5,7,2,6,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,4,7,3,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,3,7,4,2]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,1,7,4,2]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,2,1,3,6]=>[1,7,3,4,8,6,2,5]=>[8,2,6,5,1,3,7,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,4,1,8,2]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,5,1,2,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,1,6,2,4]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,5,1,4,8,7]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,1,6,4,3]=>[1,2,7,4,5,3,8,6]=>[8,7,2,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,5,1,4,2]=>[1,8,2,7,4,6,3,5]=>[8,1,7,2,5,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,6,1,5,7]=>[1,2,8,7,5,6,3,4]=>[8,7,1,2,4,3,6,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,6,1,8,5]=>[1,2,7,8,5,6,3,4]=>[8,7,2,1,4,3,6,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,8,1,5,6]=>[1,3,7,5,8,6,2,4]=>[8,6,2,4,1,3,7,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,7,1,8,6]=>[1,4,5,7,8,6,2,3]=>[8,5,4,2,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,8,1,6,7]=>[1,4,5,8,7,6,2,3]=>[8,5,4,1,2,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,7,1,6,5]=>[1,3,8,5,7,6,2,4]=>[8,6,1,4,2,3,7,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,5,1,6,3]=>[1,8,3,4,7,6,2,5]=>[8,1,6,5,2,3,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,1,6,5,2]=>[1,3,4,7,5,2,8,6]=>[8,6,5,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,7,6,1,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,5,7,1,3]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,6,7,1,5]=>[1,2,3,8,5,6,7,4]=>[8,7,6,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,8,7,1,6]=>[1,2,4,5,8,6,7,3]=>[8,7,5,4,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,6,8,1,7]=>[1,3,4,5,6,8,7,2]=>[8,6,5,4,3,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,4,2,7,3]=>[1,5,4,2,6,3,8,7]=>[8,4,5,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,4,6,2,3]=>[1,2,5,4,8,3,7,6]=>[8,7,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,8,6,2,4]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,8,2,7,4]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,8,1,7,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,2,1,7,3]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,8,3,7,4]=>[1,5,8,4,6,3,2,7]=>[8,4,1,5,3,6,7,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,8,6,3,4]=>[1,2,5,8,4,7,3,6]=>[8,7,4,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,2,8,3,4]=>[1,6,8,4,5,2,3,7]=>[8,3,1,5,4,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,6,3,4,2]=>[1,5,6,3,7,4,8,2]=>[8,4,3,6,2,5,1,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,4,6,1,3]=>[1,5,4,8,3,7,2,6]=>[8,4,5,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,8,6,1,4]=>[1,3,5,8,4,7,2,6]=>[8,6,4,1,5,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,1,8,3,4]=>[1,6,8,4,5,2,3,7]=>[8,3,1,5,4,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,5,8,3,4]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,4,1,8,3]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,5,3,8,1,4]=>[1,6,8,4,5,3,2,7]=>[8,3,1,5,4,6,7,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,2,1,8,3]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,6,3,1,4]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,1,8,2,4]=>[1,6,8,4,5,2,3,7]=>[8,3,1,5,4,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,4,2,8,3]=>[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,4,1,2,3]=>[1,5,4,6,2,7,3,8]=>[8,4,5,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,6,5,8,3]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,5,6,8,3]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,5,2,8,3]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,5,2,8,3]=>[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,5,8,2,4]=>[1,2,6,8,4,7,3,5]=>[8,7,3,1,5,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,5,8,2,4]=>[1,6,8,4,7,2,3,5]=>[8,3,1,5,2,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,8,6,1,4]=>[1,2,5,8,4,7,3,6]=>[8,7,4,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,5,8,1,4]=>[1,6,8,4,7,2,3,5]=>[8,3,1,5,2,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,5,1,8,3]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,5,1,8,3]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,5,8,1,4]=>[1,6,8,4,7,2,3,5]=>[8,3,1,5,2,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,3,2,8,7]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,3,8,2,4]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,3,8,4,2]=>[1,7,4,6,8,2,5,3]=>[8,2,5,3,1,7,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,3,8,4,5]=>[1,2,7,4,3,6,8,5]=>[8,7,2,5,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,3,8,5,4]=>[1,2,7,5,3,6,8,4]=>[8,7,2,4,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,8,6,2,4]=>[1,3,5,8,4,2,7,6]=>[8,6,4,1,5,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,5,8,3,4]=>[1,2,6,8,4,3,7,5]=>[8,7,3,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,1,8,3,5]=>[1,2,6,8,5,3,7,4]=>[8,7,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,3,8,5,4]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,1,8,5,3]=>[1,2,6,8,3,7,5,4]=>[8,7,3,1,6,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,5,8,4,3]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,8,4,2,7]=>[1,3,5,8,7,2,6,4]=>[8,6,4,1,2,7,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,8,1,6,2]=>[1,3,5,8,2,7,6,4]=>[8,6,4,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,8,1,2,6]=>[1,3,5,8,6,2,7,4]=>[8,6,4,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,8,7,3,2]=>[1,4,5,8,2,6,7,3]=>[8,5,4,1,7,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,8,7,2,3]=>[1,4,5,8,3,2,6,7]=>[8,5,4,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,8,2,7,3]=>[1,4,5,8,3,2,6,7]=>[8,5,4,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,2,8,3,4]=>[1,7,3,2,5,4,6,8]=>[8,2,6,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,8,3,6,2]=>[1,4,5,8,2,7,6,3]=>[8,5,4,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,8,1,6,5]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,3,2,7,1]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,3,7,2,1]=>[1,6,7,2,8,3,5,4]=>[8,3,2,7,1,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,2,1,7,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,3,1,6,2]=>[1,8,2,7,6,3,5,4]=>[8,1,7,2,3,6,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,2,1,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,1,8,4,7]=>[1,3,6,8,7,4,2,5]=>[8,6,3,1,2,5,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,8,4,1,7]=>[1,3,2,5,8,7,4,6]=>[8,6,7,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,8,4,1,6]=>[1,7,2,5,8,6,4,3]=>[8,2,7,4,1,3,5,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,3,8,6,1]=>[1,2,4,7,6,8,3,5]=>[8,7,5,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,8,3,1,7]=>[1,4,6,3,5,8,7,2]=>[8,5,3,6,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,5,6,3,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,8,4,3,7]=>[1,2,5,8,7,3,6,4]=>[8,7,4,1,2,6,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,8,1,4,2,7]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,1,3,2,7]=>[1,4,8,7,2,5,3,6]=>[8,5,1,2,7,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,8,3,2,7]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,2,8,5,1]=>[1,6,8,2,4,3,7,5]=>[8,3,1,7,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,8,4,2,6]=>[1,5,8,6,4,3,7,2]=>[8,4,1,3,5,6,2,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,1,8,6,3]=>[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,4,8,6,2]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,7,8,5,2]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,8,4,2,1]=>[1,5,8,2,6,4,7,3]=>[8,4,1,7,3,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,7,8,4,2]=>[1,5,7,4,3,2,6,8]=>[8,4,2,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,8,3,4,2]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,4,8,5,2]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,1,8,5,3]=>[1,6,8,3,2,7,5,4]=>[8,3,1,6,7,2,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,4,3,8,5]=>[1,6,3,2,7,8,5,4]=>[8,3,6,7,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,1,2,8,5]=>[1,6,2,4,3,7,8,5]=>[8,3,7,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,2,7,8,4]=>[1,5,2,6,7,8,4,3]=>[8,4,7,3,2,1,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,2,7,8,4]=>[1,5,2,6,7,8,4,3]=>[8,4,7,3,2,1,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,1,7,8,4]=>[1,5,2,6,7,8,4,3]=>[8,4,7,3,2,1,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,1,7,8,4]=>[1,2,5,3,6,7,8,4]=>[8,7,4,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,3,1,8,5]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,8,4,5,1]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,8,4,1,5]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,6,4,2,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,6,2,1,5]=>[1,7,2,3,8,5,6,4]=>[8,2,7,6,1,4,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,2,1,6,4]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,5,2,1,4]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,8,5,3,1]=>[1,4,7,3,2,6,5,8]=>[8,5,2,6,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,7,8,5,3]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,1,2,6,3]=>[1,7,6,2,4,8,3,5]=>[8,2,3,7,5,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,3,8,6,4]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,3,8,5,4]=>[1,6,8,4,2,7,5,3]=>[8,3,1,5,7,2,4,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,8,2,4,3]=>[1,5,8,3,6,2,4,7]=>[8,4,1,6,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,8,5,2,4]=>[1,6,5,8,4,2,3,7]=>[8,3,4,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,3,8,5,4]=>[1,6,8,4,7,5,3,2]=>[8,3,1,5,2,4,6,7]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,8,5,4,3]=>[1,6,5,8,3,7,4,2]=>[8,3,4,1,6,2,5,7]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,8,2,5,7]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,6,8,1,5,7]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,2,1,7,4]=>[1,3,5,2,6,4,8,7]=>[8,6,4,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,8,1,3,7]=>[1,2,4,5,8,7,3,6]=>[8,7,5,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,6,8,4,7]=>[1,5,6,8,7,4,2,3]=>[8,4,3,1,2,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,5,8,2,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,7,6,3,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,7,3,6,5]=>[1,8,5,7,6,3,4,2]=>[8,1,4,2,3,6,5,7]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,1,2,6,3]=>[1,5,2,8,3,7,6,4]=>[8,4,7,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,8,6,7,1]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,6,8,7,2]=>[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,8,1,7,5]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,6,7,1,4]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,8,7,1,4]=>[1,3,5,8,4,6,7,2]=>[8,6,4,1,5,3,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,6,7,3,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,5,6,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,7,3,4,5]=>[1,8,5,7,4,6,3,2]=>[8,1,4,2,5,3,6,7]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,8,4,2,6]=>[1,2,7,3,5,8,6,4]=>[8,7,2,6,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,5,3,1,6]=>[1,7,2,3,4,8,6,5]=>[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,2,7,6,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,4,1,8,6]=>[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,7,1,5,6]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,1,3,5,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,7,1,3,5]=>[1,8,5,7,3,4,6,2]=>[8,1,4,2,6,5,3,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,6,7,1,5]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,6,1,8,4]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,1,6,7,4]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,4,1,6,3]=>[1,5,4,7,6,2,8,3]=>[8,4,5,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,8,7,6,3]=>[1,5,8,3,4,2,6,7]=>[8,4,1,6,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,8,2,1,3]=>[1,4,5,8,3,6,2,7]=>[8,5,4,1,6,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,6,2,8,4]=>[1,5,6,2,3,7,8,4]=>[8,4,3,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,7,1,3,4]=>[1,5,7,3,6,2,4,8]=>[8,4,2,6,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,8,5,7,4]=>[1,6,5,8,4,2,3,7]=>[8,3,4,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,1,8,6,3]=>[1,2,7,6,8,3,5,4]=>[8,7,2,3,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,8,7,1,3]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,5,6,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,5,6,7,2]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,6,7,1,3]=>[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,7,1,8,6,3]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,1,8,6,2]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,3,2,5,7]=>[1,8,7,5,3,4,2,6]=>[8,1,2,4,6,5,7,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,5,2,4,7]=>[1,8,7,4,6,2,3,5]=>[8,1,2,5,3,7,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,6,5,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,1,8,7,4]=>[1,3,5,2,6,8,4,7]=>[8,6,4,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,6,5,1,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,6,5,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,6,5,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,1,5,3,7]=>[1,8,7,3,4,2,6,5]=>[8,1,2,6,5,7,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,1,5,2,7]=>[1,8,7,2,3,6,5,4]=>[8,1,2,7,6,3,4,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,5,1,7]=>[1,8,7,2,3,6,5,4]=>[8,1,2,7,6,3,4,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,5,7,2,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,6,2,3,1]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,5,8,2,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,4,8,7,6]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,5,8,3,2]=>[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,6,3,1,2]=>[1,5,6,3,8,2,4,7]=>[8,4,3,6,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,4,7,6,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,8,6,7,2]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,8,6,7,2]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,4,7,1,2]=>[1,6,7,2,5,4,8,3]=>[8,3,2,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,2,1,6,5]=>[1,3,7,6,2,4,8,5]=>[8,6,2,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,8,6,7,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,8,6,7,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,8,6,7,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,6,8,7,4]=>[1,5,6,8,4,3,2,7]=>[8,4,3,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,8,1,6,5]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,7,4,1,5]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,6,4,7,5]=>[1,8,5,6,4,3,2,7]=>[8,1,4,3,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,8,4,2,6]=>[1,3,2,5,8,6,4,7]=>[8,6,7,4,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,8,3,1,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,2,1,6,5]=>[1,3,8,5,2,4,7,6]=>[8,6,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,7,2,1,5]=>[1,6,2,4,8,5,7,3]=>[8,3,7,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,4,1,2,5]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,4,8,1,6]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,3,1,5,6]=>[1,8,6,2,4,3,7,5]=>[8,1,3,7,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,3,2,5,6]=>[1,8,6,2,4,3,7,5]=>[8,1,3,7,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,1,3,5,6]=>[1,8,6,3,7,5,2,4]=>[8,1,3,6,2,4,7,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,1,3,7,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,6,1,8,4]=>[1,3,7,8,4,2,5,6]=>[8,6,2,1,5,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,5,7,2,4]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,4,7,6,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,4,6,2,3]=>[1,2,5,4,7,3,8,6]=>[8,7,4,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,4,5,8,3]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,6,5,8,3]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,6,8,2,4]=>[1,3,2,5,6,8,4,7]=>[8,6,7,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,1,3,7,4]=>[1,5,2,8,4,6,3,7]=>[8,4,7,1,5,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,4,1,6,3]=>[1,2,5,4,8,3,7,6]=>[8,7,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,5,6,7,3]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,6,8,7,3]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,1,6,7,3]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,2,6,7,3]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,2,1,3,7,4]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,5,6,7,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,8,1,7,2]=>[1,4,5,8,2,6,3,7]=>[8,5,4,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,8,6,7,2]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,5,6,7,2]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,8,2,1,7]=>[1,3,5,8,7,2,4,6]=>[8,6,4,1,2,7,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,1,8,6,2]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,8,2,6,1]=>[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,8,5,1,7]=>[1,3,6,5,8,7,2,4]=>[8,6,3,4,1,2,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,1,5,6,7]=>[1,3,8,7,6,5,2,4]=>[8,6,1,2,3,4,7,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,7,8,1,4]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,4,1,6,7]=>[1,3,2,5,4,8,7,6]=>[8,6,7,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,8,4,1,7]=>[1,3,6,4,2,5,8,7]=>[8,6,3,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,4,8,6,1]=>[1,3,7,6,8,2,5,4]=>[8,6,2,3,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,8,4,6,1]=>[1,3,7,6,4,2,5,8]=>[8,6,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,8,5,4,7]=>[1,3,2,6,5,8,7,4]=>[8,6,7,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,4,8,5,1]=>[1,3,7,5,4,2,6,8]=>[8,6,2,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,8,5,4,1]=>[1,3,7,4,2,6,5,8]=>[8,6,2,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,4,5,1,2]=>[1,3,7,2,6,5,4,8]=>[8,6,2,7,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,4,5,1,7]=>[1,3,8,7,2,6,5,4]=>[8,6,1,2,7,3,4,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,4,8,6,5]=>[1,3,2,7,6,8,5,4]=>[8,6,7,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,8,5,6,4]=>[1,3,2,7,6,5,8,4]=>[8,6,7,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,4,5,6,1]=>[1,3,2,7,6,5,4,8]=>[8,6,7,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,4,5,6,1]=>[1,3,8,2,7,6,5,4]=>[8,6,1,7,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,4,5,6,7]=>[1,3,2,8,7,6,5,4]=>[8,6,7,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,7,3,8,6,2]=>[1,4,7,6,8,2,3,5]=>[8,5,2,3,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,7,8,5,2]=>[1,4,3,6,8,2,5,7]=>[8,5,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,8,5,2,7]=>[1,4,3,6,5,8,7,2]=>[8,5,6,3,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,3,8,5,2]=>[1,4,7,5,3,6,8,2]=>[8,5,2,4,6,3,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,3,5,2,7]=>[1,4,8,7,2,3,6,5]=>[8,5,1,2,7,6,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,2,8,6,5]=>[1,4,3,7,6,8,5,2]=>[8,5,6,2,3,1,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,8,3,5,6,2]=>[1,4,8,2,3,7,6,5]=>[8,5,1,7,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,2,5,6,7]=>[1,4,3,8,7,6,5,2]=>[8,5,6,1,2,3,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,7,8,3,1]=>[1,4,6,8,2,5,7,3]=>[8,5,3,1,7,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,8,1,3,7]=>[1,4,6,2,5,8,7,3]=>[8,5,3,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,3,1,2,7]=>[1,4,8,7,2,5,3,6]=>[8,5,1,2,7,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,8,1,6,2]=>[1,4,3,7,6,2,5,8]=>[8,5,6,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,7,8,5,1]=>[1,4,3,2,6,8,5,7]=>[8,5,6,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,8,5,1,7]=>[1,4,3,2,6,5,8,7]=>[8,5,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,3,8,5,1]=>[1,4,7,5,3,2,6,8]=>[8,5,2,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,2,8,5,1]=>[1,4,3,7,5,2,6,8]=>[8,5,6,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,1,8,6,5]=>[1,4,3,2,7,6,8,5]=>[8,5,6,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,3,5,6,1]=>[1,4,8,2,7,6,5,3]=>[8,5,1,7,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,1,5,6,7]=>[1,4,3,2,8,7,6,5]=>[8,5,6,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,8,4,3,7]=>[1,5,8,7,3,2,4,6]=>[8,4,1,2,6,7,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,4,8,6,3]=>[1,5,4,7,6,8,3,2]=>[8,4,5,2,3,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,8,4,6,3]=>[1,5,8,3,2,4,7,6]=>[8,4,1,6,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,8,4,3,6,7]=>[1,5,4,8,7,6,3,2]=>[8,4,5,1,2,3,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,8,4,2,7]=>[1,5,8,7,2,3,6,4]=>[8,4,1,2,7,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,4,8,2,3]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,8,4,2,3]=>[1,5,8,3,6,4,7,2]=>[8,4,1,6,3,5,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,4,2,6,7]=>[1,5,4,3,8,7,6,2]=>[8,4,5,6,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,8,4,1,7]=>[1,5,8,7,2,6,4,3]=>[8,4,1,2,7,3,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,8,4,1,3]=>[1,5,8,3,2,6,4,7]=>[8,4,1,6,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,4,8,6,1]=>[1,5,4,3,2,7,6,8]=>[8,4,5,6,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,8,4,6,1]=>[1,5,8,2,7,6,4,3]=>[8,4,1,7,2,3,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,4,1,6,7]=>[1,5,4,3,2,8,7,6]=>[8,4,5,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,8,5,4,7]=>[1,6,5,8,7,4,3,2]=>[8,3,4,1,2,5,6,7]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,8,5,4,3]=>[1,6,5,8,3,2,4,7]=>[8,3,4,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,4,5,3,7]=>[1,6,5,4,8,7,3,2]=>[8,3,4,5,1,2,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,3,4,8,5,2]=>[1,6,8,2,3,7,5,4]=>[8,3,1,7,6,2,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,4,5,2,7]=>[1,6,5,4,3,8,7,2]=>[8,3,4,5,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,8,5,4,1]=>[1,6,5,8,2,7,4,3]=>[8,3,4,1,7,2,5,6]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,4,5,3,1]=>[1,6,5,4,8,2,7,3]=>[8,3,4,5,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,4,5,1,7]=>[1,6,5,4,3,2,8,7]=>[8,3,4,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,8,6,5]=>[1,7,6,8,5,4,3,2]=>[8,2,3,1,4,5,6,7]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,4,5,6,3]=>[1,7,6,5,4,8,3,2]=>[8,2,3,4,5,1,6,7]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,4,5,6,2]=>[1,7,6,5,4,3,8,2]=>[8,2,3,4,5,6,1,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,4,3,7,6]=>[1,5,4,2,8,6,3,7]=>[8,4,5,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,2,6,4,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,1,2,4,7]=>[1,3,8,7,4,6,2,5]=>[8,6,1,2,5,3,7,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,1,5,7,4]=>[1,3,2,6,5,4,8,7]=>[8,6,7,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,3,8,4,6]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,4,6,1,3]=>[1,8,3,5,4,7,2,6]=>[8,1,6,4,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,7,6,4,5]=>[1,8,5,7,4,3,2,6]=>[8,1,4,2,5,6,7,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,4,8,1,3]=>[1,7,2,6,8,3,5,4]=>[8,2,7,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,3,2,4,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,4,8,3,7]=>[1,6,8,7,3,2,5,4]=>[8,3,1,2,6,7,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,4,2,3,5]=>[1,7,3,2,8,5,4,6]=>[8,2,6,7,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,5,6,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,2,6,4,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,5,1,8,4]=>[1,7,8,4,6,2,3,5]=>[8,2,1,5,3,7,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,5,6,1,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,4,6,2,1]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,4,3,5,1]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,5,6,2,1]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,5,3,2,4]=>[1,2,8,4,6,3,7,5]=>[8,7,1,5,3,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,3,4,5,1]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,5,2,3,4]=>[1,2,8,4,6,3,7,5]=>[8,7,1,5,3,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,4,6,1,3]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,5,1,7,4]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,5,6,3,1]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,3,1,7,2]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,4,1,3,7,2]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,5,3,7,2]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,5,2,7,4]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,8,6,7,5]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,4,1,7,2]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,3,6,1,4]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,3,4,2,8]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,8,3,1,5]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,2,6,3,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,7,8,5,6]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,7,2,5,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,5,1,7,2]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,5,8,4,7]=>[1,2,6,8,7,4,3,5]=>[8,7,3,1,2,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,5,4,7,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,5,8,4,2]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,4,3,7,6]=>[1,2,5,4,8,6,3,7]=>[8,7,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,6,8,2,7]=>[1,2,3,5,6,8,7,4]=>[8,7,6,4,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,5,8,2,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,5,2,7,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,6,8,3,1]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,1,7,3,5]=>[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,8,4,3,6]=>[1,7,3,5,8,6,4,2]=>[8,2,6,4,1,3,5,7]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,5,4,8,6]=>[1,2,7,8,6,4,3,5]=>[8,7,2,1,3,5,6,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,5,1,7,2]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,1,2,7,3]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,6,2,5,1]=>[1,3,7,5,6,2,4,8]=>[8,6,2,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,4,7,3,2]=>[1,6,7,3,2,5,4,8]=>[8,3,2,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,8,1,6,5]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,7,2,8,5]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,1,5,2,4]=>[1,8,4,6,5,2,7,3]=>[8,1,5,3,4,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,8,2,5,1]=>[1,7,5,8,2,4,6,3]=>[8,2,4,1,7,5,3,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,8,5,6,1]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,5,7,3,4]=>[1,2,8,4,3,6,7,5]=>[8,7,1,5,6,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,4,3,1,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,2,7,6,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,4,2,6,1]=>[1,8,2,5,4,7,6,3]=>[8,1,7,4,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,7,1,5,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,2,5,8,4]=>[1,2,7,8,4,3,6,5]=>[8,7,2,1,5,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,6,2,7,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,1,7,4,3]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,7,2,1,3]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,5,2,7,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,3,6,2,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,8,7,6,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,2,7,3,5]=>[1,6,7,3,2,8,5,4]=>[8,3,2,6,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,5,6,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,6,1,8,4]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,7,6,8,2]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,5,7,8,2]=>[1,3,4,6,7,8,2,5]=>[8,6,5,3,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,5,6,8,2]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,6,4,8,7,2]=>[1,5,4,6,8,2,3,7]=>[8,4,5,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,5,8,6,4]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,8,4,7,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,5,8,4,7]=>[1,3,2,4,6,8,7,5]=>[8,6,7,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,8,5,3,7]=>[1,4,6,5,8,7,3,2]=>[8,5,3,4,1,2,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,8,7,6,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,8,7,5,3]=>[1,2,3,6,7,5,8,4]=>[8,7,6,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,5,8,4,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,5,4,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,5,7,4,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,8,7,3,6]=>[1,2,4,5,8,6,7,3]=>[8,7,5,4,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,8,7,3,6]=>[1,2,5,8,6,7,3,4]=>[8,7,4,1,3,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,8,7,3,5]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,5,6,3,4]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,5,7,3,4]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,2,7,3,4]=>[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,6,7,4,5]=>[1,2,3,8,5,6,7,4]=>[8,7,6,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,8,6,3,5]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,2,5,3,4]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,3,7,5,4]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,2,3,6,4]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,8,4,6,3]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,8,3,6,5]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,4,8,5,2]=>[1,2,6,8,3,7,5,4]=>[8,7,3,1,6,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,4,8,6,2]=>[1,2,5,4,7,6,8,3]=>[8,7,4,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,5,3,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,5,7,2,6]=>[1,3,4,2,8,6,7,5]=>[8,6,5,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,2,8,6,5]=>[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,2,7,6,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,7,3,6,5]=>[1,2,3,8,5,7,6,4]=>[8,7,6,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,8,3,6,5]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,8,3,7,5]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,7,2,3,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,2,7,4,6]=>[1,2,8,6,7,4,5,3]=>[8,7,1,3,2,5,4,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,1,4,7,6]=>[1,2,8,6,4,5,3,7]=>[8,7,1,3,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,1,4,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,2,7,4,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,7,2,3,4]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,5,3,7,4]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,7,3,6,4]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,7,3,5,4]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,5,2,3,4]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,6,2,3,4]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,8,2,3,5]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,2,8,4,5]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,4,1,6,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,7,6,3,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,7,6,3,4]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,7,5,3,4]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,6,5,3,4]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,7,6,3,8,1]=>[1,5,6,3,4,7,8,2]=>[8,4,3,6,5,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,7,8,3,4]=>[1,5,7,3,2,6,8,4]=>[8,4,2,6,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,4,8,7,3]=>[1,5,4,2,6,8,3,7]=>[8,4,5,7,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,5,8,7,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,6,3,8,1]=>[1,5,6,3,2,4,7,8]=>[8,4,3,6,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,4,5,8,1]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,5,8,3,4]=>[1,2,6,8,4,7,3,5]=>[8,7,3,1,5,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,4,8,5,3]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,8,4,3,6]=>[1,5,8,6,4,7,3,2]=>[8,4,1,3,5,2,6,7]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,4,8,3,5]=>[1,2,6,8,5,4,7,3]=>[8,7,3,1,4,5,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,3,8,7,2]=>[1,5,3,6,8,2,4,7]=>[8,4,6,3,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,4,8,7,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,7,8,5,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,8,6,7,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,8,7,3,6]=>[1,5,8,6,7,3,2,4]=>[8,4,1,3,2,6,7,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,8,7,6,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,5,4,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,5,7,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,8,6,4,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,5,6,4,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,6,4,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,6,5,4,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,5,4,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,8,6,3,7]=>[1,5,8,7,3,2,4,6]=>[8,4,1,2,6,7,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,8,3,7,6]=>[1,5,8,6,3,2,4,7]=>[8,4,1,3,6,7,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,1,8,6,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,1,8,7,2]=>[1,3,5,2,6,8,4,7]=>[8,6,4,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,7,8,4,3]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,8,7,3,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,7,8,6,4,5]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,7,8,5,6,4]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,1,7,8,6,3]=>[1,5,7,6,8,3,4,2]=>[8,4,2,3,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,6,7,5]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,8,6,7,3]=>[1,5,8,3,4,2,6,7]=>[8,4,1,6,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,8,5,7,4]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,6,7,4,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,7,5,4,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,7,4,5,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,5,7,4,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,8,7,4,5]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,8,7,6,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,8,7,5,4]=>[1,3,6,7,5,8,4,2]=>[8,6,3,2,4,1,5,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,6,5,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,9,4,5,6,7,8]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,9,3,4,5,6,7,8]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,9,7,6,8]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,8,7,6,5,4,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,9,6,5,7,8]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,6,5,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,7,6,5,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,8,4,5,3,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,9,5,4,6,7,8]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,6,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,3,4,2,5,6,7]=>[1,2,8,7,6,5,3,4]=>[8,7,1,2,3,4,6,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,9,4,3,5,6,7,8]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,1,2,3,4,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,4,3,2,5,6,7]=>[1,2,8,7,6,5,3,4]=>[8,7,1,2,3,4,6,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,3,2,1]=>[1,8,2,4,6,3,7,5]=>[8,1,7,5,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,6,3,2,1]=>[1,8,2,5,6,3,7,4]=>[8,1,7,4,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,5,4,2,1]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,5,4,2,1]=>[1,8,2,6,4,3,7,5]=>[8,1,7,3,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,6,4,2,1]=>[1,8,2,5,6,4,3,7]=>[8,1,7,4,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,5,3,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,6,5,4,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,6,5,4,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,5,4,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,6,4,3,1]=>[1,8,2,5,6,4,3,7]=>[8,1,7,4,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,4,3,1]=>[1,8,2,6,4,3,7,5]=>[8,1,7,3,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,5,4,3,1]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,6,5,3,2]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,6,5,4,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,5,4,3]=>[1,8,3,7,4,2,5,6]=>[8,1,6,2,5,7,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,5,4,3]=>[1,8,3,7,4,2,5,6]=>[8,1,6,2,5,7,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,5,3,4,1]=>[1,8,2,7,4,3,6,5]=>[8,1,7,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,2,3,1]=>[1,8,2,4,6,3,7,5]=>[8,1,7,5,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,4,1,3,2]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,1,3,2]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,5,1,4,3]=>[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,5,2,4,3]=>[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,2,5,3,7]=>[1,6,5,2,8,7,3,4]=>[8,3,4,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,1,4,2,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,3,6,1,4]=>[1,7,2,8,4,5,3,6]=>[8,2,7,1,5,4,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,1,4,3,6]=>[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,3,6,2,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,3,7,2,6]=>[1,5,3,2,8,6,7,4]=>[8,4,6,7,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,1,4,3,7]=>[1,6,4,5,2,8,7,3]=>[8,3,5,4,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,3,7,1,4]=>[1,6,7,2,8,4,5,3]=>[8,3,2,7,1,5,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,4,7,1,3]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,6,8,1,4]=>[1,2,5,6,8,4,7,3]=>[8,7,4,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,3,7,6,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,3,7,5,8]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,8,1,4,3,7]=>[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,3,7,4,8]=>[1,2,6,7,4,5,3,8]=>[8,7,3,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,4,8,1,5]=>[1,2,6,8,5,4,7,3]=>[8,7,3,1,4,5,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,5,8,1,3]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,3,7,1,5]=>[1,4,6,7,2,8,5,3]=>[8,5,3,2,7,1,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,2,6,3,7]=>[1,4,5,2,8,7,3,6]=>[8,5,4,7,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,1,5,2,6]=>[1,4,7,2,8,6,5,3]=>[8,5,2,7,1,3,4,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,1,4,2,5]=>[1,6,4,7,2,8,5,3]=>[8,3,5,2,7,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,2,6,4,7]=>[1,5,2,8,7,4,3,6]=>[8,4,7,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,1,3,2,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,1,3,2,5]=>[1,6,3,4,7,2,8,5]=>[8,3,6,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,2,4,1,3]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,1,3,2,5]=>[1,4,8,5,2,7,3,6]=>[8,5,1,4,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,1,3,2,6]=>[1,4,8,6,3,5,2,7]=>[8,5,1,3,6,4,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,2,6,5,8]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,4,2,6,5,8]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,1,4,2,6]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,2,5,1,4]=>[1,3,6,5,2,7,4,8]=>[8,6,3,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,2,5,1,3]=>[1,4,8,3,6,5,2,7]=>[8,5,1,6,3,4,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,3,6,1,2]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,2,6,1,4]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,1,5,2,6]=>[1,3,4,8,6,5,2,7]=>[8,6,5,1,3,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,2,6,4,8]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,1,5,4,8]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,5,8,1,4]=>[1,3,2,7,4,6,8,5]=>[8,6,7,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,5,8,1,2]=>[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,8,4,7,1,3]=>[1,2,6,7,3,5,4,8]=>[8,7,3,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,8,3,7,1,4]=>[1,2,6,7,3,5,4,8]=>[8,7,3,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,1,5,4,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,8,5,3,1]=>[1,7,3,4,2,6,5,8]=>[8,2,6,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,2,5,1]=>[1,7,5,8,2,6,3,4]=>[8,2,4,1,7,3,6,5]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,7,2,1,5]=>[1,6,2,8,5,7,3,4]=>[8,3,7,1,4,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,5,1,8,2]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,4,8,2,1]=>[1,6,8,2,7,3,4,5]=>[8,3,1,7,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,5,2,4,1]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,8,2,4,1]=>[1,7,4,5,8,2,6,3]=>[8,2,5,4,1,7,3,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,2,4,8,1]=>[1,7,8,2,6,4,5,3]=>[8,2,1,7,3,5,4,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,5,1,8,3]=>[1,7,8,3,4,2,6,5]=>[8,2,1,6,5,7,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,8,4,1,5,3]=>[1,7,5,4,8,3,2,6]=>[8,2,4,5,1,6,7,3]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,2,4,1,5]=>[1,7,2,6,4,8,5,3]=>[8,2,7,3,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,8,2,5,1]=>[1,7,5,8,2,6,3,4]=>[8,2,4,1,7,3,6,5]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,4,5,2,1]=>[1,6,5,4,7,2,8,3]=>[8,3,4,5,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,6,2,1,4]=>[1,5,6,2,7,3,8,4]=>[8,4,3,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,8,7,2,5,1]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,1,7,5,3]=>[1,6,7,5,2,3,8,4]=>[8,3,2,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,1,5,3,8]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,7,5,8,2,1]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,8,2,1,4]=>[1,5,8,4,6,2,7,3]=>[8,4,1,5,3,7,2,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,3,5,2,1]=>[1,4,8,2,6,5,3,7]=>[8,5,1,7,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,5,7,2,1]=>[1,4,3,8,2,6,7,5]=>[8,5,6,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,6,8,2,1]=>[1,4,5,6,8,2,7,3]=>[8,5,4,3,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,8,2,6,1]=>[1,4,5,8,2,7,6,3]=>[8,5,4,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,8,2,1,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,4,1,6,7]=>[1,5,4,2,3,8,7,6]=>[8,4,5,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,2,6,1,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,7,2,6,1]=>[1,4,5,7,6,2,8,3]=>[8,5,4,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,6,7,2,1]=>[1,4,5,6,7,2,8,3]=>[8,5,4,3,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,5,6,2,1]=>[1,4,3,8,2,7,5,6]=>[8,5,6,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,6,2,5,1]=>[1,4,3,8,2,7,5,6]=>[8,5,6,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,7,2,5,1]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,2,7,6,1]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,4,1,7,6]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,1,8,7,3]=>[1,6,8,3,2,4,5,7]=>[8,3,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,8,2,1,7]=>[1,6,2,4,5,8,7,3]=>[8,3,7,5,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,8,2,1,6]=>[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,3,1,6,7]=>[1,5,3,4,2,8,7,6]=>[8,4,6,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,3,1,7,6]=>[1,5,3,4,2,8,6,7]=>[8,4,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,5,3,1,7]=>[1,6,3,2,4,8,7,5]=>[8,3,6,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,3,1,8,5]=>[1,6,2,4,7,8,5,3]=>[8,3,7,5,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,7,1,8,2]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,3,1,6,8]=>[1,5,3,4,2,7,6,8]=>[8,4,6,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,1,8,2,4]=>[1,5,2,6,8,4,7,3]=>[8,4,7,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,7,1,8,2]=>[1,5,7,8,2,6,3,4]=>[8,4,2,1,7,3,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,8,2,1,7]=>[1,5,8,7,2,6,3,4]=>[8,4,1,2,7,3,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,7,4,8,2,1]=>[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,7,8,2,1]=>[1,6,8,2,3,5,7,4]=>[8,3,1,7,6,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,1,7,3,8]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,4,1,6,8]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,2,6,1,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,8,2,5,1]=>[1,4,6,2,7,5,8,3]=>[8,5,3,7,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,5,8,2,1]=>[1,4,3,7,2,6,8,5]=>[8,5,6,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,3,6,2,1]=>[1,4,8,2,5,3,7,6]=>[8,5,1,7,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,3,7,2,6,1]=>[1,4,3,8,2,5,7,6]=>[8,5,6,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,6,8,2,1,7]=>[1,5,8,7,2,3,4,6]=>[8,4,1,2,7,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,8,2,1,4,7]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,1,8,2,4]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,6,7,1,8,2]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,6,8,2,1]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,3,7,2,1]=>[1,4,8,2,5,3,6,7]=>[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,6,3,2,1]=>[1,5,6,3,4,8,2,7]=>[8,4,3,6,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,2,8,4,1]=>[1,3,6,8,2,5,4,7]=>[8,6,3,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,6,9,8,1]=>[1,3,5,7,9,2,4,6,8]=>[9,7,5,3,1,8,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,2,1]=>[1,3,5,7,9,2,4,6,8]=>[9,7,5,3,1,8,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,10,2,1]=>[1,3,5,7,9,2,4,6,8,10]=>[10,8,6,4,2,9,7,5,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,6,2,5,3,4,8,7]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,4,6,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,6,4,8,5]=>[1,2,7,8,5,6,4,3]=>[8,7,2,1,4,3,5,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,5,3,7,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,3,4,7,6]=>[1,2,8,6,4,5,3,7]=>[8,7,1,3,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,6,4,7,5]=>[1,2,8,5,6,4,3,7]=>[8,7,1,4,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,5,4,6,8]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,3,4,6,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,3,5,4,7]=>[1,2,6,5,3,8,7,4]=>[8,7,3,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,2,4,8,7]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,4,2,3,6]=>[1,7,3,5,4,8,6,2]=>[8,2,6,4,5,1,3,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,4,2,3,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,8,2,3,6]=>[1,7,3,4,5,8,6,2]=>[8,2,6,5,4,1,3,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,2,8,3,5]=>[1,7,3,2,4,6,8,5]=>[8,2,6,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,2,6,3,5]=>[1,8,5,2,4,7,3,6]=>[8,1,4,7,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,7,2,3,6]=>[1,8,6,2,3,5,7,4]=>[8,1,3,7,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,8,3,4,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,8,2,3,6]=>[1,7,3,5,8,6,2,4]=>[8,2,6,4,1,3,7,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,5,2,3,6]=>[1,7,3,4,8,6,2,5]=>[8,2,6,5,1,3,7,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,2,4,6,5]=>[1,7,6,4,2,8,5,3]=>[8,2,3,5,7,1,4,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,4,2,3,5]=>[1,8,5,4,6,2,7,3]=>[8,1,4,5,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,4,2,3,5]=>[1,8,5,4,7,3,2,6]=>[8,1,4,5,2,6,7,3]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,2,4,6,5]=>[1,8,5,2,3,7,6,4]=>[8,1,4,7,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,1,2,4,8,5]=>[1,7,8,5,2,3,6,4]=>[8,2,1,4,7,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,4,2,3,5]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,5,3,4,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,2,4,8,5]=>[1,7,8,5,2,6,4,3]=>[8,2,1,4,7,3,5,6]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,2,7,4,5]=>[1,6,7,4,2,8,5,3]=>[8,3,2,5,7,1,4,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,2,8,4,5]=>[1,6,8,5,2,7,4,3]=>[8,3,1,4,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,2,3,8,5]=>[1,6,3,2,7,8,5,4]=>[8,3,6,7,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,4,6,3,5]=>[1,7,3,2,8,5,4,6]=>[8,2,6,7,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,1,3,6,7]=>[1,2,4,5,3,8,7,6]=>[8,7,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,8,4,2,7]=>[1,3,6,4,2,5,8,7]=>[8,6,3,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,7,4,2,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,7,3,4,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,8,4,3,2]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,5,7,3,6]=>[1,4,2,8,6,7,3,5]=>[8,5,7,1,3,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,7,2,5,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,6,2,5,3]=>[1,2,7,5,6,3,8,4]=>[8,7,2,4,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,5,1,6,2]=>[1,3,4,8,2,7,6,5]=>[8,6,5,1,7,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,1,5,8,4,6]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,7,4,1,5]=>[1,3,8,5,7,2,6,4]=>[8,6,1,4,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,7,8,1,6,5]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,7,5,6,8,2]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,7,4,2,5]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,1,4,2,3]=>[1,6,4,7,2,5,3,8]=>[8,3,5,2,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,5,3,8,2]=>[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,5,8,4,7]=>[1,6,8,7,4,2,3,5]=>[8,3,1,2,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,8,5,3,6]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,2,4,1,3]=>[1,5,2,6,4,7,3,8]=>[8,4,7,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,1,2,4,3]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,7,5,6,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,1,6,3,5]=>[1,7,3,8,5,2,4,6]=>[8,2,6,1,4,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,6,5,3,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,4,6,3,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,7,1,6,3]=>[1,4,5,7,6,2,8,3]=>[8,5,4,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,5,3,7,2]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,8,3,1,7]=>[1,5,8,7,2,3,6,4]=>[8,4,1,2,7,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,4,5,8,2]=>[1,6,5,4,3,2,7,8]=>[8,3,4,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,4,8,5,6]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,3,4,8,2]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,2,8,7,5,1]=>[1,6,7,5,8,2,3,4]=>[8,3,2,4,1,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,2,3,5,1]=>[1,6,3,7,5,2,8,4]=>[8,3,6,2,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,5,4,2,7]=>[1,8,7,2,6,4,3,5]=>[8,1,2,7,3,5,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,1,2,4,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,8,7,4,1]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,8,7,2,1]=>[1,6,7,2,3,5,8,4]=>[8,3,2,7,6,4,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,5,3,8,1]=>[1,4,2,7,8,3,6,5]=>[8,5,7,2,1,6,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,8,1,4,3]=>[1,7,4,6,2,5,8,3]=>[8,2,5,3,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,8,6,2,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,8,6,2,7]=>[1,5,8,7,2,4,3,6]=>[8,4,1,2,7,5,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,8,3,7,6,1]=>[1,4,8,2,5,3,6,7]=>[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,6,4,5,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,7,6,3,1]=>[1,5,7,3,2,8,4,6]=>[8,4,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,3,4,7,1]=>[1,6,4,5,3,2,8,7]=>[8,3,5,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,6,4,8,1,3]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,8,2,3,5]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,8,2,6,4]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,5,6,7,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,2,6,7,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,8,5,4,6]=>[1,3,7,4,2,5,8,6]=>[8,6,2,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,7,2,8,5]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,7,2,3,6]=>[1,2,5,7,3,8,6,4]=>[8,7,4,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,5,8,1,3]=>[1,6,8,3,7,2,4,5]=>[8,3,1,6,2,7,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,5,7,3,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,4,3,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,5,3,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,6,3,8,5]=>[1,2,7,8,5,6,3,4]=>[8,7,2,1,4,3,6,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,8,1,3,2]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,1,3,6,7]=>[1,2,8,7,6,3,5,4]=>[8,7,1,2,3,6,4,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,2,3,8,6]=>[1,5,2,3,7,8,6,4]=>[8,4,7,6,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,6,5,2,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,7,3,6,1]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,3,7,6,1]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,2,3,6,1]=>[1,8,2,4,5,3,7,6]=>[8,1,7,5,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,8,4,6,1,3]=>[1,7,2,5,4,8,3,6]=>[8,2,7,4,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,6,2,8,1]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,2,8,3,4]=>[1,6,8,4,2,7,3,5]=>[8,3,1,5,7,2,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,3,4,7,1]=>[1,5,3,6,4,8,2,7]=>[8,4,6,3,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,5,8,3,1]=>[1,7,3,2,6,8,4,5]=>[8,2,6,7,3,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,7,2,5,1]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,4,2,5,1]=>[1,7,5,4,8,2,6,3]=>[8,2,4,5,1,7,3,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,8,3,1,4]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,8,3,7,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,6,4,7,3]=>[1,5,6,4,2,8,3,7]=>[8,4,3,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,2,7,4,5]=>[1,2,6,7,4,3,8,5]=>[8,7,3,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,8,4,1,3]=>[1,6,4,2,5,8,3,7]=>[8,3,5,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,4,3,6,1]=>[1,5,4,7,6,3,2,8]=>[8,4,5,2,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,4,8,2,1]=>[1,5,4,6,8,2,7,3]=>[8,4,5,3,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,8,2,7,3]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,5,7,8,4]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,5,7,8,2]=>[1,2,4,3,6,7,8,5]=>[8,7,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,4,7,8,2]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,2,7,8,5]=>[1,3,2,6,7,8,5,4]=>[8,6,7,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,1,7,8,5]=>[1,2,4,3,6,7,8,5]=>[8,7,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,2,7,8,4]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,3,8,5,7]=>[1,2,3,6,8,7,5,4]=>[8,7,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,5,8,7,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,8,5,4,7]=>[1,2,3,6,5,8,7,4]=>[8,7,6,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,6,8,3,5]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,1,8,4,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,4,8,6,2]=>[1,3,7,6,8,2,4,5]=>[8,6,2,3,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,4,8,5,3]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,6,8,5,4]=>[1,2,3,7,5,6,8,4]=>[8,7,6,2,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,8,5,7,4]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,8,7,6,2]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,4,7,3,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,5,4,7,3]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,5,2,7,4]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,8,2,1,6]=>[1,3,7,2,5,8,6,4]=>[8,6,2,7,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,6,8,3,1,5]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,3,5,2,7]=>[1,2,4,8,7,3,6,5]=>[8,7,5,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,5,2,4,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,5,4,3,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,4,3,7,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,2,4,7,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,2,5,4,7]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,3,2,5,7]=>[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,8,1,2,6]=>[1,3,7,2,5,8,6,4]=>[8,6,2,7,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,5,8,2,3]=>[1,4,7,2,6,8,3,5]=>[8,5,2,7,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,5,8,1,4]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,6,8,2,4]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,8,1,7,4]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,5,8,3,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,3,8,5,4]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,3,8,6,4]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,8,7,5,3]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,8,7,1,4]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,6,8,5,3]=>[1,2,3,7,5,6,8,4]=>[8,7,6,2,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,6,8,4,3]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,5,8,4,2]=>[1,3,6,8,2,4,7,5]=>[8,6,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,5,8,3,1]=>[1,4,7,3,2,6,8,5]=>[8,5,2,6,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,6,8,3,5,1]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,2,5,7,4]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,2,7,4,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,4,7,6,3]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,7,3,6,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,7,4,3,6]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,7,2,4,6]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,8,5,1,4]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,5,7,4,3]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,7,4,6,3]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,7,6,3,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,2,8,1,6]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,6,8,1,5]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,7,1,4,8]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,4,7,1,5,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,4,5,8,1,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,6,8,1,2]=>[1,3,4,5,6,8,2,7]=>[8,6,5,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,6,8,1,4]=>[1,2,5,6,8,4,3,7]=>[8,7,4,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,3,8,1,5]=>[1,4,2,7,3,6,8,5]=>[8,5,7,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,4,8,1,6]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,5,8,1,3]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,3,4,8,1,7]=>[1,6,8,7,2,5,4,3]=>[8,3,1,2,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,3,7,1,4,8]=>[1,6,2,5,7,4,3,8]=>[8,3,7,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,3,4,6,8]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,3,4,6,7]=>[1,5,3,2,4,8,7,6]=>[8,4,6,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,8,4,6,5]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,8,5,7,2]=>[1,6,5,8,2,4,3,7]=>[8,3,4,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,7,1,4,6]=>[1,8,6,2,3,5,7,4]=>[8,1,3,7,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,1,5,3]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,6,1,4,7]=>[1,8,7,4,3,2,5,6]=>[8,1,2,5,6,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,2,4,5,1]=>[1,8,2,6,4,7,5,3]=>[8,1,7,3,5,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,4,5,6,1]=>[1,8,2,3,7,6,5,4]=>[8,1,7,6,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,3,4,5,7]=>[1,8,7,5,3,6,4,2]=>[8,1,2,4,6,3,5,7]=>[8,2,3,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,4,5,6,2]=>[1,8,2,3,7,6,5,4]=>[8,1,7,6,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,4,5,6,1]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,3,4,5,6,1]=>[1,7,6,5,4,3,8,2]=>[8,2,3,4,5,6,1,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,4,5,6,2]=>[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,3,6,7,2]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,8,3,6,4]=>[1,2,5,8,4,3,7,6]=>[8,7,4,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,8,4,5,3]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,8,5,6,2]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,4,5,7,3]=>[1,2,6,5,4,8,3,7]=>[8,7,3,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,8,2,7,5]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,6,8,2,7,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,7,1,2,3]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,7,1,2,6]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,1,4,6,5]=>[1,3,8,5,2,4,7,6]=>[8,6,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,2,4,6,5]=>[1,3,8,5,2,4,7,6]=>[8,6,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,1,2,4,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,5,1,4,7]=>[1,6,2,8,7,4,3,5]=>[8,3,7,1,2,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,2,6,1,3,5]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,4,5,6,2]=>[1,3,7,6,5,4,2,8]=>[8,6,2,3,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,3,4,5,7]=>[1,2,8,7,5,3,6,4]=>[8,7,1,2,4,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,3,4,5,8]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,3,4,5,8]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,3,4,5,7]=>[1,2,8,7,5,3,6,4]=>[8,7,1,2,4,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,4,5,6,1]=>[1,2,8,3,7,6,5,4]=>[8,7,1,6,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,4,5,6,1]=>[1,3,7,6,5,4,2,8]=>[8,6,2,3,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,2,4,5,1]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,2,3,6,4]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,4,5,2]=>[1,8,2,7,5,3,6,4]=>[8,1,7,2,4,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,7,1,8,5]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,5,1,8,6]=>[1,3,7,8,6,2,4,5]=>[8,6,2,1,3,7,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,8,5,3,7]=>[1,2,3,6,5,8,7,4]=>[8,7,6,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,5,7,1,4,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,7,5,4,6]=>[1,2,3,8,6,5,7,4]=>[8,7,6,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,8,5,4,7]=>[1,6,5,8,7,4,2,3]=>[8,3,4,1,2,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,8,4,3,7]=>[1,5,8,7,3,2,6,4]=>[8,4,1,2,6,7,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,7,4,2,5]=>[1,2,6,4,8,5,7,3]=>[8,7,3,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,2,6,7,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,5,1,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,6,1,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,1,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,1,7,9]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,6,8,7,1,2,5,4]=>[1,3,8,4,7,5,2,6]=>[8,6,1,5,2,4,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,4,7,1,3]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,4,8,1,3]=>[1,6,8,3,7,2,5,4]=>[8,3,1,6,2,7,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,5,8,7,2]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,4,8,7,6]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,1,4,6,8]=>[1,3,5,2,7,6,4,8]=>[8,6,4,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,7,4,1,6]=>[1,3,5,7,2,8,6,4]=>[8,6,4,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,7,3,1,6]=>[1,5,7,2,3,8,6,4]=>[8,4,2,7,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,1,3,6,8]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,2,8,7,6]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,2,8,7,3]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,1,8,7,2]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,7,2,1,6]=>[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,2,1,6,3]=>[1,8,3,7,6,2,4,5]=>[8,1,6,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,2,3,6,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,3,4,6,2]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,7,4,2,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,5,7,1,2,3]=>[1,6,2,4,5,7,3,8]=>[8,3,7,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,3,7,2,5]=>[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,3,8,1,2]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,5,8,1,2]=>[1,4,7,2,6,8,3,5]=>[8,5,2,7,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,8,6,2,7]=>[1,4,5,8,7,2,3,6]=>[8,5,4,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,8,1,2,6]=>[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,7,6,5,2]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,1,6,5,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,7,6,4,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,6,5,4,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,7,5,4,2]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,8,5,1,4]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,5,6,1,4]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,5,6,4,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,5,7,4,2]=>[1,8,2,3,4,6,7,5]=>[8,1,7,6,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,6,1,5,7]=>[1,8,7,5,6,2,3,4]=>[8,1,2,4,3,7,6,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,4,3,6,2]=>[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,3,2,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,4,2,5,8]=>[1,7,5,4,3,6,2,8]=>[8,2,4,5,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,4,2,5,3]=>[1,6,2,8,3,7,5,4]=>[8,3,7,1,6,2,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,2,7,5,8]=>[1,3,2,6,7,5,4,8]=>[8,6,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,5,7,6,2]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,2,8,4,7]=>[1,3,5,2,6,8,7,4]=>[8,6,4,7,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,7,2,1,4]=>[1,3,5,7,2,8,4,6]=>[8,6,4,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,2,4,3,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,4,2,3,7]=>[1,8,7,3,6,2,5,4]=>[8,1,2,6,3,7,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,7,1,3,2]=>[1,8,2,6,3,5,7,4]=>[8,1,7,3,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,7,2,3,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,7,2,4,5]=>[1,8,5,7,4,2,3,6]=>[8,1,4,2,5,7,6,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,7,3,4,2]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,6,8,4,2]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,5,8,3,2]=>[1,7,3,2,4,6,8,5]=>[8,2,6,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,7,6,3,2]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,6,7,3,4]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,8,7,3,6]=>[1,4,5,8,6,7,3,2]=>[8,5,4,1,3,2,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,6,1,7,3,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,8,7,4,2]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,6,1,8,2,7]=>[1,3,4,6,8,7,2,5]=>[8,6,5,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,8,7,2,3]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,7,2,8,5]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,5,2,8,4]=>[1,2,7,8,4,6,3,5]=>[8,7,2,1,5,3,6,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,4,1,7,3]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,5,4,1,8]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,5,4,3,1,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,6,3,1,8]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,6,2,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,1,6,4,3]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,5,1,7,4]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,4,1,6,3]=>[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,6,1,7,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,2,8,5,4]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,2,7,5,4]=>[1,8,4,6,7,5,2,3]=>[8,1,5,3,2,4,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,3,8,6,5]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,2,7,5,4]=>[1,3,8,4,6,7,5,2]=>[8,6,1,5,3,2,4,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,2,7,4,3]=>[1,5,2,6,7,4,8,3]=>[8,4,7,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,1,7,5,4]=>[1,3,8,4,6,7,5,2]=>[8,6,1,5,3,2,4,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,6,5,4,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,6,5,4,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,6,5,4,2]=>[1,3,7,4,2,8,5,6]=>[8,6,2,5,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,1,6,3,2]=>[1,4,5,2,8,3,7,6]=>[8,5,4,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,4,1,7,2]=>[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,1,6,4,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,2,7,5,3]=>[1,2,4,6,7,5,3,8]=>[8,7,5,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,8,1,3,2]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,2,8,6,4]=>[1,7,6,8,4,2,3,5]=>[8,2,3,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,3,8,7,5]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,4,8,6,5]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,3,8,5,4]=>[1,7,5,3,2,4,6,8]=>[8,2,4,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,6,4,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,7,3,8,6]=>[1,4,2,5,7,8,6,3]=>[8,5,7,4,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,2,8,4,3]=>[1,5,2,6,8,3,7,4]=>[8,4,7,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,2,8,6,3]=>[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,2,8,5,4]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,8,6,5,4]=>[1,2,7,5,8,4,3,6]=>[8,7,2,4,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,7,5,4,3]=>[1,8,3,2,6,5,7,4]=>[8,1,6,7,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,8,6,5,4]=>[1,2,7,5,8,4,3,6]=>[8,7,2,4,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,6,5,4,3]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,2,7,5,4]=>[1,3,2,8,4,6,7,5]=>[8,6,7,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,2,7,6,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,2,7,4,3]=>[1,5,2,6,7,4,3,8]=>[8,4,7,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,7,4,8,6,5]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,6,8,1,5]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,2,8,1,7]=>[1,5,2,3,6,8,7,4]=>[8,4,7,6,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,4,7,5,1,8]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,5,8,1,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,2,8,1,5]=>[1,7,2,3,6,8,5,4]=>[8,2,7,6,3,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,2,8,1,3]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,8,2,7,6]=>[1,5,8,6,2,4,3,7]=>[8,4,1,3,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,7,3,1,8]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,2,6,3,8]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,3,2,6,7]=>[1,5,3,2,4,8,7,6]=>[8,4,6,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,3,4,7,1]=>[1,6,4,8,2,5,3,7]=>[8,3,5,1,7,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,8,2,7,1]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,8,2,7,5]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,7,3,1,6]=>[1,5,7,2,8,6,3,4]=>[8,4,2,7,1,3,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,7,3,1,5]=>[1,8,5,7,2,3,6,4]=>[8,1,4,2,7,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,7,4,1,3]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,4,3,1,8]=>[1,7,2,5,4,6,3,8]=>[8,2,7,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,5,6,4,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,3,2,4,5]=>[1,2,7,4,8,5,3,6]=>[8,7,2,5,1,4,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,4,2,6,3]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,3,2,5,7]=>[1,6,2,3,8,7,5,4]=>[8,3,7,6,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,2,5,3,8]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,4,6,5,8]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,3,5,6,2]=>[1,2,7,6,5,3,8,4]=>[8,7,2,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,3,5,7,4]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,3,5,4,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,4,2,6,7]=>[1,3,5,4,8,7,6,2]=>[8,6,4,5,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,8,2,7,5]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,3,2,1,6]=>[1,5,3,4,8,6,2,7]=>[8,4,6,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,7,3,1,6]=>[1,5,7,2,4,3,8,6]=>[8,4,2,7,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,3,4,1,6]=>[1,5,3,8,6,4,7,2]=>[8,4,6,1,3,5,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,3,2,1,8]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,6,2,4,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,6,4,1,5]=>[1,7,2,3,8,5,6,4]=>[8,2,7,6,1,4,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,7,3,1,5]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,2,5,4,3]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,5,6,1,2]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,3,5,1,7]=>[1,2,8,7,3,6,5,4]=>[8,7,1,2,6,3,4,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,5,4,1,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,2,4,3,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,3,2,4,7]=>[1,2,8,7,4,5,3,6]=>[8,7,1,2,5,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,6,2,4,1]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,5,2,3,4]=>[1,7,3,8,4,6,2,5]=>[8,2,6,1,5,3,7,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,5,4,7,1]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,4,3,6,2]=>[1,2,5,4,8,3,7,6]=>[8,7,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,5,4,7,2]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,4,1,3,8]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,4,3,7,1]=>[1,2,5,4,8,3,6,7]=>[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,8,1,6,3]=>[1,2,4,5,8,3,7,6]=>[8,7,5,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,1,8,6,3]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,7,6,4,3]=>[1,5,7,4,8,3,2,6]=>[8,4,2,5,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,5,3,1,2]=>[1,4,7,2,8,3,6,5]=>[8,5,2,7,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,2,1,7,3]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,8,2,6,3]=>[1,2,5,8,3,7,6,4]=>[8,7,4,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,2,8,6,4]=>[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,7,6,4,1]=>[1,5,7,4,2,8,3,6]=>[8,4,2,5,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,3,6,7,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,2,6,1,8]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,5,1,2,7,8]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,7,6,2,8]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,1,6,2,8]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,6,1,2,8]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,6,7,1,2]=>[1,3,5,6,7,2,4,8]=>[8,6,4,3,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,6,8,7,2]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,6,8,7,3]=>[1,4,5,6,8,3,2,7]=>[8,5,4,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,10,9,7,8]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,6,5,3,4,8,7,10,9]=>[1,2,3,6,4,5,7,8,9,10]=>[10,9,8,5,7,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,7,3,8,4,6,5]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,7,3,6,5]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,8,3,6,5]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,8,4,6,5]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,4,3,6,5]=>[1,7,6,3,8,5,4,2]=>[8,2,3,6,1,4,5,7]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,5,3,6,4]=>[1,8,4,2,3,7,6,5]=>[8,1,5,7,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,8,3,6,4]=>[1,7,6,3,5,8,4,2]=>[8,2,3,6,4,1,5,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,8,3,6,4]=>[1,5,8,4,2,3,7,6]=>[8,4,1,5,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,7,3,6,4]=>[1,5,7,6,3,8,4,2]=>[8,4,2,3,6,1,5,7]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,4,3,7,6]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,4,3,7,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,4,3,7,5]=>[1,6,3,8,5,4,2,7]=>[8,3,6,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,5,3,7,4]=>[1,6,3,8,4,2,5,7]=>[8,3,6,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,7,3,5,4]=>[1,6,3,8,4,2,5,7]=>[8,3,6,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,8,3,5,4]=>[1,6,3,7,5,8,4,2]=>[8,3,6,2,4,1,5,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,4,3,8,5]=>[1,6,3,7,8,5,4,2]=>[8,3,6,2,1,4,5,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,4,3,8,7]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,4,3,8,6]=>[1,7,8,6,3,5,4,2]=>[8,2,1,3,6,4,5,7]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,4,3,8,5]=>[1,7,8,5,4,2,3,6]=>[8,2,1,4,5,7,6,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,5,3,8,4]=>[1,7,8,4,2,3,6,5]=>[8,2,1,5,7,6,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,6,3,5,4]=>[1,7,5,6,3,8,4,2]=>[8,2,4,3,6,1,5,7]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,5,4,6,3]=>[1,2,8,3,4,7,6,5]=>[8,7,1,6,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,4,3,5,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,7,2,3,5]=>[1,2,8,5,7,3,6,4]=>[8,7,1,4,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,6,3,5,7]=>[1,2,8,7,5,6,3,4]=>[8,7,1,2,4,3,6,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,6,3,5,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,3,6,2,8]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,2,4,1,6]=>[1,7,2,5,3,8,6,4]=>[8,2,7,4,6,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,3,7,2,6]=>[1,2,8,6,7,3,5,4]=>[8,7,1,3,2,6,4,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,7,2,6,3]=>[1,2,8,3,5,7,6,4]=>[8,7,1,6,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,5,3,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,2,6,7,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,2,3,6,1]=>[1,7,6,3,4,8,2,5]=>[8,2,3,6,5,1,7,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,1,3,7,5]=>[1,6,3,8,5,2,4,7]=>[8,3,6,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,5,6,2,4]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,6,8,4,5]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,2,6,8,3]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,1,2,8,6]=>[1,5,2,4,7,8,6,3]=>[8,4,7,5,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,2,5,7,8]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,7,1,8,2]=>[1,6,2,5,7,8,3,4]=>[8,3,7,4,2,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,1,6,8,3]=>[1,5,2,4,7,8,3,6]=>[8,4,7,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,3,8,2,4]=>[1,6,8,4,7,2,5,3]=>[8,3,1,5,2,7,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,5,7,1,4]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,8,2,7,1]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,6,1,3,2]=>[1,7,3,4,8,2,5,6]=>[8,2,6,5,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,7,5,2,4]=>[1,6,5,7,2,3,8,4]=>[8,3,4,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,1,7,4,2]=>[1,6,7,4,3,8,2,5]=>[8,3,2,5,6,1,7,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,1,7,3,6]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,1,6,2,7]=>[1,5,2,4,8,7,3,6]=>[8,4,7,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,1,6,2,8]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,5,1,3,7]=>[1,6,2,4,8,7,3,5]=>[8,3,7,5,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,3,6,4,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,8,2,3,5]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,2,7,6,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,3,8,1,6]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,2,8,6,7]=>[1,4,3,5,2,6,8,7]=>[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,8,7,4,5]=>[1,3,6,7,4,2,5,8]=>[8,6,3,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,8,5,2,4]=>[1,6,5,8,4,7,2,3]=>[8,3,4,1,5,2,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,8,2,6,3]=>[1,5,8,3,2,4,7,6]=>[8,4,1,6,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,7,8,3,2]=>[1,6,8,2,5,7,3,4]=>[8,3,1,7,4,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,6,7,2,8]=>[1,5,6,7,2,4,3,8]=>[8,4,3,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,7,8,3,1]=>[1,6,8,2,5,7,3,4]=>[8,3,1,7,4,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,3,8,7,1]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,2,6,8,7]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,6,7,8,3]=>[1,5,6,7,8,3,2,4]=>[8,4,3,2,1,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,6,7,8,2]=>[1,5,6,7,8,2,4,3]=>[8,4,3,2,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,2,5,7,4]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,2,5,8,4]=>[1,3,7,8,4,2,6,5]=>[8,6,2,1,5,7,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,2,5,6,4]=>[1,7,6,5,2,8,4,3]=>[8,2,3,4,7,1,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,2,4,6,5]=>[1,7,6,4,3,2,8,5]=>[8,2,3,5,6,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,3,5,4,6]=>[1,7,4,2,8,6,5,3]=>[8,2,5,7,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,1,8,6,4]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,1,8,7,4]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,1,8,4,5]=>[1,2,6,8,5,3,7,4]=>[8,7,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,3,5,4,8]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,1,7,4,5]=>[1,6,7,4,3,8,5,2]=>[8,3,2,5,6,1,4,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,1,8,4,6]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,7,8,6,5]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,3,6,4,8]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,8,2,3,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,8,2,3,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,2,4,8,5]=>[1,2,6,4,3,7,8,5]=>[8,7,3,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,2,7,8,4]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,2,6,8,4]=>[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,7,8,1,6,3]=>[1,5,8,3,4,7,6,2]=>[8,4,1,6,5,2,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,6,1,8,3]=>[1,4,7,8,3,5,6,2]=>[8,5,2,1,6,4,3,7]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,2,6,7,4]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,2,4,7,5]=>[1,6,4,3,8,5,2,7]=>[8,3,5,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,3,6,4,7]=>[1,5,3,2,4,8,7,6]=>[8,4,6,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,8,7,5,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,2,1,8,3]=>[1,7,8,3,5,2,6,4]=>[8,2,1,6,4,7,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,8,1,3,2]=>[1,7,3,5,8,2,6,4]=>[8,2,6,4,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,1,7,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,1,8,3,2]=>[1,7,3,5,2,6,8,4]=>[8,2,6,4,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,8,1,4,3]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,1,3,2]=>[1,7,3,5,4,8,2,6]=>[8,2,6,4,5,1,7,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,2,1,4,3]=>[1,7,4,5,2,6,3,8]=>[8,2,5,4,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,2,1,5,4]=>[1,7,5,2,8,4,3,6]=>[8,2,4,7,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,2,1,6,5]=>[1,8,5,2,7,6,3,4]=>[8,1,4,7,2,3,6,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,9,10,4,5,6,2,1,3]=>[1,7,6,5,4,10,3,9,2,8]=>[10,4,5,6,7,1,8,2,9,3]=>[10,9,8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,2,4,5,1,3,6]=>[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,5,1,3,8]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,2,4,5,6]=>[1,7,5,2,8,6,4,3]=>[8,2,4,7,1,3,5,6]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,5,2,3,6]=>[1,7,3,4,2,8,6,5]=>[8,2,6,5,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,1,4,5,8]=>[1,3,7,5,2,6,4,8]=>[8,6,2,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,1,4,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,1,4,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,1,4,5,8]=>[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,5,2,3,8]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,5,8,1,2]=>[1,4,3,7,2,6,8,5]=>[8,5,6,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,5,2,3,8]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,1,4,7,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,1,4,7,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,7,2,3,8]=>[1,5,7,3,4,6,2,8]=>[8,4,2,6,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,7,2,3,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,2,4,5,8]=>[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,2,4,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,6,2,4,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,6,7,1,3,8]=>[1,5,7,3,4,6,2,8]=>[8,4,2,6,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,7,1,3,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,5,1,3,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,5,1,3,8]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,7,1,3,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,7,1,3,8]=>[1,4,6,2,5,7,3,8]=>[8,5,3,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,2,4,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,5,2,3,8]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,5,8,1,2]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,7,2,3,8]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,3,4,7,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,4,1,6,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,2,1,6,8]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,4,1,6,8]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,1,4,3,8]=>[1,7,3,5,2,6,4,8]=>[8,2,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,5,2,8,4]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,6,2,5,8]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,6,5,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,5,6,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,1,6,4,8]=>[1,7,4,5,2,3,6,8]=>[8,2,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,1,3,2,8]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,5,2,6,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,2,5,8,4]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,6,2,8,5,3]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,7,2,6,8,5]=>[1,4,7,8,5,2,3,6]=>[8,5,2,1,4,7,6,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,7,3,8,2]=>[1,5,7,8,2,6,3,4]=>[8,4,2,1,7,3,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,7,4,8,6]=>[1,5,7,8,6,4,2,3]=>[8,4,2,1,3,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,8,7,2,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,6,8,7,3]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,6,8,7,4]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,6,8,1,2]=>[1,3,5,6,8,2,7,4]=>[8,6,4,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,5,8,2,7]=>[1,3,4,6,8,7,2,5]=>[8,6,5,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,6,1,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,1,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,6,8,2,1]=>[1,3,5,6,8,2,7,4]=>[8,6,4,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,7,5,6,8,2]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,7,6,5,8,2]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,6,8,7,3]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,6,8,1,4]=>[1,3,5,6,8,4,2,7]=>[8,6,4,3,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,6,8,4,1]=>[1,3,5,6,8,2,7,4]=>[8,6,4,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,4,7,8,1]=>[1,6,7,8,2,3,5,4]=>[8,3,2,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,4,7,8,6]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,2,7,8,6]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,4,7,8,6]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,6,8,4,3]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,6,1,8,5,3]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,1,5,8,4]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,5,1,8,4]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,7,1,8,5]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,6,8,1,4]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,6,8,2,3]=>[1,7,2,3,5,6,8,4]=>[8,2,7,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,8,6,1,2]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,8,1,6,2]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,8,1,2,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,8,6,2,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,8,2,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,8,6,2,1]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,6,8,3,2]=>[1,7,3,5,6,8,2,4]=>[8,2,6,4,3,1,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,1,8,3,2]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,8,2,1,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,8,2,6,1]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,8,2,5,3]=>[1,4,2,7,5,8,3,6]=>[8,5,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,7,5,2,3]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,2,6,1,5,3]=>[1,4,2,7,5,6,3,8]=>[8,5,7,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,8,3,5,1]=>[1,7,5,8,2,6,3,4]=>[8,2,4,1,7,3,6,5]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,7,5,3,1]=>[1,8,2,6,5,7,3,4]=>[8,1,7,3,4,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,5,1,2]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,5,3,2]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,8,3,2,5]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,6,1,5,2]=>[1,7,5,6,2,4,3,8]=>[8,2,4,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,6,2,5,1]=>[1,7,5,6,2,8,3,4]=>[8,2,4,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,3,5,4,7]=>[1,2,3,8,7,4,6,5]=>[8,7,6,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,3,6,7,5]=>[1,4,8,5,3,2,6,7]=>[8,5,1,4,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,3,5,7,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,1,4,8,5,6]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,4,5,7,8]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,7,8,4,6]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,6,8,4,5]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,6,1,8,2]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,5,1,7,2]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,3,5,7,4]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,3,7,4,5]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,5,7,4,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,6,8,4,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,7,4,6,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,5,1,6,2]=>[1,3,4,7,6,2,8,5]=>[8,6,5,2,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,1,7,5,2]=>[1,8,2,4,6,7,5,3]=>[8,1,7,5,3,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,3,5,4,6]=>[1,8,6,5,3,2,4,7]=>[8,1,3,4,6,7,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,3,5,4,7]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,1,5,6,4,8]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,1,6,3,8]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,7,5,3,6]=>[1,8,6,5,7,3,4,2]=>[8,1,3,4,2,6,5,7]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,8,5,3,6]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,1,6,3,7]=>[1,2,4,5,3,8,7,6]=>[8,7,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,3,4,8,5]=>[1,6,4,7,8,5,3,2]=>[8,3,5,2,1,4,6,7]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,8,3,5,4]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,6,4,5,7]=>[1,2,3,8,7,5,6,4]=>[8,7,6,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,7,4,5,8]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,4,5,6,8]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,4,5,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,6,7,4,5]=>[1,2,3,8,5,6,7,4]=>[8,7,6,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,1,6,7,3]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,6,1,7,2]=>[1,4,5,6,2,3,8,7]=>[8,5,4,3,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,4,5,6,7]=>[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,7,2,4,5]=>[1,2,6,3,8,5,7,4]=>[8,7,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,4,7,3,5]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,2,4,7,3]=>[1,6,4,8,3,5,2,7]=>[8,3,5,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,3,6,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,8,3,6,5]=>[1,4,7,6,3,2,5,8]=>[8,5,2,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,8,6,1,2]=>[1,3,7,2,5,8,4,6]=>[8,6,2,7,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,7,6,1,2]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,5,4,6,3]=>[1,8,3,2,7,6,4,5]=>[8,1,6,7,2,3,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,3,7,6,4]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,3,5,7,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,7,6,4,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,8,4,5,3]=>[1,7,5,8,3,6,4,2]=>[8,2,4,1,6,3,5,7]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,8,5,4,7]=>[1,2,3,6,5,8,7,4]=>[8,7,6,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,3,6,4,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,8,5,4,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,8,6,3,5]=>[1,4,7,3,2,5,8,6]=>[8,5,2,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,4,3,5,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,7,3,5,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,2,4,5,7]=>[1,2,8,7,5,3,6,4]=>[8,7,1,2,4,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,8,4,5,6]=>[1,2,7,5,8,6,4,3]=>[8,7,2,4,1,3,5,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,4,5,6,3]=>[1,2,8,3,7,6,5,4]=>[8,7,1,6,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,5,6,2,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,7,4,5,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,6,4,5,7]=>[1,2,8,7,5,6,4,3]=>[8,7,1,2,4,3,5,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,2,4,5,8]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,3,7,5,6]=>[1,2,3,8,6,7,5,4]=>[8,7,6,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,2,4,6,3]=>[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,6,1,2]=>[1,5,4,7,2,3,8,6]=>[8,4,5,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,7,4,5,3]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,8,6,4,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,3,6,4,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,7,5,4,8]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,5,4,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,6,5,1,2]=>[1,3,4,8,2,7,5,6]=>[8,6,5,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,6,4,5,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,5,1,4,3]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,1,5,8,4]=>[1,2,7,8,4,3,6,5]=>[8,7,2,1,5,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,6,5,2,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,5,3,2,7]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,6,5,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,3,5,2,8]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,5,2,6,8]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,4,6,5,8]=>[1,7,5,4,2,3,6,8]=>[8,2,4,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,4,5,2,7]=>[1,2,8,7,3,6,5,4]=>[8,7,1,2,6,3,4,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,4,2,5,3]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,4,8,5,7]=>[1,3,2,6,8,7,5,4]=>[8,6,7,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,5,2,8,6]=>[1,3,7,8,6,2,4,5]=>[8,6,2,1,3,7,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,1,5,8,2]=>[1,3,7,8,2,6,5,4]=>[8,6,2,1,7,3,4,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,1,2,3,7]=>[1,5,2,4,6,3,8,7]=>[8,4,7,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,4,3,1,2]=>[1,5,4,7,2,6,3,8]=>[8,4,5,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,4,3,6,5]=>[1,2,8,5,4,7,6,3]=>[8,7,1,4,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,3,2,4]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,6,3,7,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,6,4,7,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,5,8,2,7]=>[1,4,3,6,8,7,2,5]=>[8,5,6,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,3,2,7,6,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,2,6,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,6,5,8,3]=>[1,4,7,8,3,2,5,6]=>[8,5,2,1,6,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,7,8,5,3]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,6,2,7,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,2,8,1,4]=>[1,5,2,6,8,4,3,7]=>[8,4,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,6,8,4,1]=>[1,2,5,6,8,3,7,4]=>[8,7,4,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,2,8,6,7]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,1,2,6,5]=>[1,3,7,6,2,4,8,5]=>[8,6,2,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,1,4,5,2]=>[1,3,7,5,2,6,4,8]=>[8,6,2,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,1,5,4,7]=>[1,3,2,6,5,4,8,7]=>[8,6,7,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,5,1,4,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,5,1,4]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,4,6,1,2]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,8,4,1,6,3]=>[1,7,6,2,5,4,8,3]=>[8,2,3,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,3,5,1,7]=>[1,6,5,3,2,4,8,7]=>[8,3,4,6,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,3,6,2,1]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,8,3,6,2]=>[1,7,6,3,5,8,2,4]=>[8,2,3,6,4,1,7,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,8,4,6,1]=>[1,7,6,4,5,8,2,3]=>[8,2,3,5,4,1,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,2,5,1]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,8,5,1,2]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,3,4,1,7]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,7,5,3,1]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,4,3,1]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,4,3,1,7]=>[1,2,5,4,8,7,3,6]=>[8,7,4,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,4,1,3,6]=>[1,2,5,4,8,6,3,7]=>[8,7,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,4,1,3,2]=>[1,6,2,5,4,8,3,7]=>[8,3,7,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,2,4,1,3]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,8,5,1,3]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,2,4,1,7]=>[1,3,6,4,8,7,2,5]=>[8,6,3,5,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,1,4,5,3]=>[1,2,6,4,8,3,7,5]=>[8,7,3,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,1,4,2,5]=>[1,3,7,2,6,4,8,5]=>[8,6,2,7,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,2,1,4,6]=>[1,3,7,4,8,6,2,5]=>[8,6,2,5,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,1,4,3,5]=>[1,2,6,4,8,5,3,7]=>[8,7,3,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,3,1,4,2]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,3,1,4,6]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,8,1,5,6]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,8,1,5,2]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,8,1,2,5]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,8,2,1,5]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,4,8,1,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,8,2,1,7]=>[1,5,8,7,2,4,3,6]=>[8,4,1,2,7,5,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,8,1,6,2]=>[1,5,8,2,4,3,7,6]=>[8,4,1,7,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,3,1,6,4]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,3,1,2,6]=>[1,4,8,6,2,5,3,7]=>[8,5,1,3,7,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,2,3,1,7]=>[1,4,8,7,2,5,3,6]=>[8,5,1,2,7,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,8,3,1,7]=>[1,5,8,7,2,4,3,6]=>[8,4,1,2,7,5,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,8,4,1,7]=>[1,5,8,7,2,3,4,6]=>[8,4,1,2,7,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,8,1,3,6]=>[1,5,8,6,2,4,3,7]=>[8,4,1,3,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,2,1,3,6]=>[1,4,8,6,2,5,3,7]=>[8,5,1,3,7,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,1,3,2,5]=>[1,4,8,5,2,6,3,7]=>[8,5,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,1,5,3,4]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,1,5,2,3]=>[1,4,8,3,7,2,6,5]=>[8,5,1,6,2,7,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,8,1,6,3]=>[1,5,8,3,7,6,2,4]=>[8,4,1,6,2,3,7,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,8,1,6,4]=>[1,5,8,4,7,6,2,3]=>[8,4,1,5,2,3,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,1,2,5,4]=>[1,3,7,5,2,6,4,8]=>[8,6,2,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,1,5,2,4]=>[1,3,7,2,6,5,4,8]=>[8,6,2,7,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,1,5,4,3]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,1,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,1,2,10]=>[1,3,5,7,9,2,4,6,8,10]=>[10,8,6,4,2,9,7,5,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,5,6,7,8,9,2,4]=>[1,2,3,5,7,9,4,6,8]=>[9,8,7,5,3,1,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,5,6,7,8,9,10,2,3]=>[1,2,4,6,8,10,3,5,7,9]=>[10,9,7,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,9,10,11,2]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[4,2,7,1,5,3,8,6]=>[1,4,2,3,7,8,6,5]=>[8,5,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,5,1,4,8]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,5,4,8,6]=>[1,2,7,8,6,4,3,5]=>[8,7,2,1,3,5,6,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,5,8,6,3]=>[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,5,8,6,4]=>[1,7,6,8,4,3,2,5]=>[8,2,3,1,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,7,1,5,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,2,7,5,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,2,6,7,5]=>[1,3,4,8,5,2,6,7]=>[8,6,5,1,4,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,1,5,7,3]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,5,1,7,2]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,5,1,8,2]=>[1,6,2,4,3,7,8,5]=>[8,3,7,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,1,8,2,3]=>[1,6,8,3,7,2,4,5]=>[8,3,1,6,2,7,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,6,8,2,4]=>[1,7,2,3,5,6,8,4]=>[8,2,7,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,6,1,8,2]=>[1,4,5,6,2,7,8,3]=>[8,5,4,3,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,5,1,7,2]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,5,7,4,6]=>[1,2,8,6,7,4,3,5]=>[8,7,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,6,1,4,5,8]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,5,8,4,7]=>[1,2,6,8,7,4,3,5]=>[8,7,3,1,2,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,6,1,4,8]=>[1,7,4,5,6,2,3,8]=>[8,2,5,4,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,6,1,3,8]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,1,5,3,7]=>[1,4,8,7,3,2,6,5]=>[8,5,1,2,6,7,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,5,3,6]=>[1,8,6,5,7,3,2,4]=>[8,1,3,4,2,6,7,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,7,1,3,8]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,4,8,3,5]=>[1,2,6,8,5,4,7,3]=>[8,7,3,1,4,5,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,1,5,6,3]=>[1,2,7,6,5,3,8,4]=>[8,7,2,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,5,6,3,4]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,6,7,3,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,6,1,7,2]=>[1,3,4,5,6,2,8,7]=>[8,6,5,4,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,3,7,6,1,2]=>[1,4,3,8,2,5,7,6]=>[8,5,6,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,7,1,6,5]=>[1,4,3,8,5,7,6,2]=>[8,5,6,1,4,2,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,8,1,6,5]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,8,1,5,6]=>[1,7,5,8,6,2,3,4]=>[8,2,4,1,3,7,6,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,8,5,1,2]=>[1,7,2,6,5,8,3,4]=>[8,2,7,3,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,4,5,1,2]=>[1,7,2,6,5,4,8,3]=>[8,2,7,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,5,1,4,6]=>[1,7,4,8,6,2,3,5]=>[8,2,5,1,3,7,6,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,1,5,7,3]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,4,1,5,6]=>[1,7,5,4,8,6,2,3]=>[8,2,4,5,1,3,7,6]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,8,1,4,6]=>[1,7,4,5,8,6,2,3]=>[8,2,5,4,1,3,7,6]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,6,1,4,5]=>[1,7,4,3,2,8,5,6]=>[8,2,5,6,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,7,1,5,8]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,8,1,6,4]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,1,3,7,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,1,7,5,2]=>[1,3,4,8,2,6,7,5]=>[8,6,5,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,1,8,7,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,4,2,3,8]=>[1,7,3,5,4,2,6,8]=>[8,2,6,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,2,4,3,8]=>[1,7,3,5,2,6,4,8]=>[8,2,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,2,4,8,3]=>[1,7,8,3,5,2,6,4]=>[8,2,1,6,4,7,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,3,2,4,8]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,5,1,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,1,5,8,7]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,1,8,5,7]=>[1,2,6,8,7,5,3,4]=>[8,7,3,1,2,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,1,8,7,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,1,2,6,7]=>[1,3,8,7,6,2,5,4]=>[8,6,1,2,3,7,4,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,1,6,2,7]=>[1,3,8,7,2,5,4,6]=>[8,6,1,2,7,4,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,6,1,7,5]=>[1,4,3,8,5,6,2,7]=>[8,5,6,1,4,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,1,7,8,5]=>[1,3,4,2,6,7,8,5]=>[8,6,5,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,1,7,5,8]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,1,8,7,2]=>[1,3,6,8,2,5,4,7]=>[8,6,3,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,1,3,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,2,8,3,4]=>[1,7,3,5,2,6,8,4]=>[8,2,6,4,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,8,2,4,3]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,8,2,3,4]=>[1,7,3,5,8,4,2,6]=>[8,2,6,4,1,5,7,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,4,8,2,3]=>[1,7,2,6,8,3,5,4]=>[8,2,7,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,5,1,7,2,8]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,1,7,8,3]=>[1,2,5,3,6,7,8,4]=>[8,7,4,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,1,6,3,2]=>[1,7,3,5,2,8,4,6]=>[8,2,6,4,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,1,7,3,8]=>[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,5,1,7,8,2]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,4,8,3,2]=>[1,7,3,5,4,2,6,8]=>[8,2,6,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,8,3,4,2]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,6,2,8,5,3]=>[1,4,6,8,3,7,5,2]=>[8,5,3,1,6,2,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,1,3,5,4]=>[1,7,5,2,8,4,3,6]=>[8,2,4,7,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,2,8,4,5]=>[1,3,6,8,5,2,7,4]=>[8,6,3,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,1,4,8,7]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,3,2,8,7]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,2,5,8,7]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,7,8,1,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,5,2,4,3]=>[1,8,3,2,7,4,6,5]=>[8,1,6,7,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,6,8,1,3,4]=>[1,7,3,5,8,4,6,2]=>[8,2,6,4,1,5,3,7]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,1,8,7,3]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,5,7,3,2]=>[1,8,2,4,6,7,3,5]=>[8,1,7,5,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,7,5,1,6]=>[1,2,8,6,5,7,3,4]=>[8,7,1,3,4,2,6,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,5,1,6,3,2]=>[1,4,5,2,7,3,8,6]=>[8,5,4,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,7,3,5,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,7,3,2,5]=>[1,4,2,8,5,7,3,6]=>[8,5,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,1,7,2,4,6]=>[1,3,5,7,4,2,8,6]=>[8,6,4,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,3,2,4,5]=>[1,6,2,8,5,3,7,4]=>[8,3,7,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,4,5,6,2]=>[1,3,2,7,6,5,4,8]=>[8,6,7,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,6,4,5,2]=>[1,7,5,6,4,8,2,3]=>[8,2,4,3,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,6,7,4,1]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,8,6,5,3]=>[1,7,5,8,3,2,4,6]=>[8,2,4,1,6,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,5,8,3,1]=>[1,4,2,6,8,3,7,5]=>[8,5,7,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,5,3,8,1,4]=>[1,7,2,6,8,4,5,3]=>[8,2,7,3,1,5,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,3,4,8,7,5]=>[1,6,8,5,4,3,2,7]=>[8,3,1,4,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,8,1,5,3]=>[1,4,2,7,5,8,3,6]=>[8,5,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,7,8,3,2]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,7,8,6,5]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,8,6,7,5]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,3,1,2,7]=>[1,6,2,4,8,7,3,5]=>[8,3,7,5,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,5,6,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,5,2,4,7]=>[1,3,8,7,4,2,6,5]=>[8,6,1,2,5,7,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,7,4,2,1]=>[1,6,4,5,7,2,3,8]=>[8,3,5,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,5,1,2,3]=>[1,7,2,4,8,3,6,5]=>[8,2,7,5,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,7,5,3,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,3,7,5,4]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,4,1,5,7]=>[1,3,8,7,5,4,2,6]=>[8,6,1,2,4,5,7,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,8,1,3,7]=>[1,2,6,3,5,8,7,4]=>[8,7,3,6,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,8,1,7,2]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,5,1,7,6]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,5,3,6,7]=>[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,6,2,1,3,5]=>[1,7,3,8,5,2,4,6]=>[8,2,6,1,4,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,3,7,5,1]=>[1,4,8,2,6,7,5,3]=>[8,5,1,7,3,2,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,3,6,4,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,6,7,1,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,4,1,3,2]=>[1,7,3,5,4,6,2,8]=>[8,2,6,4,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,5,7,6,2]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,9,6,7,4,5,1,3,2]=>[1,8,3,6,5,4,7,2,9]=>[9,2,7,4,5,6,3,8,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,6,7,4,5,2,3,1]=>[1,8,3,6,5,4,7,2,9]=>[9,2,7,4,5,6,3,8,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,6,3,5,1,4,2]=>[1,7,4,3,6,2,8,5]=>[8,2,5,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,6,1,4,2]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,7,1,3,2]=>[1,6,2,5,7,3,8,4]=>[8,3,7,4,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,6,1,3,2]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,6,3,1,8]=>[1,7,2,4,5,6,3,8]=>[8,2,7,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,5,6,3,1,8]=>[1,4,5,6,3,7,2,8]=>[8,5,4,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,6,2,1,8]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,6,2,1,8]=>[1,4,5,6,2,7,3,8]=>[8,5,4,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,6,4,1,8]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,6,1,4,2]=>[1,7,4,5,6,2,8,3]=>[8,2,5,4,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,2,7,4,3]=>[1,2,6,7,4,5,3,8]=>[8,7,3,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,1,7,4,3]=>[1,6,7,4,5,2,3,8]=>[8,3,2,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,6,1,5,4]=>[1,3,7,5,6,2,4,8]=>[8,6,2,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,2,3,7,5]=>[1,6,3,4,2,8,5,7]=>[8,3,6,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,6,3,2,7]=>[1,4,5,6,3,8,7,2]=>[8,5,4,3,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,6,4,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,2,7,6,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,3,7,6,4]=>[1,8,4,5,3,2,6,7]=>[8,1,5,4,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,6,7,8,3]=>[1,2,5,6,7,8,3,4]=>[8,7,4,3,2,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,6,7,8,2]=>[1,4,3,5,6,7,8,2]=>[8,5,6,4,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,6,3,2,8,5]=>[1,7,8,5,3,4,6,2]=>[8,2,1,4,6,5,3,7]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,1,7,8,5]=>[1,3,6,7,8,5,2,4]=>[8,6,3,2,1,4,7,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,1,2,8,5]=>[1,7,8,5,2,6,3,4]=>[8,2,1,4,7,3,6,5]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,1,7,2,4]=>[1,8,4,5,2,6,7,3]=>[8,1,5,4,7,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,6,7,8,2]=>[1,4,2,5,6,7,8,3]=>[8,5,7,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,6,7,8,4]=>[1,3,2,5,6,7,8,4]=>[8,6,7,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,6,7,8,4]=>[1,5,6,7,8,4,2,3]=>[8,4,3,2,1,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,6,7,8,4]=>[1,2,5,6,7,8,4,3]=>[8,7,4,3,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,1,7,8,4]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,6,1,4,5]=>[1,3,8,5,6,2,4,7]=>[8,6,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,2,1,3,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,6,1,2,4]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,6,1,3,4]=>[1,8,4,5,6,2,3,7]=>[8,1,5,4,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,1,7,3,2]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,1,5,8,3]=>[1,7,8,3,4,2,6,5]=>[8,2,1,6,5,7,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,1,3,8,2]=>[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,3,1,2,5]=>[1,8,5,3,4,7,2,6]=>[8,1,4,6,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,7,1,8,6]=>[1,5,7,8,6,2,3,4]=>[8,4,2,1,3,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,7,1,8,6]=>[1,3,4,2,5,7,8,6]=>[8,6,5,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,3,5,2,7]=>[1,8,7,2,6,5,3,4]=>[8,1,2,7,3,4,6,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,2,6,8,3]=>[1,7,8,3,4,2,5,6]=>[8,2,1,6,5,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,3,7,6,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,6,4,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,2,5,3,7]=>[1,6,5,2,8,7,3,4]=>[8,3,4,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,5,2,8,3]=>[1,7,8,3,4,2,6,5]=>[8,2,1,6,5,7,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,4,7,2,3]=>[1,8,3,2,6,7,4,5]=>[8,1,6,7,3,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,6,7,8,2]=>[1,3,2,5,6,7,8,4]=>[8,6,7,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,6,7,8,3]=>[1,5,6,7,8,3,2,4]=>[8,4,3,2,1,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,6,7,8,2]=>[1,5,6,7,8,2,4,3]=>[8,4,3,2,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,3,7,2,6]=>[1,8,6,7,2,4,5,3]=>[8,1,3,2,7,5,4,6]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,3,2,8,6]=>[1,7,8,6,2,5,3,4]=>[8,2,1,3,7,4,6,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,4,7,8,6]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,5,2,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,4,7,2,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,6,7,8,2]=>[1,5,6,7,8,2,3,4]=>[8,4,3,2,1,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,5,7,4,6]=>[1,3,8,6,7,4,2,5]=>[8,6,1,3,2,5,7,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,1,4,7,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,4,3,7,5]=>[1,2,8,5,4,6,3,7]=>[8,7,1,4,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,8,7,5,4]=>[1,2,6,7,5,8,4,3]=>[8,7,3,2,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,3,8,6,4]=>[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,5,7,4,3]=>[1,2,6,7,4,3,8,5]=>[8,7,3,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,8,4,6,3]=>[1,2,7,6,4,5,8,3]=>[8,7,2,3,5,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,6,5,3,8,4]=>[1,2,7,8,4,6,3,5]=>[8,7,2,1,5,3,6,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,6,5,4,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,6,5,4,2]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,4,2,5,8]=>[1,3,6,2,7,5,4,8]=>[8,6,3,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,4,6,8,2]=>[1,3,5,4,2,7,8,6]=>[8,6,4,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,1,4,7,2]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,2,1,4,6]=>[1,7,4,8,6,2,3,5]=>[8,2,5,1,3,7,6,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,1,6,5,3]=>[1,7,5,2,4,8,3,6]=>[8,2,4,7,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,2,1,6,4]=>[1,8,4,3,5,2,7,6]=>[8,1,5,6,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,1,8,3,5]=>[1,7,3,6,8,5,2,4]=>[8,2,6,3,1,4,7,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,2,1,7,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,3,8,6,2]=>[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,5,3,2,8]=>[1,4,2,7,3,6,5,8]=>[8,5,7,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,3,8,2,4]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,4,2,8,3]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,6,4,3,2]=>[1,5,6,4,7,3,8,2]=>[8,4,3,5,2,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,3,7,2,5]=>[1,4,6,7,2,3,8,5]=>[8,5,3,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,7,3,1,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,5,7,1,2]=>[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,3,6,1,2]=>[1,5,3,8,2,4,7,6]=>[8,4,6,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,7,1,2,5]=>[1,6,2,4,8,5,7,3]=>[8,3,7,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,4,8,1,5]=>[1,6,8,5,4,2,3,7]=>[8,3,1,4,5,7,6,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,2,7,3,1]=>[1,5,2,6,7,3,8,4]=>[8,4,7,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,8,1,3,6]=>[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,1,7,3]=>[1,8,3,5,2,6,4,7]=>[8,1,6,4,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,1,8,2,5]=>[1,6,8,5,2,4,3,7]=>[8,3,1,4,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,8,6,1,2]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,8,3,5,2,1]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,4,7,6,9,8]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,1,5,4,7,6,8,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,1,5,4,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,1,5,4,7,6,9,8,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,1,5,4,7,6,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,1,5,4,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,6,3,7,4,2,1,8]=>[1,5,4,7,2,6,3,8]=>[8,4,5,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,3,2,5,7]=>[1,6,2,4,3,8,7,5]=>[8,3,7,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,6,3,1,5,2]=>[1,7,5,3,8,2,4,6]=>[8,2,4,6,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,5,3,1,8]=>[1,4,6,3,7,2,5,8]=>[8,5,3,6,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,6,5,1,8]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,5,2,6,7]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,2,5,3,7]=>[1,2,6,5,3,8,7,4]=>[8,7,3,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,1,5,7,3]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,5,1,2,3]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,5,1,6,4]=>[1,3,7,6,2,4,8,5]=>[8,6,2,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,5,4,6,7]=>[1,3,8,7,6,4,2,5]=>[8,6,1,2,3,5,7,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,2,6,7,3]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,3,7,2,5]=>[1,6,7,2,3,8,5,4]=>[8,3,2,7,6,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,4,2,5,8,6]=>[1,3,2,7,8,6,5,4]=>[8,6,7,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,5,3,2,7,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,6,3,8,5,2]=>[1,7,5,3,4,6,8,2]=>[8,2,4,6,5,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,1,8,7,5]=>[1,3,6,8,5,2,4,7]=>[8,6,3,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,8,7,6,4]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,8,6,4,7]=>[1,2,5,8,7,4,3,6]=>[8,7,4,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,7,8,6,3]=>[1,5,7,6,8,3,2,4]=>[8,4,2,3,1,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,5,1,3,4]=>[1,8,4,6,2,3,7,5]=>[8,1,5,3,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,2,8,5,4]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,1,8,5,4]=>[1,7,5,2,6,8,4,3]=>[8,2,4,7,3,1,5,6]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,4,1,2,5]=>[1,8,5,4,7,2,6,3]=>[8,1,4,5,2,7,3,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,7,1,8,6]=>[1,5,7,8,6,2,3,4]=>[8,4,2,1,3,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,4,5,7,2]=>[1,8,2,6,5,4,3,7]=>[8,1,7,3,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,5,4,2,8]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,4,5,6,7]=>[1,8,7,6,5,4,2,3]=>[8,1,2,3,4,5,7,6]=>[8,2,3,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,2,3,6,5]=>[1,8,5,2,4,7,6,3]=>[8,1,4,7,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,5,4,7,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,6,4,7,2]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,2,5,7,3]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,5,2,3,8]=>[1,7,3,4,2,6,5,8]=>[8,2,6,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,4,7,3,2]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,6,7,2,8]=>[1,3,2,5,6,7,4,8]=>[8,6,7,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,7,6,3,8]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,1,3,7,6]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,1,4,6,7]=>[1,5,2,8,7,6,4,3]=>[8,4,7,1,2,3,5,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,6,2,8,7]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,3,6,2,7]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,4,6,8,7]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,5,6,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,4,6,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,6,2,7,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,5,7,6,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,4,7,6,9,8]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,5,2,7,4,9,6,10,8]=>[1,3,5,7,9,10,8,6,4,2]=>[10,8,6,4,2,1,3,5,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,5,2,4,7,6,9,8]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,2,5,4,7,6,9,8,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,6,7,2,5,1,4,8]=>[1,3,7,4,2,6,5,8]=>[8,6,2,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,1,5,2,8]=>[1,4,3,7,2,6,5,8]=>[8,5,6,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,4,5,7,2]=>[1,6,5,4,2,8,3,7]=>[8,3,4,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,8,2,3,6,4]=>[1,7,6,3,2,5,4,8]=>[8,2,3,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,3,4,7,5]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,6,3,7,2]=>[1,5,6,3,8,2,4,7]=>[8,4,3,6,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,5,7,2,6]=>[1,4,3,8,6,7,2,5]=>[8,5,6,1,3,2,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,3,6,8,1]=>[1,4,2,5,3,7,8,6]=>[8,5,7,4,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,1,6,8,3]=>[1,4,7,8,3,2,5,6]=>[8,5,2,1,6,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,5,8,2,7]=>[1,3,2,4,6,8,7,5]=>[8,6,7,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,5,7,3,6]=>[1,4,8,6,7,3,2,5]=>[8,5,1,3,2,6,7,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,6,2,7,3]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,7,4,2,8]=>[1,5,7,2,6,4,3,8]=>[8,4,2,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,8,5,2,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,7,1,5,3]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,1,5,3,6]=>[1,7,3,4,8,6,5,2]=>[8,2,6,5,1,3,4,7]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,5,1,4,8]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,5,2,4,6]=>[1,7,4,8,6,2,3,5]=>[8,2,5,1,3,7,6,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,1,8,4,5]=>[1,3,6,8,5,2,4,7]=>[8,6,3,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,7,8,5,2]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,7,8,5,3]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,8,7,5,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,9,1,2,3]=>[1,4,7,2,5,8,3,6,9]=>[9,6,3,8,5,2,7,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,5,6,7,8,9,2,3,1]=>[1,4,7,2,5,8,3,6,9]=>[9,6,3,8,5,2,7,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,7,8,9,2,3,4,1]=>[1,5,9,2,6,3,7,4,8]=>[9,5,1,8,4,7,3,6,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,7,8,9,3,4,1,2]=>[1,5,9,2,6,3,7,4,8]=>[9,5,1,8,4,7,3,6,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,7,8,9,3,4,2,1]=>[1,5,9,2,6,3,7,4,8]=>[9,5,1,8,4,7,3,6,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,9,2,3,4,5,1]=>[1,6,3,8,5,2,7,4,9]=>[9,4,7,2,5,8,3,6,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,9,3,4,5,1,2]=>[1,6,4,9,2,7,5,3,8]=>[9,4,6,1,8,3,5,7,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,9,3,4,5,2,1]=>[1,6,4,9,2,7,5,3,8]=>[9,4,6,1,8,3,5,7,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,9,5,6,3,4,1,2]=>[1,7,4,5,6,3,9,2,8]=>[9,3,6,5,4,7,1,8,2]=>[9,8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,9,5,6,3,4,2,1]=>[1,7,4,5,6,3,9,2,8]=>[9,3,6,5,4,7,1,8,2]=>[9,8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,5,6,7,8,9,10,1,2,3]=>[1,4,7,10,3,6,9,2,5,8]=>[10,7,4,1,8,5,2,9,6,3]=>[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,6,7,8,9,10,2,3,4,1]=>[1,5,9,4,8,3,7,2,6,10]=>[10,6,2,7,3,8,4,9,5,1]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,10,3,4,5,6,1,2]=>[1,7,5,3,9,2,8,6,4,10]=>[10,4,6,8,2,9,3,5,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,10,3,4,5,6,2,1]=>[1,7,5,3,9,2,8,6,4,10]=>[10,4,6,8,2,9,3,5,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,10,4,5,6,1,2,3]=>[1,7,6,5,4,10,3,9,2,8]=>[10,4,5,6,7,1,8,2,9,3]=>[10,9,8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,9,10,5,6,7,3,4,1,2]=>[1,8,4,5,6,7,3,10,2,9]=>[10,3,7,6,5,4,8,1,9,2]=>[10,9,8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,9,10,5,6,7,3,4,2,1]=>[1,8,4,5,6,7,3,10,2,9]=>[10,3,7,6,5,4,8,1,9,2]=>[10,9,8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,8,3,7,6,5,1,2]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,5,4,1,2]=>[1,6,4,7,2,3,8,5]=>[8,3,5,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,6,4,1,2]=>[1,5,6,4,7,2,3,8]=>[8,4,3,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,1,5,4,3]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,6,1,4,3]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,5,1,4,3]=>[1,7,4,6,2,8,3,5]=>[8,2,5,3,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,5,4,3,2]=>[1,6,4,7,3,8,2,5]=>[8,3,5,2,6,1,7,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,6,5,4,2]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,7,1,5,4,3]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,7,6,5,3]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,6,1,5,3]=>[1,4,7,5,6,2,8,3]=>[8,5,2,4,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,1,6,5,4]=>[1,3,7,5,2,8,4,6]=>[8,6,2,4,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,1,4,3,2]=>[1,6,4,7,3,8,2,5]=>[8,3,5,2,6,1,7,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,6,5,3,2]=>[1,4,7,3,2,8,5,6]=>[8,5,2,6,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,7,6,3,2]=>[1,5,7,3,2,4,8,6]=>[8,4,2,6,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,7,5,3,2]=>[1,6,5,7,3,8,2,4]=>[8,3,4,2,6,1,7,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,6,5,3,2]=>[1,7,3,4,2,8,5,6]=>[8,2,6,5,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,8,7,4,2]=>[1,6,7,4,2,5,8,3]=>[8,3,2,5,7,4,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,8,7,5,2]=>[1,6,7,5,8,2,4,3]=>[8,3,2,4,1,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,8,7,6,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,3,6,5,7]=>[1,8,7,5,3,4,2,6]=>[8,1,2,4,6,5,7,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,3,6,5,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,1,4,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,1,4,5,7]=>[1,6,4,8,7,5,2,3]=>[8,3,5,1,2,4,7,6]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,8,1,5,7]=>[1,4,3,2,6,5,8,7]=>[8,5,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,4,1,5,7]=>[1,8,7,5,4,6,2,3]=>[8,1,2,4,5,3,7,6]=>[8,2,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,6,1,5,7]=>[1,2,8,7,5,6,3,4]=>[8,7,1,2,4,3,6,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,4,1,5,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,2,1,5,7]=>[1,6,2,3,8,7,5,4]=>[8,3,7,6,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,1,4,5,7]=>[1,2,6,4,8,7,5,3]=>[8,7,3,5,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,1,4,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,4,1,5,7]=>[1,2,8,7,5,4,6,3]=>[8,7,1,2,4,5,3,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,3,8,4,5,7]=>[1,6,4,3,2,5,8,7]=>[8,3,5,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,6,4,5,7]=>[1,8,7,5,6,4,3,2]=>[8,1,2,4,3,5,6,7]=>[8,2,3,5,4,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,4,1,5,7]=>[1,6,2,3,8,7,5,4]=>[8,3,7,6,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,8,5,1,2]=>[1,3,4,7,2,6,5,8]=>[8,6,5,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,5,6,8,3]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,2,7,8,3]=>[1,2,6,7,8,3,5,4]=>[8,7,3,2,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,6,2,8,4]=>[1,7,8,4,3,5,6,2]=>[8,2,1,5,6,4,3,7]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,4,8,7,3]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,8,5,7,3]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,2,5,6,3]=>[1,7,6,5,2,8,3,4]=>[8,2,3,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,3,1,6,2,7]=>[1,4,3,5,2,8,7,6]=>[8,5,6,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,4,2,3,5]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,7,3,6,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,7,5,2,4]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,4,7,6,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,5,7,8,4]=>[1,6,7,8,4,2,3,5]=>[8,3,2,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,7,5,3,8]=>[1,4,2,6,5,7,3,8]=>[8,5,7,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,8,5,2,4]=>[1,2,6,5,8,4,7,3]=>[8,7,3,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,7,8,1,5]=>[1,4,3,2,6,8,5,7]=>[8,5,6,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,5,7,8,6]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,5,1,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,6,3,1,5]=>[1,7,2,8,5,6,3,4]=>[8,2,7,1,4,3,6,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,1,7,2,6]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,1,2,7,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,4,2,1,7]=>[1,6,2,5,4,8,7,3]=>[8,3,7,4,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,5,6,4,2]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,3,6,4,1]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,5,3,4,2]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,2,6,4,3]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,2,3,7,1]=>[1,5,2,4,6,3,8,7]=>[8,4,7,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,2,5,7,3]=>[1,6,5,2,4,8,3,7]=>[8,3,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,5,8,7,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,8,5,7,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,5,8,7,6]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,5,8,7,2]=>[1,4,3,2,6,8,5,7]=>[8,5,6,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,5,8,7,2]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,5,8,7,2]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,6,5,7,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,3,5,7,8]=>[1,4,6,5,3,2,7,8]=>[8,5,3,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,3,5,7,4]=>[1,6,5,3,2,4,8,7]=>[8,3,4,6,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,3,8,5,7,4]=>[1,6,5,8,4,3,2,7]=>[8,3,4,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,8,5,7,2]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,6,5,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,6,5,7,2]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,6,5,7,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,3,5,7,6]=>[1,8,6,5,3,2,4,7]=>[8,1,3,4,6,7,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,3,5,7,2]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,3,5,7,2]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,3,5,7,2]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,3,5,7,2]=>[1,6,5,3,2,4,8,7]=>[8,3,4,6,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,3,5,7,2]=>[1,4,8,2,6,5,3,7]=>[8,5,1,7,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,3,5,7,2]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,8,5,7,2]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,8,5,7,2]=>[1,4,3,2,6,5,8,7]=>[8,5,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,3,5,7,4]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,8,5,7,2]=>[1,2,4,6,5,8,3,7]=>[8,7,5,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,6,5,7,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,6,5,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,3,5,7,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,3,5,7,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,6,5,7,2]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,6,5,7,2]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,3,5,7,2]=>[1,4,6,5,3,2,8,7]=>[8,5,3,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,3,5,7,2]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,3,5,7,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,3,5,7,8]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,3,5,7,2]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,3,5,7,4]=>[1,8,4,2,6,5,3,7]=>[8,1,5,7,3,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,3,5,7,6]=>[1,8,6,5,3,2,4,7]=>[8,1,3,4,6,7,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,2,1,4,3]=>[1,7,4,5,2,8,3,6]=>[8,2,5,4,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,8,6,3,2]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,8,3,7,1]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,6,3,2,8]=>[1,5,6,3,2,7,4,8]=>[8,4,3,6,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,5,8,2,1]=>[1,3,7,2,6,8,4,5]=>[8,6,2,7,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,7,2,5,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,7,8,3,2]=>[1,5,7,3,6,8,2,4]=>[8,4,2,6,3,1,7,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,1,8,7,3,2]=>[1,5,8,2,6,7,3,4]=>[8,4,1,7,3,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,6,7,2,1]=>[1,3,8,2,5,6,7,4]=>[8,6,1,7,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,5,7,2,1]=>[1,3,8,2,6,7,4,5]=>[8,6,1,7,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,5,6,2,1]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,5,3,7,2]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,4,6,2,8]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,4,6,7,2]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,5,3,8,2]=>[1,6,3,2,7,8,4,5]=>[8,3,6,7,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,6,3,8,2]=>[1,5,6,3,2,7,8,4]=>[8,4,3,6,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,7,3,8,1]=>[1,5,7,8,2,6,3,4]=>[8,4,2,1,7,3,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,8,3,1,6]=>[1,5,8,6,3,7,2,4]=>[8,4,1,3,6,2,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,8,3,6,1]=>[1,5,8,2,4,3,7,6]=>[8,4,1,7,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,8,3,1,7]=>[1,5,8,7,2,6,3,4]=>[8,4,1,2,7,3,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,5,4,2,7,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,4,2,5,7]=>[1,6,2,8,7,5,4,3]=>[8,3,7,1,2,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,4,2,8,5]=>[1,6,2,7,8,5,4,3]=>[8,3,7,2,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,7,6,5,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,6,8,7,5]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,4,7,2,5]=>[1,6,7,2,8,5,4,3]=>[8,3,2,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,7,3,2,6]=>[1,5,7,2,8,6,3,4]=>[8,4,2,7,1,3,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,5,3,2,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,4,7,2,6]=>[1,3,2,8,6,7,4,5]=>[8,6,7,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,4,2,5,8]=>[1,6,2,7,5,4,3,8]=>[8,3,7,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,4,2,7,5]=>[1,6,2,8,5,4,3,7]=>[8,3,7,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,4,6,2,5]=>[1,7,2,8,5,4,3,6]=>[8,2,7,1,4,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,6,5,1,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,3,4,2,1]=>[1,6,4,7,2,5,3,8]=>[8,3,5,2,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,4,6,5,2]=>[1,7,5,4,2,8,3,6]=>[8,2,4,5,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,4,2,6,8]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,7,3,6,2]=>[1,5,7,6,3,2,8,4]=>[8,4,2,3,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,7,5,3,1]=>[1,6,5,7,3,4,2,8]=>[8,3,4,2,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,8,5,3,1]=>[1,6,5,8,2,4,3,7]=>[8,3,4,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,4,8,5,2]=>[1,6,8,2,3,7,5,4]=>[8,3,1,7,6,2,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,4,7,5,2]=>[1,6,7,5,4,2,8,3]=>[8,3,2,4,5,7,1,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,4,8,6,2]=>[1,3,2,7,6,8,4,5]=>[8,6,7,2,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,8,5,7,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,5,8,7,6]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,4,2,8,6]=>[1,3,2,7,8,6,4,5]=>[8,6,7,2,1,3,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,4,5,8,2]=>[1,6,5,4,2,7,8,3]=>[8,3,4,5,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,4,5,2,6]=>[1,7,2,3,8,6,5,4]=>[8,2,7,6,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,4,5,6,2]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,4,5,2,7]=>[1,6,5,4,2,8,7,3]=>[8,3,4,5,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,3,2,1,5]=>[1,8,5,3,4,6,2,7]=>[8,1,4,6,5,3,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,5,4,1,3]=>[1,8,3,6,4,2,7,5]=>[8,1,6,3,5,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,3,2,1,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,5,2,1,4]=>[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,3,2,1,7]=>[1,6,2,5,3,8,7,4]=>[8,3,7,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,3,2,1,5]=>[1,8,5,3,7,2,4,6]=>[8,1,4,6,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,3,2,1,6]=>[1,5,3,7,2,8,6,4]=>[8,4,6,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,3,5,7,1]=>[1,4,6,5,3,2,8,7]=>[8,5,3,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,5,8,6,3]=>[1,4,2,3,7,6,8,5]=>[8,5,7,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,8,4,3,7]=>[1,2,6,4,5,8,7,3]=>[8,7,3,5,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,4,5,3,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,8,5,2,4]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,2,3,7,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,1,6,5,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,8,6,3,4]=>[1,5,8,4,2,3,7,6]=>[8,4,1,5,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,8,7,4,5]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,1,7,3,4]=>[1,6,7,3,2,5,4,8]=>[8,3,2,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,1,7,4,6]=>[1,2,8,6,7,4,5,3]=>[8,7,1,3,2,5,4,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,7,1,6,2]=>[1,5,7,6,2,4,8,3]=>[8,4,2,3,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,7,2,6,1]=>[1,8,2,5,7,6,3,4]=>[8,1,7,4,2,3,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,2,6,5,1]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,4,1,7,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,1,7,5,6]=>[1,2,8,6,7,5,3,4]=>[8,7,1,3,2,4,6,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,3,1,7,6]=>[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,1,7,6,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,1,7,6,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,2,6,4,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,8,2,1,6]=>[1,7,2,5,8,6,3,4]=>[8,2,7,4,1,3,6,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,1,2,6,4]=>[1,3,8,4,5,2,7,6]=>[8,6,1,5,4,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,1,2,5,3]=>[1,4,6,2,7,5,3,8]=>[8,5,3,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,2,4,3]=>[1,5,2,7,4,6,3,8]=>[8,4,7,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,3,1,2,5]=>[1,6,2,4,8,5,3,7]=>[8,3,7,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,2,1,5,6]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,3,1,4,2]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,1,5,7,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,1,6,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,1,6,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,3,1,5,2]=>[1,6,2,4,7,5,3,8]=>[8,3,7,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,3,2,5,1]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,2,5,6,1]=>[1,8,2,3,4,7,6,5]=>[8,1,7,6,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,1,5,6,2]=>[1,3,8,2,4,7,6,5]=>[8,6,1,7,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,1,4,7,3]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,2,4,6,1]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,2,3,5,1]=>[1,8,2,4,7,5,3,6]=>[8,1,7,5,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,1,3,7,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,1,3,4,2]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,2,1,3,5]=>[1,7,3,6,2,4,8,5]=>[8,2,6,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,1,8,6,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,8,1,5,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,3,5,2,7]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,2,1,3,7]=>[1,5,2,4,6,3,8,7]=>[8,4,7,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,1,5,4,7]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,4,7,8,3]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,4,7,3,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,6,8,4,2]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,1,4,5,3]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,3,2,5,4]=>[1,2,8,4,6,3,7,5]=>[8,7,1,5,3,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,2,3,4,1]=>[1,5,2,7,4,6,3,8]=>[8,4,7,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,8,5,3,4]=>[1,2,7,3,6,5,8,4]=>[8,7,2,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,6,1,5,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,4,1,2,6]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,2,7,6,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,4,1,6,2]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,8,5,1,3]=>[1,2,7,3,6,5,8,4]=>[8,7,2,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,6,8,1,2]=>[1,7,2,3,5,6,8,4]=>[8,2,7,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,7,1,8,2]=>[1,6,2,3,5,7,8,4]=>[8,3,7,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,8,7,2]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,8,5,2,4]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,6,4,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,6,2,5,7]=>[1,2,8,7,5,6,3,4]=>[8,7,1,2,4,3,6,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,6,4,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,8,5,4,2]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,6,8,2,1]=>[1,7,2,3,5,6,8,4]=>[8,2,7,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,8,5,3,1]=>[1,2,7,3,6,5,8,4]=>[8,7,2,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,2,6,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,4,6,2,1]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,5,8,1,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,5,1,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,5,1,6,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,1,6,5,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,1,6,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,1,8,7,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,4,2,7,1]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,3,2,1,6]=>[1,7,2,4,5,3,8,6]=>[8,2,7,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,2,3,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,4,2,1,7]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,6,8,3,7,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,6,3,2,8]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,6,3,7,1]=>[1,5,6,3,8,2,4,7]=>[8,4,3,6,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,4,6,7,2,1]=>[1,3,5,6,7,2,8,4]=>[8,6,4,3,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,5,7,2,1]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,6,3,8,1]=>[1,2,5,6,3,7,8,4]=>[8,7,4,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,8,3,2,6]=>[1,5,8,6,3,2,4,7]=>[8,4,1,3,6,7,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,8,3,6,1]=>[1,5,8,2,4,7,6,3]=>[8,4,1,7,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,8,3,2,7]=>[1,5,8,7,2,3,4,6]=>[8,4,1,2,7,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,5,3,2,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,4,6,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,4,3,5,6]=>[1,8,6,3,2,7,5,4]=>[8,1,3,6,7,2,4,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,4,3,5,8]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,4,6,5,1]=>[1,8,2,7,5,4,3,6]=>[8,1,7,2,4,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,5,7,1]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,4,3,6,8]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,5,3,6,1]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,7,3,6,1]=>[1,5,7,6,3,2,8,4]=>[8,4,2,3,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,4,7,5,1]=>[1,6,7,5,4,2,8,3]=>[8,3,2,4,5,7,1,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,4,5,2,6]=>[1,8,6,5,4,3,2,7]=>[8,1,3,4,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,4,5,2,7]=>[1,8,7,2,3,6,5,4]=>[8,1,2,7,6,3,4,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,4,3,6,7]=>[1,8,7,6,3,2,4,5]=>[8,1,2,3,6,7,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,5,2,6,1]=>[1,3,8,2,4,7,6,5]=>[8,6,1,7,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,1,5,4,7]=>[1,3,8,7,4,6,5,2]=>[8,6,1,2,5,3,4,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,4,2,5,1]=>[1,8,2,7,5,4,6,3]=>[8,1,7,2,4,5,3,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,5,4,6,1]=>[1,3,7,6,4,2,8,5]=>[8,6,2,3,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,5,6,3,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,1,4,8,6]=>[1,3,2,7,8,6,4,5]=>[8,6,7,2,1,3,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,6,2,3,4,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,8,6,3,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,8,2,5,4]=>[1,3,6,2,7,5,8,4]=>[8,6,3,7,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,8,2,4,5]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,1,4,7,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,3,4,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,4,7,2,5]=>[1,8,5,4,6,7,2,3]=>[8,1,4,5,3,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,5,7,4,6]=>[1,8,6,7,4,3,2,5]=>[8,1,3,2,5,6,7,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,3,8,2,6]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,3,4,1,6]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,5,8,4,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,5,8,4,6]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,3,6,2,5]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,5,7,4,6]=>[1,8,6,7,4,3,2,5]=>[8,1,3,2,5,6,7,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,5,8,4,6]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,7,3,2,5]=>[1,8,5,7,2,6,3,4]=>[8,1,4,2,7,3,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,1,4,8,5]=>[1,2,6,4,7,8,5,3]=>[8,7,3,5,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,1,4,7,5]=>[1,2,6,4,8,5,3,7]=>[8,7,3,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,1,3,2,6]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,1,3,2,6]=>[1,8,6,3,4,7,2,5]=>[8,1,3,6,5,2,7,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,5,4,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,3,4,2,7]=>[1,8,7,2,6,4,3,5]=>[8,1,2,7,3,5,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,6,3,4,2]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,6,1,8,5,2]=>[1,3,7,5,2,4,6,8]=>[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,7,1,8,4]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,1,3,2,6]=>[1,8,6,3,7,2,4,5]=>[8,1,3,6,2,7,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,5,2,7,4]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,3,4,7,5]=>[1,6,4,8,5,3,2,7]=>[8,3,5,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,5,1,7,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,3,8,4,1,6]=>[1,2,7,3,5,8,6,4]=>[8,7,2,6,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,7,2,6,5]=>[1,8,5,7,6,2,3,4]=>[8,1,4,2,3,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,4,7,1,5]=>[1,2,8,5,4,6,7,3]=>[8,7,1,4,5,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,8,1,2,5]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,7,1,2,5]=>[1,8,5,7,2,3,6,4]=>[8,1,4,2,7,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,5,7,4,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,5,7,4,6]=>[1,2,8,6,7,4,3,5]=>[8,7,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,4,2,8,3]=>[1,6,2,5,4,7,8,3]=>[8,3,7,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,8,2,1,5]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,3,5,2,8]=>[1,4,7,2,6,5,3,8]=>[8,5,2,7,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,3,4,2,8]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,3,4,2,8,5]=>[1,6,2,3,7,8,5,4]=>[8,3,7,6,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,6,5,2,4]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,6,5,2,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,2,8,6,3]=>[1,5,2,3,7,6,8,4]=>[8,4,7,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,5,1,7,3]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,5,1,7,3]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,1,5,2,3]=>[1,8,3,4,7,2,6,5]=>[8,1,6,5,2,7,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,8,1,5,2,3]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,2,3,8,7]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,6,5,2,4]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,1,6,7,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,7,1,6,8,5]=>[1,2,4,7,8,5,3,6]=>[8,7,5,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,2,3,7,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,1,5,2,3]=>[1,6,5,2,4,8,3,7]=>[8,3,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,1,5,2,3]=>[1,8,3,4,6,5,2,7]=>[8,1,6,5,3,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,8,1,5,6]=>[1,3,4,7,5,8,6,2]=>[8,6,5,2,4,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,7,1,5,6]=>[1,3,4,8,6,2,5,7]=>[8,6,5,1,3,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,1,4,2,3]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,1,4,2,3]=>[1,8,3,5,2,6,4,7]=>[8,1,6,4,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,4,2,3,8]=>[1,5,4,7,3,6,2,8]=>[8,4,5,2,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,1,5,2,3]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,1,5,2,3]=>[1,8,3,7,2,4,6,5]=>[8,1,6,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,7,1,5,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,8,1,5,6]=>[1,7,5,8,6,2,3,4]=>[8,2,4,1,3,7,6,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,1,6,4,8]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,1,5,2,3]=>[1,7,2,4,8,3,6,5]=>[8,2,7,5,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,4,2,3,7]=>[1,5,4,8,7,3,6,2]=>[8,4,5,1,2,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,1,6,2,4]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,7,1,6,5,8]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,5,8,6,3]=>[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,6,1,5,8]=>[1,3,4,7,5,6,2,8]=>[8,6,5,2,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,1,5,2,3]=>[1,4,8,3,6,5,2,7]=>[8,5,1,6,3,4,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,1,4,2,3]=>[1,8,3,6,4,7,2,5]=>[8,1,6,3,5,2,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,1,4,2,3]=>[1,8,3,7,2,6,4,5]=>[8,1,6,2,7,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,1,4,2,3]=>[1,6,4,5,2,8,3,7]=>[8,3,5,4,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,1,4,2,3]=>[1,5,2,6,4,7,3,8]=>[8,4,7,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,7,1,5,2,3]=>[1,4,7,2,6,5,3,8]=>[8,5,2,7,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,1,4,2,3]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,4,2,8,6]=>[1,3,7,8,6,2,4,5]=>[8,6,2,1,3,7,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,4,6,3,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,2,3,6,7]=>[1,4,5,2,3,8,7,6]=>[8,5,4,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,6,7,2,8]=>[1,5,6,7,2,4,3,8]=>[8,4,3,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,5,3,4,6]=>[1,8,6,3,7,4,2,5]=>[8,1,3,6,2,5,7,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,5,8,4,6]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,5,4,2,8]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,8,4,2,6]=>[1,7,2,3,5,8,6,4]=>[8,2,7,6,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,5,4,2,7]=>[1,3,8,7,2,6,4,5]=>[8,6,1,2,7,3,5,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,5,4,2,7]=>[1,6,4,2,8,7,3,5]=>[8,3,5,7,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,5,3,4,7]=>[1,8,7,4,2,6,3,5]=>[8,1,2,5,7,3,6,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,5,7,4,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,6,3,8,5]=>[1,4,2,7,8,5,6,3]=>[8,5,7,2,1,4,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,5,3,4,6]=>[1,2,7,4,3,8,6,5]=>[8,7,2,5,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,1,4,3,2]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,4,3,2]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,6,5,3,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,7,6,8,2]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,7,5,3,8]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,1,4,3,2]=>[1,5,2,6,4,7,3,8]=>[8,4,7,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,1,4,3,2]=>[1,8,2,6,4,7,3,5]=>[8,1,7,3,5,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,1,4,3,2]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,1,4,3,2]=>[1,6,4,8,2,5,3,7]=>[8,3,5,1,7,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,5,6,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,6,5,3,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,5,6,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,8,6,7,2]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,4,6,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,4,5,3,7]=>[1,8,7,3,6,5,4,2]=>[8,1,2,6,3,4,5,7]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,4,5,3,7]=>[1,6,5,4,2,3,8,7]=>[8,3,4,5,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,6,3,8,7]=>[1,4,5,6,3,2,7,8]=>[8,5,4,3,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,6,8,3,2]=>[1,7,3,4,5,6,8,2]=>[8,2,6,5,4,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,1,4,3,2]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,1,4,3,2]=>[1,7,3,8,2,6,4,5]=>[8,2,6,1,7,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,1,4,3,2]=>[1,6,4,5,2,8,3,7]=>[8,3,5,4,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,4,5,3,8]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,4,6,8,2]=>[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,1,4,3,2]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,1,8,7,4]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,1,4,6,8]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,8,3,1,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,1,3,6,8]=>[1,7,6,3,4,5,2,8]=>[8,2,3,6,5,4,7,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,2,8,7,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,1,2,6,8]=>[1,3,4,5,2,7,6,8]=>[8,6,5,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,8,2,1,6]=>[1,3,4,5,8,6,2,7]=>[8,6,5,4,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,6,3,5,8]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,2,1,6,3]=>[1,8,3,4,5,2,7,6]=>[8,1,6,5,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,8,4,2,5]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,6,3,2,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,6,3,1,2]=>[1,5,6,3,4,8,2,7]=>[8,4,3,6,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,6,7,1,2]=>[1,4,5,6,7,2,8,3]=>[8,5,4,3,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,6,7,2,3]=>[1,4,5,6,7,2,8,3]=>[8,5,4,3,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,6,7,2,8]=>[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,6,1,2,7]=>[1,5,6,2,8,7,3,4]=>[8,4,3,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,6,7,3,2]=>[1,2,5,6,7,3,8,4]=>[8,7,4,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,6,7,5,2]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,1,7,5,6]=>[1,4,2,3,8,6,7,5]=>[8,5,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,6,7,4,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,6,7,4,2]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,6,7,1,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,6,7,4,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,6,7,4,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,6,2,5,8]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,6,2,1,5]=>[1,7,2,8,5,6,3,4]=>[8,2,7,1,4,3,6,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,5,7,6,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,8,7,5,2]=>[1,4,6,7,5,8,2,3]=>[8,5,3,2,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,2,7,4,5]=>[1,6,7,4,8,5,2,3]=>[8,3,2,5,1,4,7,6]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,2,7,1,4]=>[1,6,7,2,3,5,4,8]=>[8,3,2,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,6,2,3,5]=>[1,7,3,4,8,5,6,2]=>[8,2,6,5,1,4,3,7]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,6,2,3,8]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,3,6,7,4,2]=>[1,2,8,3,5,6,7,4]=>[8,7,1,6,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,7,3,2]=>[1,8,2,4,5,6,7,3]=>[8,1,7,5,4,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,6,7,1,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,6,7,3,2]=>[1,4,5,6,7,3,8,2]=>[8,5,4,3,2,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,6,7,3,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,6,7,3,8]=>[1,4,5,6,7,3,2,8]=>[8,5,4,3,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,6,7,4,2]=>[1,2,5,6,7,4,8,3]=>[8,7,4,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,6,7,3,2]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,1,7,2,6]=>[1,4,8,6,7,2,3,5]=>[8,5,1,3,2,7,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,6,1,2,7]=>[1,3,4,8,7,2,5,6]=>[8,6,5,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,6,7,2,3]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,6,7,1,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,6,3,4,8]=>[1,2,7,4,5,6,3,8]=>[8,7,2,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,3,6,5,8]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,5,6,8,1]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,4,5,8,7]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,6,8,2,3]=>[1,4,5,6,8,3,2,7]=>[8,5,4,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,5,7,1,6]=>[1,8,6,7,2,4,3,5]=>[8,1,3,2,7,5,6,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,5,6,1,8]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,6,2,8,1,7]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,2,8,1,6]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,3,8,1,5]=>[1,6,8,5,3,7,2,4]=>[8,3,1,4,6,2,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,4,8,6,1]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,8,3,4,7]=>[1,2,6,3,5,8,7,4]=>[8,7,3,6,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,4,5,2,3]=>[1,8,3,6,5,4,2,7]=>[8,1,6,3,4,5,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,2,5,4]=>[1,8,4,2,7,5,3,6]=>[8,1,5,7,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,1,6,2,3]=>[1,8,3,4,5,2,7,6]=>[8,1,6,5,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,1,7,2,3]=>[1,8,3,6,7,2,5,4]=>[8,1,6,3,2,7,4,5]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,3,1,7,5]=>[1,8,5,3,6,2,4,7]=>[8,1,4,6,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,2,1,7,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,2,1,8,6]=>[1,5,2,7,8,6,3,4]=>[8,4,7,2,1,3,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,3,1,8,5]=>[1,6,2,7,8,5,3,4]=>[8,3,7,2,1,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,3,1,2,8,4]=>[1,6,2,7,8,4,3,5]=>[8,3,7,2,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,1,8,2,3]=>[1,6,8,3,5,2,7,4]=>[8,3,1,6,4,7,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,3,1,2,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,2,3]=>[10,1,2,3,4,5,6,7,9,8]=>[10,2,3,4,5,6,7,8,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,2,4,3,8,7,5,1]=>[1,6,7,5,8,2,3,4]=>[8,3,2,4,1,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,1,8,6,2]=>[1,7,6,8,2,3,5,4]=>[8,2,3,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,3,4,8,6]=>[1,5,3,7,8,6,4,2]=>[8,4,6,2,1,3,5,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,3,1,4,8]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,3,1,8,4]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,7,8,5,2]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,3,4,5,7]=>[1,6,4,2,8,7,5,3]=>[8,3,5,7,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,4,5,2,6]=>[1,3,2,7,4,8,6,5]=>[8,6,7,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,3,7,8,5]=>[1,4,6,7,8,5,3,2]=>[8,5,3,2,1,4,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,8,6,1,2]=>[1,7,2,4,5,8,3,6]=>[8,2,7,5,4,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,3,1,4,5]=>[1,2,7,4,8,5,3,6]=>[8,7,2,5,1,4,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,8,6,2,1]=>[1,7,2,4,5,8,3,6]=>[8,2,7,5,4,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,7,8,6,5]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,4,3,6,2]=>[1,5,4,7,6,3,2,8]=>[8,4,5,2,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,2,1,4,5]=>[1,3,8,5,2,7,4,6]=>[8,6,1,4,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,3,5,6,7]=>[1,4,8,7,6,5,3,2]=>[8,5,1,2,3,4,6,7]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,6,7,5,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,7,5,6,8]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,8,6,5,1]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,3,8,7,5]=>[1,4,6,8,5,3,2,7]=>[8,5,3,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,3,5,6,8]=>[1,4,7,6,5,3,2,8]=>[8,5,2,3,4,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,2,1,4,8]=>[1,3,7,4,5,2,6,8]=>[8,6,2,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,7,3,5,1]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,2,6,8,1,5]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,2,4,8,1]=>[1,3,7,8,2,6,4,5]=>[8,6,2,1,7,3,5,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,3,6,5,8]=>[1,4,7,5,3,2,6,8]=>[8,5,2,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,3,6,8,5]=>[1,4,7,8,5,3,2,6]=>[8,5,2,1,4,6,7,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,4,2,5,1]=>[1,3,6,2,7,5,4,8]=>[8,6,3,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,4,2,6,3]=>[1,5,4,7,6,2,8,3]=>[8,4,5,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,2,4,5,1]=>[1,3,8,2,7,5,4,6]=>[8,6,1,7,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,8,6,7,5]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,7,6,5,8]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,5,7,6,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,3,7,6,5]=>[1,4,8,5,3,2,6,7]=>[8,5,1,4,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,5,6,8,7]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,1,3,6,5]=>[1,7,6,3,2,8,5,4]=>[8,2,3,6,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,4,7,8,3]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,8,7,1,2]=>[1,4,5,8,2,6,7,3]=>[8,5,4,1,7,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,4,8,7,2]=>[1,3,6,8,2,5,4,7]=>[8,6,3,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,4,1,5,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,1,3,6,8]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,1,5,3,2]=>[1,6,5,2,7,3,8,4]=>[8,3,4,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,4,5,3,2]=>[1,7,3,6,5,4,8,2]=>[8,2,6,3,4,5,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,2,8,1,3]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,4,2,3,8]=>[1,7,3,5,4,6,2,8]=>[8,2,6,4,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,8,1,3,2]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,4,6,3,2]=>[1,5,4,2,7,3,8,6]=>[8,4,5,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,4,6,3,2]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,7,5,3,2]=>[1,6,5,7,3,8,2,4]=>[8,3,4,2,6,1,7,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,6,1,7,3,2]=>[1,4,6,7,3,8,2,5]=>[8,5,3,2,6,1,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,6,7,3,2]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,6,7,3,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,4,2,3,8]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,1,5,7,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,1,6,7,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,2,6,3,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,2,5,3,7]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,3,4,7,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,6,2,5,7]=>[1,8,7,5,6,2,3,4]=>[8,1,2,4,3,7,6,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,2,6,4,7]=>[1,3,2,5,4,8,7,6]=>[8,6,7,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,8,4,7,6]=>[1,3,2,5,8,6,4,7]=>[8,6,7,4,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,6,7,1,5]=>[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,5,1,7,4]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,4,6,5,3]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,5,4,6,3]=>[1,8,3,7,6,4,2,5]=>[8,1,6,2,3,5,7,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,6,8,1,4]=>[1,7,2,3,5,6,8,4]=>[8,2,7,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,6,2,4,8]=>[1,7,4,5,6,2,3,8]=>[8,2,5,4,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,6,2,4,8]=>[1,3,5,6,2,7,4,8]=>[8,6,4,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,1,6,5,3]=>[1,8,3,2,7,5,4,6]=>[8,1,6,7,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,3,6,5,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,6,4,3,5]=>[1,2,7,3,8,5,6,4]=>[8,7,2,6,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,2,6,4,5]=>[1,2,7,4,8,5,3,6]=>[8,7,2,5,1,4,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,3,2,4,6]=>[1,7,4,8,6,2,3,5]=>[8,2,5,1,3,7,6,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,4,3,7,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,2,4,6,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,7,3,5,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,4,6,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,5,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,6,8,3,1]=>[1,2,4,5,6,8,3,7]=>[8,7,5,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,4,7,6,1]=>[1,2,5,4,8,3,6,7]=>[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,3,6,4,1]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,2,7,6,4]=>[1,3,8,4,5,2,6,7]=>[8,6,1,5,4,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,1,6,4,2]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,4,5,7,2]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,4,5,7,1]=>[1,2,6,5,4,3,8,7]=>[8,7,3,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,4,8,6,1]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,3,6,4,1]=>[1,2,7,4,5,3,8,6]=>[8,7,2,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,4,8,5,1]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,2,6,4,5]=>[1,3,8,5,2,4,7,6]=>[8,6,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,1,4,5,2]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,3,6,5,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,2,6,4,5]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,1,6,4,2]=>[1,7,4,5,2,3,8,6]=>[8,2,5,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,1,4,8,5,2]=>[1,7,5,4,2,3,6,8]=>[8,2,4,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,1,4,5,2]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,2,3,6,5]=>[1,7,6,3,8,5,2,4]=>[8,2,3,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,1,2,5,3]=>[1,8,3,4,6,2,7,5]=>[8,1,6,5,3,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,3,4,8,6]=>[1,7,8,6,4,2,5,3]=>[8,2,1,3,5,7,4,6]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,2,8,3,5]=>[1,7,3,6,8,5,2,4]=>[8,2,6,3,1,4,7,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,8,5,7,3]=>[1,6,5,8,3,2,4,7]=>[8,3,4,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,3,6,4,8]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,2,7,4,5]=>[1,3,8,5,2,6,7,4]=>[8,6,1,4,7,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,2,3,7,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,2,7,3,6]=>[1,4,5,2,8,6,7,3]=>[8,5,4,7,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,3,8,7,6]=>[1,4,5,3,2,6,8,7]=>[8,5,4,6,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,7,5,2,6]=>[1,3,4,8,6,5,7,2]=>[8,6,5,1,3,4,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,7,5,1,2]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,2,7,6,3]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,2,7,3,6]=>[1,5,2,4,8,6,7,3]=>[8,4,7,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,1,2,5,3]=>[1,8,3,7,5,2,6,4]=>[8,1,6,2,4,7,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,4,8,5,2]=>[1,6,8,2,7,5,4,3]=>[8,3,1,7,2,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,7,1,4,2]=>[1,5,7,4,8,2,6,3]=>[8,4,2,5,1,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,8,2,7,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,2,8,6,3]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,2,8,3,5]=>[1,6,8,5,2,7,3,4]=>[8,3,1,4,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,3,7,8,4]=>[1,6,7,8,4,2,5,3]=>[8,3,2,1,5,7,4,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,2,3,7,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,2,5,3,8]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,5,7,1,8]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,7,2,5,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,3,1,7,4]=>[1,8,4,5,3,2,6,7]=>[8,1,5,4,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,1,7,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,2,7,5,6]=>[1,2,8,6,7,5,3,4]=>[8,7,1,3,2,4,6,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,1,6,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,1,6,5,4]=>[1,8,4,3,2,7,5,6]=>[8,1,5,6,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,6,1,7,5]=>[1,3,2,8,5,6,4,7]=>[8,6,7,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,3,1,7,6]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,7,2,6,8]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,5,7,2,4,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,5,3,6,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,2,5,4,8]=>[1,7,4,6,5,2,3,8]=>[8,2,5,3,4,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,2,4,7,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,5,4,6]=>[1,2,3,8,6,5,7,4]=>[8,7,6,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,1,4,7,3]=>[1,6,4,8,3,5,2,7]=>[8,3,5,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,1,6,7,4]=>[1,3,8,4,5,2,6,7]=>[8,6,1,5,4,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,5,7,4,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,5,6,4,2]=>[1,3,7,4,2,8,5,6]=>[8,6,2,5,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,6,1,7,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,1,6,5,2]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,2,7,3,5]=>[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,5,4,7,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,4,6,5,8]=>[1,7,5,4,2,3,6,8]=>[8,2,4,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,4,5,7,6]=>[1,8,6,5,4,2,3,7]=>[8,1,3,4,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,2,4,7,6]=>[1,8,6,4,3,2,5,7]=>[8,1,3,5,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,2,6,4,8]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,5,3,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,3,2,7,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,2,6,3,8]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,2,6,5,8]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,2,5,3,8]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,5,6,4,8]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,4,3,7,5]=>[1,8,5,4,2,6,3,7]=>[8,1,4,5,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,6,7,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,5,3,6,4]=>[1,7,6,3,2,8,4,5]=>[8,2,3,6,7,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,5,3,8,4]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,2,8,4,6]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,3,8,4,2]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,2,3,8,4]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,6,5,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,6,3,4,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,2,5,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,2,3,4,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,2,5,7,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,5,7,6,2]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,3,5,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,2,6,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,3,5,7,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,8,2,4,1]=>[1,6,2,5,8,3,7,4]=>[8,3,7,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,5,8,3,1]=>[1,4,7,3,6,8,2,5]=>[8,5,2,6,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,2,1,8,4,3]=>[1,6,8,3,5,2,7,4]=>[8,3,1,6,4,7,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,5,2,1,6]=>[1,3,8,6,2,4,7,5]=>[8,6,1,3,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,1,7,2,4]=>[1,5,2,6,7,3,8,4]=>[8,4,7,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,3,2,7,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,8,6,2,5]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,2,1,5,7]=>[1,3,6,2,4,8,7,5]=>[8,6,3,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,3,8,6,1]=>[1,4,7,6,8,2,3,5]=>[8,5,2,3,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,3,8,1,6]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,8,3,4,7]=>[1,5,8,7,4,6,3,2]=>[8,4,1,2,5,3,6,7]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,4,1,3,7]=>[1,5,4,8,7,3,6,2]=>[8,4,5,1,2,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,3,4,2,7]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,6,3,2,7]=>[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,8,2,6,1]=>[1,4,3,7,6,2,5,8]=>[8,5,6,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,7,8,2,6]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,4,8,2,6]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,4,6,1,2]=>[1,5,4,8,2,7,3,6]=>[8,4,5,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,3,8,6,2]=>[1,2,4,7,6,8,3,5]=>[8,7,5,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,7,8,4,2]=>[1,2,5,7,4,6,8,3]=>[8,7,4,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,3,8,5,2]=>[1,4,7,5,3,2,6,8]=>[8,5,2,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,8,4,5,2]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,8,1,5,3]=>[1,6,2,7,5,8,3,4]=>[8,3,7,2,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,7,3,8,5]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,7,8,1,4]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,2,8,4,5]=>[1,6,8,5,2,7,4,3]=>[8,3,1,4,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,3,4,8,5]=>[1,6,4,2,3,7,8,5]=>[8,3,5,7,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,3,8,4,6]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,1,8,3,5]=>[1,6,8,5,2,4,7,3]=>[8,3,1,4,7,5,2,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,7,8,1,5]=>[1,4,3,6,8,5,7,2]=>[8,5,6,3,1,4,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,7,8,5,1]=>[1,4,3,6,8,2,5,7]=>[8,5,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,2,4,5,1]=>[1,6,4,8,2,7,5,3]=>[8,3,5,1,7,2,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,4,1,8,5]=>[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,1,4,8,5]=>[1,6,4,2,7,8,5,3]=>[8,3,5,7,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,4,2,5,6]=>[1,7,5,4,3,8,6,2]=>[8,2,4,5,6,1,3,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,8,3,5,6]=>[1,7,5,8,6,3,4,2]=>[8,2,4,1,3,6,5,7]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,6,1,3,5]=>[1,7,3,4,8,5,6,2]=>[8,2,6,5,1,4,3,7]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,6,2,1,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,1,8,6,4]=>[1,3,7,6,8,4,2,5]=>[8,6,2,3,1,5,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,5,1,4]=>[1,6,5,2,7,3,8,4]=>[8,3,4,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,2,5,4,1]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,7,1,8,5,3]=>[1,6,8,3,4,7,5,2]=>[8,3,1,6,5,2,4,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,1,8,5,3]=>[1,4,7,5,2,6,8,3]=>[8,5,2,4,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,1,6,3,4]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,8,2,5,3]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,7,8,4,3]=>[1,5,7,4,2,6,8,3]=>[8,4,2,5,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,5,4,1,3]=>[1,6,4,8,3,2,7,5]=>[8,3,5,1,6,7,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,6,3,5,7]=>[1,2,8,7,5,6,3,4]=>[8,7,1,2,4,3,6,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,3,6,2,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,3,6,2,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,3,4,7,2,6]=>[1,2,8,6,7,3,5,4]=>[8,7,1,3,2,6,4,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,6,3,7,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,4,6,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,1,4,5,8]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,2,4,7,5]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,6,2,8,5]=>[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,6,1,8,7]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,7,1,8,2]=>[1,4,3,5,7,8,2,6]=>[8,5,6,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,1,6,8,3]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,5,1,7,3]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,1,3,7,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,4,8,3,7,1]=>[1,6,3,5,8,2,4,7]=>[8,3,6,4,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,8,2,7,1]=>[1,6,2,4,5,8,3,7]=>[8,3,7,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,7,1,6,8]=>[1,3,2,5,7,6,4,8]=>[8,6,7,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,1,6,2,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,1,6,2,8]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,3,8,1,5]=>[1,4,7,2,3,6,8,5]=>[8,5,2,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,2,8,6,3]=>[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,8,6,4,5]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,1,8,6,3]=>[1,4,7,6,8,3,2,5]=>[8,5,2,3,1,6,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,7,8,1,2]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,7,8,3,1]=>[1,5,7,3,6,8,2,4]=>[8,4,2,6,3,1,7,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,3,8,5,1]=>[1,4,7,5,3,6,8,2]=>[8,5,2,4,6,3,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,3,8,7,1]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,3,1,8,7]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,3,1,8,7]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,3,8,7,1]=>[1,6,8,2,4,5,3,7]=>[8,3,1,7,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,5,2,3,1]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,4,5,3,1]=>[1,8,2,6,5,4,7,3]=>[8,1,7,3,4,5,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,8,7,3,1]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,3,8,7,1]=>[1,4,5,3,2,6,8,7]=>[8,5,4,6,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,3,8,7,1]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,5,2,3,1]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,5,2,3,1]=>[1,4,7,3,6,2,8,5]=>[8,5,2,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,5,2,3,1]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,4,5,3,1]=>[1,6,5,4,7,3,2,8]=>[8,3,4,5,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,5,3,1]=>[1,8,2,6,5,7,3,4]=>[8,1,7,3,4,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,7,5,3,1]=>[1,6,5,7,3,2,8,4]=>[8,3,4,2,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,7,5,3,1]=>[1,4,6,5,7,3,2,8]=>[8,5,3,4,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,4,5,3,1]=>[1,6,5,4,2,8,3,7]=>[8,3,4,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,7,5,3,1]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,7,5,3,1]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,7,5,3,1]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,8,7,3,1]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,8,7,3,1]=>[1,6,7,3,4,5,8,2]=>[8,3,2,6,5,4,1,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,4,5,3,1]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,4,5,3,1]=>[1,8,2,6,5,4,3,7]=>[8,1,7,3,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,8,7,3,1]=>[1,6,7,3,5,8,2,4]=>[8,3,2,6,4,1,7,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,6,8,7,5,1]=>[1,4,6,7,5,8,2,3]=>[8,5,3,2,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,7,2,3,1]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,2,5,3,1]=>[1,8,2,6,5,3,7,4]=>[8,1,7,3,4,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,5,2,3,1]=>[1,6,2,4,7,3,8,5]=>[8,3,7,5,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,7,5,2,3,1]=>[1,4,7,3,8,2,6,5]=>[8,5,2,6,1,7,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,7,4,5,3]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,7,5,3,1]=>[1,2,4,6,5,7,3,8]=>[8,7,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,7,5,3,1]=>[1,6,5,7,3,8,2,4]=>[8,3,4,2,6,1,7,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,7,5,3,1]=>[1,8,2,3,6,5,7,4]=>[8,1,7,6,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,7,5,3,1]=>[1,6,5,7,3,8,2,4]=>[8,3,4,2,6,1,7,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,7,5,3,1]=>[1,4,2,6,5,7,3,8]=>[8,5,7,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,7,2,5,3,1]=>[1,4,7,3,8,2,6,5]=>[8,5,2,6,1,7,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,4,7,5,3]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,4,7,5,3]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,2,5,3,1]=>[1,6,5,2,8,3,7,4]=>[8,3,4,7,1,6,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,7,5,3,1]=>[1,2,8,3,6,5,7,4]=>[8,7,1,6,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,7,5,3,1]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,7,4,8,3,1]=>[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,4,7,6,3]=>[1,8,3,2,5,4,6,7]=>[8,1,6,7,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,7,8,5,1]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,6,3,4,1]=>[1,5,6,3,8,2,7,4]=>[8,4,3,6,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,5,8,4,2]=>[1,7,4,3,6,8,2,5]=>[8,2,5,6,3,1,7,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,8,4,5,2]=>[1,6,4,7,5,8,2,3]=>[8,3,5,2,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,5,8,6,4]=>[1,7,6,8,4,2,3,5]=>[8,2,3,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,2,4,8,7]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,5,7,4,1]=>[1,6,7,4,8,2,3,5]=>[8,3,2,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,5,3,7,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,6,2,7,5]=>[1,3,8,5,6,2,4,7]=>[8,6,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,4,5,7,2]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,1,2,8,3]=>[1,7,8,3,5,2,6,4]=>[8,2,1,6,4,7,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,3,4,2,1]=>[1,5,3,6,4,8,2,7]=>[8,4,6,3,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,5,7,4,3]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,5,3,7,1]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,6,1,8,4]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,6,7,3,5]=>[1,8,5,6,7,3,2,4]=>[8,1,4,3,2,6,7,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,4,8,6,1]=>[1,5,4,7,6,8,2,3]=>[8,4,5,2,3,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,4,3,1,7]=>[1,5,4,8,7,2,3,6]=>[8,4,5,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,4,3,6,2]=>[1,7,6,3,2,8,4,5]=>[8,2,3,6,7,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,5,3,6,1]=>[1,7,6,3,4,8,2,5]=>[8,2,3,6,5,1,7,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,8,4,6,2]=>[1,3,5,8,2,7,6,4]=>[8,6,4,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,4,6,1,3]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,8,6,2,1]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,3,5,2,7]=>[1,4,6,5,3,2,8,7]=>[8,5,3,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,4,5,7,6]=>[1,3,8,6,5,4,2,7]=>[8,6,1,3,4,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,6,2,4,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,7,1,4,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,5,7,1,6]=>[1,4,8,6,7,2,3,5]=>[8,5,1,3,2,7,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,8,5,7,1]=>[1,3,4,2,6,5,8,7]=>[8,6,5,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,5,1,8,6]=>[1,4,2,7,8,6,3,5]=>[8,5,7,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,5,8,6,1]=>[1,3,4,7,6,8,2,5]=>[8,6,5,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,6,5,1,7]=>[1,4,8,7,2,3,5,6]=>[8,5,1,2,7,6,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,1,8,6,7]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,4,6,5,7]=>[1,3,8,7,5,4,2,6]=>[8,6,1,2,4,5,7,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,4,7,2,5]=>[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,3,2,7,5]=>[1,4,8,5,3,2,6,7]=>[8,5,1,4,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,1,2,6,5]=>[1,4,3,8,5,2,7,6]=>[8,5,6,1,4,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,2,3,7,5]=>[1,4,8,5,2,6,3,7]=>[8,5,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,2,3,7,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,1,3,7,5]=>[1,4,8,5,2,6,3,7]=>[8,5,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,4,7,5,1]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,4,7,1,5]=>[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,8,3,7,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,8,3,7,6]=>[1,4,5,8,6,3,2,7]=>[8,5,4,1,3,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,3,8,7,6]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,8,7,1,6]=>[1,3,5,8,6,7,2,4]=>[8,6,4,1,3,2,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,3,8,7,6]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,8,2,7,6]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,8,7,2,6]=>[1,3,5,8,6,7,2,4]=>[8,6,4,1,3,2,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,8,7,2,6]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,7,1,2,4]=>[1,3,5,7,2,6,4,8]=>[8,6,4,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,7,3,4,1]=>[1,2,5,7,4,8,3,6]=>[8,7,4,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,8,7,2,6]=>[1,3,5,8,6,7,2,4]=>[8,6,4,1,3,2,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,8,7,2,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,8,2,7,6]=>[1,4,5,8,6,2,3,7]=>[8,5,4,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,2,1,7,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,3,7,5,1]=>[1,2,4,8,3,6,7,5]=>[8,7,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,8,7,1,6]=>[1,3,5,8,6,7,2,4]=>[8,6,4,1,3,2,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,2,8,7,6]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,2,8,7,6]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,8,1,7,6]=>[1,4,5,8,6,2,3,7]=>[8,5,4,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,8,7,1,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,8,7,1,6]=>[1,3,4,5,8,6,7,2]=>[8,6,5,4,1,3,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,8,1,7,6]=>[1,4,5,8,6,2,3,7]=>[8,5,4,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,4,1,3,7]=>[1,8,7,3,2,6,4,5]=>[8,1,2,6,7,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,2,8,3,1]=>[1,6,8,2,5,3,7,4]=>[8,3,1,7,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,3,4,5,7]=>[1,8,7,5,3,2,4,6]=>[8,1,2,4,6,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,2,4,1,7]=>[1,8,7,2,3,5,4,6]=>[8,1,2,7,6,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,3,5,4,7]=>[1,8,7,4,2,6,5,3]=>[8,1,2,5,7,3,4,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,6,5,7]=>[1,8,7,5,4,3,2,6]=>[8,1,2,4,5,6,7,3]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,8,4,5,1]=>[1,6,4,7,5,8,2,3]=>[8,3,5,2,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,6,3,4,1]=>[1,7,4,2,5,6,3,8]=>[8,2,5,7,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,3,4,8,2]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,1,4,5,3]=>[1,6,4,2,7,5,3,8]=>[8,3,5,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,7,2,6,1]=>[1,5,7,6,2,3,8,4]=>[8,4,2,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,6,4,2,5]=>[1,8,5,6,4,7,2,3]=>[8,1,4,3,5,2,7,6]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,8,6,2,4]=>[1,5,8,4,7,2,3,6]=>[8,4,1,5,2,7,6,3]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,3,1,7,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,7,1,3,5]=>[1,8,5,7,3,6,2,4]=>[8,1,4,2,6,3,7,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,2,1,7,4]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,2,5,6,1]=>[1,8,2,3,7,6,5,4]=>[8,1,7,6,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,2,6,7,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,1,5,2]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,1,5,7,2]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,2,8,4,3]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,7,4,1,3]=>[1,6,4,5,7,2,8,3]=>[8,3,5,4,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,6,3,1,8,4]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,1,5,6,7]=>[1,4,3,8,7,6,5,2]=>[8,5,6,1,2,3,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,8,4,6,1]=>[1,2,5,8,3,7,6,4]=>[8,7,4,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,7,5,6,3]=>[1,4,8,3,2,5,7,6]=>[8,5,1,6,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,7,1,5,4,2]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,8,6,4,2]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,3,1,6,2]=>[1,5,3,8,2,7,6,4]=>[8,4,6,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,8,3,6,1]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,4,8,6,2]=>[1,3,7,6,8,2,5,4]=>[8,6,2,3,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,1,4,6,3]=>[1,7,6,4,5,2,3,8]=>[8,2,3,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,3,6,2,1]=>[1,5,3,4,8,2,7,6]=>[8,4,6,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,3,5,2,7]=>[1,4,2,8,7,3,6,5]=>[8,5,7,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,4,7,5,6]=>[1,2,8,6,7,5,4,3]=>[8,7,1,3,2,4,5,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,5,7,1,6]=>[1,8,6,7,2,4,3,5]=>[8,1,3,2,7,5,6,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,5,8,1,6]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,8,5,6,1]=>[1,3,4,7,6,5,8,2]=>[8,6,5,2,3,4,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,8,5,1,7]=>[1,2,6,5,8,7,3,4]=>[8,7,3,4,1,2,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,4,5,7,6]=>[1,8,6,5,4,3,2,7]=>[8,1,3,4,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,5,4,1,7]=>[1,3,6,4,8,7,2,5]=>[8,6,3,5,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,8,7,6,1]=>[1,4,3,5,8,2,6,7]=>[8,5,6,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,5,3,1,7]=>[1,4,6,3,2,8,7,5]=>[8,5,3,6,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,4,1,3,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,5,4,2,7]=>[1,3,8,7,2,4,6,5]=>[8,6,1,2,7,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,3,2,6,1]=>[1,5,3,8,2,4,7,6]=>[8,4,6,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,7,2,5,1]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,2,1,8,5]=>[1,4,6,2,7,8,5,3]=>[8,5,3,7,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,1,8,2,6]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,6,2,1,3]=>[1,5,6,2,4,7,3,8]=>[8,4,3,7,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,3,1,6,2]=>[1,4,7,6,2,8,3,5]=>[8,5,2,3,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,3,7,6,2]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,7,1,5,2]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,1,6,5,2]=>[1,4,3,8,2,7,5,6]=>[8,5,6,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,6,4,2,1]=>[1,8,2,7,3,5,6,4]=>[8,1,7,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,8,7,5,2]=>[1,4,3,2,6,7,5,8]=>[8,5,6,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,7,4,5,3]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,5,6,8,4]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,5,8,1,4]=>[1,3,6,8,4,2,7,5]=>[8,6,3,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,3,8,1,5]=>[1,4,6,8,5,3,2,7]=>[8,5,3,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,4,8,7,5,1]=>[1,6,7,5,8,2,3,4]=>[8,3,2,4,1,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,6,1,8,5]=>[1,3,2,7,8,5,6,4]=>[8,6,7,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,8,1,4,6]=>[1,5,8,6,2,3,7,4]=>[8,4,1,3,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,6,5,1,4]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,1,7,6,3]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,7,6,3,4]=>[1,5,7,3,8,4,2,6]=>[8,4,2,6,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,7,5,2,4]=>[1,3,2,6,5,7,4,8]=>[8,6,7,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,1,5,4,3]=>[1,2,7,4,8,3,6,5]=>[8,7,2,5,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,6,4,3,2]=>[1,5,6,4,2,8,3,7]=>[8,4,3,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,7,2,1,6]=>[1,8,6,2,5,7,3,4]=>[8,1,3,7,4,2,6,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,3,2,7,1]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,2,8,5,1]=>[1,7,5,2,6,8,3,4]=>[8,2,4,7,3,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,8,2,5,6]=>[1,7,5,8,6,2,3,4]=>[8,2,4,1,3,7,6,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,5,8,3,6]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,5,1,3,8]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,6,2,8,3]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,3,2,8,6]=>[1,7,8,6,2,5,3,4]=>[8,2,1,3,7,4,6,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,3,8,5,2]=>[1,6,8,2,4,3,7,5]=>[8,3,1,7,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,3,1,6,8]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,7,6,8,3]=>[1,4,2,5,7,8,3,6]=>[8,5,7,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,3,1,2,7]=>[1,5,3,6,2,4,8,7]=>[8,4,6,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,3,7,2,5]=>[1,6,7,2,4,3,8,5]=>[8,3,2,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,8,5,2,7]=>[1,4,3,2,6,5,8,7]=>[8,5,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,5,7,2,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,5,3,1,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,3,5,1,7]=>[1,2,6,5,3,8,7,4]=>[8,7,3,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,2,8,5,6]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,7,2,5,8]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,2,1,3,4]=>[1,7,3,8,4,6,2,5]=>[8,2,6,1,5,3,7,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,5,4,1,6]=>[1,2,8,6,4,3,7,5]=>[8,7,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,8,7,1,5]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,6,1,8,5]=>[1,7,8,5,6,2,4,3]=>[8,2,1,4,3,7,5,6]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,6,5,7,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,3,7,1,4]=>[1,2,8,4,6,7,3,5]=>[8,7,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,8,1,6,3]=>[1,7,6,2,4,5,8,3]=>[8,2,3,7,5,4,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,4,5,1,6]=>[1,2,7,3,8,6,5,4]=>[8,7,2,6,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,4,6,5,8]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,2,1,4,3]=>[1,7,4,8,3,6,2,5]=>[8,2,5,1,6,3,7,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,2,7,4,8]=>[1,3,6,7,4,5,2,8]=>[8,6,3,2,5,4,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,5,1,3,8]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,2,5,8,6]=>[1,3,4,2,7,8,6,5]=>[8,6,5,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,5,2,8,3]=>[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,5,1,8,2]=>[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,6,8,5,2]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,5,6,8,3]=>[1,4,7,8,3,2,5,6]=>[8,5,2,1,6,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,6,7,1,5]=>[1,3,4,8,5,6,7,2]=>[8,6,5,1,4,3,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,8,5,2,7]=>[1,3,6,5,8,7,2,4]=>[8,6,3,4,1,2,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,5,8,2,3]=>[1,4,7,2,3,6,8,5]=>[8,5,2,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,6,8,2,5]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,6,8,2,1]=>[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,6,5,2,8]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,5,3,1,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,3,5,1,6]=>[1,2,8,6,5,3,7,4]=>[8,7,1,3,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,6,2,5,8]=>[1,4,3,7,5,6,2,8]=>[8,5,6,2,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,1,2,4,3]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,2,1,3,4]=>[1,5,2,8,4,6,3,7]=>[8,4,7,1,5,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,6,8,5,3]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,6,1,8,5]=>[1,4,3,7,8,5,6,2]=>[8,5,6,2,1,4,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,5,6,7,1]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,1,6,7,5]=>[1,3,2,8,5,4,6,7]=>[8,6,7,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,2,4,1,7]=>[1,3,5,2,8,7,4,6]=>[8,6,4,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,3,7,1,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,4,6,7,5]=>[1,3,2,8,5,4,6,7]=>[8,6,7,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,4,6,7,1]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,5,6,1,8,3]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,4,5,1,6]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,1,3,4,2]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,2,3,4,1]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,6,2,3,8]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,3,4,1,6]=>[1,2,8,6,4,5,3,7]=>[8,7,1,3,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,4,3,1,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,6,3,2,8]=>[1,4,5,6,3,7,2,8]=>[8,5,4,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,1,3,2,4]=>[1,5,2,8,4,6,3,7]=>[8,4,7,1,5,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,7,6,8,1]=>[1,5,7,8,2,4,3,6]=>[8,4,2,1,7,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,2,8,1,6]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,5,1,6,3]=>[1,8,3,7,6,2,4,5]=>[8,1,6,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,3,5,8,1]=>[1,7,8,2,4,3,6,5]=>[8,2,1,7,5,6,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,2,6,8,3]=>[1,4,2,5,3,7,8,6]=>[8,5,7,4,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,3,6,8,2]=>[1,5,3,2,4,7,8,6]=>[8,4,6,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,1,3,8,2]=>[1,4,6,3,5,2,7,8]=>[8,5,3,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,3,1,8,2]=>[1,5,3,6,2,7,8,4]=>[8,4,6,3,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,1,4,8,2]=>[1,5,2,7,8,3,6,4]=>[8,4,7,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,4,8,1,6]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,4,1,6,2]=>[1,8,2,7,6,3,5,4]=>[8,1,7,2,3,6,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,4,8,5,2]=>[1,7,5,4,3,2,6,8]=>[8,2,4,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,7,8,1,4]=>[1,3,5,7,2,6,8,4]=>[8,6,4,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,7,1,4,5]=>[1,3,8,5,7,4,6,2]=>[8,6,1,4,2,5,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,5,2,1,7]=>[1,4,6,2,8,7,3,5]=>[8,5,3,7,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,3,5,4,6]=>[1,2,8,6,5,3,7,4]=>[8,7,1,3,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,5,3,4,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,8,2,6,4]=>[1,3,5,8,4,2,7,6]=>[8,6,4,1,5,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,2,5,3,4]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,8,6,2,3]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,2,8,1,3]=>[1,5,2,7,3,6,8,4]=>[8,4,7,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,6,8,7,2]=>[1,5,6,8,2,3,4,7]=>[8,4,3,1,7,6,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,8,2,1,3]=>[1,4,6,2,5,8,3,7]=>[8,5,3,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,3,6,5,1]=>[1,7,5,3,8,2,4,6]=>[8,2,4,6,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,5,2,1,3]=>[1,6,2,4,8,3,7,5]=>[8,3,7,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,5,1,2,7]=>[1,3,4,8,7,2,6,5]=>[8,6,5,1,2,7,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,2,6,5,1]=>[1,7,5,2,4,8,3,6]=>[8,2,4,7,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,5,4,6,2]=>[1,8,2,7,6,4,3,5]=>[8,1,7,2,3,5,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,1,4,5,2]=>[1,7,5,2,6,4,3,8]=>[8,2,4,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,2,5,7,6]=>[1,3,4,8,6,5,2,7]=>[8,6,5,1,3,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,1,3,6,7]=>[1,4,2,8,7,6,3,5]=>[8,5,7,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,3,1,4,7]=>[1,5,3,2,8,7,4,6]=>[8,4,6,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,4,5,3,6]=>[1,8,6,5,4,2,3,7]=>[8,1,3,4,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,2,5,4,7]=>[1,8,7,4,6,5,2,3]=>[8,1,2,5,3,4,7,6]=>[8,2,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,4,3,6,8]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,4,2,6,7]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,2,3,7,4]=>[1,8,4,6,3,5,2,7]=>[8,1,5,3,6,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,3,2,6,7]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,5,2,6,7]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,5,3,6,8]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,5,4,7,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,5,4,7,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,5,2,6,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,4,2,6,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,2,5,4,8]=>[1,7,4,6,5,2,3,8]=>[8,2,5,3,4,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,2,5,4,8]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,4,5,2,6,8]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,5,4,7,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,5,4,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,1,6,7,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,5,2,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,5,3,7,8]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,5,3,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,3,7,4,8]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,3,7,4,8]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,5,4,3,8]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,3,7,4,8]=>[1,5,3,2,6,7,4,8]=>[8,4,6,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,5,3,7,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,5,2,6,8]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,2,6,3,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,2,3,8,4]=>[1,5,2,7,8,4,6,3]=>[8,4,7,2,1,5,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,2,7,4,8]=>[1,5,2,6,7,4,3,8]=>[8,4,7,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,1,6,7,8]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,3,4,1,7]=>[1,6,4,2,8,7,3,5]=>[8,3,5,7,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,7,1,4,3]=>[1,8,3,6,2,5,7,4]=>[8,1,6,3,7,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,7,8,4,3]=>[1,6,8,3,2,5,7,4]=>[8,3,1,6,7,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,5,3,8,2]=>[1,4,2,7,8,3,6,5]=>[8,5,7,2,1,6,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,1,3,8,2]=>[1,5,2,7,8,3,6,4]=>[8,4,7,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,3,8,4,2]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,3,1,4,2]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,1,6,4,3]=>[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,7,8,5,2]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,7,2,3,1]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,4,1,2,7,3]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,7,2,4,3]=>[1,5,7,4,2,8,3,6]=>[8,4,2,5,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,2,6,4,1]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,2,6,4,3]=>[1,8,3,5,2,4,7,6]=>[8,1,6,4,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,5,6,3,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,5,1,3,4]=>[1,6,2,8,4,3,7,5]=>[8,3,7,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,1,6,3,4]=>[1,5,2,8,4,3,7,6]=>[8,4,7,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,2,6,7,3]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,1,6,2,4]=>[1,3,8,4,5,2,7,6]=>[8,6,1,5,4,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,8,1,4,3]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,5,6,3,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,2,3,4]=>[1,8,4,2,6,3,7,5]=>[8,1,5,7,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,5,2,3,4]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,1,6,4,3]=>[1,8,3,5,2,7,4,6]=>[8,1,6,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,8,6,2,4]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,6,8,7,2]=>[1,5,6,8,2,3,4,7]=>[8,4,3,1,7,6,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,8,2,7,1]=>[1,4,6,2,5,8,3,7]=>[8,5,3,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,8,1,7,2]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,3,4,7,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,6,3,4,7,2]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,5,3,7,2]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,3,2,7,1]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,1,2,7,4]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,5,2,7,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,5,2,1,4]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,5,2,7,4]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,5,6,2,4]=>[1,8,4,3,2,7,5,6]=>[8,1,5,6,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,5,1,2,4]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,3,6,7,1]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,1,6,7,4]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,4,3,7,2]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,4,3,5,2]=>[1,6,3,2,7,5,4,8]=>[8,3,6,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,1,4,3,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,8,1,6,4,5]=>[1,2,7,4,8,5,3,6]=>[8,7,2,5,1,4,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,8,2,4,6,3]=>[1,7,6,4,8,3,2,5]=>[8,2,3,5,1,6,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,1,6,3,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,1,3,8,7]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,7,6,3,1]=>[1,4,5,7,3,2,8,6]=>[8,5,4,2,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,4,1,8,7]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,2,3,8,7]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,1,4,8,7]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,1,8,4,3]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,5,3,4,7]=>[1,8,7,4,2,6,3,5]=>[8,1,2,5,7,3,6,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,8,3,4,1]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,7,6,3,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,5,3,2,1]=>[1,7,2,4,8,3,6,5]=>[8,2,7,5,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,7,4,6,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,6,7,2,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,1,6,7,2,4]=>[1,3,5,6,7,2,8,4]=>[8,6,4,3,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,8,1,3,4]=>[1,5,8,4,2,6,3,7]=>[8,4,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,6,7,4,3]=>[1,2,5,6,7,4,8,3]=>[8,7,4,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,6,7,4,2]=>[1,3,2,5,6,7,4,8]=>[8,6,7,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,6,7,4,1]=>[1,5,6,7,4,8,2,3]=>[8,4,3,2,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,6,7,1,2]=>[1,8,2,3,5,6,7,4]=>[8,1,7,6,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,6,7,4,2]=>[1,5,6,7,4,8,2,3]=>[8,4,3,2,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,6,7,4,1]=>[1,3,5,6,7,4,8,2]=>[8,6,4,3,2,5,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,3,8,7,4]=>[1,6,8,4,5,3,2,7]=>[8,3,1,5,4,6,7,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,8,1,4,7]=>[1,5,8,7,4,2,6,3]=>[8,4,1,2,5,7,3,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,3,2,5,1]=>[1,4,8,2,7,5,3,6]=>[8,5,1,7,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,1,3,4,6]=>[1,2,7,4,8,6,3,5]=>[8,7,2,5,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,8,5,1,4,3]=>[1,7,4,8,3,2,6,5]=>[8,2,5,1,6,7,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,5,2,6,4]=>[1,8,4,7,6,2,3,5]=>[8,1,5,2,3,7,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,5,1,6,2]=>[1,3,8,2,4,7,6,5]=>[8,6,1,7,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,4,2,5,7]=>[1,6,2,3,8,7,5,4]=>[8,3,7,6,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,7,4,1,2]=>[1,6,4,5,7,2,3,8]=>[8,3,5,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,5,1,3,2]=>[1,7,3,6,2,4,8,5]=>[8,2,6,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,7,5,6,3]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,6,7,3,1]=>[1,4,2,5,6,7,3,8]=>[8,5,7,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,6,7,3,1]=>[1,2,5,6,7,3,8,4]=>[8,7,4,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,6,7,2,1]=>[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,6,7,1,5]=>[1,8,5,6,7,2,4,3]=>[8,1,4,3,2,7,5,6]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,6,7,3,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,6,7,3,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,2,1,5,6]=>[1,3,8,6,2,4,7,5]=>[8,6,1,3,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,6,4,2,1]=>[1,7,2,8,3,5,6,4]=>[8,2,7,1,6,4,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,6,7,2,3]=>[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,6,7,2,5]=>[1,3,2,8,5,6,7,4]=>[8,6,7,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,6,7,1,5]=>[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,8,5,1,6]=>[1,7,2,4,3,5,8,6]=>[8,2,7,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,4,6,1,7]=>[1,5,4,8,7,2,3,6]=>[8,4,5,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,5,4,1,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,4,6,1,7]=>[1,3,8,7,2,5,4,6]=>[8,6,1,2,7,4,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,4,2,1,7]=>[1,5,4,6,2,8,7,3]=>[8,4,5,3,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,5,3,1,7]=>[1,4,2,8,7,3,6,5]=>[8,5,7,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,2,8,7,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,1,2,6,8]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,5,1,4,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,6,4,1,2,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,3,8,5,4]=>[1,6,8,4,7,5,3,2]=>[8,3,1,5,2,4,6,7]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,3,8,6,5]=>[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,8,7,4,6]=>[1,5,8,6,7,4,2,3]=>[8,4,1,3,2,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,2,6,5,4]=>[1,2,8,4,7,5,3,6]=>[8,7,1,5,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,3,7,2,6]=>[1,5,3,4,8,6,7,2]=>[8,4,6,5,1,3,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,5,4,7,3]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,2,5,3,8]=>[1,4,2,7,3,6,5,8]=>[8,5,7,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,3,2,7,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,3,2,6,8]=>[1,5,3,7,6,2,4,8]=>[8,4,6,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,2,1,3,6]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,1,5,3,8]=>[1,7,3,6,5,2,4,8]=>[8,2,6,3,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,8,5,7,4]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,8,4,7,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,8,1,4,6]=>[1,5,8,6,2,7,4,3]=>[8,4,1,3,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,8,1,2,3]=>[1,6,2,4,5,8,3,7]=>[8,3,7,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,1,6,3,2]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,1,7,4,2]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,1,7,5,3]=>[1,8,3,4,2,6,7,5]=>[8,1,6,5,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,8,5,2,3]=>[1,7,2,6,5,8,3,4]=>[8,2,7,3,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,7,5,3,2]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,2,8,6,4]=>[1,7,6,8,4,3,2,5]=>[8,2,3,1,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,5,8,6,3]=>[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,2,7,5,3]=>[1,6,7,5,2,8,3,4]=>[8,3,2,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,2,6,4,3]=>[1,7,4,2,5,3,8,6]=>[8,2,5,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,6,3,5,2]=>[1,7,5,6,3,8,2,4]=>[8,2,4,3,6,1,7,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,7,3,6,4]=>[1,5,7,6,3,2,8,4]=>[8,4,2,3,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,2,4,7,5]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,6,2,5,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,7,3,2,6]=>[1,5,7,2,4,8,6,3]=>[8,4,2,7,5,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,7,2,4,6]=>[1,3,2,5,7,4,8,6]=>[8,6,7,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,3,7,2,5]=>[1,4,8,5,3,2,6,7]=>[8,5,1,4,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,7,6,2,3]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,5,4,3,2]=>[1,8,2,6,4,7,3,5]=>[8,1,7,3,5,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,6,4,3,2]=>[1,7,3,5,6,4,8,2]=>[8,2,6,4,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,3,6,4,2]=>[1,5,3,8,2,4,7,6]=>[8,4,6,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,6,5,2,4]=>[1,3,8,4,7,2,5,6]=>[8,6,1,5,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,2,3,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,2,3,6,8]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,2,4,6,8]=>[1,2,7,6,4,5,3,8]=>[8,7,2,3,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,2,4,7,8]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,2,5,7,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,3,4,2,6]=>[1,2,8,6,4,7,3,5]=>[8,7,1,3,5,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,2,6,5,8]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,4,7,3,6]=>[1,2,5,4,8,6,7,3]=>[8,7,4,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,2,4,5,8]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,6,2,3,5,8]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,5,6,4,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,5,6,3,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,4,6,3,7]=>[1,2,5,4,8,7,3,6]=>[8,7,4,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,4,5,3,7]=>[1,2,6,5,4,8,7,3]=>[8,7,3,4,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,5,3,6,7]=>[1,8,7,6,3,2,4,5]=>[8,1,2,3,6,7,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,5,7,8,9,1]=>[1,2,3,4,6,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,6,7,5,8,9,1]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,6,8,9,10,1]=>[1,2,3,4,5,7,8,9,10,6]=>[10,9,8,7,6,4,3,2,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,6,7,4,5,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,9,10,11,6,7,2,3,4,5,12]=>[1,2,8,3,9,4,10,5,11,6,7,12]=>[12,11,5,10,4,9,3,8,2,7,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,6,4,7,2,1,3,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,2,8,3,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,3,5,1,7]=>[1,8,7,2,4,3,6,5]=>[8,1,2,7,5,6,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,2,3,1,6]=>[1,7,2,4,5,3,8,6]=>[8,2,7,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,3,5,1,7]=>[1,4,2,8,7,3,6,5]=>[8,5,7,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,4,8,2,6]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,8,2,3,5]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,1,2,3,6]=>[1,5,2,8,6,3,7,4]=>[8,4,7,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,4,1,2,7]=>[1,6,2,8,7,3,5,4]=>[8,3,7,1,2,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,2,1,4,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,3,7,2,4]=>[1,8,4,6,7,2,5,3]=>[8,1,5,3,2,7,4,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,5,8,2,6]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,8,2,3,5]=>[1,7,3,6,2,4,5,8]=>[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,8,2,4,6]=>[1,5,8,6,2,3,7,4]=>[8,4,1,3,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,6,1,2,3,5]=>[1,7,3,8,5,2,4,6]=>[8,2,6,1,4,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,2,3,5,8]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,1,2,3,7]=>[1,6,2,5,3,8,7,4]=>[8,3,7,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,1,6,2,3]=>[1,7,2,4,5,3,8,6]=>[8,2,7,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,1,7,4,5]=>[1,8,5,2,6,7,4,3]=>[8,1,4,7,3,2,5,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,6,3,4,5]=>[1,2,7,4,8,5,6,3]=>[8,7,2,5,1,4,3,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,3,6,2,4]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,2,3,6,7]=>[1,5,2,4,8,7,6,3]=>[8,4,7,5,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,2,3,5,6]=>[1,2,4,7,5,3,8,6]=>[8,7,5,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,8,2,4,6]=>[1,5,8,6,2,7,4,3]=>[8,4,1,3,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,5,2,3,4]=>[1,7,3,8,4,2,6,5]=>[8,2,6,1,5,7,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,6,2,3,4]=>[1,7,3,5,6,2,4,8]=>[8,2,6,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,4,5,3,2]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,6,5,4,2]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,3,4,2,6]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,2,5,6,8]=>[1,7,6,5,2,3,4,8]=>[8,2,3,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,8,5,7,1]=>[1,6,5,8,2,4,3,7]=>[8,3,4,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,7,5,8,3,6]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,6,5,3,8,2]=>[1,7,8,2,3,4,6,5]=>[8,2,1,7,6,5,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,6,5,3,2,8]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,6,8,5,1]=>[1,3,7,5,6,8,2,4]=>[8,6,2,4,3,1,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,6,8,2,5]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,6,8,5,2]=>[1,3,7,5,6,8,2,4]=>[8,6,2,4,3,1,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,8,5,1,7]=>[1,6,5,8,7,2,4,3]=>[8,3,4,1,2,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,5,8,1,3]=>[1,6,8,3,2,4,7,5]=>[8,3,1,6,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,5,3,1,8]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,6,8,1,5]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,6,8,2,1]=>[1,5,6,8,2,4,3,7]=>[8,4,3,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,6,5,1,8]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,5,6,1,7]=>[1,4,2,8,7,3,5,6]=>[8,5,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,5,1,2,6]=>[1,4,3,7,2,8,6,5]=>[8,5,6,2,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,3,5,2,6]=>[1,4,2,8,6,5,3,7]=>[8,5,7,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,2,6,5,7]=>[1,4,2,8,7,5,3,6]=>[8,5,7,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,6,2,5,8]=>[1,3,7,5,6,2,4,8]=>[8,6,2,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,2,6,7,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,3,4,2,7]=>[1,5,3,2,8,7,4,6]=>[8,4,6,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,3,7,2,4]=>[1,6,7,2,8,4,3,5]=>[8,3,2,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,3,4,7,2]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,2,6,7,1]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,6,2,8,1]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,6,1,8,3]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,5,1,2,8]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,5,1,8,2]=>[1,6,2,4,7,8,3,5]=>[8,3,7,5,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,3,1,5,8,7]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,1,6,4,7]=>[1,5,2,8,7,4,3,6]=>[8,4,7,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,3,1,2,6]=>[1,5,3,7,2,8,6,4]=>[8,4,6,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,6,2,1,8]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,6,5,1,7]=>[1,4,8,7,2,3,5,6]=>[8,5,1,2,7,6,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,6,1,4,7]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,5,1,2,6]=>[1,4,8,6,2,3,7,5]=>[8,5,1,3,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,4,1,2,6]=>[1,5,4,8,6,2,3,7]=>[8,4,5,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,3,1,4,7]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,1,6,2]=>[1,5,4,7,6,2,3,8]=>[8,4,5,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,6,2,4,1]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,7,2,4,1]=>[1,8,2,6,3,5,7,4]=>[8,1,7,3,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,8,2,6,1]=>[1,7,6,2,5,8,3,4]=>[8,2,3,7,4,1,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,8,2,5,1]=>[1,7,5,8,2,4,3,6]=>[8,2,4,1,7,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,8,2,4,1]=>[1,7,4,3,6,2,5,8]=>[8,2,5,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,7,2,4,1]=>[1,8,2,5,7,4,3,6]=>[8,1,7,4,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,5,2,8,1]=>[1,7,8,2,4,3,6,5]=>[8,2,1,7,5,6,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,5,2,7,1]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,5,2,6,1]=>[1,8,2,4,3,7,6,5]=>[8,1,7,5,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,4,2,6,1]=>[1,8,2,5,4,3,7,6]=>[8,1,7,4,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,3,2,6,1]=>[1,7,6,2,5,3,8,4]=>[8,2,3,7,4,6,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,3,2,7,1]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,4,2,7,1]=>[1,6,2,5,4,3,8,7]=>[8,3,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,4,2,6,1]=>[1,7,6,2,5,4,3,8]=>[8,2,3,7,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,6,2,3,1]=>[1,7,3,8,2,5,6,4]=>[8,2,6,1,7,4,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,6,2,5,1]=>[1,7,5,6,2,4,3,8]=>[8,2,4,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,5,2,6,1]=>[1,7,6,2,4,3,8,5]=>[8,2,3,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,5,2,7,1]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,5,2,8,1]=>[1,6,2,4,3,7,8,5]=>[8,3,7,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,7,2,6,1]=>[1,5,7,6,2,4,3,8]=>[8,4,2,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,7,2,4,1]=>[1,6,2,5,7,4,3,8]=>[8,3,7,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,7,2,3,1]=>[1,6,2,5,7,3,8,4]=>[8,3,7,4,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,8,2,5,1]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,8,2,6,1]=>[1,5,8,2,4,3,7,6]=>[8,4,1,7,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,4,7,8,1]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,6,8,7,2]=>[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,8,6,7,3]=>[1,4,5,8,3,2,6,7]=>[8,5,4,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,8,7,6,3]=>[1,4,5,8,3,2,6,7]=>[8,5,4,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,7,5,8,6,2]=>[1,4,7,6,8,2,3,5]=>[8,5,2,3,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,4,8,2,5]=>[1,6,8,5,4,2,7,3]=>[8,3,1,4,5,7,2,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,4,8,2,6]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,7,8,2,6]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,5,4,6,7]=>[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,5,7,4,6]=>[1,3,2,4,8,6,7,5]=>[8,6,7,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,8,4,3,5]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,8,4,5,3]=>[1,6,4,2,7,5,8,3]=>[8,3,5,7,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,8,5,7,3]=>[1,4,6,5,8,3,2,7]=>[8,5,3,4,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,8,5,3,7]=>[1,4,6,5,8,7,3,2]=>[8,5,3,4,1,2,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,8,4,3,7]=>[1,5,8,7,3,6,4,2]=>[8,4,1,2,6,3,5,7]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,8,7,4,3]=>[1,5,8,3,6,7,4,2]=>[8,4,1,6,3,2,5,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,8,7,3,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,5,8,2,4]=>[1,6,8,4,2,7,3,5]=>[8,3,1,5,7,2,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,8,6,3,5]=>[1,4,7,3,2,5,8,6]=>[8,5,2,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,7,6,4,5]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,6,4,7,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,4,6,7,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,4,7,6,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,7,4,6,5]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,8,3,6,5]=>[1,4,7,6,3,2,5,8]=>[8,5,2,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,8,3,6,4]=>[1,5,8,4,2,3,7,6]=>[8,4,1,5,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,8,3,4,6]=>[1,5,8,6,3,7,4,2]=>[8,4,1,3,6,2,5,7]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,8,2,5,6]=>[1,7,5,8,6,2,4,3]=>[8,2,4,1,3,7,5,6]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,5,6,1,3]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,2,4,6,1]=>[1,7,6,4,5,2,3,8]=>[8,2,3,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,5,6,2,1]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,4,5,1,7]=>[1,6,5,4,2,3,8,7]=>[8,3,4,5,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,5,7,4,1]=>[1,6,7,4,2,3,8,5]=>[8,3,2,5,7,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,1,5,2,7]=>[1,6,5,2,4,8,7,3]=>[8,3,4,7,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,8,2,4,1]=>[1,5,8,2,6,3,7,4]=>[8,4,1,7,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,4,6,7,1]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,7,5,1,3]=>[1,6,5,7,2,4,3,8]=>[8,3,4,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,4,2,7,8]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,8,2,4,1]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,2,4,7,1]=>[1,5,2,6,4,8,3,7]=>[8,4,7,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,4,5,1,8]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,5,8,4,1]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,8,2,4,7,1]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,3,8,1,7]=>[1,5,3,6,8,7,2,4]=>[8,4,6,3,1,2,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,4,2,1,7]=>[1,3,8,7,2,5,4,6]=>[8,6,1,2,7,4,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,2,1,8,7]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,2,1,5,8,7]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,1,3,8,7]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,4,1,6,3]=>[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,5,4,1,7]=>[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,7,6,2,1]=>[1,4,5,7,2,3,8,6]=>[8,5,4,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,6,4,3,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,5,6,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,8,4,1,7]=>[1,2,5,8,7,3,6,4]=>[8,7,4,1,2,6,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,2,1,8,5,7]=>[1,6,8,7,5,2,3,4]=>[8,3,1,2,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,6,4,2,1]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,1,8,5,7]=>[1,3,4,2,6,8,7,5]=>[8,6,5,7,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,2,1,5,7]=>[1,3,6,2,8,7,5,4]=>[8,6,3,7,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,6,2,4,1]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,1,8,5,3]=>[1,7,5,2,6,8,3,4]=>[8,2,4,7,3,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,6,4,3,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,3,7,8,5]=>[1,2,3,6,7,8,5,4]=>[8,7,6,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,4,2,1,5]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,6,3,5]=>[1,7,3,4,2,8,5,6]=>[8,2,6,5,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,3,8,4,1]=>[1,5,3,6,8,2,7,4]=>[8,4,6,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,4,3,7,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,5,8,4,3]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,7,5,6,1]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,2,1,4,3]=>[1,8,3,7,4,6,2,5]=>[8,1,6,2,5,3,7,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,6,2,1,3]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,1,3,8,5]=>[1,4,2,7,8,5,3,6]=>[8,5,7,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,6,1,7,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,3,2,1,5]=>[1,6,2,4,8,5,3,7]=>[8,3,7,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,5,2,1,8]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,8,4,1,7]=>[1,6,4,2,5,8,7,3]=>[8,3,5,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,8,4,1,3]=>[1,6,4,7,2,5,8,3]=>[8,3,5,2,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,5,4,1,8]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,3,1,7,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,4,2,8,5]=>[1,2,7,8,5,4,3,6]=>[8,7,2,1,4,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,1,4,6,3]=>[1,8,3,5,2,7,6,4]=>[8,1,6,4,7,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,2,1,4,6,3]=>[1,7,6,4,2,8,3,5]=>[8,2,3,5,7,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,2,3,1,7,4]=>[1,5,3,6,2,8,4,7]=>[8,4,6,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,4,2,8,6]=>[1,5,4,3,7,8,6,2]=>[8,4,5,6,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,4,5,7,3]=>[1,6,5,4,2,3,8,7]=>[8,3,4,5,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,1,5,6,4]=>[1,3,8,4,7,6,5,2]=>[8,6,1,5,2,3,4,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,1,4,6,3]=>[1,5,2,8,3,7,6,4]=>[8,4,7,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,3,4,5,2]=>[1,6,4,2,8,3,7,5]=>[8,3,5,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,4,5,6,3]=>[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,3,4,5,2]=>[1,8,2,6,4,3,7,5]=>[8,1,7,3,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,3,4,5,2]=>[1,7,5,3,8,2,6,4]=>[8,2,4,6,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,3,1,7,4]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,2,6,7,4]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,1,5,6,3]=>[1,8,3,2,4,7,6,5]=>[8,1,6,7,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,1,5,6,3]=>[1,7,6,5,2,4,8,3]=>[8,2,3,4,7,5,1,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,3,1,7,5]=>[1,6,2,4,8,5,3,7]=>[8,3,7,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,8,1,7,6]=>[1,5,8,6,2,4,3,7]=>[8,4,1,3,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,1,6,8,7]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,4,7,8,6]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,2,6,7,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,4,2,8,7]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,5,3,8,7]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,3,6,8,5]=>[1,4,2,7,8,5,3,6]=>[8,5,7,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,2,6,8,4]=>[1,5,2,7,8,4,3,6]=>[8,4,7,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,4,5,8,3]=>[1,6,5,4,2,7,8,3]=>[8,3,4,5,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,5,6,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,4,5,6,3]=>[1,8,3,2,7,6,5,4]=>[8,1,6,7,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,4,5,6,3]=>[1,7,6,5,4,2,8,3]=>[8,2,3,4,5,7,1,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,2,6,7,4]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,3,6,7,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,5,7,8,6]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,3,7,8,6]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,2,3,7,6]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,3,2,5,8]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,7,6,1,5]=>[1,4,2,8,5,7,3,6]=>[8,5,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,7,1,6,5]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,1,7,6,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,3,2,5,6]=>[1,4,7,5,3,8,6,2]=>[8,5,2,4,6,1,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,2,5,3,6]=>[1,4,2,7,3,8,6,5]=>[8,5,7,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,7,1,6,8,5]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,4,1,8,5]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,4,7,8,1,5]=>[1,2,6,8,5,7,3,4]=>[8,7,3,1,4,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,3,4,1,5]=>[1,2,6,4,8,5,3,7]=>[8,7,3,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,4,2,5,6]=>[1,3,7,5,4,8,6,2]=>[8,6,2,4,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,8,7,5,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,6,4,1,5]=>[1,3,8,5,6,4,2,7]=>[8,6,1,4,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,1,6,7,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,4,2,5,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,4,1,6,5]=>[1,3,7,6,2,4,8,5]=>[8,6,2,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,3,1,7,5]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,8,1,6,5]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,7,2,5,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,1,8,6,5]=>[1,3,4,7,6,8,5,2]=>[8,6,5,2,3,1,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,6,8,1,5]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,8,2,3,6]=>[1,4,5,8,6,2,7,3]=>[8,5,4,1,3,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,8,2,5,6]=>[1,3,7,5,8,6,2,4]=>[8,6,2,4,1,3,7,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,8,4,1,5]=>[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,7,1,8,5]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,6,3,4,1]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,7,3,4,1]=>[1,8,2,6,3,5,7,4]=>[8,1,7,3,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,6,3,2,1]=>[1,7,2,4,5,6,3,8]=>[8,2,7,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,7,5,8,3]=>[1,2,3,6,5,7,8,4]=>[8,7,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,4,2,6,8]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,4,7,1,2]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,4,7,8,3]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,8,5,7,3]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,2,3,6,7]=>[1,4,5,2,8,7,6,3]=>[8,5,4,7,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,4,3,2,7]=>[1,5,4,8,7,2,6,3]=>[8,4,5,1,2,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,6,4,3,2,7]=>[1,5,4,6,3,8,7,2]=>[8,4,5,3,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,8,7,2,4]=>[1,5,8,4,3,6,7,2]=>[8,4,1,5,6,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,4,3,2,5]=>[1,6,3,8,5,4,7,2]=>[8,3,6,1,4,5,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,8,3,6,4]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,7,5,2,8]=>[1,4,3,6,5,7,2,8]=>[8,5,6,3,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,8,5,2,4]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,7,8,5,3]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,7,8,2,5]=>[1,4,3,6,8,5,7,2]=>[8,5,6,3,1,4,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,6,3,2,5]=>[1,7,2,8,5,6,3,4]=>[8,2,7,1,4,3,6,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,2,3,7,6]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,3,7,2,5]=>[1,4,8,5,3,6,7,2]=>[8,5,1,4,6,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,3,8,2,7]=>[1,5,3,6,8,7,2,4]=>[8,4,6,3,1,2,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,4,3,2,7]=>[1,6,3,8,7,2,5,4]=>[8,3,6,1,2,7,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,6,8,2,4]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,6,2,8,4]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,2,6,8,4]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,7,6,4,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,6,2,4,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,4,6,8,2]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,4,6,2,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,4,2,6,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,7,2,6,8]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,7,8,2,6]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,7,2,8,6]=>[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,4,2,8,6]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,4,8,2,6]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,4,8,6,2]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,8,4,6,2]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,7,8,6,4]=>[1,2,3,5,7,6,8,4]=>[8,7,6,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,2,8,6,4]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,8,2,6,4]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,7,4,8,5]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,2,8,7,4]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,4,3,8,5]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,5,2,8,6]=>[1,2,4,3,7,8,6,5]=>[8,7,5,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,3,8,1,6]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,3,8,6,5]=>[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,1,8,6,5]=>[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,8,2,7,5]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,8,7,6,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,8,2,6,5]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,8,4,6,3]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,8,1,5,4]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,8,4,1,6]=>[1,3,2,5,8,6,4,7]=>[8,6,7,4,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,8,4,7,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,7,8,3,5]=>[1,4,2,6,8,5,7,3]=>[8,5,7,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,7,8,2,1]=>[1,5,7,2,3,6,8,4]=>[8,4,2,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,8,4,7,1]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,8,7,1,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,8,7,5,4]=>[1,2,3,6,7,5,8,4]=>[8,7,6,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,8,7,2,5]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,3,8,6,1]=>[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,4,8,6,3]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,2,8,5,1]=>[1,4,7,5,2,6,8,3]=>[8,5,2,4,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,8,6,2,5]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,8,6,1,3]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,8,5,1,4]=>[1,3,6,5,8,4,7,2]=>[8,6,3,4,1,5,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,2,4,3,7]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,2,4,1,6]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,3,1,5,6]=>[1,2,4,8,6,3,7,5]=>[8,7,5,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,1,5,6,7]=>[1,3,4,8,7,6,5,2]=>[8,6,5,1,2,3,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,3,2,4,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,2,3,1,5]=>[1,8,5,2,4,7,3,6]=>[8,1,4,7,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,2,3,1,5]=>[1,4,8,5,2,6,3,7]=>[8,5,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,2,3,1,5]=>[1,7,2,4,8,5,3,6]=>[8,2,7,5,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,3,1,5,6]=>[1,2,4,7,5,3,8,6]=>[8,7,5,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,2,3,1,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,2,3,1,4]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,2,3,1,5]=>[1,6,3,8,5,2,4,7]=>[8,3,6,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,2,3,1,4]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,2,3,1,5]=>[1,4,8,5,2,7,3,6]=>[8,5,1,4,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,2,3,1,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,4,1,6,5]=>[1,8,5,4,7,6,2,3]=>[8,1,4,5,2,3,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,2,5,1,6]=>[1,3,4,8,6,5,2,7]=>[8,6,5,1,3,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,2,3,1,5]=>[1,4,6,3,8,5,2,7]=>[8,5,3,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,1,5,8,6]=>[1,2,4,3,7,8,6,5]=>[8,7,5,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,2,3,1,4]=>[1,8,4,6,3,7,2,5]=>[8,1,5,3,6,2,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,2,3,1,4]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,2,3,8,5]=>[1,7,8,5,2,3,6,4]=>[8,2,1,4,7,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,2,3,1,5]=>[1,4,6,3,7,2,8,5]=>[8,5,3,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,2,3,1,4]=>[1,6,3,7,2,8,4,5]=>[8,3,6,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,5,8,7,2]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,1,8,7,2]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,5,8,7,2]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,3,8,7,2]=>[1,4,5,3,2,6,8,7]=>[8,5,4,6,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,8,1,7,3,4]=>[1,2,6,7,3,5,4,8]=>[8,7,3,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,8,3,7,2]=>[1,4,5,8,2,6,3,7]=>[8,5,4,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,8,3,7,2]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,8,3,7,2]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,8,7,3,2]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,7,1,5,2]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,7,1,5,2]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,3,7,1,4]=>[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,5,7,3,2]=>[1,4,2,6,7,3,8,5]=>[8,5,7,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,5,7,3,2]=>[1,2,4,8,3,6,7,5]=>[8,7,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,3,1,7,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,1,7,3,4]=>[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,5,1,7,2]=>[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,1,5,7,2]=>[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,8,5,7,2]=>[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,1,5,7,2]=>[1,4,8,2,6,5,3,7]=>[8,5,1,7,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,1,5,7,2]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,8,5,7,2]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,8,7,5,2]=>[1,4,6,7,5,8,2,3]=>[8,5,3,2,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,8,7,5,2]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,7,1,3,4]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,1,7,5,2]=>[1,4,8,2,6,7,5,3]=>[8,5,1,7,3,2,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,8,7,5,2]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,3,7,5,2]=>[1,4,8,2,6,7,5,3]=>[8,5,1,7,3,2,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,3,7,5,2]=>[1,4,2,6,7,5,3,8]=>[8,5,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,7,3,1,4]=>[1,6,3,8,4,5,7,2]=>[8,3,6,1,5,4,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,7,1,3,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,1,5,3,6]=>[1,2,4,7,3,8,6,5]=>[8,7,5,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,5,3,1,6]=>[1,4,7,2,3,8,6,5]=>[8,5,2,7,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,7,3,5,2]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,5,1,3,6]=>[1,4,7,3,8,6,2,5]=>[8,5,2,6,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,3,5,1,6]=>[1,2,4,7,3,8,6,5]=>[8,7,5,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,9,7,1]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,7,1,8,6,5]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,8,9,6,1]=>[1,2,3,4,5,7,9,6,8]=>[9,8,7,6,5,3,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,5,6,7,8,9,4,1]=>[1,2,3,5,7,9,4,6,8]=>[9,8,7,5,3,1,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,9,10,8,1]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,7,8,5,6,1]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,1,9,7,6]=>[1,2,3,4,5,8,7,9,6]=>[9,8,7,6,5,2,3,1,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,9,10,7,1]=>[1,2,3,4,5,6,8,10,7,9]=>[10,9,8,7,6,5,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,6,7,4,8,5,1]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,7,8,1,4]=>[1,2,5,7,3,6,8,4]=>[8,7,4,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,4,8,6,5]=>[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,7,8,9,10,5,1]=>[1,2,3,4,6,8,10,5,7,9]=>[10,9,8,7,5,3,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,10,1,8,9]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,8,7,6,5,4,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,8,9,6,7,1]=>[1,2,3,4,5,8,7,6,9]=>[9,8,7,6,5,2,3,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,7,8,5,9,6,1]=>[1,2,3,4,7,9,5,8,6]=>[9,8,7,6,3,1,5,2,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,7,8,4,5,6,1]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,4,8,5,1]=>[1,2,6,8,3,7,5,4]=>[8,7,3,1,6,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,6,4,7,8]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,6,7,4,8]=>[1,2,5,6,7,4,3,8]=>[8,7,4,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,5,8,4,6]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,5,4,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,4,3,7,1,8]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,2,1,5,7]=>[1,3,4,8,7,5,2,6]=>[8,6,5,1,2,4,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,5,3,4,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,7,5,1,8]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,6,5,1,8]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,5,6,1,8]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,4,6,1,8]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,4,7,1,8]=>[1,5,4,6,7,2,3,8]=>[8,4,5,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,5,7,1,8]=>[1,4,3,2,6,7,5,8]=>[8,5,6,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,8,4,3,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,8,6,4,7]=>[1,3,2,5,8,7,4,6]=>[8,6,7,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,2,1,5,7]=>[1,3,8,7,5,2,6,4]=>[8,6,1,2,4,7,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,1,8,5,7]=>[1,4,6,8,7,5,2,3]=>[8,5,3,1,2,4,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,7,4,3,6]=>[1,2,5,7,3,8,6,4]=>[8,7,4,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,8,6,5]=>[1,2,7,6,8,5,4,3]=>[8,7,2,3,1,4,5,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,4,1,7,5]=>[1,6,2,8,5,4,3,7]=>[8,3,7,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,4,5,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,4,5,8,6]=>[1,7,8,6,5,4,2,3]=>[8,2,1,3,4,5,7,6]=>[8,3,2,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,3,5,2,6]=>[1,7,2,8,6,5,3,4]=>[8,2,7,1,3,4,6,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,6,8,5]=>[1,7,8,5,4,3,2,6]=>[8,2,1,4,5,6,7,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,8,7,5]=>[1,6,8,5,4,3,2,7]=>[8,3,1,4,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,7,6,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,6,7,5]=>[1,8,5,4,3,2,6,7]=>[8,1,4,5,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,3,5,2,6]=>[1,8,6,5,3,2,7,4]=>[8,1,3,4,6,7,2,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,4,5,7,6]=>[1,8,6,5,4,2,3,7]=>[8,1,3,4,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,3,5,2,6]=>[1,7,2,4,8,6,5,3]=>[8,2,7,5,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,3,5,2,6]=>[1,8,6,5,3,2,4,7]=>[8,1,3,4,6,7,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,6,2,1,5,7]=>[1,3,4,6,2,8,7,5]=>[8,6,5,3,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,3,1,6,7]=>[1,8,7,6,2,4,5,3]=>[8,1,2,3,7,5,4,6]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,4,1,6,7]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,1,8,6,7]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,1,8,6,7]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,5,4,2,6]=>[1,2,8,6,4,3,7,5]=>[8,7,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,7,4,3,6]=>[1,5,7,3,8,6,4,2]=>[8,4,2,6,1,3,5,7]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,5,3,4,7]=>[1,6,3,2,4,8,7,5]=>[8,3,6,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,4,5,1,6]=>[1,7,2,3,4,8,6,5]=>[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,3,5,1,6]=>[1,2,7,3,8,6,5,4]=>[8,7,2,6,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,4,6,1,5]=>[1,7,2,8,5,4,3,6]=>[8,2,7,1,4,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,4,8,2,5]=>[1,6,8,5,4,3,2,7]=>[8,3,1,4,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,4,7,2,5]=>[1,6,7,2,8,5,4,3]=>[8,3,2,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,6,8,5]=>[1,2,7,8,5,4,3,6]=>[8,7,2,1,4,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,4,8,7,5]=>[1,2,6,8,5,4,3,7]=>[8,7,3,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,4,1,8,5]=>[1,7,8,5,4,3,2,6]=>[8,2,1,4,5,6,7,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,4,1,7,5]=>[1,8,5,4,3,2,6,7]=>[8,1,4,5,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,5,4,2,6]=>[1,8,6,4,3,7,2,5]=>[8,1,3,5,6,2,7,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,4,1,8,5]=>[1,6,2,7,8,5,4,3]=>[8,3,7,2,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,4,8,1,5]=>[1,7,2,6,8,5,4,3]=>[8,2,7,3,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,4,7,1,5]=>[1,8,5,4,3,2,6,7]=>[8,1,4,5,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,5,6,1,2]=>[1,4,3,7,2,8,5,6]=>[8,5,6,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,3,6,1,2]=>[1,4,5,3,7,2,8,6]=>[8,5,4,6,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,1,6,7,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,2,6,7,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,6,1,8,4]=>[1,5,6,2,3,7,8,4]=>[8,4,3,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,4,7,6,3]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,1,7,6,3]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,2,6,5,3]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,2,7,6,3]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,4,7,6,3]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,6,7,1,4]=>[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,2,4,1,5]=>[1,3,7,2,8,5,4,6]=>[8,6,2,7,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,4,1,3,5]=>[1,2,8,5,4,6,3,7]=>[8,7,1,4,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,5,1,3,4]=>[1,7,3,2,8,4,6,5]=>[8,2,6,7,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,4,2,3,5]=>[1,2,8,5,4,6,3,7]=>[8,7,1,4,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,5,6,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,6,5,8,4]=>[1,3,7,8,4,2,5,6]=>[8,6,2,1,5,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,6,5,8,4]=>[1,3,7,8,4,2,5,6]=>[8,6,2,1,5,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,5,7,3,4]=>[1,6,7,3,2,4,8,5]=>[8,3,2,6,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,5,7,3,4]=>[1,6,7,3,2,4,8,5]=>[8,3,2,6,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,5,7,2,4]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,5,2,7,4]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,6,8,5,4]=>[1,2,3,7,5,6,8,4]=>[8,7,6,2,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,6,8,5,4]=>[1,2,3,7,5,6,8,4]=>[8,7,6,2,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,5,3,1,4]=>[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,4,3,1,5]=>[1,2,8,5,4,6,3,7]=>[8,7,1,4,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,1,2,5,4]=>[1,3,7,5,2,8,4,6]=>[8,6,2,4,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,2,1,5,4]=>[1,3,7,5,2,8,4,6]=>[8,6,2,4,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,1,3,2,5]=>[1,4,6,3,7,2,8,5]=>[8,5,3,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,4,1,2,5]=>[1,3,7,2,8,5,4,6]=>[8,6,2,7,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,5,1,2,4]=>[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,6,8,1,4]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,4,2,1,5]=>[1,3,7,2,8,5,4,6]=>[8,6,2,7,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,8,2,3,7]=>[1,5,8,7,3,4,6,2]=>[8,4,1,2,6,5,3,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,5,1,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,5,7,2,8]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,7,3,4,2]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,8,6,3,7]=>[1,2,4,5,8,7,3,6]=>[8,7,5,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,5,8,3,7]=>[1,4,2,6,8,7,3,5]=>[8,5,7,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,1,4,8,3]=>[1,5,2,6,4,3,7,8]=>[8,4,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,1,2,4,3]=>[1,7,4,5,2,8,3,6]=>[8,2,5,4,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,7,8,2,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,4,1,7,3]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,8,5,7,4]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,1,4,8,6]=>[1,7,8,6,4,5,2,3]=>[8,2,1,3,5,4,7,6]=>[8,3,2,4,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,3,6,8,5]=>[1,7,8,5,3,4,2,6]=>[8,2,1,4,6,5,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,4,6,7,2]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,4,7,6,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,6,5,4,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,1,7,8,6]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,6,2,1,5]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,6,7,3,4]=>[1,5,6,7,3,2,8,4]=>[8,4,3,2,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,6,4,1,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,6,3,1,5]=>[1,2,7,3,8,5,6,4]=>[8,7,2,6,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,2,6,8,3]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,6,1,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,6,1,7,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,3,7,1,5]=>[1,2,8,5,3,6,7,4]=>[8,7,1,4,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,4,7,1,5]=>[1,8,5,4,6,7,2,3]=>[8,1,4,5,3,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,6,5,1,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,3,6,5,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,3,6,1,5]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,1,2,6,3]=>[1,4,7,6,2,5,3,8]=>[8,5,2,3,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,3,2,6,4]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,3,2,1,6]=>[1,4,7,2,5,3,8,6]=>[8,5,2,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,7,2,1,5]=>[1,3,8,5,7,2,6,4]=>[8,6,1,4,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,3,7,6,1,4]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,7,6,1,5]=>[1,3,8,5,7,2,4,6]=>[8,6,1,4,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,7,2,6,4]=>[1,2,5,7,6,3,8,4]=>[8,7,4,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,3,7,1,4]=>[1,5,3,8,4,2,6,7]=>[8,4,6,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,2,7,5,3]=>[1,2,6,7,5,3,8,4]=>[8,7,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,2,7,6,3]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,3,7,6,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,3,7,6,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,1,2,7,3]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,3,2,7,4]=>[1,5,3,8,4,2,6,7]=>[8,4,6,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,6,2,5,3]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,6,2,5,4]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,3,6,1,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,7,5,4,3]=>[1,2,6,5,7,4,8,3]=>[8,7,3,4,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,7,2,5,3]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,7,6,1,4]=>[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,7,2,6,4]=>[1,3,5,7,6,2,4,8]=>[8,6,4,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,2,7,5,3]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,2,7,6,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,3,2,7,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,8,2,5,3]=>[1,7,5,8,3,2,6,4]=>[8,2,4,1,6,7,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,8,2,5,4]=>[1,7,5,8,4,3,2,6]=>[8,2,4,1,5,6,7,3]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,8,2,1,5]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,8,6,1,4]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,8,6,5,3]=>[1,7,5,8,3,2,4,6]=>[8,2,4,1,6,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,8,6,5,4]=>[1,7,5,8,4,3,2,6]=>[8,2,4,1,5,6,7,3]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,8,6,1,5]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,8,2,1,6]=>[1,7,2,3,5,8,6,4]=>[8,2,7,6,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,8,7,4,3]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,8,7,1,6]=>[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,8,2,1,7]=>[1,3,5,8,7,2,6,4]=>[8,6,4,1,2,7,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,3,8,1,4]=>[1,7,2,6,8,4,3,5]=>[8,2,7,3,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,2,8,5,3]=>[1,7,5,2,6,8,3,4]=>[8,2,4,7,3,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,2,8,6,3]=>[1,7,6,8,3,5,2,4]=>[8,2,3,1,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,3,8,6,4]=>[1,7,6,8,4,2,3,5]=>[8,2,3,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,3,8,1,7]=>[1,2,6,8,7,3,5,4]=>[8,7,3,1,2,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,3,2,8,5]=>[1,7,8,5,3,2,6,4]=>[8,2,1,4,6,7,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,3,2,8,6]=>[1,7,8,6,2,3,5,4]=>[8,2,1,3,7,6,4,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,7,8,1,5]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,6,8,7,5]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,6,1,7,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,5,4,1,8]=>[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,5,4,1,7]=>[1,2,6,4,3,8,7,5]=>[8,7,3,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,7,5,4,8]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,6,8,4,5]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,2,6,1,8,5]=>[1,7,8,5,6,2,3,4]=>[8,2,1,4,3,7,6,5]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,8,5,3,6]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,1,5,3,6]=>[1,8,6,5,2,7,3,4]=>[8,1,3,4,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,6,5,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,5,6,8,2]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,5,8,3,2]=>[1,6,8,2,7,3,4,5]=>[8,3,1,7,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,6,8,3,2]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,7,6,8,2]=>[1,4,2,5,7,8,3,6]=>[8,5,7,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,7,5,3,8]=>[1,4,2,6,5,7,3,8]=>[8,5,7,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,6,5,4,8]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,6,5,3,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,1,5,6,7,2]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,8,6,7,2]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,3,1,7,2]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,8,6,7,2]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,1,6,7,2]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,1,6,7,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,5,1,4,7]=>[1,6,2,8,7,4,3,5]=>[8,3,7,1,2,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,6,8,3,2]=>[1,5,6,8,2,7,3,4]=>[8,4,3,1,7,2,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,7,6,8,2]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,7,5,3,8]=>[1,6,5,7,3,4,2,8]=>[8,3,4,2,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,1,6,8,2]=>[1,5,2,4,7,8,3,6]=>[8,4,7,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,1,8,3,2]=>[1,6,8,2,7,3,5,4]=>[8,3,1,7,2,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,1,5,3,8]=>[1,7,3,4,2,6,5,8]=>[8,2,6,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,5,4,1,3]=>[1,8,3,7,2,4,6,5]=>[8,1,6,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,5,4,1,3]=>[1,8,3,2,7,4,6,5]=>[8,1,6,7,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,6,5,1,4]=>[1,3,8,4,7,2,5,6]=>[8,6,1,5,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,5,3,1,2]=>[1,4,6,3,7,2,8,5]=>[8,5,3,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,5,4,3,2]=>[1,7,3,6,4,2,8,5]=>[8,2,6,3,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,6,3,2,1]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,6,5,2,1]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,3,5,4,1]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,3,2,4,7]=>[1,8,7,4,2,5,3,6]=>[8,1,2,5,7,4,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,3,2,4,6]=>[1,7,4,5,3,2,8,6]=>[8,2,5,4,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,5,2,3,7]=>[1,8,7,3,2,6,4,5]=>[8,1,2,6,7,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,5,2,4,7]=>[1,8,7,4,2,6,3,5]=>[8,1,2,5,7,3,6,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,5,2,3,7]=>[1,8,7,3,6,2,4,5]=>[8,1,2,6,3,7,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,5,4,3,7]=>[1,8,7,3,2,6,4,5]=>[8,1,2,6,7,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,1,4,3,7]=>[1,8,7,3,2,5,4,6]=>[8,1,2,6,7,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,7,4,3,6]=>[1,8,6,4,2,5,7,3]=>[8,1,3,5,7,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,5,4,3,6]=>[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,5,2,4,6]=>[1,7,4,2,8,6,3,5]=>[8,2,5,7,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,1,3,4,6]=>[1,8,6,3,7,4,5,2]=>[8,1,3,6,2,5,4,7]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,5,2,3,6]=>[1,8,6,2,4,7,3,5]=>[8,1,3,7,5,2,6,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,5,4,3,6]=>[1,8,6,4,2,3,7,5]=>[8,1,3,5,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,7,4,3,5]=>[1,8,5,7,3,6,4,2]=>[8,1,4,2,6,3,5,7]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,3,2,6,4]=>[1,8,4,7,6,2,3,5]=>[8,1,5,2,3,7,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,5,7,3,4]=>[1,8,4,2,3,6,7,5]=>[8,1,5,7,6,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,7,2,3,4]=>[1,5,7,3,2,8,4,6]=>[8,4,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,8,2,3,4]=>[1,5,8,4,2,7,3,6]=>[8,4,1,5,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,5,1,8,3,4]=>[1,6,8,4,5,2,7,3]=>[8,3,1,5,4,7,2,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,8,2,3,4]=>[1,7,3,2,5,8,4,6]=>[8,2,6,7,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,1,8,2,3,4]=>[1,6,2,5,8,4,3,7]=>[8,3,7,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,1,2,4,5]=>[1,6,2,7,4,8,5,3]=>[8,3,7,2,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,8,2,3,6]=>[1,7,3,4,2,5,8,6]=>[8,2,6,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,7,2,3,5]=>[1,8,5,7,3,6,2,4]=>[8,1,4,2,6,3,7,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,3,2,4,6]=>[1,7,4,2,5,3,8,6]=>[8,2,5,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,1,2,5,6]=>[1,8,6,2,3,7,5,4]=>[8,1,3,7,6,2,4,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,3,2,4,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,3,2,4,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,3,6,2,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,6,4,2,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,7,2,3,6]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,7,2,3,4]=>[1,5,7,3,8,4,2,6]=>[8,4,2,6,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,2,7,3,4]=>[1,6,7,3,8,4,2,5]=>[8,3,2,6,1,5,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,5,6,2,4]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,3,1,5,4]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,3,2,6,4]=>[1,5,3,2,8,4,7,6]=>[8,4,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,3,2,6,5]=>[1,8,5,3,2,4,7,6]=>[8,1,4,6,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,1,2,6,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,1,3,6,5]=>[1,8,5,2,3,7,6,4]=>[8,1,4,7,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,1,3,6,5]=>[1,7,6,3,8,5,2,4]=>[8,2,3,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,3,1,6,4]=>[1,8,4,2,7,6,3,5]=>[8,1,5,7,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,3,4,7,1]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,8,1,4,7]=>[1,3,2,5,8,7,4,6]=>[8,6,7,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,3,6,8,1]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,6,8,1,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,6,8,1,3,7]=>[1,5,8,7,3,4,6,2]=>[8,4,1,2,6,5,3,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,6,8,2,7]=>[1,5,6,8,7,2,3,4]=>[8,4,3,1,2,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,6,8,1,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,7,2,6,8,1]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,2,5,8,1]=>[1,4,7,8,2,6,5,3]=>[8,5,2,1,7,3,4,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,7,8,2,5]=>[1,4,2,6,8,5,7,3]=>[8,5,7,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,7,8,2,6]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,4,8,2,6]=>[1,5,4,3,2,7,6,8]=>[8,4,5,6,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,4,6,8,2]=>[1,5,4,3,2,7,8,6]=>[8,4,5,6,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,3,6,8,2]=>[1,4,2,5,3,7,8,6]=>[8,5,7,4,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,1,5,8,2]=>[1,4,7,8,2,3,6,5]=>[8,5,2,1,7,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,1,7,8,2]=>[1,4,5,2,6,7,8,3]=>[8,5,4,7,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,7,2,8,1]=>[1,4,5,7,8,2,6,3]=>[8,5,4,2,1,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,1,7,8,2]=>[1,3,6,7,8,2,5,4]=>[8,6,3,2,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,7,4,8,2]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,4,5,8,2]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,5,8,1,3]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,8,1,3,5]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,2,7,8,4]=>[1,5,2,3,6,7,8,4]=>[8,4,7,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,1,7,8,4]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,7,4,8,1]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,7,4,8,1]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,1,7,8,4]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,3,5,8,1]=>[1,4,7,8,2,3,6,5]=>[8,5,2,1,7,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,4,5,8,1]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,8,1,4,6]=>[1,3,7,4,2,5,8,6]=>[8,6,2,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,8,1,5,6]=>[1,3,2,7,5,8,6,4]=>[8,6,7,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,6,8,2,5]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,6,8,1,5]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,5,8,1,4]=>[1,6,8,4,2,3,7,5]=>[8,3,1,5,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,7,2,8,1,4]=>[1,6,8,4,7,2,3,5]=>[8,3,1,5,2,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,7,3,8,1]=>[1,6,3,4,5,7,8,2]=>[8,3,6,5,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,1,7,8,3]=>[1,6,7,8,3,4,5,2]=>[8,3,2,1,6,5,4,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,5,6,8,3]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,8,1,3,4]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,2,5,8,3]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,7,3,8,1]=>[1,5,7,8,2,6,3,4]=>[8,4,2,1,7,3,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,7,3,8,1]=>[1,5,7,8,2,4,6,3]=>[8,4,2,1,7,5,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,1,7,8,3]=>[1,5,2,4,6,7,8,3]=>[8,4,7,5,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,2,7,8,3]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,2,7,8,3]=>[1,6,7,8,3,5,2,4]=>[8,3,2,1,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,8,1,3,4]=>[1,6,2,5,8,4,3,7]=>[8,3,7,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,1,3,8,2]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,1,7,8,2]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,4,8,1,6]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,6,1,3,7]=>[1,8,7,3,5,6,2,4]=>[8,1,2,6,4,3,7,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,6,3,7]=>[1,8,7,3,4,2,5,6]=>[8,1,2,6,5,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,1,6,2,7]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,1,8,3,6]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,1,6,8,3]=>[1,7,8,3,4,2,5,6]=>[8,2,1,6,5,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,1,6,8,2]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,6,1,8,2]=>[1,7,8,2,4,5,6,3]=>[8,2,1,7,5,4,3,6]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,1,4,8,2]=>[1,5,2,6,4,3,7,8]=>[8,4,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,1,8,2,4]=>[1,5,2,6,8,4,3,7]=>[8,4,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,8,1,2,4]=>[1,5,8,4,7,2,6,3]=>[8,4,1,5,2,7,3,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,2,4,8,1]=>[1,5,2,6,4,7,8,3]=>[8,4,7,3,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,3,8,1,4]=>[1,5,3,7,2,6,8,4]=>[8,4,6,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,8,1,3,6]=>[1,7,3,5,8,6,2,4]=>[8,2,6,4,1,3,7,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,4,8,1,5]=>[1,6,8,5,4,2,7,3]=>[8,3,1,4,5,7,2,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,1,3,8,5]=>[1,7,8,5,2,6,3,4]=>[8,2,1,4,7,3,6,5]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,1,2,8,5]=>[1,7,8,5,2,6,3,4]=>[8,2,1,4,7,3,6,5]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,5,1,8,4]=>[1,6,2,7,8,4,3,5]=>[8,3,7,2,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,1,2,8,3]=>[1,7,8,3,5,2,4,6]=>[8,2,1,6,4,7,5,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,1,2,8,4]=>[1,6,2,7,8,4,5,3]=>[8,3,7,2,1,5,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,1,2,8,3]=>[1,5,2,6,3,7,8,4]=>[8,4,7,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,4,1,8,3]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,3,1,8,2]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,6,4,1,2]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,6,1,4,2]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,6,3,4,2]=>[1,2,7,4,5,6,3,8]=>[8,7,2,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,6,3,4,2]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,6,1,4,2]=>[1,3,5,6,2,7,4,8]=>[8,6,4,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,6,4,1,2]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,6,3,4,2]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,3,6,4,2]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,1,6,4,2]=>[1,3,7,4,8,2,5,6]=>[8,6,2,5,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,1,6,4,2]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,6,1,4,2]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,6,1,4,2]=>[1,7,4,5,6,2,3,8]=>[8,2,5,4,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,6,3,4,2]=>[1,7,4,5,6,3,2,8]=>[8,2,5,4,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,6,3,4,2]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,3,6,4,2]=>[1,5,3,7,4,8,2,6]=>[8,4,6,2,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,5,6,4,2]=>[1,3,7,4,8,2,5,6]=>[8,6,2,5,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,5,6,4,2]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,8,6,4,2]=>[1,3,7,4,5,8,2,6]=>[8,6,2,5,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,3,6,4,2]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,3,6,4,2]=>[1,7,4,5,3,2,8,6]=>[8,2,5,4,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,1,6,4,2]=>[1,7,4,5,2,8,3,6]=>[8,2,5,4,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,1,6,4,2]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,8,6,4,2]=>[1,3,7,4,2,5,8,6]=>[8,6,2,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,1,6,4,2]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,3,6,4,2]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,3,6,4,2]=>[1,2,7,4,5,3,8,6]=>[8,7,2,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,1,6,4,2]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,6,1,4,2]=>[1,5,6,2,7,4,3,8]=>[8,4,3,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,3,1,4,2]=>[1,5,3,8,2,7,4,6]=>[8,4,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,6,3,4,2]=>[1,5,6,3,8,2,7,4]=>[8,4,3,6,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,3,6,4,2]=>[1,5,3,8,2,7,4,6]=>[8,4,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,5,6,4,2]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,5,6,4,2]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,5,6,4,2]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,5,6,4,2]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,3,6,4,2]=>[1,5,3,2,7,4,8,6]=>[8,4,6,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,6,3,4,2]=>[1,5,6,3,2,7,4,8]=>[8,4,3,6,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,6,3,4,2]=>[1,7,4,2,5,6,3,8]=>[8,2,5,7,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,3,6,4,2]=>[1,7,4,2,5,3,8,6]=>[8,2,5,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,8,6,4,2]=>[1,7,4,3,2,5,8,6]=>[8,2,5,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,8,6,4,2]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,8,6,4,2]=>[1,7,4,5,8,2,3,6]=>[8,2,5,4,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,5,6,4,2]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,5,6,4,2]=>[1,7,4,3,2,8,5,6]=>[8,2,5,6,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,5,6,4,2]=>[1,7,4,3,8,2,5,6]=>[8,2,5,6,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,5,6,4,2]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,8,6,4,2]=>[1,7,4,5,8,2,3,6]=>[8,2,5,4,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,8,6,4,2]=>[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,6,8,1,2]=>[1,5,6,8,2,7,3,4]=>[8,4,3,1,7,2,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,8,6,1,2]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,8,1,6,2]=>[1,5,8,2,7,6,3,4]=>[8,4,1,7,2,3,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,1,8,6,2]=>[1,5,2,7,6,8,3,4]=>[8,4,7,2,3,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,1,6,8,2]=>[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,1,2,8,4]=>[1,7,8,4,6,2,3,5]=>[8,2,1,5,3,7,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,4,6,2,8]=>[1,5,4,2,7,3,6,8]=>[8,4,5,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,4,8,2,6]=>[1,5,4,2,7,3,6,8]=>[8,4,5,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,1,2,8,6]=>[1,5,2,3,7,8,6,4]=>[8,4,7,6,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,1,2,6,8]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,4,2,6,8]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,2,8,6,4]=>[1,3,5,2,7,6,8,4]=>[8,6,4,7,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,1,2,6,4]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,2,6,4,8]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,2,6,8,4]=>[1,3,5,2,7,8,4,6]=>[8,6,4,7,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,5,2,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,6,1,3,2]=>[1,5,6,2,4,8,3,7]=>[8,4,3,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,2,8,3,1,4]=>[1,7,2,5,8,4,3,6]=>[8,2,7,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,8,3,1,6]=>[1,4,5,8,6,3,2,7]=>[8,5,4,1,3,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,1,3,8,7]=>[1,6,3,4,5,2,7,8]=>[8,3,6,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,5,4,1,2]=>[1,3,6,4,7,2,8,5]=>[8,6,3,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,3,4,1,5]=>[1,6,4,8,5,3,7,2]=>[8,3,5,1,4,6,2,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,3,4,7,6]=>[1,5,3,8,6,4,2,7]=>[8,4,6,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,5,4,6,2]=>[1,3,8,2,7,6,4,5]=>[8,6,1,7,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,7,1,4,2]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,8,3,5,2]=>[1,4,2,7,5,8,3,6]=>[8,5,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,3,8,5,1]=>[1,4,6,8,2,7,5,3]=>[8,5,3,1,7,2,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,6,7,3,5]=>[1,2,3,8,5,6,7,4]=>[8,7,6,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,3,1,2,5]=>[1,4,6,2,7,3,8,5]=>[8,5,3,7,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,6,7,2,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,8,1,7,6]=>[1,3,4,5,8,6,2,7]=>[8,6,5,4,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,2,3,8,1]=>[1,6,3,7,8,2,4,5]=>[8,3,6,2,1,7,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,7,3,2,5]=>[1,6,3,8,5,7,2,4]=>[8,3,6,1,4,2,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,7,5,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,3,5,2,4]=>[1,7,2,6,5,3,8,4]=>[8,2,7,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,2,3,1,8,4]=>[1,6,2,7,8,4,3,5]=>[8,3,7,2,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,5,1,8,3]=>[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,8,5,7,3]=>[1,6,5,8,3,2,4,7]=>[8,3,4,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,4,1,5,3]=>[1,8,3,2,7,5,4,6]=>[8,1,6,7,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,5,3,1,4]=>[1,6,3,8,4,2,7,5]=>[8,3,6,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,6,8,5,4]=>[1,2,3,7,5,6,8,4]=>[8,7,6,2,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,8,4,6,3]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,3,6,1,4]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,3,2,8,5]=>[1,6,2,3,7,8,5,4]=>[8,3,7,6,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,2,1,7,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,5,7,8,3]=>[1,4,2,3,6,7,8,5]=>[8,5,7,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,7,4,1,2]=>[1,6,4,3,8,2,5,7]=>[8,3,5,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,5,7,6,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,8,6,1,4]=>[1,3,7,2,5,8,4,6]=>[8,6,2,7,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,8,6,1,3]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,5,2,8,4]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,5,1,8,4]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,7,5,1,3]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,8,5,1,4]=>[1,6,5,8,4,2,3,7]=>[8,3,4,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,7,6,1,3]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,6,5,1,3]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,7,6,1,3]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,6,1,8,4]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,2,8,7,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,1,8,7,4]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,8,1,6,5]=>[1,4,3,7,6,2,5,8]=>[8,5,6,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,7,3,8,6]=>[1,2,5,7,8,6,3,4]=>[8,7,4,2,1,3,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,7,2,5,4]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,2,8,7,4]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,3,8,7,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,8,7,6,3]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,2,8,6,4]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,2,8,7,6]=>[1,4,3,5,2,6,8,7]=>[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,3,8,7,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,1,8,6,4]=>[1,7,6,8,4,5,2,3]=>[8,2,3,1,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,8,6,5,2]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,8,7,5,2]=>[1,6,7,5,8,2,3,4]=>[8,3,2,4,1,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,8,7,6,2]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,8,7,6,3]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,8,7,5,3]=>[1,2,6,7,5,8,3,4]=>[8,7,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,8,7,4,2]=>[1,5,8,2,6,7,4,3]=>[8,4,1,7,3,2,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,8,1,7,4]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,1,8,7,3]=>[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,2,8,7,4]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,2,7,6,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,3,1,7,6,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,1,7,6,3]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,5,1,4,8,7]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,3,7,6,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,4,7,6,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,4,7,6,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,2,8,6,5]=>[1,3,2,4,7,6,8,5]=>[8,6,7,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,7,4,8,6]=>[1,3,2,5,7,8,6,4]=>[8,6,7,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,2,8,5,4]=>[1,6,8,4,7,5,2,3]=>[8,3,1,5,2,4,7,6]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,8,7,5,4]=>[1,2,6,7,5,8,4,3]=>[8,7,3,2,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,8,7,6,3]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,8,6,5,3]=>[1,7,5,8,3,2,4,6]=>[8,2,4,1,6,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,2,8,6,4]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,3,7,6,4]=>[1,5,3,8,4,2,6,7]=>[8,4,6,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,3,7,6,5]=>[1,4,8,5,3,2,6,7]=>[8,5,1,4,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,5,3,1,2]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,4,1,3,8]=>[1,7,3,2,5,4,6,8]=>[8,2,6,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,5,8,4,2]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,4,1,5,8]=>[1,7,5,4,3,6,2,8]=>[8,2,4,5,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,5,1,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,5,3,1,2]=>[1,6,3,4,7,2,8,5]=>[8,3,6,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,6,3,1,2]=>[1,4,5,6,3,7,2,8]=>[8,5,4,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,4,5,1,2]=>[1,3,7,2,8,4,6,5]=>[8,6,2,7,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,1,4,5,8]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,2,1,4,7]=>[1,6,2,8,7,4,3,5]=>[8,3,7,1,2,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,5,1,3,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,4,1,3,8]=>[1,5,4,6,2,7,3,8]=>[8,4,5,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,5,8,4,2]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,3,7,5,2]=>[1,8,2,3,6,7,5,4]=>[8,1,7,6,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,8,6,3,5]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,7,5,4,2]=>[1,2,8,3,6,5,7,4]=>[8,7,1,6,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,3,6,5,4]=>[1,2,8,4,7,5,3,6]=>[8,7,1,5,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,4,7,5,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,4,3,6,5]=>[1,8,5,4,7,6,3,2]=>[8,1,4,5,2,3,6,7]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,8,4,7,2]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,7,1,4,3,5]=>[1,6,4,7,3,8,5,2]=>[8,3,5,2,6,1,4,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,5,4,3,6]=>[1,8,6,4,2,7,3,5]=>[8,1,3,5,7,2,6,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,1,5,6,7]=>[1,2,4,3,8,7,6,5]=>[8,7,5,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,7,1,5,6,8]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,2,1,5,6]=>[1,4,8,6,2,7,5,3]=>[8,5,1,3,7,2,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,1,4,6,8]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,8,4,6,5]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,8,6,7,3]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,2,1,4,7]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,7,1,3,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,7,1,3,8]=>[1,5,7,3,6,2,4,8]=>[8,4,2,6,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,8,4,5,2]=>[1,7,5,8,2,6,4,3]=>[8,2,4,1,7,3,5,6]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,3,7,5,2]=>[1,6,7,5,3,4,2,8]=>[8,3,2,4,6,5,7,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,1,3,8,4,2]=>[1,6,8,2,5,3,7,4]=>[8,3,1,7,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,7,4,6,2]=>[1,5,7,6,4,2,8,3]=>[8,4,2,3,5,7,1,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,5,4,6,2]=>[1,8,2,3,4,7,6,5]=>[8,1,7,6,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,4,6,5,2]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,6,3,5,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,6,4,3,5]=>[1,8,5,6,4,7,3,2]=>[8,1,4,3,5,2,6,7]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,7,4,5,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,7,6,3,4]=>[1,5,7,3,2,8,4,6]=>[8,4,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,8,5,3,4]=>[1,6,5,8,4,2,3,7]=>[8,3,4,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,6,5,4,2]=>[1,7,4,3,8,2,5,6]=>[8,2,5,6,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,9,3,4,5,6,7]=>[1,2,3,8,6,4,9,7,5]=>[9,8,7,2,4,6,1,3,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,7,8,4,6,3,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,2,6,4,1]=>[1,3,8,2,5,4,7,6]=>[8,6,1,7,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,5,2,1,4]=>[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,5,2,1,7]=>[1,4,8,7,2,6,3,5]=>[8,5,1,2,7,3,6,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,2,6,1,4]=>[1,3,7,2,5,4,8,6]=>[8,6,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,1,3,8,7]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,6,1,5,7]=>[1,8,7,5,6,2,3,4]=>[8,1,2,4,3,7,6,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,6,1,8,5]=>[1,7,8,5,6,2,3,4]=>[8,2,1,4,3,7,6,5]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,7,5,1,6]=>[1,8,6,5,7,2,3,4]=>[8,1,3,4,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,5,1,4,2]=>[1,7,4,6,2,8,3,5]=>[8,2,5,3,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,6,1,5,8,7]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,5,1,6,2]=>[1,4,7,6,2,8,3,5]=>[8,5,2,3,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,7,1,6,5]=>[1,8,5,7,6,2,3,4]=>[8,1,4,2,3,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,8,7,1,6]=>[1,5,8,6,7,2,3,4]=>[8,4,1,3,2,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,6,8,1,7]=>[1,5,6,8,7,2,3,4]=>[8,4,3,1,2,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,7,6,1,3]=>[1,4,5,7,2,3,8,6]=>[8,5,4,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,5,1,8,2]=>[1,3,6,2,7,8,4,5]=>[8,6,3,7,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,5,8,2,1]=>[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,5,2,1,6]=>[1,4,7,2,8,6,3,5]=>[8,5,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,5,1,2,4]=>[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,1,6,3,4]=>[1,8,4,5,2,3,7,6]=>[8,1,5,4,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,5,8,6,3,1]=>[1,4,5,8,2,3,7,6]=>[8,5,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,3,6,4,2]=>[1,5,3,2,8,4,7,6]=>[8,4,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,4,6,3,1]=>[1,5,4,8,2,3,7,6]=>[8,4,5,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,7,6,1,4]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,1,6,4,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,5,7,1,4]=>[1,6,7,2,8,4,3,5]=>[8,3,2,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,4,2,1]=>[1,6,4,8,2,7,3,5]=>[8,3,5,1,7,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,1,8,5,7]=>[1,6,8,7,5,2,3,4]=>[8,3,1,2,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,8,7,5,1]=>[1,6,7,5,8,2,3,4]=>[8,3,2,4,1,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,7,5,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,3,4,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,3,5,6,7]=>[1,2,8,7,6,5,3,4]=>[8,7,1,2,3,4,6,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,1,5,3,2]=>[1,8,2,6,5,3,7,4]=>[8,1,7,3,4,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,5,1,3,2]=>[1,4,7,3,6,2,8,5]=>[8,5,2,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,6,5,2,3]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,4,6,2,3]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,4,6,3,2]=>[1,8,2,5,4,3,7,6]=>[8,1,7,4,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,5,6,3,2]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,5,6,3,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,6,1,3,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,4,6,2,3]=>[1,8,3,5,4,2,7,6]=>[8,1,6,4,5,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,1,4,6,3]=>[1,8,3,2,7,6,4,5]=>[8,1,6,7,2,3,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,5,1,6,3]=>[1,4,2,8,3,7,6,5]=>[8,5,7,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,5,2,7,3]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,2,5,6,3]=>[1,8,3,2,7,6,5,4]=>[8,1,6,7,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,4,6,3]=>[1,8,3,5,2,7,6,4]=>[8,1,6,4,7,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,2,5,6,4]=>[1,3,7,6,5,2,8,4]=>[8,6,2,3,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,7,1,6,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,5,6,2,4]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,1,6,2,4]=>[1,3,8,4,7,2,5,6]=>[8,6,1,5,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,7,5,1,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,2,6,5,3]=>[1,8,3,4,2,7,5,6]=>[8,1,6,5,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,7,5,2,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,2,6,3,4]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,5,6,3,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,2,4,6,3]=>[1,8,3,2,7,6,4,5]=>[8,1,6,7,2,3,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,7,2,6,4]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,2,5,6,4]=>[1,2,8,4,7,6,5,3]=>[8,7,1,5,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,3,5,6,4]=>[1,2,8,4,3,7,6,5]=>[8,7,1,5,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,2,3,6,4]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,3,5,6,4]=>[1,7,6,5,3,8,4,2]=>[8,2,3,4,6,1,5,7]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,4,1,5,2]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,7,5,1,3]=>[1,4,6,5,7,2,3,8]=>[8,5,3,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,5,6,1,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,1,7,5,2]=>[1,4,6,7,5,2,8,3]=>[8,5,3,2,4,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,5,1,6,2]=>[1,8,2,3,4,7,6,5]=>[8,1,7,6,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,5,6,1,3]=>[1,8,3,4,2,7,5,6]=>[8,1,6,5,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,6,2,3,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,1,5,6,3]=>[1,8,3,2,7,6,5,4]=>[8,1,6,7,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,7,2,5,3]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,2,6,5,3]=>[1,4,8,3,2,7,5,6]=>[8,5,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,7,1,5,3]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,3,4,5]=>[1,8,5,6,3,7,4,2]=>[8,1,4,3,6,2,5,7]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,3,6,4,5]=>[1,8,5,3,7,4,2,6]=>[8,1,4,6,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,6,3,4,5]=>[1,2,8,5,6,3,7,4]=>[8,7,1,4,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,6,2,4,5]=>[1,2,8,5,6,3,7,4]=>[8,7,1,4,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,6,3,4,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,1,5,6,3]=>[1,8,3,7,6,5,2,4]=>[8,1,6,2,3,4,7,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,5,6,2,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,5,6,1,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,7,5,2,4]=>[1,8,4,6,5,7,2,3]=>[8,1,5,3,4,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,6,7,4,3]=>[1,8,3,2,5,6,7,4]=>[8,1,6,7,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,6,7,4,3]=>[1,2,5,6,7,4,8,3]=>[8,7,4,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,7,5,3,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,7,5,1,4]=>[1,8,4,6,5,7,2,3]=>[8,1,5,3,4,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,5,6,1,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,5,6,2,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,5,6,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,7,5,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,7,3,5,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,3,6,4,5]=>[1,8,5,3,2,4,7,6]=>[8,1,4,6,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,3,4,5]=>[1,8,5,6,3,7,4,2]=>[8,1,4,3,6,2,5,7]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,3,6,4,5]=>[1,8,5,3,7,4,2,6]=>[8,1,4,6,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,3,6,5,4]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,2,5,6,4]=>[1,8,4,2,3,7,6,5]=>[8,1,5,7,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,3,6,4,5]=>[1,8,5,3,2,7,4,6]=>[8,1,4,6,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,4,6,3,1]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,7,4,2,6]=>[1,3,8,6,4,5,7,2]=>[8,6,1,3,5,4,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,4,2,6,1]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,4,5,7,1]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,5,4,7,1]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,4,6,3,1]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,6,3,2,5]=>[1,4,7,2,8,5,6,3]=>[8,5,2,7,1,4,3,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,6,2,3,5,8]=>[1,4,6,3,7,5,2,8]=>[8,5,3,6,2,4,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,8,4,2,6]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,4,2,6,1]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,2,8,5,1]=>[1,7,5,2,3,6,8,4]=>[8,2,4,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,1,6,3,5]=>[1,7,3,8,5,2,4,6]=>[8,2,6,1,4,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,3,2,5,1]=>[1,8,2,7,5,3,4,6]=>[8,1,7,2,4,6,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,2,1,4,3,6]=>[1,7,3,5,2,8,6,4]=>[8,2,6,4,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,1,4,8,6]=>[1,7,8,6,4,3,2,5]=>[8,2,1,3,5,6,7,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,8,1,3,2,7]=>[1,4,8,7,2,6,3,5]=>[8,5,1,2,7,3,6,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,3,6,2,5]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,4,6,2,8]=>[1,5,4,3,2,7,6,8]=>[8,4,5,6,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,2,3,6,8]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,2,4,6,7]=>[1,5,2,8,7,6,4,3]=>[8,4,7,1,2,3,5,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,3,2,7,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,2,3,6,1]=>[1,5,2,4,7,6,3,8]=>[8,4,7,5,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,2,5,4,1]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,2,3,7,1]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,8,3,6,1]=>[1,5,8,2,7,6,3,4]=>[8,4,1,7,2,3,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,1,8,3,5]=>[1,6,8,5,2,4,3,7]=>[8,3,1,4,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,1,2,8,7]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,1,3,2,7]=>[1,6,3,5,2,8,7,4]=>[8,3,6,4,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,6,1,5,3,8]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,6,1,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,1,5,7,3]=>[1,6,5,2,4,8,3,7]=>[8,3,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,2,5,1,4]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,4,2,1,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,5,6,2,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,6,1,3,8]=>[1,7,3,5,6,2,4,8]=>[8,2,6,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,6,7,4,1]=>[1,5,6,7,4,2,3,8]=>[8,4,3,2,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,5,4,7,1]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,2,6,4,1]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,6,2,1,3]=>[1,5,6,2,7,3,8,4]=>[8,4,3,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,6,7,1,2]=>[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,4,7,2,1,3]=>[1,5,7,2,8,3,6,4]=>[8,4,2,7,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,6,3,2,1]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,5,3,2,1]=>[1,4,7,2,8,3,6,5]=>[8,5,2,7,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,2,4,1,5]=>[1,6,4,7,2,3,8,5]=>[8,3,5,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,2,6,4,1]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,7,2,4,1]=>[1,5,7,4,6,2,3,8]=>[8,4,2,5,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,8,2,1,3]=>[1,5,8,3,6,2,7,4]=>[8,4,1,6,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,7,2,1,3]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,1,7,3,5]=>[1,6,7,3,2,4,8,5]=>[8,3,2,6,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,4,3,7,8,1]=>[1,6,7,8,2,5,3,4]=>[8,3,2,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,7,2,4,1]=>[1,5,7,4,8,2,6,3]=>[8,4,2,5,1,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,1,8,2,5]=>[1,6,8,5,2,7,3,4]=>[8,3,1,4,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,6,8,1,2]=>[1,5,6,8,2,7,3,4]=>[8,4,3,1,7,2,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,6,7,3,2,1]=>[1,4,6,3,8,2,5,7]=>[8,5,3,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,7,3,2,1]=>[1,4,5,7,2,6,3,8]=>[8,5,4,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,7,2,4,1]=>[1,5,7,4,3,8,2,6]=>[8,4,2,5,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,2,7,1,3]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,2,5,1,4]=>[1,3,7,2,6,5,4,8]=>[8,6,2,7,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,6,4,1,3]=>[1,5,6,4,2,7,3,8]=>[8,4,3,5,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,7,1,4,2]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,6,2,3,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,8,6,1,3]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,1,8,4,2]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,7,1,8,3]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,5,1,6,4]=>[1,8,4,7,6,2,3,5]=>[8,1,5,2,3,7,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,5,1,8,4]=>[1,7,8,4,3,6,2,5]=>[8,2,1,5,6,3,7,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,7,2,4,5]=>[1,8,5,7,4,6,2,3]=>[8,1,4,2,5,3,7,6]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,6,3,7]=>[1,8,7,3,4,2,5,6]=>[8,1,2,6,5,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,7,5,3,6]=>[1,8,6,5,7,3,4,2]=>[8,1,3,4,2,6,5,7]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,2,7,4,5]=>[1,6,7,4,8,5,2,3]=>[8,3,2,5,1,4,7,6]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,1,7,8,5]=>[1,3,2,6,7,8,5,4]=>[8,6,7,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,1,5,8,4]=>[1,6,5,2,3,7,8,4]=>[8,3,4,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,5,8,6,2]=>[1,7,6,8,2,3,4,5]=>[8,2,3,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,8,6,3,4]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,7,8,4,2]=>[1,5,7,4,2,6,8,3]=>[8,4,2,5,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,2,6,3,7]=>[1,2,5,3,8,7,4,6]=>[8,7,4,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,2,6,4,8]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,2,6,3,5]=>[1,4,8,5,2,7,3,6]=>[8,5,1,4,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,1,3,2,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,2,5,4,8]=>[1,6,5,2,7,4,3,8]=>[8,3,4,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,1,5,4,6]=>[1,7,4,3,2,8,6,5]=>[8,2,5,6,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,3,5,1,6]=>[1,7,2,8,6,5,3,4]=>[8,2,7,1,3,4,6,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,1,5,3,6]=>[1,7,3,2,8,6,5,4]=>[8,2,6,7,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,5,7,3,8]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,1,5,3,8]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,1,5,4,8]=>[1,6,5,2,7,4,3,8]=>[8,3,4,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,4,8,1,2]=>[1,6,8,2,7,3,4,5]=>[8,3,1,7,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,5,7,3,8]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,7,4,8,1,2]=>[1,3,5,4,7,2,6,8]=>[8,6,4,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,3,7,1,8]=>[1,5,3,2,6,7,4,8]=>[8,4,6,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,3,7,2,8]=>[1,5,3,2,6,7,4,8]=>[8,4,6,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,2,7,4,8]=>[1,5,2,6,7,4,3,8]=>[8,4,7,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,1,3,2,8]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,1,3,2,8]=>[1,6,3,4,5,2,7,8]=>[8,3,6,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,1,3,2,4]=>[1,6,3,5,2,7,4,8]=>[8,3,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,2,7,6,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,1,3,2,8]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,2,7,5,8]=>[1,4,3,2,6,7,5,8]=>[8,5,6,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,2,7,5,8]=>[1,2,4,6,7,5,3,8]=>[8,7,5,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,5,7,2,8]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,1,7,6,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,6,8,1,2]=>[1,4,7,2,5,6,8,3]=>[8,5,2,7,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,3,8,1,2]=>[1,4,7,2,6,8,3,5]=>[8,5,2,7,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,2,3,1,8]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,4,7,2,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,2,7,4,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,1,7,4,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,4,7,1,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,1,7,5,8]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,1,7,5,8]=>[1,4,3,2,6,7,5,8]=>[8,5,6,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,1,7,5,8]=>[1,2,4,6,7,5,3,8]=>[8,7,5,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,1,7,4,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,3,5,8,1]=>[1,4,7,8,2,6,5,3]=>[8,5,2,1,7,3,4,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,5,4,8,1]=>[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,3,8,2,5]=>[1,4,7,2,6,8,5,3]=>[8,5,2,7,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,3,8,6,5]=>[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,6,4,8,1]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,3,8,2,6]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,1,8,6,4]=>[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,8,3,6,4]=>[1,2,5,8,4,3,7,6]=>[8,7,4,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,1,8,4,6]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,4,8,2,6]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,1,8,4,3]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,8,5,6,4]=>[1,2,3,7,6,5,8,4]=>[8,7,6,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,8,4,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,8,4,3,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,8,6,4,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,8,5,4,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,8,5,4,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,1,8,3,5]=>[1,4,7,3,2,6,8,5]=>[8,5,2,6,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,7,8,3,2]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,8,6,3,4]=>[1,2,5,8,4,7,3,6]=>[8,7,4,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,8,7,4,5]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,8,4,7,3]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,8,4,7,5]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,8,7,3,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,7,8,4,1]=>[1,3,5,7,4,2,6,8]=>[8,6,4,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,7,5,8,3,1]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,4,2,6,3]=>[1,2,5,4,8,3,7,6]=>[8,7,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,8,6,2,5]=>[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,5,7,2,1]=>[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,8,7,3,1]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,1,7,4,3]=>[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,8,7,3,2]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,1,8,7,2]=>[1,4,3,6,8,2,5,7]=>[8,5,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,1,7,5,8]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,1,7,5,8]=>[1,4,2,6,7,5,3,8]=>[8,5,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,7,5,2,8]=>[1,4,2,6,5,7,3,8]=>[8,5,7,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,6,1,8,2]=>[1,4,7,8,2,5,6,3]=>[8,5,2,1,7,4,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,4,3,8,6]=>[1,2,5,4,3,7,8,6]=>[8,7,4,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,7,6,1,8,2]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,6,4,7,8]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,2,7,4,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,7,5,3,8]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,4,2,5,8]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,5,3,2,8]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,2,1,7,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,4,1,7,8]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,3,7,4,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,1,7,8,5]=>[1,4,3,6,7,8,5,2]=>[8,5,6,3,2,1,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,7,4,5,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,4,1,5,8]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,8,6,4,1]=>[1,3,7,4,2,5,8,6]=>[8,6,2,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,5,2,4,8]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,3,1,7,8]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,6,3,7,8]=>[1,5,6,3,2,4,7,8]=>[8,4,3,6,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,3,1,7,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,5,4,8,2]=>[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,4,3,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,5,4,7,8]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,3,2,7,8]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,3,2,7,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,6,2,7,8]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,5,4,8,2]=>[1,7,8,2,3,4,6,5]=>[8,2,1,7,6,5,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,1,5,4,3,6]=>[1,7,3,8,6,4,2,5]=>[8,2,6,1,3,5,7,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,5,4,1,7]=>[1,3,2,8,7,4,6,5]=>[8,6,7,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,5,4,6,8]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,1,4,3,5]=>[1,7,3,8,5,2,4,6]=>[8,2,6,1,4,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,6,8,4,1,3]=>[1,5,8,3,7,2,4,6]=>[8,4,1,6,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,5,4,1,6]=>[1,3,7,2,8,6,4,5]=>[8,6,2,7,1,3,5,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,8,4,3,2]=>[1,7,3,2,5,8,4,6]=>[8,2,6,7,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,5,6,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,5,1,3,4]=>[1,7,3,8,4,6,2,5]=>[8,2,6,1,5,3,7,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,7,4,1,8]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,5,6,1,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,7,1,5,8]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,5,2,4,8]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,4,7,1,8]=>[1,3,6,7,2,5,4,8]=>[8,6,3,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,2,4,6,1]=>[1,3,8,2,5,4,7,6]=>[8,6,1,7,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,4,3,6,1]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,7,1,3,8]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,3,5,2,8]=>[1,4,6,5,3,2,7,8]=>[8,5,3,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,7,8,2,6]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,7,6,3,5]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,1,5,4,2]=>[1,8,2,7,4,6,5,3]=>[8,1,7,2,5,3,4,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,4,6,1,3]=>[1,2,5,4,7,3,8,6]=>[8,7,4,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,7,8,3,6]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,1,8,3,5]=>[1,4,2,7,3,6,8,5]=>[8,5,7,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,1,7,5,4]=>[1,8,4,2,3,6,7,5]=>[8,1,5,7,6,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,4,2,1,5]=>[1,8,5,4,6,2,3,7]=>[8,1,4,5,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,4,7,6,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,6,5,1,3]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,4,7,3,2]=>[1,8,2,6,7,3,5,4]=>[8,1,7,3,2,6,4,5]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,7,3,6,2]=>[1,8,2,5,7,6,3,4]=>[8,1,7,4,2,3,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,2,7,5,4]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,1,8,5,3]=>[1,6,8,3,7,5,2,4]=>[8,3,1,6,2,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,3,8,6,4]=>[1,2,7,6,8,4,3,5]=>[8,7,2,3,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,3,8,2,5]=>[1,2,7,3,6,8,5,4]=>[8,7,2,6,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,8,6,5,1]=>[1,3,2,7,5,8,4,6]=>[8,6,7,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,7,6,1,5]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,2,7,8,6]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,4,1,8,5]=>[1,3,6,2,7,8,5,4]=>[8,6,3,7,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,5,7,4,3]=>[1,2,6,7,4,3,8,5]=>[8,7,3,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,1,3,8,5]=>[1,2,7,8,5,3,6,4]=>[8,7,2,1,4,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,3,1,8,4]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,4,6,3,1]=>[1,5,4,8,2,7,3,6]=>[8,4,5,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,8,4,6,2]=>[1,5,8,2,7,6,4,3]=>[8,4,1,7,2,3,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,1,6,5,2]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,7,4,1,3]=>[1,2,6,4,5,7,3,8]=>[8,7,3,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,2,1,8,3]=>[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,3,4,2,5]=>[1,6,4,8,5,3,2,7]=>[8,3,5,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,1,8,3,4]=>[1,5,2,6,8,4,7,3]=>[8,4,7,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,3,8,1,5]=>[1,6,8,5,3,2,7,4]=>[8,3,1,4,6,7,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,6,7,1,5]=>[1,2,4,8,5,6,7,3]=>[8,7,5,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,4,5,3,6]=>[1,2,8,6,5,4,7,3]=>[8,7,1,3,4,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,5,6,4,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,4,7,1,2]=>[1,3,5,4,6,7,2,8]=>[8,6,4,5,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,4,8,1,2]=>[1,5,4,6,8,2,7,3]=>[8,4,5,3,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,1,6,4,8]=>[1,5,2,7,4,3,6,8]=>[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,3,6,1,8]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,1,5,3,8]=>[1,4,7,3,2,6,5,8]=>[8,5,2,6,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,1,4,2,8]=>[1,5,2,6,4,7,3,8]=>[8,4,7,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,3,4,2,8]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,4,7,2,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,4,8,2,3]=>[1,5,4,6,8,3,2,7]=>[8,4,5,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,4,2,8,5,6]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,2,8,6,7]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,8,2,3,1,7]=>[1,4,8,7,2,6,3,5]=>[8,5,1,2,7,3,6,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,5,8,1,7]=>[1,3,2,4,6,8,7,5]=>[8,6,7,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,6,2,8,1,7]=>[1,3,4,6,8,7,2,5]=>[8,6,5,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,7,1,8,5,6]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,1,8,5,6]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,4,7,1,6]=>[1,2,5,4,8,6,7,3]=>[8,7,4,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,1,7,4,5]=>[1,2,6,7,4,8,5,3]=>[8,7,3,2,5,1,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,3,6,4,5]=>[1,2,7,4,8,5,3,6]=>[8,7,2,5,1,4,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,4,6,3,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,6,1,5,2]=>[1,3,4,8,2,7,5,6]=>[8,6,5,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,7,6,2,3]=>[1,4,8,3,2,5,7,6]=>[8,5,1,6,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,7,6,3,4]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,8,7,6,3,4]=>[1,5,7,3,2,4,8,6]=>[8,4,2,6,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,7,6,2,3]=>[1,4,8,3,5,7,2,6]=>[8,5,1,6,4,2,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,7,4,5,1]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,2,6,3,1]=>[1,4,8,2,5,3,7,6]=>[8,5,1,7,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,2,7,3,1]=>[1,4,8,2,5,3,6,7]=>[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,7,4,5,2]=>[1,3,6,4,8,2,5,7]=>[8,6,3,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,7,2,5,3]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,7,1,6,2]=>[1,5,7,6,2,8,3,4]=>[8,4,2,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,7,1,4,2]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,6,4,5,2]=>[1,3,7,5,6,4,8,2]=>[8,6,2,4,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,3,6,4,1]=>[1,5,3,7,4,8,2,6]=>[8,4,6,2,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,2,5,3,1]=>[1,4,8,2,6,5,3,7]=>[8,5,1,7,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,2,6,3,1]=>[1,7,3,8,2,5,4,6]=>[8,2,6,1,7,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,2,7,5,1]=>[1,6,7,5,2,3,8,4]=>[8,3,2,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,8,6,2,1]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,8,5,2,1]=>[1,3,7,2,6,5,8,4]=>[8,6,2,7,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,3,7,4,1]=>[1,5,3,2,6,7,4,8]=>[8,4,6,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,2,6,4,1]=>[1,5,2,7,4,3,8,6]=>[8,4,7,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,2,7,4,1]=>[1,5,2,6,7,4,3,8]=>[8,4,7,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,2,7,5,1]=>[1,3,8,2,6,7,5,4]=>[8,6,1,7,3,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,7,3,6,4]=>[1,2,5,7,6,3,8,4]=>[8,7,4,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,3,7,4,2]=>[1,5,3,8,2,6,7,4]=>[8,4,6,1,7,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,1,5,3,2]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,3,6,4,1]=>[1,5,3,2,7,4,8,6]=>[8,4,6,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,6,2,5,3]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,6,1,5,3]=>[1,7,5,6,2,4,8,3]=>[8,2,4,3,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,7,2,4,1]=>[1,6,2,8,3,5,7,4]=>[8,3,7,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,8,6,4,1]=>[1,7,4,3,2,5,8,6]=>[8,2,5,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,8,6,2,1]=>[1,3,4,5,8,2,7,6]=>[8,6,5,4,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,8,5,2,1]=>[1,3,4,7,2,6,5,8]=>[8,6,5,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,8,6,3,1]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,4,7,5,2]=>[1,6,7,5,4,3,8,2]=>[8,3,2,4,5,6,1,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,5,7,3,1]=>[1,6,7,3,4,2,8,5]=>[8,3,2,6,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,4,6,2,1]=>[1,7,2,5,4,3,8,6]=>[8,2,7,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,4,5,6,9,1]=>[1,7,6,5,4,3,2,8,9]=>[9,3,4,5,6,7,8,2,1]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,1,7,3,4,5,8,2]=>[1,6,5,4,3,7,8,2]=>[8,3,4,5,6,2,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,4,1,8,6]=>[1,5,4,3,2,7,8,6]=>[8,4,5,6,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,4,5,6,3]=>[1,2,7,6,5,4,8,3]=>[8,7,2,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,4,5,1,7]=>[1,2,6,5,4,3,8,7]=>[8,7,3,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,9,3,4,5,6,7,1]=>[1,2,8,7,6,5,4,3,9]=>[9,8,2,3,4,5,6,7,1]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,8,3,4,5,6,9,2]=>[1,7,6,5,4,3,8,9,2]=>[9,3,4,5,6,7,2,1,8]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,8,2,3,4,5,1,9,7]=>[1,6,5,4,3,2,8,9,7]=>[9,4,5,6,7,8,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,1,2,7,4,5,8,3]=>[1,6,5,4,7,8,3,2]=>[8,3,4,5,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,1,5,8,6]=>[1,4,3,2,7,8,6,5]=>[8,5,6,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,8,5,6,4]=>[1,2,7,6,5,8,4,3]=>[8,7,2,3,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,4,5,3,1]=>[1,2,6,5,4,8,3,7]=>[8,7,3,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,9,4,5,6,7,3]=>[1,2,8,7,6,5,4,9,3]=>[9,8,2,3,4,5,6,1,7]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,5,8,3,4,1,6,7]=>[1,2,5,4,3,8,7,6]=>[8,7,4,5,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,9,3,4,5,6,1,8]=>[1,2,7,6,5,4,3,9,8]=>[9,8,3,4,5,6,7,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,9,2,3,4,5,6,1,10,8]=>[1,7,6,5,4,3,2,9,10,8]=>[10,4,5,6,7,8,9,2,1,3]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,8,2,3,4,1,6,9,7]=>[1,5,4,3,2,8,9,7,6]=>[9,5,6,7,8,2,1,3,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,8,1,3,9,5,6,7,4]=>[1,2,8,7,6,5,9,4,3]=>[9,8,2,3,4,5,1,6,7]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,6,1,8,4,5,3,7]=>[1,2,6,5,4,8,7,3]=>[8,7,3,4,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,4,3,6,1]=>[1,2,5,4,8,3,7,6]=>[8,7,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,9,3,4,5,1,7,8]=>[1,2,6,5,4,3,9,8,7]=>[9,8,4,5,6,7,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,8,10,3,4,5,6,7,1,9]=>[1,2,8,7,6,5,4,3,10,9]=>[10,9,3,4,5,6,7,8,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,6,8,4,5,7,1,2]=>[1,3,8,2,6,7,4,5]=>[8,6,1,7,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,7,2,3,5]=>[1,2,6,3,8,5,7,4]=>[8,7,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,8,6,1,2]=>[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,8,5,1,2]=>[1,3,7,2,6,5,8,4]=>[8,6,2,7,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,8,7,1,2]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,3,6,4,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,6,2,3,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,8,2,5,3]=>[1,2,6,3,7,5,8,4]=>[8,7,3,6,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,8,2,7,3]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,6,2,7,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,3,4,7,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,3,5,8,4]=>[1,2,6,5,3,7,8,4]=>[8,7,3,4,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,5,4,6]=>[1,7,4,2,8,6,5,3]=>[8,2,5,7,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,3,5,4,8]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,6,2,3,8]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,3,6,4,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,3,6,8,4]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,5,2,3,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,5,2,7,3]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,3,4,7,5]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,3,7,4,5]=>[1,2,6,7,4,3,8,5]=>[8,7,3,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,6,2,8,3]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,5,2,6,3]=>[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,4,6,5]=>[1,7,6,4,2,8,5,3]=>[8,2,3,5,7,1,4,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,6,4,5]=>[1,7,4,2,8,5,3,6]=>[8,2,5,7,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,3,8,5,4]=>[1,2,6,8,4,3,7,5]=>[8,7,3,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,3,8,7,4]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,1,6,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,5,1,8,7]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,5,8,7,3]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,1,8,7,3]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,6,7,3,5]=>[1,4,2,8,5,6,7,3]=>[8,5,7,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,3,1,5,7]=>[1,8,7,5,3,2,6,4]=>[8,1,2,4,6,7,3,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,3,1,7,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,6,5,3,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,8,5,7,3]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,8,3,7,1]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,3,5,7,1]=>[1,6,5,3,2,4,8,7]=>[8,3,4,6,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,3,5,1,7]=>[1,8,7,2,4,6,5,3]=>[8,1,2,7,5,3,4,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,5,8,7,1]=>[1,4,3,6,8,2,5,7]=>[8,5,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,6,5,1,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,6,5,3,7]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,4,8,5,7,3]=>[1,6,5,8,3,2,4,7]=>[8,3,4,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,2,1,3,7]=>[1,8,7,3,6,2,4,5]=>[8,1,2,6,3,7,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,5,7,2,1,3]=>[1,6,2,4,5,7,3,8]=>[8,3,7,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,6,7,3,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,7,5,1,3]=>[1,2,4,6,5,7,3,8]=>[8,7,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,5,7,1,3]=>[1,4,6,7,2,3,8,5]=>[8,5,3,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,5,1,3,7]=>[1,8,7,3,6,2,4,5]=>[8,1,2,6,3,7,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,4,3,7,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,2,1,3,5]=>[1,6,2,8,5,3,7,4]=>[8,3,7,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,7,1,3,5]=>[1,2,8,5,7,3,6,4]=>[8,7,1,4,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,1,7,3,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,3,5,1,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,3,5,1,6]=>[1,7,2,3,8,6,5,4]=>[8,2,7,6,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,5,3,6,7]=>[1,8,7,6,3,2,4,5]=>[8,1,2,3,6,7,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,2,3,6,7]=>[1,8,7,6,3,2,5,4]=>[8,1,2,3,6,7,4,5]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,3,2,6,7]=>[1,8,7,6,2,4,5,3]=>[8,1,2,3,7,5,4,6]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,4,2,1,5]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,3,5,2,6]=>[1,7,2,3,8,6,5,4]=>[8,2,7,6,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,3,5,2,6]=>[1,2,7,3,8,6,5,4]=>[8,7,2,6,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,3,5,2,6]=>[1,7,2,3,4,8,6,5]=>[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,5,6,2,3]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,3,5,6,2]=>[1,7,6,5,3,8,2,4]=>[8,2,3,4,6,1,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,8,4,5,2]=>[1,6,4,2,7,5,8,3]=>[8,3,5,7,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,4,5,2,1]=>[1,6,5,4,8,2,7,3]=>[8,3,4,5,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,4,3,2,5]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,8,4,5,3,6]=>[1,7,3,2,4,8,6,5]=>[8,2,6,7,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,8,4,3,5]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,4,3,5,1]=>[1,6,3,7,5,4,8,2]=>[8,3,6,2,4,5,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,8,3,5,1]=>[1,2,6,3,7,5,8,4]=>[8,7,3,6,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,8,3,1,5]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,6,2,4,5]=>[1,7,4,3,2,8,5,6]=>[8,2,5,6,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,6,3,4,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,8,5,3,4]=>[1,2,6,5,8,4,3,7]=>[8,7,3,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,5,3,1,4]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,5,3,4,1]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,8,4,5,6,3]=>[1,7,6,5,4,8,3,2]=>[8,2,3,4,5,1,6,7]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,4,5,6,3]=>[1,2,7,6,5,4,8,3]=>[8,7,2,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,1,5,2,4]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,6,5,8,4]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,7,4,8,3]=>[1,5,7,8,3,2,4,6]=>[8,4,2,1,6,7,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,3,2,5,8]=>[1,4,7,5,3,2,6,8]=>[8,5,2,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,3,2,5,7]=>[1,4,8,7,5,3,2,6]=>[8,5,1,2,4,6,7,3]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,3,5,2,6]=>[1,4,8,6,5,3,2,7]=>[8,5,1,3,4,6,7,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,8,6,2,3,5]=>[1,4,8,5,6,2,3,7]=>[8,5,1,4,3,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,7,3,4,2]=>[1,2,6,3,5,7,4,8]=>[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,6,2,3,5]=>[1,4,7,3,8,5,6,2]=>[8,5,2,6,1,4,3,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,3,5,2,6]=>[1,4,7,2,8,6,5,3]=>[8,5,2,7,1,3,4,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,3,2,5,7]=>[1,4,6,2,8,7,5,3]=>[8,5,3,7,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,3,2,5,8]=>[1,4,6,2,7,5,3,8]=>[8,5,3,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,7,5,4,8]=>[1,6,5,7,4,3,2,8]=>[8,3,4,2,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,3,7,2,4]=>[1,6,7,2,8,4,5,3]=>[8,3,2,7,1,5,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,4,1,6,3]=>[1,8,3,5,4,2,7,6]=>[8,1,6,4,5,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,4,8,6,2]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,4,7,6,2]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,5,6,4,8]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,5,6,4,7]=>[1,8,7,4,3,2,5,6]=>[8,1,2,5,6,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,5,4,7,6]=>[1,8,6,4,3,2,5,7]=>[8,1,3,5,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,6,3,2,5]=>[1,7,2,3,8,5,6,4]=>[8,2,7,6,1,4,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,3,1,5,7]=>[1,6,2,8,7,5,3,4]=>[8,3,7,1,2,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,4,5,7,6]=>[1,3,2,8,6,5,4,7]=>[8,6,7,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,6,4,2,5]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,7,5,8,4]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,6,4,2,5]=>[1,3,2,8,5,6,4,7]=>[8,6,7,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,3,5,1,6]=>[1,8,6,5,3,2,7,4]=>[8,1,3,4,6,7,2,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,3,2,5]=>[1,8,5,6,3,7,2,4]=>[8,1,4,3,6,2,7,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,3,2,4]=>[1,8,4,6,3,7,2,5]=>[8,1,5,3,6,2,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,4,6,8,2]=>[1,2,5,4,3,7,8,6]=>[8,7,4,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,3,6,1,4]=>[1,8,4,5,3,2,7,6]=>[8,1,5,4,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,5,4,8,6]=>[1,7,8,6,4,3,2,5]=>[8,2,1,3,5,6,7,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,5,8,4,7]=>[1,6,8,7,4,3,2,5]=>[8,3,1,2,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,5,7,4,8]=>[1,6,7,4,3,2,5,8]=>[8,3,2,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,7,6,4,8]=>[1,5,7,4,3,2,6,8]=>[8,4,2,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,8,6,4,7]=>[1,5,8,7,4,3,2,6]=>[8,4,1,2,5,6,7,3]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,4,7,8,2]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,3,8,6,1]=>[1,7,6,8,2,4,3,5]=>[8,2,3,1,7,5,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,1,2,8,7]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,1,5,8,7]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,5,8,6,1]=>[1,7,6,8,2,3,4,5]=>[8,2,3,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,7,1,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,8,5,1,2]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,1,8,6,2]=>[1,3,4,5,2,7,6,8]=>[8,6,5,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,7,4,5,1]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,6,7,3,2]=>[1,4,5,6,7,3,2,8]=>[8,5,4,3,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,6,7,1,3]=>[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,4,2,7,5]=>[1,6,2,8,5,4,3,7]=>[8,3,7,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,8,5,3,4]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,4,8,5,2]=>[1,7,5,4,6,8,2,3]=>[8,2,4,5,3,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,8,5,2,3]=>[1,7,2,6,5,8,3,4]=>[8,2,7,3,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,8,4,1,5]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,7,1,4,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,5,1,7,2]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,6,7,1,2]=>[1,5,6,7,2,4,3,8]=>[8,4,3,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,4,6,7,2]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,4,5,2,7]=>[1,3,2,6,5,4,8,7]=>[8,6,7,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,5,2,7,1]=>[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,2,4,1,6]=>[1,5,2,7,3,8,6,4]=>[8,4,7,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,1,4,5,7]=>[1,6,4,3,2,8,7,5]=>[8,3,5,6,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,8,3,1,6]=>[1,5,8,6,3,7,2,4]=>[8,4,1,3,6,2,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,8,4,1,6]=>[1,3,5,8,6,4,2,7]=>[8,6,4,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,8,5,1,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,8,2,5,6]=>[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,8,1,2,5]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,2,6,1,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,5,6,2,8]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,4,5,7,6]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,3,7,5,2]=>[1,8,2,4,6,7,5,3]=>[8,1,7,5,3,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,1,6,3,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,7,4,1,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,7,6,4,2]=>[1,2,5,7,4,8,3,6]=>[8,7,4,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,5,6,3,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,5,7,2,3]=>[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,8,2,3,7]=>[1,2,6,3,5,8,7,4]=>[8,7,3,6,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,7,4,3,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,7,4,3,6]=>[1,5,7,3,2,4,8,6]=>[8,4,2,6,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,8,1,4,7]=>[1,5,8,7,4,3,6,2]=>[8,4,1,2,5,6,3,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,3,1,7,5]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,4,6,2,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,4,6,3,2]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,6,3,7,2]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,6,2,1,7]=>[1,5,6,2,8,7,3,4]=>[8,4,3,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,6,7,5,2]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,1,7,6,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,5,1,6,7]=>[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,5,1,7,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,6,5,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,5,7,6,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,4,7,8,3]=>[1,6,7,8,3,5,4,2]=>[8,3,2,1,6,4,5,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,2,7,6,3]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,3,6,2,7]=>[1,4,2,8,7,3,5,6]=>[8,5,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,5,7,2,8,4]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,8,5,7,4]=>[1,6,5,8,4,2,3,7]=>[8,3,4,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,3,7,5,6]=>[1,4,2,3,8,6,7,5]=>[8,5,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,8,2,3,1]=>[1,6,2,4,5,8,3,7]=>[8,3,7,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,2,6,3,1]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,6,8,3,2]=>[1,5,6,8,2,7,3,4]=>[8,4,3,1,7,2,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,7,1,3,2]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,1,7,3,2]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,7,8,3,2]=>[1,5,7,3,2,6,8,4]=>[8,4,2,6,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,4,8,3,1]=>[1,5,4,2,6,8,3,7]=>[8,4,5,7,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,4,8,2,1]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,6,7,4,1]=>[1,5,6,7,4,8,2,3]=>[8,4,3,2,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,5,7,2,3,1]=>[1,6,2,4,5,7,3,8]=>[8,3,7,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,6,2,1,3]=>[1,7,2,4,5,6,3,8]=>[8,2,7,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,7,2,3,1]=>[1,4,5,7,3,8,2,6]=>[8,5,4,2,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,4,7,3,1]=>[1,5,4,2,6,7,3,8]=>[8,4,5,7,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,8,7,2,1]=>[1,4,5,8,2,6,7,3]=>[8,5,4,1,7,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,2,7,4,1]=>[1,5,2,6,7,4,8,3]=>[8,4,7,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,7,2,4,1]=>[1,3,5,7,4,8,2,6]=>[8,6,4,2,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,6,8,3,1]=>[1,5,6,8,2,4,3,7]=>[8,4,3,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,6,8,4,1]=>[1,5,6,8,2,3,4,7]=>[8,4,3,1,7,6,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,2,4,1]=>[1,6,2,7,4,8,3,5]=>[8,3,7,2,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,5,3,8,1]=>[1,6,3,7,8,2,4,5]=>[8,3,6,2,1,7,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,1,4,8,3]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,3,6,1,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,4,2,5,1]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,4,6,2,1]=>[1,3,7,2,5,4,8,6]=>[8,6,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,4,6,2,1]=>[1,5,4,8,2,3,7,6]=>[8,4,5,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,4,6,3,1]=>[1,5,4,2,7,3,8,6]=>[8,4,5,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,3,7,6,1]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,7,3,5,1]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,6,2,1,5]=>[1,3,4,8,5,6,2,7]=>[8,6,5,1,4,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,2,7,6,1]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,8,6,2,1]=>[1,4,5,8,2,3,7,6]=>[8,5,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,4,7,2,1]=>[1,3,6,7,2,5,4,8]=>[8,6,3,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,8,6,3,2]=>[1,7,3,4,2,5,8,6]=>[8,2,6,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,7,6,3,2]=>[1,8,2,5,7,3,4,6]=>[8,1,7,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,6,3,4,7]=>[1,2,8,7,4,5,6,3]=>[8,7,1,2,5,4,3,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,6,2,4,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,3,5,2,8]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,3,7,4,6]=>[1,2,8,6,7,4,3,5]=>[8,7,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,3,6,7,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,2,1,6,4]=>[1,7,6,2,5,3,8,4]=>[8,2,3,7,4,6,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,1,5,6,3]=>[1,7,6,5,2,3,8,4]=>[8,2,3,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,4,7,8,3]=>[1,2,5,4,6,7,8,3]=>[8,7,4,5,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,2,3,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,7,1,4,8,3]=>[1,6,4,7,8,3,5,2]=>[8,3,5,2,1,6,4,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,8,1,7,2]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,8,5,2,4,1]=>[1,7,4,8,2,3,6,5]=>[8,2,5,1,7,6,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,6,5,1,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,4,6,3,1]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,8,3,4,1,7]=>[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,4,1,3,7]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,6,1,3,5]=>[1,2,7,3,8,5,6,4]=>[8,7,2,6,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,3,7,4,5]=>[1,6,7,4,8,5,3,2]=>[8,3,2,5,1,4,6,7]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,3,8,1,4]=>[1,2,6,8,4,7,3,5]=>[8,7,3,1,5,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,5,8,4,3]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,8,5,6,4]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,8,7,3,4]=>[1,6,7,3,2,5,8,4]=>[8,3,2,6,7,4,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,7,8,4,1]=>[1,2,6,8,3,5,7,4]=>[8,7,3,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,3,8,7,1,4]=>[1,6,7,2,5,8,4,3]=>[8,3,2,7,4,1,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,3,8,6,7]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,6,3,8,7]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,2,5,4,3]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,9,8,7,6]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,9,8,7,6]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,9,8,7]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,9,8,7]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,9,8,7]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,6,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,10,9,8,7]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,10,9,8,7]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,10,9,8]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,6,10,9,8]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,6,10,9,8]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,2,7,4,1,6,3,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,1,5,6,2,8]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,1,6,7,2]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,5,6,2,3]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,2,6,7,3]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,5,2,7,4]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,1,6,4,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,5,1,4,8]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,8,6,2,5]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,1,6,5,4]=>[1,8,4,2,7,5,3,6]=>[8,1,5,7,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,2,3,4,6]=>[1,8,6,3,2,5,4,7]=>[8,1,3,6,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,3,7,1,6]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,2,1,7,5]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,8,2,7,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,3,2,7,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,2,8,7,6]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,1,8,7,5]=>[1,3,6,8,5,2,4,7]=>[8,6,3,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,7,8,1,5]=>[1,3,6,8,5,7,2,4]=>[8,6,3,1,4,2,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,3,7,2,5]=>[1,8,5,3,4,6,7,2]=>[8,1,4,6,5,3,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,3,7,5,2]=>[1,8,2,3,4,6,7,5]=>[8,1,7,6,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,1,7,4,8]=>[1,3,6,7,4,2,5,8]=>[8,6,3,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,7,3,4,2]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,8,7,2,5]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,8,7,2,4]=>[1,3,6,7,2,5,8,4]=>[8,6,3,2,7,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,6,7,4,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,6,7,5,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,7,1,5,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,6,7,5,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,1,7,4,3]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,8,7,4,2]=>[1,3,6,7,4,2,5,8]=>[8,6,3,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,8,7,5,2]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,7,1,5,2]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,7,8,4,2]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,7,8,3,2]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,7,3,8,2]=>[1,4,2,5,7,8,3,6]=>[8,5,7,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,7,4,8,2]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,7,4,2,3]=>[1,8,3,5,7,2,4,6]=>[8,1,6,4,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,7,4,3,2]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,7,4,2,8]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,7,3,2,8]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,4,3,1,2]=>[1,6,3,8,2,5,4,7]=>[8,3,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,8,5,1,3]=>[1,6,5,8,3,2,4,7]=>[8,3,4,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,7,5,2,3]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,4,7,3,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,4,7,3,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,8,5,2,3]=>[1,6,5,8,3,2,4,7]=>[8,3,4,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,4,8,2,5]=>[1,7,2,6,8,5,4,3]=>[8,2,7,3,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,4,7,2,5]=>[1,8,5,4,3,6,7,2]=>[8,1,4,5,6,3,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,4,7,2,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,4,8,3,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,5,4,8,3,6]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,4,8,3,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,4,7,1,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,4,7,3,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,5,4,8,3,6]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,4,8,3,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,4,8,1,6]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,7,3,1,6]=>[1,2,5,7,3,8,6,4]=>[8,7,4,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,4,8,1,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,4,7,1,5]=>[1,6,7,2,8,5,4,3]=>[8,3,2,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,4,8,1,6]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,4,8,2,6]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,4,8,2,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,7,3,2,6]=>[1,2,5,7,3,8,6,4]=>[8,7,4,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,7,3,2,6]=>[1,5,7,2,3,8,6,4]=>[8,4,2,7,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,7,3,1,6]=>[1,5,7,2,8,6,3,4]=>[8,4,2,7,1,3,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,2,1,4,3]=>[1,8,3,5,2,7,4,6]=>[8,1,6,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,7,3,1,6]=>[1,8,6,3,2,5,7,4]=>[8,1,3,6,7,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,4,8,2,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,4,7,2,5]=>[1,8,5,4,2,6,7,3]=>[8,1,4,5,7,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,7,5,1,3]=>[1,8,3,4,2,6,5,7]=>[8,1,6,5,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,7,2,5,3]=>[1,8,3,4,2,6,5,7]=>[8,1,6,5,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,6,8,2,1]=>[1,5,6,8,2,3,7,4]=>[8,4,3,1,7,6,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,7,8,5,6]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,7,8,5,6]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,7,8,5,6]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,5,4,8,1,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,6,8,2,1]=>[1,5,6,8,2,7,3,4]=>[8,4,3,1,7,2,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,4,8,1,6]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,7,8,5,6]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,4,3,5,2]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,1,6,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,2,1,4,8]=>[1,7,4,5,2,3,6,8]=>[8,2,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,2,1,7,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,4,2,1,3]=>[1,7,2,5,4,6,3,8]=>[8,2,7,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,4,1,3,7]=>[1,5,4,6,2,8,7,3]=>[8,4,5,3,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,1,4,7,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,3,1,4,7]=>[1,2,5,3,8,7,4,6]=>[8,7,4,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,1,4,7,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,1,5,7,4]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,2,7,1,4]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,1,4,8]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,6,3,1,4,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,3,1,5,4]=>[1,2,8,4,6,3,7,5]=>[8,7,1,5,3,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,6,3,1,4]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,6,5,7,3]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,6,1,4,5]=>[1,2,8,5,6,3,7,4]=>[8,7,1,4,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,1,4,6,8]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,1,3,7,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,1,4,7,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,3,1,4,5]=>[1,2,7,4,6,3,8,5]=>[8,7,2,5,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,2,1,4,6]=>[1,7,4,5,2,3,8,6]=>[8,2,5,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,8,4,7,5]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,1,4,5,7]=>[1,2,8,7,5,3,6,4]=>[8,7,1,2,4,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,1,4,6,7]=>[1,8,7,6,4,2,3,5]=>[8,1,2,3,5,7,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,7,3,6,4]=>[1,2,5,7,6,3,8,4]=>[8,7,4,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,7,3,6,4]=>[1,2,8,4,5,7,6,3]=>[8,7,1,5,4,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,4,7,5,2]=>[1,8,2,3,6,7,5,4]=>[8,1,7,6,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,5,7,3,4]=>[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,8,3,4,6]=>[1,2,7,4,5,8,6,3]=>[8,7,2,5,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,6,3,8,4,5]=>[1,2,7,4,6,8,5,3]=>[8,7,2,5,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,8,5,2,3]=>[1,4,2,7,3,6,5,8]=>[8,5,7,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,1,2,6,4]=>[1,3,5,2,7,6,4,8]=>[8,6,4,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,1,2,8,4,5]=>[1,7,4,2,3,6,8,5]=>[8,2,5,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,6,5,2,3]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,8,2,5,3]=>[1,7,5,8,3,6,2,4]=>[8,2,4,1,6,3,7,5]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,6,1,2,3]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,1,7,2,3]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,2,3,8,4]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,2,8,3,4]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,6,2,3,4]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,2,7,3,4]=>[1,8,4,6,7,3,2,5]=>[8,1,5,3,2,6,7,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,4,7,5,2]=>[1,3,2,6,7,5,4,8]=>[8,6,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,5,2,3]=>[1,8,3,6,5,7,2,4]=>[8,1,6,3,4,2,7,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,7,2,3,6]=>[1,4,8,6,2,5,7,3]=>[8,5,1,3,7,4,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,1,2,5,6]=>[1,3,8,6,2,4,7,5]=>[8,6,1,3,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,1,2,5,3]=>[1,6,2,4,7,5,3,8]=>[8,3,7,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,7,1,4,2]=>[1,5,7,4,3,8,2,6]=>[8,4,2,5,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,2,8,5,3]=>[1,6,8,3,7,5,2,4]=>[8,3,1,6,2,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,2,7,3,4]=>[1,6,7,3,2,5,4,8]=>[8,3,2,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,2,7,3,4]=>[1,8,4,2,6,7,3,5]=>[8,1,5,7,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,7,2,3,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,7,2,3,4]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,2,8,3,4]=>[1,6,8,4,7,3,2,5]=>[8,3,1,5,2,6,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,8,2,3,6]=>[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,4,1,2,3]=>[1,5,4,7,2,6,3,8]=>[8,4,5,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,4,1,2,3]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,3,6,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,3,4,6,7,1]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,3,6,8,5]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,5,7,8,3]=>[1,4,2,6,7,8,3,5]=>[8,5,7,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,1,7,8,6]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,4,1,8,5]=>[1,3,6,2,4,7,8,5]=>[8,6,3,7,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,1,4,8,3]=>[1,5,2,6,4,7,8,3]=>[8,4,7,3,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,1,7,4,5]=>[1,6,7,4,8,5,2,3]=>[8,3,2,5,1,4,7,6]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,4,7,1,5]=>[1,2,6,7,3,8,5,4]=>[8,7,3,2,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,5,1,3,8]=>[1,4,7,3,2,6,5,8]=>[8,5,2,6,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,4,8,1,6]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,8,7,4,5]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,7,8,1,2]=>[1,3,6,8,2,5,7,4]=>[8,6,3,1,7,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,2,8,7,1]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,5,7,3,6]=>[1,4,2,3,8,6,7,5]=>[8,5,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,4,1,7,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,5,3,8,7]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,7,6,8,3]=>[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,1,6,3,8]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,7,2,4,6]=>[1,5,7,4,2,8,6,3]=>[8,4,2,5,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,5,2,4,7]=>[1,6,2,8,7,4,3,5]=>[8,3,7,1,2,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,6,3,5,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,2,6,3,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,1,5,3,7]=>[1,6,5,2,8,7,3,4]=>[8,3,4,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,1,7,3,4]=>[1,6,7,3,5,2,8,4]=>[8,3,2,6,4,7,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,1,5,7,2]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,1,5,7,3]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,1,4,5,7]=>[1,6,4,2,8,7,5,3]=>[8,3,5,7,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,2,4,6,8]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,3,6,7,4]=>[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,6,2,7,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,1,6,8,3]=>[1,5,2,4,3,7,8,6]=>[8,4,7,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,3,4,8,6]=>[1,5,3,2,4,7,8,6]=>[8,4,6,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,7,5,8,2]=>[1,6,5,7,8,2,4,3]=>[8,3,4,2,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,2,6,8,4]=>[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,6,4,8,5]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,5,8,3,7]=>[1,4,6,8,7,3,2,5]=>[8,5,3,1,2,6,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,5,7,3,6]=>[1,4,8,6,7,3,2,5]=>[8,5,1,3,2,6,7,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,8,5,6,2]=>[1,7,6,5,8,2,4,3]=>[8,2,3,4,1,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,8,5,6,3]=>[1,7,6,5,8,3,2,4]=>[8,2,3,4,1,6,7,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,7,4,5,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,8,6,3,4]=>[1,7,3,2,5,8,4,6]=>[8,2,6,7,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,2,7,3,5]=>[1,6,7,3,8,5,2,4]=>[8,3,2,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,3,7,4,5]=>[1,6,7,4,8,5,3,2]=>[8,3,2,5,1,4,6,7]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,3,6,4,8]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,6,1,4,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,6,1,4,7]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,7,1,4,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,4,7,3,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,8,1,6,7]=>[1,4,5,8,7,6,2,3]=>[8,5,4,1,2,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,7,1,6,8]=>[1,4,5,7,6,2,3,8]=>[8,5,4,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,2,8,6,3]=>[1,5,2,4,7,6,8,3]=>[8,4,7,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,7,8,4,2]=>[1,6,8,2,5,7,4,3]=>[8,3,1,7,4,2,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,6,7,3,8]=>[1,5,6,7,3,2,4,8]=>[8,4,3,2,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,6,7,4,8]=>[1,5,6,7,4,2,3,8]=>[8,4,3,2,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,7,8,5,3]=>[1,6,8,3,2,4,5,7]=>[8,3,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,8,7,5,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,6,8,5,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,1,7,8,5]=>[1,4,6,7,8,5,2,3]=>[8,5,3,2,1,4,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,6,7,8,4]=>[1,5,6,7,8,4,2,3]=>[8,4,3,2,1,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,5,7,2,3]=>[1,8,3,2,6,7,4,5]=>[8,1,6,7,3,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,5,7,1,2]=>[1,3,6,7,2,8,4,5]=>[8,6,3,2,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,7,4,2,5]=>[1,2,8,5,7,3,6,4]=>[8,7,1,4,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,3,6,7,1]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,3,6,1,8]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,3,6,1,7]=>[1,5,3,2,4,8,7,6]=>[8,4,6,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,4,7,2,1]=>[1,6,7,2,5,4,8,3]=>[8,3,2,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,3,7,1,6]=>[1,5,3,8,6,7,2,4]=>[8,4,6,1,3,2,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,3,1,8,6]=>[1,5,3,2,4,7,8,6]=>[8,4,6,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,1,2,8,5]=>[1,6,2,4,7,8,5,3]=>[8,3,7,5,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,1,2,7,5]=>[1,6,2,4,8,5,3,7]=>[8,3,7,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,1,6,3,4]=>[1,7,3,8,4,5,2,6]=>[8,2,6,1,5,4,7,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,3,1,5,6]=>[1,7,5,3,8,6,2,4]=>[8,2,4,6,1,3,7,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,4,2,6,1]=>[1,7,6,2,5,4,8,3]=>[8,2,3,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,3,1,5,8]=>[1,6,2,4,7,5,3,8]=>[8,3,7,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,8,2,3,5,1]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,2,5,3,4]=>[1,7,3,8,4,2,6,5]=>[8,2,6,1,5,7,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,3,8,7,2]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,8,2,3,4]=>[1,6,2,5,8,4,7,3]=>[8,3,7,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,3,8,2,6]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,7,3,4,2]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,7,6,2,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,5,2,8,4,7]=>[1,6,8,7,4,5,2,3]=>[8,3,1,2,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,5,2,1,6]=>[1,4,7,2,3,8,6,5]=>[8,5,2,7,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,8,3,5,1]=>[1,2,7,5,8,3,6,4]=>[8,7,2,4,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,1,4,8,3]=>[1,6,4,7,8,3,2,5]=>[8,3,5,2,1,6,7,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,3,2,8,5]=>[1,7,8,5,3,6,2,4]=>[8,2,1,4,6,3,7,5]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,3,1,5,2]=>[1,8,2,4,6,3,7,5]=>[8,1,7,5,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,6,3,8,2]=>[1,7,8,2,4,5,6,3]=>[8,2,1,7,5,4,3,6]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,6,3,8,1]=>[1,2,4,5,6,3,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,6,2,8,3]=>[1,5,6,2,4,7,8,3]=>[8,4,3,7,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,1,4,8,2]=>[1,3,6,4,7,8,2,5]=>[8,6,3,5,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,3,4,8,5]=>[1,2,7,8,5,3,6,4]=>[8,7,2,1,4,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,1,6,3,8,4]=>[1,5,6,3,2,7,8,4]=>[8,4,3,6,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,6,3,8,1]=>[1,4,5,6,3,2,7,8]=>[8,5,4,3,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,7,1,4,3]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,3,8,1,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,3,2,5,4]=>[1,6,2,8,4,3,7,5]=>[8,3,7,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,7,1,4,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,2,6,7,1]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,2,4,7,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,2,4,7,3]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,3,2,7,5]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,8,6,7,3]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,8,6,4,5]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,2,8,1,4]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,8,6,7,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,1,6,7,3]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,7,8,4,6]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,7,8,3,6]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,6,3,4,7,1]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,3,2,7,1]=>[1,5,3,8,2,6,4,7]=>[8,4,6,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,4,2,1,5]=>[1,3,7,2,6,4,8,5]=>[8,6,2,7,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,2,1,7,5]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,3,1,6,7,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,2,6,7,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,2,4,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,4,6,1,5]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,3,4,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,1,6,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,5,8,1,3]=>[1,6,8,3,7,2,4,5]=>[8,3,1,6,2,7,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,3,6,1,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,5,2,4,7]=>[1,8,7,4,3,2,6,5]=>[8,1,2,5,6,7,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,1,3,2,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,2,8,1,6]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,6,1,8,2]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,7,8,5,1]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,8,4,5,3]=>[1,6,4,7,5,8,3,2]=>[8,3,5,2,4,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,5,4,8,2]=>[1,7,8,2,6,4,3,5]=>[8,2,1,7,3,5,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,1,7,8,3]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,6,8,2,3]=>[1,2,4,5,6,8,3,7]=>[8,7,5,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,4,6,8,1]=>[1,3,5,4,2,7,8,6]=>[8,6,4,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,4,2,8,3]=>[1,5,4,7,8,3,2,6]=>[8,4,5,2,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,7,1,8,4,2]=>[1,3,5,2,6,8,4,7]=>[8,6,4,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,2,1,3,5]=>[1,6,2,4,8,5,3,7]=>[8,3,7,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,4,1,2,5]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,4,6,1,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,1,3,2,6]=>[1,7,2,5,3,8,6,4]=>[8,2,7,4,6,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,3,1,2,6]=>[1,4,8,6,2,7,3,5]=>[8,5,1,3,7,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,3,5,7,6]=>[1,4,2,8,6,5,3,7]=>[8,5,7,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,2,4,3,5]=>[1,7,3,8,5,2,6,4]=>[8,2,6,1,4,7,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,1,3,2,4]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,6,1,7,3]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,7,6,1,3]=>[1,8,3,5,7,2,4,6]=>[8,1,6,4,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,2,5,3]=>[1,8,3,6,2,7,5,4]=>[8,1,6,3,7,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,5,2,8,4]=>[1,6,2,7,8,4,3,5]=>[8,3,7,2,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,6,8,1,4]=>[1,5,6,8,4,3,2,7]=>[8,4,3,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,7,6,1,4]=>[1,8,4,2,5,7,3,6]=>[8,1,5,7,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,5,8,1,2]=>[1,3,6,8,2,4,7,5]=>[8,6,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,6,1,8,2]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,7,8,3,1]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,1,6,2,7,4]=>[1,3,5,6,2,8,4,7]=>[8,6,4,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,6,8,7,4]=>[1,2,5,6,8,4,3,7]=>[8,7,4,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,3,7,8,2]=>[1,5,3,6,7,8,2,4]=>[8,4,6,3,2,1,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,8,1,5,2]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,1,8,2,5]=>[1,3,6,8,5,2,7,4]=>[8,6,3,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,1,5,6,2]=>[1,3,8,2,7,6,5,4]=>[8,6,1,7,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,2,1,6,3]=>[1,8,3,5,2,7,6,4]=>[8,1,6,4,7,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,7,4,2,1]=>[1,3,8,2,5,7,4,6]=>[8,6,1,7,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,7,3,4,2]=>[1,5,7,4,6,3,2,8]=>[8,4,2,5,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,5,1,8,4,3]=>[1,6,8,3,2,7,4,5]=>[8,3,1,6,7,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,6,7,4,3]=>[1,5,6,7,4,2,8,3]=>[8,4,3,2,5,7,1,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,8,6,3,7,1]=>[1,4,8,2,5,6,3,7]=>[8,5,1,7,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,4,8,3,7]=>[1,2,6,8,7,3,5,4]=>[8,7,3,1,2,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,4,7,3,6]=>[1,2,5,4,8,6,7,3]=>[8,7,4,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,8,2,4,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,7,3,4,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,1,3,7,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,8,6,7,5]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,1,2,6,5]=>[1,8,5,2,4,7,6,3]=>[8,1,4,7,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,8,2,6,4]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,6,7,3,5]=>[1,2,8,5,6,7,3,4]=>[8,7,1,4,3,2,6,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,7,2,4,5]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,8,3,4,5]=>[1,7,4,6,3,2,5,8]=>[8,2,5,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,6,8,3,5]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,3,6,8,4]=>[1,5,3,7,8,4,2,6]=>[8,4,6,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,3,5,8,4]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,7,8,3,6]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,4,6,7,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,4,6,8,5]=>[1,7,8,5,4,2,3,6]=>[8,2,1,4,5,7,6,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,7,2,5,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,1,2,7,4,6]=>[1,3,8,6,7,4,2,5]=>[8,6,1,3,2,5,7,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,2,4,7,5]=>[1,3,8,5,2,6,4,7]=>[8,6,1,4,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,7,2,6,5]=>[1,4,8,5,7,6,2,3]=>[8,5,1,4,2,3,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,8,2,6,5]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,2,3,7,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,7,3,4,5]=>[1,2,6,3,8,5,7,4]=>[8,7,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,8,5,6,4]=>[1,3,7,6,5,8,4,2]=>[8,6,2,3,4,1,5,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,8,1,5,4]=>[1,2,6,3,7,5,8,4]=>[8,7,3,6,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,3,6,2,5]=>[1,8,5,3,2,4,7,6]=>[8,1,4,6,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,7,1,5,4]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,4,2,6,3]=>[1,5,4,7,6,2,3,8]=>[8,4,5,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,3,6,5,1]=>[1,4,8,2,7,5,3,6]=>[8,5,1,7,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,8,5,3,6,2]=>[1,4,8,2,3,7,6,5]=>[8,5,1,7,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,8,3,6,2]=>[1,5,8,2,3,7,6,4]=>[8,4,1,7,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,5,3,6,2]=>[1,4,7,6,3,8,2,5]=>[8,5,2,3,6,1,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,3,5,8,1]=>[1,4,6,5,3,2,7,8]=>[8,5,3,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,3,7,5,1]=>[1,6,7,5,3,2,8,4]=>[8,3,2,4,6,7,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,4,1,5,6]=>[1,3,7,5,4,2,8,6]=>[8,6,2,4,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,4,1,5,6]=>[1,3,8,6,2,7,5,4]=>[8,6,1,3,7,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,4,5,7,1]=>[1,3,8,2,6,5,4,7]=>[8,6,1,7,3,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,4,5,8,1]=>[1,3,7,8,2,6,5,4]=>[8,6,2,1,7,3,4,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,3,5,4]=>[1,8,4,2,7,5,3,6]=>[8,1,5,7,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,6,2,8,7]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,1,6,2,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,7,1,6,4]=>[1,3,5,7,6,2,8,4]=>[8,6,4,2,3,7,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,5,3,4,1]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,3,6,4,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,2,4,7,1]=>[1,3,5,2,6,4,8,7]=>[8,6,4,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,7,3,4,6]=>[1,5,7,4,8,6,3,2]=>[8,4,2,5,1,3,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,7,3,8,1]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,8,3,5,4]=>[1,6,3,7,5,8,4,2]=>[8,3,6,2,4,1,5,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,6,4,3]=>[1,8,3,5,2,7,4,6]=>[8,1,6,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,7,1,6,5]=>[1,8,5,7,6,2,4,3]=>[8,1,4,2,3,7,5,6]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,2,7,5,6]=>[1,4,3,2,8,6,7,5]=>[8,5,6,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,7,5,2,6]=>[1,3,2,8,6,5,7,4]=>[8,6,7,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,4,5,1,2]=>[1,6,5,4,7,2,3,8]=>[8,3,4,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,6,2,1,3]=>[1,8,3,7,2,5,6,4]=>[8,1,6,2,7,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,2,1,5,3]=>[1,8,3,4,6,2,7,5]=>[8,1,6,5,3,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,5,2,8,4]=>[1,7,8,4,3,2,6,5]=>[8,2,1,5,6,7,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,3,1,7,4]=>[1,8,4,5,3,6,2,7]=>[8,1,5,4,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,5,2,3,1]=>[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,4,3,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,5,3,8,4]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,3,5,8,4]=>[1,2,7,8,4,3,6,5]=>[8,7,2,1,5,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,2,5,8,3]=>[1,4,2,7,8,3,6,5]=>[8,5,7,2,1,6,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,8,5,6,2]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,1,8,6,2]=>[1,7,6,8,2,5,3,4]=>[8,2,3,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,7,3,1,4]=>[1,8,4,2,5,7,3,6]=>[8,1,5,7,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,6,1,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,1,7,8,2]=>[1,6,7,8,2,3,5,4]=>[8,3,2,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,5,8,3,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,8,3,2,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,8,3,5,1]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,8,3,1,5]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,7,8,3,5]=>[1,2,3,6,8,5,7,4]=>[8,7,6,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,8,1,3,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,3,1,8,4,6]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,8,1,5,2]=>[1,3,4,7,5,8,2,6]=>[8,6,5,2,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,1,8,2,5]=>[1,4,7,2,3,6,8,5]=>[8,5,2,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,8,1,2,5]=>[1,3,4,7,2,6,5,8]=>[8,6,5,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,1,7,8,5]=>[1,2,3,6,7,8,5,4]=>[8,7,6,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,5,3,8,6]=>[1,4,2,7,8,6,3,5]=>[8,5,7,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,2,1,8,6]=>[1,3,4,5,2,7,8,6]=>[8,6,5,4,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,7,2,8,5]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,2,7,8,6]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,3,7,8,6]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,8,2,5,4]=>[1,2,6,3,7,5,8,4]=>[8,7,3,6,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,7,8,5,2,3]=>[1,6,5,8,3,4,7,2]=>[8,3,4,1,6,5,2,7]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,1,8,5,4]=>[1,6,8,4,3,7,5,2]=>[8,3,1,5,6,2,4,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,7,8,1,5,3]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,1,8,5,4]=>[1,2,6,8,4,3,7,5]=>[8,7,3,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,3,2,4,7]=>[1,8,7,4,2,6,3,5]=>[8,1,2,5,7,3,6,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,3,2,5,1]=>[1,6,2,4,8,3,7,5]=>[8,3,7,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,1,2,5,6]=>[1,3,4,7,5,2,8,6]=>[8,6,5,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,5,4,3,7]=>[1,8,7,3,2,6,4,5]=>[8,1,2,6,7,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,5,3,2,7]=>[1,4,2,8,7,3,6,5]=>[8,5,7,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,5,2,1,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,4,2,3,1]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,1,6,4,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,7,4,5,3]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,1,3,7,2]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,3,6,4,1]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,5,6,2,1]=>[1,3,4,8,2,7,5,6]=>[8,6,5,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,5,1,2,3]=>[1,6,2,4,7,3,8,5]=>[8,3,7,5,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,4,6,2,3]=>[1,5,4,8,3,2,7,6]=>[8,4,5,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,2,1,4,5]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,5,6,1,4]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,5,1,2,4]=>[1,3,6,2,7,4,8,5]=>[8,6,3,7,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,5,1,3,4]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,1,6,3,5]=>[1,2,4,8,5,3,7,6]=>[8,7,5,1,4,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,2,6,3,1]=>[1,5,2,4,8,3,7,6]=>[8,4,7,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,1,2,7,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,5,2,3,4]=>[1,6,2,8,4,3,7,5]=>[8,3,7,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,7,6,1,4]=>[1,5,7,2,8,4,3,6]=>[8,4,2,7,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,8,6,7,1]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,1,4,7,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,5,2,7,3]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,7,6,1,4]=>[1,5,7,2,8,4,3,6]=>[8,4,2,7,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,3,2,7,1]=>[1,4,5,3,8,2,6,7]=>[8,5,4,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,5,1,7,3]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,5,6,2,1]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,8,6,1,4]=>[1,7,2,5,8,4,3,6]=>[8,2,7,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,8,6,7,3]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,3,6,7,2]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,1,6,7,2]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,5,6,1,2]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,7,2,4,8,3]=>[1,6,4,7,8,3,5,2]=>[8,3,5,2,1,6,4,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,2,3,8,6]=>[1,7,8,6,3,5,2,4]=>[8,2,1,3,6,4,7,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,2,8,5,6]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,2,1,5,3]=>[1,8,3,7,5,2,4,6]=>[8,1,6,2,4,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,7,1,3,2]=>[1,8,2,4,5,7,3,6]=>[8,1,7,5,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,5,8,3,6]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,3,5,8,2]=>[1,7,8,2,4,6,5,3]=>[8,2,1,7,5,3,4,6]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,1,3,8,6]=>[1,4,2,7,8,6,3,5]=>[8,5,7,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,6,4,8,1]=>[1,5,6,4,3,2,7,8]=>[8,4,3,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,7,1,4,5]=>[1,8,5,7,4,3,2,6]=>[8,1,4,2,5,6,7,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,8,3,6,1]=>[1,5,8,2,7,6,3,4]=>[8,4,1,7,2,3,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,8,6,3,5]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,5,4,8,3,2]=>[1,7,3,2,6,8,4,5]=>[8,2,6,7,3,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,1,8,5,6]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,5,8,4,6]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,1,2,5,3]=>[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,3,2,5,4]=>[1,7,5,3,6,2,8,4]=>[8,2,4,6,3,7,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,4,1,3,5]=>[1,2,8,5,4,7,3,6]=>[8,7,1,4,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,5,7,4,6]=>[1,3,2,8,6,7,4,5]=>[8,6,7,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,2,7,3,1]=>[1,6,7,3,5,2,8,4]=>[8,3,2,6,4,7,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,2,4,5,7]=>[1,6,4,2,8,7,5,3]=>[8,3,5,7,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,7,3,1,5,2]=>[1,4,7,5,3,8,2,6]=>[8,5,2,4,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,8,4,1,2]=>[1,6,4,7,2,5,8,3]=>[8,3,5,2,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,7,5,6,2]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,8,1,3,5]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,1,6,3,7]=>[1,8,7,3,5,2,4,6]=>[8,1,2,6,4,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,8,1,7,5]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,3,8,2,4]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,7,8,3,6]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,8,1,6,7]=>[1,3,4,2,5,8,7,6]=>[8,6,5,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,4,2,7,6]=>[1,5,4,8,6,2,3,7]=>[8,4,5,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,3,6,5,2]=>[1,7,5,3,8,2,4,6]=>[8,2,4,6,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,7,4,2,5]=>[1,3,6,4,8,5,7,2]=>[8,6,3,5,1,4,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,2,1,5,3]=>[1,7,5,2,4,8,3,6]=>[8,2,4,7,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,3,1,2,7]=>[1,6,2,5,3,8,7,4]=>[8,3,7,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,3,6,7,4,1]=>[1,2,5,6,7,4,3,8]=>[8,7,4,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,7,4,6,2]=>[1,8,2,5,7,6,4,3]=>[8,1,7,4,2,3,5,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,7,4,2,6]=>[1,2,5,7,3,8,6,4]=>[8,7,4,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,1,5,6,4]=>[1,3,2,8,4,7,6,5]=>[8,6,7,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,6,4,1,7]=>[1,5,6,4,3,2,8,7]=>[8,4,3,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,4,7,5,1]=>[1,6,7,5,4,3,2,8]=>[8,3,2,4,5,6,7,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,4,2,6,1]=>[1,3,8,2,5,4,7,6]=>[8,6,1,7,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,8,4,2,6,3]=>[1,7,6,2,5,4,8,3]=>[8,2,3,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,2,7,4,1]=>[1,3,8,2,6,7,4,5]=>[8,6,1,7,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,4,6,5,3]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,3,5,8,6]=>[1,2,3,7,8,6,5,4]=>[8,7,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,4,6,1,2]=>[1,3,7,2,5,4,8,6]=>[8,6,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,5,7,1,4]=>[1,8,4,3,2,6,7,5]=>[8,1,5,6,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,3,1,5,6]=>[1,7,5,3,2,8,6,4]=>[8,2,4,6,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,1,5,4,2]=>[1,7,4,8,2,6,5,3]=>[8,2,5,1,7,3,4,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,3,5,8,4]=>[1,6,5,3,7,8,4,2]=>[8,3,4,6,2,1,5,7]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,3,5,4,7]=>[1,6,5,3,8,7,4,2]=>[8,3,4,6,1,2,5,7]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,6,3,8,5]=>[1,7,8,5,6,3,4,2]=>[8,2,1,4,3,6,5,7]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,2,6,4,1]=>[1,7,4,5,2,3,8,6]=>[8,2,5,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,5,2,6,3]=>[1,4,8,3,2,7,6,5]=>[8,5,1,6,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,8,7,1,6]=>[1,5,8,6,7,2,3,4]=>[8,4,1,3,2,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,6,8,1,7]=>[1,5,6,8,7,2,3,4]=>[8,4,3,1,2,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,3,8,2,1]=>[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,2,3,1,6]=>[1,4,7,2,8,6,3,5]=>[8,5,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,5,8,3,6,1]=>[1,4,5,8,2,3,7,6]=>[8,5,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,1,4,6,2]=>[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,3,4,6,1]=>[1,5,3,2,8,4,7,6]=>[8,4,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,5,3,8,1]=>[1,6,3,2,7,8,4,5]=>[8,3,6,7,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,3,6,1,4]=>[1,5,3,2,7,4,8,6]=>[8,4,6,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,6,4,2,8,7]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,4,6,2,3]=>[1,5,4,7,2,3,8,6]=>[8,4,5,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,5,4,2,1]=>[1,6,4,7,2,8,3,5]=>[8,3,5,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,4,8,5,7]=>[1,6,8,7,5,4,2,3]=>[8,3,1,2,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,4,7,8,5]=>[1,6,7,8,5,4,2,3]=>[8,3,2,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,5,7,4,1]=>[1,6,7,4,3,8,2,5]=>[8,3,2,5,6,1,7,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,6,4,8,7]=>[1,5,6,4,3,2,7,8]=>[8,4,3,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,4,8,5,6,3]=>[1,7,6,5,8,3,2,4]=>[8,2,3,4,1,6,7,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,4,8,6,5]=>[1,7,6,8,5,4,2,3]=>[8,2,3,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,4,5,8,6]=>[1,7,8,6,5,4,3,2]=>[8,2,1,3,4,5,6,7]=>[8,3,2,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,4,2,1,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,3,2,8,7]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,4,6,5,2]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,4,7,5,1]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,5,8,3,4]=>[1,6,8,4,7,3,2,5]=>[8,3,1,5,2,6,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,5,8,4,3]=>[1,6,8,3,2,7,4,5]=>[8,3,1,6,7,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,5,4,3,2]=>[1,7,3,8,2,6,4,5]=>[8,2,6,1,7,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,6,1,3,2]=>[1,5,6,2,4,7,3,8]=>[8,4,3,7,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,7,4,3,2]=>[1,6,4,2,5,7,3,8]=>[8,3,5,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,4,1,3,2]=>[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,3,2,5,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,6,2,4,7]=>[1,2,8,7,4,5,6,3]=>[8,7,1,2,5,4,3,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,3,7,4,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,2,3,5,7]=>[1,6,3,4,8,7,5,2]=>[8,3,6,5,1,2,4,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,6,1,4,3]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,2,3,8,6]=>[1,5,2,7,8,6,3,4]=>[8,4,7,2,1,3,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,5,3,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,4,1,6,8]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,5,6,1,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,3,1,5,7]=>[1,6,2,8,7,5,3,4]=>[8,3,7,1,2,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,4,1,6,8]=>[1,3,5,4,2,7,6,8]=>[8,6,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,8,4,5,6]=>[1,7,5,8,6,4,2,3]=>[8,2,4,1,3,5,7,6]=>[8,4,5,2,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,8,3,5,6]=>[1,2,3,7,5,8,6,4]=>[8,7,6,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,6,1,3,4,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,4,5,6,7]=>[1,2,8,7,6,5,4,3]=>[8,7,1,2,3,4,5,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,3,1,5,6]=>[1,7,5,3,8,6,2,4]=>[8,2,4,6,1,3,7,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,1,4,5,6]=>[1,8,6,4,2,3,7,5]=>[8,1,3,5,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,4,7,1,3,8]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,1,8,2,3]=>[1,6,8,3,7,2,5,4]=>[8,3,1,6,2,7,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,1,8,2,3]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,8,3,5,6]=>[1,7,5,8,6,3,2,4]=>[8,2,4,1,3,6,7,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,5,7,2,6]=>[1,4,3,2,8,6,7,5]=>[8,5,6,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,3,6,2,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,1,8,2,5,6]=>[1,4,2,7,5,8,6,3]=>[8,5,7,2,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,7,3,5,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,4,7,6,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,3,7,6,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,8,7,6,2]=>[1,4,3,5,8,2,6,7]=>[8,5,6,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,8,7,6,3]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,8,1,4,3]=>[1,5,8,3,2,6,4,7]=>[8,4,1,6,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,3,7,5,1,2]=>[1,4,3,6,5,7,2,8]=>[8,5,6,3,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,7,5,1,3]=>[1,4,2,6,5,7,3,8]=>[8,5,7,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,4,1,8,3]=>[1,5,4,7,8,3,2,6]=>[8,4,5,2,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,3,1,8,4]=>[1,5,3,7,8,4,2,6]=>[8,4,6,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,8,3,1,4]=>[1,5,8,4,2,6,3,7]=>[8,4,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,1,8,3,4]=>[1,5,2,6,8,4,3,7]=>[8,4,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,1,3,8,4]=>[1,5,2,6,3,7,8,4]=>[8,4,7,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,8,2,4,3]=>[1,5,8,3,2,6,4,7]=>[8,4,1,6,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,2,4,8,3]=>[1,5,2,6,4,7,8,3]=>[8,4,7,3,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,7,3,5,2]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,7,5,3,2]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,4,8,3,2]=>[1,5,4,7,3,6,8,2]=>[8,4,5,2,6,3,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,8,4,2,3]=>[1,5,8,3,2,6,4,7]=>[8,4,1,6,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,7,5,2,3]=>[1,4,2,6,5,7,3,8]=>[8,5,7,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,7,5,3,2]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,8,3,2,4]=>[1,5,8,4,2,6,3,7]=>[8,4,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,3,8,2,4]=>[1,5,3,7,2,6,8,4]=>[8,4,6,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,3,2,8,4]=>[1,5,3,7,8,4,2,6]=>[8,4,6,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,1,2,8,4]=>[1,5,2,6,3,7,8,4]=>[8,4,7,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,4,2,1,3]=>[1,5,4,7,2,6,3,8]=>[8,4,5,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,3,5,1,8]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,3,2,5,7]=>[1,2,4,6,3,8,7,5]=>[8,7,5,3,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,3,8,5,2]=>[1,7,5,3,2,4,6,8]=>[8,2,4,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,1,8,3,2]=>[1,7,3,5,2,4,6,8]=>[8,2,6,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,6,3,2,7]=>[1,4,8,7,2,3,5,6]=>[8,5,1,2,7,6,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,1,8,5,4]=>[1,3,7,5,2,4,6,8]=>[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,6,8,2,3]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,2,7,4,3]=>[1,8,3,5,2,6,7,4]=>[8,1,6,4,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,4,8,7,6]=>[1,3,5,4,2,6,8,7]=>[8,6,4,5,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,3,2,7,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,6,8,7,5]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,7,1,6,2]=>[1,5,7,6,2,4,3,8]=>[8,4,2,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,3,5,2,7]=>[1,8,7,2,4,3,6,5]=>[8,1,2,7,5,6,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,8,1,6]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,7,8,1,6]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,2,5,3,4]=>[1,8,4,7,3,6,5,2]=>[8,1,5,2,6,3,4,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,6,5,8,2,4]=>[1,3,7,2,4,6,8,5]=>[8,6,2,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,6,8,3,4]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,6,8,4,5]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,4,7,1,5]=>[1,3,8,5,4,6,7,2]=>[8,6,1,4,5,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,3,2,1,5]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,3,7,2,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,6,7,1,4]=>[1,8,4,3,5,6,7,2]=>[8,1,5,6,4,3,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,7,6,1,4]=>[1,3,5,7,2,8,4,6]=>[8,6,4,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,3,1,8,6,2]=>[1,4,3,5,2,7,6,8]=>[8,5,6,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,8,1,7,2]=>[1,4,6,2,5,8,3,7]=>[8,5,3,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,1,8,7,4]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,7,2,8,4]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,7,8,2,3]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,7,2,1,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,6,8,1,3]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,8,7,1,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,4,3,2,8,7]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,4,7,3,8]=>[1,2,6,7,3,5,4,8]=>[8,7,3,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,5,2,1,8,7]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,3,8,6,2]=>[1,5,3,4,2,7,6,8]=>[8,4,6,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,3,8,1,6]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,3,1,4,8]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,6,1,5,7]=>[1,2,4,8,7,5,6,3]=>[8,7,5,1,2,4,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,5,6,2,4]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,5,6,2,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,3,4,6,2]=>[1,5,3,7,6,4,8,2]=>[8,4,6,2,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,3,4,6,2]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,2,5,6,4]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,5,2,6,4]=>[1,3,7,6,2,4,8,5]=>[8,6,2,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,8,2,6,4]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,8,2,6,4]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,8,4,6,2]=>[1,3,7,6,4,2,5,8]=>[8,6,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,1,4,6,2]=>[1,3,7,6,4,8,2,5]=>[8,6,2,3,5,1,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,4,6,1,2]=>[1,5,4,8,2,3,7,6]=>[8,4,5,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,4,1,6,2]=>[1,5,4,8,2,3,7,6]=>[8,4,5,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,1,4,6,2]=>[1,5,2,3,7,6,4,8]=>[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,8,4,6,2]=>[1,5,8,2,3,7,6,4]=>[8,4,1,7,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,4,5,8,7]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,1,3,8,7]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,3,2,4,5]=>[1,8,5,3,2,6,4,7]=>[8,1,4,6,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,7,3,4,6]=>[1,2,5,7,4,3,8,6]=>[8,7,4,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,3,1,4,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,4,3,6,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,7,1,4,6]=>[1,5,7,4,2,8,6,3]=>[8,4,2,5,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,6,1,3,7]=>[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,7,1,4,5]=>[1,2,6,3,8,5,7,4]=>[8,7,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,6,2,3,7]=>[1,5,6,2,8,7,3,4]=>[8,4,3,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,6,2,3,7]=>[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,6,2,3,7]=>[1,4,2,8,7,3,5,6]=>[8,5,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,8,3,6,7]=>[1,2,3,5,8,7,6,4]=>[8,7,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,1,5,6,7]=>[1,2,4,8,7,6,5,3]=>[8,7,5,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,2,5,6,7]=>[1,3,8,7,6,5,2,4]=>[8,6,1,2,3,4,7,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,1,5,6,7]=>[1,3,4,2,8,7,6,5]=>[8,6,5,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,1,5,6,7]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,1,5,6,7]=>[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,7,1,4,6]=>[1,3,5,7,4,2,8,6]=>[8,6,4,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,6,1,3,7]=>[1,4,2,8,7,3,5,6]=>[8,5,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,5,3,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,1,5,6,7]=>[1,3,8,7,6,5,2,4]=>[8,6,1,2,3,4,7,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,1,5,6,7]=>[1,2,8,7,6,5,3,4]=>[8,7,1,2,3,4,6,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,6,2,8,3]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,8,1,6,2]=>[1,5,8,2,7,6,3,4]=>[8,4,1,7,2,3,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,8,2,6,1]=>[1,5,8,2,7,6,3,4]=>[8,4,1,7,2,3,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,6,7,5,1]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,6,7,5,2]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,2,8,4,3]=>[1,6,8,3,7,4,5,2]=>[8,3,1,6,2,5,4,7]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,2,8,1,7]=>[1,5,2,6,8,7,3,4]=>[8,4,7,3,1,2,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,3,8,4,1]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,2,5,3,1]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,5,3,8,4]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,1,6,7,5]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,8,2,1,6]=>[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,1,2,4,3]=>[1,6,2,7,4,8,3,5]=>[8,3,7,2,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,3,1,2,5]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,2,4,3,1]=>[1,6,4,8,2,7,3,5]=>[8,3,5,1,7,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,3,1,4,2]=>[1,6,2,7,4,8,3,5]=>[8,3,7,2,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,5,7,6,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,6,1,4,8,3]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,2,3,5,1]=>[1,6,3,4,8,2,7,5]=>[8,3,6,5,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,1,3,5,2]=>[1,6,3,4,8,2,7,5]=>[8,3,6,5,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,1,3,8,4]=>[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,4,1,3,2]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,2,1,3,5]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,1,2,3,5]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,5,8,2,7]=>[1,2,4,6,8,7,3,5]=>[8,7,5,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,7,2,6,5]=>[1,8,5,7,6,2,3,4]=>[8,1,4,2,3,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,3,5,4,1]=>[1,6,5,3,8,2,7,4]=>[8,3,4,6,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,7,6,2,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,6,5,4,1]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,5,2,6,4]=>[1,3,2,8,4,7,6,5]=>[8,6,7,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,7,2,5,3]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,4,6,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,4,3,6,5]=>[1,8,5,4,7,6,3,2]=>[8,1,4,5,2,3,6,7]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,5,4,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,7,2,6,3]=>[1,8,3,5,7,6,2,4]=>[8,1,6,4,2,3,7,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,7,4,2,3]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,7,6,2,3]=>[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,7,3,6,1]=>[1,2,4,5,7,6,3,8]=>[8,7,5,4,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,5,7,2,1]=>[1,4,6,7,2,3,8,5]=>[8,5,3,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,6,3,4,1]=>[1,5,6,3,7,4,8,2]=>[8,4,3,6,2,5,1,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,7,3,5,1]=>[1,4,6,3,8,2,5,7]=>[8,5,3,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,5,4,6,1]=>[1,3,8,2,4,7,6,5]=>[8,6,1,7,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,5,6,2,4]=>[1,3,8,4,7,2,5,6]=>[8,6,1,5,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,7,5,2,3]=>[1,4,6,5,7,2,3,8]=>[8,5,3,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,5,4,2,3]=>[1,6,4,8,3,2,7,5]=>[8,3,5,1,6,7,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,6,1,7,5]=>[1,3,8,5,6,2,4,7]=>[8,6,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,5,6,3,2]=>[1,7,3,4,2,8,5,6]=>[8,2,6,5,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,1,6,3,2]=>[1,7,3,4,5,2,8,6]=>[8,2,6,5,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,1,6,7,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,6,3,7,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,4,6,7,2]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,1,5,3,7]=>[1,4,8,7,3,6,5,2]=>[8,5,1,2,6,3,4,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,1,5,3,6]=>[1,7,3,2,4,8,6,5]=>[8,2,6,7,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,4,5,3,7]=>[1,6,5,4,8,7,3,2]=>[8,3,4,5,1,2,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,5,3,4,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,5,4,1,2]=>[1,6,4,8,2,3,7,5]=>[8,3,5,1,7,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,8,4,3,2]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,5,6,7,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,6,5,3,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,6,5,3,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,5,1,4,6]=>[1,3,7,4,8,6,2,5]=>[8,6,2,5,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,5,1,4,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,8,5,1,4,6]=>[1,2,7,4,8,6,3,5]=>[8,7,2,5,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,5,1,4,7]=>[1,3,2,6,4,8,7,5]=>[8,6,7,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,7,5,3,6]=>[1,2,4,8,6,5,7,3]=>[8,7,5,1,3,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,4,5,3,7]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,8,4,3,2]=>[1,7,3,6,4,5,8,2]=>[8,2,6,3,5,4,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,1,8,4,3,2]=>[1,6,4,2,5,8,3,7]=>[8,3,5,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,8,4,3,2]=>[1,5,8,2,7,3,6,4]=>[8,4,1,7,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,4,1,2]=>[1,6,4,8,2,7,3,5]=>[8,3,5,1,7,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,4,5,3,6]=>[1,7,3,2,4,8,6,5]=>[8,2,6,7,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,3,2,4,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,2,5,3,6]=>[1,2,8,6,5,3,7,4]=>[8,7,1,3,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,5,3,6,1]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,2,5,3,8]=>[1,7,3,6,5,2,4,8]=>[8,2,6,3,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,7,1,3,8]=>[1,2,6,3,5,7,4,8]=>[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,6,4,2,8]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,7,4,2,6]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,6,3,5,1]=>[1,7,5,6,3,2,4,8]=>[8,2,4,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,8,7,4,2]=>[1,5,8,2,3,6,7,4]=>[8,4,1,7,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,4,6,1,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,7,5,4,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,2,1,6]=>[1,5,4,7,2,3,8,6]=>[8,4,5,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,8,6,3,5]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,7,4,2,1]=>[1,8,2,6,4,5,7,3]=>[8,1,7,3,5,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,2,1,7,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,4,2,1,5]=>[1,8,5,4,7,2,6,3]=>[8,1,4,5,2,7,3,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,7,5,1,3]=>[1,2,8,3,6,5,7,4]=>[8,7,1,6,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,6,3,7,4,2]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,1,8,5,2]=>[1,6,8,2,3,7,5,4]=>[8,3,1,7,6,2,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,3,7,4,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,4,2,5,1]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,4,7,5,1]=>[1,8,2,6,7,5,4,3]=>[8,1,7,3,2,4,5,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,3,8,7,6]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,5,8,6,3]=>[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,7,4,2,5]=>[1,8,5,7,2,6,4,3]=>[8,1,4,2,7,3,5,6]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,7,4,2,6]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,5,3,2,6]=>[1,4,7,2,3,8,6,5]=>[8,5,2,7,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,3,2,7,5]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,5,2,7,4]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,3,1,7,4]=>[1,8,4,6,2,5,3,7]=>[8,1,5,3,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,2,6,3,1]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,7,4,6,3]=>[1,2,8,3,5,7,6,4]=>[8,7,1,6,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,4,6,3,1]=>[1,8,2,5,4,7,3,6]=>[8,1,7,4,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,1,8,5,2]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,4,8,5,2]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,5,7,4,2]=>[1,8,2,6,7,4,3,5]=>[8,1,7,3,2,5,6,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,8,6,3,2]=>[1,4,5,8,2,3,7,6]=>[8,5,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,5,8,6,4]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,7,4,6,3]=>[1,8,3,2,5,7,6,4]=>[8,1,6,7,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,6,3,8,5,2]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,1,4,8,7]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,1,4,8,7]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,1,4,2,6]=>[1,3,7,2,5,4,8,6]=>[8,6,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,7,3,2,6]=>[1,4,5,7,2,3,8,6]=>[8,5,4,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,8,3,2,6]=>[1,4,5,8,6,3,7,2]=>[8,5,4,1,3,6,2,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,7,4,3,6]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,8,3,2,6]=>[1,5,8,6,3,7,2,4]=>[8,4,1,3,6,2,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,3,1,8,5]=>[1,4,7,8,5,3,2,6]=>[8,5,2,1,4,6,7,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,4,1,6,5]=>[1,3,8,5,4,2,7,6]=>[8,6,1,4,5,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,4,1,6,5]=>[1,3,7,6,2,8,5,4]=>[8,6,2,3,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,1,7,3,5]=>[1,6,7,3,8,5,2,4]=>[8,3,2,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,1,6,2,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,8,1,7,2,5]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,1,2,7,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,1,2,7,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,1,2,7,6]=>[1,3,4,8,6,2,5,7]=>[8,6,5,1,3,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,1,2,7,6]=>[1,4,8,6,2,5,3,7]=>[8,5,1,3,7,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,1,6,2,5]=>[1,7,2,4,8,5,3,6]=>[8,2,7,5,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,7,1,2,4]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,1,7,2,5]=>[1,4,8,5,2,6,7,3]=>[8,5,1,4,7,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,1,7,3,5]=>[1,2,6,7,3,8,5,4]=>[8,7,3,2,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,6,1,2,4]=>[1,3,5,6,2,7,4,8]=>[8,6,4,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,6,1,3,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,7,1,3,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,6,7,1,3,4]=>[1,5,7,3,8,4,6,2]=>[8,4,2,6,1,5,3,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,7,6,4,5]=>[1,2,8,5,7,4,3,6]=>[8,7,1,4,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,6,1,3,4]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,1,6,2,5]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,6,1,3,4]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,8,1,2,3]=>[1,7,2,4,5,8,3,6]=>[8,2,7,5,4,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,5,1,2,4]=>[1,3,7,2,6,4,8,5]=>[8,6,2,7,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,7,5,1,3,4]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,5,2,3,4]=>[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,5,1,3,4]=>[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,8,1,2,3]=>[1,5,8,3,6,2,7,4]=>[8,4,1,6,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,1,3,5,6]=>[1,2,8,6,3,7,5,4]=>[8,7,1,3,6,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,1,3,2,6]=>[1,5,2,4,7,3,8,6]=>[8,4,7,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,3,2,5,7]=>[1,4,2,8,7,5,3,6]=>[8,5,7,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,4,5,3,6]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,2,8,7,4]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,5,4,1,6]=>[1,8,6,4,3,2,7,5]=>[8,1,3,5,6,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,8,7,2,6]=>[1,5,8,6,7,2,3,4]=>[8,4,1,3,2,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,8,7,1,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,1,5,2,4]=>[1,3,6,5,2,7,4,8]=>[8,6,3,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,6,8,2,4]=>[1,3,5,6,8,4,2,7]=>[8,6,4,3,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,1,4,7,2]=>[1,3,5,2,6,4,8,7]=>[8,6,4,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,4,7,2,3]=>[1,8,3,5,4,6,7,2]=>[8,1,6,4,5,3,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,1,8,2,5]=>[1,3,7,2,6,8,5,4]=>[8,6,2,7,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,6,8,2,5,3]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,1,8,5,4]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,3,1,8,5]=>[1,6,2,4,3,7,8,5]=>[8,3,7,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,4,6,2,7]=>[1,5,4,8,7,2,3,6]=>[8,4,5,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,7,4,2,5]=>[1,3,2,8,5,7,4,6]=>[8,6,7,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,6,8,1,5]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,1,5,3,7]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,3,2,5,7]=>[1,8,7,5,3,2,4,6]=>[8,1,2,4,6,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,5,2,1,6]=>[1,4,8,6,2,7,3,5]=>[8,5,1,3,7,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,8,5,2,6]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,5,2,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,6,7,5,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,7,5,4,2]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,8,6,1,4]=>[1,7,2,5,8,4,3,6]=>[8,2,7,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,1,3,7,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,6,1,7,5,2]=>[1,3,4,6,7,5,2,8]=>[8,6,5,3,2,4,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,6,5,2,8,1]=>[1,3,4,6,2,7,8,5]=>[8,6,5,3,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,1,5,8,3]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,5,7,6,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,8,4,7,2]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,7,3,8,4,2]=>[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,8,4,1,3]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,6,7,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,7,4,1,5]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,4,7,3,2]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,6,4,7,3]=>[1,2,5,6,4,3,8,7]=>[8,7,4,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,2,1,6,5]=>[1,8,5,2,3,7,6,4]=>[8,1,4,7,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,3,1,7,4]=>[1,5,3,6,2,4,8,7]=>[8,4,6,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,1,8,4,5,2]=>[1,7,5,8,2,3,6,4]=>[8,2,4,1,7,6,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,4,6,5,1]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,4,8,7,5]=>[1,6,8,5,4,2,3,7]=>[8,3,1,4,5,7,6,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,3,6,1,5]=>[1,8,5,3,4,2,7,6]=>[8,1,4,6,5,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,4,2,3,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,2,8,6,4]=>[1,3,2,7,6,8,4,5]=>[8,6,7,2,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,4,1,3,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,2,4,3,5]=>[1,7,3,8,5,2,4,6]=>[8,2,6,1,4,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,8,5,3,4]=>[1,7,3,6,5,8,4,2]=>[8,2,6,3,4,1,5,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,7,2,8,5]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,5,1,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,3,8,6,4]=>[1,5,3,7,6,8,4,2]=>[8,4,6,2,3,1,5,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,1,7,6,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,4,8,2,5]=>[1,7,2,6,8,5,4,3]=>[8,2,7,3,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,3,8,1,5]=>[1,7,2,3,6,8,5,4]=>[8,2,7,6,3,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,3,8,2,6]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,4,8,2,6]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,6,3,7,5]=>[1,8,5,6,3,4,2,7]=>[8,1,4,3,6,5,7,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,1,6,4,3]=>[1,8,3,7,4,5,2,6]=>[8,1,6,2,5,4,7,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,3,2,8,5,4]=>[1,6,8,4,3,7,5,2]=>[8,3,1,5,6,2,4,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,6,3,8,5]=>[1,4,2,7,8,5,6,3]=>[8,5,7,2,1,4,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,3,8,4,7]=>[1,6,8,7,4,5,3,2]=>[8,3,1,2,5,4,6,7]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,2,8,4,7]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,1,5,2,6]=>[1,7,2,4,8,6,5,3]=>[8,2,7,5,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,5,3,2,6]=>[1,7,2,4,3,8,6,5]=>[8,2,7,5,6,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,2,8,5,1,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,7,4,2,6]=>[1,8,6,4,3,2,5,7]=>[8,1,3,5,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,5,2,7,4]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,7,5,2,4]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,1,7,3,2]=>[1,4,6,7,3,5,2,8]=>[8,5,3,2,6,4,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,8,5,2,4]=>[1,6,5,8,4,3,2,7]=>[8,3,4,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,5,2,8,4]=>[1,3,7,8,4,2,6,5]=>[8,6,2,1,5,7,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,1,3,8,4]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,1,3,7,4]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,7,5,2,4]=>[1,6,5,7,2,3,8,4]=>[8,3,4,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,5,8,3,6]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,8,3,2,6]=>[1,7,2,4,5,8,6,3]=>[8,2,7,5,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,7,4,2,6]=>[1,5,7,2,3,8,6,4]=>[8,4,2,7,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,1,5,2,6]=>[1,7,2,4,3,8,6,5]=>[8,2,7,5,6,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,5,2,7,3]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,5,2,8,3]=>[1,7,8,3,6,2,4,5]=>[8,2,1,6,3,7,5,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,1,6,8,4]=>[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,8,6,1,3]=>[1,4,2,5,8,3,7,6]=>[8,5,7,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,2,6,8,4]=>[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,1,5,8,3]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,3,8,5,2]=>[1,4,2,6,8,3,7,5]=>[8,5,7,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,5,8,3,2]=>[1,4,2,6,8,3,7,5]=>[8,5,7,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,4,8,5,2]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,4,8,5,6]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,7,6,3,8]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,3,8,6,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,5,8,6,4]=>[1,3,2,7,6,8,4,5]=>[8,6,7,2,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,4,8,5,3]=>[1,6,8,3,7,5,4,2]=>[8,3,1,6,2,4,5,7]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,1,8,5,6]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,1,8,6,4]=>[1,7,6,8,4,3,5,2]=>[8,2,3,1,5,6,4,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,2,8,6,3]=>[1,7,6,8,3,2,5,4]=>[8,2,3,1,6,7,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,3,8,6,2]=>[1,7,6,8,2,5,3,4]=>[8,2,3,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,7,6,4,8]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,8,1,6,5]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,8,3,5,1]=>[1,7,5,8,2,6,3,4]=>[8,2,4,1,7,3,6,5]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,8,1,5,2]=>[1,7,5,8,2,3,6,4]=>[8,2,4,1,7,6,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,1,6,4,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,3,6,2,1]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,4,6,3,1]=>[1,8,2,5,4,3,7,6]=>[8,1,7,4,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,1,3,2,5]=>[1,8,5,2,4,7,3,6]=>[8,1,4,7,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,4,1,5,3]=>[1,7,5,4,8,3,6,2]=>[8,2,4,5,1,6,3,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,4,2,7,3]=>[1,6,2,5,4,3,8,7]=>[8,3,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,1,3,7,2]=>[1,6,3,8,2,5,4,7]=>[8,3,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,2,1,7,6]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,1,6,5,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,4,3,7,6]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,1,3,6,2]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,8,2,6,3]=>[1,5,8,3,2,7,6,4]=>[8,4,1,6,7,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,8,3,6,5]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,4,2,7,6]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,3,1,7,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,8,3,5,4]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,3,5,1,6]=>[1,4,7,2,3,8,6,5]=>[8,5,2,7,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,6,2,3,5]=>[1,4,7,3,2,8,5,6]=>[8,5,2,6,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,6,4,2,5]=>[1,7,2,3,8,5,6,4]=>[8,2,7,6,1,4,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,5,3,2,6]=>[1,4,2,7,3,8,6,5]=>[8,5,7,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,3,6,4,2]=>[1,5,3,7,4,2,8,6]=>[8,4,6,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,1,6,4,5]=>[1,3,7,4,2,8,5,6]=>[8,6,2,5,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,6,3,5,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,1,3,5,2]=>[1,4,6,3,7,5,2,8]=>[8,5,3,6,2,4,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,5,2,4,3]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,3,1,2,6]=>[1,5,3,8,6,2,7,4]=>[8,4,6,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,4,3,2,1,7]=>[1,5,3,6,2,8,7,4]=>[8,4,6,3,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,4,2,1,5]=>[1,8,5,4,6,2,7,3]=>[8,1,4,5,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,5,3,7,8]=>[1,6,3,4,2,5,7,8]=>[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,5,4,2,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,4,7,3,8]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,4,7,8,2]=>[1,5,4,3,6,7,8,2]=>[8,4,5,6,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,8,6,1,2]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,5,3,8,6]=>[1,2,4,3,7,8,6,5]=>[8,7,5,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,4,8,5,2]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,3,1,8,4]=>[1,2,7,8,4,5,3,6]=>[8,7,2,1,5,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,4,7,8,3]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,4,1,7,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,1,3,6,8]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,4,7,8,2]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,4,2,7,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,6,3,8,5]=>[1,2,7,8,5,6,3,4]=>[8,7,2,1,4,3,6,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,2,3,6,8]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,8,5,1,2]=>[1,4,3,6,5,8,2,7]=>[8,5,6,3,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,5,1,2,8,4]=>[1,3,6,2,7,8,4,5]=>[8,6,3,7,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,1,3,8,5]=>[1,4,6,3,2,7,8,5]=>[8,5,3,6,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,6,8,3,5,4]=>[1,2,7,5,8,4,6,3]=>[8,7,2,4,1,5,3,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,9,7,8,1]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,10,9,1]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,2,8,7,6,4,3,1]=>[1,5,6,4,7,3,8,2]=>[8,4,3,5,2,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,1,5,4,3]=>[1,8,3,7,4,6,5,2]=>[8,1,6,2,5,3,4,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,7,8,1,6]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,4,3,5,1]=>[1,6,3,7,5,4,2,8]=>[8,3,6,2,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,5,8,1,6]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,2,4,3,7]=>[1,6,4,5,2,8,7,3]=>[8,3,5,4,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,5,8,1,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,7,8,2,5,1]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,1,7,2,5]=>[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,8,6,2,5]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,4,1,2,6]=>[1,3,8,6,2,7,4,5]=>[8,6,1,3,7,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,8,4,1,3]=>[1,5,8,3,6,4,2,7]=>[8,4,1,6,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,8,3,4,2]=>[1,6,3,7,4,5,8,2]=>[8,3,6,2,5,4,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,1,3,8,2]=>[1,7,8,2,5,3,6,4]=>[8,2,1,7,4,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,4,7,3,2]=>[1,2,5,4,8,3,6,7]=>[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,7,6,5,8,2]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,5,8,6,2]=>[1,3,2,4,7,6,8,5]=>[8,6,7,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,3,1,6,2]=>[1,8,2,5,3,7,6,4]=>[8,1,7,4,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,7,2,4,3]=>[1,6,2,8,3,5,7,4]=>[8,3,7,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,2,3,6,5]=>[1,8,5,2,3,7,6,4]=>[8,1,4,7,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,3,5,6,4]=>[1,2,8,4,3,7,6,5]=>[8,7,1,5,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,6,7,5,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,5,7,6,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,2,7,6,5]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,4,1,8,5,6]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,2,7,8,5]=>[1,6,7,8,5,2,4,3]=>[8,3,2,1,4,7,5,6]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,1,3,6,4]=>[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,8,2,4,3]=>[1,6,2,7,4,5,8,3]=>[8,3,7,2,5,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,2,3,5,1]=>[1,4,6,3,7,5,2,8]=>[8,5,3,6,2,4,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,8,2,1,4]=>[1,6,2,5,8,4,3,7]=>[8,3,7,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,2,5,6,3]=>[1,8,3,4,7,6,5,2]=>[8,1,6,5,2,3,4,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,1,5,8,2]=>[1,7,8,2,3,4,6,5]=>[8,2,1,7,6,5,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,7,1,6,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,8,1,4,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,6,1,5,7]=>[1,4,8,7,5,6,2,3]=>[8,5,1,2,4,3,7,6]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,4,6,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,8,7,4,6]=>[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,3,8,4,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,4,8,5,6]=>[1,3,7,5,4,2,6,8]=>[8,6,2,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,6,8,4,5]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,8,7,4,5]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,8,4,6,5]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,8,4,7,5]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,8,6,4,5]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,7,5,1,4]=>[1,6,5,7,2,3,8,4]=>[8,3,4,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,7,5,6,1]=>[1,4,3,8,2,5,7,6]=>[8,5,6,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,6,5,1,2]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,7,2,6,1]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,7,2,6,1]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,7,4,5,1]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,6,2,5,1]=>[1,7,5,6,2,4,8,3]=>[8,2,4,3,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,7,2,6,1]=>[1,3,4,8,2,5,7,6]=>[8,6,5,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,4,5,2,1]=>[1,3,7,2,6,5,4,8]=>[8,6,2,7,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,4,7,3,1]=>[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,4,7,3,2]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,8,3,2,1]=>[1,7,2,4,5,8,3,6]=>[8,2,7,5,4,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,5,7,3,1]=>[1,4,6,7,3,8,2,5]=>[8,5,3,2,6,1,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,5,4,6,1]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,4,5,6,3]=>[1,2,8,3,4,7,6,5]=>[8,7,1,6,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,3,4,5,1]=>[1,7,5,3,8,2,4,6]=>[8,2,4,6,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,6,7,3,1]=>[1,4,5,6,7,3,8,2]=>[8,5,4,3,2,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,7,2,5,1]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,6,2,4,1]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,5,6,3,1]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,4,6,2,1]=>[1,3,5,4,8,2,7,6]=>[8,6,4,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,8,3,2,1]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,5,7,3,1]=>[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,3,8,5,6]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,3,8,6,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,7,2,4,8]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,5,8,6,4]=>[1,3,2,7,6,8,4,5]=>[8,6,7,2,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,2,8,5,6]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,4,8,6,2]=>[1,7,6,8,2,5,4,3]=>[8,2,3,1,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,4,8,6,3]=>[1,7,6,8,3,2,5,4]=>[8,2,3,1,6,7,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,7,1,5,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,1,2,5,4]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,8,1,6,5]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,7,1,4,5]=>[1,8,5,7,4,3,6,2]=>[8,1,4,2,5,6,3,7]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,7,4,5,3]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,4,6,3]=>[1,8,3,7,6,4,2,5]=>[8,1,6,2,3,5,7,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,3,4,6,2]=>[1,8,2,5,3,7,6,4]=>[8,1,7,4,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,1,3,5,4]=>[1,8,4,7,5,2,6,3]=>[8,1,5,2,4,7,3,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,1,2,4,7]=>[1,3,5,2,8,7,4,6]=>[8,6,4,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,1,2,4,6]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,8,1,3,5,2]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,8,1,6,5]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,2,5,1,3,6]=>[1,4,2,7,3,8,6,5]=>[8,5,7,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,1,4,5,3]=>[1,6,4,7,5,2,8,3]=>[8,3,5,2,4,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,3,5,6,2]=>[1,4,2,8,3,7,6,5]=>[8,5,7,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,2,4,6,5]=>[1,3,7,6,4,2,8,5]=>[8,6,2,3,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,2,4,6,3]=>[1,5,2,8,3,7,6,4]=>[8,4,7,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,2,5,3,6]=>[1,7,3,4,2,8,6,5]=>[8,2,6,5,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,7,5,3,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,7,2,5,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,6,3,5,4]=>[1,7,5,6,3,2,8,4]=>[8,2,4,3,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,5,4,3,8]=>[1,6,4,7,3,2,5,8]=>[8,3,5,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,5,4,3,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,6,4,8,2]=>[1,5,6,4,3,7,8,2]=>[8,4,3,5,6,2,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,7,4,3,8]=>[1,6,4,5,7,3,2,8]=>[8,3,5,4,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,4,1,5,8]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,5,6,1,2]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,4,1,5,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,8,6,4,1,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,6,4,5,2]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,2,1,8,3]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,5,7,8,2]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,6,2,7,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,7,6,8,3]=>[1,5,7,8,3,2,4,6]=>[8,4,2,1,6,7,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,2,6,3,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,6,7,3,5]=>[1,4,2,8,5,6,7,3]=>[8,5,7,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,6,5,3,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,6,8,7,5]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,5,7,6,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,4,7,1,6]=>[1,3,8,6,7,2,4,5]=>[8,6,1,3,2,7,5,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,7,6,1,2]=>[1,4,5,7,2,3,8,6]=>[8,5,4,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,6,3,7,5]=>[1,4,2,8,5,6,3,7]=>[8,5,7,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,2,7,1,4]=>[1,3,6,7,2,8,4,5]=>[8,6,3,2,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,1,7,4,2]=>[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,2,1,6,4]=>[1,3,8,4,5,2,7,6]=>[8,6,1,5,4,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,4,6,5,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,1,6,4,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,5,1,4,3]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,6,7,2,8]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,7,5,2,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,7,3,5,6]=>[1,8,6,3,4,2,5,7]=>[8,1,3,6,5,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,2,3,7,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,3,7,2,5]=>[1,2,6,7,3,8,5,4]=>[8,7,3,2,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,3,8,2,5]=>[1,6,8,5,3,7,2,4]=>[8,3,1,4,6,2,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,8,2,6,5]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,1,3,7,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,8,3,5,6]=>[1,2,7,5,8,6,3,4]=>[8,7,2,4,1,3,6,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,2,3,6,5]=>[1,2,7,6,3,8,5,4]=>[8,7,2,3,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,8,2,6,5]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,4,2,6,5]=>[1,8,5,4,3,2,7,6]=>[8,1,4,5,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,6,2,8,5]=>[1,2,7,8,5,6,3,4]=>[8,7,2,1,4,3,6,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,6,5,2,1,7]=>[1,3,4,6,2,8,7,5]=>[8,6,5,3,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,7,5,8,1,6]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,6,2,8,5]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,2,6,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,7,2,8,5]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,6,2,7,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,5,7,1,6]=>[1,4,8,6,7,2,3,5]=>[8,5,1,3,2,7,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,3,4,1,6]=>[1,2,8,6,4,7,3,5]=>[8,7,1,3,5,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,4,3,1,6]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,8,7,1,6]=>[1,4,5,8,6,7,2,3]=>[8,5,4,1,3,2,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,4,7,1,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,4,2,7,5]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,6,2,1,7]=>[1,3,4,5,6,2,8,7]=>[8,6,5,4,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,3,2,6,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,6,5,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,6,3,2,7]=>[1,5,6,3,4,8,7,2]=>[8,4,3,6,5,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,4,7,2,6]=>[1,5,4,8,6,7,2,3]=>[8,4,5,1,3,2,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,5,7,2,6]=>[1,4,2,3,8,6,7,5]=>[8,5,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,5,7,4,8]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,6,5,3,8]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,4,8,2,1]=>[1,7,2,5,4,6,8,3]=>[8,2,7,4,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,5,1,6,3]=>[1,8,3,2,7,6,4,5]=>[8,1,6,7,2,3,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,8,6,3,1]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,3,6,4]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,4,1,6,2]=>[1,5,4,7,6,2,8,3]=>[8,4,5,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,2,6,5,3]=>[1,8,3,7,5,2,4,6]=>[8,1,6,2,4,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,8,4,7,2]=>[1,5,8,2,6,4,3,7]=>[8,4,1,7,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,8,6,3,2]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,8,6,2,1]=>[1,3,7,2,5,8,4,6]=>[8,6,2,7,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,5,8,3,1]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,5,8,3,2]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,1,4,7,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,8,2,7,1]=>[1,5,8,2,4,6,3,7]=>[8,4,1,7,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,4,8,2,1]=>[1,6,8,2,5,4,7,3]=>[8,3,1,7,4,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,1,6,3,2]=>[1,7,3,8,2,5,4,6]=>[8,2,6,1,7,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,5,1,6,3]=>[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,4,1,6,2]=>[1,5,4,8,2,7,6,3]=>[8,4,5,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,1,4,7,2]=>[1,5,2,6,4,8,3,7]=>[8,4,7,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,5,6,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,1,6,5,2]=>[1,3,8,2,7,5,4,6]=>[8,6,1,7,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,2,6,4,3]=>[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,5,2,6,3]=>[1,8,3,2,7,6,4,5]=>[8,1,6,7,2,3,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,5,4,2,6]=>[1,8,6,4,2,7,3,5]=>[8,1,3,5,7,2,6,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,5,4,8,7]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,1,4,8,7]=>[1,3,6,4,5,2,7,8]=>[8,6,3,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,7,4,3,6]=>[1,2,5,7,3,8,6,4]=>[8,7,4,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,5,4,8,1,3]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,1,8,5,6]=>[1,4,3,7,5,2,6,8]=>[8,5,6,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,4,3,7,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,6,7,1,3]=>[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,1,5,7,6]=>[1,3,4,8,6,5,2,7]=>[8,6,5,1,3,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,1,7,6,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,7,2,6,8,5]=>[1,4,7,8,5,2,3,6]=>[8,5,2,1,4,7,6,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,2,1,5,4]=>[1,6,2,8,4,7,5,3]=>[8,3,7,1,5,2,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,6,8,3,2]=>[1,5,6,8,2,3,7,4]=>[8,4,3,1,7,6,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,8,2,6,4]=>[1,5,8,4,2,3,7,6]=>[8,4,1,5,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,4,8,3,5]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,8,7,3,6]=>[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,2,6,1,3]=>[1,5,2,4,7,3,8,6]=>[8,4,7,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,6,2,7,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,4,2,1,7,6]=>[1,3,5,2,8,6,4,7]=>[8,6,4,7,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,2,7,1,3]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,5,4,1,6]=>[1,3,8,6,4,7,2,5]=>[8,6,1,3,5,2,7,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,3,1,8,7]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,3,1,4,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,2,8,4,1]=>[1,7,4,5,2,3,6,8]=>[8,2,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,4,8,5,1]=>[1,7,5,4,3,2,6,8]=>[8,2,4,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,1,4,2,6]=>[1,8,6,4,3,5,2,7]=>[8,1,3,5,6,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,2,8,5,1]=>[1,3,6,8,2,7,5,4]=>[8,6,3,1,7,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,4,8,5,3]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,4,3,5,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,2,1,4,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,2,1,5,6]=>[1,3,7,5,2,8,6,4]=>[8,6,2,4,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,5,1,4,6]=>[1,7,4,3,2,8,6,5]=>[8,2,5,6,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,8,3,6,2]=>[1,5,8,2,7,6,3,4]=>[8,4,1,7,2,3,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,4,8,3,2]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,5,8,3,4,2]=>[1,7,4,5,8,2,6,3]=>[8,2,5,4,1,7,3,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,1,3,2,4]=>[1,8,4,5,2,6,3,7]=>[8,1,5,4,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,1,7,3,4]=>[1,8,4,6,7,3,2,5]=>[8,1,5,3,2,6,7,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,8,3,7,1]=>[1,5,8,2,4,6,3,7]=>[8,4,1,7,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,1,3,6,5]=>[1,7,6,3,2,4,8,5]=>[8,2,3,6,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,5,6,3,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,1,2,7,5]=>[1,3,8,5,2,6,4,7]=>[8,6,1,4,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,5,3,6,7]=>[1,4,2,8,7,6,3,5]=>[8,5,7,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,3,5,6,7]=>[1,8,7,6,5,3,2,4]=>[8,1,2,3,4,6,7,5]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,5,7,8,9,10,1]=>[1,2,3,4,6,7,8,9,10,5]=>[10,9,8,7,5,4,3,2,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,5,6,4,7,8,9,1]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,8,5,4,7,3,2,1]=>[1,6,3,5,7,2,8,4]=>[8,3,6,4,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,2,5,4,1]=>[1,3,7,4,6,5,2,8]=>[8,6,2,5,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,3,2,5,1]=>[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,5,2,1,4]=>[1,3,7,2,8,4,6,5]=>[8,6,2,7,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,5,1,4,3]=>[1,7,4,2,6,3,8,5]=>[8,2,5,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,7,6,1,8]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,2,6,1,8]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,6,1,2,8]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,6,1,8,2]=>[1,3,4,7,8,2,5,6]=>[8,6,5,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,4,6,1,8]=>[1,3,5,4,7,2,6,8]=>[8,6,4,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,6,4,1,8]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,2,4,1,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,1,2,8,4]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,1,4,2,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,4,1,2,8]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,6,1,4,8]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,6,1,4,8]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,4,1,8,2]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,1,8,2,6]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,1,8,6,2]=>[1,3,5,2,7,6,8,4]=>[8,6,4,7,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,4,8,6,2]=>[1,3,5,4,2,7,6,8]=>[8,6,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,4,8,2,6]=>[1,3,5,4,2,7,6,8]=>[8,6,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,2,6,8,4]=>[1,3,7,8,4,2,5,6]=>[8,6,2,1,5,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,1,6,8,4]=>[1,3,7,8,4,2,5,6]=>[8,6,2,1,5,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,1,6,4,8]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,1,6,4,8]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,4,6,2,8]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,1,4,6,8]=>[1,3,7,6,4,2,5,8]=>[8,6,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,1,4,6,8]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,4,1,6,8]=>[1,3,5,4,7,6,2,8]=>[8,6,4,5,2,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,4,1,6,8]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,1,6,8,2]=>[1,3,4,7,8,2,5,6]=>[8,6,5,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,7,1,6,8]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,1,6,8]=>[1,3,5,7,6,2,4,8]=>[8,6,4,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,1,8,4,2]=>[1,5,2,7,4,3,6,8]=>[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,1,8,2,4]=>[1,5,2,7,3,6,8,4]=>[8,4,7,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,1,2,8,6]=>[1,3,7,8,6,2,5,4]=>[8,6,2,1,3,7,4,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,2,1,8,6]=>[1,3,7,8,6,2,5,4]=>[8,6,2,1,3,7,4,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,4,1,8,6]=>[1,3,5,4,7,8,6,2]=>[8,6,4,5,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,1,4,8,6]=>[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,1,4,8,6]=>[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,1,4,8,6]=>[1,3,7,8,6,4,2,5]=>[8,6,2,1,3,5,7,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,4,2,8,6]=>[1,3,7,8,6,2,5,4]=>[8,6,2,1,3,7,4,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,1,8,6,4]=>[1,3,5,2,7,6,8,4]=>[8,6,4,7,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,1,8,6,4]=>[1,3,2,7,6,8,4,5]=>[8,6,7,2,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,1,8,6,4]=>[1,3,7,6,8,4,5,2]=>[8,6,2,3,1,5,4,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,1,8,4,6]=>[1,3,7,4,5,2,6,8]=>[8,6,2,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,1,8,4,6]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,1,8,4,6]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,7,4,8,3]=>[1,6,4,5,7,8,3,2]=>[8,3,5,4,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,8,4,6,3]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,4,7,5,6]=>[1,2,3,8,6,7,5,4]=>[8,7,6,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,4,8,3,6]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,7,1,8,5]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,9,2,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,9,3]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,2,9]=>[1,3,4,5,6,7,8,2,9]=>[9,7,6,5,4,3,2,8,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,8,3,4,1,7,6,2]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,1,7,5,2]=>[1,3,6,7,5,2,8,4]=>[8,6,3,2,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,8,1,7,2]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,1,8,5,2]=>[1,3,6,8,2,7,5,4]=>[8,6,3,1,7,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,8,6,5,2]=>[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,7,6,5,2]=>[1,3,4,2,8,5,7,6]=>[8,6,5,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,1,5,4,8]=>[1,3,7,4,6,5,2,8]=>[8,6,2,5,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,6,1,5,4]=>[1,3,8,4,7,5,6,2]=>[8,6,1,5,2,4,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,1,6,3,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,5,1,3,7]=>[1,8,7,3,2,4,6,5]=>[8,1,2,6,7,5,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,7,1,5,4]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,5,6,1,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,5,1,3,6]=>[1,8,6,2,4,7,3,5]=>[8,1,3,7,5,2,6,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,5,1,3,6]=>[1,7,3,2,4,8,6,5]=>[8,2,6,7,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,1,8,3,4]=>[1,2,6,8,4,7,3,5]=>[8,7,3,1,5,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,7,4,3,6]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,1,6,2,7]=>[1,8,7,2,3,5,4,6]=>[8,1,2,7,6,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,1,5,2,7]=>[1,8,7,2,6,5,3,4]=>[8,1,2,7,3,4,6,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,8,2,3,1]=>[1,5,8,2,4,6,3,7]=>[8,4,1,7,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,3,7,6,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,3,4,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,6,8,7,3,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,4,5,7,2]=>[1,2,6,5,4,3,8,7]=>[8,7,3,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,7,8,1,3]=>[1,5,7,2,4,6,8,3]=>[8,4,2,7,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,1,3,6,5]=>[1,8,5,2,7,6,3,4]=>[8,1,4,7,2,3,6,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,2,5,6,4]=>[1,8,4,3,2,7,6,5]=>[8,1,5,6,7,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,1,7,5,4]=>[1,6,7,5,2,8,4,3]=>[8,3,2,4,7,1,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,6,8,5,1]=>[1,7,5,6,8,2,4,3]=>[8,2,4,3,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,8,5,6,1]=>[1,2,7,6,5,8,3,4]=>[8,7,2,3,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,1,5,6,4]=>[1,8,4,2,3,7,6,5]=>[8,1,5,7,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,4,3,1,6]=>[1,5,4,2,7,3,8,6]=>[8,4,5,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,4,8,1,6]=>[1,3,5,4,7,2,6,8]=>[8,6,4,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,4,1,5,6]=>[1,8,6,2,3,7,5,4]=>[8,1,3,7,6,2,4,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,8,6,4,3]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,6,5,7,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,8,7,2,4]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,1,3,8,4]=>[1,5,2,7,8,4,3,6]=>[8,4,7,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,2,6,8,3]=>[1,4,5,2,3,7,8,6]=>[8,5,4,7,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,5,1,8,3]=>[1,7,8,3,2,6,4,5]=>[8,2,1,6,7,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,2,5,8,6,1]=>[1,7,6,8,2,3,4,5]=>[8,2,3,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,6,7,1,3]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,1,3,7,4]=>[1,8,4,2,5,3,6,7]=>[8,1,5,7,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,6,7,8,3]=>[1,4,5,6,7,8,3,2]=>[8,5,4,3,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,5,1,7,8,2]=>[1,3,6,7,8,2,4,5]=>[8,6,3,2,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,4,6,1,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,4,6,1,8]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,4,6,1,8]=>[1,3,5,4,2,7,6,8]=>[8,6,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,4,6,1,8]=>[1,5,4,2,7,3,6,8]=>[8,4,5,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,4,7,6,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,1,4,6,8]=>[1,5,2,7,6,4,3,8]=>[8,4,7,2,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,4,1,6,8]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,4,7,6,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,7,4,6,8]=>[1,5,7,6,4,2,3,8]=>[8,4,2,3,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,5,4,6,8]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,2,4,6,8]=>[1,7,6,4,5,2,3,8]=>[8,2,3,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,2,4,6,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,2,4,6,8]=>[1,3,5,2,7,6,4,8]=>[8,6,4,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,2,4,6,8]=>[1,5,2,7,6,4,3,8]=>[8,4,7,2,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,2,4,6,8]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,4,1,6,8]=>[1,5,4,7,6,2,3,8]=>[8,4,5,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,7,1,6,8]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,4,7,6,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,7,4,6,8]=>[1,5,7,6,4,2,3,8]=>[8,4,2,3,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,5,4,6,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,5,4,6,8]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,5,4,6,8]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,7,4,6,8]=>[1,5,7,6,4,2,3,8]=>[8,4,2,3,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,4,7,6,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,4,7,6,8]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,2,4,6,8]=>[1,7,6,4,5,2,3,8]=>[8,2,3,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,2,4,6,8]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,2,4,6,8]=>[1,7,6,4,3,2,5,8]=>[8,2,3,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,2,4,6,8]=>[1,5,2,7,6,4,3,8]=>[8,4,7,2,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,2,4,6,8]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,5,4,6,8]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,5,4,6,8]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,5,4,6,8]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,5,4,6,8]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,5,4,6,8]=>[1,3,7,6,4,2,5,8]=>[8,6,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,9,5,7,8]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,9,4,6,7,8]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,6,5,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,9,3,5,6,7,8]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,9,2,4,5,6,7,8]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,8,7,4,2,6,5,3]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,3,2,6,5]=>[1,2,8,5,3,7,6,4]=>[8,7,1,4,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,2,7,6,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,2,8,1,6]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,2,4,7,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,7,4,2,1]=>[1,8,2,5,7,3,6,4]=>[8,1,7,4,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,7,4,3,1]=>[1,8,2,5,7,3,6,4]=>[8,1,7,4,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,4,1,5,2]=>[1,8,2,7,5,4,3,6]=>[8,1,7,2,4,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,6,8,5,4]=>[1,2,7,5,6,8,4,3]=>[8,7,2,4,3,1,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,8,2,7,1]=>[1,3,6,2,5,8,4,7]=>[8,6,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,8,2,7,6]=>[1,3,2,5,8,6,4,7]=>[8,6,7,4,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,6,4,8,2]=>[1,3,5,6,4,2,7,8]=>[8,6,4,3,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,8,1,3,6]=>[1,2,7,3,5,8,6,4]=>[8,7,2,6,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,8,6,1,3]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,8,6,3,2]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,8,7,3,6]=>[1,2,5,8,6,7,3,4]=>[8,7,4,1,3,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,8,7,1,5]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,8,1,2,7]=>[1,3,6,2,5,8,7,4]=>[8,6,3,7,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,8,7,2,3]=>[1,2,5,8,3,6,7,4]=>[8,7,4,1,6,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,8,7,2,5]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,8,5,2,7]=>[1,2,6,5,8,7,3,4]=>[8,7,3,4,1,2,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,5,8,2,6]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,5,4,8,2]=>[1,7,8,2,6,4,3,5]=>[8,2,1,7,3,5,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,5,8,4,6]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,8,5,3,7]=>[1,2,6,5,8,7,3,4]=>[8,7,3,4,1,2,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,2,4,3,1]=>[1,7,3,5,2,6,4,8]=>[8,2,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,8,5,7,1]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,5,8,6,4]=>[1,7,6,8,4,2,3,5]=>[8,2,3,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,1,4,8,2]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,4,8,6,5]=>[1,7,6,8,5,4,2,3]=>[8,2,3,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,4,8,6,1]=>[1,7,6,8,2,3,4,5]=>[8,2,3,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,8,3,7,2]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,8,3,1,7]=>[1,2,5,8,7,3,6,4]=>[8,7,4,1,2,6,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,4,7,8,2]=>[1,3,6,7,8,2,5,4]=>[8,6,3,2,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,4,5,8,2]=>[1,7,8,2,6,5,4,3]=>[8,2,1,7,3,4,5,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,4,8,5,6]=>[1,7,5,4,2,3,6,8]=>[8,2,4,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,5,3,4,8,2]=>[1,7,8,2,6,4,5,3]=>[8,2,1,7,3,5,4,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,1,3,2,4]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,7,2,1,5]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,3,7,8,6]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,3,1,8,7]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,1,7,2,4]=>[1,3,6,7,2,5,4,8]=>[8,6,3,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,3,2,8,7]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,7,2,8,6]=>[1,4,2,5,7,8,6,3]=>[8,5,7,4,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,2,7,8,6]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,3,8,6,1]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,8,4,2,6]=>[1,3,7,2,5,8,6,4]=>[8,6,2,7,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,2,7,8,6]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,2,7,5,8]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,4,6,7,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,4,5,2,8]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,3,7,5,8]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,3,7,5,8]=>[1,4,2,6,7,5,3,8]=>[8,5,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,7,4,8,5]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,6,5,2,8]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,1,5,8,4]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,2,5,8,4]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,4,7,8,1]=>[1,2,6,7,8,3,5,4]=>[8,7,3,2,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,5,4,2,8]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,5,1,8,7]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,1,8,3,7]=>[1,6,8,7,3,4,5,2]=>[8,3,1,2,6,5,4,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,1,4,5,3]=>[1,8,3,6,4,7,5,2]=>[8,1,6,3,5,2,4,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,7,2,3,1]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,4,7,5,3]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,8,5,3,7]=>[1,2,6,5,8,7,3,4]=>[8,7,3,4,1,2,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,6,1,8,5,7]=>[1,4,6,8,7,5,2,3]=>[8,5,3,1,2,4,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,6,8,5,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,6,1,7,5]=>[1,4,8,5,6,2,3,7]=>[8,5,1,4,3,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,4,5,1,3]=>[1,8,3,7,2,6,5,4]=>[8,1,6,2,7,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,3,6,7,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,3,6,7,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,6,3,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,5,1,3]=>[1,8,3,2,6,5,7,4]=>[8,1,6,7,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,4,5,7,3]=>[1,2,6,5,4,3,8,7]=>[8,7,3,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,4,5,7,3]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,6,7,3,5]=>[1,2,8,5,6,7,3,4]=>[8,7,1,4,3,2,6,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,3,7,5,1]=>[1,4,2,8,3,6,7,5]=>[8,5,7,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,7,3,1,5]=>[1,8,5,7,2,4,6,3]=>[8,1,4,2,7,5,3,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,3,4,8,2]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,8,2,3,4]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,3,4,7,1]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,7,4,1,5]=>[1,6,4,8,5,7,2,3]=>[8,3,5,1,4,2,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,5,8,6,1]=>[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,1,8,4,6]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,1,4,6,7]=>[1,5,2,3,8,7,6,4]=>[8,4,7,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,6,5,7,1]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,6,4,7,2]=>[1,5,6,4,3,2,8,7]=>[8,4,3,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,3,6,2,7]=>[1,5,3,2,8,7,4,6]=>[8,4,6,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,3,7,6,2]=>[1,5,3,4,2,8,6,7]=>[8,4,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,6,2,8,7]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,1,7,3,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,5,8,7,1]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,6,1,8,7]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,6,8,3,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,6,5,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,5,7,1,6]=>[1,4,3,8,6,7,2,5]=>[8,5,6,1,3,2,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,5,7,1,2]=>[1,4,6,7,2,3,8,5]=>[8,5,3,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,2,5,8,7]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,3,6,8,2]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,4,1,7,6]=>[1,5,4,8,6,2,3,7]=>[8,4,5,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,8,2,1,6]=>[1,7,2,5,8,6,3,4]=>[8,2,7,4,1,3,6,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,3,4,1,5,6]=>[1,7,5,4,3,8,6,2]=>[8,2,4,5,6,1,3,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,5,2,6,1]=>[1,7,6,2,4,8,3,5]=>[8,2,3,7,5,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,3,1,5,8]=>[1,4,7,5,3,2,6,8]=>[8,5,2,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,1,3,4,6]=>[1,7,4,5,2,3,8,6]=>[8,2,5,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,8,2,4,5]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,7,8,3,1]=>[1,4,5,7,3,6,8,2]=>[8,5,4,2,6,3,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,5,8,1,3]=>[1,4,7,2,3,6,8,5]=>[8,5,2,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,8,1,4,5]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,7,2,1,4]=>[1,3,8,4,5,7,2,6]=>[8,6,1,5,4,2,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,1,7,2,4]=>[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,7,6,2,5]=>[1,3,8,5,7,2,4,6]=>[8,6,1,4,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,5,1,3,2]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,7,1,6,4]=>[1,5,7,6,2,3,8,4]=>[8,4,2,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,6,1,3,2]=>[1,7,3,5,6,2,4,8]=>[8,2,6,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,7,1,5,2]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,7,1,4,2]=>[1,3,5,7,4,8,2,6]=>[8,6,4,2,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,2,6,3,1]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,1,7,4,2]=>[1,5,2,6,7,4,3,8]=>[8,4,7,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,2,7,5,1]=>[1,4,8,2,6,7,5,3]=>[8,5,1,7,3,2,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,7,2,6,4]=>[1,5,7,6,2,3,8,4]=>[8,4,2,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,2,7,4,1]=>[1,6,7,4,8,2,5,3]=>[8,3,2,5,1,7,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,3,7,5,2]=>[1,6,7,5,3,8,2,4]=>[8,3,2,4,6,1,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,4,7,5,1]=>[1,6,7,5,4,3,8,2]=>[8,3,2,4,5,6,1,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,4,2,5,8]=>[1,7,5,4,2,6,3,8]=>[8,2,4,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,7,8,2,6]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,5,3,1,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,1,7,8,6]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,6,3,1,5]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,3,1,5,8]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,5,2,4,8]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,6,4,3,5]=>[1,2,8,5,6,4,7,3]=>[8,7,1,4,3,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,6,4,2,1]=>[1,8,2,3,5,6,4,7]=>[8,1,7,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,7,6,3,1]=>[1,8,2,4,5,7,3,6]=>[8,1,7,5,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,8,6,3,1]=>[1,7,3,2,5,8,4,6]=>[8,2,6,7,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,4,6,3,1]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,6,3,7,4,1]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,2,6,3,1]=>[1,8,2,4,5,3,7,6]=>[8,1,7,5,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,7,5,2,1]=>[1,8,2,3,6,5,7,4]=>[8,1,7,6,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,5,3,6,4]=>[1,2,8,4,7,6,3,5]=>[8,7,1,5,2,3,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,3,1,8,4]=>[1,7,8,4,6,2,5,3]=>[8,2,1,5,3,7,4,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,1,8,6,3]=>[1,5,2,3,7,6,8,4]=>[8,4,7,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,4,1,6,3]=>[1,5,4,7,6,2,3,8]=>[8,4,5,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,6,3,1,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,1,3,6,4]=>[1,8,4,2,7,6,3,5]=>[8,1,5,7,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,5,8,2,4]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,5,2,1,3]=>[1,8,3,4,7,2,6,5]=>[8,1,6,5,2,7,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,5,2,1,3]=>[1,6,2,4,7,3,8,5]=>[8,3,7,5,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,2,1,3,8]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,8,7,5,2]=>[1,6,7,5,8,2,3,4]=>[8,3,2,4,1,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,4,7,5,2]=>[1,8,2,6,7,5,4,3]=>[8,1,7,3,2,4,5,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,3,1,4,2]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,4,7,5,3]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,6,4,8,3]=>[1,7,8,3,2,5,6,4]=>[8,2,1,6,7,4,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,1,5,2,8]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,6,3,5,2]=>[1,7,5,6,3,2,4,8]=>[8,2,4,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,2,1,8,3]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,5,3,8,2]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,2,7,4,1]=>[1,8,2,6,7,4,5,3]=>[8,1,7,3,2,5,4,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,8,7,4,1]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,7,4,1,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,6,3,1,8]=>[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,5,2,6,8]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,1,6,7,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,1,6,5,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,5,1,7,2]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,5,2,6,8]=>[1,4,3,7,6,2,5,8]=>[8,5,6,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,4,2,5,8]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,2,7,4,5]=>[1,3,6,7,4,8,5,2]=>[8,6,3,2,5,1,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,1,6,7,5]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,8,1,6,3]=>[1,4,2,5,8,3,7,6]=>[8,5,7,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,3,1,7,2]=>[1,4,8,2,5,3,6,7]=>[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,2,6,5,8]=>[1,3,7,5,2,4,6,8]=>[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,1,2,6,5,8]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,3,6,4,8]=>[1,5,3,7,4,2,6,8]=>[8,4,6,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,4,3,6,5]=>[1,7,6,3,2,8,5,4]=>[8,2,3,6,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,2,5,7,6]=>[1,4,2,8,6,5,3,7]=>[8,5,7,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,5,7,8,2]=>[1,4,6,7,8,2,3,5]=>[8,5,3,2,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,2,8,5,7]=>[1,6,8,7,5,2,3,4]=>[8,3,1,2,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,7,6,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,5,7,6,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,1,7,8,4]=>[1,2,6,7,8,4,3,5]=>[8,7,3,2,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,5,7,6,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,6,8,2,5]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,1,8,4,5]=>[1,2,7,4,3,6,8,5]=>[8,7,2,5,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,3,7,5,1]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,6,5,4,2]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,4,2,6,3]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,7,1,4,2]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,7,1,5,3]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,3,4,2,7]=>[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,7,2,6,3]=>[1,8,3,5,7,6,2,4]=>[8,1,6,4,2,3,7,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,5,8,3,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,7,4,1,2]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,5,6,3,1]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,7,4,1,2]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,6,4,2,1]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,4,5,3,1]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,5,3,4,2]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,5,3,1,8]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,6,1,4,2]=>[1,3,5,6,2,8,4,7]=>[8,6,4,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,2,6,5,4]=>[1,3,7,5,2,4,8,6]=>[8,6,2,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,2,7,5,4]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,7,5,4,3]=>[1,8,3,6,5,7,4,2]=>[8,1,6,3,4,2,5,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,1,5,4,2]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,1,7,5,3]=>[1,2,6,7,5,3,8,4]=>[8,7,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,2,8,5,3]=>[1,4,2,6,8,3,7,5]=>[8,5,7,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,2,7,5,4]=>[1,3,2,6,7,5,4,8]=>[8,6,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,2,8,6,3]=>[1,5,2,7,6,8,3,4]=>[8,4,7,2,3,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,2,8,5,4]=>[1,6,8,4,2,3,7,5]=>[8,3,1,5,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,3,7,5,4]=>[1,6,7,5,3,2,4,8]=>[8,3,2,4,6,7,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,3,2,4,7]=>[1,8,7,4,6,2,3,5]=>[8,1,2,5,3,7,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,5,2,4,6]=>[1,2,7,4,3,8,6,5]=>[8,7,2,5,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,8,5,3,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,7,4,3,5,1]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,8,4,3,5]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,4,1,3,6]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,4,5,3,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,7,3,6,2]=>[1,8,2,5,7,6,3,4]=>[8,1,7,4,2,3,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,3,6,1,2]=>[1,8,2,4,5,3,7,6]=>[8,1,7,5,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,7,3,5,2]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,7,4,1,2]=>[1,3,8,2,5,7,4,6]=>[8,6,1,7,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,7,1,5,2]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,6,8,2,5]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,6,8,2,4]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,7,1,8,4]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,2,1,8,6]=>[1,3,5,2,7,8,6,4]=>[8,6,4,7,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,4,2,8,5]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,2,7,5,1]=>[1,3,4,8,2,6,7,5]=>[8,6,5,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,2,7,8,5]=>[1,2,4,3,6,7,8,5]=>[8,7,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,6,3,2,4]=>[1,8,4,5,6,3,2,7]=>[8,1,5,4,3,6,7,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,5,3,2,4]=>[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,6,5,3,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,6,4,5,3]=>[1,2,7,5,6,4,3,8]=>[8,7,2,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,4,6,1,3]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,3,1,6,4]=>[1,8,4,5,3,2,7,6]=>[8,1,5,4,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,3,1,5,4]=>[1,8,4,7,5,3,6,2]=>[8,1,5,2,4,6,3,7]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,5,6,4,3]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,4,6,5,3]=>[1,2,7,5,4,8,3,6]=>[8,7,2,4,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,4,5,3,2]=>[1,8,2,7,3,6,5,4]=>[8,1,7,2,6,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,7,2,6,1]=>[1,3,8,2,5,7,6,4]=>[8,6,1,7,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,4,6,1,2,7]=>[1,3,5,6,2,8,7,4]=>[8,6,4,3,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,7,3,6,1]=>[1,2,5,7,6,3,8,4]=>[8,7,4,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,6,2,7,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,7,6,2,3]=>[1,4,2,5,7,3,8,6]=>[8,5,7,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,7,1,6,2]=>[1,3,8,2,5,7,6,4]=>[8,6,1,7,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,7,3,6,2]=>[1,2,5,7,6,3,8,4]=>[8,7,4,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,7,8,5,2]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,8,6,5,2]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,7,8,3,5]=>[1,2,6,8,5,7,3,4]=>[8,7,3,1,4,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,7,1,8,5]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,7,8,3,5]=>[1,2,6,8,5,7,3,4]=>[8,7,3,1,4,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,8,6,5,1]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,8,5,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,6,1,4,2,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,3,4,1,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,5,6,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,1,6,5,4]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,5,6,4,1]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,7,1,5,3]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,7,6,2,3]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,5,8,2,4]=>[1,7,2,6,8,4,3,5]=>[8,2,7,3,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,5,6,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,2,6,5,4]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,8,2,7,3]=>[1,4,5,8,3,6,2,7]=>[8,5,4,1,6,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,8,4,7,2]=>[1,3,6,4,5,8,2,7]=>[8,6,3,5,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,8,4,7,1]=>[1,3,6,4,5,8,2,7]=>[8,6,3,5,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,6,5,8,2]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,8,2,7,3]=>[1,5,8,3,6,2,4,7]=>[8,4,1,6,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,8,1,7,3]=>[1,5,8,3,6,2,4,7]=>[8,4,1,6,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,8,1,6,2]=>[1,4,5,8,2,3,7,6]=>[8,5,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,8,2,6,1]=>[1,4,5,8,2,3,7,6]=>[8,5,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,8,2,6,1]=>[1,5,8,2,3,7,6,4]=>[8,4,1,7,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,8,1,6,2]=>[1,5,8,2,3,7,6,4]=>[8,4,1,7,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,1,8,5]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,5,2,8,6]=>[1,4,2,3,7,8,6,5]=>[8,5,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,6,2,8,5]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,6,3,7,1]=>[1,5,6,3,8,2,4,7]=>[8,4,3,6,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,6,3,7,2]=>[1,5,6,3,8,2,4,7]=>[8,4,3,6,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,3,5,1,6]=>[1,4,8,6,5,3,2,7]=>[8,5,1,3,4,6,7,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,3,7,4,5]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,6,5,8,3]=>[1,7,8,3,4,2,5,6]=>[8,2,1,6,5,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,3,1,6,2]=>[1,7,6,2,5,3,8,4]=>[8,2,3,7,4,6,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,6,3,5,1]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,5,8,4,3]=>[1,6,8,3,2,4,7,5]=>[8,3,1,6,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,8,5,6,1]=>[1,4,3,7,6,5,8,2]=>[8,5,6,2,3,4,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,5,7,6,1]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,4,7,2,1]=>[1,6,7,2,8,3,5,4]=>[8,3,2,7,1,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,2,3,5,1]=>[1,8,2,4,6,3,7,5]=>[8,1,7,5,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,5,3,7,2]=>[1,6,3,4,2,8,5,7]=>[8,3,6,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,6,2,5,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,2,6,7,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,1,4,7,2]=>[1,6,4,5,2,8,3,7]=>[8,3,5,4,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,3,7,6,1]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,5,6,4,7]=>[1,8,7,4,3,2,5,6]=>[8,1,2,5,6,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,5,4,7,6]=>[1,8,6,4,3,2,5,7]=>[8,1,3,5,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,4,6,7,5]=>[1,8,5,4,3,2,6,7]=>[8,1,4,5,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,2,6,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,5,3,7,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,4,2,7,1]=>[1,6,2,5,4,8,3,7]=>[8,3,7,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,6,2,8,1]=>[1,4,5,6,2,7,8,3]=>[8,5,4,3,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,1,3,5,2]=>[1,6,3,8,2,7,5,4]=>[8,3,6,1,7,2,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,4,7,5,2]=>[1,3,6,7,5,4,8,2]=>[8,6,3,2,4,5,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,8,6,1,4]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,8,1,6,3]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,8,1,5,3]=>[1,2,4,7,5,8,3,6]=>[8,7,5,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,1,7,5,3]=>[1,2,4,8,3,6,7,5]=>[8,7,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,3,5,6,1]=>[1,2,4,8,3,7,6,5]=>[8,7,5,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,1,8,4,5]=>[1,3,7,4,6,8,5,2]=>[8,6,2,5,3,1,4,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,1,7,4,5]=>[1,3,6,7,4,8,5,2]=>[8,6,3,2,5,1,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,5,8,1,7]=>[1,3,4,2,6,8,7,5]=>[8,6,5,7,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,7,5,8,1]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,3,6,7,1]=>[1,5,3,4,2,8,6,7]=>[8,4,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,2,1,7,6]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,2,1,7,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,3,7,5,1]=>[1,6,7,5,3,4,2,8]=>[8,3,2,4,6,5,7,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,2,7,1,5]=>[1,6,7,2,4,3,8,5]=>[8,3,2,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,2,1,6,4]=>[1,5,2,8,4,7,6,3]=>[8,4,7,1,5,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,7,1,8,3]=>[1,2,5,7,8,3,6,4]=>[8,7,4,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,1,6,7,3]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,8,2,1,5]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,2,1,8,5]=>[1,6,2,7,8,5,3,4]=>[8,3,7,2,1,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,8,7,3,4]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,4,6,7,3]=>[1,2,5,4,8,3,6,7]=>[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,4,6,8,3]=>[1,2,5,4,7,8,3,6]=>[8,7,4,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,3,6,8,4]=>[1,5,3,2,4,7,8,6]=>[8,4,6,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,8,3,6,7,4]=>[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,8,7,2,1]=>[1,5,8,2,6,7,3,4]=>[8,4,1,7,3,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,3,6,7,5]=>[1,4,8,5,3,2,6,7]=>[8,5,1,4,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,3,6,8,5]=>[1,4,7,8,5,3,2,6]=>[8,5,2,1,4,6,7,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,4,6,2,1]=>[1,7,2,5,4,8,3,6]=>[8,2,7,4,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,4,6,2,1]=>[1,8,2,5,4,7,3,6]=>[8,1,7,4,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,3,6,4,5]=>[1,7,4,8,5,3,2,6]=>[8,2,5,1,4,6,7,3]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,3,5,8,4]=>[1,6,5,3,7,8,4,2]=>[8,3,4,6,2,1,5,7]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,4,5,7,3]=>[1,2,6,5,4,3,8,7]=>[8,7,3,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,5,6,2,1]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,4,6,5,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,3,5,8,4]=>[1,7,8,4,2,3,6,5]=>[8,2,1,5,7,6,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,3,5,6,4]=>[1,8,4,2,3,7,6,5]=>[8,1,5,7,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,4,5,2,1]=>[1,6,5,4,3,7,2,8]=>[8,3,4,5,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,4,5,3,6]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,3,4,7,5]=>[1,8,5,3,2,6,4,7]=>[8,1,4,6,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,1,4,8,2]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,7,3,6,1]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,7,2,6,4]=>[1,2,8,4,5,7,6,3]=>[8,7,1,5,4,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,8,5,7,1]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,4,8,6,1]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,7,8,5,1]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,8,6,3,4]=>[1,2,5,8,4,3,7,6]=>[8,7,4,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,2,4,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,8,4,5,3]=>[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,6,7,1,5]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,5,6,3,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,8,5,3,4]=>[1,2,6,5,8,4,7,3]=>[8,7,3,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,7,8,4,1]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,7,5,3,6]=>[1,2,8,6,5,7,3,4]=>[8,7,1,3,4,2,6,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,7,4,2,6]=>[1,8,6,4,2,5,7,3]=>[8,1,3,5,7,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,8,4,2,5]=>[1,3,6,4,7,2,5,8]=>[8,6,3,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,5,6,2,7]=>[1,3,4,8,7,2,5,6]=>[8,6,5,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,5,7,2,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,9,1,2,3,4,5,10]=>[1,6,2,7,3,8,4,9,5,10]=>[10,5,9,4,8,3,7,2,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,1,2,3,4,5,9]=>[1,6,3,8,5,2,7,4,9]=>[9,4,7,2,5,8,3,6,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,7,8,9,10,2,3,4,5,6]=>[1,2,7,3,8,4,9,5,10,6]=>[10,9,4,8,3,7,2,6,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,6,7,8,9,1,2,3,4,10]=>[1,5,9,4,8,3,7,2,6,10]=>[10,6,2,7,3,8,4,9,5,1]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,6,2,3,5,1,4,7]=>[1,8,7,4,3,2,6,5]=>[8,1,2,5,6,7,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,7,3,1,6]=>[1,8,6,3,4,5,7,2]=>[8,1,3,6,5,4,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,7,5,4,1]=>[1,2,6,5,7,4,8,3]=>[8,7,3,4,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,5,4,1,6]=>[1,8,6,4,7,2,3,5]=>[8,1,3,5,2,7,6,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,5,4,1,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,2,4,3,7]=>[1,8,7,3,2,6,4,5]=>[8,1,2,6,7,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,5,4,2,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,5,4,2,6]=>[1,8,6,4,7,2,3,5]=>[8,1,3,5,2,7,6,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,7,5,4,2]=>[1,3,2,6,5,7,4,8]=>[8,6,7,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,7,6,4,1]=>[1,3,2,5,7,4,8,6]=>[8,6,7,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,7,6,5,1]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,1,6,5,2]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,7,6,4,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,7,6,3,2]=>[1,4,5,7,3,8,2,6]=>[8,5,4,2,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,4,5,6,3]=>[1,8,3,7,6,5,4,2]=>[8,1,6,2,3,4,5,7]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,4,6,2,5]=>[1,8,5,4,3,7,2,6]=>[8,1,4,5,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,4,6,5,1]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,3,6,5,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,4,3,5]=>[1,8,5,6,4,2,3,7]=>[8,1,4,3,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,2,4,3,6]=>[1,8,6,4,5,2,3,7]=>[8,1,3,5,4,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,7,6,3,1]=>[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,3,1,5,6]=>[1,8,6,2,3,7,5,4]=>[8,1,3,7,6,2,4,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,7,6,4,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,5,2,6,4]=>[1,8,4,3,7,6,2,5]=>[8,1,5,6,2,3,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,7,6,4,3]=>[1,8,3,5,7,4,2,6]=>[8,1,6,4,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,7,6,5,1]=>[1,4,3,8,2,5,7,6]=>[8,5,6,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,7,6,5,3]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,2,6,4,3]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,7,6,2,4]=>[1,5,7,2,8,4,3,6]=>[8,4,2,7,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,1,7,6,3]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,7,6,5,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,7,6,5,2]=>[1,4,3,2,8,5,7,6]=>[8,5,6,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,7,6,5,2]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,3,2,1,7,4]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,2,4,1,8]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,4,3,1,8]=>[1,6,3,7,2,5,4,8]=>[8,3,6,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,2,8,6,4]=>[1,5,2,7,6,8,4,3]=>[8,4,7,2,3,1,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,2,7,4,6]=>[1,5,2,8,6,7,4,3]=>[8,4,7,1,3,2,5,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,2,4,6,7]=>[1,8,7,6,4,3,2,5]=>[8,1,2,3,5,6,7,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,2,4,8,6]=>[1,7,8,6,4,3,2,5]=>[8,2,1,3,5,6,7,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,1,4,3,6]=>[1,7,3,8,6,4,2,5]=>[8,2,6,1,3,5,7,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,5,4,8,3]=>[1,6,4,2,7,8,3,5]=>[8,3,5,7,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,8,6,4,5]=>[1,7,4,3,2,5,8,6]=>[8,2,5,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,2,3,7,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,3,5,6,4]=>[1,2,7,6,5,3,8,4]=>[8,7,2,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,3,1,4,6]=>[1,7,4,2,5,3,8,6]=>[8,2,5,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,6,8,3,5]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,5,7,3,4]=>[1,6,7,3,8,4,2,5]=>[8,3,2,6,1,5,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,1,8,6,3]=>[1,7,6,8,3,5,2,4]=>[8,2,3,1,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,2,1,8,6]=>[1,7,8,6,2,3,5,4]=>[8,2,1,3,7,6,4,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,5,6,1,4]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,6,8,5,2]=>[1,2,7,5,6,8,3,4]=>[8,7,2,4,3,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,7,2,1,3]=>[1,5,7,2,4,8,3,6]=>[8,4,2,7,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,1,8,5,4]=>[1,6,8,4,2,7,5,3]=>[8,3,1,5,7,2,4,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,2,8,4,5]=>[1,2,7,4,3,6,8,5]=>[8,7,2,5,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,7,3,6,8]=>[1,5,7,6,3,2,4,8]=>[8,4,2,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,4,1,7,2]=>[1,6,2,5,4,3,8,7]=>[8,3,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,5,3,6,7]=>[1,4,8,7,6,3,2,5]=>[8,5,1,2,3,6,7,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,6,5,2,8]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,5,2,8,4]=>[1,3,6,2,7,8,4,5]=>[8,6,3,7,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,5,8,4,3]=>[1,2,7,4,3,6,8,5]=>[8,7,2,5,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,8,4,2,3]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,5,1,2,7]=>[1,4,8,7,2,3,6,5]=>[8,5,1,2,7,6,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,8,4,3,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,8,4,3,5]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,4,5,1,8]=>[1,7,2,3,6,5,4,8]=>[8,2,7,6,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,5,3,1]=>[1,6,5,2,7,3,8,4]=>[8,3,4,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,7,8,4,3]=>[1,6,8,3,2,4,5,7]=>[8,3,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,8,5,3,6]=>[1,4,7,3,2,5,8,6]=>[8,5,2,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,1,2,6,8,5]=>[1,4,2,7,8,5,3,6]=>[8,5,7,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,5,8,2,4]=>[1,3,6,8,4,2,7,5]=>[8,6,3,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,7,8,5,1]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,5,8,3,1,6]=>[1,4,5,8,6,3,7,2]=>[8,5,4,1,3,6,2,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,3,8,6,5]=>[1,4,2,3,7,6,8,5]=>[8,5,7,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,7,8,3,6]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,4,8,1]=>[1,5,3,2,6,4,7,8]=>[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,5,4,7,2]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,5,1,3,4]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,5,3,1,4]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,4,2,3,7]=>[1,2,5,4,6,3,8,7]=>[8,7,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,4,1,7,3]=>[1,2,5,4,6,3,8,7]=>[8,7,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,5,7,3,8]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,1,6,8,5]=>[1,4,3,2,7,8,5,6]=>[8,5,6,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,5,4,8,2]=>[1,6,4,2,7,8,3,5]=>[8,3,5,7,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,8,3,5,1]=>[1,7,5,8,2,4,3,6]=>[8,2,4,1,7,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,4,8,2,6]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,8,6,2,1]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,6,7,5,1]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,5,7,1,6]=>[1,4,2,3,8,6,7,5]=>[8,5,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,6,4,7,2,3]=>[1,5,4,6,7,2,3,8]=>[8,4,5,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,8,4,1,6]=>[1,7,2,5,8,6,4,3]=>[8,2,7,4,1,3,5,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,6,3,8,2]=>[1,4,7,8,2,5,6,3]=>[8,5,2,1,7,4,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,2,3,4,6]=>[1,8,6,3,7,4,5,2]=>[8,1,3,6,2,5,4,7]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,2,8,7,3]=>[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,1,7,2,5]=>[1,4,6,7,2,8,5,3]=>[8,5,3,2,7,1,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,3,4,5,1]=>[1,6,4,8,2,3,7,5]=>[8,3,5,1,7,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,2,3,4,5,6,7,8,1]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,3,4,5,6,7,1,9]=>[1,8,2,3,4,5,6,7,9]=>[9,2,8,7,6,5,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,2,3,4,5,6,1,8,9]=>[1,7,2,3,4,5,6,8,9]=>[9,3,8,7,6,5,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,3,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,3,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,6,8,5,7,3]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,8,6,3,4]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,6,5,2,1]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,6,5,1,2]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,6,5,1,2]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,5,8,1,2]=>[1,7,2,4,6,8,3,5]=>[8,2,7,5,3,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,2,6,1,3]=>[1,4,7,2,5,3,8,6]=>[8,5,2,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,5,1,4,2]=>[1,3,6,2,8,4,7,5]=>[8,6,3,7,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,2,7,6,1]=>[1,4,8,2,5,3,6,7]=>[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,4,1,7,6,2]=>[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,5,8,3,1]=>[1,6,8,2,4,3,7,5]=>[8,3,1,7,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,1,2,8,7]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,5,7,1,2]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,7,6,1,3]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,7,8,3,6]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,3,8,6,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,4,3,6,7]=>[1,5,4,2,3,8,7,6]=>[8,4,5,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,7,8,2,6]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,6,7,2,5]=>[1,4,2,8,5,6,7,3]=>[8,5,7,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,6,5,7,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,6,8,1,5]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,8,1,2,5]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,5,8,1,4]=>[1,3,7,2,6,8,4,5]=>[8,6,2,7,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,3,7,2,4]=>[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,3,4,7,2]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,3,4,7,2]=>[1,5,3,8,2,6,4,7]=>[8,4,6,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,3,4,7,1]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,5,4,7,2]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,1,7,3,5]=>[1,6,7,3,4,8,5,2]=>[8,3,2,6,5,1,4,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,5,4,6,2]=>[1,3,7,6,4,8,2,5]=>[8,6,2,3,5,1,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,4,8,5,3]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,4,3,5,6]=>[1,2,7,5,4,8,6,3]=>[8,7,2,4,5,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,3,2,4,5]=>[1,6,2,7,4,8,5,3]=>[8,3,7,2,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,8,1,3,4]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,7,2,3,4]=>[1,5,7,3,6,2,4,8]=>[8,4,2,6,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,5,3,1,2]=>[1,7,2,4,8,3,6,5]=>[8,2,7,5,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,8,3,6,4]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,7,1,8,3]=>[1,4,5,7,8,3,2,6]=>[8,5,4,2,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,5,1,2,4]=>[1,3,6,2,8,4,7,5]=>[8,6,3,7,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,6,3,1,2]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,2,5,4,7]=>[1,2,6,5,3,8,7,4]=>[8,7,3,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,3,2,6,4]=>[1,7,6,2,8,4,3,5]=>[8,2,3,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,5,4,7,3]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,6,2,8,3]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,5,1,8,4]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,3,2,7,4]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,8,5,7,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,6,3,1,7]=>[1,2,5,6,3,8,7,4]=>[8,7,4,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,8,3,2,6]=>[1,7,2,3,5,8,6,4]=>[8,2,7,6,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,5,3,2,8]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,8,1,5,3]=>[1,2,7,5,8,3,6,4]=>[8,7,2,4,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,6,1,5,4]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,8,1,6,4]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,1,2,6,7]=>[1,5,2,3,8,7,6,4]=>[8,4,7,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,7,1,5,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,1,6,3,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,4,3,6,2]=>[1,5,4,7,6,3,8,2]=>[8,4,5,2,3,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,4,6,1,5]=>[1,3,7,2,8,5,4,6]=>[8,6,2,7,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,2,4,8,6]=>[1,5,2,7,8,6,4,3]=>[8,4,7,2,1,3,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,2,3,5,6]=>[1,8,6,3,7,5,2,4]=>[8,1,3,6,2,4,7,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,3,8,7,4,2]=>[1,6,7,4,3,2,5,8]=>[8,3,2,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,5,3,7,2,4]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,7,4,3,2]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,4,3,1,8]=>[1,5,4,7,2,6,3,8]=>[8,4,5,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,4,1,3,5]=>[1,8,5,4,7,3,2,6]=>[8,1,4,5,2,6,7,3]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,6,1,4,5]=>[1,3,8,5,6,2,7,4]=>[8,6,1,4,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,2,1,4,6]=>[1,3,8,6,2,7,4,5]=>[8,6,1,3,7,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,3,1,5,2]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,1,2,7,3]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,1,2,3,7]=>[1,4,5,2,8,7,3,6]=>[8,5,4,7,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,7,6,8,2]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,5,1,2,4]=>[1,3,7,2,8,4,6,5]=>[8,6,2,7,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,1,8,4,3]=>[1,5,2,7,4,6,8,3]=>[8,4,7,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,1,3,8,4]=>[1,5,2,7,8,4,6,3]=>[8,4,7,2,1,5,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,1,4,7,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,6,1,4,2]=>[1,3,7,4,5,6,2,8]=>[8,6,2,5,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,2,1,5,3]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,5,2,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,3,5,6,7]=>[1,4,2,8,7,6,5,3]=>[8,5,7,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,4,3,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,4,8,1,5]=>[1,2,6,8,5,4,3,7]=>[8,7,3,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,4,3,8,6]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,5,6,2,3]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,8,7,5,2]=>[1,6,7,5,8,2,4,3]=>[8,3,2,4,1,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,6,8,3,5]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,6,8,3,5]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,7,3,5,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,2,3,5,4]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,5,7,6,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,6,7,5,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,6,1,5,3]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,7,8,9,10,3]=>[1,2,4,5,6,7,8,9,10,3]=>[10,9,7,6,5,4,3,2,1,8]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,9,1,10,8]=>[1,2,3,4,5,6,7,9,10,8]=>[10,9,8,7,6,5,4,2,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,5,1,6,7,8,9,10,4]=>[1,2,3,5,6,7,8,9,10,4]=>[10,9,8,6,5,4,3,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,1,9,10,7]=>[1,2,3,4,5,6,8,9,10,7]=>[10,9,8,7,6,5,3,2,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,6,1,7,8,9,10,5]=>[1,2,3,4,6,7,8,9,10,5]=>[10,9,8,7,5,4,3,2,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,1,8,9,10,6]=>[1,2,3,4,5,7,8,9,10,6]=>[10,9,8,7,6,4,3,2,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,1,9]=>[1,3,4,5,6,7,8,2,9]=>[9,7,6,5,4,3,2,8,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,8,4,3,1,6,7,2]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,5,7,6,3]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,5,4,8,1]=>[1,6,4,2,3,7,8,5]=>[8,3,5,7,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,2,6,8,1]=>[1,5,2,4,3,7,8,6]=>[8,4,7,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,6,2,8,1]=>[1,3,5,6,2,7,8,4]=>[8,6,4,3,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,1,7,4,5]=>[1,6,7,4,2,8,5,3]=>[8,3,2,5,7,1,4,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,5,3,2,6]=>[1,4,7,2,8,6,3,5]=>[8,5,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,2,8,6,1]=>[1,5,2,4,7,6,8,3]=>[8,4,7,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,7,2,8,4,1]=>[1,3,5,2,6,8,4,7]=>[8,6,4,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,8,7,3,1,4]=>[1,2,6,3,5,7,4,8]=>[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,1,7,2,5]=>[1,6,7,2,3,8,5,4]=>[8,3,2,7,6,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,1,6,4,3,5]=>[1,7,3,8,5,6,4,2]=>[8,2,6,1,4,3,5,7]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,6,4,1,5]=>[1,3,8,5,6,4,7,2]=>[8,6,1,4,3,5,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,3,5,1,7]=>[1,8,7,2,3,6,5,4]=>[8,1,2,7,6,3,4,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,3,1,4,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,1,4,8,7]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,5,3,1,6]=>[1,2,4,8,6,3,7,5]=>[8,7,5,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,4,1,8,7]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,3,2,4,1]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,8,5,3,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,5,7,4,2]=>[1,8,2,3,4,6,7,5]=>[8,1,7,6,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,3,1,4,2]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,2,6,4,1]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,5,8,3,4]=>[1,6,8,4,7,3,2,5]=>[8,3,1,5,2,6,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,1,4,6,8,5]=>[1,2,7,8,5,4,3,6]=>[8,7,2,1,4,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,6,5,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,7,1,2,4]=>[1,3,5,7,2,8,4,6]=>[8,6,4,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,8,4,7,3]=>[1,6,4,2,5,8,3,7]=>[8,3,5,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,4,6,7,3]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,4,6,3]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,1,6,5,2]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,2,6,5,1]=>[1,8,2,7,5,3,4,6]=>[8,1,7,2,4,6,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,7,1,6]=>[1,8,6,7,2,4,3,5]=>[8,1,3,2,7,5,6,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,3,8,1,6]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,2,8,3,1]=>[1,6,8,2,4,5,3,7]=>[8,3,1,7,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,6,4,8,2]=>[1,7,8,2,5,6,4,3]=>[8,2,1,7,4,3,5,6]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,3,7,8,4,1]=>[1,6,8,2,5,7,4,3]=>[8,3,1,7,4,2,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,5,7,6,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,5,7,6,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,1,7,6,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,3,7,1,6,4]=>[1,2,5,7,6,3,8,4]=>[8,7,4,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,4,7,6,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,8,7,5,3]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,1,6,5,3]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,8,7,5,3]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,1,7,6,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,7,5,3,4]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,5,7,6,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,5,7,6,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,5,7,6,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,5,7,6,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,7,5,3,4]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,7,5,3,4]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,7,5,2,4]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,7,5,1,4]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,5,7,6,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,4,6,5,3]=>[1,7,5,4,2,8,3,6]=>[8,2,4,5,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,7,5,1,4]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,7,2,5,4]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,1,6,2,7]=>[1,3,4,5,2,8,7,6]=>[8,6,5,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,7,2,3,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,6,3,2,5]=>[1,8,5,6,3,4,7,2]=>[8,1,4,3,6,5,2,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,4,7,2,5]=>[1,8,5,4,6,7,2,3]=>[8,1,4,5,3,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,5,7,2,4]=>[1,8,4,2,3,6,7,5]=>[8,1,5,7,6,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,1,2,5,7]=>[1,8,7,5,2,4,3,6]=>[8,1,2,4,7,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,6,2,3,7]=>[1,2,5,6,3,8,7,4]=>[8,7,4,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,4,2,3,7]=>[1,5,4,2,6,3,8,7]=>[8,4,5,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,1,2,3,6]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,3,7,4,6]=>[1,8,6,7,4,5,3,2]=>[8,1,3,2,5,4,6,7]=>[8,2,4,3,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,2,6,3,5]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,6,2,3,4]=>[1,8,4,5,6,2,7,3]=>[8,1,5,4,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,7,2,3,4]=>[1,2,6,3,5,7,4,8]=>[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,5,8,3,4]=>[1,6,8,4,2,3,7,5]=>[8,3,1,5,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,8,2,3,4]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,7,2,3,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,7,2,4,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,4,6,8,5]=>[1,2,7,8,5,4,3,6]=>[8,7,2,1,4,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,8,4,6,5]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,8,7,3,4]=>[1,5,8,4,6,7,3,2]=>[8,4,1,5,3,2,6,7]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,5,7,3,4]=>[1,2,8,4,3,6,7,5]=>[8,7,1,5,6,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,2,6,3,4]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,6,2,3,4]=>[1,8,4,7,3,5,6,2]=>[8,1,5,2,6,4,3,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,5,2,3,4]=>[1,7,3,6,2,4,8,5]=>[8,2,6,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,8,4,6,5]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,7,6,4,5]=>[1,8,5,7,4,2,3,6]=>[8,1,4,2,5,7,6,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,6,2,3,4]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,5,2,3,4]=>[1,7,3,6,2,8,4,5]=>[8,2,6,3,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,3,4,5,6,7,8,2]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,3,4,5,6,7,8,1,10]=>[1,9,2,3,4,5,6,7,8,10]=>[10,2,9,8,7,6,5,4,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,10,3,4,5,6,7,8,9,2]=>[1,2,10,3,4,5,6,7,8,9]=>[10,9,1,8,7,6,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,7,4,8,2,5,3,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,1,5,3,2]=>[1,7,3,8,2,6,5,4]=>[8,2,6,1,7,3,4,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,7,2,6,8]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,8,1,3,2]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,6,8,5,2]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,6,8,5,4]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,4,6,1,7]=>[1,3,5,4,2,8,7,6]=>[8,6,4,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,3,5,2,7]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,6,3,7,2]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,2,6,7,1]=>[1,3,4,5,2,8,6,7]=>[8,6,5,4,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,5,3,7,2]=>[1,4,6,3,8,2,5,7]=>[8,5,3,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,6,3,2,1]=>[1,5,6,3,8,2,7,4]=>[8,4,3,6,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,4,8,6,1]=>[1,7,6,8,2,5,4,3]=>[8,2,3,1,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,2,8,6,1]=>[1,7,6,8,2,3,5,4]=>[8,2,3,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,2,4,7,8]=>[1,5,2,6,4,3,7,8]=>[8,4,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,1,8,6,5]=>[1,4,2,3,7,6,8,5]=>[8,5,7,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,1,3,5,8]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,1,5,7,8]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,5,4,1,8]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,3,6,1,8]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,4,1,6,8]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,8,6,5,1]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,7,5,8,6,1]=>[1,3,2,4,7,6,8,5]=>[8,6,7,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,7,8,6,2]=>[1,3,5,7,6,8,2,4]=>[8,6,4,2,3,1,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,3,1,8,6]=>[1,4,2,5,3,7,8,6]=>[8,5,7,4,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,4,6,5,2]=>[1,3,8,2,7,5,4,6]=>[8,6,1,7,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,4,1,3,6]=>[1,2,5,4,7,3,8,6]=>[8,7,4,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,5,3,8,1]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,7,1,3,8,5]=>[1,6,3,4,7,8,5,2]=>[8,3,6,5,2,1,4,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,4,2,8,6]=>[1,7,8,6,2,3,5,4]=>[8,2,1,3,7,6,4,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,3,2,8,6]=>[1,5,3,7,8,6,2,4]=>[8,4,6,2,1,3,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,7,5,3,8,2]=>[1,6,3,4,7,8,2,5]=>[8,3,6,5,2,1,7,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,7,3,2,5]=>[1,6,3,8,5,7,2,4]=>[8,3,6,1,4,2,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,1,2,8,5]=>[1,4,6,2,7,8,5,3]=>[8,5,3,7,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,3,1,8,5]=>[1,4,2,7,8,5,3,6]=>[8,5,7,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,5,3,4,1]=>[1,7,4,2,6,3,8,5]=>[8,2,5,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,8,7,5,4]=>[1,2,3,6,7,5,8,4]=>[8,7,6,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,7,5,3,1,4]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,5,2,8,3]=>[1,6,2,4,7,8,3,5]=>[8,3,7,5,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,2,5,6,3]=>[1,4,2,8,3,7,6,5]=>[8,5,7,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,1,5,6,3]=>[1,2,8,3,7,6,5,4]=>[8,7,1,6,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,5,7,4,3]=>[1,8,3,2,6,7,4,5]=>[8,1,6,7,3,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,5,2,1,4]=>[1,3,6,2,8,4,7,5]=>[8,6,3,7,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,5,8,2,4]=>[1,6,8,4,7,2,3,5]=>[8,3,1,5,2,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,3,4,8,1]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,7,3,8,1]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,7,2,5,3]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,6,8,1,3]=>[1,4,2,5,6,8,3,7]=>[8,5,7,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,2,7,4,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,7,2,4,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,6,1,4,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,8,6,1,3,5]=>[1,4,8,5,6,2,3,7]=>[8,5,1,4,3,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,6,2,4,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,5,2,3,1]=>[1,7,3,6,2,4,8,5]=>[8,2,6,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,8,2,1,4]=>[1,7,2,5,8,4,6,3]=>[8,2,7,4,1,5,3,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,8,1,3,4]=>[1,5,8,4,7,3,6,2]=>[8,4,1,5,2,6,3,7]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,7,1,3,5]=>[1,4,8,5,7,3,6,2]=>[8,5,1,4,2,6,3,7]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,7,2,3,5]=>[1,2,4,8,5,7,3,6]=>[8,7,5,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,1,7,2,6]=>[1,3,8,6,7,2,5,4]=>[8,6,1,3,2,7,4,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,2,3,7,1]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,8,1,3,4]=>[1,7,3,6,2,4,5,8]=>[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,4,8,1]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,4,5,3,6]=>[1,8,6,5,4,7,3,2]=>[8,1,3,4,5,2,6,7]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,6,1,3,8]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,5,3,8,2]=>[1,6,3,7,8,2,4,5]=>[8,3,6,2,1,7,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,1,7,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,5,6,4,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,8,6,7,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,7,8,2,3]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,1,3,8,5]=>[1,6,3,2,7,8,5,4]=>[8,3,6,7,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,2,7,1,6]=>[1,8,6,7,2,5,3,4]=>[8,1,3,2,7,4,6,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,5,6,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,1,6,5,2]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,6,1,5,3]=>[1,8,3,2,7,5,6,4]=>[8,1,6,7,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,2,8,4,1]=>[1,3,7,4,5,2,6,8]=>[8,6,2,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,8,1,3,2]=>[1,5,8,2,4,7,3,6]=>[8,4,1,7,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,2,1,3,6]=>[1,5,2,4,7,3,8,6]=>[8,4,7,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,6,2,8,1]=>[1,5,6,2,3,7,8,4]=>[8,4,3,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,7,4,5,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,3,5,6,1]=>[1,8,2,3,4,7,6,5]=>[8,1,7,6,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,7,3,4,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,7,3,8,1]=>[1,4,2,5,7,8,3,6]=>[8,5,7,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,5,2,8,3]=>[1,7,8,3,6,2,4,5]=>[8,2,1,6,3,7,5,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,2,5,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,3,8,7,4]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,7,1,8,2]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,5,4,1,7]=>[1,6,4,8,7,2,3,5]=>[8,3,5,1,2,7,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,2,8,6,7]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,5,2,6,7]=>[1,3,4,2,8,7,6,5]=>[8,6,5,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,8,1,6,7]=>[1,2,5,8,7,6,3,4]=>[8,7,4,1,2,3,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,3,1,6,8]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,7,1,6,8]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,1,2,6,8]=>[1,3,5,2,7,6,4,8]=>[8,6,4,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,3,8,7,6]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,2,7,6,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,7,2,6,8]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,5,2,7,8]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,5,6,4,8]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,2,1,6,8]=>[1,3,5,2,7,6,4,8]=>[8,6,4,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,1,6,5,8]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,7,4,3,5]=>[1,2,8,5,7,3,6,4]=>[8,7,1,4,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,1,3,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,1,3,7,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,3,2,4,8]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,5,4,6,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,5,3,7,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,5,4,3,8]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,6,3,7,4]=>[1,8,4,5,6,3,2,7]=>[8,1,5,4,3,6,7,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,6,4,7,3]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,3,2,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,5,2,7,8]=>[1,3,4,6,2,5,7,8]=>[8,6,5,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,3,2,8,7]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,3,7,5,4]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,7,6,4,2]=>[1,5,7,4,2,8,3,6]=>[8,4,2,5,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,8,5,1,4]=>[1,7,2,6,5,8,4,3]=>[8,2,7,3,4,1,5,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,7,2,6,1]=>[1,4,5,7,6,2,3,8]=>[8,5,4,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,4,1,2,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,5,1,2,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,2,8,6,7]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,3,8,6,7]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,8,5,6,1]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,2,8,6,7]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,1,8,6,7]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,3,1,6,2]=>[1,5,3,7,6,2,8,4]=>[8,4,6,2,3,7,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,4,5,7,2]=>[1,6,5,4,3,2,8,7]=>[8,3,4,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,1,6,7,4]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,2,5,4,6]=>[1,3,7,4,8,6,5,2]=>[8,6,2,5,1,3,4,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,1,2,5,8]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,6,5,1,4]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,1,2,4,8]=>[1,3,7,4,5,2,6,8]=>[8,6,2,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,8,2,3,6]=>[1,7,3,5,8,6,2,4]=>[8,2,6,4,1,3,7,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,8,4,5,6]=>[1,7,5,8,6,4,2,3]=>[8,2,4,1,3,5,7,6]=>[8,4,5,2,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,7,5,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,4,2,6,1]=>[1,5,4,8,2,3,7,6]=>[8,4,5,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,2,4,5,1]=>[1,6,4,8,2,3,7,5]=>[8,3,5,1,7,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,3,1,7,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,3,1,8,6]=>[1,7,8,6,2,5,3,4]=>[8,2,1,3,7,4,6,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,8,1,7,2]=>[1,3,6,2,5,8,4,7]=>[8,6,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,6,7,1,8,2]=>[1,3,4,6,2,5,7,8]=>[8,6,5,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,5,8,7,3]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,4,8,7,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,3,8,7,6]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,3,8,7,6]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,4,8,6,2]=>[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,4,7,5,2]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,6,4,8,5,3]=>[1,2,7,5,4,6,8,3]=>[8,7,2,4,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,6,3,8,5,4]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,4,8,6,3]=>[1,2,5,4,7,6,8,3]=>[8,7,4,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,5,7,6,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,4,7,6,2]=>[1,2,5,4,8,3,6,7]=>[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,3,6,5,2]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,1,5,4,7]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,2,6,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,5,2,1,6]=>[1,4,3,7,2,8,6,5]=>[8,5,6,2,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,5,2,4,1]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,5,4,2,7]=>[1,8,7,2,6,4,3,5]=>[8,1,2,7,3,5,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,5,3,2,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,1,3,2,7]=>[1,8,7,2,6,3,5,4]=>[8,1,2,7,3,6,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,6,2,1]=>[1,5,4,7,2,3,8,6]=>[8,4,5,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,4,6,1,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,4,1,2,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,1,5,4,2]=>[1,6,5,2,8,3,7,4]=>[8,3,4,7,1,6,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,4,6,3,1]=>[1,2,5,4,7,3,8,6]=>[8,7,4,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,5,1,3,2]=>[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,1,6,2,4]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,5,6,1,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,2,1,3,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,5,2,1,4]=>[1,6,2,8,4,3,7,5]=>[8,3,7,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,5,2,7,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,7,5,3,4]=>[1,6,5,7,3,2,8,4]=>[8,3,4,2,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,1,2,7,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,5,2,1,3]=>[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,1,6,2,3]=>[1,4,5,2,8,3,7,6]=>[8,5,4,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,8,6,7,3]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,4,6,1,3]=>[1,5,4,8,3,2,7,6]=>[8,4,5,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,4,8,5,1]=>[1,6,8,2,7,5,4,3]=>[8,3,1,7,2,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,5,1,3,4]=>[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,4,1,3,6]=>[1,5,4,8,6,2,3,7]=>[8,4,5,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,4,1,3,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,2,8,4,1]=>[1,7,4,5,2,6,8,3]=>[8,2,5,4,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,7,2,4,3]=>[1,8,3,5,7,4,2,6]=>[8,1,6,4,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,7,3,2,4]=>[1,6,3,5,7,2,8,4]=>[8,3,6,4,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,7,4,2,5]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,4,8,1,7]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,8,1,7,6]=>[1,3,2,5,8,6,4,7]=>[8,6,7,4,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,4,1,7,5]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,5,4,2,1]=>[1,6,4,7,2,3,8,5]=>[8,3,5,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,1,7,5,3]=>[1,6,7,5,2,8,3,4]=>[8,3,2,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,3,8,1,7]=>[1,5,3,6,8,7,2,4]=>[8,4,6,3,1,2,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,4,8,2,7]=>[1,6,8,7,2,5,4,3]=>[8,3,1,2,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,6,4,2,5]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,6,2,5,4]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,4,2,5,3]=>[1,8,3,7,5,4,6,2]=>[8,1,6,2,4,5,3,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,2,4,3,6]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,4,8,3,7]=>[1,6,8,7,3,5,4,2]=>[8,3,1,2,6,4,5,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,8,2,4,7]=>[1,2,5,8,7,4,3,6]=>[8,7,4,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,6,5,2,4]=>[1,8,4,3,2,7,5,6]=>[8,1,5,6,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,3,8,5,1]=>[1,2,6,8,3,7,5,4]=>[8,7,3,1,6,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,2,4,6,3]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,3,6,5,2]=>[1,2,4,7,5,3,8,6]=>[8,7,5,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,5,1,6,4]=>[1,8,4,2,3,7,6,5]=>[8,1,5,7,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,1,5,4,6]=>[1,3,2,7,4,8,6,5]=>[8,6,7,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,5,8,4,7]=>[1,3,6,8,7,4,2,5]=>[8,6,3,1,2,5,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,5,8,4,3,6]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,1,4,3,6,5]=>[1,7,6,3,8,5,4,2]=>[8,2,3,6,1,4,5,7]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,2,6,5,4]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,8,3,2,6]=>[1,2,7,3,5,8,6,4]=>[8,7,2,6,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,4,3,8,2,7]=>[1,6,8,7,2,3,5,4]=>[8,3,1,2,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,6,8,2,3]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,9,8,2]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,9,8,1,10]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,3,4,5,6,8,1,2,9]=>[1,7,2,3,4,5,6,8,9]=>[9,3,8,7,6,5,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,6,8,1,9]=>[1,2,3,4,5,7,8,6,9]=>[9,8,7,6,5,3,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,8,7,9,2]=>[1,2,3,4,5,6,8,9,7]=>[9,8,7,6,5,4,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,10,9,2]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,6,4,2,3,5,7,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,3,4,5,6]=>[1,2,8,6,4,3,7,5]=>[8,7,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,2,3,4,7]=>[1,2,5,3,8,7,4,6]=>[8,7,4,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,2,3,4,8]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,6,4,5,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,6,4,5,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,3,7,6,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,3,8,6,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,6,4,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,2,3,4,6]=>[1,2,7,4,8,6,3,5]=>[8,7,2,5,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,2,3,4,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,6,1,7,3]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,6,1,7,4]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,6,1,7,4]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,1,3,7,2]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,2,6,4,1]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,7,6,5,3]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,5,7,6,2]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,5,7,6,2]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,5,2,7,1]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,4,2,7,1]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,8,2,7,5]=>[1,3,4,2,6,5,8,7]=>[8,6,5,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,1,3,7,2]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,4,6,1,8,5]=>[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,1,3,8,2]=>[1,6,3,7,8,2,5,4]=>[8,3,6,2,1,7,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,5,7,8,1]=>[1,2,4,3,6,7,8,5]=>[8,7,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,5,7,8,1]=>[1,3,4,2,6,7,8,5]=>[8,6,5,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,5,7,8,4]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,5,7,8,1]=>[1,4,2,3,6,7,8,5]=>[8,5,7,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,5,7,8,3]=>[1,4,2,6,7,8,3,5]=>[8,5,7,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,5,7,8,3]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,5,7,8,3]=>[1,2,4,6,7,8,3,5]=>[8,7,5,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,6,1,8,3]=>[1,7,8,3,4,2,5,6]=>[8,2,1,6,5,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,1,8,6,5,2]=>[1,4,2,7,5,8,3,6]=>[8,5,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,8,2,1,7]=>[1,5,8,7,2,3,6,4]=>[8,4,1,2,7,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,4,1,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,1,8,6,4]=>[1,7,6,8,4,5,2,3]=>[8,2,3,1,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,8,2,1,5]=>[1,4,3,6,2,7,5,8]=>[8,5,6,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,6,2,1,5]=>[1,4,8,5,6,2,7,3]=>[8,5,1,4,3,7,2,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,6,1,8,4]=>[1,5,6,2,7,8,4,3]=>[8,4,3,7,2,1,5,6]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,6,4,1,8]=>[1,5,6,4,2,7,3,8]=>[8,4,3,5,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,3,1,8,6,4]=>[1,2,7,6,8,4,3,5]=>[8,7,2,3,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,8,2,1,6]=>[1,4,5,8,6,2,3,7]=>[8,5,4,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,7,2,1,6]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,8,6,1,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,8,2,1,7]=>[1,4,6,2,5,8,7,3]=>[8,5,3,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,9,7,8,6]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,9,6,7,8,5]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,9,5,6,7,8,4]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,9,4,5,6,7,8,3]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,10,8,9,7]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,9,7,6,8,5]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,10,7,8,9,6]=>[1,2,3,4,5,6,10,7,8,9]=>[10,9,8,7,6,5,1,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,8,6,4,5,7,3]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,9,6,5,7,8,4]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,10,6,7,8,9,5]=>[1,2,3,4,5,10,6,7,8,9]=>[10,9,8,7,6,1,5,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,5,3,4,6,7,2]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,9,5,4,6,7,8,3]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,10,5,6,7,8,9,4]=>[1,2,3,4,10,5,6,7,8,9]=>[10,9,8,7,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,9,4,3,5,6,7,8,2]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,10,4,5,6,7,8,9,3]=>[1,2,3,10,4,5,6,7,8,9]=>[10,9,8,1,7,6,5,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,3,2,4,5,6,7,8,1]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,2,3,4,5,6,7,8,9,1]=>[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,4,1,6,3,5,2]=>[1,7,5,6,3,4,2,8]=>[8,2,4,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,1,3,4,2]=>[1,8,2,7,4,6,3,5]=>[8,1,7,2,5,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,7,4,6,9,8]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,6,4,7,5,9,8]=>[1,2,3,4,6,7,5,8,9]=>[9,8,7,6,4,3,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,8,5,7,9]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,7,5,8,6,9]=>[1,2,3,4,5,7,8,6,9]=>[9,8,7,6,5,3,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,5,7,3,6,9,8]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,5,6,3,7,4,9,8]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,6,4,1,8,5,7]=>[1,3,6,8,7,5,2,4]=>[8,6,3,1,2,4,7,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,3,1,4,7]=>[1,2,8,7,4,5,3,6]=>[8,7,1,2,5,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,2,3,1,7]=>[1,5,2,4,6,3,8,7]=>[8,4,7,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,2,3,1,6]=>[1,4,5,2,8,6,3,7]=>[8,5,4,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,7,6,8,3,1]=>[1,5,6,8,2,3,4,7]=>[8,4,3,1,7,6,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,3,2,4,1]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,2,7,3,6]=>[1,2,8,6,7,3,5,4]=>[8,7,1,3,2,6,4,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,2,7,4,1]=>[1,3,5,2,6,7,4,8]=>[8,6,4,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,4,6,5,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,3,8,4,5]=>[1,7,4,2,3,6,8,5]=>[8,2,5,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,3,2,8,5]=>[1,6,2,4,3,7,8,5]=>[8,3,7,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,7,2,6,4]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,5,3,4]=>[1,8,4,6,5,2,7,3]=>[8,1,5,3,4,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,4,8,3,6]=>[1,7,3,5,4,2,6,8]=>[8,2,6,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,1,3,8,6]=>[1,7,8,6,3,5,2,4]=>[8,2,1,3,6,4,7,5]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,5,6,2,3]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,9,4,5,6,7,8]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,9,1,2,4,5,6,7,8]=>[1,3,2,9,8,7,6,5,4]=>[9,7,8,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,8,2,3,4,5,6,7,9]=>[1,2,8,7,6,5,4,3,9]=>[9,8,2,3,4,5,6,7,1]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,4,6,1,3,2,5,8]=>[1,7,5,3,6,2,4,8]=>[8,2,4,6,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,6,3,2,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,7,2,6,1,3]=>[1,8,3,5,2,4,7,6]=>[8,1,6,4,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,3,6,2,4]=>[1,8,4,5,3,7,2,6]=>[8,1,5,4,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,1,7,8,4]=>[1,5,2,3,6,7,8,4]=>[8,4,7,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,6,7,8,2]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,2,3,8,4]=>[1,5,2,7,8,4,3,6]=>[8,4,7,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,5,2,4,3]=>[1,2,7,4,8,3,6,5]=>[8,7,2,5,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,1,2,4,3]=>[1,5,2,7,4,8,3,6]=>[8,4,7,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,1,4,8,2]=>[1,5,2,6,4,7,8,3]=>[8,4,7,3,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,5,7,2,1]=>[1,3,6,7,2,8,4,5]=>[8,6,3,2,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,4,5,2,3]=>[1,7,2,8,3,6,5,4]=>[8,2,7,1,6,3,4,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,6,7,2,3]=>[1,2,8,3,5,6,7,4]=>[8,7,1,6,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,7,2,1,4]=>[1,6,2,5,7,3,8,4]=>[8,3,7,4,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,2,6,5,1]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,2,6,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,2,1,7,5]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,2,7,6,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,1,2,7,4]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,3,2,4,5]=>[1,7,4,2,8,5,3,6]=>[8,2,5,7,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,2,7,5,6]=>[1,2,8,6,7,5,3,4]=>[8,7,1,3,2,4,6,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,2,1,6,7]=>[1,5,2,4,8,7,6,3]=>[8,4,7,5,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,2,6,7,1]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,6,7,8,9,3]=>[1,4,2,5,6,7,8,9,3]=>[9,6,8,5,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,4,2,3,5,1,8,7]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,1,4,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,4,8,1,6]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,5,4,7,1]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,5,8,1,6]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,7,2,5,1]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,4,5,7,3]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,7,8,2,1,5]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,3,6,7,2]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,2,6,4,1]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,3,7,6,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,7,8,5,1]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,6,7,1,5]=>[1,8,5,6,7,2,4,3]=>[8,1,4,3,2,7,5,6]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,4,5,1,6]=>[1,3,2,7,4,8,6,5]=>[8,6,7,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,4,6,2,7]=>[1,3,2,5,4,8,7,6]=>[8,6,7,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,5,8,3,7]=>[1,4,6,8,7,3,2,5]=>[8,5,3,1,2,6,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,5,8,1,3,6]=>[1,4,5,8,6,2,3,7]=>[8,5,4,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,8,3,1,5]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,8,2,5,7]=>[1,4,3,2,6,5,8,7]=>[8,5,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,1,8,7,5]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,1,6,2,8]=>[1,3,4,5,2,7,6,8]=>[8,6,5,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,5,8,2,1,7]=>[1,3,4,5,8,7,2,6]=>[8,6,5,4,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,1,6,3,8]=>[1,7,3,4,5,2,6,8]=>[8,2,6,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,6,3,2,7]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,3,6,4,2]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,1,6,2,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,6,3,2,7]=>[1,8,7,2,5,6,3,4]=>[8,1,2,7,4,3,6,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,6,5,3,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,6,7,3,4]=>[1,8,4,5,6,7,3,2]=>[8,1,5,4,3,2,6,7]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,4,7,2,5]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,6,3,2,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,6,7,2,3]=>[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,8,2,1,5]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,4,7,2,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,2,7,1,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,8,2,1,6]=>[1,5,8,6,2,3,7,4]=>[8,4,1,3,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,1,6,2,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,4,7,2,6]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,1,6,2,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,6,7,4,2]=>[1,2,5,6,7,4,3,8]=>[8,7,4,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,6,5,2,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,5,7,2,4]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,5,3,7]=>[1,8,7,3,4,2,5,6]=>[8,1,2,6,5,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,4,8,2,6]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,7,8,2,6]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,3,7,6,1]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,4,6,8,1]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,8,6,1,7]=>[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,8,1,2,6]=>[1,3,4,5,8,6,2,7]=>[8,6,5,4,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,4,5,2,6]=>[1,3,8,6,5,4,2,7]=>[8,6,1,3,4,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,5,3,6,1]=>[1,2,4,8,3,7,6,5]=>[8,7,5,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,7,2,8,6]=>[1,5,7,8,6,2,3,4]=>[8,4,2,1,3,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,1,2,7,6]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,8,3,6,1]=>[1,2,4,5,8,3,7,6]=>[8,7,5,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,2,1,7,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,3,1,2,6]=>[1,4,7,2,8,6,3,5]=>[8,5,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,1,3,2,6]=>[1,4,5,2,8,6,3,7]=>[8,5,4,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,1,3,6,7]=>[1,4,5,2,3,8,7,6]=>[8,5,4,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,8,2,1,6]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,2,4,3,6]=>[1,2,8,6,4,7,3,5]=>[8,7,1,3,5,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,2,3,6,7]=>[1,2,8,7,6,3,5,4]=>[8,7,1,2,3,6,4,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,5,4,2,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,2,7,4,5]=>[1,2,6,7,4,8,5,3]=>[8,7,3,2,5,1,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,5,8,3,6]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,6,7,5,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,2,7,5,4]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,3,8,2,7]=>[1,2,6,8,7,3,5,4]=>[8,7,3,1,2,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,5,6,2,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,2,4,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,3,6,2,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,4,5,3,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,3,6,5,1]=>[1,7,5,3,8,2,4,6]=>[8,2,4,6,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,7,5,4,1,3]=>[1,6,4,7,2,3,8,5]=>[8,3,5,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,3,7,1,5]=>[1,6,7,2,3,8,5,4]=>[8,3,2,7,6,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,2,6,8,5]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,6,2,8,4]=>[1,2,5,6,3,7,8,4]=>[8,7,4,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,1,5,4,8]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,8,7,2,5]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,6,8,2,4]=>[1,2,5,6,8,4,7,3]=>[8,7,4,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,7,8,2,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,7,8,1,3]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,8,4,7,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,4,7,2,5]=>[1,3,8,5,4,6,7,2]=>[8,6,1,4,5,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,5,4,2,7]=>[1,3,6,4,8,7,2,5]=>[8,6,3,5,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,7,6,1,4]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,3,7,2,1]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,3,7,2,6]=>[1,4,2,8,6,7,3,5]=>[8,5,7,1,3,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,8,1,2,5,3]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,3,2,1,5]=>[1,8,5,3,4,7,2,6]=>[8,1,4,6,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,2,7,1,4]=>[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,6,7,1,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,6,2,8,7]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,6,7,2,3]=>[1,4,8,3,5,6,7,2]=>[8,5,1,6,4,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,1,2,8,3]=>[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,6,2,8,1]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,6,7,2,1]=>[1,3,5,6,7,2,4,8]=>[8,6,4,3,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,6,7,4,3]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,7,1,2,6]=>[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,6,2,8,3]=>[1,4,5,6,2,7,8,3]=>[8,5,4,3,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,1,3,8,5]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,4,7,2,1]=>[1,5,4,6,7,2,3,8]=>[8,4,5,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,7,8,3,2]=>[1,6,8,2,4,5,7,3]=>[8,3,1,7,5,4,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,6,1,7,2,5]=>[1,3,4,6,7,2,8,5]=>[8,6,5,3,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,4,7,2,1]=>[1,3,5,4,6,7,2,8]=>[8,6,4,5,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,6,7,2,1]=>[1,3,4,5,6,7,2,8]=>[8,6,5,4,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,2,7,4,1]=>[1,3,6,7,4,5,2,8]=>[8,6,3,2,5,4,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,1,7,2,4]=>[1,3,6,7,2,8,4,5]=>[8,6,3,2,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,3,2,8,5]=>[1,6,2,4,7,8,5,3]=>[8,3,7,5,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,7,2,8,3]=>[1,5,7,8,3,4,6,2]=>[8,4,2,1,6,5,3,7]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,1,3,8,2]=>[1,6,3,4,7,8,2,5]=>[8,3,6,5,2,1,7,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,3,7,8,4]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,7,2,3,8,5]=>[1,6,3,4,7,8,5,2]=>[8,3,6,5,2,1,4,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,1,4,5,6,8,9,7]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,8,9,7]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,6,4,3,1,8,2,7]=>[1,5,2,6,8,7,3,4]=>[8,4,7,3,1,2,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,3,8,4,5]=>[1,6,8,5,3,2,7,4]=>[8,3,1,4,6,7,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,8,3,2,6]=>[1,5,8,6,3,4,2,7]=>[8,4,1,3,6,5,7,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,8,3,6,2]=>[1,4,5,8,2,3,7,6]=>[8,5,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,3,8,5,2]=>[1,2,6,8,3,7,5,4]=>[8,7,3,1,6,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,2,8,5,3]=>[1,6,8,3,7,5,2,4]=>[8,3,1,6,2,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,4,3,8,5]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,1,8,4,5]=>[1,6,8,5,2,7,4,3]=>[8,3,1,4,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,8,4,5,1]=>[1,6,4,2,7,5,8,3]=>[8,3,5,7,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,4,3,8,5]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,4,6,3,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,1,6,3,4]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,4,5,3,2]=>[1,6,5,4,8,2,7,3]=>[8,3,4,5,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,1,2,5,4]=>[1,8,4,6,2,3,7,5]=>[8,1,5,3,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,6,2,5,1]=>[1,8,2,7,5,6,3,4]=>[8,1,7,2,4,3,6,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,1,4,6,3]=>[1,8,3,5,2,4,7,6]=>[8,1,6,4,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,1,5,6,3]=>[1,8,3,4,7,6,5,2]=>[8,1,6,5,2,3,4,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,7,1,5,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,6,2,4,1]=>[1,8,2,7,4,5,6,3]=>[8,1,7,2,5,4,3,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,6,1,4,2]=>[1,8,2,3,5,6,4,7]=>[8,1,7,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,2,1,5,4]=>[1,8,4,6,2,7,5,3]=>[8,1,5,3,7,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,6,2,1,5]=>[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,5,2,1,3]=>[1,8,3,4,6,2,7,5]=>[8,1,6,5,3,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,7,4,3,1]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,4,1,3,2]=>[1,8,2,5,4,7,3,6]=>[8,1,7,4,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,4,1,2,3]=>[1,8,3,7,2,5,4,6]=>[8,1,6,2,7,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,5,1,6,3]=>[1,8,3,2,4,7,6,5]=>[8,1,6,7,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,7,5,6,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,1,2,3]=>[1,8,3,7,2,4,6,5]=>[8,1,6,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,7,4,6,1]=>[1,8,2,3,5,7,6,4]=>[8,1,7,6,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,7,3,1,4]=>[1,8,4,5,7,2,6,3]=>[8,1,5,4,2,7,3,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,3,1,5]=>[1,8,5,7,2,6,3,4]=>[8,1,4,2,7,3,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,7,4,1,6]=>[1,8,6,4,3,2,5,7]=>[8,1,3,5,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,7,6,4,1]=>[1,8,2,5,7,4,3,6]=>[8,1,7,4,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,4,3,2,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,3,1,6,7]=>[1,2,4,8,7,6,3,5]=>[8,7,5,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,5,1,6,7]=>[1,2,4,8,7,6,3,5]=>[8,7,5,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,5,4,6,1]=>[1,7,6,4,2,8,3,5]=>[8,2,3,5,7,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,8,3,2,7]=>[1,2,6,3,5,8,7,4]=>[8,7,3,6,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,8,4,6,2]=>[1,2,7,6,4,5,8,3]=>[8,7,2,3,5,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,4,8,5,3]=>[1,7,5,4,6,8,3,2]=>[8,2,4,5,3,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,4,6,5,1]=>[1,3,7,5,4,2,8,6]=>[8,6,2,4,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,4,8,5,2]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,6,4,2,5]=>[1,3,8,5,6,4,7,2]=>[8,6,1,4,3,5,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,5,4,2,6]=>[1,3,8,6,4,7,2,5]=>[8,6,1,3,5,2,7,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,5,3,2,7]=>[1,4,6,3,2,8,7,5]=>[8,5,3,6,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,6,3,2,8]=>[1,5,6,3,2,4,7,8]=>[8,4,3,6,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,5,3,2,7]=>[1,6,3,2,4,8,7,5]=>[8,3,6,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,5,3,2,8]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,4,3,2,8]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,4,3,2,7]=>[1,8,7,2,5,4,3,6]=>[8,1,2,7,4,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,4,3,2,8]=>[1,5,4,2,7,3,6,8]=>[8,4,5,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,4,3,2,8]=>[1,6,3,5,4,2,7,8]=>[8,3,6,4,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,4,3,2,7]=>[1,8,7,2,6,3,5,4]=>[8,1,2,7,3,6,4,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,2,5,3,4]=>[1,8,4,7,3,2,6,5]=>[8,1,5,2,6,7,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,4,2,5,7]=>[1,2,8,7,5,4,3,6]=>[8,7,1,2,4,5,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,5,8,7,2]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,5,7,2,8]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,7,2,5,1,3]=>[1,4,7,2,6,5,3,8]=>[8,5,2,7,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,4,5,2,1]=>[1,7,2,6,5,4,8,3]=>[8,2,7,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,1,4,3,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,1,4,3,6]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,4,1,2,7]=>[1,5,4,8,7,2,6,3]=>[8,4,5,1,2,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,1,4,5,3]=>[1,8,3,7,5,2,4,6]=>[8,1,6,2,4,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,7,1,6,8]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,1,6,8,4]=>[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,7,8,1,6]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,1,6,4,2]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,8,5,2,3,6]=>[1,2,4,8,6,3,7,5]=>[8,7,5,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,4,1,5,8]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,2,4,8,3]=>[1,6,4,7,8,3,2,5]=>[8,3,5,2,1,6,7,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,4,2,5,8]=>[1,3,7,5,4,2,6,8]=>[8,6,2,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,2,1,3,6]=>[1,4,8,6,2,7,3,5]=>[8,5,1,3,7,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,3,7,2,4]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,3,2,6,4]=>[1,2,8,4,5,3,7,6]=>[8,7,1,5,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,4,2,3,6]=>[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,4,6,3,8]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,5,4,2,3]=>[1,6,4,7,2,8,3,5]=>[8,3,5,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,2,8,5,4]=>[1,7,5,2,6,8,4,3]=>[8,2,4,7,3,1,5,6]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,4,8,1,3]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,8,2,4,5]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,8,4,6,3]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,3,2,8,5]=>[1,6,2,7,8,5,3,4]=>[8,3,7,2,1,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,4,3,5,6]=>[1,2,7,5,4,8,6,3]=>[8,7,2,4,5,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,7,8,2,4]=>[1,2,6,8,4,5,7,3]=>[8,7,3,1,5,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,8,3,2,5]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,5,2,7,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,7,8,2,6]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,7,8,2,3]=>[1,5,7,2,4,6,8,3]=>[8,4,2,7,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,7,8,2,3]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,7,5,4,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,6,3,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,8,5,2,3]=>[1,6,5,8,3,4,2,7]=>[8,3,4,1,6,5,7,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,5,7,3,2]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,7,1,6,8]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,4,3,6,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,5,8,4,6]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,7,8,2,5]=>[1,2,3,6,8,5,7,4]=>[8,7,6,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,7,8,2,6]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,7,8,4,6]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,7,8,2,5]=>[1,2,6,8,5,7,3,4]=>[8,7,3,1,4,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,1,5,2,8]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,1,3,2,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,1,2,7,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,7,8,2,4]=>[1,2,5,7,3,6,8,4]=>[8,7,4,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,7,2,4,1]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,3,8,7,6]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,2,1,4,3]=>[1,8,3,5,2,6,4,7]=>[8,1,6,4,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,4,5,7,2]=>[1,2,6,5,4,8,3,7]=>[8,7,3,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,6,3,8,1]=>[1,7,8,2,5,6,3,4]=>[8,2,1,7,4,3,6,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,6,7,8,9,1]=>[1,2,4,5,6,7,8,9,3]=>[9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,8,4,7,5,6,1]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,8,2,4,1]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,1,7,3,6]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,1,6,4,7]=>[1,2,8,7,4,5,3,6]=>[8,7,1,2,5,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,3,7,5,1]=>[1,8,2,3,4,6,7,5]=>[8,1,7,6,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,2,1,7,6]=>[1,4,8,6,2,5,3,7]=>[8,5,1,3,7,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,5,1,6,7]=>[1,4,2,8,7,6,3,5]=>[8,5,7,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,3,8,6,4]=>[1,5,3,7,6,8,4,2]=>[8,4,6,2,3,1,5,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,9,2,1,3]=>[1,4,7,2,5,8,3,6,9]=>[9,6,3,8,5,2,7,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,9,2,1,3,4,5]=>[1,6,2,7,3,8,4,9,5]=>[9,4,8,3,7,2,6,1,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,6,2,7,5,3,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,1,4,6,3]=>[1,8,3,7,6,4,5,2]=>[8,1,6,2,3,5,4,7]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,6,8,3,5,2]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,5,6,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,5,6,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,5,8,6,3]=>[1,7,6,8,3,4,2,5]=>[8,2,3,1,6,5,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,5,4,6,3]=>[1,7,6,4,2,8,3,5]=>[8,2,3,5,7,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,6,5,3,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,2,6,3,7]=>[1,2,4,5,3,8,7,6]=>[8,7,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,6,3,8,7]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,8,1,6,4]=>[1,5,8,4,7,6,2,3]=>[8,4,1,5,2,3,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,1,8,7,4]=>[1,6,8,4,5,2,3,7]=>[8,3,1,5,4,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,5,7,1,4]=>[1,8,4,2,6,7,3,5]=>[8,1,5,7,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,3,7,1,8,4]=>[1,6,2,3,5,7,8,4]=>[8,3,7,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,7,2,1,4]=>[1,8,4,6,2,5,7,3]=>[8,1,5,3,7,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,3,6,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,4,6,7,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,3,4,6,8]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,6,8,4,5]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,4,3,5,6]=>[1,8,6,3,7,5,4,2]=>[8,1,3,6,2,4,5,7]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,6,8,4,5]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,8,3,4,5]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,6,5,3,2]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,1,4,2,7]=>[1,3,8,7,2,5,4,6]=>[8,6,1,2,7,4,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,7,6,3,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,6,5,4,2]=>[1,7,4,8,2,3,5,6]=>[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,6,5,4,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,7,3,6,5]=>[1,2,4,8,5,7,6,3]=>[8,7,5,1,4,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,6,1,5,4,2]=>[1,7,4,6,5,2,3,8]=>[8,2,5,3,4,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,2,1,6,3]=>[1,5,2,4,8,3,7,6]=>[8,4,7,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,8,4,2,7]=>[1,5,8,7,2,3,6,4]=>[8,4,1,2,7,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,1,5,4,2]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,5,3,2,8]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,1,8,5,7]=>[1,3,6,8,7,5,2,4]=>[8,6,3,1,2,4,7,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,1,6,3,8]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,3,2,1,7]=>[1,5,3,4,8,7,2,6]=>[8,4,6,5,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,2,1,6,3]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,6,2,8,3]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,1,4,2,5]=>[1,6,4,3,7,2,8,5]=>[8,3,5,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,7,3,2,4]=>[1,8,4,2,5,7,3,6]=>[8,1,5,7,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,7,8,3,2]=>[1,4,6,8,2,5,7,3]=>[8,5,3,1,7,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,6,8,3,5,2]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,4,8,5,3]=>[1,6,8,3,2,7,5,4]=>[8,3,1,6,7,2,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,7,8,5,2]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,7,5,8,1]=>[1,2,3,6,5,7,8,4]=>[8,7,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,4,5,6,2]=>[1,7,6,5,4,3,2,8]=>[8,2,3,4,5,6,7,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,7,3,4,5]=>[1,2,8,5,7,4,6,3]=>[8,7,1,4,2,5,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,8,1,5,6]=>[1,4,2,7,5,8,6,3]=>[8,5,7,2,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,3,8,5,4]=>[1,7,5,3,2,4,6,8]=>[8,2,4,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,3,7,5,4]=>[1,8,4,6,7,5,3,2]=>[8,1,5,3,2,4,6,7]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,1,6,2,5]=>[1,4,3,7,2,8,5,6]=>[8,5,6,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,1,6,2,5]=>[1,4,3,8,5,2,7,6]=>[8,5,6,1,4,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,6,2,8,5]=>[1,7,8,5,6,2,4,3]=>[8,2,1,4,3,7,5,6]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,8,6,2,5]=>[1,7,2,4,3,5,8,6]=>[8,2,7,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,4,8,1,5]=>[1,3,6,8,5,4,2,7]=>[8,6,3,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,3,8,7,4]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,3,8,6,4]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,1,7,4,5]=>[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,3,5,7,4]=>[1,6,5,3,2,4,8,7]=>[8,3,4,6,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,7,6,1,5]=>[1,8,5,7,2,4,3,6]=>[8,1,4,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,7,6,3,2]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,8,6,1,5]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,8,6,1,5]=>[1,7,2,4,3,5,8,6]=>[8,2,7,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,5,2,1,4]=>[1,6,2,8,4,7,3,5]=>[8,3,7,1,5,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,3,2,1,6]=>[1,5,3,8,6,2,7,4]=>[8,4,6,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,5,2,1,7]=>[1,6,2,4,8,7,3,5]=>[8,3,7,5,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,7,6,1,3]=>[1,8,3,5,7,2,4,6]=>[8,1,6,4,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,8,6,1,3]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,8,6,1,7]=>[1,4,2,5,8,7,3,6]=>[8,5,7,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,8,6,1,7]=>[1,3,5,8,7,2,4,6]=>[8,6,4,1,2,7,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,5,4,1,7]=>[1,3,8,7,2,4,6,5]=>[8,6,1,2,7,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,5,2,1,6]=>[1,8,6,2,4,7,3,5]=>[8,1,3,7,5,2,6,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,5,4,1,6]=>[1,3,7,2,4,8,6,5]=>[8,6,2,7,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,3,2,1,5]=>[1,6,2,8,5,3,7,4]=>[8,3,7,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,7,2,6,4]=>[1,5,7,6,2,8,4,3]=>[8,4,2,3,7,1,5,6]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,8,2,6,3]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,8,7,4,5]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,8,7,4,5]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,8,5,6,2]=>[1,3,7,6,5,8,2,4]=>[8,6,2,3,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,7,5,6,2]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,8,3,6,4]=>[1,7,6,3,5,8,4,2]=>[8,2,3,6,4,1,5,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,7,5,6,3]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,1,7,5,2]=>[1,8,2,3,6,7,5,4]=>[8,1,7,6,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,2,8,6,4]=>[1,7,6,8,4,5,2,3]=>[8,2,3,1,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,2,8,5,3]=>[1,7,5,2,3,6,8,4]=>[8,2,4,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,5,8,6,2]=>[1,3,4,2,7,6,8,5]=>[8,6,5,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,3,7,5,2]=>[1,6,7,5,3,2,8,4]=>[8,3,2,4,6,7,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,4,7,5,3]=>[1,6,7,5,4,2,8,3]=>[8,3,2,4,5,7,1,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,8,3,5,2]=>[1,7,5,8,2,3,6,4]=>[8,2,4,1,7,6,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,1,7,4,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,2,7,4,3]=>[1,8,3,6,7,4,2,5]=>[8,1,6,3,2,5,7,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,4,7,3,1]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,2,4,6,1]=>[1,8,2,5,3,7,6,4]=>[8,1,7,4,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,4,3,6,7]=>[1,8,7,6,3,2,5,4]=>[8,1,2,3,6,7,4,5]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,3,6,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,5,6,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,2,7,8,5]=>[1,6,7,8,5,2,3,4]=>[8,3,2,1,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,7,2,4,5]=>[1,2,8,5,7,4,6,3]=>[8,7,1,4,2,5,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,7,4,6,5]=>[1,2,3,8,5,7,6,4]=>[8,7,6,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,4,3,1,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,4,2,6,1]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,2,5,4,6]=>[1,3,2,7,4,8,6,5]=>[8,6,7,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,6,1,3,7,2]=>[1,4,6,3,8,2,5,7]=>[8,5,3,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,6,2,7,3,1]=>[1,4,6,7,3,8,2,5]=>[8,5,3,2,6,1,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,1,8,5,3]=>[1,4,2,6,8,3,7,5]=>[8,5,7,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,6,7,8,2]=>[1,4,5,6,7,8,2,3]=>[8,5,4,3,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,5,1,6,2]=>[1,3,8,2,7,6,4,5]=>[8,6,1,7,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,3,7,1,5]=>[1,4,2,6,7,3,8,5]=>[8,5,7,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,4,5,2,6]=>[1,3,2,8,6,5,4,7]=>[8,6,7,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,6,2,5,1]=>[1,3,8,2,7,5,6,4]=>[8,6,1,7,2,4,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,4,7,1,6]=>[1,3,2,8,6,7,4,5]=>[8,6,7,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,5,1,7,4]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,2,6,1,4]=>[1,3,8,4,5,2,7,6]=>[8,6,1,5,4,7,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,4,1,6,2]=>[1,3,8,2,7,6,4,5]=>[8,6,1,7,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,3,1,7,2]=>[1,4,5,3,8,2,6,7]=>[8,5,4,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,6,4,8,2]=>[1,5,6,4,7,8,2,3]=>[8,4,3,5,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,7,8,1,3]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,3,4,8,7]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,7,3,8,2]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,2,4,8,6]=>[1,5,2,7,8,6,4,3]=>[8,4,7,2,1,3,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,1,7,4,8]=>[1,6,7,4,5,2,3,8]=>[8,3,2,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,4,8,5,3,7]=>[1,6,5,8,7,3,2,4]=>[8,3,4,1,2,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,2,5,8,4]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,5,1,4,6]=>[1,3,2,7,4,8,6,5]=>[8,6,7,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,4,7,1,8]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,1,7,2,4]=>[1,3,5,2,6,7,4,8]=>[8,6,4,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,5,8,6,7,2,4]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,3,6,8,2]=>[1,5,3,4,2,7,8,6]=>[8,4,6,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,6,5,8,2]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,5,3,2,4]=>[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,4,5,3,2]=>[1,7,3,6,5,4,2,8]=>[8,2,6,3,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,3,4,2,8]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,3,1,4,5]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,5,3,4,6]=>[1,2,7,4,3,8,6,5]=>[8,7,2,5,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,2,5,6,4]=>[1,3,8,4,2,7,6,5]=>[8,6,1,5,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,3,4,6,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,5,1,6,3]=>[1,8,3,7,6,2,4,5]=>[8,1,6,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,4,3,6,2]=>[1,8,2,7,6,3,5,4]=>[8,1,7,2,3,6,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,3,4,2,6]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,7,5,6,2]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,7,5,6,2]=>[1,4,3,2,8,5,7,6]=>[8,5,6,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,5,3,4,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,8,6,7,2]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,5,3,4,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,3,8,1,2,4]=>[1,6,2,7,3,5,8,4]=>[8,3,7,2,6,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,7,1,8,5]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,3,1,2,4]=>[1,6,2,8,4,7,3,5]=>[8,3,7,1,5,2,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,4,7,1,8,5]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,4,2,3,7]=>[1,2,5,4,8,7,3,6]=>[8,7,4,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,6,1,2,4]=>[1,5,6,2,7,3,8,4]=>[8,4,3,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,2,4,3,7]=>[1,2,5,3,8,7,4,6]=>[8,7,4,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,2,6,8,4]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,6,2,4,3,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,3,7,1,2,4]=>[1,5,7,2,8,4,3,6]=>[8,4,2,7,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,8,6,7,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,3,1,2,4]=>[1,5,3,6,2,7,4,8]=>[8,4,6,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,3,1,2,4]=>[1,6,2,8,4,5,3,7]=>[8,3,7,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,6,8,7,4]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,1,4,8,2,5]=>[1,7,2,3,6,8,5,4]=>[8,2,7,6,3,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,5,3,4,2]=>[1,7,4,6,3,2,8,5]=>[8,2,5,3,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,1,4,6,5]=>[1,8,5,2,7,6,4,3]=>[8,1,4,7,2,3,5,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,7,4,2,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,4,1,7,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,8,5,7,1]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,5,8,6,4]=>[1,2,7,6,8,4,3,5]=>[8,7,2,3,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,5,1,7,8]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,5,1,6,4]=>[1,2,8,4,7,6,3,5]=>[8,7,1,5,2,3,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,2,1,5,3]=>[1,6,2,4,7,5,3,8]=>[8,3,7,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,6,7,1,5]=>[1,2,8,5,6,7,3,4]=>[8,7,1,4,3,2,6,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,2,4,3,5]=>[1,2,6,4,8,5,3,7]=>[8,7,3,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,6,4,1,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,2,5,1,4]=>[1,7,2,6,5,3,8,4]=>[8,2,7,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,6,4,5,3]=>[1,2,7,5,6,4,3,8]=>[8,7,2,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,5,3,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,4,6,2,7]=>[1,5,4,8,7,2,3,6]=>[8,4,5,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,5,1,6,8,4]=>[1,2,7,8,4,5,3,6]=>[8,7,2,1,5,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,2,1,4,3]=>[1,5,2,7,4,8,3,6]=>[8,4,7,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,2,7,4,8]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,3,4,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,6,8,3,4]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,8,3,5,6]=>[1,2,7,5,8,6,3,4]=>[8,7,2,4,1,3,6,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,5,3,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,4,5,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,4,3,5,7]=>[1,2,6,3,8,7,5,4]=>[8,7,3,6,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,5,3,4,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,6,7,4,5]=>[1,2,3,8,5,6,7,4]=>[8,7,6,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,3,4,8,6]=>[1,2,7,8,6,4,5,3]=>[8,7,2,1,3,5,4,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,3,4,5,6,7,8,9,1,2]=>[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,3,4,5,6,7,8,1,10,2]=>[1,9,10,2,3,4,5,6,7,8]=>[10,2,1,9,8,7,6,5,4,3]=>[10,3,2,9,8,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,3,1,5,6,7,8,9,10,2]=>[1,4,5,6,7,8,9,10,2,3]=>[10,7,6,5,4,3,2,1,9,8]=>[10,8,7,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,10,2,9]=>[1,3,4,5,6,7,8,10,9,2]=>[10,8,7,6,5,4,3,1,2,9]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,2,1,4,6,7,3,5]=>[1,8,5,6,7,3,2,4]=>[8,1,4,3,2,6,7,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,1,3,4,8,5]=>[1,7,8,5,3,6,4,2]=>[8,2,1,4,6,3,5,7]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,1,3,8,4]=>[1,6,3,7,8,4,5,2]=>[8,3,6,2,1,5,4,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,2,3,8,4]=>[1,2,7,8,4,6,3,5]=>[8,7,2,1,5,3,6,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,5,7,2,4]=>[1,8,4,3,2,6,7,5]=>[8,1,5,6,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,8,2,5,6]=>[1,2,7,5,8,6,3,4]=>[8,7,2,4,1,3,6,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,3,4,8,2,7]=>[1,6,8,7,2,3,5,4]=>[8,3,1,2,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,2,8,1,4]=>[1,3,7,2,6,8,4,5]=>[8,6,2,7,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,5,6,2,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,7,1,5,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,8,3,6,7]=>[1,2,3,5,8,7,6,4]=>[8,7,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,2,4,5,6]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,7,2,5,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,8,2,3,5]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,7,8,1,4]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,5,6,2,4]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,5,1,3,4]=>[1,8,4,7,3,6,2,5]=>[8,1,5,2,6,3,7,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,7,1,3,6]=>[1,2,5,7,3,8,6,4]=>[8,7,4,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,1,2,3,6]=>[1,4,7,3,8,6,2,5]=>[8,5,2,6,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,7,2,3,6]=>[1,4,5,7,3,8,6,2]=>[8,5,4,2,6,1,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,6,2,3,5]=>[1,2,8,5,6,3,7,4]=>[8,7,1,4,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,1,8,3,7]=>[1,2,6,8,7,3,5,4]=>[8,7,3,1,2,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,4,8,3,7]=>[1,6,8,7,3,5,4,2]=>[8,3,1,2,6,4,5,7]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,2,8,1,7]=>[1,6,8,7,2,3,5,4]=>[8,3,1,2,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,4,2,6,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,1,5,2,6]=>[1,8,6,5,2,7,3,4]=>[8,1,3,4,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,1,6,7,2]=>[1,3,4,5,2,8,6,7]=>[8,6,5,4,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,3,6,7,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,5,6,4,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,3,1,2]=>[1,8,2,4,6,3,7,5]=>[8,1,7,5,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,7,6,3,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,5,7,6,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,7,6,3,5]=>[1,8,5,7,3,2,4,6]=>[8,1,4,2,6,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,4,2,6,5]=>[1,8,5,4,7,6,2,3]=>[8,1,4,5,2,3,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,1,6,5,4]=>[1,8,4,3,7,5,2,6]=>[8,1,5,6,2,4,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,3,7,6,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,7,4,6,5]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,4,3,7,6]=>[1,8,6,3,2,5,4,7]=>[8,1,3,6,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,4,1,6,5]=>[1,2,8,5,4,7,6,3]=>[8,7,1,4,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,7,6,4,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,3,1,5,6]=>[1,4,7,5,3,8,6,2]=>[8,5,2,4,6,1,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,7,2,5,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,6,7,2,5]=>[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,6,7,1,5]=>[1,3,8,5,6,7,2,4]=>[8,6,1,4,3,2,7,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,5,6,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,4,1,7,3]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,1,7,2,3]=>[1,6,7,2,8,3,5,4]=>[8,3,2,7,1,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,4,2,3]=>[1,8,3,7,2,5,6,4]=>[8,1,6,2,7,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,3,6,5,1]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,1,6,5,3]=>[1,8,3,7,5,2,4,6]=>[8,1,6,2,4,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,6,5,2,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,1,7,4,6,2]=>[1,3,8,2,5,7,6,4]=>[8,6,1,7,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,3,6,5,2]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,6,9,1,7]=>[1,8,2,3,4,5,6,7,9]=>[9,2,8,7,6,5,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,3,4,5,6,7,10,1,8]=>[1,9,2,3,4,5,6,7,8,10]=>[10,2,9,8,7,6,5,4,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,7,6,8,1,5]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,5,6,4,8]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,4,6,7,3]=>[1,8,3,2,5,4,6,7]=>[8,1,6,7,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,5,2,7,3]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,8,5,7,1]=>[1,4,3,6,5,8,2,7]=>[8,5,6,3,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,6,3,5,8]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,2,7,1,6]=>[1,8,6,7,2,3,5,4]=>[8,1,3,2,7,6,4,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,7,3,1,5]=>[1,2,8,5,7,3,6,4]=>[8,7,1,4,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,2,6,7,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,1,5,7,6]=>[1,3,2,8,6,5,4,7]=>[8,6,7,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,4,1,7,6]=>[1,5,4,2,8,6,3,7]=>[8,4,5,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,4,8,1,7]=>[1,6,8,7,2,5,4,3]=>[8,3,1,2,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,6,1,3,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,6,8,1,5]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,7,5,1,2]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,7,6,3,2]=>[1,4,5,7,3,2,8,6]=>[8,5,4,2,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,6,8,2,5,1]=>[1,3,4,6,2,7,5,8]=>[8,6,5,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,8,1,7,3,6]=>[1,4,8,6,7,3,2,5]=>[8,5,1,3,2,6,7,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,8,6,1,4]=>[1,3,5,8,4,2,7,6]=>[8,6,4,1,5,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,6,7,1,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,1,2,7,3]=>[1,5,2,4,6,3,8,7]=>[8,4,7,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,7,5,2,3]=>[1,8,3,6,5,7,2,4]=>[8,1,6,3,4,2,7,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,6,4,8,1,3]=>[1,5,4,6,8,3,7,2]=>[8,4,5,3,1,6,2,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,5,1,7,4]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,4,1,3,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,6,8,1,3]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,4,6,3,2]=>[1,7,3,5,4,8,2,6]=>[8,2,6,4,5,1,7,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,7,1,5,2]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,2,8,5,6]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,4,2,8,7]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,1,5,6,3]=>[1,7,6,5,2,3,4,8]=>[8,2,3,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,2,5,6,3]=>[1,7,6,5,2,3,8,4]=>[8,2,3,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,8,1,7,3]=>[1,6,2,4,5,8,3,7]=>[8,3,7,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,8,3,6,4]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,6,2,1,4]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,3,7,4,2]=>[1,6,7,4,8,2,3,5]=>[8,3,2,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,6,3,1,2]=>[1,7,2,4,5,6,3,8]=>[8,2,7,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,1,5,6,2]=>[1,7,6,5,2,8,3,4]=>[8,2,3,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,2,5,6,4]=>[1,7,6,5,2,3,4,8]=>[8,2,3,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,1,5,6,4]=>[1,7,6,5,2,3,4,8]=>[8,2,3,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,3,2,1,5]=>[1,6,2,4,7,3,8,5]=>[8,3,7,5,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,6,3,1,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,3,1,7,5]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,8,2,4,7]=>[1,5,8,7,4,3,6,2]=>[8,4,1,2,5,6,3,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,4,8,7,2]=>[1,3,5,4,2,6,8,7]=>[8,6,4,5,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,8,4,1,5]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,4,7,2,3]=>[1,6,7,2,5,4,8,3]=>[8,3,2,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,1,6,2,3]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,7,1,2,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,1,4,2,7]=>[1,3,6,4,8,7,2,5]=>[8,6,3,5,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,3,1,5,8]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,4,2,7,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,1,4,2,5]=>[1,7,2,8,5,3,6,4]=>[8,2,7,1,4,6,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,4,6,3,1]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,7,1,8,2]=>[1,5,7,8,2,6,3,4]=>[8,4,2,1,7,3,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,2,4,8,1]=>[1,6,4,7,8,2,5,3]=>[8,3,5,2,1,7,4,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,4,3,7,1]=>[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,6,8,2,1]=>[1,5,6,8,2,7,3,4]=>[8,4,3,1,7,2,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,6,7,8,3]=>[1,5,6,7,8,3,2,4]=>[8,4,3,2,1,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,8,2,7,1]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,1,7,8,3]=>[1,5,2,3,6,7,8,4]=>[8,4,7,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,6,2,7,1]=>[1,5,6,2,4,8,3,7]=>[8,4,3,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,8,3,7,1]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,2,3,5,1]=>[1,6,3,7,5,2,4,8]=>[8,3,6,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,4,8,1,6]=>[1,3,5,4,2,7,6,8]=>[8,6,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,3,8,6,1]=>[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,8,4,6,1]=>[1,5,8,2,7,6,4,3]=>[8,4,1,7,2,3,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,8,4,6,1]=>[1,5,8,2,3,7,6,4]=>[8,4,1,7,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,5,8,6,1]=>[1,4,2,3,7,6,8,5]=>[8,5,7,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,5,8,6,1]=>[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,6,4,8,1]=>[1,7,8,2,5,6,4,3]=>[8,2,1,7,4,3,5,6]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,7,3,4,1]=>[1,8,2,5,7,4,6,3]=>[8,1,7,4,2,5,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,3,7,5,1]=>[1,8,2,4,6,7,5,3]=>[8,1,7,5,3,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,3,8,5,1]=>[1,7,5,3,6,8,2,4]=>[8,2,4,6,3,1,7,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,3,8,5,1]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,5,8,1,4]=>[1,7,2,6,8,4,3,5]=>[8,2,7,3,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,10,4,5,6,7,8,9,1,3]=>[1,2,10,3,4,5,6,7,8,9]=>[10,9,1,8,7,6,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,3,8,5,4,7,2,1]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,4,6,3,8,7,5,1]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,8,7,3,5]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,8,7,1,5]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,8,7,1,5]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,8,7,1,3]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,5,7,3,1]=>[1,2,4,8,3,6,7,5]=>[8,7,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,5,7,1,3]=>[1,2,4,8,3,6,7,5]=>[8,7,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,3,7,1,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,1,7,3,5]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,1,8,7,3]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,8,3,7,1]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,8,1,7,3]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,7,1,3,5]=>[1,2,4,8,5,7,3,6]=>[8,7,5,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,5,1,3,7]=>[1,2,4,8,7,3,6,5]=>[8,7,5,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,1,8,3,7]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,1,3,8,7]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,3,8,1,7]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,8,3,1,7]=>[1,2,4,5,8,7,3,6]=>[8,7,5,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,5,3,1,7]=>[1,2,4,8,7,3,6,5]=>[8,7,5,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,7,3,1,5]=>[1,2,4,8,5,7,3,6]=>[8,7,5,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,2,1,3,6]=>[1,4,5,2,8,6,3,7]=>[8,5,4,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,3,2,7,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,8,5,3,2]=>[1,4,7,3,2,6,5,8]=>[8,5,2,6,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,8,4,5,3]=>[1,6,4,7,5,8,3,2]=>[8,3,5,2,4,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,7,4,8,2]=>[1,5,7,8,2,6,4,3]=>[8,4,2,1,7,3,5,6]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,1,6,5,2]=>[1,4,7,5,2,8,3,6]=>[8,5,2,4,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,5,1,4,3]=>[1,8,3,2,7,4,6,5]=>[8,1,6,7,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,1,7,6,4]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,1,7,6,2]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,7,6,5,1]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,6,5,3,1]=>[1,4,7,3,2,8,5,6]=>[8,5,2,6,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,2,5,1,4]=>[1,3,7,2,8,4,6,5]=>[8,6,2,7,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,6,2,5,1]=>[1,4,7,5,6,2,8,3]=>[8,5,2,4,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,6,5,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,5,3,7,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,7,3,4,5]=>[1,2,8,5,7,4,3,6]=>[8,7,1,4,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,4,5,7,8]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,4,3,7,8]=>[1,2,5,4,6,3,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,6,3,7,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,3,7,4,5]=>[1,2,8,5,3,6,7,4]=>[8,7,1,4,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,6,3,4,7]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,2,7,4,5]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,2,5,6,7]=>[1,2,4,8,7,6,5,3]=>[8,7,5,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,2,5,6,7]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,5,4,3,7]=>[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,2,7,4,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,5,6,3,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,2,8,4,6]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,6,8,4,5]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,6,8,4,5]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,2,5,6,7]=>[1,2,4,3,8,7,6,5]=>[8,7,5,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,8,3,4,6]=>[1,2,7,4,5,8,6,3]=>[8,7,2,5,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,5,6,9,8,1]=>[1,7,9,2,3,4,5,6,8]=>[9,3,1,8,7,6,5,4,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,9,4,5,6,7,8,1]=>[1,3,9,2,4,5,6,7,8]=>[9,7,1,8,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,9,3,4,5,6,7,8,1]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,3,4,5,6,7,8,10,1]=>[1,9,10,2,3,4,5,6,7,8]=>[10,2,1,9,8,7,6,5,4,3]=>[10,3,2,9,8,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,2,3,4,1,7,9,8,6]=>[1,5,2,3,4,6,7,9,8]=>[9,5,8,7,6,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,2,4,8,1,6,7,3]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,9,5,6,7,8,3]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,9,4,5,6,7,8,2]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,3,4,5,6,7,8,9,1]=>[1,2,10,3,4,5,6,7,8,9]=>[10,9,1,8,7,6,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,5,6,4,7,8,1,9]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,6,7,5,8,9,2]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,6,7,5,8,9,1,10]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,6,5,7,4,8,1,9]=>[1,2,3,6,4,5,7,8,9]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,6,4,5,7,3,1,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,4,7,1,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,6,8,4,2]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,4,5,8,2]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,4,2,7,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,4,7,2,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,4,2,7,8]=>[1,2,5,4,6,3,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,3,8,4,2]=>[1,2,7,4,6,8,3,5]=>[8,7,2,5,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,6,4,2,8]=>[1,2,5,6,4,7,3,8]=>[8,7,4,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,7,4,2,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,7,4,2,8]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,3,4,8,2]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,6,4,8,2]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,8,7,2,4]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,8,2,1,7]=>[1,4,5,8,7,2,6,3]=>[8,5,4,1,2,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,6,3,1,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,1,8,6,3]=>[1,7,6,8,3,5,2,4]=>[8,2,3,1,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,1,8,6,3]=>[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,2,1,7,4]=>[1,8,4,6,2,5,3,7]=>[8,1,5,3,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,1,2,8,6]=>[1,4,3,7,8,6,2,5]=>[8,5,6,2,1,3,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,3,2,7,6]=>[1,4,8,6,2,5,3,7]=>[8,5,1,3,7,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,4,1,7,6]=>[1,2,5,4,8,6,3,7]=>[8,7,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,1,7,5,4]=>[1,8,4,3,2,6,7,5]=>[8,1,5,6,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,1,8,6,4]=>[1,7,6,8,4,3,2,5]=>[8,2,3,1,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,4,8,7,5]=>[1,6,8,5,4,2,3,7]=>[8,3,1,4,5,7,6,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,3,6,1,8]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,5,1,2,7]=>[1,3,8,7,2,6,4,5]=>[8,6,1,2,7,3,5,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,6,4,1,8]=>[1,5,6,4,7,2,3,8]=>[8,4,3,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,3,4,1,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,4,1,3,7]=>[1,8,7,3,6,2,4,5]=>[8,1,2,6,3,7,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,5,1,3,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,8,5,6,4]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,1,4,3,6]=>[1,7,3,8,6,4,5,2]=>[8,2,6,1,3,5,4,7]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,4,2,3,5]=>[1,8,5,4,2,6,3,7]=>[8,1,4,5,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,1,2,5,6]=>[1,4,3,7,5,2,8,6]=>[8,5,6,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,3,1,5,7]=>[1,4,2,8,7,5,3,6]=>[8,5,7,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,2,1,6,7]=>[1,4,8,7,6,2,5,3]=>[8,5,1,2,3,7,4,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,7,6,2,5]=>[1,3,4,2,8,5,7,6]=>[8,6,5,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,8,4,6,5]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,5,2,3,4]=>[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,6,3,4]=>[1,8,4,2,5,7,3,6]=>[8,1,5,7,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,7,6,4,5]=>[1,3,2,8,5,7,4,6]=>[8,6,7,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,2,4,6,1]=>[1,3,7,6,4,8,2,5]=>[8,6,2,3,5,1,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,4,3,6,1]=>[1,7,6,3,2,8,4,5]=>[8,2,3,6,7,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,8,2,6,1]=>[1,4,7,6,2,5,8,3]=>[8,5,2,3,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,3,6,2,8]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,8,4,5,2]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,7,3,5,1]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,5,1,8,2]=>[1,4,3,6,2,7,8,5]=>[8,5,6,3,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,4,6,1,3]=>[1,2,5,4,8,3,7,6]=>[8,7,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,2,1,4,8]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,4,5,3,8]=>[1,6,5,4,7,3,2,8]=>[8,3,4,5,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,7,5,3,8]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,6,7,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,4,8,3,2]=>[1,6,8,2,7,3,5,4]=>[8,3,1,7,2,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,5,3,8,2]=>[1,7,8,2,4,6,3,5]=>[8,2,1,7,5,3,6,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,3,6,4,1]=>[1,5,3,2,8,4,7,6]=>[8,4,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,3,8,4,2]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,4,2,7,3]=>[1,2,5,4,8,3,6,7]=>[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,8,2,6,3]=>[1,7,6,2,5,8,3,4]=>[8,2,3,7,4,1,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,7,6,4,3]=>[1,8,3,5,7,4,2,6]=>[8,1,6,4,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,8,2,5,1]=>[1,6,2,7,5,8,3,4]=>[8,3,7,2,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,4,3,2,5]=>[1,7,2,8,5,4,3,6]=>[8,2,7,1,4,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,6,1,3,5]=>[1,2,4,8,5,6,3,7]=>[8,7,5,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,5,2,4,1]=>[1,3,8,2,7,4,6,5]=>[8,6,1,7,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,8,6,3,1]=>[1,4,7,3,2,5,8,6]=>[8,5,2,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,3,1,7,8]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,3,2,7,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,4,1,3,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,1,5,2,8]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,4,3,2,8]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,3,1,5,2]=>[1,7,5,3,6,2,8,4]=>[8,2,4,6,3,7,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,8,2,6,3]=>[1,4,5,8,3,2,7,6]=>[8,5,4,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,1,8,4,5]=>[1,3,6,8,5,2,7,4]=>[8,6,3,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,3,6,4,1]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,6,5,3,1]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,2,6,3,1]=>[1,7,3,4,8,2,5,6]=>[8,2,6,5,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,6,5,2,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,7,8,1,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,2,6,7,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,5,2,1,6]=>[1,7,2,3,4,8,6,5]=>[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,1,5,6,2]=>[1,7,6,5,2,3,8,4]=>[8,2,3,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,1,8,3,6]=>[1,7,3,4,5,2,6,8]=>[8,2,6,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,8,5,6,4]=>[1,7,6,5,8,4,2,3]=>[8,2,3,4,1,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,5,7,6,1]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,8,6,7,1]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,5,3,2,1]=>[1,6,3,4,8,2,7,5]=>[8,3,6,5,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,1,7,8,2]=>[1,4,6,7,8,2,3,5]=>[8,5,3,2,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,4,7,8,1]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,4,7,8,2]=>[1,3,5,4,6,7,8,2]=>[8,6,4,5,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,7,5,8,2]=>[1,3,4,6,5,7,8,2]=>[8,6,5,3,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,2,6,8,5]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,8,7,5,2]=>[1,3,6,7,5,8,2,4]=>[8,6,3,2,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,1,5,8,4]=>[1,3,6,5,2,7,8,4]=>[8,6,3,4,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,3,7,8,5]=>[1,4,2,3,6,7,8,5]=>[8,5,7,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,7,6,3,1]=>[1,8,2,5,7,3,4,6]=>[8,1,7,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,7,1,3,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,4,6,7,3]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,2,6,5,1]=>[1,3,8,2,7,5,4,6]=>[8,6,1,7,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,7,1,3,4]=>[1,5,7,3,2,6,4,8]=>[8,4,2,6,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,4,5,6,2]=>[1,7,6,5,4,8,2,3]=>[8,2,3,4,5,1,7,6]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,3,5,6,2]=>[1,7,6,5,3,2,8,4]=>[8,2,3,4,6,7,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,8,1,5,4]=>[1,3,7,5,8,4,2,6]=>[8,6,2,4,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,3,5,8,4]=>[1,2,6,5,3,7,8,4]=>[8,7,3,4,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,8,2,5,4]=>[1,3,7,5,8,4,2,6]=>[8,6,2,4,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,7,2,6,5]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,2,8,6,4]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,7,2,6,5]=>[1,3,2,8,5,7,6,4]=>[8,6,7,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,2,7,6,5]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,2,7,6,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,1,7,6,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,7,1,6,5]=>[1,3,4,2,8,5,7,6]=>[8,6,5,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,7,6,1,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,7,1,6,5]=>[1,3,2,8,5,7,6,4]=>[8,6,7,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,1,8,6,4]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,3,7,6,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,3,7,6,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,8,7,1,5]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,1,2,8,3]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,8,2,3,1]=>[1,4,5,8,2,6,3,7]=>[8,5,4,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,6,8,3,2]=>[1,4,2,5,6,8,3,7]=>[8,5,7,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,6,8,2,3]=>[1,4,7,2,5,6,8,3]=>[8,5,2,7,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,3,1,4,5]=>[1,6,2,7,4,8,5,3]=>[8,3,7,2,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,2,8,4,5]=>[1,7,4,2,6,8,5,3]=>[8,2,5,7,3,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,4,1,3,5]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,4,1,2,5]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,3,7,8,6]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,2,7,8,6]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,5,2,7,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,2,7,8,6]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,4,7,8,6]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,5,4,1,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,2,6,7,3]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,8,2,1,4]=>[1,5,8,4,7,2,3,6]=>[8,4,1,5,2,7,6,3]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,6,2,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,6,1,7,3]=>[1,8,3,5,6,2,4,7]=>[8,1,6,4,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,3,7,5,1]=>[1,4,2,6,7,5,3,8]=>[8,5,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,3,6,1,8]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,4,8,1,5]=>[1,6,8,5,4,3,2,7]=>[8,3,1,4,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,6,7,8,1]=>[1,3,2,5,6,7,8,4]=>[8,6,7,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,7,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,7,6,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,5,4,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,3,5,8,4,7,1,2]=>[1,6,7,2,3,5,4,8]=>[8,3,2,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,5,1,6,3]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,2,6,7,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,1,7,8,4]=>[1,6,7,8,4,5,2,3]=>[8,3,2,1,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,2,7,8,5]=>[1,2,6,7,8,5,3,4]=>[8,7,3,2,1,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,1,6,7,4]=>[1,8,4,2,5,3,6,7]=>[8,1,5,7,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,3,6,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,3,6,7,4]=>[1,8,4,5,3,2,6,7]=>[8,1,5,4,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,3,8,2,1,4]=>[1,6,2,7,3,5,8,4]=>[8,3,7,2,6,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,6,7,1,3]=>[1,4,8,3,5,6,7,2]=>[8,5,1,6,4,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,1,8,6,5]=>[1,3,2,7,6,8,5,4]=>[8,6,7,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,5,1,3,6]=>[1,2,4,8,6,3,7,5]=>[8,7,5,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,4,1,6,7]=>[1,2,5,4,8,7,6,3]=>[8,7,4,5,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,1,3,4,2]=>[1,5,2,7,4,8,3,6]=>[8,4,7,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,5,6,2,8]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,4,3,5,6]=>[1,8,6,3,7,5,4,2]=>[8,1,3,6,2,4,5,7]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,4,7,5,6]=>[1,2,3,8,6,7,5,4]=>[8,7,6,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,4,6,5,8]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,4,6,5,8]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,4,2,5,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,4,2,5,6]=>[1,8,6,2,7,5,4,3]=>[8,1,3,7,2,4,5,6]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,4,1,5,6]=>[1,3,8,6,2,4,7,5]=>[8,6,1,3,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,4,6,5,8]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,1,7,8,4]=>[1,3,6,7,8,4,5,2]=>[8,6,3,2,1,5,4,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,7,1,8,4]=>[1,5,7,8,4,6,2,3]=>[8,4,2,1,5,3,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,7,4,1,5]=>[1,3,8,5,7,2,4,6]=>[8,6,1,4,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,7,3,1,5]=>[1,8,5,7,2,4,3,6]=>[8,1,4,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,7,2,1,5]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,8,7,1,5]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,6,5,1,2]=>[1,3,4,7,2,8,5,6]=>[8,6,5,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,6,3,5,1]=>[1,7,5,6,3,4,2,8]=>[8,2,4,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,6,4,5,1]=>[1,3,7,5,6,4,8,2]=>[8,6,2,4,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,3,2,4,1]=>[1,5,3,8,2,7,4,6]=>[8,4,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,1,7,8,3]=>[1,6,7,8,3,4,2,5]=>[8,3,2,1,6,5,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,7,6,3,8]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,2,7,8,3]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,7,2,8,3]=>[1,5,7,8,3,2,4,6]=>[8,4,2,1,6,7,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,1,7,2,4]=>[1,6,7,2,8,4,3,5]=>[8,3,2,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,8,7,1,4]=>[1,5,8,4,3,6,7,2]=>[8,4,1,5,6,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,3,4,2,5]=>[1,8,5,3,2,6,4,7]=>[8,1,4,6,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,7,4,2,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,2,7,8,4]=>[1,2,6,7,8,4,5,3]=>[8,7,3,2,1,5,4,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,2,6,4,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,2,6,4,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,2,7,3,5]=>[1,6,7,3,4,8,5,2]=>[8,3,2,6,5,1,4,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,3,7,1,5]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,2,3,4]=>[1,8,4,6,2,3,7,5]=>[8,1,5,3,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,8,2,4,3]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,5,4,2,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,5,4,8,2]=>[1,2,6,4,3,7,8,5]=>[8,7,3,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,6,8,4,2]=>[1,2,7,4,5,6,8,3]=>[8,7,2,5,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,6,4,5,2]=>[1,2,7,5,6,4,3,8]=>[8,7,2,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,4,5,2,3]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,6,4,1,3]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,6,8,3,2]=>[1,7,3,5,6,8,2,4]=>[8,2,6,4,3,1,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,6,8,3,2]=>[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,3,1,8,2]=>[1,5,3,7,8,2,6,4]=>[8,4,6,2,1,7,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,5,3,7,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,5,4,7,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,5,4,7,3]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,6,3,7,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,3,5,7,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,2,6,8,3]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,2,8,5,4]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,8,4,3,5]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,4,3,7,6]=>[1,2,5,4,8,6,3,7]=>[8,7,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,3,6,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,6,3,4,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,5,8,4,3]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,2,6,3,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,8,2,5,3]=>[1,2,7,5,8,3,6,4]=>[8,7,2,4,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,6,5,4,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,6,4,8,3]=>[1,2,5,6,4,7,8,3]=>[8,7,4,3,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,8,7,5,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,2,4,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,4,2,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,8,6,5,3]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,7,5,4,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,5,4,3,7]=>[1,2,3,8,7,4,6,5]=>[8,7,6,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,6,5,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,6,5,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,2,6,4,7]=>[1,5,2,8,7,4,3,6]=>[8,4,7,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,5,2,3,6]=>[1,4,7,3,2,8,6,5]=>[8,5,2,6,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,5,2,6,3]=>[1,4,7,6,2,8,3,5]=>[8,5,2,3,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,2,6,3,7]=>[1,8,7,3,2,5,4,6]=>[8,1,2,6,7,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,1,6,4,7]=>[1,8,7,4,2,5,3,6]=>[8,1,2,5,7,4,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,2,6,3,7]=>[1,8,7,3,5,2,4,6]=>[8,1,2,6,4,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,1,6,3,7]=>[1,8,7,3,2,5,4,6]=>[8,1,2,6,7,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,5,2,6,3]=>[1,4,2,8,3,7,6,5]=>[8,5,7,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,1,3,2,5]=>[1,7,2,6,3,8,5,4]=>[8,2,7,3,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,1,3,5,2]=>[1,7,5,2,6,3,8,4]=>[8,2,4,7,3,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,4,1,2,6]=>[1,3,7,2,8,6,4,5]=>[8,6,2,7,1,3,5,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,5,1,3,6]=>[1,4,7,3,2,8,6,5]=>[8,5,2,6,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,1,5,2,3]=>[1,7,2,6,5,3,8,4]=>[8,2,7,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,6,3,5,2]=>[1,7,5,6,3,4,8,2]=>[8,2,4,3,6,5,1,7]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,3,4,7,2]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,3,4,7,1]=>[1,8,2,6,4,5,3,7]=>[8,1,7,3,5,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,3,4,7,2]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,3,6,2,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,3,6,2,4]=>[1,8,4,5,3,2,7,6]=>[8,1,5,4,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,5,4,7,2]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,6,3,5,1]=>[1,7,5,6,3,8,2,4]=>[8,2,4,3,6,1,7,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,6,3,1,5]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,6,4,5,2]=>[1,8,2,7,5,6,4,3]=>[8,1,7,2,4,3,5,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,4,6,5,2]=>[1,8,2,7,5,4,3,6]=>[8,1,7,2,4,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,7,5,6,1]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,1,8,5,2]=>[1,7,5,2,6,8,3,4]=>[8,2,4,7,3,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,2,5,1,3]=>[1,7,2,8,3,6,5,4]=>[8,2,7,1,6,3,4,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,6,5,1,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,4,6,1,3]=>[1,8,3,5,4,2,7,6]=>[8,1,6,4,5,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,6,4,2,8]=>[1,5,6,4,7,2,3,8]=>[8,4,3,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,4,2,5,3]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,7,5,3,2]=>[1,2,4,6,5,7,3,8]=>[8,7,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,7,4,3,1]=>[1,8,2,6,4,5,7,3]=>[8,1,7,3,5,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,8,5,4,2]=>[1,7,4,6,5,8,2,3]=>[8,2,5,3,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,4,3,5,7]=>[1,2,8,7,5,4,6,3]=>[8,7,1,2,4,5,3,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,6,4,3,5,8]=>[1,2,7,5,4,6,3,8]=>[8,7,2,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,4,6,3,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,8,1,4,3]=>[1,6,2,5,8,3,7,4]=>[8,3,7,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,8,1,4,3]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,5,8,1,4,3]=>[1,6,2,7,4,5,8,3]=>[8,3,7,2,5,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,8,1,4,2]=>[1,6,2,5,8,3,7,4]=>[8,3,7,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,2,5,3,1]=>[1,8,2,7,3,6,5,4]=>[8,1,7,2,6,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,2,3,5,1]=>[1,8,2,7,5,3,4,6]=>[8,1,7,2,4,6,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,7,3,2,1]=>[1,6,3,4,5,7,2,8]=>[8,3,6,5,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,4,3,8,2]=>[1,6,3,5,4,2,7,8]=>[8,3,6,4,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,6,1,3,4]=>[1,5,6,2,8,4,7,3]=>[8,4,3,7,1,5,2,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,3,4,2,6]=>[1,5,3,8,6,4,7,2]=>[8,4,6,1,3,5,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,7,1,4,5]=>[1,8,5,7,4,6,2,3]=>[8,1,4,2,5,3,7,6]=>[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,5,8,6,7]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,4,8,7,5,3,1,6]=>[1,2,4,7,3,8,6,5]=>[8,7,5,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,7,5,3,4,1]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,4,3,8,7]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,1,2,8,7]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,3,1,2,6]=>[1,4,5,3,7,2,8,6]=>[8,5,4,6,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,3,1,4,2]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,3,1,4,2]=>[1,8,2,7,4,6,3,5]=>[8,1,7,2,5,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,6,5,1,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,7,3,6,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,1,2,6,5]=>[1,8,5,2,7,6,3,4]=>[8,1,4,7,2,3,6,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,6,5,2,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,6,5,1,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,4,6,5,1]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,6,5,1,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,6,5,3,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,6,5,3,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,4,3,6,5]=>[1,8,5,4,2,7,6,3]=>[8,1,4,5,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,3,4,6,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,4,3,6]=>[1,8,6,4,2,7,3,5]=>[8,1,3,5,7,2,6,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,4,3,6,5]=>[1,2,8,5,4,3,7,6]=>[8,7,1,4,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,4,1,6,5]=>[1,2,8,5,4,3,7,6]=>[8,7,1,4,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,6,3,4,1]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,1,4,6,5]=>[1,2,8,5,3,7,6,4]=>[8,7,1,4,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,8,7,5,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,6,8,7,5]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,3,1,6,4]=>[1,2,8,4,5,3,7,6]=>[8,7,1,5,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,3,6,4,1]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,6,1,4,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,7,5,1,4,3]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,1,2,4,3]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,1,2,4,3]=>[1,8,3,5,2,7,4,6]=>[8,1,6,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,4,6,5,3]=>[1,8,3,2,7,5,4,6]=>[8,1,6,7,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,3,6,5,1]=>[1,2,4,7,5,3,8,6]=>[8,7,5,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,3,6,5,1]=>[1,8,2,7,5,3,4,6]=>[8,1,7,2,4,6,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,2,6,5,3]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,1,2,6,4]=>[1,8,4,3,5,2,7,6]=>[8,1,5,6,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,6,4,1,2]=>[1,8,2,7,3,5,6,4]=>[8,1,7,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,3,6,5,2]=>[1,8,2,7,5,3,4,6]=>[8,1,7,2,4,6,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,1,6,5,2]=>[1,8,2,7,5,3,4,6]=>[8,1,7,2,4,6,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,3,2,4,5,6,7,8,9,1]=>[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,1,2,3,5,4,6,8]=>[1,7,6,4,3,2,5,8]=>[8,2,3,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,4,5,3,8]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,5,1,2,8]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,8,3,1,6]=>[1,7,2,5,8,6,3,4]=>[8,2,7,4,1,3,6,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,5,7,2,4]=>[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,1,8,4,6,3]=>[1,5,8,3,2,7,6,4]=>[8,4,1,6,7,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,4,3,1,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,4,2,1,5]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,2,4,5,7]=>[1,8,7,5,2,6,4,3]=>[8,1,2,4,7,3,5,6]=>[8,2,3,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,5,8,6,2]=>[1,4,3,7,6,8,2,5]=>[8,5,6,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,5,2,1,6]=>[1,8,6,2,4,3,7,5]=>[8,1,3,7,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,3,2,6,7]=>[1,5,3,8,7,6,2,4]=>[8,4,6,1,2,3,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,7,2,4,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,6,2,4,5]=>[1,2,7,4,8,5,6,3]=>[8,7,2,5,1,4,3,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,3,7,5,4]=>[1,8,4,2,6,7,5,3]=>[8,1,5,7,3,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,7,6,3,5]=>[1,8,5,7,3,4,2,6]=>[8,1,4,2,6,5,7,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,2,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,10,2,9]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,9,3,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,3,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,9,2,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,5,7,3,6,8,2,4]=>[1,2,5,6,8,4,3,7]=>[8,7,4,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,6,8,2,5]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,8,5,3,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,6,8,2,5]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,2,4,7,1,3]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,5,7,1,4]=>[1,3,2,8,4,6,7,5]=>[8,6,7,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,7,4,1,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,6,3,1,4]=>[1,8,4,5,6,3,2,7]=>[8,1,5,4,3,6,7,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,4,3,2,5]=>[1,8,5,4,6,3,2,7]=>[8,1,4,5,3,6,7,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,5,4,3,6]=>[1,2,8,6,4,7,3,5]=>[8,7,1,3,5,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,7,3,2,4]=>[1,5,7,2,8,4,3,6]=>[8,4,2,7,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,8,4,3,5]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,6,5,4,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,6,5,4,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,6,8,2,5]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,8,3,1,2]=>[1,5,8,2,4,6,3,7]=>[8,4,1,7,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,6,3,2,4]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,2,1,4]=>[1,8,4,5,6,2,3,7]=>[8,1,5,4,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,5,4,1,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,5,4,2,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,4,3,1,5]=>[1,8,5,4,6,3,7,2]=>[8,1,4,5,3,6,2,7]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,4,3,2,5]=>[1,8,5,4,6,3,7,2]=>[8,1,4,5,3,6,2,7]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,3,6,5,2]=>[1,4,7,5,3,8,2,6]=>[8,5,2,4,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,1,7,3,2]=>[1,5,2,6,7,3,8,4]=>[8,4,7,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,3,1,6,2]=>[1,4,7,6,2,5,3,8]=>[8,5,2,3,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,7,6,5,2]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,3,7,6,2]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,5,6,4,3]=>[1,8,3,7,4,2,5,6]=>[8,1,6,2,5,7,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,2,7,6,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,4,8,6,3]=>[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,7,5,8,3]=>[1,2,4,6,5,7,8,3]=>[8,7,5,3,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,6,3,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,8,6,4,3]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,8,7,4,1]=>[1,3,6,7,4,2,5,8]=>[8,6,3,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,7,6,3,8]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,6,4,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,6,7,1,4]=>[1,8,4,5,6,7,2,3]=>[8,1,5,4,3,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,7,6,2,1]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,2,8,1,7]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,8,5,1,6]=>[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,6,8,2,5]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,6,5,8,2]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,5,8,6,1]=>[1,3,4,2,7,6,8,5]=>[8,6,5,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,4,8,7,6]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,6,8,5,4]=>[1,2,7,5,6,8,4,3]=>[8,7,2,4,3,1,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,1,8,6,5]=>[1,3,4,2,7,6,8,5]=>[8,6,5,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,4,1,5,6]=>[1,8,6,2,3,7,5,4]=>[8,1,3,7,6,2,4,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,1,4,3,5]=>[1,8,5,2,6,4,3,7]=>[8,1,4,7,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,1,2,6,4]=>[1,8,4,5,2,3,7,6]=>[8,1,5,4,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,2,1,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,5,1,4,2]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,6,1,4,2]=>[1,8,2,7,4,5,6,3]=>[8,1,7,2,5,4,3,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,1,6,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,6,4,7,2]=>[1,8,2,5,6,4,3,7]=>[8,1,7,4,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,4,5,6,2]=>[1,8,2,7,6,5,4,3]=>[8,1,7,2,3,4,5,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,5,6,2,3]=>[1,8,3,4,2,7,5,6]=>[8,1,6,5,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,7,5,2,3]=>[1,8,3,4,2,6,5,7]=>[8,1,6,5,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,7,4,5,2]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,1,4,2,5]=>[1,7,2,6,4,8,5,3]=>[8,2,7,3,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,6,1,5,3]=>[1,7,5,6,2,4,3,8]=>[8,2,4,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,5,2,3,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,6,3,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,2,7,5,3]=>[1,8,3,4,2,6,7,5]=>[8,1,6,5,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,2,5,3,6]=>[1,8,6,5,2,7,3,4]=>[8,1,3,4,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,3,6,4]=>[1,8,4,2,7,6,3,5]=>[8,1,5,7,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,4,2,1,8]=>[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,4,2,5,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,5,2,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,2,5,3,7]=>[1,2,8,7,3,6,5,4]=>[8,7,1,2,6,3,4,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,6,1,5,2]=>[1,7,5,6,2,8,3,4]=>[8,2,4,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,2,7,3,5]=>[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,3,5,6,8]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,1,4,7,3]=>[1,6,4,5,2,8,3,7]=>[8,3,5,4,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,6,8,7,3]=>[1,4,2,5,6,8,3,7]=>[8,5,7,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,1,4,5,3]=>[1,8,3,2,7,5,4,6]=>[8,1,6,7,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,2,4,3,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,2,4,7,6]=>[1,8,6,4,2,5,3,7]=>[8,1,3,5,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,5,3,4,7]=>[1,8,7,4,6,3,2,5]=>[8,1,2,5,3,6,7,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,6,4,5,7]=>[1,3,8,7,5,6,4,2]=>[8,6,1,2,4,3,5,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,7,6,4,8]=>[1,5,7,4,3,2,6,8]=>[8,4,2,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,8,3,7,6]=>[1,5,8,6,3,2,4,7]=>[8,4,1,3,6,7,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,2,3,7,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,5,3,4,6,8]=>[1,7,6,4,5,3,2,8]=>[8,2,3,5,4,6,7,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,2,8,4,5]=>[1,2,6,8,5,3,7,4]=>[8,7,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,2,7,4,5]=>[1,2,8,5,3,6,7,4]=>[8,7,1,4,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,2,8,4,6]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,8,5,3,7]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,8,4,3,7]=>[1,2,5,8,7,3,6,4]=>[8,7,4,1,2,6,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,1,7,5,8]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,6,5,7,2,1]=>[1,3,8,2,4,6,7,5]=>[8,6,1,7,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,3,6,5,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,4,3,6,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,4,6,8,3]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,6,8,3,5]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,1,7,4,5]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,8,6,4,5]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,7,8,5,3,4]=>[1,2,6,5,8,4,7,3]=>[8,7,3,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,6,7,1,3]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,6,7,3,2]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,6,5,7,2]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,4,2,7,3]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,2,1,7,3]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,5,4,2,3]=>[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,5,1,3,2]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,5,4,2,8,7]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,6,8,4,1]=>[1,5,6,8,2,3,7,4]=>[8,4,3,1,7,6,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,4,6,8,1]=>[1,5,4,3,2,7,8,6]=>[8,4,5,6,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,2,5,6,4]=>[1,2,8,4,3,7,6,5]=>[8,7,1,5,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,3,8,6,4]=>[1,5,3,2,7,6,8,4]=>[8,4,6,7,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,4,1,5,3]=>[1,7,5,4,2,8,3,6]=>[8,2,4,5,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,6,1,5,3]=>[1,7,5,6,2,3,8,4]=>[8,2,4,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,8,1,5,3]=>[1,7,5,8,3,6,2,4]=>[8,2,4,1,6,3,7,5]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,2,3,6,4]=>[1,7,6,3,5,2,4,8]=>[8,2,3,6,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,8,2,1,5,3]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,2,3,5,7]=>[1,6,3,8,7,5,2,4]=>[8,3,6,1,2,4,7,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,1,8,5,4]=>[1,7,5,2,3,6,8,4]=>[8,2,4,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,8,4,7,3]=>[1,5,8,3,2,6,4,7]=>[8,4,1,6,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,5,7,3,4]=>[1,2,8,4,6,7,3,5]=>[8,7,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,3,8,7,2]=>[1,5,3,6,8,2,4,7]=>[8,4,6,3,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,1,3,7,2]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,5,4,6,2]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,3,4,2,5,6,7,8,1]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,9,8,6]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,9,8,5]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,8,9,7,5]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,9,8,7,5]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,9,8,4]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,8,9,7,4]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,9,8,7,4]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,7,9,8,6,4]=>[1,2,3,4,5,7,8,6,9]=>[9,8,7,6,5,3,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,5,7,8,9,6,3]=>[1,2,3,4,5,7,9,6,8]=>[9,8,7,6,5,3,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,5,7,9,8,6,3]=>[1,2,3,4,5,7,8,6,9]=>[9,8,7,6,5,3,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,10,9,7]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,10,9,6]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,9,10,8,6]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,10,9,8,6]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,10,9,5]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,9,10,8,5]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,10,9,8,5]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,9,10,8,4]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,10,9,8,4]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,8,9,10,7,4]=>[1,2,3,4,5,6,8,10,7,9]=>[10,9,8,7,6,5,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,4,1,8,2,5,6,3]=>[1,7,6,5,2,4,8,3]=>[8,2,3,4,7,5,1,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,5,6,8,4]=>[1,3,7,8,4,2,5,6]=>[8,6,2,1,5,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,2,8,5,3]=>[1,6,8,3,2,4,7,5]=>[8,3,1,6,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,2,8,5,4]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,3,1,6,7]=>[1,4,5,3,2,8,7,6]=>[8,5,4,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,7,1,8,5,2]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,3,4,6,2]=>[1,7,6,4,2,8,3,5]=>[8,2,3,5,7,1,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,5,6,8,2]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,6,3,1,4]=>[1,8,4,7,2,5,6,3]=>[8,1,5,2,7,4,3,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,6,1,7,4]=>[1,8,4,5,6,2,3,7]=>[8,1,5,4,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,6,8,7,3]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,8,6,1,3]=>[1,5,8,3,2,4,7,6]=>[8,4,1,6,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,5,2,4,1]=>[1,3,6,2,7,4,8,5]=>[8,6,3,7,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,2,6,3,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,8,1,5,3]=>[1,7,5,8,3,2,6,4]=>[8,2,4,1,6,7,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,8,6,2,4]=>[1,2,5,8,4,3,7,6]=>[8,7,4,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,8,2,3,4]=>[1,6,2,7,3,5,8,4]=>[8,3,7,2,6,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,5,3,8,4]=>[1,6,3,2,7,8,4,5]=>[8,3,6,7,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,7,1,6,5]=>[1,4,8,5,7,6,2,3]=>[8,5,1,4,2,3,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,7,6,5,2]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,1,6,4,2]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,1,6,4,2]=>[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,6,5,1,4]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,1,7,6,3]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,1,7,6,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,1,7,6,2]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,4,7,2,3]=>[1,8,3,6,7,2,5,4]=>[8,1,6,3,2,7,4,5]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,2,5,8,3]=>[1,2,6,5,3,7,8,4]=>[8,7,3,4,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,8,3,2,4]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,7,4,1,2]=>[1,3,6,4,5,7,2,8]=>[8,6,3,5,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,7,4,3,2]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,8,4,7,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,4,2,3,1]=>[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,4,2,1,3]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,3,1,6,2,8]=>[1,4,3,5,2,7,6,8]=>[8,5,6,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,3,8,1,6,2]=>[1,4,3,5,8,2,7,6]=>[8,5,6,4,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,6,3,4,1]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,8,3,1,4]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,3,6,8,1,2]=>[1,4,3,5,6,8,2,7]=>[8,5,6,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,3,8,4,1]=>[1,2,7,4,6,8,3,5]=>[8,7,2,5,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,1,4,6,2]=>[1,8,2,7,6,4,3,5]=>[8,1,7,2,3,5,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,3,1,4,8,6]=>[1,2,7,8,6,4,3,5]=>[8,7,2,1,3,5,6,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,3,4,8,6,1]=>[1,2,7,6,8,3,5,4]=>[8,7,2,3,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,8,3,1,4]=>[1,5,8,4,2,7,3,6]=>[8,4,1,5,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,2,4,8,7]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,8,3,2,4]=>[1,5,8,4,2,7,3,6]=>[8,4,1,5,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,1,5,4,6]=>[1,3,7,4,2,8,6,5]=>[8,6,2,5,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,8,4,3,5]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,2,5,4,6]=>[1,7,4,3,8,6,5,2]=>[8,2,5,6,1,3,4,7]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,1,5,4,6]=>[1,2,7,4,3,8,6,5]=>[8,7,2,5,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,7,2,1,3]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,2,7,4,1,3]=>[1,5,7,2,8,3,6,4]=>[8,4,2,7,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,8,5,1,3]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,8,3,1,5]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,8,5,1,3]=>[1,4,2,7,3,6,5,8]=>[8,5,7,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,2,6,4,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,8,3,7,4]=>[1,5,8,4,2,6,3,7]=>[8,4,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,7,6,2,3]=>[1,8,3,5,7,2,4,6]=>[8,1,6,4,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,7,2,4,3]=>[1,8,3,6,2,5,7,4]=>[8,1,6,3,7,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,3,8,4,2]=>[1,5,3,6,8,2,7,4]=>[8,4,6,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,2,8,5,3]=>[1,6,8,3,2,7,5,4]=>[8,3,1,6,7,2,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,8,3,7,5]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,3,8,6,2]=>[1,7,6,8,2,4,3,5]=>[8,2,3,1,7,5,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,4,2,3,6]=>[1,2,5,4,8,6,3,7]=>[8,7,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,2,5,7,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,3,6,2,4]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,2,4,3,6]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,3,2,1,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,2,7,1,3]=>[1,6,7,2,8,3,5,4]=>[8,3,2,7,1,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,3,2,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,4,2,7,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,4,6,8,5]=>[1,7,8,5,4,2,3,6]=>[8,2,1,4,5,7,6,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,6,7,5,3]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,6,3,4,8]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,6,5,1,7]=>[1,4,3,8,7,2,5,6]=>[8,5,6,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,7,8,6,1,3]=>[1,5,8,3,4,7,2,6]=>[8,4,1,6,5,2,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,4,8,5,6]=>[1,7,5,4,3,2,6,8]=>[8,2,4,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,1,8,6,3]=>[1,2,4,7,6,8,3,5]=>[8,7,5,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,3,4,7,5]=>[1,8,5,3,6,4,2,7]=>[8,1,4,6,3,5,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,5,7,8,3]=>[1,6,7,8,3,4,2,5]=>[8,3,2,1,6,5,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,5,2,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,4,7,2,5]=>[1,2,8,5,4,6,7,3]=>[8,7,1,4,5,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,2,6,1,4]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,6,7,2,1,5]=>[1,3,8,5,7,2,4,6]=>[8,6,1,4,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,8,4,3,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,8,3,5,2]=>[1,2,4,7,5,8,3,6]=>[8,7,5,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,6,8,7,2]=>[1,4,3,5,6,8,2,7]=>[8,5,6,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,6,8,4,2]=>[1,3,5,6,8,2,7,4]=>[8,6,4,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,6,5,1,3]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,4,6,2,1]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,2,6,3,1]=>[1,4,5,2,8,3,7,6]=>[8,5,4,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,5,6,3,1]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,5,2,7,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,4,5,1,3]=>[1,2,6,5,4,8,3,7]=>[8,7,3,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,5,6,3,2]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,2,6,4,3]=>[1,5,2,7,4,8,3,6]=>[8,4,7,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,7,6,2,1]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,3,7,6,2,1]=>[1,4,3,8,2,5,7,6]=>[8,5,6,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,6,4,5,3]=>[1,2,7,5,6,4,8,3]=>[8,7,2,4,3,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,1,6,2,4]=>[1,3,7,2,5,4,8,6]=>[8,6,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,7,6,1,3]=>[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,5,1,7,4]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,6,7,3,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,6,3,1,7]=>[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,6,1,2,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,1,7,2,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,1,8,2,7]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,7,3,2,4]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,6,5,2,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,4,7,2,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,4,3,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,6,8,3,2,5]=>[1,4,6,3,7,2,5,8]=>[8,5,3,6,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,7,3,2,6]=>[1,8,6,3,4,5,7,2]=>[8,1,3,6,5,4,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,6,2,3,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,1,7,4,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,4,8,5,1]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,8,2,5,3]=>[1,4,7,5,8,3,2,6]=>[8,5,2,4,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,4,5,6,1]=>[1,7,6,5,4,8,2,3]=>[8,2,3,4,5,1,7,6]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,7,2,1,6]=>[1,5,7,2,8,6,3,4]=>[8,4,2,7,1,3,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,4,6,1,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,6,2,8,3]=>[1,4,7,8,3,2,5,6]=>[8,5,2,1,6,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,6,3,4,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,3,5,4,1]=>[1,7,4,8,2,3,6,5]=>[8,2,5,1,7,6,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,6,2,5,3]=>[1,4,7,5,6,2,8,3]=>[8,5,2,4,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,6,5,2,3]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,8,4,3,1]=>[1,7,3,5,8,2,6,4]=>[8,2,6,4,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,7,4,3,2]=>[1,6,4,8,2,5,7,3]=>[8,3,5,1,7,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,6,1,4,2]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,1,5,4,2]=>[1,3,7,4,6,5,2,8]=>[8,6,2,5,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,1,3,2,4]=>[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,2,7,4,3]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,4,2,1,7]=>[1,6,2,8,7,3,5,4]=>[8,3,7,1,2,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,4,3,1,7]=>[1,8,7,2,5,4,6,3]=>[8,1,2,7,4,5,3,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,1,4,7,3]=>[1,8,3,2,5,4,6,7]=>[8,1,6,7,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,1,8,5,4]=>[1,3,6,8,4,7,5,2]=>[8,6,3,1,5,2,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,8,2,1,5]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,8,4,1,5]=>[1,3,6,4,7,2,5,8]=>[8,6,3,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,8,5,4,2]=>[1,6,5,8,2,7,4,3]=>[8,3,4,1,7,2,5,6]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,5,2,4,3]=>[1,6,2,7,4,8,3,5]=>[8,3,7,2,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,8,5,3,4]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,8,3,2,5]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,8,3,2,5]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,2,6,4,5]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,5,4,6,3]=>[1,8,3,2,7,6,4,5]=>[8,1,6,7,2,3,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,6,5,3,1]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,2,3,5,4]=>[1,6,3,8,4,7,5,2]=>[8,3,6,1,5,2,4,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,7,3,4,5]=>[1,8,5,7,4,2,6,3]=>[8,1,4,2,5,7,3,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,5,4,1,3]=>[1,6,4,2,8,3,7,5]=>[8,3,5,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,8,7,5,1]=>[1,3,6,7,5,8,2,4]=>[8,6,3,2,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,6,5,1,3]=>[1,4,8,3,2,7,5,6]=>[8,5,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,6,5,3,2]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,3,6,1,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,6,1,5,2]=>[1,4,8,2,7,5,6,3]=>[8,5,1,7,2,4,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,7,2,5,1]=>[1,4,8,2,3,6,5,7]=>[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,5,7,6,1]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,8,7,2,5]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,7,5,2,3]=>[1,4,8,3,6,5,7,2]=>[8,5,1,6,3,4,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,5,7,2,6]=>[1,3,2,8,6,7,4,5]=>[8,6,7,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,2,5,7,6]=>[1,3,2,8,6,5,4,7]=>[8,6,7,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,6,8,7,1,5]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,5,7,6,1]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,7,1,3,6]=>[1,4,5,7,3,8,6,2]=>[8,5,4,2,6,1,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,1,3,2,8]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,1,3,2,5]=>[1,7,2,8,5,3,6,4]=>[8,2,7,1,4,6,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,5,6,3,8]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,4,6,5,8]=>[1,7,5,4,2,3,6,8]=>[8,2,4,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,5,6,2,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,5,8,7,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,7,1,6,8,5]=>[1,4,7,8,5,2,3,6]=>[8,5,2,1,4,7,6,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,5,6,3,2]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,5,3,7,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,5,3,7,4]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,3,6,7,1]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,3,6,7,1]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,4,8,7,1]=>[1,5,4,6,8,2,3,7]=>[8,4,5,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,8,6,7,1]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,8,6,7,1]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,8,6,7,1]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,5,6,8,3]=>[1,4,7,8,3,2,5,6]=>[8,5,2,1,6,7,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,2,8,3,1]=>[1,5,2,6,8,3,7,4]=>[8,4,7,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,6,8,3,1]=>[1,2,5,6,8,3,7,4]=>[8,7,4,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,3,8,6,1]=>[1,7,6,8,2,5,3,4]=>[8,2,3,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,5,4,7,3]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,5,2,7,3]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,5,4,7,3]=>[1,2,6,4,8,3,5,7]=>[8,7,3,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,5,4,7,2]=>[1,3,6,4,8,2,5,7]=>[8,6,3,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,4,6,7,1]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,4,6,7,1]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,2,6,7,1]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,3,6,7,1]=>[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,2,6,7,1]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,3,6,7,1]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,5,4,7,2]=>[1,6,4,3,8,2,5,7]=>[8,3,5,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,2,6,7,1]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,8,5,4,3]=>[1,6,5,8,3,2,4,7]=>[8,3,4,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,3,2,5,1]=>[1,7,5,3,6,2,4,8]=>[8,2,4,6,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,7,1,6,8]=>[1,3,5,7,6,2,4,8]=>[8,6,4,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,3,2,8,4]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,3,2,5,1]=>[1,8,2,4,7,5,3,6]=>[8,1,7,5,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,3,1,5,7]=>[1,8,7,5,3,6,2,4]=>[8,1,2,4,6,3,7,5]=>[8,2,3,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,5,4,2,6]=>[1,3,7,2,4,8,6,5]=>[8,6,2,7,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,1,8,6,7]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,6,1,2,3]=>[1,7,2,4,5,6,3,8]=>[8,2,7,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,1,3,7,4]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,1,5,3,8]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,3,6,2,8]=>[1,5,3,4,2,7,6,8]=>[8,4,6,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,3,8,2,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,7,3,2,5]=>[1,2,8,5,7,3,6,4]=>[8,7,1,4,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,6,3,5,2]=>[1,4,8,2,7,5,6,3]=>[8,5,1,7,2,4,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,2,1,7,5]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,4,1,7,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,4,6,5,1]=>[1,7,5,4,2,8,3,6]=>[8,2,4,5,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,7,3,6,1]=>[1,2,5,7,6,3,4,8]=>[8,7,4,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,7,4,2,5]=>[1,3,8,5,7,2,6,4]=>[8,6,1,4,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,8,3,1,6]=>[1,2,7,3,5,8,6,4]=>[8,7,2,6,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,2,1,3,4]=>[1,6,2,8,4,5,3,7]=>[8,3,7,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,2,8,4,3]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,7,8,4,3]=>[1,2,6,8,3,5,7,4]=>[8,7,3,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,5,6,2,3,1]=>[1,4,5,6,2,7,3,8]=>[8,5,4,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,6,1,4,3]=>[1,2,7,4,5,6,3,8]=>[8,7,2,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,1,5,3]=>[1,6,2,7,5,3,8,4]=>[8,3,7,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,2,5,7,3]=>[1,8,3,4,2,6,5,7]=>[8,1,6,5,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,7,2,5,8,3]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,5,4,2,1]=>[1,6,4,3,8,2,7,5]=>[8,3,5,6,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,1,5,3,4]=>[1,6,5,2,7,3,8,4]=>[8,3,4,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,7,4,1,8]=>[1,5,7,2,6,4,3,8]=>[8,4,2,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,5,4,8,1]=>[1,7,8,2,6,4,3,5]=>[8,2,1,7,3,5,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,3,6,1,7]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,4,1,6,3]=>[1,8,3,7,6,2,5,4]=>[8,1,6,2,3,7,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,8,1,4,3]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,8,5,1,4]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,6,4,2,5]=>[1,8,5,6,4,2,3,7]=>[8,1,4,3,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,3,7,2,4]=>[1,5,3,8,4,2,6,7]=>[8,4,6,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,6,1,2,5]=>[1,3,4,8,5,6,2,7]=>[8,6,5,1,4,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,3,2,4,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,7,4,2,3]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,6,1,3,5]=>[1,7,3,8,5,6,2,4]=>[8,2,6,1,4,3,7,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,3,8,1,5]=>[1,6,8,5,3,7,2,4]=>[8,3,1,4,6,2,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,6,2,3,5]=>[1,2,7,3,8,5,6,4]=>[8,7,2,6,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,6,2,3,5]=>[1,7,3,8,5,6,2,4]=>[8,2,6,1,4,3,7,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,7,3,8,2]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,6,2,8,5]=>[1,7,8,5,6,2,3,4]=>[8,2,1,4,3,7,6,5]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,6,5,8,7,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,7,2,8,5,3,1,6]=>[1,4,8,6,3,2,7,5]=>[8,5,1,3,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,6,3,2,5]=>[1,8,5,6,3,2,7,4]=>[8,1,4,3,6,7,2,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,4,7,1,3]=>[1,6,7,2,5,4,8,3]=>[8,3,2,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,8,6,3,2]=>[1,2,4,5,8,3,7,6]=>[8,7,5,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,4,7,2,5]=>[1,6,7,2,3,8,5,4]=>[8,3,2,7,6,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,8,4,1,7]=>[1,3,5,8,7,2,6,4]=>[8,6,4,1,2,7,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,2,3,7,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,8,4,2,1]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,2,1,3,6]=>[1,5,2,8,6,3,7,4]=>[8,4,7,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,7,8,6,4]=>[1,3,5,7,6,8,4,2]=>[8,6,4,2,3,1,5,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,2,5,4,6]=>[1,2,8,6,5,3,7,4]=>[8,7,1,3,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,8,7,3,6]=>[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,6,3,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,7,3,8,6]=>[1,2,5,7,8,6,3,4]=>[8,7,4,2,1,3,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,7,4,1,2]=>[1,8,2,6,4,5,7,3]=>[8,1,7,3,5,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,1,4,7,6]=>[1,8,6,4,2,5,3,7]=>[8,1,3,5,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,8,4,3,5]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,5,7,8,4]=>[1,2,6,7,8,4,3,5]=>[8,7,3,2,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,8,4,2,7]=>[1,2,6,4,5,8,7,3]=>[8,7,3,5,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,4,6,3,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,2,3,7,5]=>[1,4,6,3,8,5,2,7]=>[8,5,3,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,3,8,5,2]=>[1,2,7,5,3,6,8,4]=>[8,7,2,4,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,7,8,4,2]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,2,7,8,4]=>[1,2,5,3,6,7,8,4]=>[8,7,4,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,5,3,2,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,4,3,7,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,6,4,1,8]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,6,1,7,4]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,5,3,1,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,3,5,1,8]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,1,6,3,5]=>[1,8,5,2,4,7,3,6]=>[8,1,4,7,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,8,1,7,5]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,4,3,5,2]=>[1,8,2,7,5,4,3,6]=>[8,1,7,2,4,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,5,4,2]=>[1,8,2,7,4,3,6,5]=>[8,1,7,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,5,4,2,3]=>[1,8,3,6,4,2,7,5]=>[8,1,6,3,5,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,1,5,3,4]=>[1,8,4,7,3,2,6,5]=>[8,1,5,2,6,7,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,8,1,6,4]=>[1,5,8,4,2,3,7,6]=>[8,4,1,5,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,1,5,2,6]=>[1,7,2,8,6,5,3,4]=>[8,2,7,1,3,4,6,5]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,1,5,2,4]=>[1,8,4,7,2,6,5,3]=>[8,1,5,2,7,3,4,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,5,4,3]=>[1,8,3,6,5,2,7,4]=>[8,1,6,3,4,7,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,4,2,5,3]=>[1,8,3,6,2,7,5,4]=>[8,1,6,3,7,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,6,1,3,2]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,1,2,6,3]=>[1,8,3,5,2,7,6,4]=>[8,1,6,4,7,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,3,2,4]=>[1,8,4,2,6,3,7,5]=>[8,1,5,7,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,3,4,2,8]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,3,4,2,6]=>[1,5,3,8,6,4,2,7]=>[8,4,6,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,4,2,6,8]=>[1,7,6,2,5,4,3,8]=>[8,2,3,7,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,4,2,8,6]=>[1,5,4,3,2,7,8,6]=>[8,4,5,6,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,4,8,1,2]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,8,4,6,2]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,8,2,6,4]=>[1,2,5,8,4,3,7,6]=>[8,7,4,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,8,4,2,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,8,6,2,4]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,3,6,2,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,3,4,2,6]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,3,4,2,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,4,1,2,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,4,1,2,6]=>[1,3,5,4,8,6,2,7]=>[8,6,4,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,8,1,2,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,5,8,4,6]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,5,8,4,6]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,7,8,6,4]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,4,6,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,2,6,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,8,5,6,4]=>[1,3,2,7,6,5,8,4]=>[8,6,7,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,2,6,8,4]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,5,6,1,2]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,2,3,1,8]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,5,6,1,3]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,6,1,3,7]=>[1,5,6,2,8,7,3,4]=>[8,4,3,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,5,2,7,3]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,1,6,7,2]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,2,1,5,3]=>[1,6,2,8,3,7,5,4]=>[8,3,7,1,6,2,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,5,2,7,4]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,5,6,4,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,2,6,7,3]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,4,6,7,3]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,3,6,7,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,1,7,4,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,1,6,4,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,6,3,5,4]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,3,2,8,4]=>[1,5,3,6,2,7,8,4]=>[8,4,6,3,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,3,6,4,2]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,7,4,2,1]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,6,1,7,8,2]=>[1,3,4,6,7,8,2,5]=>[8,6,5,3,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,6,3,7,2]=>[1,8,2,3,5,6,4,7]=>[8,1,7,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,6,4,3,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,5,4,3,1]=>[1,8,2,6,4,7,3,5]=>[8,1,7,3,5,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,8,6,1,3]=>[1,5,8,3,7,2,4,6]=>[8,4,1,6,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,1,7,2,8]=>[1,3,6,7,2,5,4,8]=>[8,6,3,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,7,4,3,8]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,6,5,4,3]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,1,4,5,7]=>[1,6,4,3,8,7,5,2]=>[8,3,5,6,1,2,4,7]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,1,4,5,6]=>[1,2,7,5,3,8,6,4]=>[8,7,2,4,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,3,2,6,7,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,6,3,2,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,3,2,8,4]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,3,4,8,6]=>[1,2,7,8,6,4,3,5]=>[8,7,2,1,3,5,6,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,4,8,6,3]=>[1,2,7,6,8,3,5,4]=>[8,7,2,3,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,3,2,4,5]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,2,3,5,7]=>[1,2,4,6,3,8,7,5]=>[8,7,5,3,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,6,7,2,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,3,4,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,3,5,7,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,4,3,5,6]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,4,2,3,5]=>[1,2,8,5,4,7,3,6]=>[8,7,1,4,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,4,2,3,5]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,3,4,2,5]=>[1,2,6,4,8,5,3,7]=>[8,7,3,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,3,8,5,6]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,2,3,5,6]=>[1,2,7,5,3,8,6,4]=>[8,7,2,4,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,6,2,8,4]=>[1,2,7,8,4,5,6,3]=>[8,7,2,1,5,4,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,8,5,4,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,6,3,8,5]=>[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,2,3,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,4,5,2,6]=>[1,2,7,3,8,6,5,4]=>[8,7,2,6,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,5,6,3,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,6,2,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,2,6,1,4]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,2,5,1,6]=>[1,4,3,7,2,8,6,5]=>[8,5,6,2,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,6,7,4,2]=>[1,5,6,7,4,2,3,8]=>[8,4,3,2,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,3,7,6,4]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,6,2,7,5]=>[1,3,8,5,6,2,4,7]=>[8,6,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,5,2,3,7]=>[1,8,7,3,2,4,6,5]=>[8,1,2,6,7,5,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,4,3,5,2]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,5,3,4,2]=>[1,6,3,8,2,4,7,5]=>[8,3,6,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,2,4,1,5]=>[1,6,4,3,7,2,8,5]=>[8,3,5,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,6,8,4,1]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,5,8,1,6]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,4,5,1,3]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,3,1,5,2]=>[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,7,6,8,1]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,4,7,8,1]=>[1,5,4,6,7,8,2,3]=>[8,4,5,3,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,7,4,8,1]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,6,4,8,1]=>[1,5,6,4,7,8,2,3]=>[8,4,3,5,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,8,4,6,1]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,4,6,8,1]=>[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,4,6,8,1]=>[1,3,5,4,7,8,2,6]=>[8,6,4,5,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,4,8,6,1]=>[1,3,7,6,8,2,4,5]=>[8,6,2,3,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,4,8,6,1]=>[1,3,5,4,2,7,6,8]=>[8,6,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,6,4,7,2]=>[1,8,2,3,5,6,4,7]=>[8,1,7,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,1,3,7,2]=>[1,8,2,4,6,3,5,7]=>[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,1,3,6,7]=>[1,5,2,3,8,7,6,4]=>[8,4,7,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,1,6,3,8]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,3,4,2,5]=>[1,8,5,3,6,4,7,2]=>[8,1,4,6,3,5,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,7,4,3,5]=>[1,8,5,7,3,2,4,6]=>[8,1,4,2,6,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,9,5,6,8,7]=>[1,2,3,4,5,9,7,6,8]=>[9,8,7,6,5,1,3,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,8,5,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,9,6,8,7]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,9,6,8,7]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,9,10,7,8]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,5,2,3,6,8,7,4]=>[1,2,5,6,8,4,3,7]=>[8,7,4,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,9,8,7]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,1,2,5,6,8,9,7]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,4,9,5,6,8,7]=>[1,2,3,4,5,9,7,6,8]=>[9,8,7,6,5,1,3,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,11,10,9]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,10,9,8,7,6,5,4,3,1,2]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,5,7,4,1,8,2,6]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,5,1,2,3]=>[1,8,3,4,7,2,6,5]=>[8,1,6,5,2,7,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,2,5,3,7]=>[1,8,7,3,4,2,6,5]=>[8,1,2,6,5,7,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,1,6,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,1,4,7,2]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,5,4,2,1]=>[1,6,4,3,7,2,8,5]=>[8,3,5,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,5,7,4,6]=>[1,3,2,4,8,6,7,5]=>[8,6,7,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,5,8,4,6]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,2,1,4,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,5,7,4,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,8,4,5,6]=>[1,7,5,8,6,4,2,3]=>[8,2,4,1,3,5,7,6]=>[8,4,5,2,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,6,3,5,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,3,8,1,6]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,6,7,3,1]=>[1,8,2,4,5,6,7,3]=>[8,1,7,5,4,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,3,7,8,2]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,6,7,8,2]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,4,8,2,3]=>[1,6,8,3,7,2,4,5]=>[8,3,1,6,2,7,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,6,8,4,5]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,4,7,6,3]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,4,7,3,2]=>[1,5,4,6,7,3,2,8]=>[8,4,5,3,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,7,2,4,1]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,7,3,5,2]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,7,4,5,3]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,8,3,2,4]=>[1,5,8,4,6,3,2,7]=>[8,4,1,5,3,6,7,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,8,3,4,7]=>[1,5,8,7,4,2,6,3]=>[8,4,1,2,5,7,3,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,7,1,4,3]=>[1,8,3,5,7,4,6,2]=>[8,1,6,4,2,5,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,6,8,3,1,5]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,7,8,1,3,5]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,2,8,5,7]=>[1,6,8,7,5,2,3,4]=>[8,3,1,2,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,6,1,5,3]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,5,7,3,1]=>[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,4,2,5,1]=>[1,3,8,2,7,5,4,6]=>[8,6,1,7,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,7,5,1,3]=>[1,6,5,7,2,3,8,4]=>[8,3,4,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,6,8,1,2]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,6,5,1,2]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,5,1,4,8]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,4,1,5,8]=>[1,3,7,5,4,6,2,8]=>[8,6,2,4,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,7,1,4,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,8,5,2,4]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,1,6,3,7]=>[1,4,5,2,3,8,7,6]=>[8,5,4,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,4,2,3,7]=>[1,6,2,5,4,3,8,7]=>[8,3,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,1,5,7,8]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,1,6,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,1,6,2,8]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,8,5,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,5,8,7,3]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,8,4,3,6,2]=>[1,7,6,3,2,5,4,8]=>[8,2,3,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,7,6,4,2]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,4,6,3,2]=>[1,5,4,7,3,8,2,6]=>[8,4,5,2,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,5,1,3,6]=>[1,2,4,7,3,8,6,5]=>[8,7,5,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,1,8,4,2]=>[1,3,7,4,6,8,2,5]=>[8,6,2,5,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,2,8,4,1]=>[1,3,7,4,6,8,2,5]=>[8,6,2,5,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,8,7,5,2]=>[1,6,7,5,8,2,3,4]=>[8,3,2,4,1,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,7,4,2,5]=>[1,6,4,8,5,7,2,3]=>[8,3,5,1,4,2,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,8,7,4,1]=>[1,5,8,2,3,6,7,4]=>[8,4,1,7,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,3,7,6,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,8,7,6,2]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,8,1,2,6]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,5,4,3,1]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,1,4,3,5]=>[1,7,3,6,4,8,5,2]=>[8,2,6,3,5,1,4,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,7,4,5,2]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,7,1,8,6,5]=>[1,2,4,7,6,8,5,3]=>[8,7,5,2,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,3,8,4,1]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,4,1,5,3]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,7,1,8,3]=>[1,2,6,3,5,7,8,4]=>[8,7,3,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,6,1,7,2]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,2,5,8,3]=>[1,6,5,2,3,7,8,4]=>[8,3,4,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,5,4,2,3]=>[1,6,4,2,8,3,7,5]=>[8,3,5,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,5,7,6,2]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,7,1,6,4]=>[1,5,7,6,2,3,8,4]=>[8,4,2,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,2,7,1,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,1,5,3,4]=>[1,8,4,7,3,6,5,2]=>[8,1,5,2,6,3,4,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,6,3,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,3,4,5,2]=>[1,6,4,8,2,7,5,3]=>[8,3,5,1,7,2,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,8,4,5,2]=>[1,3,2,7,5,8,4,6]=>[8,6,7,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,6,7,1,4]=>[1,3,5,6,7,2,8,4]=>[8,6,4,3,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,7,1,4,8]=>[1,3,5,7,4,2,6,8]=>[8,6,4,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,7,1,5,2]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,6,3,5,2]=>[1,7,5,6,3,8,2,4]=>[8,2,4,3,6,1,7,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,7,1,5,2]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,4,8,6,5,2]=>[1,3,2,7,5,8,4,6]=>[8,6,7,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,4,5,2,8,6]=>[1,3,2,7,8,6,4,5]=>[8,6,7,2,1,3,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,5,8,1,4]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,8,2,1,4]=>[1,3,7,2,5,8,4,6]=>[8,6,2,7,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,7,5,2,8]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,7,5,1,8]=>[1,4,3,6,5,7,2,8]=>[8,5,6,3,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,6,4,1,8]=>[1,5,6,4,3,7,2,8]=>[8,4,3,5,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,5,4,1,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,5,4,1,7]=>[1,6,4,2,3,8,7,5]=>[8,3,5,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,6,5,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,5,4,1,6]=>[1,8,6,4,2,3,7,5]=>[8,1,3,5,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,6,4,1,7]=>[1,5,6,4,3,8,7,2]=>[8,4,3,5,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,6,5,1,7]=>[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,1,6,3,7]=>[1,8,7,3,5,2,4,6]=>[8,1,2,6,4,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,7,5,2,6]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,4,8,5,3,7]=>[1,6,5,8,7,3,2,4]=>[8,3,4,1,2,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,8,6,3,7]=>[1,5,8,7,3,2,4,6]=>[8,4,1,2,6,7,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,7,4,1,6]=>[1,5,7,2,3,8,6,4]=>[8,4,2,7,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,4,1,5]=>[1,8,5,6,4,2,3,7]=>[8,1,4,3,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,8,5,2,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,8,5,2,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,7,4,1,5]=>[1,8,5,7,2,3,6,4]=>[8,1,4,2,7,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,8,4,1,5]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,8,4,1,6]=>[1,5,8,6,4,3,7,2]=>[8,4,1,3,5,6,2,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,8,5,1,6]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,8,4,1,7]=>[1,5,8,7,2,3,6,4]=>[8,4,1,2,7,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,8,4,1,6]=>[1,7,2,3,5,8,6,4]=>[8,2,7,6,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,7,4,1,6]=>[1,8,6,4,3,5,7,2]=>[8,1,3,5,6,4,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,8,5,2,7]=>[1,2,3,6,5,8,7,4]=>[8,7,6,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,8,6,2,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,7,5,1,6]=>[1,8,6,5,7,2,3,4]=>[8,1,3,4,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,8,5,1,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,8,6,1,7]=>[1,5,8,7,2,3,4,6]=>[8,4,1,2,7,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,1,7,6,8]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,3,1,7,5,8]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,1,6,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,7,6,3,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,3,1,7,4,8]=>[1,6,7,4,3,5,2,8]=>[8,3,2,5,6,4,7,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,1,7,5,8]=>[1,3,6,7,5,2,4,8]=>[8,6,3,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,1,6,5,8]=>[1,3,7,5,2,4,6,8]=>[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,1,6,5,8]=>[1,4,3,7,5,2,6,8]=>[8,5,6,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,1,6,4,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,1,5,4,8]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,8,6,3,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,4,7,5,8]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,1,5,3,7]=>[1,6,5,2,3,8,7,4]=>[8,3,4,7,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,5,6,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,4,8,1,7]=>[1,6,8,7,2,3,5,4]=>[8,3,1,2,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,7,4,3,6]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,1,4,3,6]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,2,6,8,4]=>[1,7,8,4,3,5,2,6]=>[8,2,1,5,6,4,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,8,6,2,4]=>[1,3,5,8,4,7,2,6]=>[8,6,4,1,5,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,1,5,7,4]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,4,8,6,3]=>[1,2,5,4,7,6,8,3]=>[8,7,4,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,3,6,8,5]=>[1,2,4,7,8,5,3,6]=>[8,7,5,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,2,4,8,5]=>[1,2,7,8,5,3,6,4]=>[8,7,2,1,4,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,7,8,5,3]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,4,7,8,5]=>[1,2,6,7,8,5,4,3]=>[8,7,3,2,1,4,5,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,5,8,4,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,5,6,2,3]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,2,4,5,8]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,8,4,5,6,1]=>[1,2,7,6,5,4,8,3]=>[8,7,2,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,8,3,4,1]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,5,6,2,3]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,5,7,2,3]=>[1,6,7,2,4,3,8,5]=>[8,3,2,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,6,3,5,7]=>[1,2,3,8,7,5,6,4]=>[8,7,6,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,4,6,3,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,4,5,7,2]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,6,3,7,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,4,1,7,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,4,7,5,3]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,6,3,5,4]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,4,7,1,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,7,3,5,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,7,1,6,5]=>[1,8,5,7,6,2,4,3]=>[8,1,4,2,3,7,5,6]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,7,3,1,6]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,1,3,7,4]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,2,7,4,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,6,7,1,5]=>[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,1,8,5,3]=>[1,4,6,8,3,7,5,2]=>[8,5,3,1,6,2,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,6,3,5,1]=>[1,7,5,6,3,4,8,2]=>[8,2,4,3,6,5,1,7]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,1,8,4,7]=>[1,3,5,2,6,8,7,4]=>[8,6,4,7,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,2,1,6,8]=>[1,4,7,6,2,5,3,8]=>[8,5,2,3,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,1,6,7,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,3,2,7,1,6]=>[1,4,3,8,6,7,2,5]=>[8,5,6,1,3,2,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,2,3,6,1]=>[1,5,2,4,8,3,7,6]=>[8,4,7,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,1,6,7,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,2,4,5,6,7,8,3]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,3,4,5,6,7,8,2]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,6,7,4,5,2,8,1]=>[1,3,7,8,2,6,4,5]=>[8,6,2,1,7,3,5,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,2,4,8,1]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,3,1,5,2]=>[1,6,2,4,8,3,7,5]=>[8,3,7,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,1,5,6,2]=>[1,8,2,4,3,7,6,5]=>[8,1,7,5,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,8,3,4,2]=>[1,5,8,2,6,3,7,4]=>[8,4,1,7,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,2,5,4,3]=>[1,7,4,6,5,2,3,8]=>[8,2,5,3,4,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,6,4,7,3]=>[1,2,5,6,4,3,8,7]=>[8,7,4,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,6,8,3,2]=>[1,2,5,6,8,3,7,4]=>[8,7,4,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,6,8,3,2]=>[1,2,4,5,6,8,3,7]=>[8,7,5,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,8,1,3,2]=>[1,5,8,2,6,3,7,4]=>[8,4,1,7,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,4,5,7,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,5,4,8,3]=>[1,2,6,4,3,7,8,5]=>[8,7,3,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,5,8,1,4]=>[1,3,7,2,4,6,8,5]=>[8,6,2,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,5,8,2,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,5,6,3,2]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,1,3,4,5,6,7,8,9,2]=>[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,11,9,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,10,9,8,7,6,5,4,3,1,2]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,2,7,4,5,8,3,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,5,8,1,4]=>[1,6,8,4,2,7,3,5]=>[8,3,1,5,7,2,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,2,8,7,3]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,1,6,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,4,6,3,2]=>[1,2,5,4,7,3,8,6]=>[8,7,4,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,8,1,5,4]=>[1,3,2,7,5,8,4,6]=>[8,6,7,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,5,1,4,3]=>[1,2,7,4,8,3,6,5]=>[8,7,2,5,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,7,3,8,2]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,8,6,2,3]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,8,2,5,4]=>[1,7,5,8,4,6,2,3]=>[8,2,4,1,5,3,7,6]=>[8,4,6,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,5,2,4,3]=>[1,7,4,8,3,6,2,5]=>[8,2,5,1,6,3,7,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,6,2,4,3]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,4,7,8,5]=>[1,3,2,6,7,8,5,4]=>[8,6,7,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,9,1,6,7]=>[1,2,3,4,5,8,6,9,7]=>[9,8,7,6,5,2,4,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,6,3,2,1,5,4,7]=>[1,8,7,4,2,6,5,3]=>[8,1,2,5,7,3,4,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,4,1,7,6]=>[1,8,6,2,5,4,3,7]=>[8,1,3,7,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,6,3,2,7]=>[1,8,7,2,5,6,3,4]=>[8,1,2,7,4,3,6,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,3,4,2,7]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,1,5,2,7]=>[1,8,7,2,4,6,5,3]=>[8,1,2,7,5,3,4,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,8,7,1,5]=>[1,6,7,2,4,3,5,8]=>[8,3,2,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,3,7,2,6]=>[1,8,6,7,2,5,3,4]=>[8,1,3,2,7,4,6,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,3,7,6]=>[1,8,6,3,4,2,5,7]=>[8,1,3,6,5,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,1,8,5,2]=>[1,4,6,8,2,7,5,3]=>[8,5,3,1,7,2,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,1,5,8,3]=>[1,7,8,3,2,6,5,4]=>[8,2,1,6,7,3,4,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,7,4,2,5]=>[1,8,5,7,2,3,6,4]=>[8,1,4,2,7,6,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,6,7,1,4]=>[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,3,7,1,5]=>[1,8,5,3,4,6,7,2]=>[8,1,4,6,5,3,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,3,5,8,1]=>[1,7,8,2,3,6,5,4]=>[8,2,1,7,6,3,4,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,4,5,8,1]=>[1,7,8,2,3,6,5,4]=>[8,2,1,7,6,3,4,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,1,4,6,5]=>[1,8,5,2,3,7,6,4]=>[8,1,4,7,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,3,2,8,5]=>[1,7,8,5,3,4,2,6]=>[8,2,1,4,6,5,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,1,5,6,4]=>[1,7,6,5,2,3,8,4]=>[8,2,3,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,7,4,3,8,1]=>[1,6,3,5,4,7,8,2]=>[8,3,6,4,5,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,4,8,7,1,3]=>[1,6,7,2,3,5,8,4]=>[8,3,2,7,6,4,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,8,5,1,3]=>[1,4,6,5,8,3,7,2]=>[8,5,3,4,1,6,2,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,7,4,8,3,2]=>[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,7,8,3,4,2]=>[1,6,3,5,8,2,4,7]=>[8,3,6,4,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,1,8,5,2]=>[1,4,3,7,5,2,6,8]=>[8,5,6,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,5,8,7,3]=>[1,6,8,3,4,2,5,7]=>[8,3,1,6,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,4,6,2,7]=>[1,2,5,4,8,7,3,6]=>[8,7,4,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,8,4,1,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,8,5,1,3]=>[1,7,2,6,5,8,3,4]=>[8,2,7,3,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,8,5,3,2]=>[1,2,7,3,6,5,8,4]=>[8,7,2,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,3,2,6,5]=>[1,8,5,3,4,2,7,6]=>[8,1,4,6,5,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,3,6,2,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,7,6,2,3]=>[1,4,5,7,2,3,8,6]=>[8,5,4,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,4,2,1,6]=>[1,3,5,4,8,6,2,7]=>[8,6,4,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,3,4,2,7]=>[1,6,4,8,7,2,3,5]=>[8,3,5,1,2,7,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,7,3,4,8]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,3,7,1,5]=>[1,4,8,5,3,6,7,2]=>[8,5,1,4,6,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,4,2,3,7]=>[1,6,2,8,7,3,5,4]=>[8,3,7,1,2,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,1,3,6,2]=>[1,7,6,3,4,5,2,8]=>[8,2,3,6,5,4,7,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,3,4,6,2]=>[1,2,7,6,4,5,3,8]=>[8,7,2,3,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,6,4,7,2]=>[1,2,5,6,4,3,8,7]=>[8,7,4,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,4,2,7,5]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,6,3,7,2]=>[1,4,5,6,3,2,8,7]=>[8,5,4,3,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,2,6,5,4]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,6,5,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,5,3,6,2]=>[1,8,2,4,3,7,6,5]=>[8,1,7,5,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,4,6,1,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,5,3,1,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,6,2,7,1]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,3,4,5,8]=>[1,7,5,3,2,4,6,8]=>[8,2,4,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,6,3,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,6,2,5,8]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,4,2,3,8]=>[1,7,3,6,2,4,5,8]=>[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,1,7,2,6]=>[1,5,2,8,6,7,3,4]=>[8,4,7,1,3,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,2,4,7,1]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,3,2,6,1]=>[1,5,3,8,2,7,6,4]=>[8,4,6,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,7,2,6,5]=>[1,2,3,8,5,7,6,4]=>[8,7,6,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,5,8,6,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,2,8,5,4]=>[1,6,8,4,3,2,7,5]=>[8,3,1,5,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,7,2,8,6]=>[1,5,7,8,6,2,4,3]=>[8,4,2,1,3,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,8,2,6,1]=>[1,5,8,2,4,7,6,3]=>[8,4,1,7,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,6,2,4,1]=>[1,3,5,6,2,8,4,7]=>[8,6,4,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,7,2,5,4]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,4,2,3,6]=>[1,5,4,2,8,6,3,7]=>[8,4,5,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,1,4,5,8]=>[1,2,6,4,7,5,3,8]=>[8,7,3,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,3,1,5,2]=>[1,7,5,3,8,2,6,4]=>[8,2,4,6,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,4,1,3,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,5,8,3,2]=>[1,4,2,7,3,6,8,5]=>[8,5,7,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,1,3,2,4,5,6,7,8]=>[1,9,8,7,6,5,4,2,3]=>[9,1,2,3,4,5,6,8,7]=>[9,2,3,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,8,7,1,5,4,3,2]=>[1,6,4,2,8,3,7,5]=>[8,3,5,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,6,9,8,1,10]=>[1,3,5,7,9,2,4,6,8,10]=>[10,8,6,4,2,9,7,5,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,4,3,6,5,8,7,10,9,1]=>[1,2,4,6,8,10,3,5,7,9]=>[10,9,7,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,2,6,1,5,8,3,4]=>[1,7,3,6,8,4,2,5]=>[8,2,6,3,1,5,7,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,6,2,5,1]=>[1,4,8,2,7,5,6,3]=>[8,5,1,7,2,4,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,8,2,1,5]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,8,2,1,6]=>[1,5,8,6,2,4,3,7]=>[8,4,1,3,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,6,3,5,1]=>[1,8,2,7,5,6,3,4]=>[8,1,7,2,4,3,6,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,5,4,3,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,7,1,4,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,7,3,6,1]=>[1,5,7,6,3,4,2,8]=>[8,4,2,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,4,6,3,7]=>[1,8,7,3,5,4,2,6]=>[8,1,2,6,4,5,7,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,4,5,7,2]=>[1,8,2,6,5,4,3,7]=>[8,1,7,3,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,4,6,7,3]=>[1,8,3,2,5,4,6,7]=>[8,1,6,7,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,7,3,4,5,1]=>[1,2,6,4,7,5,3,8]=>[8,7,3,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,6,4,2,3]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,4,6,7,5]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,8,2,4,6]=>[1,3,7,4,5,8,6,2]=>[8,6,2,5,4,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,4,2,3,7]=>[1,8,7,3,5,4,6,2]=>[8,1,2,6,4,5,3,7]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,4,3,2,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,5,4,3,7]=>[1,2,6,4,3,8,7,5]=>[8,7,3,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,6,3,8,4]=>[1,5,6,3,2,4,7,8]=>[8,4,3,6,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,1,4,7,6]=>[1,3,8,6,4,2,5,7]=>[8,6,1,3,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,3,7,6,1]=>[1,4,5,3,8,2,6,7]=>[8,5,4,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,3,7,2,6]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,7,4,5,1]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,5,6,2,1]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,7,6,2,4]=>[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,5,7,3,4]=>[1,8,4,6,7,3,2,5]=>[8,1,5,3,2,6,7,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,4,5,8,3]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,1,8,3,4]=>[1,7,3,6,8,4,5,2]=>[8,2,6,3,1,5,4,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,6,3,1,7]=>[1,4,5,6,3,8,7,2]=>[8,5,4,3,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,8,7,3,5]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,5,1,6,8]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,8,7,1,6]=>[1,4,3,5,8,6,7,2]=>[8,5,6,4,1,3,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,7,4,5,2]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,5,4,6,1]=>[1,8,2,7,6,4,3,5]=>[8,1,7,2,3,5,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,8,3,2,4]=>[1,7,2,5,8,4,3,6]=>[8,2,7,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,7,3,1,8]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,1,6,2,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,4,1,8,6,5]=>[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,7,5,3,8]=>[1,2,4,6,5,7,3,8]=>[8,7,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,5,2,4,8]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,6,5,2,3]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,8,6,7,2]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,5,8,1,3]=>[1,4,7,2,6,8,3,5]=>[8,5,2,7,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,1,8,4,6]=>[1,7,4,5,2,3,6,8]=>[8,2,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,2,3,5,6]=>[1,7,5,2,8,6,3,4]=>[8,2,4,7,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,1,3,7,6]=>[1,8,6,3,2,5,4,7]=>[8,1,3,6,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,3,6,8,7]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,3,7,6,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,5,3,1,4]=>[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,1,5,4,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,5,2,6,7]=>[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,7,2,8,5]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,8,2,6,3]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,4,5,8,7]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,5,2,4,3]=>[1,7,4,6,2,8,3,5]=>[8,2,5,3,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,5,1,2,4]=>[1,3,8,4,6,2,7,5]=>[8,6,1,5,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,7,3,1,6]=>[1,4,2,5,7,3,8,6]=>[8,5,7,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,7,3,1,4]=>[1,6,3,8,4,2,5,7]=>[8,3,6,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,7,3,1,5]=>[1,6,3,8,5,7,2,4]=>[8,3,6,1,4,2,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,6,4,2,5]=>[1,7,2,8,5,6,4,3]=>[8,2,7,1,4,3,5,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,3,2,1,6]=>[1,4,8,6,2,5,3,7]=>[8,5,1,3,7,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,2,6,8,1]=>[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,3,6,8,1]=>[1,5,3,4,2,7,8,6]=>[8,4,6,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,2,8,1,6]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,4,5,1,7]=>[1,6,5,4,2,8,7,3]=>[8,3,4,5,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,6,1,2,7]=>[1,5,6,2,8,7,3,4]=>[8,4,3,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,5,1,2,7]=>[1,6,2,4,8,7,3,5]=>[8,3,7,5,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,2,3,1,7]=>[1,5,2,4,8,7,3,6]=>[8,4,7,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,1,2,3,7]=>[1,5,2,6,3,8,7,4]=>[8,4,7,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,3,1,4,6]=>[1,5,3,8,6,2,7,4]=>[8,4,6,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,3,1,2,4,7]=>[1,5,2,8,7,4,3,6]=>[8,4,7,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,1,3,4,7]=>[1,6,3,5,2,8,7,4]=>[8,3,6,4,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,2,4,8,7]=>[1,5,2,6,4,3,7,8]=>[8,4,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,6,2,7,3]=>[1,8,3,5,6,2,4,7]=>[8,1,6,4,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,8,5,7,1]=>[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,1,8,6,4]=>[1,5,2,3,7,6,8,4]=>[8,4,7,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,7,2,1,6]=>[1,5,7,2,4,3,8,6]=>[8,4,2,7,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,2,1,7,4]=>[1,3,8,4,5,2,6,7]=>[8,6,1,5,4,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,4,7,2,8,3]=>[1,6,2,3,5,7,8,4]=>[8,3,7,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,8,2,7,4]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,2,7,1,6]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,2,1,6,8]=>[1,5,2,4,7,6,3,8]=>[8,4,7,5,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,8,2,1,6]=>[1,5,8,6,2,4,7,3]=>[8,4,1,3,7,5,2,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,2,9,1]=>[1,3,5,7,2,4,6,8,9]=>[9,7,5,3,8,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,2,10,1]=>[1,3,5,7,9,10,2,4,6,8]=>[10,8,6,4,2,1,9,7,5,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,2,1,9,8]=>[1,3,5,7,2,4,6,8,9]=>[9,7,5,3,8,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,5,6,7,8,9,4,3]=>[1,2,3,5,7,9,4,6,8]=>[9,8,7,5,3,1,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,5,6,7,8,9,10,3,1]=>[1,2,4,6,8,10,3,5,7,9]=>[10,9,7,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,2,5,3,8,4,1]=>[1,6,8,2,7,4,5,3]=>[8,3,1,7,2,5,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,8,1,2,7,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,7,4,5,3]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,6,5,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,4,6,2,1]=>[1,3,8,2,5,4,7,6]=>[8,6,1,7,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,3,4,2,1]=>[1,6,4,7,2,8,3,5]=>[8,3,5,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,8,4,2,1,7]=>[1,5,4,8,7,2,3,6]=>[8,4,5,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,4,1,5,7]=>[1,6,2,3,8,7,5,4]=>[8,3,7,6,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,7,6,3,5]=>[1,2,4,8,5,7,3,6]=>[8,7,5,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,4,7,2,6]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,5,1,6,4]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,6,1,3,2]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,4,1,3,6]=>[1,5,4,2,8,6,3,7]=>[8,4,5,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,6,2,8,7]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,1,7,4,2]=>[1,6,7,4,5,2,3,8]=>[8,3,2,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,1,3,7,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,8,2,7,1]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,6,1,7,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,5,2,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,8,1,5,6]=>[1,2,7,5,8,6,3,4]=>[8,7,2,4,1,3,6,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,6,4,1,5]=>[1,3,2,8,5,6,4,7]=>[8,6,7,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,1,8,4,7]=>[1,5,2,3,6,8,7,4]=>[8,4,7,6,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,2,7,1,5]=>[1,4,6,7,2,3,8,5]=>[8,5,3,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,2,7,5,4]=>[1,3,6,7,5,2,4,8]=>[8,6,3,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,7,2,1,4]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,7,6,4,3]=>[1,2,5,7,4,8,3,6]=>[8,7,4,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,6,5,3,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,6,5,8,3]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,8,7,3,1]=>[1,4,6,7,3,5,8,2]=>[8,5,3,2,6,4,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,7,4,2,1]=>[1,6,4,3,8,2,5,7]=>[8,3,5,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,6,3,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,1,6,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,6,3,2,4]=>[1,7,2,8,4,5,6,3]=>[8,2,7,1,5,4,3,6]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,2,5,4,6]=>[1,2,7,4,3,8,6,5]=>[8,7,2,5,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,2,5,6,4]=>[1,7,6,5,2,8,4,3]=>[8,2,3,4,7,1,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,5,4,6,2]=>[1,7,6,4,3,2,8,5]=>[8,2,3,5,6,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,5,2,4,6]=>[1,7,4,3,2,8,6,5]=>[8,2,5,6,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,5,2,4,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,5,2,6,4]=>[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,2,5,6,4]=>[1,2,7,6,5,3,8,4]=>[8,7,2,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,4,6,1,2]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,4,8,1,2]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,5,4,2,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,2,5,4,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,8,5,4,6]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,8,4,1,2]=>[1,3,7,2,5,8,4,6]=>[8,6,2,7,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,8,3,4,2]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,3,8,5,6]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,5,4,1,6]=>[1,7,2,3,4,8,6,5]=>[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,7,6,3,8,2]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,3,8,5,10,7,9]=>[1,2,4,6,8,10,9,7,5,3]=>[10,9,7,5,3,1,2,4,6,8]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,4,8,2,3,6,5,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,3,5,2,8]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,6,7,5,3]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,4,5,6,8]=>[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,4,5,8,6]=>[1,2,7,8,6,5,4,3]=>[8,7,2,1,3,4,5,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,2,5,7,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,3,1,7,8]=>[1,4,5,3,6,2,7,8]=>[8,5,4,6,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,8,7,4,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,1,7,6,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,4,2,6,1]=>[1,3,8,2,7,6,4,5]=>[8,6,1,7,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,5,6,1,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,7,4,2,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,5,4,6,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,6,3,5,7]=>[1,2,4,8,7,5,6,3]=>[8,7,5,1,2,4,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,5,3,4,7]=>[1,6,3,8,7,4,2,5]=>[8,3,6,1,2,5,7,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,2,7,1,5]=>[1,3,6,7,2,8,5,4]=>[8,6,3,2,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,3,6,8,7]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,3,4,8,7]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,8,6,7,5]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,5,8,7,4,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,8,4,7,3]=>[1,6,4,2,5,8,3,7]=>[8,3,5,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,8,1,4,6]=>[1,3,5,8,6,2,7,4]=>[8,6,4,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,3,2,8,6]=>[1,5,3,4,7,8,6,2]=>[8,4,6,5,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,8,6,1,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,7,5,1,8]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,4,8,1,6]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,1,5,8,4]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,1,7,6,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,2,5,8,4]=>[1,3,6,5,2,7,8,4]=>[8,6,3,4,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,8,5,3,2]=>[1,4,6,5,8,2,7,3]=>[8,5,3,4,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,3,5,2,7]=>[1,4,6,5,3,8,7,2]=>[8,5,3,4,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,6,2,3,7]=>[1,4,8,7,3,5,6,2]=>[8,5,1,2,6,4,3,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,6,2,8,7,1]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,3,7,1,2]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,8,2,6,1]=>[1,5,8,2,7,6,3,4]=>[8,4,1,7,2,3,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,7,8,3,1]=>[1,5,7,3,4,2,6,8]=>[8,4,2,6,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,4,1,2,8]=>[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,3,8,1,2]=>[1,6,8,2,4,5,3,7]=>[8,3,1,7,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,8,3,1,2]=>[1,5,8,2,7,3,6,4]=>[8,4,1,7,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,3,1,6,2]=>[1,5,3,4,8,2,7,6]=>[8,4,6,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,8,7,2,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,1,8,4,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,3,1,7,4]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,3,6,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,5,3,6,8]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,3,2,6,8]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,3,5,2,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,4,8,2,1,7]=>[1,3,6,2,5,8,7,4]=>[8,6,3,7,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,5,2,3,8]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,7,4,3,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,2,5,7,4]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,4,6,3,2]=>[1,7,3,8,2,5,4,6]=>[8,2,6,1,7,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,8,1,5,3]=>[1,4,7,5,8,3,6,2]=>[8,5,2,4,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,8,1,5,2]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,3,2,6,1,7]=>[1,4,3,5,2,8,7,6]=>[8,5,6,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,3,6,1,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,2,4,7,6]=>[1,8,6,4,3,5,2,7]=>[8,1,3,5,6,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,2,7,4,5]=>[1,8,5,2,6,7,4,3]=>[8,1,4,7,3,2,5,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,8,1,5,4]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,1,5,4,2]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,8,1,5,4]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,7,5,6,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,3,2,6,7]=>[1,2,4,5,3,8,7,6]=>[8,7,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,4,1,5,3]=>[1,8,3,7,5,4,6,2]=>[8,1,6,2,4,5,3,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,8,5,1,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,3,1,5,4]=>[1,6,2,8,4,7,5,3]=>[8,3,7,1,5,2,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,1,7,5]=>[1,8,5,4,3,6,2,7]=>[8,1,4,5,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,3,6,7,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,1,3,2,6]=>[1,4,7,2,8,6,3,5]=>[8,5,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,7,4,6,3]=>[1,5,7,6,4,8,3,2]=>[8,4,2,3,5,1,6,7]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,4,6,3,5]=>[1,8,5,4,7,3,2,6]=>[8,1,4,5,2,6,7,3]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,3,6,7,1]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,3,2,7,4]=>[1,5,3,6,2,4,8,7]=>[8,4,6,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,8,2,7,3]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,4,1,3,6]=>[1,5,4,2,7,3,8,6]=>[8,4,5,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,8,4,7,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,8,4,3,5]=>[1,6,4,7,3,2,5,8]=>[8,3,5,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,8,4,7,6]=>[1,5,8,6,4,3,2,7]=>[8,4,1,3,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,5,4,1]=>[1,6,5,2,7,4,3,8]=>[8,3,4,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,4,8,1,3]=>[1,5,4,6,8,3,2,7]=>[8,4,5,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,7,8,5,1]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,3,7,5,8,4]=>[1,6,5,7,8,4,3,2]=>[8,3,4,2,1,5,6,7]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,4,5,1,2]=>[1,6,5,4,3,7,2,8]=>[8,3,4,5,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,8,1,4,5]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,5,8,1,6]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,5,8,1,6]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,2,3,5,8]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,8,6,4,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,7,2,8,5,3]=>[1,6,8,3,4,7,5,2]=>[8,3,1,6,5,2,4,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,4,2,3,6]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,4,8,5,3]=>[1,2,6,8,3,7,5,4]=>[8,7,3,1,6,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,6,2,8,1]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,1,7,4,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,6,2,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,1,7,4,6]=>[1,8,6,7,4,3,5,2]=>[8,1,3,2,5,6,4,7]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,1,7,4,2]=>[1,6,7,4,8,2,3,5]=>[8,3,2,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,6,1,7,2]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,8,4,6,1]=>[1,7,6,4,3,2,5,8]=>[8,2,3,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,4,8,3,6]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,2,8,3,4]=>[1,5,2,7,3,6,8,4]=>[8,4,7,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,1,8,2,3]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,6,8,4,5]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,8,1,6,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,2,4,6,5]=>[1,2,7,6,4,8,5,3]=>[8,7,2,3,5,1,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,5,3,1,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,4,2,7,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,6,2,7,3]=>[1,5,6,2,4,8,3,7]=>[8,4,3,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,1,3,2,7]=>[1,5,2,4,8,7,3,6]=>[8,4,7,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,5,7,2,1]=>[1,6,7,2,4,3,8,5]=>[8,3,2,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,1,3,6,5]=>[1,7,6,3,8,5,2,4]=>[8,2,3,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,7,2,6,1]=>[1,8,2,4,5,7,6,3]=>[8,1,7,5,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,3,8,7,6]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,2,4,7,1]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,4,6,3,5]=>[1,2,8,5,4,3,7,6]=>[8,7,1,4,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,8,1,4,3]=>[1,5,8,3,6,2,7,4]=>[8,4,1,6,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,2,5,4,7]=>[1,6,5,2,3,8,7,4]=>[8,3,4,7,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,2,8,3,1]=>[1,7,3,5,2,6,8,4]=>[8,2,6,4,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,5,8,7,10,9,2]=>[1,2,4,6,8,10,3,5,7,9]=>[10,9,7,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,5,7,2,4,3,6,8]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,3,2,4,7,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,6,5,3,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,7,4,3,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,3,5,8,6]=>[1,2,3,7,8,6,5,4]=>[8,7,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,7,4,3,5]=>[1,2,6,4,8,5,7,3]=>[8,7,3,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,3,5,8,6]=>[1,2,7,8,6,5,3,4]=>[8,7,2,1,3,4,6,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,5,2,3,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,2,8,6,3]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,4,2,8,5]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,5,3,2,6]=>[1,2,4,7,3,8,6,5]=>[8,7,5,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,5,8,6,3]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,6,2,4,3]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,7,6,2,4]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,3,6,8,7]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,5,3,2,4]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,4,3,8,6]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,6,8,7,4]=>[1,2,5,6,8,4,3,7]=>[8,7,4,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,8,7,5,3]=>[1,2,4,6,7,5,8,3]=>[8,7,5,3,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,3,2,7,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,8,5,4,7]=>[1,2,6,5,8,7,4,3]=>[8,7,3,4,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,4,2,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,4,2,8,1]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,1,6,4,5]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,6,7,3,1]=>[1,8,2,5,6,7,3,4]=>[8,1,7,4,3,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,1,6,7,8,3]=>[1,5,6,7,8,3,4,2]=>[8,4,3,2,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,6,8,3,5]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,6,4,7,1,3]=>[1,5,4,6,7,2,3,8]=>[8,4,5,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,7,2,8,5]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,5,3,1,6]=>[1,8,6,3,7,2,4,5]=>[8,1,3,6,2,7,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,2,1,7,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,7,3,5,2]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,2,8,4,1]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,2,4,8,1]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,7,1,5,3]=>[1,8,3,4,2,6,5,7]=>[8,1,6,5,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,7,5,2,3]=>[1,8,3,2,6,5,7,4]=>[8,1,6,7,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,6,7,4,3]=>[1,2,5,6,7,4,3,8]=>[8,7,4,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,5,2,8,4]=>[1,7,8,4,6,2,3,5]=>[8,2,1,5,3,7,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,5,7,6,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,4,2,8,3]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,6,5,1,8,4]=>[1,2,7,8,4,6,3,5]=>[8,7,2,1,5,3,6,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,3,7,4,2]=>[1,8,2,6,7,4,3,5]=>[8,1,7,3,2,5,6,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,4,8,1,3]=>[1,5,4,2,7,3,6,8]=>[8,4,5,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,1,7,5,3]=>[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,7,3,5,1]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,6,5,3,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,7,1,4,2]=>[1,3,8,2,5,7,4,6]=>[8,6,1,7,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,8,5,3,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,6,2,4,7]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,8,1,3,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,4,7,8,1,3]=>[1,6,8,3,2,5,7,4]=>[8,3,1,6,7,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,7,1,6,5]=>[1,2,4,8,5,7,6,3]=>[8,7,5,1,4,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,4,3,1,2]=>[1,6,3,7,2,8,4,5]=>[8,3,6,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,6,2,7,1]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,6,2,7,1]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,6,1,8,7]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,6,8,2,1,5]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,2,3,5,6]=>[1,8,6,3,4,7,5,2]=>[8,1,3,6,5,2,4,7]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,5,2,7,3,4]=>[1,6,7,3,8,4,5,2]=>[8,3,2,6,1,5,4,7]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,3,1,4,5]=>[1,8,5,3,2,7,4,6]=>[8,1,4,6,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,4,5,2,3]=>[1,8,3,2,7,4,6,5]=>[8,1,6,7,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,7,2,8,6]=>[1,5,7,8,6,2,4,3]=>[8,4,2,1,3,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,6,2,1,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,5,2,4,6]=>[1,3,8,6,2,4,7,5]=>[8,6,1,3,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,2,4,3,1]=>[1,6,4,7,3,8,2,5]=>[8,3,5,2,6,1,7,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,8,2,1,7]=>[1,4,5,8,7,2,3,6]=>[8,5,4,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,7,1,4,5]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,6,7,1,4]=>[1,3,8,4,5,6,7,2]=>[8,6,1,5,4,3,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,2,3,6,8]=>[1,7,6,3,2,5,4,8]=>[8,2,3,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,7,8,6,3]=>[1,5,7,6,8,3,2,4]=>[8,4,2,3,1,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,7,2,3,4]=>[1,8,4,6,2,5,7,3]=>[8,1,5,3,7,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,4,6,8,3]=>[1,7,8,3,2,5,4,6]=>[8,2,1,6,7,4,5,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,7,3,4,5]=>[1,8,5,7,4,2,3,6]=>[8,1,4,2,5,7,6,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,5,3,4,6]=>[1,8,6,3,7,4,2,5]=>[8,1,3,6,2,5,7,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,4,5,6,3]=>[1,8,3,2,4,7,6,5]=>[8,1,6,7,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,4,5,6,2]=>[1,2,8,3,4,7,6,5]=>[8,7,1,6,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,5,2,3,4]=>[1,8,4,7,3,6,2,5]=>[8,1,5,2,6,3,7,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,5,6,7,4]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,7,4,5,8]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,2,3,5,8]=>[1,6,3,7,5,2,4,8]=>[8,3,6,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,6,8,5,2]=>[1,2,7,5,6,8,3,4]=>[8,7,2,4,3,1,6,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,4,5,6,2]=>[1,2,7,6,5,4,8,3]=>[8,7,2,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,4,5,8,2]=>[1,2,6,5,4,7,8,3]=>[8,7,3,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,5,1,6,8]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,4,1,6,8]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,1,6,5,8]=>[1,3,7,5,2,4,6,8]=>[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,5,1,4,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,3,6,8,5]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,4,6,3,8]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,6,5,4,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,4,3,6,8]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,1,4,6,8]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,1,5,2,8]=>[1,4,7,2,6,5,3,8]=>[8,5,2,7,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,8,1,4,6]=>[1,5,8,6,2,7,4,3]=>[8,4,1,3,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,1,8,4,3]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,4,1,7,2]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,1,3,6,2]=>[1,5,2,4,8,3,7,6]=>[8,4,7,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,4,6,8,3]=>[1,2,5,4,3,7,8,6]=>[8,7,4,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,6,3,8,5]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,1,7,6,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,5,6,1,9,8]=>[1,7,2,3,4,5,6,8,9]=>[9,3,8,7,6,5,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,9,4,5,6,7,8,3]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,6,1,4,2,3,5,8]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,3,2,5,6]=>[1,8,6,2,7,5,3,4]=>[8,1,3,7,2,4,6,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,4,2,3,6]=>[1,8,6,2,7,3,5,4]=>[8,1,3,7,2,6,4,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,5,3,6,7]=>[1,8,7,6,3,2,4,5]=>[8,1,2,3,6,7,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,4,2,6,3]=>[1,8,3,5,4,2,7,6]=>[8,1,6,4,5,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,1,5,4,2]=>[1,8,2,7,4,3,6,5]=>[8,1,7,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,4,5,6,1]=>[1,2,8,3,4,7,6,5]=>[8,7,1,6,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,4,3,6,1]=>[1,8,2,7,6,3,5,4]=>[8,1,7,2,3,6,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,3,1,6,7]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,3,2,6,7]=>[1,8,7,6,2,4,3,5]=>[8,1,2,3,7,5,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,7,2,6,8]=>[1,3,2,5,7,6,4,8]=>[8,6,7,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,7,8,3,6]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,5,2,6,8]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,4,2,7,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,7,2,5,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,3,1,5,8]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,7,3,5,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,4,5,1,8]=>[1,6,5,4,7,2,3,8]=>[8,3,4,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,3,6,8,5]=>[1,7,8,5,3,4,2,6]=>[8,2,1,4,6,5,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,7,1,4,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,5,6,4,8]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,5,7,8,4]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,5,7,4,8]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,2,7,3,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,4,3,7,8]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,4,3,7,8]=>[1,2,5,4,6,3,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,6,3,7,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,3,7,2,4,8]=>[1,2,6,3,5,7,4,8]=>[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,7,3,6,8]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,4,8,7,6]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,6,1,8,4,3]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,1,7,4,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,6,2,7,4]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,4,5,2,3]=>[1,6,5,4,2,8,3,7]=>[8,3,4,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,7,3,8,5]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,3,5,6,4]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,2,1,5,3]=>[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,8,1,6,3]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,5,4,3,7]=>[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,8,2,1,3]=>[1,6,2,4,5,8,3,7]=>[8,3,7,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,2,5,8,1]=>[1,6,5,2,3,7,8,4]=>[8,3,4,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,7,3,8,1]=>[1,4,5,7,8,2,6,3]=>[8,5,4,2,1,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,3,6,1,7]=>[1,4,5,3,8,7,2,6]=>[8,5,4,6,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,4,5,6,3]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,1,2,8,4]=>[1,7,8,4,3,5,2,6]=>[8,2,1,5,6,4,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,7,8,4,5]=>[1,6,8,5,7,4,2,3]=>[8,3,1,4,2,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,7,2,4,5]=>[1,3,8,5,7,4,6,2]=>[8,6,1,4,2,5,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,8,6,7,3]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,1,6,8,2]=>[1,4,7,8,2,5,3,6]=>[8,5,2,1,7,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,3,6,7,1]=>[1,4,5,3,8,2,6,7]=>[8,5,4,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,5,4,7,1]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,6,4,8,2]=>[1,7,8,2,3,5,6,4]=>[8,2,1,7,6,4,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,2,6,8,3]=>[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,6,4,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,8,5,6,3]=>[1,2,7,6,5,8,3,4]=>[8,7,2,3,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,1,3,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,5,3,7,1]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,2,1,5,4]=>[1,8,4,6,2,3,7,5]=>[8,1,5,3,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,6,1,4,3]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,5,4,8,1]=>[1,2,6,4,7,8,3,5]=>[8,7,3,5,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,3,8,6,2]=>[1,5,3,7,6,8,2,4]=>[8,4,6,2,3,1,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,4,7,3,6]=>[1,2,8,6,7,3,5,4]=>[8,7,1,3,2,6,4,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,3,4,2,5]=>[1,8,5,3,7,2,4,6]=>[8,1,4,6,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,7,3,6]=>[1,8,6,7,3,4,2,5]=>[8,1,3,2,6,5,7,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,8,4,3,1]=>[1,7,3,6,4,5,8,2]=>[8,2,6,3,5,4,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,6,2,7,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,4,6,1,7]=>[1,5,4,3,2,8,7,6]=>[8,4,5,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,2,5,7,8]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,2,4,7,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,2,4,6,1]=>[1,7,6,4,5,2,8,3]=>[8,2,3,5,4,7,1,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,3,6,1,8]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,1,6,4,7,8]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,3,4,2,7,8]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,2,6,1,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,5,3,6,2]=>[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,1,6,3,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,3,6,2,8]=>[1,5,3,4,7,2,6,8]=>[8,4,6,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,5,2,1,8]=>[1,4,3,6,2,7,5,8]=>[8,5,6,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,7,4,2,3]=>[1,2,6,4,8,3,5,7]=>[8,7,3,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,8,2,5,4]=>[1,7,5,8,4,6,2,3]=>[8,2,4,1,5,3,7,6]=>[8,4,6,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,8,2,4,1]=>[1,3,7,4,5,8,2,6]=>[8,6,2,5,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,2,8,6,3]=>[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,1,8,6,3]=>[1,7,6,8,3,4,2,5]=>[8,2,3,1,6,5,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,2,8,5,1]=>[1,3,7,5,2,6,8,4]=>[8,6,2,4,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,7,8,5,1]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,4,2,5,8]=>[1,7,5,4,3,2,6,8]=>[8,2,4,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,4,5,3,1]=>[1,7,3,2,8,4,6,5]=>[8,2,6,7,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,6,1,3,8]=>[1,7,3,5,6,2,4,8]=>[8,2,6,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,4,5,6,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,5,6,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,7,5,4,8]=>[1,3,2,6,5,7,4,8]=>[8,6,7,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,1,5,4,8]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,7,5,3,8]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,5,6,4,3,1]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,1,3,2]=>[1,7,3,8,2,6,4,5]=>[8,2,6,1,7,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,6,5,3,2]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,5,3,2,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,4,3,2,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,6,2,7,5]=>[1,4,8,5,6,2,3,7]=>[8,5,1,4,3,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,8,1,7,4]=>[1,5,8,4,2,6,3,7]=>[8,4,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,7,4,3,1]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,4,7,6,1]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,6,8,4,5]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,3,4,5,1]=>[1,6,4,8,2,7,5,3]=>[8,3,5,1,7,2,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,6,5,7,2]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,8,4,7,5]=>[1,6,4,3,2,5,8,7]=>[8,3,5,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,5,2,3,7]=>[1,8,7,3,6,2,4,5]=>[8,1,2,6,3,7,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,5,2,7,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,2,3,5,1]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,2,3,7,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,2,5,1,3]=>[1,8,3,7,2,6,5,4]=>[8,1,6,2,7,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,5,3,7,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,5,3,1,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,7,3,1,5]=>[1,8,5,7,2,6,3,4]=>[8,1,4,2,7,3,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,5,7,2,3]=>[1,8,3,4,2,6,7,5]=>[8,1,6,5,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,1,5,7,3]=>[1,8,3,4,2,6,5,7]=>[8,1,6,5,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,7,2,5,3]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,5,2,3,7]=>[1,8,7,3,4,2,6,5]=>[8,1,2,6,5,7,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,4,5,2,3]=>[1,8,3,7,2,6,5,4]=>[8,1,6,2,7,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,2,7,3,1]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,2,1,5,3]=>[1,8,3,7,5,2,6,4]=>[8,1,6,2,4,7,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,5,7,3,1]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,5,1,7,3]=>[1,8,3,4,2,6,5,7]=>[8,1,6,5,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,5,7,1,3]=>[1,8,3,4,2,6,7,5]=>[8,1,6,5,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,8,2,6,1]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,6,5,2,3]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[9,6,7,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,11,12,1]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[7,4,5,1,2,8,6,3]=>[1,7,6,8,3,5,2,4]=>[8,2,3,1,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,3,8,6,1]=>[1,5,3,4,2,7,6,8]=>[8,4,6,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,1,7,4,6]=>[1,3,2,8,6,7,4,5]=>[8,6,7,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,3,7,1,6]=>[1,5,3,4,2,8,6,7]=>[8,4,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,1,7,3,6]=>[1,4,2,8,6,7,3,5]=>[8,5,7,1,3,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,1,2,4,3]=>[1,8,3,7,4,6,2,5]=>[8,1,6,2,5,3,7,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,2,4,1,3]=>[1,6,4,5,2,8,3,7]=>[8,3,5,4,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,4,1,3,2]=>[1,5,4,8,2,7,3,6]=>[8,4,5,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,8,5,4,2]=>[1,7,4,6,5,8,2,3]=>[8,2,5,3,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,4,8,6,2]=>[1,5,4,7,6,8,2,3]=>[8,4,5,2,3,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,6,4,5,2]=>[1,7,5,6,4,8,2,3]=>[8,2,4,3,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,7,3,2,5]=>[1,8,5,7,2,6,3,4]=>[8,1,4,2,7,3,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,4,7,1,6]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,7,2,1,5]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,7,4,1,5]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,7,3,1,5]=>[1,6,3,4,2,8,5,7]=>[8,3,6,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,9,1,4,3,2]=>[1,5,9,2,6,3,7,4,8]=>[9,5,1,8,4,7,3,6,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,7,8,5,1,2,6]=>[1,3,7,2,4,8,6,5]=>[8,6,2,7,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,5,6,8,1]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,1,8,7,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,6,4,7,5]=>[1,8,5,6,4,2,3,7]=>[8,1,4,3,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,1,3,2,6]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,6,1,7,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,7,4,1,5]=>[1,3,6,4,8,5,7,2]=>[8,6,3,5,1,4,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,8,7,4,5]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,8,7,6,4]=>[1,5,8,4,3,2,6,7]=>[8,4,1,5,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,4,3,6,7]=>[1,2,5,4,3,8,7,6]=>[8,7,4,5,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,1,5,2,7]=>[1,4,8,7,2,3,6,5]=>[8,5,1,2,7,6,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,3,1,7,2]=>[1,5,3,6,2,4,8,7]=>[8,4,6,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,5,1,7,2]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,2,4,3,5]=>[1,8,5,2,6,4,7,3]=>[8,1,4,7,3,5,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,1,8,5,4]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,6,4,1,5]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,1,4,7,5]=>[1,6,4,3,8,5,2,7]=>[8,3,5,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,7,4,6,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,7,4,5,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,2,4,7,5]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,7,5,4]=>[1,8,4,6,7,5,2,3]=>[8,1,5,3,2,4,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,7,6,4,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,7,6,4,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,2,5,4,8]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,6,3,5,8]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,4,1,3,7]=>[1,5,4,8,7,3,2,6]=>[8,4,5,1,2,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,1,6,7,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,2,1,6,7]=>[1,3,8,7,6,2,5,4]=>[8,6,1,2,3,7,4,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,3,1,4,6,7]=>[1,2,5,3,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,5,7,4,6]=>[1,2,8,6,7,4,3,5]=>[8,7,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,3,2,6,1]=>[1,5,3,7,6,2,4,8]=>[8,4,6,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,5,1,4,7]=>[1,3,8,7,4,2,6,5]=>[8,6,1,2,5,7,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,2,5,4,1]=>[1,3,8,2,6,5,4,7]=>[8,6,1,7,3,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,8,3,5,1]=>[1,2,4,7,5,8,3,6]=>[8,7,5,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,8,5,3,7]=>[1,2,4,6,5,8,7,3]=>[8,7,5,3,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,3,5,4,7]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,5,4,2,7]=>[1,2,6,4,3,8,7,5]=>[8,7,3,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,4,6,8,7]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,6,3,2,4]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,3,2,4,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,4,8,7,5]=>[1,2,6,8,5,4,3,7]=>[8,7,3,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,4,3,5,8]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,2,4,6,3]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,4,6,3,8]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,5,3,6,8]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,5,2,6,3]=>[1,2,8,3,4,7,6,5]=>[8,7,1,6,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,3,6,4,8]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,6,3,4,8]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,4,2,5,8]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,2,6,3,8]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,8,7,5,2]=>[1,2,3,6,7,5,8,4]=>[8,7,6,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,4,2,5,8]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,8,5,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,5,2,4,6]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,2,7,5,8]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,2,8,7,5]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,4,2,3,8]=>[1,2,5,4,6,3,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,2,7,4,8]=>[1,2,6,7,4,5,3,8]=>[8,7,3,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,5,2,4,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,5,3,8,2]=>[1,6,3,7,8,2,4,5]=>[8,3,6,2,1,7,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,6,5,7,1]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,3,4,7,5]=>[1,2,6,4,8,5,3,7]=>[8,7,3,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,8,2,3,6]=>[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,1,4,3,8,2]=>[1,6,3,7,8,2,5,4]=>[8,3,6,2,1,7,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,2,4,8,3]=>[1,5,2,7,8,3,6,4]=>[8,4,7,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,8,5,7,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,4,8,3,1]=>[1,5,4,2,7,3,6,8]=>[8,4,5,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,8,5,7,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,2,6,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,2,5,3,8]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,2,6,3,7]=>[1,5,2,4,8,7,3,6]=>[8,4,7,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,2,6,4,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,2,6,3,8]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,4,2,7,3,8]=>[1,6,7,3,2,5,4,8]=>[8,3,2,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,4,5,2,6]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,9,3,4,5,6,7,2]=>[1,2,8,7,6,5,4,3,9]=>[9,8,2,3,4,5,6,7,1]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,8,7,4,5,2,3,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,7,3,4,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,4,5,6,2]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,9,10,11,12,2]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,4,2,3,1,6,5,7]=>[1,8,7,5,2,4,3,6]=>[8,1,2,4,7,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,3,1,7,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,8,5,3,7]=>[1,6,5,8,7,3,2,4]=>[8,3,4,1,2,6,7,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,5,1,7,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,7,4,8,5]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,3,2,7,4]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,2,8,6,5]=>[1,2,4,7,6,8,5,3]=>[8,7,5,2,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,5,3,2,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,4,5,7,6]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,8,4,5,3]=>[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,5,6,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,8,4,5,1]=>[1,3,6,4,7,5,8,2]=>[8,6,3,5,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,8,7,6,2]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,2,7,8,5,1]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,1,6,3,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,1,3,5,4]=>[1,6,3,7,5,2,4,8]=>[8,3,6,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,3,7,2,6]=>[1,5,3,8,6,7,2,4]=>[8,4,6,1,3,2,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,1,4,5,6,3]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,5,6,7,3]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,10,9,7]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,10,8,9,5]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,6,5,3,8,7,10,9]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,10,7,8,9,3]=>[1,2,3,4,5,6,10,7,8,9]=>[10,9,8,7,6,5,1,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,6,4,5,1,8,7,10,9]=>[1,2,3,6,4,5,7,8,9,10]=>[10,9,8,5,7,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,10,6,7,8,9,1]=>[1,2,3,4,5,10,6,7,8,9]=>[10,9,8,7,6,1,5,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,5,2,3,6,8,4,1]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,6,5,2,3]=>[1,8,3,4,7,2,5,6]=>[8,1,6,5,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,6,5,4,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,6,7,2,3]=>[1,4,2,5,6,7,3,8]=>[8,5,7,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,1,5,7,4]=>[1,3,8,4,6,5,2,7]=>[8,6,1,5,3,4,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,5,8,4,6,1]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,1,5,2,3]=>[1,6,5,2,7,3,8,4]=>[8,3,4,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,5,1,4,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,5,3,1,8]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,3,4,1,7]=>[1,6,4,5,3,2,8,7]=>[8,3,5,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,4,1,2,3]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,1,8,2,3]=>[1,7,2,4,6,8,3,5]=>[8,2,7,5,3,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,4,5,2,3]=>[1,6,5,4,7,2,3,8]=>[8,3,4,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,6,3,2,5]=>[1,4,2,8,5,6,3,7]=>[8,5,7,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,8,7,4,5]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,5,4,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,2,3,5,4]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,8,3,6,7]=>[1,2,5,8,7,6,3,4]=>[8,7,4,1,2,3,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,8,6,3,7]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,5,4,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,5,4,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,2,4,8,3]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,7,2,3,8]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,5,8,3,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,7,5,2,8]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,7,2,3,8]=>[1,2,6,3,5,7,4,8]=>[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,6,4,8,5]=>[1,2,7,8,5,6,4,3]=>[8,7,2,1,4,3,5,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,3,6,7,4]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,8,5,4,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,7,4,5,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,3,6,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,5,3,8,6]=>[1,2,4,7,8,6,3,5]=>[8,7,5,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,2,4,3,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,3,2,6,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,2,6,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,6,5,8,3]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,3,7,4,2]=>[1,2,6,7,4,8,3,5]=>[8,7,3,2,5,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,4,5,2,7]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,3,2,8,5]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,4,5,6,1]=>[1,8,2,3,4,7,6,5]=>[8,1,7,6,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,3,6,4,1]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,5,4,8,2,3]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,1,8,4,5]=>[1,7,4,2,6,8,5,3]=>[8,2,5,7,3,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,4,6,1,5]=>[1,2,8,5,4,3,7,6]=>[8,7,1,4,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,4,5,2,6]=>[1,7,2,3,8,6,5,4]=>[8,2,7,6,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,4,2,1,5]=>[1,6,2,8,5,4,3,7]=>[8,3,7,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,2,4,5,6]=>[1,3,7,5,2,8,6,4]=>[8,6,2,4,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,4,3,8,2]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,4,5,8,2]=>[1,7,8,2,3,4,6,5]=>[8,2,1,7,6,5,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,6,4,8,2]=>[1,7,8,2,3,5,6,4]=>[8,2,1,7,6,4,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,2,6,3,4]=>[1,5,2,8,4,3,7,6]=>[8,4,7,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,4,7,1,5]=>[1,6,7,2,8,5,4,3]=>[8,3,2,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,4,7,8,5]=>[1,6,7,8,5,4,2,3]=>[8,3,2,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,3,4,7,8,5]=>[1,6,7,8,5,4,3,2]=>[8,3,2,1,4,5,6,7]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,8,9,5]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,5,2,6,7,8,9,4]=>[1,2,3,5,6,7,8,9,4]=>[9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,8,9,5]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,5,6,7,8,9,4]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,1,7,8,9,10,2,6]=>[1,3,5,7,9,2,4,6,8,10]=>[10,8,6,4,2,9,7,5,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,5,8,7,4,1,6]=>[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,7,3,1,6]=>[1,4,8,6,3,5,7,2]=>[8,5,1,3,6,4,2,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,6,5,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,5,7,2,1]=>[1,3,4,8,2,6,7,5]=>[8,6,5,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,8,7,2,5]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,7,2,4,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,5,7,3,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,7,1,4,6]=>[1,3,5,7,4,8,6,2]=>[8,6,4,2,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,7,1,6,3]=>[1,2,5,7,6,3,8,4]=>[8,7,4,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,8,5,7,3]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,8,7,2,4]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,3,6,7,1,2]=>[1,4,3,5,6,7,2,8]=>[8,5,6,4,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,3,4,7,6,2]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,6,4,5,8]=>[1,2,7,5,6,4,3,8]=>[8,7,2,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,5,7,1,6]=>[1,3,4,8,6,7,2,5]=>[8,6,5,1,3,2,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,7,5,6,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,3,1,7,2]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,5,7,3,4]=>[1,8,4,2,6,7,3,5]=>[8,1,5,7,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,1,5,3,6]=>[1,8,6,5,2,7,3,4]=>[8,1,3,4,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,8,6,2,1]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,4,6,7,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,1,2,7,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,6,5,2,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,6,3,1,5]=>[1,4,2,8,5,6,3,7]=>[8,5,7,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,6,3,5,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,4,3,5,6]=>[1,8,6,3,2,7,5,4]=>[8,1,3,6,7,2,4,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,6,3,4,5]=>[1,2,8,5,6,3,7,4]=>[8,7,1,4,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,6,5,1,3]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,2,4,3,1]=>[1,6,4,5,2,8,3,7]=>[8,3,5,4,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,4,8,6,3]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,4,5,2,1]=>[1,6,5,4,7,2,3,8]=>[8,3,4,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,2,8,1,7]=>[1,4,3,5,2,6,8,7]=>[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,1,5,6,7]=>[1,2,8,7,6,5,3,4]=>[8,7,1,2,3,4,6,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,1,8,2,7]=>[1,4,3,6,8,7,2,5]=>[8,5,6,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,3,6,8,7]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,8,4,2,7]=>[1,2,5,8,7,3,6,4]=>[8,7,4,1,2,6,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,4,2,6,1]=>[1,5,4,8,2,7,6,3]=>[8,4,5,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,8,4,1,7]=>[1,5,8,7,2,3,6,4]=>[8,4,1,2,7,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,8,2,6,1]=>[1,3,5,8,2,7,6,4]=>[8,6,4,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,2,8,4,6]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,2,5,4,1]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,1,6,7,4,5,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,6,7,5,3]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,4,7,5,3]=>[1,8,3,2,4,6,7,5]=>[8,1,6,7,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,2,7,5,3]=>[1,8,3,2,4,6,7,5]=>[8,1,6,7,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,6,7,5,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,6,7,5,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,4,7,5,3]=>[1,8,3,6,7,5,4,2]=>[8,1,6,3,2,4,5,7]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,8,5,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,8,9,10,5]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,3,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,3,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,3,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,9,10,3]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,8,5,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,8,9,10,5]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,1,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,9,10,11,12,7]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,8,5,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,8,5,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,8,9,10,5,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,8,9,10,11,12,5]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,3,8,7,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,3,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,3,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,3,8,9,10,11,12,7]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,3,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,3,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,9,10,3,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,9,10,11,12,3]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,8,7,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,8,9,10,11,12,7]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,8,5,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,8,5,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,8,9,10,5,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,8,9,10,11,12,5]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,7,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,9,10,11,12,7]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,1,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,1,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,1,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[5,4,7,6,3,1,2,8]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,1,5,2,7]=>[1,3,4,8,7,2,6,5]=>[8,6,5,1,2,7,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,1,5,2,7]=>[1,3,8,7,2,6,5,4]=>[8,6,1,2,7,3,4,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,2,3,5,6]=>[1,8,6,3,2,7,5,4]=>[8,1,3,6,7,2,4,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,7,1,3,4]=>[1,8,4,5,7,3,6,2]=>[8,1,5,4,2,6,3,7]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,2,8,7,5]=>[1,4,3,2,6,8,5,7]=>[8,5,6,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,5,2,8,7]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,4,8,7,3]=>[1,6,8,3,2,4,5,7]=>[8,3,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,3,5,6,2]=>[1,8,2,4,7,6,5,3]=>[8,1,7,5,2,3,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,5,7,3,6]=>[1,8,6,7,3,2,4,5]=>[8,1,3,2,6,7,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,8,3,1,7]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,6,2,1,7]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,6,3,7,2]=>[1,4,8,2,5,6,3,7]=>[8,5,1,7,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,8,9,2,7]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,3,7,2,1,6,5,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,2,5,1,3]=>[1,8,3,7,2,4,6,5]=>[8,1,6,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,2,1,5]=>[1,8,5,6,2,4,3,7]=>[8,1,4,3,7,5,6,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,6,4,1,2]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,6,2,1,4]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,6,2,4,1]=>[1,3,7,4,5,6,2,8]=>[8,6,2,5,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,6,4,1,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,6,7,8,9,1]=>[1,4,3,2,5,6,7,8,9]=>[9,6,7,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,3,2,5,6,7,8,9,1]=>[1,4,5,6,7,8,9,2,3]=>[9,6,5,4,3,2,1,8,7]=>[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,3,2,5,6,7,8,9,10,1]=>[1,4,5,6,7,8,9,10,2,3]=>[10,7,6,5,4,3,2,1,9,8]=>[10,8,7,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,6,3,8,4,7,1,5]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,5,7,8,1,4]=>[1,2,6,8,4,5,7,3]=>[8,7,3,1,5,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,7,2,8,4]=>[1,2,5,7,8,4,3,6]=>[8,7,4,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,4,2,8,6]=>[1,2,5,4,3,7,8,6]=>[8,7,4,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,4,2,7,6]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,7,2,8,6]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,8,2,7,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,2,8,6,3]=>[1,2,7,6,8,3,5,4]=>[8,7,2,3,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,8,5,2,1,4,7,6]=>[1,3,5,2,8,6,4,7]=>[8,6,4,7,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,2,6,7,1]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,8,6,3,2]=>[1,5,8,2,4,3,7,6]=>[8,4,1,7,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,6,5,3,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,6,2,4,7]=>[1,8,7,4,3,2,5,6]=>[8,1,2,5,6,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,8,3,4,2,6]=>[1,7,2,5,3,4,8,6]=>[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,7,4,3,6]=>[1,5,7,3,8,6,4,2]=>[8,4,2,6,1,3,5,7]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,6,7,3,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,8,7,3,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,2,7,4,3]=>[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,6,4,8,5]=>[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,7,3,4,2]=>[1,2,5,7,4,6,3,8]=>[8,7,4,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,7,2,4,3]=>[1,2,6,3,5,7,4,8]=>[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,2,8,3,4]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,6,7,4,3]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,7,3,8,4]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,1,2,7,4]=>[1,3,5,2,6,4,8,7]=>[8,6,4,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,1,6,3,2]=>[1,5,2,4,8,3,7,6]=>[8,4,7,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,1,3,7,4]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,8,1,2,7,4]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,2,3,7,1]=>[1,4,8,2,5,3,6,7]=>[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,1,6,4,3]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,3,6,2,1]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,5,2,4,1]=>[1,3,8,2,6,4,7,5]=>[8,6,1,7,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,5,1,3,2]=>[1,6,2,4,8,3,7,5]=>[8,3,7,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,5,1,3,2]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,1,6,3,4]=>[1,2,8,4,5,3,7,6]=>[8,7,1,5,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,2,1,5,3]=>[1,8,3,6,2,7,5,4]=>[8,1,6,3,7,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,1,2,6,4]=>[1,3,7,6,2,8,4,5]=>[8,6,2,3,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,2,6,5,1]=>[1,3,7,5,2,8,4,6]=>[8,6,2,4,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,4,7,6,1]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,2,6,5,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,4,6,1,7]=>[1,5,4,2,3,8,7,6]=>[8,4,5,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,3,2,6,1,7]=>[1,4,3,8,7,2,5,6]=>[8,5,6,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,3,6,2,7]=>[1,4,8,7,2,3,5,6]=>[8,5,1,2,7,6,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,3,6,1,2,7]=>[1,4,3,8,7,2,5,6]=>[8,5,6,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,8,5,4,6]=>[1,3,7,4,2,5,8,6]=>[8,6,2,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,5,2,3,1,6]=>[1,4,5,2,7,3,8,6]=>[8,5,4,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,1,5,3,4]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,4,1,3,5]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,4,3,1,5]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,2,5,3,6]=>[1,7,3,2,4,8,6,5]=>[8,2,6,7,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,8,3,6,4,5]=>[1,7,4,8,5,3,2,6]=>[8,2,5,1,4,6,7,3]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,1,2,4,5]=>[1,6,2,8,5,3,7,4]=>[8,3,7,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,1,2,6,5]=>[1,7,6,2,4,3,8,5]=>[8,2,3,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,1,6,7,2]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,6,7,4,5]=>[1,8,5,6,7,4,2,3]=>[8,1,4,3,2,5,7,6]=>[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,4,1,3,5]=>[1,7,3,6,2,4,8,5]=>[8,2,6,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,6,2,5,8]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,2,4,6,1]=>[1,3,5,2,7,6,4,8]=>[8,6,4,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,3,4,8,7]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,6,2,8,7]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,7,2,6,1]=>[1,3,4,5,7,6,2,8]=>[8,6,5,4,2,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,5,6,2,1]=>[1,3,4,7,2,8,5,6]=>[8,6,5,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,3,7,5,1]=>[1,4,6,7,5,3,8,2]=>[8,5,3,2,4,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,5,3,6,2]=>[1,7,6,3,2,4,8,5]=>[8,2,3,6,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,4,7,1,2]=>[1,3,6,7,2,5,4,8]=>[8,6,3,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,6,7,2,3]=>[1,5,6,7,2,4,8,3]=>[8,4,3,2,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,2,6,5,1]=>[1,4,8,2,7,5,3,6]=>[8,5,1,7,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,2,5,8,4]=>[1,6,5,2,3,7,8,4]=>[8,3,4,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,8,2,6,3]=>[1,5,8,3,4,7,6,2]=>[8,4,1,6,5,2,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,1,3,6,4]=>[1,7,6,3,5,2,4,8]=>[8,2,3,6,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,2,1,6,4]=>[1,3,7,6,2,8,4,5]=>[8,6,2,3,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,2,7,4,1]=>[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,8,7,3,2]=>[1,4,6,7,3,5,8,2]=>[8,5,3,2,6,4,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,6,7,5,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,6,2,7,1]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,9,7,6]=>[1,8,7,9,6,5,4,3,2]=>[9,2,3,1,4,5,6,7,8]=>[9,4,3,2,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,3,7,4,5,6,2]=>[1,8,2,3,4,7,6,5]=>[8,1,7,6,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,6,4,7,2]=>[1,8,2,3,5,6,4,7]=>[8,1,7,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,1,5,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,5,8,7,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,6,2,7,8]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,7,3,6,2]=>[1,8,2,3,5,7,6,4]=>[8,1,7,6,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,1,8,2,3]=>[1,7,2,6,8,3,5,4]=>[8,2,7,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,5,7,2,8]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,7,6,3,2]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,5,7,8,2]=>[1,3,4,2,6,7,8,5]=>[8,6,5,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,3,5,8,6]=>[1,2,7,8,6,5,3,4]=>[8,7,2,1,3,4,6,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,4,2,6,5]=>[1,3,2,8,5,4,7,6]=>[8,6,7,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,3,5,6,2]=>[1,8,2,3,7,6,5,4]=>[8,1,7,6,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,5,3,7,1]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,4,7,5,6]=>[1,2,8,6,7,5,4,3]=>[8,7,1,3,2,4,5,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,7,4,1,5]=>[1,8,5,7,2,6,4,3]=>[8,1,4,2,7,3,5,6]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,1,8,4,5,6]=>[1,2,7,5,8,6,4,3]=>[8,7,2,4,1,3,5,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,5,6,4,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,1,2,5,7]=>[1,3,8,7,5,2,6,4]=>[8,6,1,2,4,7,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,5,2,1,3,6]=>[1,4,5,2,7,3,8,6]=>[8,5,4,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,8,7,3,4]=>[1,6,7,3,5,8,4,2]=>[8,3,2,6,4,1,5,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,4,7,2,6]=>[1,3,8,6,7,2,4,5]=>[8,6,1,3,2,7,5,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,8,5,2,7]=>[1,3,6,5,8,7,2,4]=>[8,6,3,4,1,2,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,2,6,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,8,3,6,7]=>[1,5,8,7,6,3,2,4]=>[8,4,1,2,3,6,7,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,8,7,3,6]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,3,2,5,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,5,7,2,4]=>[1,8,4,2,6,7,3,5]=>[8,1,5,7,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,4,7,6,2]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,7,8,3,6]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,6,4,7,5]=>[1,2,8,5,6,4,3,7]=>[8,7,1,4,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,5,3,6,8]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,7,8,5,4]=>[1,3,6,8,4,2,5,7]=>[8,6,3,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,8,3,5,2]=>[1,7,5,8,2,6,3,4]=>[8,2,4,1,7,3,6,5]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,5,8,2,3]=>[1,7,2,4,6,8,3,5]=>[8,2,7,5,3,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,6,7,3,2]=>[1,8,2,5,6,7,3,4]=>[8,1,7,4,3,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,4,7,8,3]=>[1,5,4,6,7,8,3,2]=>[8,4,5,3,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,5,7,8,4]=>[1,2,6,7,8,4,3,5]=>[8,7,3,2,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,5,2,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,1,7,3,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,3,6,8,4]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,8,4,1,6]=>[1,3,5,8,6,4,7,2]=>[8,6,4,1,3,5,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,6,2,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,4,1,2,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,1,5,4,7]=>[1,8,7,4,6,5,2,3]=>[8,1,2,5,3,4,7,6]=>[8,2,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,4,6,2,3]=>[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,4,3,6,2]=>[1,8,2,5,4,7,6,3]=>[8,1,7,4,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,2,1,3,4]=>[1,8,4,6,2,5,3,7]=>[8,1,5,3,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,1,7,2,6]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,3,2,7,6]=>[1,5,3,4,8,6,2,7]=>[8,4,6,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,6,5,2,3]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,2,6,1,5]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,4,3,6,1]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,5,4,1,2]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,6,1,5,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,3,1,7,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,1,3,7,6]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,6,3,5,2]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,7,2,6,5]=>[1,2,4,8,5,7,6,3]=>[8,7,5,1,4,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,6,2,3,8]=>[1,7,3,5,6,2,4,8]=>[8,2,6,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,6,2,5,8]=>[1,7,5,6,2,4,3,8]=>[8,2,4,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,1,7,4,5]=>[1,2,6,7,4,3,8,5]=>[8,7,3,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,1,7,3,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,8,3,4,1]=>[1,7,4,5,8,2,3,6]=>[8,2,5,4,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,4,2,7,8]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,4,8,7,1]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,3,4,7,8]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,4,5,1,8]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,5,1,6,2]=>[1,3,7,6,2,4,8,5]=>[8,6,2,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,8,7,2,1]=>[1,5,8,2,3,6,7,4]=>[8,4,1,7,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,6,2,7,3]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,6,3,8,1]=>[1,4,7,8,2,5,6,3]=>[8,5,2,1,7,4,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,2,7,6,4]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,2,3,6,7]=>[1,4,2,8,7,6,3,5]=>[8,5,7,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,5,1,3,7]=>[1,8,7,3,2,6,4,5]=>[8,1,2,6,7,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,8,6,2,7]=>[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,6,8,5,1]=>[1,7,5,6,8,2,4,3]=>[8,2,4,3,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,4,5,3,1]=>[1,7,3,6,5,4,8,2]=>[8,2,6,3,4,5,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,8,5,1,4,2]=>[1,7,4,8,2,3,6,5]=>[8,2,5,1,7,6,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,6,2,4,3]=>[1,7,4,2,5,6,3,8]=>[8,2,5,7,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,5,1,4,3]=>[1,7,4,8,3,6,2,5]=>[8,2,5,1,6,3,7,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,8,3,1,6]=>[1,7,2,5,8,6,3,4]=>[8,2,7,4,1,3,6,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,3,1,5,2]=>[1,6,2,7,5,3,8,4]=>[8,3,7,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,8,1,4,6,3]=>[1,7,6,4,8,3,2,5]=>[8,2,3,5,1,6,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,1,6,4,5]=>[1,3,8,5,2,7,4,6]=>[8,6,1,4,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,1,5,4,2]=>[1,6,5,2,7,4,3,8]=>[8,3,4,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,3,4,7,2]=>[1,5,3,6,4,8,2,7]=>[8,4,6,3,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,5,4,3,2]=>[1,7,3,6,4,8,2,5]=>[8,2,6,3,5,1,7,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,2,3,7,4]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,7,6,5,3]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,8,5,7,3]=>[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,5,2,1,8]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,2,1,3,6]=>[1,5,2,7,3,8,6,4]=>[8,4,7,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,5,2,1,7]=>[1,6,2,4,3,8,7,5]=>[8,3,7,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,5,7,4,8]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,2,5,6,8]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,7,9,5,8,6]=>[1,2,3,4,5,7,6,9,8]=>[9,8,7,6,5,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,6,8,3,7,5]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,2,6,7,4]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,2,8,5,4]=>[1,6,8,4,7,5,2,3]=>[8,3,1,5,2,4,7,6]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,6,7,2,5]=>[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,2,8,3,5]=>[1,2,6,8,5,3,7,4]=>[8,7,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,3,6,2,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,4,3,2,6]=>[1,2,5,4,7,3,8,6]=>[8,7,4,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,3,6,8,5]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,7,8,5,4]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,4,2,7,5]=>[1,3,2,8,5,4,6,7]=>[8,6,7,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,7,8,2,5]=>[1,2,6,8,5,7,3,4]=>[8,7,3,1,4,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,6,2,8,4]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,2,7,8,5]=>[1,6,7,8,5,2,3,4]=>[8,3,2,1,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,8,3,2,5]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,6,2,7,5]=>[1,4,8,5,6,2,3,7]=>[8,5,1,4,3,7,6,2]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,8,7,6,4]=>[1,3,5,8,4,2,6,7]=>[8,6,4,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,3,7,6,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,7,4,3,5]=>[1,2,6,4,8,5,7,3]=>[8,7,3,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,6,2,4,7]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,8,6,3,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,4,2,5,7]=>[1,8,7,5,4,6,2,3]=>[8,1,2,4,5,3,7,6]=>[8,2,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,3,5,2,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,8,5,1,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,1,7,5,4]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,6,3,7,4]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,1,7,3,5]=>[1,2,8,5,3,6,7,4]=>[8,7,1,4,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,7,5,3,6]=>[1,2,8,6,5,7,3,4]=>[8,7,1,3,4,2,6,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,5,3,6,4]=>[1,2,8,4,7,6,3,5]=>[8,7,1,5,2,3,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,6,4,3,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,6,3,5,2]=>[1,4,7,5,6,3,8,2]=>[8,5,2,4,3,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,3,5,1,7]=>[1,4,6,5,3,2,8,7]=>[8,5,3,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,3,6,2,7]=>[1,4,5,3,8,7,2,6]=>[8,5,4,6,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,3,1,7,8]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,2,7,4,6]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,3,2,7,8]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,4,6,2,7]=>[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,7,1,6,8,2]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,3,6,7,2]=>[1,4,5,3,8,2,6,7]=>[8,5,4,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,5,1,7,2]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,5,7,4,3]=>[1,2,6,7,4,8,3,5]=>[8,7,3,2,5,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,5,2,1,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,2,3,4,1]=>[1,6,3,8,2,5,4,7]=>[8,3,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,5,2,7,1]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,5,3,7,4]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,5,4,7,1]=>[1,3,6,4,8,2,5,7]=>[8,6,3,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,2,6,3,7]=>[1,4,5,2,3,8,7,6]=>[8,5,4,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,5,2,4,7]=>[1,3,6,2,4,8,7,5]=>[8,6,3,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,4,1,2,3]=>[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,4,2,1,3]=>[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,2,4,1,3]=>[1,6,4,7,2,5,3,8]=>[8,3,5,2,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,5,7,1,3]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,5,8,6,1]=>[1,4,3,7,6,8,2,5]=>[8,5,6,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,8,5,7,1]=>[1,3,2,6,5,8,4,7]=>[8,6,7,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,3,8,6,1]=>[1,2,7,6,8,3,5,4]=>[8,7,2,3,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,4,7,6,2]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,5,4,7,2]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,7,6,5,1]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,5,7,4,1]=>[1,3,8,2,6,7,4,5]=>[8,6,1,7,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,4,3,7,1]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,5,4,7,1]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,2,5,7,1]=>[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,3,5,7,1]=>[1,4,8,2,6,5,3,7]=>[8,5,1,7,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,7,4,6,1]=>[1,3,8,2,5,7,6,4]=>[8,6,1,7,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,7,4,3,1]=>[1,2,6,4,5,7,3,8]=>[8,7,3,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,6,3,5,1]=>[1,2,4,7,5,6,3,8]=>[8,7,5,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,3,2,8,4]=>[1,7,8,4,6,2,5,3]=>[8,2,1,5,3,7,4,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,4,1,8,5]=>[1,2,7,8,5,4,3,6]=>[8,7,2,1,4,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,1,2,8,4]=>[1,5,2,7,8,4,3,6]=>[8,4,7,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,7,5,6,3]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,7,2,4,1]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,6,2,3,7]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,7,6,2,4]=>[1,3,2,5,7,4,8,6]=>[8,6,7,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,6,5,8,7,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,4,6,5,8,7,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,2,4,6,5,8,7,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,2,6,5,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,6,2,7,8,1,3,4]=>[1,5,8,4,7,3,2,6]=>[8,4,1,5,2,6,7,3]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,6,1,2,8]=>[1,4,5,6,2,7,3,8]=>[8,5,4,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,5,6,1,2]=>[1,4,3,8,2,7,5,6]=>[8,5,6,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,6,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,5,6,8,4,7,1]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,6,3,7,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,8,3,7,1]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,7,8,1,6]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,1,6,8,2,5]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,8,1,3,5]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,6,3,1,8]=>[1,4,5,6,3,2,7,8]=>[8,5,4,3,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,3,7,2,4]=>[1,6,7,2,3,5,4,8]=>[8,3,2,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,7,8,2,6]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,4,3,2,7]=>[1,6,3,5,4,8,7,2]=>[8,3,6,4,5,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,1,8,3,2,7]=>[1,5,8,7,2,6,3,4]=>[8,4,1,2,7,3,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,7,8,3,6]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,4,3,5,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,9,3,4,5,6,2,8]=>[1,7,6,5,4,3,9,8,2]=>[9,3,4,5,6,7,1,2,8]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,2,3,1,8,5,4,7]=>[1,6,5,8,7,4,2,3]=>[8,3,4,1,2,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,7,5,1,4]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,5,6,1,7]=>[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,8,4,1,3]=>[1,5,8,3,7,2,6,4]=>[8,4,1,6,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,2,7,1,6]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,1,6,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,7,4,2,6]=>[1,3,2,5,7,4,8,6]=>[8,6,7,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,8,2,7,5]=>[1,4,3,2,6,5,8,7]=>[8,5,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,3,5,7,4]=>[1,8,4,2,6,5,3,7]=>[8,1,5,7,3,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,3,2,4,6]=>[1,5,3,7,4,8,6,2]=>[8,4,6,2,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,6,2,8,5,4]=>[1,3,7,5,2,4,6,8]=>[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,6,7,3,1]=>[1,5,6,7,3,2,4,8]=>[8,4,3,2,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,8,7,3,5]=>[1,6,7,3,4,2,5,8]=>[8,3,2,6,5,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,8,4,5,1]=>[1,3,2,7,5,8,4,6]=>[8,6,7,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,7,8,3,1]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,7,8,3,1]=>[1,5,7,3,6,8,2,4]=>[8,4,2,6,3,1,7,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,5,7,4,3]=>[1,6,7,4,8,3,2,5]=>[8,3,2,5,1,6,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,3,1,8,7]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,8,3,1,5]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,8,4,5,1]=>[1,6,4,7,5,8,2,3]=>[8,3,5,2,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,7,6,5,3]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,9,10,5,6,7]=>[1,2,3,4,5,8,6,9,7,10]=>[10,9,8,7,6,3,5,2,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,10,6,9,7]=>[1,2,3,4,5,6,8,7,10,9]=>[10,9,8,7,6,5,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,7,3,1,5,2,8,6]=>[1,4,2,7,8,6,3,5]=>[8,5,7,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,5,3,8,6]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,5,2,8,1]=>[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,3,8,5,1,6]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,2,1,4,8,3]=>[1,6,4,2,7,8,3,5]=>[8,3,5,7,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,3,4,7,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,3,2,4,7]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,3,5,6,4]=>[1,2,8,4,7,6,5,3]=>[8,7,1,5,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,6,5,3,2]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,5,7,4,8,2]=>[1,2,6,4,5,7,8,3]=>[8,7,3,5,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,2,8,3,6]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,6,1,7,4]=>[1,3,5,6,2,8,4,7]=>[8,6,4,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,5,2,6,1]=>[1,3,4,8,2,7,6,5]=>[8,6,5,1,7,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,5,3,4,7]=>[1,8,7,4,6,3,2,5]=>[8,1,2,5,3,6,7,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,5,6,1,8]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,6,7,5,1]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,1,4,2,5]=>[1,3,8,5,2,7,4,6]=>[8,6,1,4,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,2,5,6,1]=>[1,3,8,2,7,6,5,4]=>[8,6,1,7,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,5,1,6,7]=>[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,5,4,1,3]=>[1,6,4,7,2,8,3,5]=>[8,3,5,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,7,6,2,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,7,1,6,2]=>[1,4,5,7,6,2,3,8]=>[8,5,4,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,8,7,2,1,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,7,1,6,2]=>[1,5,7,6,2,3,8,4]=>[8,4,2,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,1,4,6,3]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,1,6,4,5]=>[1,3,8,5,2,4,7,6]=>[8,6,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,1,6,4,5]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,1,4,6,3]=>[1,2,7,6,4,5,3,8]=>[8,7,2,3,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,4,1,6,2]=>[1,3,8,2,5,4,7,6]=>[8,6,1,7,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,3,5,1,2]=>[1,7,2,4,8,3,6,5]=>[8,2,7,5,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,3,6,4,5]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,4,5,6,3]=>[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,2,4,1,5]=>[1,3,7,2,6,4,8,5]=>[8,6,2,7,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,6,3,1,2]=>[1,4,8,2,5,6,3,7]=>[8,5,1,7,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,7,3,1,2]=>[1,5,7,2,4,8,3,6]=>[8,4,2,7,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,6,7,1,3,2]=>[1,4,6,2,5,7,3,8]=>[8,5,3,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,2,1,3,4]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,7,3,1,2]=>[1,4,8,2,5,7,3,6]=>[8,5,1,7,4,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,2,1,6,8]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,5,4,7,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,8,3,1,5]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,5,1,4,3]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,1,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,7,3,1,8]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,8,4,1,7]=>[1,3,6,4,5,8,7,2]=>[8,6,3,5,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,8,7,1,4]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,8,7,1,3]=>[1,4,5,8,3,6,7,2]=>[8,5,4,1,6,3,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,8,2,1,3]=>[1,5,8,3,7,2,4,6]=>[8,4,1,6,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,8,3,1,2]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,5,8,6,1,3]=>[1,4,5,8,3,7,2,6]=>[8,5,4,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,8,4,1,6]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,8,5,1,7]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,8,6,1,4]=>[1,5,8,4,2,3,7,6]=>[8,4,1,5,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,8,7,1,5]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,8,4,1,3]=>[1,6,4,5,8,3,7,2]=>[8,3,5,4,1,6,2,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,5,4,6,1]=>[1,3,8,2,7,6,4,5]=>[8,6,1,7,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,5,3,2]=>[1,8,2,7,3,6,5,4]=>[8,1,7,2,6,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,4,8,1,6]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,7,8,6,1]=>[1,4,3,5,7,6,8,2]=>[8,5,6,4,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,4,1,8,7]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,3,5,4,1]=>[1,7,4,2,8,3,6,5]=>[8,2,5,7,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,3,7,4,1]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,7,5,6,1]=>[1,4,3,2,8,5,7,6]=>[8,5,6,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,4,3,8,1]=>[1,2,7,8,3,5,4,6]=>[8,7,2,1,6,4,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,6,4,2,1]=>[1,3,5,6,4,7,2,8]=>[8,6,4,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,5,4,2,1]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,6,3,8,1]=>[1,7,8,2,4,5,6,3]=>[8,2,1,7,5,4,3,6]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,3,8,4,1]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,7,5,6,1]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,5,6,2,1]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,3,7,4,1]=>[1,6,7,4,8,2,3,5]=>[8,3,2,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,2,5,6,1]=>[1,4,8,2,7,6,5,3]=>[8,5,1,7,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,3,7,4,1]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,1,2,6,8]=>[1,4,7,6,2,5,3,8]=>[8,5,2,3,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,8,4,1,5]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,6,3,2,5]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,3,8,1,5]=>[1,2,6,8,5,3,7,4]=>[8,7,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,3,4,6,1]=>[1,5,3,2,7,6,4,8]=>[8,4,6,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,5,6,4,1]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,4,5,7,1]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,4,7,5,1]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,7,4,5,1]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,4,7,5,1]=>[1,3,2,6,7,5,4,8]=>[8,6,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,7,4,6,1]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,7,5,4,1]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,6,4,2,7]=>[1,2,5,6,4,3,8,7]=>[8,7,4,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,3,4,2,7]=>[1,2,5,3,8,7,4,6]=>[8,7,4,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,2,6,4,1]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,4,6,2,3]=>[1,5,4,2,7,3,8,6]=>[8,4,5,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,3,4,7,8]=>[1,6,4,5,3,2,7,8]=>[8,3,5,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,7,3,2,8]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,4,1,2,8]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,3,5,4,2]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,6,5,3,8]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,3,7,6,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,8,4,7,5]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,1,6,7,3]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,4,2,6,3]=>[1,8,3,7,6,2,4,5]=>[8,1,6,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,7,3,5,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,7,2,5,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,2,6,1,4]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,9,8,7,1]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,8,7,9,6,1]=>[1,2,3,4,5,8,6,7,9]=>[9,8,7,6,5,2,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,11,10,1]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,10,9,8,7,6,5,4,3,1,2]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,10,9,8,1]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,8,9,7,6,1]=>[1,2,3,4,5,8,6,9,7]=>[9,8,7,6,5,2,4,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,4,5,1,3,7,6,2]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,1,5,2]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,1,3,2,4]=>[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,4,2,3,1]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,6,5,2,4]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,1,2,8,9]=>[1,3,5,7,2,4,6,8,9]=>[9,7,5,3,8,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,7,3,1,4,8,6,5]=>[1,2,7,6,8,5,4,3]=>[8,7,2,3,1,4,5,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,7,8,4,2]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,8,7,6,2]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,2,5,6,8]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,6,8,4,3]=>[1,2,7,4,5,6,8,3]=>[8,7,2,5,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,3,1,5,2]=>[1,4,8,2,7,5,3,6]=>[8,5,1,7,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,1,8,6,2]=>[1,3,4,7,6,8,2,5]=>[8,6,5,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,2,3,6,8]=>[1,7,6,3,5,2,4,8]=>[8,2,3,6,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,4,5,2,8]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,3,6,5,4]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,3,1,2,7,4]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,1,3,6,4]=>[1,5,2,8,4,7,6,3]=>[8,4,7,1,5,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,4,1,3,7,8]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,8,7,3,6]=>[1,5,8,6,7,3,2,4]=>[8,4,1,3,2,6,7,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,7,8,5,3]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,6,8,7,3]=>[1,2,4,5,6,8,3,7]=>[8,7,5,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,7,8,4,1]=>[1,2,5,7,4,6,8,3]=>[8,7,4,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,4,3,5,7]=>[1,2,8,7,5,4,3,6]=>[8,7,1,2,4,5,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,7,8,1,6]=>[1,3,4,5,7,2,6,8]=>[8,6,5,4,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,5,8,6,1]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,7,4,3,1]=>[1,6,4,8,2,5,7,3]=>[8,3,5,1,7,4,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,3,1,4]=>[1,8,4,2,6,3,7,5]=>[8,1,5,7,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,8,4,5,3]=>[1,2,6,4,7,5,8,3]=>[8,7,3,5,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,3,8,6,2]=>[1,5,3,7,6,8,2,4]=>[8,4,6,2,3,1,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,2,4,1,5]=>[1,8,5,2,6,4,7,3]=>[8,1,4,7,3,5,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,4,2,3,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,4,1,3,5]=>[1,7,3,8,5,4,6,2]=>[8,2,6,1,4,5,3,7]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,3,2,8,5]=>[1,2,7,8,5,3,6,4]=>[8,7,2,1,4,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,4,2,5,8]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,3,8,6,5]=>[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,3,8,7,6]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,4,6,7,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,3,7,8,6]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,3,5,8,4]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,6,5,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,8,1,6,5]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,6,1,8,4]=>[1,3,7,8,4,5,6,2]=>[8,6,2,1,5,4,3,7]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,8,2,6,5]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,6,3,8,2]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,8,3,5,1]=>[1,4,6,3,7,5,8,2]=>[8,5,3,6,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,5,2,7,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,7,1,4,3]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,5,7,1,3,2]=>[1,6,2,4,5,7,3,8]=>[8,3,7,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,6,2,8,7]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,4,1,8,2]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,6,8,1,4,3]=>[1,5,8,3,7,4,6,2]=>[8,4,1,6,2,5,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,1,6,3,5,4]=>[1,7,5,6,3,8,4,2]=>[8,2,4,3,6,1,5,7]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,4,7,6,9,8,10]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,5,1,4,7,6,9,8]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,1,5,2,7,6,9,8]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,2,5,3,7,6,9,8,10]=>[1,2,4,5,3,6,7,8,9,10]=>[10,9,7,6,8,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,3,6,5,4,1,2,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,4,6,3,2]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,3,8,6,5]=>[1,7,6,8,5,3,4,2]=>[8,2,3,1,4,6,5,7]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,3,7,6,4]=>[1,8,4,5,3,2,6,7]=>[8,1,5,4,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,4,1,7,8]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,6,7,1,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,5,8,6,3]=>[1,7,6,8,3,4,2,5]=>[8,2,3,1,6,5,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,2,4,3,6]=>[1,7,3,5,2,8,6,4]=>[8,2,6,4,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,3,6,7,2]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,6,4,1,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,7,4,1,6]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,1,2,4,8]=>[1,5,2,7,4,3,6,8]=>[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,8,1,3,5]=>[1,4,7,3,2,6,5,8]=>[8,5,2,6,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,9,1,3,5,7]=>[1,4,2,6,3,8,5,9,7]=>[9,6,8,4,7,2,5,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,6,7,8,2,1,3,5]=>[1,4,8,5,2,6,3,7]=>[8,5,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,1,7,5,4]=>[1,8,4,2,6,7,5,3]=>[8,1,5,7,3,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,7,8,2,6]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,2,5,8,7]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,6,2,4,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,8,2,4,3]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,8,4,2,6]=>[1,5,8,6,4,3,2,7]=>[8,4,1,3,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,3,7,8,5]=>[1,2,6,7,8,5,3,4]=>[8,7,3,2,1,4,6,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,3,5,8,7]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,1,8,4,2]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,3,8,4,2]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,1,5,8,4,2]=>[1,7,4,2,3,6,8,5]=>[8,2,5,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,8,5,4,2]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,1,8,4,2]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,4,8,1,2]=>[1,5,4,3,6,8,2,7]=>[8,4,5,6,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,6,1,2,8]=>[1,3,5,6,2,7,4,8]=>[8,6,4,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,6,8,1,2]=>[1,5,6,8,2,3,4,7]=>[8,4,3,1,7,6,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,4,1,2,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,1,2,6,8]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,2,7,6,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,3,2,4,8]=>[1,5,3,6,2,7,4,8]=>[8,4,6,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,2,7,6,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,2,5,4,6]=>[1,7,4,2,8,6,5,3]=>[8,2,5,7,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,3,2,4,6]=>[1,7,4,2,8,6,3,5]=>[8,2,5,7,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,8,6,2,4]=>[1,7,2,5,8,4,3,6]=>[8,2,7,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,7,2,6,8]=>[1,3,5,7,6,2,4,8]=>[8,6,4,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,3,8,2,4]=>[1,5,3,6,8,4,2,7]=>[8,4,6,3,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,6,2,4,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,2,4,5,8]=>[1,2,6,4,7,5,3,8]=>[8,7,3,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,8,1,7,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,2,7,1,4]=>[1,6,7,2,8,4,3,5]=>[8,3,2,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,5,1,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,5,1,8,7,2]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,3,2,6,4]=>[1,8,4,5,3,2,7,6]=>[8,1,5,4,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,7,2,8,6]=>[1,3,2,5,7,8,6,4]=>[8,6,7,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,7,3,2,6]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,9,7,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,3,7,5,9,6,8]=>[1,2,3,4,5,7,9,8,6]=>[9,8,7,6,5,3,1,2,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,10,7,9]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,1,3,4,2,7,8,5]=>[1,6,7,8,5,2,3,4]=>[8,3,2,1,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,4,2,7,6]=>[1,2,5,4,8,6,3,7]=>[8,7,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,8,3,7,6]=>[1,5,8,6,3,2,4,7]=>[8,4,1,3,6,7,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,3,5,1,6]=>[1,7,2,4,3,8,6,5]=>[8,2,7,5,6,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,7,3,1,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,4,2,7,5]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,3,6,7,4]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,9,6,7,8,1]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,9,5,6,7,8,1]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,9,4,5,6,7,8,1]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,10,8,9,1]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,9,7,6,8,1]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,10,7,8,9,1]=>[1,2,3,4,5,6,10,7,8,9]=>[10,9,8,7,6,5,1,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,9,6,5,7,8,1]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,9,5,4,6,7,8,1]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,10,5,6,7,8,9,1]=>[1,2,3,4,10,5,6,7,8,9]=>[10,9,8,7,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,9,4,3,5,6,7,8,1]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,10,4,5,6,7,8,9,1]=>[1,2,3,10,4,5,6,7,8,9]=>[10,9,8,1,7,6,5,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,9,7,8,6,1]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,2,3,7,4,1,8]=>[1,5,7,2,6,4,3,8]=>[8,4,2,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,3,6,7,2]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,2,6,7,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,1,2,8,3]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,7,3,8,2,5]=>[1,6,8,5,3,4,7,2]=>[8,3,1,4,6,5,2,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,4,8,2,5]=>[1,7,2,3,6,8,5,4]=>[8,2,7,6,3,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,3,1,5,7]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,5,1,4,7]=>[1,8,7,4,3,6,2,5]=>[8,1,2,5,6,3,7,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,5,8,2,6]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,3,8,2,4]=>[1,6,8,4,2,7,3,5]=>[8,3,1,5,7,2,6,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,6,7,2,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,4,1,3,5]=>[1,7,3,6,2,8,5,4]=>[8,2,6,3,7,1,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,8,4,7,2]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,7,2,8,4]=>[1,5,7,8,4,3,2,6]=>[8,4,2,1,5,6,7,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,2,3,7,4]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,8,4,7,3]=>[1,5,8,3,2,6,4,7]=>[8,4,1,6,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,6,4,2,5]=>[1,3,8,5,6,4,2,7]=>[8,6,1,4,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,3,4,2,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,6,4,2,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,6,4,2,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,6,4,2,3]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,6,4,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,6,4,2,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,9,8,10,7]=>[1,2,3,4,5,6,7,9,10,8]=>[10,9,8,7,6,5,4,2,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,6,5,7,4,8,3,10,9]=>[1,2,3,6,4,5,7,8,9,10]=>[10,9,8,5,7,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,5,4,7,6,9,8,10,1]=>[1,3,5,7,9,10,2,4,6,8]=>[10,8,6,4,2,1,9,7,5,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,11,10,12,9]=>[1,2,3,4,5,6,7,8,9,11,12,10]=>[12,11,10,9,8,7,6,5,4,2,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,5,1,6,2,3,4,7]=>[1,8,7,4,6,3,2,5]=>[8,1,2,5,3,6,7,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,3,8,4,5]=>[1,7,4,2,6,8,5,3]=>[8,2,5,7,3,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,1,3,5,6]=>[1,2,7,5,3,8,6,4]=>[8,7,2,4,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,3,7,4,5]=>[1,6,7,4,2,8,5,3]=>[8,3,2,5,7,1,4,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,6,7,2,4]=>[1,8,4,5,6,7,2,3]=>[8,1,5,4,3,2,7,6]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,5,7,8,3]=>[1,4,6,7,8,3,2,5]=>[8,5,3,2,1,6,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,2,1,4,3]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,4,5,3,7]=>[1,2,3,8,7,4,6,5]=>[8,7,6,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,6,3,4,2]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,5,7,3,2]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,2,7,3,4]=>[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,4,2,3,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,5,2,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,4,1,8,2]=>[1,6,2,5,4,7,8,3]=>[8,3,7,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,2,3,6,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,4,6,1,3]=>[1,5,4,2,7,3,8,6]=>[8,4,5,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,1,3,6,5]=>[1,8,5,2,7,6,3,4]=>[8,1,4,7,2,3,6,5]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,4,6,5,2]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,7,4,5,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,6,2,5,4]=>[1,3,7,5,6,2,4,8]=>[8,6,2,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,6,5,7,3]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,3,7,2,4]=>[1,5,3,2,6,7,4,8]=>[8,4,6,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,6,3,8,4]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,7,6,8,3]=>[1,4,5,7,8,3,2,6]=>[8,5,4,2,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,7,8,6,2]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,4,5,6,3]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,9,7,10,8]=>[1,2,3,4,5,6,7,9,10,8]=>[10,9,8,7,6,5,4,2,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,9,10,1,7,8]=>[1,2,3,4,5,6,9,7,10,8]=>[10,9,8,7,6,5,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,5,6,4,8,1,7]=>[1,3,5,4,6,8,7,2]=>[8,6,4,5,3,1,2,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,1,7,5,8]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,5,8,4,6]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,7,5,8,4]=>[1,2,3,6,5,7,8,4]=>[8,7,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,1,7,4,8]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,1,7,8,3]=>[1,4,2,6,7,8,3,5]=>[8,5,7,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,5,8,3,2]=>[1,4,7,3,2,6,8,5]=>[8,5,2,6,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,1,7,8,3]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,7,6,8,3,2]=>[1,4,7,3,5,6,8,2]=>[8,5,2,6,4,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,1,4,7,8]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,6,8,3,1]=>[1,4,7,3,5,6,8,2]=>[8,5,2,6,4,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,2,8,1,7]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,1,7,8,2]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,5,2,1,7,8]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,1,7,8,2]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,8,1,4,2,3,6,7]=>[1,5,2,8,7,6,3,4]=>[8,4,7,1,2,3,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,1,7,2,6]=>[1,3,4,8,6,7,2,5]=>[8,6,5,1,3,2,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,8,1,4,7,2]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,8,3,7,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,6,2,7,1]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,5,2,6,3]=>[1,7,6,2,4,3,8,5]=>[8,2,3,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,6,5,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,8,7,2,3]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,8,4,7,3]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,4,7,2,3]=>[1,2,5,4,8,3,6,7]=>[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,5,7,2,3]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,8,6,7,2]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,8,4,7,2]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,3,4,7,1]=>[1,5,3,8,2,6,4,7]=>[8,4,6,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,1,3,6,4]=>[1,5,2,8,4,3,7,6]=>[8,4,7,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,8,6,3,4]=>[1,5,8,4,2,3,7,6]=>[8,4,1,5,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,3,4,8,7,2]=>[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,3,2,1,4,7]=>[1,5,2,8,7,4,3,6]=>[8,4,7,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,3,5,4,2]=>[1,8,2,7,4,6,5,3]=>[8,1,7,2,5,3,4,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,2,5,3,4]=>[1,8,4,2,6,5,3,7]=>[8,1,5,7,3,4,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,1,7,5,6,2]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,4,2,3,5]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,8,5,2,6]=>[1,7,2,4,3,5,8,6]=>[8,2,7,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,3,4,5,2]=>[1,7,5,3,2,8,4,6]=>[8,2,4,6,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,3,4,2,5]=>[1,6,4,7,2,8,5,3]=>[8,3,5,2,7,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,4,2,1,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,2,5,1,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7,8,9,10,11]=>[1,3,2,4,5,6,7,8,9,10,11]=>[11,9,10,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[4,6,5,3,8,2,7,1]=>[1,4,3,5,8,2,6,7]=>[8,5,6,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,4,1,8]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,7,3,1,8]=>[1,6,3,4,5,7,2,8]=>[8,3,6,5,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,1,4,2,8]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,4,6,7,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,3,4,2,5,8]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,5,8,6,4]=>[1,3,7,6,8,4,2,5]=>[8,6,2,3,1,5,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,5,6,4,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,8,1,7,4]=>[1,3,6,2,5,8,4,7]=>[8,6,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,6,2,7,4]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,4,7,3,1]=>[1,6,7,3,5,4,8,2]=>[8,3,2,6,4,5,1,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,2,5,3,4]=>[1,7,3,6,5,2,4,8]=>[8,2,6,3,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,7,4,1,8,2]=>[1,3,5,4,7,8,2,6]=>[8,6,4,5,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,4,2,3,8]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,2,1,8,6]=>[1,3,7,8,6,2,4,5]=>[8,6,2,1,3,7,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,8,6,4,1]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,5,6,3,1]=>[1,7,3,8,2,4,5,6]=>[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,5,4,7,1]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,4,1,3,2]=>[1,7,3,8,2,5,4,6]=>[8,2,6,1,7,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,8,5,1,4]=>[1,2,7,3,6,5,8,4]=>[8,7,2,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,4,6,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,6,8,4,5]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,4,6,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,1,8,6,7]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,9,7,1,8,6]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,9,6,7,1,8,5]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,9,5,6,1,7,8,4]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,10,9,1,8]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,10,8,9,1,7]=>[1,2,3,4,5,6,10,7,8,9]=>[10,9,8,7,6,5,1,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,10,8,1,9,7]=>[1,2,3,4,5,6,10,7,8,9]=>[10,9,8,7,6,5,1,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,10,1,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,7,6,5,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,10,7,8,9,1,6]=>[1,2,3,4,5,10,6,7,8,9]=>[10,9,8,7,6,1,5,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,10,7,8,1,9,6]=>[1,2,3,4,5,10,6,7,8,9]=>[10,9,8,7,6,1,5,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,10,1,6,7,8,9]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,6,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,10,6,7,8,1,9,5]=>[1,2,3,4,10,5,6,7,8,9]=>[10,9,8,7,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,10,6,7,1,8,9,5]=>[1,2,3,4,10,5,6,7,8,9]=>[10,9,8,7,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,10,1,5,6,7,8,9]=>[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,1,2,3,4,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,8,7,2,6,4,1,3]=>[1,5,6,4,2,8,3,7]=>[8,4,3,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,7,4,3,2]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,7,4,1,3]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,6,4,3,2]=>[1,7,3,8,2,5,6,4]=>[8,2,6,1,7,4,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,1,7,5,4]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,7,9,1]=>[1,2,3,4,5,6,8,9,7]=>[9,8,7,6,5,4,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,6,8,7,1,3,5,4]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,6,2,1,4]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,1,8,6,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,3,1,4,8]=>[1,5,3,6,2,7,4,8]=>[8,4,6,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,1,3,6,8]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,3,2,6,8]=>[1,5,3,4,2,7,6,8]=>[8,4,6,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,5,3,1,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,4,1,6,8]=>[1,5,4,7,6,2,3,8]=>[8,4,5,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,3,2,7,8]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,2,4,7,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,6,3,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,4,3,7,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,7,6,2,1]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,7,5,4,2]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,7,2,3,1]=>[1,8,2,4,5,7,3,6]=>[8,1,7,5,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,4,3,6,1]=>[1,8,2,5,4,3,7,6]=>[8,1,7,4,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,4,7,2,1]=>[1,8,2,5,4,6,7,3]=>[8,1,7,4,5,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,6,7,4,1]=>[1,8,2,3,5,6,7,4]=>[8,1,7,6,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,4,7,6,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,2,1,8,3]=>[1,7,8,3,4,5,2,6]=>[8,2,1,6,5,4,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,6,3,1,5]=>[1,8,5,6,3,4,7,2]=>[8,1,4,3,6,5,2,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,4,6,3,2]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,7,2,8,5,1]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,6,4,2,5]=>[1,8,5,6,4,3,7,2]=>[8,1,4,3,5,6,2,7]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,1,5,2,7]=>[1,6,5,2,8,7,3,4]=>[8,3,4,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,3,2,6,7]=>[1,2,4,8,7,6,3,5]=>[8,7,5,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,3,8,6,1]=>[1,5,3,7,6,8,2,4]=>[8,4,6,2,3,1,7,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,4,8,5,6,1]=>[1,2,7,6,5,8,3,4]=>[8,7,2,3,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,3,5,4,1]=>[1,2,7,4,8,3,6,5]=>[8,7,2,5,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,3,8,6,1]=>[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,4,5,8,1]=>[1,6,5,4,7,8,2,3]=>[8,3,4,5,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,7,5,8,4]=>[1,2,6,5,7,8,4,3]=>[8,7,3,4,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,6,8,1,4]=>[1,7,2,3,5,6,8,4]=>[8,2,7,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,4,7,8,1]=>[1,2,5,4,6,7,8,3]=>[8,7,4,5,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,6,7,8,1]=>[1,4,3,5,6,7,8,2]=>[8,5,6,4,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,4,7,3,8]=>[1,2,6,7,3,5,4,8]=>[8,7,3,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,4,6,3,5]=>[1,2,8,5,4,3,7,6]=>[8,7,1,4,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,5,4,3,6]=>[1,2,8,6,4,3,7,5]=>[8,7,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,7,3,6,8]=>[1,2,5,7,6,3,4,8]=>[8,7,4,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,8,7,3,6]=>[1,2,5,8,6,7,3,4]=>[8,7,4,1,3,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,5,2,4,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,3,5,8,4]=>[1,2,7,8,4,3,6,5]=>[8,7,2,1,5,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,6,5,4,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,5,2,4,7]=>[1,2,3,8,7,4,6,5]=>[8,7,6,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,2,8,6,5]=>[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,2,4,7,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,3,2,5,7]=>[1,2,6,3,8,7,5,4]=>[8,7,3,6,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,2,6,4,8]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,2,4,6,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,7,6,1,3]=>[1,5,7,2,4,8,3,6]=>[8,4,2,7,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,5,7,4,1]=>[1,8,2,6,7,4,3,5]=>[8,1,7,3,2,5,6,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,6,5,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,7,1,4,3]=>[1,6,2,8,3,5,7,4]=>[8,3,7,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,1,7,4,3]=>[1,6,7,4,5,2,8,3]=>[8,3,2,5,4,7,1,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,2,1,4,3]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,7,4,1,3]=>[1,6,4,2,5,7,3,8]=>[8,3,5,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,5,8,4,3]=>[1,6,8,3,2,4,7,5]=>[8,3,1,6,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,5,3,7,2]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,8,7,1,4]=>[1,3,6,7,2,5,8,4]=>[8,6,3,2,7,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,3,4,7,8,2]=>[1,2,6,7,8,3,5,4]=>[8,7,3,2,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,8,1,3,5]=>[1,4,7,3,6,2,5,8]=>[8,5,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,3,7,8,2]=>[1,4,2,6,7,8,3,5]=>[8,5,7,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,6,4,8,3]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,6,4,8,3]=>[1,5,6,4,7,8,3,2]=>[8,4,3,5,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,6,5,8,3]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,1,5,8,3]=>[1,2,7,8,3,6,5,4]=>[8,7,2,1,6,3,4,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,7,8,1,5]=>[1,2,4,6,8,5,7,3]=>[8,7,5,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,7,3,1,4]=>[1,6,3,5,7,2,8,4]=>[8,3,6,4,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,1,8,3,6]=>[1,7,3,2,5,4,6,8]=>[8,2,6,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,2,3,6,7]=>[1,8,7,6,3,5,2,4]=>[8,1,2,3,6,4,7,5]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,2,4,8,3]=>[1,7,8,3,6,4,2,5]=>[8,2,1,6,3,5,7,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,2,3,6,8]=>[1,7,6,3,4,5,2,8]=>[8,2,3,6,5,4,7,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,7,2,3,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,5,7,2,3,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,8,3,4,2]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,8,2,3,4]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,7,8,2,3,5]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,2,4,7,3]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,5,3,4,2]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,4,5,7,6]=>[1,8,6,5,4,2,3,7]=>[8,1,3,4,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,2,3,5,8]=>[1,6,3,2,7,5,4,8]=>[8,3,6,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,8,2,3,5]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,5,6,7,8,9,4]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,3,8,5,6,2,7,1]=>[1,4,5,6,2,3,8,7]=>[8,5,4,3,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,7,2,5,1]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,5,3,4,2]=>[1,7,4,2,6,3,8,5]=>[8,2,5,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,5,3,8,2]=>[1,7,8,2,4,3,6,5]=>[8,2,1,7,5,6,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,7,2,5,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,4,7,1,8,3]=>[1,6,2,3,5,7,8,4]=>[8,3,7,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,4,8,7,5,1]=>[1,2,6,7,5,8,3,4]=>[8,7,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,1,8,3,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,7,6,1,2,3]=>[1,8,3,5,6,2,4,7]=>[8,1,6,4,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,6,7,5,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,3,5,4,1]=>[1,8,2,7,4,3,6,5]=>[8,1,7,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,5,7,4,3]=>[1,8,3,2,4,6,7,5]=>[8,1,6,7,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,5,6,4,3]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,1,5,3,4]=>[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,4,8,2,7]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,2,1,4,7]=>[1,3,8,7,4,6,2,5]=>[8,6,1,2,5,3,7,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,6,3,2,5]=>[1,2,7,3,8,5,6,4]=>[8,7,2,6,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,6,3,1,5]=>[1,8,5,6,3,2,7,4]=>[8,1,4,3,6,7,2,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,1,6,4,5]=>[1,8,5,2,7,4,3,6]=>[8,1,4,7,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,6,5,2,1]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,5,2,4,1]=>[1,8,2,7,4,6,3,5]=>[8,1,7,2,5,3,6,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,6,5,7,4]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,5,4,6,1]=>[1,3,2,8,4,7,6,5]=>[8,6,7,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,5,3,6,2]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,6,3,1,5]=>[1,2,8,5,6,3,7,4]=>[8,7,1,4,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,6,5,1,3]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,4,7,2,3,1]=>[1,5,7,3,6,2,8,4]=>[8,4,2,6,3,7,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,5,8,3,1]=>[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,7,4,2,1]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,2,4,8,3,1]=>[1,6,8,2,7,3,5,4]=>[8,3,1,7,2,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,4,6,1,5]=>[1,8,5,4,3,7,2,6]=>[8,1,4,5,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,8,1,3,2]=>[1,6,2,7,3,5,8,4]=>[8,3,7,2,6,4,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,4,7,2,1]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,5,3,2,1]=>[1,6,3,8,2,4,7,5]=>[8,3,6,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,3,2,8,5]=>[1,6,2,7,8,5,3,4]=>[8,3,7,2,1,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,4,8,3,6]=>[1,7,3,5,4,2,6,8]=>[8,2,6,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,8,4,2,5]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,3,2,8,5,4]=>[1,2,6,8,4,3,7,5]=>[8,7,3,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,2,7,6,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,2,8,7,3]=>[1,6,8,3,2,4,5,7]=>[8,3,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,1,8,2,4]=>[1,7,2,6,8,4,3,5]=>[8,2,7,3,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,7,3,6,8]=>[1,2,5,7,6,3,4,8]=>[8,7,4,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,7,4,8,3]=>[1,2,6,4,5,7,8,3]=>[8,7,3,5,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,6,3,8,4]=>[1,2,5,6,3,7,8,4]=>[8,7,4,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,7,4,3,8]=>[1,2,6,4,5,7,3,8]=>[8,7,3,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,2,4,7,8]=>[1,3,6,4,5,2,7,8]=>[8,6,3,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,4,2,7,8]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,7,2,4,8]=>[1,3,5,7,4,2,6,8]=>[8,6,4,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,1,4,7,8]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,1,2,7,8]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,3,7,2,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,3,7,8,1]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,7,1,4,2,8]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,4,7,2,8]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,7,1,2,8]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,1,3,7,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,3,7,8,2]=>[1,4,5,3,6,7,8,2]=>[8,5,4,6,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,6,1,2,5,8]=>[1,3,7,5,2,4,6,8]=>[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,6,3,8,1]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,2,7,3,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,7,2,1,4,8]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,2,4,1,8]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,3,7,1,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,7,3,1,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,1,4,6,7]=>[1,3,8,7,6,4,2,5]=>[8,6,1,2,3,5,7,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,1,4,6,7]=>[1,5,2,3,8,7,6,4]=>[8,4,7,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,2,4,6,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,2,4,6,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,2,3,6,7]=>[1,2,5,3,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,1,6,7,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,3,6,1,7]=>[1,5,3,2,8,7,4,6]=>[8,4,6,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,6,2,3,7]=>[1,5,6,2,8,7,3,4]=>[8,4,3,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,6,7,2,3]=>[1,2,5,6,7,3,8,4]=>[8,7,4,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,6,7,2,3]=>[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,7,2,5,1]=>[1,8,2,4,6,3,5,7]=>[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,7,2,1,5]=>[1,8,5,7,2,4,6,3]=>[8,1,4,2,7,5,3,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,5,3,7,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,5,3,1,7]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,2,3,5,7]=>[1,2,8,7,5,3,6,4]=>[8,7,1,2,4,6,3,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,1,4,5,7]=>[1,3,6,4,2,8,7,5]=>[8,6,3,5,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,4,1,5,7]=>[1,3,6,2,8,7,5,4]=>[8,6,3,7,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,4,5,1,7]=>[1,8,7,2,3,6,5,4]=>[8,1,2,7,6,3,4,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,2,4,5,7]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,5,1,7,3]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,6,3,5,8,4]=>[1,2,7,8,4,6,5,3]=>[8,7,2,1,5,3,4,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,5,3,7,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,7,3,6,5]=>[1,8,5,7,6,3,2,4]=>[8,1,4,2,3,6,7,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,8,4,7,3]=>[1,2,6,4,5,8,3,7]=>[8,7,3,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,1,7,4,3]=>[1,2,6,7,4,5,3,8]=>[8,7,3,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,7,3,6,4]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,7,4,8,5]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,4,3,7,1]=>[1,5,4,2,6,3,8,7]=>[8,4,5,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,6,4,7,1]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,4,7,3,5]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,8,3,5,6,1]=>[1,4,8,2,3,7,6,5]=>[8,5,1,7,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,1,4,6,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,5,3,6,4]=>[1,2,8,4,3,7,6,5]=>[8,7,1,5,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,7,6,5,1]=>[1,3,4,2,8,5,7,6]=>[8,6,5,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,7,5,6,1]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,7,5,6,1]=>[1,3,4,8,2,5,7,6]=>[8,6,5,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,5,3,4,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,8,1,4,7]=>[1,3,5,8,7,4,6,2]=>[8,6,4,1,2,5,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,4,5,2,7]=>[1,3,2,8,7,4,6,5]=>[8,6,7,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,6,3,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,1,4,8,6]=>[1,5,2,7,8,6,4,3]=>[8,4,7,2,1,3,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,3,5,6,1]=>[1,8,2,4,7,6,5,3]=>[8,1,7,5,2,3,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,7,5,3,2]=>[1,2,8,3,6,5,7,4]=>[8,7,1,6,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,8,6,3,2]=>[1,7,3,2,4,5,8,6]=>[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,3,1,2,6]=>[1,4,7,2,5,3,8,6]=>[8,5,2,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,6,4,2,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,7,4,6,3]=>[1,2,8,3,5,7,6,4]=>[8,7,1,6,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,7,5,2,3]=>[1,2,8,3,6,5,7,4]=>[8,7,1,6,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,6,3,8,5,1]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,4,7,5,3]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,9,1,2,8]=>[1,3,5,7,2,4,6,9,8]=>[9,7,5,3,8,6,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,1,2,9,10]=>[1,3,5,7,2,4,6,8,9,10]=>[10,8,6,4,9,7,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,1,8,6,3,7,5,2]=>[1,4,6,7,5,3,8,2]=>[8,5,3,2,4,6,1,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,8,1,6,2]=>[1,7,6,2,5,8,3,4]=>[8,2,3,7,4,1,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,2,8,7,4]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,7,8,2,6]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,5,7,3,8]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,7,2,4,6]=>[1,3,5,7,4,8,6,2]=>[8,6,4,2,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,8,4,6,1]=>[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,2,6,8,1]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,2,6,1,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,2,1,6,7]=>[1,5,2,3,8,7,6,4]=>[8,4,7,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,3,1,6,7]=>[1,5,3,8,7,6,2,4]=>[8,4,6,1,2,3,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,3,2,6,7]=>[1,5,3,8,7,6,2,4]=>[8,4,6,1,2,3,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,3,6,1,8]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,1,6,8,2]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,8,4,6,2]=>[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,8,4,2,6]=>[1,3,5,8,6,4,7,2]=>[8,6,4,1,3,5,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,1,3,8,6]=>[1,5,2,3,7,8,6,4]=>[8,4,7,6,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,4,8,5,1]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,4,5,1,8]=>[1,6,5,4,7,2,3,8]=>[8,3,4,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,4,5,8,2]=>[1,6,5,4,7,8,2,3]=>[8,3,4,5,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,4,3,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,4,5,2,8]=>[1,6,5,4,7,2,3,8]=>[8,3,4,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,5,3,4,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,1,6,3,2]=>[1,4,8,2,5,3,7,6]=>[8,5,1,7,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,4,6,3,1]=>[1,2,5,4,8,3,7,6]=>[8,7,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,5,3,4,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,8,6,7,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,8,6,7,2]=>[1,4,3,5,8,2,6,7]=>[8,5,6,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,4,8,6,2]=>[1,7,6,8,2,3,5,4]=>[8,2,3,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,4,5,6,8]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,4,2,5,6]=>[1,3,7,5,4,2,8,6]=>[8,6,2,4,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,2,4,3,6]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,1,7,3,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,4,6,8,7]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,7,1,8,6]=>[1,5,7,8,6,2,3,4]=>[8,4,2,1,3,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,7,1,2,6]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,3,5,6,2]=>[1,4,7,6,5,3,2,8]=>[8,5,2,3,4,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,6,8,1,7]=>[1,5,6,8,7,2,3,4]=>[8,4,3,1,2,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,5,7,8,9,6]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,7,6,3,1,4,8,5]=>[1,2,7,8,5,3,6,4]=>[8,7,2,1,4,6,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,6,8,2,1]=>[1,3,4,5,6,8,2,7]=>[8,6,5,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,2,5,3,6]=>[1,8,6,5,2,7,3,4]=>[8,1,3,4,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,7,1,5,2]=>[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,8,1,6,2]=>[1,4,5,8,2,7,6,3]=>[8,5,4,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,7,1,6,2]=>[1,8,2,4,5,7,6,3]=>[8,1,7,5,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,8,3,1,5]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,3,7,1,6]=>[1,8,6,7,2,5,3,4]=>[8,1,3,2,7,4,6,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,3,7,6,2]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,5,1,8,4]=>[1,3,7,8,4,2,6,5]=>[8,6,2,1,5,7,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,1,4,8,3]=>[1,2,6,4,7,8,3,5]=>[8,7,3,5,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,7,6,5,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,6,7,5,2]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,1,7,6,2]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,8,5,7,4]=>[1,6,5,8,4,2,3,7]=>[8,3,4,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,4,2,5,8,3,1]=>[1,6,8,2,7,3,4,5]=>[8,3,1,7,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,6,3,1,7]=>[1,8,7,2,5,6,3,4]=>[8,1,2,7,4,3,6,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,7,5,2,6]=>[1,2,3,8,6,5,7,4]=>[8,7,6,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,1,4,8,3]=>[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,6,1,2,4]=>[1,3,5,6,2,8,4,7]=>[8,6,4,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,7,2,1,5]=>[1,3,6,2,8,5,7,4]=>[8,6,3,7,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,6,8,3,1]=>[1,5,6,8,2,3,7,4]=>[8,4,3,1,7,6,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,7,6,4,5]=>[1,2,8,5,7,4,3,6]=>[8,7,1,4,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,8,1,7,3]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,5,1,6,2,3]=>[1,4,5,2,7,3,8,6]=>[8,5,4,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,6,7,8,3]=>[1,4,2,5,6,7,8,3]=>[8,5,7,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,2,8,7,6]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,2,6,8,7]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,2,6,7,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,6,2,5,7]=>[1,2,3,8,7,5,6,4]=>[8,7,6,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,3,7,5,6]=>[1,2,8,6,7,5,3,4]=>[8,7,1,3,2,4,6,5]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,2,7,6,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,5,2,4,8]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,7,5,4,3]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,4,6,2,1]=>[1,3,5,4,7,2,8,6]=>[8,6,4,5,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,5,7,1,3]=>[1,8,3,2,6,7,4,5]=>[8,1,6,7,3,2,5,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,5,2,6,1]=>[1,3,7,6,2,8,4,5]=>[8,6,2,3,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,5,8,2,1]=>[1,4,7,2,6,8,3,5]=>[8,5,2,7,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,5,2,1,7]=>[1,3,8,7,2,6,4,5]=>[8,6,1,2,7,3,5,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,3,6,1,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,7,6,3,1]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,5,1,8,3]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,3,1,6,4,5]=>[1,7,4,3,8,5,2,6]=>[8,2,5,6,1,4,7,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,1,8,5,6]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,1,3,6,5]=>[1,2,4,8,5,3,7,6]=>[8,7,5,1,4,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,1,4,3,6]=>[1,8,6,4,5,2,7,3]=>[8,1,3,5,4,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,2,4,7,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,7,4,2,3]=>[1,8,3,5,7,2,6,4]=>[8,1,6,4,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,1,2,6,3]=>[1,8,3,4,5,2,7,6]=>[8,1,6,5,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,7,1,5,4]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,1,7,6,5]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,5,6,2,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,5,2,6,3]=>[1,8,3,2,4,7,6,5]=>[8,1,6,7,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,5,1,2,6]=>[1,8,6,2,4,7,3,5]=>[8,1,3,7,5,2,6,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,2,1,3]=>[1,8,3,7,2,4,6,5]=>[8,1,6,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,6,2,4,1]=>[1,8,2,3,5,6,4,7]=>[8,1,7,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,4,6,1,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,8,2,6,7]=>[1,4,2,5,8,7,6,3]=>[8,5,7,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,3,2,8,4,5]=>[1,6,8,5,2,3,7,4]=>[8,3,1,4,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,3,4,6,7]=>[1,5,3,2,8,7,6,4]=>[8,4,6,7,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,8,3,6,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,3,5,1,6]=>[1,7,2,4,8,6,5,3]=>[8,2,7,5,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,8,6,2,5]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,5,2,4,8,1]=>[1,3,6,4,5,2,7,8]=>[8,6,3,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,8,4,6,5]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,5,7,4,1]=>[1,6,7,4,3,2,8,5]=>[8,3,2,5,6,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,6,2,8,3]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,4,6,3,2]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,8,6,2,3]=>[1,4,2,5,8,3,7,6]=>[8,5,7,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,5,2,7,1]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,5,1,7,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,1,2,6,8]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,5,7,8,4]=>[1,3,2,4,6,7,8,5]=>[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,6,8,4,1,7]=>[1,3,5,8,7,2,4,6]=>[8,6,4,1,2,7,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,5,4,3,1]=>[1,7,3,6,4,8,2,5]=>[8,2,6,3,5,1,7,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,2,4,1,8]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,2,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,2,5,1,3,6,8,7]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,7,1,8,6]=>[1,5,7,8,6,2,3,4]=>[8,4,2,1,3,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,1,3,4,7]=>[1,5,2,6,3,8,7,4]=>[8,4,7,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,3,8,4,7]=>[1,6,8,7,4,2,5,3]=>[8,3,1,2,5,7,4,6]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,6,8,1,7]=>[1,2,4,5,6,8,7,3]=>[8,7,5,4,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,7,8,4,5]=>[1,6,8,5,7,4,2,3]=>[8,3,1,4,2,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,8,5,2,3]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,1,4,3]=>[1,8,3,6,2,5,4,7]=>[8,1,6,3,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,8,4,7,1]=>[1,2,5,8,3,6,4,7]=>[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,3,1,7,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,8,3,5,4]=>[1,2,7,5,8,4,3,6]=>[8,7,2,4,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,3,2,8,4]=>[1,7,8,4,6,2,3,5]=>[8,2,1,5,3,7,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,5,2,7,6]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,4,3,1,7]=>[1,8,7,2,3,5,4,6]=>[8,1,2,7,6,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,6,5,1,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,8,6,2,7]=>[1,3,4,5,8,7,2,6]=>[8,6,5,4,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,2,8,4,6]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,3,2,4,6]=>[1,5,3,8,6,2,7,4]=>[8,4,6,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,6,7,3,5]=>[1,8,5,6,7,3,4,2]=>[8,1,4,3,2,6,5,7]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,2,4,1,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,3,6,2,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,3,5,4,2]=>[1,7,4,2,8,3,6,5]=>[8,2,5,7,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,4,3,2,6]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,3,4,1,6]=>[1,8,6,4,5,3,7,2]=>[8,1,3,5,4,6,2,7]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,3,1,5]=>[1,8,5,6,3,7,2,4]=>[8,1,4,3,6,2,7,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,8,3,6,4]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,2,1,8,5]=>[1,7,8,5,2,6,3,4]=>[8,2,1,4,7,3,6,5]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,1,7,2,6]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,8,2,1,4]=>[1,5,8,4,7,2,6,3]=>[8,4,1,5,2,7,3,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,7,2,1,5]=>[1,8,5,7,2,6,3,4]=>[8,1,4,2,7,3,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,7,5,1,2]=>[1,4,6,5,7,2,3,8]=>[8,5,3,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,7,8,3,1]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,7,1,8,3]=>[1,4,2,5,7,8,3,6]=>[8,5,7,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,1,7,8,3]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,1,7,3,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,3,1,4,5]=>[1,6,2,8,5,3,7,4]=>[8,3,7,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,3,7,4,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,1,3,8,4,6]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,1,6,8,2]=>[1,3,5,2,7,8,4,6]=>[8,6,4,7,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,2,6,3,8]=>[1,7,3,5,2,4,6,8]=>[8,2,6,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,6,8,1,3]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,8,1,7,5]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,7,9,2,1]=>[1,8,2,3,4,5,6,7,9]=>[9,2,8,7,6,5,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,9,1,8,6]=>[1,2,3,4,5,7,6,9,8]=>[9,8,7,6,5,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,5,8,1,6,7,4]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,6,8,1,3]=>[1,2,4,5,6,8,3,7]=>[8,7,5,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,7,9,2,8]=>[1,3,2,4,5,6,7,9,8]=>[9,7,8,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,9,1,8]=>[1,3,4,5,6,7,9,8,2]=>[9,7,6,5,4,3,1,2,8]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,4,5,6,7,8,10,1,2]=>[1,9,2,3,4,5,6,7,8,10]=>[10,2,9,8,7,6,5,4,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,10,1,9,7]=>[1,2,3,4,5,6,8,7,10,9]=>[10,9,8,7,6,5,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,7,6,5,2,8,3,1]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,7,6,3,4]=>[1,8,4,2,5,7,3,6]=>[8,1,5,7,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,6,4,1,8,5]=>[1,2,7,8,5,4,6,3]=>[8,7,2,1,4,5,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,4,8,2,7]=>[1,3,5,4,2,6,8,7]=>[8,6,4,5,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,6,3,8,7]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,4,2,8,7]=>[1,3,5,4,6,2,7,8]=>[8,6,4,5,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,3,1,7,2]=>[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,3,6,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,4,8,2,1]=>[1,5,4,6,8,2,3,7]=>[8,4,5,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,2,8,1,5]=>[1,3,6,8,5,2,7,4]=>[8,6,3,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,3,7,2,5]=>[1,8,5,3,2,6,7,4]=>[8,1,4,6,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,1,6,3,2]=>[1,8,2,4,5,3,7,6]=>[8,1,7,5,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,7,8,6,4]=>[1,2,3,5,7,6,8,4]=>[8,7,6,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,7,6,5,2]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,6,7,5,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,5,7,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,2,1,5]=>[1,8,5,7,2,6,3,4]=>[8,1,4,2,7,3,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,3,2,6,7]=>[1,5,3,2,8,7,6,4]=>[8,4,6,7,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,8,2,7,1]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,3,2,5,6]=>[1,7,5,3,2,8,6,4]=>[8,2,4,6,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,6,5,7,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,4,5,6,8,3]=>[1,7,8,3,2,4,5,6]=>[8,2,1,6,7,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,4,5,6,3]=>[1,2,8,3,7,6,5,4]=>[8,7,1,6,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,4,5,6,2]=>[1,8,2,7,6,5,4,3]=>[8,1,7,2,3,4,5,6]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,4,6,7,2]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,4,6,8,3]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,1,6,7,4]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,5,7,8,3]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,1,7,8,2]=>[1,6,7,8,2,5,3,4]=>[8,3,2,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,1,4,7,8,6]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,2,7,8,6]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,4,7,8,6]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,5,6,8,4]=>[1,7,8,4,3,2,5,6]=>[8,2,1,5,6,7,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,2,3,1,6]=>[1,5,2,4,7,3,8,6]=>[8,4,7,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,3,6,2,7]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,4,6,2,7]=>[1,8,7,2,3,5,4,6]=>[8,1,2,7,6,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,7,4,3,6]=>[1,5,7,3,2,8,6,4]=>[8,4,2,6,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,1,8,4,3]=>[1,6,8,3,7,4,2,5]=>[8,3,1,6,2,5,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,3,8,6,2]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,8,5,6,2]=>[1,7,6,5,8,2,4,3]=>[8,2,3,4,1,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,1,7,2,5]=>[1,3,8,5,2,6,7,4]=>[8,6,1,4,7,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,7,6,3,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,8,4,3,1]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,7,8,6,1]=>[1,3,2,5,7,6,8,4]=>[8,6,7,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,8,2,1,4]=>[1,7,2,5,8,4,3,6]=>[8,2,7,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,4,5,8,3]=>[1,2,6,5,4,7,8,3]=>[8,7,3,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,2,5,7,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,1,6,8,2]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,9,8,11,10]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,6,4,7,5,9,8]=>[1,2,3,4,6,7,5,8,9]=>[9,8,7,6,4,3,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,6,3,7,4,8,5,9]=>[1,2,3,6,4,5,7,8,9]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,4,2,7,6,1,5,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,2,6,5,3]=>[1,8,3,7,5,2,4,6]=>[8,1,6,2,4,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,1,2,5,3]=>[1,8,3,7,5,2,4,6]=>[8,1,6,2,4,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,6,2,4,3]=>[1,5,6,2,7,4,3,8]=>[8,4,3,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,5,2,1,3]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,1,5,4,3]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,2,5,1,3]=>[1,6,5,2,8,3,7,4]=>[8,3,4,7,1,6,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,7,2,1,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,6,4,8,1]=>[1,2,5,6,4,7,8,3]=>[8,7,4,3,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,6,4,2,8]=>[1,3,5,6,4,7,2,8]=>[8,6,4,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,4,7,2,8]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,3,4,7,1]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,5,2,7,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,6,4,2,8]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,5,2,7,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,5,2,7,8]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,5,7,1,8]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,5,1,7,8]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,1,3,6,8]=>[1,4,7,6,3,2,5,8]=>[8,5,2,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,5,3,7,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,4,8,7,3]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,5,7,4,2]=>[1,6,7,4,3,2,8,5]=>[8,3,2,5,6,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,7,4,6,1]=>[1,5,7,6,4,2,8,3]=>[8,4,2,3,5,7,1,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,5,4,7,2]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,5,3,7,4]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,6,4,8,3]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,6,1,7,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,6,7,4,2,8]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,5,6,2,4]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,5,3,4,8]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,5,2,4,6]=>[1,3,2,7,4,8,6,5]=>[8,6,7,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,7,1,3,5]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,4,7,2,8]=>[1,5,4,6,7,2,3,8]=>[8,4,5,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,8,7,3,6]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,5,8,6,2]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,6,5,7,3]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,8,7,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,5,7,2,9,4,6,8]=>[1,2,3,5,4,7,6,9,8]=>[9,8,7,5,6,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,1,4,8,3,2,7]=>[1,5,8,7,2,6,3,4]=>[8,4,1,2,7,3,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,6,7,8,9,10]=>[1,2,4,5,3,6,7,8,9,10]=>[10,9,7,6,8,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,4,1,3,7,8,6,5]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,7,8,4,3]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,7,8,2,3]=>[1,5,7,2,3,6,8,4]=>[8,4,2,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,5,1,2]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,2,3,5,1]=>[1,4,8,2,7,5,3,6]=>[8,5,1,7,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,1,2,6,3]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,8,1,4,2]=>[1,3,7,4,5,8,2,6]=>[8,6,2,5,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,8,2,4,1]=>[1,3,5,8,2,7,4,6]=>[8,6,4,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,6,8,4,5,3]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,2,6,3,8]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,8,3,6,2]=>[1,2,4,5,8,3,7,6]=>[8,7,5,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,5,6,2,1]=>[1,4,3,7,2,8,5,6]=>[8,5,6,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,5,4,2,8]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,6,5,7,2]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,5,8,7,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,3,4,8,7]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,3,4,8,7]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,2,4,3,7]=>[1,8,7,3,5,2,4,6]=>[8,1,2,6,4,7,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,3,2,7,8]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,3,2,6,8]=>[1,5,3,2,7,6,4,8]=>[8,4,6,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,3,7,5,8]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,2,1,6,4]=>[1,7,6,2,8,4,3,5]=>[8,2,3,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,8,4,5,3]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,2,7,5,3]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,1,8,4,6]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,8,4,6,5]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,3,2,8,6]=>[1,5,3,2,4,7,8,6]=>[8,4,6,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,1,8,6,2]=>[1,7,6,8,2,3,4,5]=>[8,2,3,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,7,4,8,1]=>[1,6,4,5,7,8,2,3]=>[8,3,5,4,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,7,6,3,8]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,3,1,4,5]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,1,7,8,4]=>[1,6,7,8,4,5,2,3]=>[8,3,2,1,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,8,2,1,5]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,8,4,2,3]=>[1,5,8,3,7,2,6,4]=>[8,4,1,6,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,6,5,2,3]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,8,6,5,4]=>[1,2,7,5,8,4,3,6]=>[8,7,2,4,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,8,6,5,4]=>[1,3,2,7,5,8,4,6]=>[8,6,7,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,6,5,3,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,7,6,3,4]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,3,4,6,2]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,6,3,1,5]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,7,6,3,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,1,6,2,3]=>[1,4,7,2,5,3,8,6]=>[8,5,2,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,6,7,5,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,4,7,6,3]=>[1,2,5,4,8,3,6,7]=>[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,1,7,6,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,1,7,6,3]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,6,7,3,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,7,6,4,5]=>[1,8,5,7,4,2,3,6]=>[8,1,4,2,5,7,6,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,6,2,5,1]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,3,1,7,2]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,3,8,1,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,7,1,3,2]=>[1,6,2,8,3,5,7,4]=>[8,3,7,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,3,4,2,6]=>[1,7,2,5,3,8,6,4]=>[8,2,7,4,6,1,3,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,8,7,2,6]=>[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,4,2,6,3]=>[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,7,4,8,3]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,4,2,8,3]=>[1,5,4,7,8,3,6,2]=>[8,4,5,2,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,2,3,7,4]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,8,6,7,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,6,2,7,3]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,6,2,7,3]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,7,2,8,3]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,7,6,2,5]=>[1,4,3,2,8,5,7,6]=>[8,5,6,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,1,8,7,5]=>[1,6,8,5,2,4,3,7]=>[8,3,1,4,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,7,6,1,5]=>[1,8,5,7,2,4,3,6]=>[8,1,4,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,2,4,3,6]=>[1,5,2,7,3,8,6,4]=>[8,4,7,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,3,5,4,2]=>[1,2,7,4,8,3,6,5]=>[8,7,2,5,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,2,1,3,8]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,1,3,2,8]=>[1,6,3,7,2,5,4,8]=>[8,3,6,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,3,5,2,7]=>[1,4,8,7,2,6,5,3]=>[8,5,1,2,7,3,4,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,3,2,5,6]=>[1,4,8,6,2,7,5,3]=>[8,5,1,3,7,2,4,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,4,5,3,2]=>[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,4,5,1,7]=>[1,3,8,7,2,4,6,5]=>[8,6,1,2,7,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,2,5,1,7]=>[1,8,7,2,4,6,5,3]=>[8,1,2,7,5,3,4,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,4,3,5,2]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,8,7,5,4]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,1,8,6,3]=>[1,5,2,7,6,8,3,4]=>[8,4,7,2,3,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,2,4,3,1]=>[1,8,2,6,4,7,3,5]=>[8,1,7,3,5,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,8,5,3,2]=>[1,7,3,6,5,8,2,4]=>[8,2,6,3,4,1,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,8,1,5,2]=>[1,7,5,8,2,4,3,6]=>[8,2,4,1,7,5,6,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,6,3,2,5]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,6,2,1,5]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,5,7,1,3]=>[1,4,2,6,7,3,8,5]=>[8,5,7,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,5,7,1,3]=>[1,6,7,2,4,3,8,5]=>[8,3,2,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,7,3,5,1]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,7,1,3,5]=>[1,8,5,7,3,6,2,4]=>[8,1,4,2,6,3,7,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,7,1,3,5]=>[1,6,2,8,5,7,3,4]=>[8,3,7,1,4,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,1,7,3,5]=>[1,6,7,3,2,8,5,4]=>[8,3,2,6,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,2,4,8,3]=>[1,7,8,3,2,5,4,6]=>[8,2,1,6,7,4,5,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,1,6,8,3]=>[1,4,7,8,3,5,2,6]=>[8,5,2,1,6,4,7,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,6,7,3,1]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,8,7,1,6]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,6,1,3,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,6,1,4,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,5,1,6,8]=>[1,4,3,7,6,2,5,8]=>[8,5,6,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,8,4,7,1]=>[1,5,8,2,6,4,3,7]=>[8,4,1,7,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,1,7,8,4]=>[1,5,2,6,7,8,4,3]=>[8,4,7,3,2,1,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,4,1,6,8]=>[1,5,4,3,2,7,6,8]=>[8,4,5,6,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,5,1,4,8]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,5,1,4,8]=>[1,7,4,3,6,2,5,8]=>[8,2,5,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,3,1,7,8,4]=>[1,6,7,8,4,3,2,5]=>[8,3,2,1,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,3,8,4,7,1]=>[1,6,4,3,2,5,8,7]=>[8,3,5,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,4,6,8,3]=>[1,7,8,3,2,5,4,6]=>[8,2,1,6,7,4,5,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,1,6,4,7]=>[1,8,7,4,3,2,5,6]=>[8,1,2,5,6,7,4,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,1,5,4,7]=>[1,8,7,4,3,2,6,5]=>[8,1,2,5,6,7,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,1,7,4,5]=>[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,2,7,5,8]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,5,6,8,3]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,5,6,3,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,1,6,4,7]=>[1,5,2,8,7,4,3,6]=>[8,4,7,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,5,6,8,3]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,1,7,5,6]=>[1,4,8,6,7,5,2,3]=>[8,5,1,3,2,4,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,3,7,6,8]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,6,7,8,4]=>[1,5,6,7,8,4,2,3]=>[8,4,3,2,1,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,2,7,6,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,2,7,5,8]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,5,8,4,6]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,3,4,5,1]=>[1,6,4,2,8,3,7,5]=>[8,3,5,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,1,4,5,6]=>[1,3,2,7,5,4,8,6]=>[8,6,7,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,4,6,1,8]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,4,5,1,8]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,4,5,1,8]=>[1,6,5,4,3,7,2,8]=>[8,3,4,5,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,2,1,6,7]=>[1,3,4,5,2,8,7,6]=>[8,6,5,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,1,3,4,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,8,3,6,1]=>[1,4,2,5,8,3,7,6]=>[8,5,7,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,6,7,8,4]=>[1,5,6,7,8,4,3,2]=>[8,4,3,2,1,5,6,7]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,2,8,3,4]=>[1,2,6,8,4,7,3,5]=>[8,7,3,1,5,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,7,8,4,3]=>[1,6,8,3,5,7,4,2]=>[8,3,1,6,4,2,5,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,2,8,4,3]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,2,8,7,3]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,6,2,8,3,7]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,8,2,3,7]=>[1,2,5,8,7,3,6,4]=>[8,7,4,1,2,6,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,8,4,7,3]=>[1,6,4,5,8,3,2,7]=>[8,3,5,4,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,4,1,3,2]=>[1,7,3,6,2,5,4,8]=>[8,2,6,3,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,1,4,2,6]=>[1,8,6,4,5,2,3,7]=>[8,1,3,5,4,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,3,6,2,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,7,1,3,4]=>[1,8,4,2,5,7,3,6]=>[8,1,5,7,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,4,7,5]=>[1,8,5,6,4,3,2,7]=>[8,1,4,3,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,5,8,1,4]=>[1,7,2,6,8,4,3,5]=>[8,2,7,3,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,8,1,6,2]=>[1,4,7,6,2,5,8,3]=>[8,5,2,3,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,1,6,7,5]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,5,7,6,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,4,3,7,8]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,6,7,4,1]=>[1,3,2,5,6,7,4,8]=>[8,6,7,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,2,8,6,1]=>[1,5,2,3,7,6,8,4]=>[8,4,7,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,3,5,6,1]=>[1,7,6,5,3,8,2,4]=>[8,2,3,4,6,1,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,7,1,4,3]=>[1,5,7,4,8,3,2,6]=>[8,4,2,5,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,2,7,8,1]=>[1,4,5,2,6,7,8,3]=>[8,5,4,7,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,4,6,8,2]=>[1,3,5,4,7,8,2,6]=>[8,6,4,5,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,5,7,8,2]=>[1,4,2,3,6,7,8,5]=>[8,5,7,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,2,6,7,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,6,7,8,2]=>[1,5,6,7,8,2,3,4]=>[8,4,3,2,1,7,6,5]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,3,5,8,2]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,4,7,2,8]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,7,8,4,6,1]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,1,7,5,8]=>[1,3,2,6,7,5,4,8]=>[8,6,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,4,8,5,1]=>[1,3,6,8,2,4,7,5]=>[8,6,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,4,5,2,6]=>[1,7,2,3,4,8,6,5]=>[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,4,6,2,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,5,8,4,1]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,4,5,3,8]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,5,7,3,8]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,6,7,3,8]=>[1,5,6,7,3,2,4,8]=>[8,4,3,2,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,4,1,3,8]=>[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,8,4,5,2]=>[1,3,6,4,7,5,8,2]=>[8,6,3,5,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,2,1,8,3]=>[1,7,8,3,5,2,4,6]=>[8,2,1,6,4,7,5,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,7,1,8,3]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,2,1,8,4]=>[1,3,5,2,7,8,4,6]=>[8,6,4,7,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,8,4,5,2]=>[1,2,7,5,8,3,6,4]=>[8,7,2,4,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,5,2,7,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,3,7,1,6]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,2,5,1,6]=>[1,7,2,3,4,8,6,5]=>[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,6,5,8,1,7]=>[1,3,4,6,8,7,2,5]=>[8,6,5,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,7,1,6,2]=>[1,3,4,8,2,5,7,6]=>[8,6,5,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,6,3,4,8]=>[1,7,4,2,5,6,3,8]=>[8,2,5,7,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,4,2,5,8]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,5,3,6,4]=>[1,8,4,2,7,6,3,5]=>[8,1,5,7,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,1,5,7,2]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,4,8,2,3]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,3,8,4,1]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,1,8,3,7]=>[1,5,2,6,8,7,3,4]=>[8,4,7,3,1,2,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,2,7,5,4]=>[1,6,7,5,2,8,4,3]=>[8,3,2,4,7,1,5,6]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,4,1,2,8]=>[1,5,4,6,2,7,3,8]=>[8,4,5,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,8,1,5,6]=>[1,7,5,8,6,2,3,4]=>[8,2,4,1,3,7,6,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,1,3,8,7]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,8,1,6,7]=>[1,2,4,5,8,7,6,3]=>[8,7,5,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,7,4,3,1]=>[1,5,7,3,2,8,4,6]=>[8,4,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,8,1,4,7]=>[1,2,6,3,5,8,7,4]=>[8,7,3,6,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,4,3,2,5]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,7,8,5,2]=>[1,4,3,2,6,8,5,7]=>[8,5,6,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,2,6,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,1,8,7,2]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,3,6,7,4]=>[1,8,4,2,5,3,6,7]=>[8,1,5,7,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,5,4,7,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,7,1,2,5]=>[1,3,6,2,8,5,7,4]=>[8,6,3,7,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,4,3,2,6]=>[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,1,3,2,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,6,2,5,8]=>[1,3,4,7,5,6,2,8]=>[8,6,5,2,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,6,2,7,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,6,3,5,8]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,5,2,4,8]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,4,6,3,8]=>[1,7,3,5,4,2,6,8]=>[8,2,6,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,2,7,4,3]=>[1,6,7,4,8,3,5,2]=>[8,3,2,5,1,6,4,7]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,5,4,7,2]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,7,4,5,2]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,6,5,2,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,1,3,6,4]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,6,3,8,7]=>[1,5,6,3,2,4,7,8]=>[8,4,3,6,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,1,3,6,5]=>[1,2,7,6,3,8,5,4]=>[8,7,2,3,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,5,8,1,3]=>[1,2,4,7,3,6,8,5]=>[8,7,5,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,3,7,8,1,5]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,8,7,1,3]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,8,3,7,1]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,3,8,1,7]=>[1,2,4,6,8,7,3,5]=>[8,7,5,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,8,5,1,7]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,4,1,6,7]=>[1,5,4,3,8,7,6,2]=>[8,4,5,6,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,2,7,8,5]=>[1,3,4,2,6,7,8,5]=>[8,6,5,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,5,3,7,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,6,5,1,3]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,6,5,1,3]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,7,1,4,3]=>[1,8,3,5,7,4,2,6]=>[8,1,6,4,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,7,1,4,3]=>[1,6,2,5,7,4,3,8]=>[8,3,7,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,1,6,4,3]=>[1,7,4,2,5,3,8,6]=>[8,2,5,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,5,8,4,7]=>[1,3,2,4,6,8,7,5]=>[8,6,7,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,5,7,3,1]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,5,8,2,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,7,6,2,5]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,8,7,2,4]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,4,1,6,3]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,4,2,6,3]=>[1,8,3,5,4,7,6,2]=>[8,1,6,4,5,2,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,5,7,1,6]=>[1,3,8,6,7,2,4,5]=>[8,6,1,3,2,7,5,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,4,5,3,7]=>[1,6,5,4,2,3,8,7]=>[8,3,4,5,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,2,7,1,5]=>[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,7,6,2,5]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,8,5,1,3]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,6,1,8,2]=>[1,5,6,2,4,7,8,3]=>[8,4,3,7,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,1,4,2,5]=>[1,8,5,2,6,4,7,3]=>[8,1,4,7,3,5,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,7,6,4,5]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,2,3,7,6]=>[1,8,6,3,4,2,5,7]=>[8,1,3,6,5,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,6,4,7,5]=>[1,8,5,6,4,2,3,7]=>[8,1,4,3,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,1,7,5,6]=>[1,2,3,8,6,7,5,4]=>[8,7,6,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,2,7,8,5]=>[1,4,3,2,6,7,8,5]=>[8,5,6,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,5,8,4,1,3]=>[1,6,4,5,8,3,2,7]=>[8,3,5,4,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,8,2,5,6,3]=>[1,4,8,3,7,6,5,2]=>[8,5,1,6,2,3,4,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,8,1,6,2]=>[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,3,5,2,6]=>[1,2,8,6,5,3,7,4]=>[8,7,1,3,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,5,3,1,4]=>[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,6,1,4,7]=>[1,2,8,7,4,5,6,3]=>[8,7,1,2,5,4,3,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,2,7,5,8]=>[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,8,1,4,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,6,1,4,7]=>[1,3,8,7,4,5,6,2]=>[8,6,1,2,5,4,3,7]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,1,2,3,6]=>[1,4,8,6,2,7,3,5]=>[8,5,1,3,7,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,2,8,1,6]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,7,8,1,6]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,3,8,1,6]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,6,3,1,2]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,7,6,2,3]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,8,1,6,7]=>[1,3,4,5,8,7,6,2]=>[8,6,5,4,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,2,7,1,5]=>[1,3,8,5,2,6,7,4]=>[8,6,1,4,7,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,6,2,1,5]=>[1,4,7,2,8,5,6,3]=>[8,5,2,7,1,4,3,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,3,8,2,5]=>[1,2,4,6,8,5,3,7]=>[8,7,5,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,7,2,8,4]=>[1,3,5,7,8,4,2,6]=>[8,6,4,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,2,8,5,3]=>[1,7,5,2,4,6,8,3]=>[8,2,4,7,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,2,4,7,5]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,3,8,2,5]=>[1,2,6,8,5,3,7,4]=>[8,7,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,5,2,8,4]=>[1,7,8,4,6,2,3,5]=>[8,2,1,5,3,7,6,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,6,2,7,3]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,5,1,6,3]=>[1,4,8,3,2,7,6,5]=>[8,5,1,6,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,1,5,4,3]=>[1,7,4,2,8,3,6,5]=>[8,2,5,7,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,3,5,1,4]=>[1,8,4,7,2,6,5,3]=>[8,1,5,2,7,3,4,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,7,5,6,4]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,3,8,5,2]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,10,7,9]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,2,1,9]=>[1,3,5,7,2,4,6,8,9]=>[9,7,5,3,8,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,2,1,8,9]=>[1,3,5,7,2,4,6,8,9]=>[9,7,5,3,8,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,5,6,7,8,1,2,3,9]=>[1,4,7,2,5,8,3,6,9]=>[9,6,3,8,5,2,7,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,8,1,6,3,7,2,5]=>[1,4,6,7,2,8,5,3]=>[8,5,3,2,7,1,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,6,3,7,2]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,4,8,5,3]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,4,3,1,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,3,5,1,7]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,6,4,5,1]=>[1,2,7,5,6,4,3,8]=>[8,7,2,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,4,1,8,3,6]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,5,3,2,7]=>[1,4,8,7,2,6,3,5]=>[8,5,1,2,7,3,6,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,1,6,4,7]=>[1,3,5,2,8,7,4,6]=>[8,6,4,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,2,6,3,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,3,7,6,2]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,4,3,2,5]=>[1,8,5,4,2,6,3,7]=>[8,1,4,5,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,3,4,7,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,2,7,4,5]=>[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,1,8,5,4]=>[1,3,6,8,4,2,7,5]=>[8,6,3,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,7,1,5,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,4,7,2,3]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,5,4,8,1,3]=>[1,6,8,3,2,7,4,5]=>[8,3,1,6,7,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,8,5,1,3]=>[1,7,2,6,5,8,3,4]=>[8,2,7,3,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,6,3,8,1]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,8,1,4,7]=>[1,3,6,2,5,8,7,4]=>[8,6,3,7,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,3,7,6,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,4,3,5,7]=>[1,6,3,8,7,5,4,2]=>[8,3,6,1,2,4,5,7]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,5,3,4,7]=>[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,4,5,1,3]=>[1,8,3,6,5,4,2,7]=>[8,1,6,3,4,5,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,4,5,3,1]=>[1,8,2,7,3,6,5,4]=>[8,1,7,2,6,3,4,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,1,2,6,3]=>[1,5,2,4,7,6,3,8]=>[8,4,7,5,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,6,5,1,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,5,6,2,3]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,5,6,2,7]=>[1,4,8,7,2,3,5,6]=>[8,5,1,2,7,6,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,3,2,5,4]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,5,6,1,8]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,5,7,4,6]=>[1,3,8,6,7,4,2,5]=>[8,6,1,3,2,5,7,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,2,1,5,8]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,1,8,3,4]=>[1,5,2,7,3,6,8,4]=>[8,4,7,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,8,6,7,1]=>[1,4,3,5,8,2,6,7]=>[8,5,6,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,8,5,6,1]=>[1,3,7,6,5,8,2,4]=>[8,6,2,3,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,6,3,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,4,2,7,1]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,3,5,2,8]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,7,4,1,6]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,1,2,7,4]=>[1,6,2,8,4,5,3,7]=>[8,3,7,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,6,4,3,2]=>[1,8,2,7,3,5,6,4]=>[8,1,7,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,7,5,2,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,8,5,2,4]=>[1,2,7,3,6,5,8,4]=>[8,7,2,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,4,5,6,2]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,4,5,6,2]=>[1,7,6,5,4,8,2,3]=>[8,2,3,4,5,1,7,6]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,4,5,6,1]=>[1,3,8,2,4,7,6,5]=>[8,6,1,7,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,5,7,6,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,7,4,6,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,3,8,6,1]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,7,8,1,2,5]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,7,1,2,6]=>[1,8,6,2,3,5,7,4]=>[8,1,3,7,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,4,1,7,8,3]=>[1,6,7,8,3,5,2,4]=>[8,3,2,1,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,3,2,4,7]=>[1,8,7,4,6,2,5,3]=>[8,1,2,5,3,7,4,6]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,3,2,5,1]=>[1,6,2,8,3,7,5,4]=>[8,3,7,1,6,2,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,6,7,3,2]=>[1,8,2,3,5,6,7,4]=>[8,1,7,6,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,3,7,6,4]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,3,7,6,1]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,1,8,2,7,3]=>[1,5,8,3,4,2,6,7]=>[8,4,1,6,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,3,8,7,2]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,5,4,8,2,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,2,5,6,4]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,6,5,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,7,6,5,1]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,4,6,5,2]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,4,6,8,7]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,2,8,4,3]=>[1,6,8,3,2,7,4,5]=>[8,3,1,6,7,2,5,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,6,4,8,2]=>[1,2,5,6,4,7,8,3]=>[8,7,4,3,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,6,2,7,5]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,4,8,6,5,1]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,8,3,6,1]=>[1,2,5,8,3,7,6,4]=>[8,7,4,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,4,7,1,3]=>[1,8,3,6,7,2,5,4]=>[8,1,6,3,2,7,4,5]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,7,1,3,2]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,3,6,4,2]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,2,8,5,6]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,3,8,5,1]=>[1,2,7,5,3,6,8,4]=>[8,7,2,4,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,2,4,6,7]=>[1,5,2,8,7,6,4,3]=>[8,4,7,1,2,3,5,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,2,3,6,7]=>[1,2,4,5,3,8,7,6]=>[8,7,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,2,3,7,6]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,6,8,3,5]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,3,5,4,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,8,1,3,5]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,7,2,3,5]=>[1,4,8,5,7,3,6,2]=>[8,5,1,4,2,6,3,7]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,2,8,3,1]=>[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,2,8,4,3,1]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,2,7,5,1]=>[1,6,7,5,2,8,3,4]=>[8,3,2,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,9,7,10,8]=>[1,2,3,4,5,6,7,9,10,8]=>[10,9,8,7,6,5,4,2,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,7,5,9,6,10,8]=>[1,2,3,4,5,7,9,10,8,6]=>[10,9,8,7,6,4,2,1,3,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,5,3,7,4,9,6,10,8]=>[1,2,3,5,7,9,10,8,6,4]=>[10,9,8,6,4,2,1,3,5,7]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,6,3,7,4,8,5,10,9]=>[1,2,3,6,4,5,7,8,9,10]=>[10,9,8,5,7,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,11,9,12,10]=>[1,2,3,4,5,6,7,8,9,11,12,10]=>[12,11,10,9,8,7,6,5,4,2,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[3,1,5,2,7,4,9,6,11,8,12,10]=>[1,3,5,7,9,11,12,10,8,6,4,2]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,1,7,3,5,8,2,4]=>[1,6,8,4,3,7,2,5]=>[8,3,1,5,6,2,7,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,4,8,2,5]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,7,3,1,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,3,5,4,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,7,4,3,2]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,7,6,3,2]=>[1,8,2,5,7,3,4,6]=>[8,1,7,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,2,4,6,5]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,5,8,4,1]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,5,8,1,4]=>[1,2,6,8,4,3,7,5]=>[8,7,3,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,1,4,8,3]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,3,2,8,1,6]=>[1,4,3,5,2,7,6,8]=>[8,5,6,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,7,4,3,6]=>[1,5,7,3,2,8,6,4]=>[8,4,2,6,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,2,4,5,7]=>[1,6,4,8,7,5,2,3]=>[8,3,5,1,2,4,7,6]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,5,8,6,3]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,8,3,1,5]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,4,3,7,2]=>[1,6,3,8,2,5,4,7]=>[8,3,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,9,10,11,2,12,3,4,5,6,7]=>[1,2,8,3,9,4,10,5,11,6,7,12]=>[12,11,5,10,4,9,3,8,2,7,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,8,9,10,11,12,2,3,4,5,6,7]=>[1,2,8,3,9,4,10,5,11,6,12,7]=>[12,11,5,10,4,9,3,8,2,7,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,6,3,5,2,1,7,4]=>[1,8,4,5,2,6,3,7]=>[8,1,5,4,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,4,7,1,2,3]=>[1,5,7,2,8,3,6,4]=>[8,4,2,7,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,8,6,1,5]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,5,1,7,2]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,4,6,8,2,5]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,1,3,2,4]=>[1,8,4,6,3,7,2,5]=>[8,1,5,3,6,2,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,1,8,4,3]=>[1,2,7,4,6,8,3,5]=>[8,7,2,5,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,4,5,8,3]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,8,1,4,5]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,8,5,4,7]=>[1,2,6,5,8,7,4,3]=>[8,7,3,4,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,3,2,5,7]=>[1,6,2,4,8,7,5,3]=>[8,3,7,5,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,2,7,3,6]=>[1,5,2,8,6,7,3,4]=>[8,4,7,1,3,2,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,8,7,4,5]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,1,7,3,5]=>[1,6,7,3,8,5,2,4]=>[8,3,2,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,7,5,6,4]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,2,4,3,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,1,2,5,4]=>[1,6,2,8,4,7,5,3]=>[8,3,7,1,5,2,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,1,5,3,7]=>[1,2,8,7,3,6,5,4]=>[8,7,1,2,6,3,4,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,6,2,4,8]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,1,3,8,2]=>[1,6,3,4,5,2,7,8]=>[8,3,6,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,3,8,2,4,7]=>[1,2,6,3,5,8,7,4]=>[8,7,3,6,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,4,3,6]=>[1,8,6,4,2,5,7,3]=>[8,1,3,5,7,4,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,4,1,7,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,1,2,5,8]=>[1,3,7,5,2,6,4,8]=>[8,6,2,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,7,3,2,5]=>[1,2,6,3,8,5,7,4]=>[8,7,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,4,8,1,2]=>[1,3,7,2,6,8,4,5]=>[8,6,2,7,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,6,3,8,1]=>[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,4,6,8,3]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,8,1,6,4]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,2,3,6,8]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,4,6,3,5]=>[1,8,5,4,2,3,7,6]=>[8,1,4,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,8,6,3,5]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,8,2,4,7]=>[1,2,5,8,7,4,6,3]=>[8,7,4,1,2,5,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,6,3,7,5]=>[1,4,2,8,5,6,3,7]=>[8,5,7,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,7,5,8,4]=>[1,2,6,5,7,8,4,3]=>[8,7,3,4,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,5,7,8,3]=>[1,4,6,7,8,3,2,5]=>[8,5,3,2,1,6,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,3,8,6,4]=>[1,2,7,6,8,4,3,5]=>[8,7,2,3,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,3,5,2,6]=>[1,8,6,5,3,4,7,2]=>[8,1,3,4,6,5,2,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,3,7,4,5]=>[1,2,6,7,4,8,5,3]=>[8,7,3,2,5,1,4,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,6,8,3,4]=>[1,2,5,6,8,4,7,3]=>[8,7,4,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,2,4,7,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,7,5,8,4]=>[1,2,3,6,5,7,8,4]=>[8,7,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,6,7,8,2]=>[1,3,5,6,7,8,2,4]=>[8,6,4,3,2,1,7,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,3,8,5,6]=>[1,7,5,3,2,4,6,8]=>[8,2,4,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,8,5,4,6]=>[1,7,4,3,2,5,8,6]=>[8,2,5,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,8,6,4,5]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,2,4,8,6]=>[1,2,7,8,6,4,3,5]=>[8,7,2,1,3,5,6,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,6,5,8,3]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,5,7,8,2]=>[1,3,2,4,6,7,8,5]=>[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,4,1,5,6]=>[1,2,8,6,3,7,5,4]=>[8,7,1,3,6,2,4,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,3,8,1,4]=>[1,5,3,6,8,4,2,7]=>[8,4,6,3,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,3,2,6,4]=>[1,5,3,7,6,2,4,8]=>[8,4,6,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,4,3,7,5]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,6,2,7,5]=>[1,4,2,8,5,6,3,7]=>[8,5,7,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,6,4,7,5]=>[1,2,8,5,6,4,3,7]=>[8,7,1,4,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,5,8,4,3]=>[1,6,8,3,7,4,2,5]=>[8,3,1,6,2,5,7,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,8,9,10,3,2]=>[1,2,4,6,8,10,3,5,7,9]=>[10,9,7,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,8,5,1,3,2,6,7]=>[1,4,2,8,7,6,3,5]=>[8,5,7,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,2,7,6,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,2,3,7,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,3,6,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,7,2,5,8]=>[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,8,3,7,5]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,7,2,5,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,3,4,7,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,7,4,5,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,2,4,1,8]=>[1,6,4,7,2,5,3,8]=>[8,3,5,2,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,1,5,4,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,3,2,4,8]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,7,2,3,8]=>[1,5,7,3,2,6,4,8]=>[8,4,2,6,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,8,6,3,4]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,4,5,3,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,4,6,3,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,1,7,4,3]=>[1,8,3,5,2,6,7,4]=>[8,1,6,4,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,7,1,5,2]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,7,1,6,5]=>[1,8,5,7,6,2,3,4]=>[8,1,4,2,3,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,6,1,5,4]=>[1,7,5,6,2,3,4,8]=>[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,6,1,4,3]=>[1,7,4,2,5,6,3,8]=>[8,2,5,7,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,7,4,1,3]=>[1,5,7,2,6,4,3,8]=>[8,4,2,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,6,5,8,3]=>[1,7,8,3,2,4,5,6]=>[8,2,1,6,7,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,6,1,8,3]=>[1,5,6,2,3,7,8,4]=>[8,4,3,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,3,1,5,2]=>[1,8,2,4,7,5,3,6]=>[8,1,7,5,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,1,2,7,3]=>[1,4,5,2,6,3,8,7]=>[8,5,4,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,4,2,5,7]=>[1,2,6,3,8,7,5,4]=>[8,7,3,6,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,3,4,2,6]=>[1,2,8,6,4,5,3,7]=>[8,7,1,3,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,4,2,3,5]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,4,3,2,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,4,2,3,6]=>[1,5,4,8,6,2,3,7]=>[8,4,5,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,6,7,5,4]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,5,8,3,6]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,7,8,3,5]=>[1,2,3,6,8,5,7,4]=>[8,7,6,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,4,2,1,6]=>[1,5,4,3,8,6,2,7]=>[8,4,5,6,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,3,8,2,6,1]=>[1,4,3,5,8,2,7,6]=>[8,5,6,4,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,8,5,3,1]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,6,1,3,2]=>[1,7,3,4,5,6,2,8]=>[8,2,6,5,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,4,6,7,3]=>[1,2,5,4,8,3,6,7]=>[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,6,7,1,3]=>[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,4,2,1,7]=>[1,6,2,5,4,3,8,7]=>[8,3,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,4,6,7,2]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,2,1,6,7]=>[1,3,5,2,4,8,7,6]=>[8,6,4,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,3,4,5,1]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,2,1,4,5]=>[1,6,2,8,5,3,7,4]=>[8,3,7,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,4,6,3,5]=>[1,7,3,2,8,5,4,6]=>[8,2,6,7,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,3,4,5,1,6]=>[1,7,2,3,8,6,5,4]=>[8,2,7,6,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,4,2,5,7]=>[1,6,2,3,8,7,5,4]=>[8,3,7,6,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,3,4,5,8]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,1,8,4,7]=>[1,6,8,7,4,2,3,5]=>[8,3,1,2,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,5,1,7,4]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,6,1,7,5]=>[1,3,4,8,5,6,2,7]=>[8,6,5,1,4,3,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,4,5,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,7,8,4,6,5]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,4,7,6,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,5,4,6,3]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,7,8,1,4]=>[1,3,6,8,4,5,7,2]=>[8,6,3,1,5,4,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,6,8,1,4]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,4,6,5,3]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,4,7,3,2]=>[1,6,7,3,5,4,8,2]=>[8,3,2,6,4,5,1,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,5,7,2,3]=>[1,2,4,8,3,6,7,5]=>[8,7,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,8,3,6,5]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,4,2,3,8,7]=>[1,6,3,5,2,4,7,8]=>[8,3,6,4,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,2,8,3,7]=>[1,6,8,7,3,5,2,4]=>[8,3,1,2,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,7,6,3,2]=>[1,8,2,4,5,7,3,6]=>[8,1,7,5,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,5,2,4,7]=>[1,8,7,4,3,6,2,5]=>[8,1,2,5,6,3,7,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,3,8,1,7]=>[1,4,5,3,2,6,8,7]=>[8,5,4,6,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,1,8,3,7]=>[1,4,2,6,8,7,3,5]=>[8,5,7,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,6,7,2,1]=>[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,6,7,4,1]=>[1,2,5,6,7,4,8,3]=>[8,7,4,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,1,8,4,7]=>[1,3,6,8,7,4,5,2]=>[8,6,3,1,2,5,4,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,1,6,2,3]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,6,7,3,2]=>[1,4,2,5,6,7,3,8]=>[8,5,7,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,1,7,2,4]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,3,7,2,4]=>[1,8,4,5,3,2,6,7]=>[8,1,5,4,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,8,1,5,4]=>[1,7,5,8,4,6,2,3]=>[8,2,4,1,5,3,7,6]=>[8,4,6,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,8,1,4,5]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,3,1,5,4]=>[1,7,5,3,8,4,6,2]=>[8,2,4,6,1,5,3,7]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,7,2,5,1]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,8,5,4,1]=>[1,7,4,6,5,8,2,3]=>[8,2,5,3,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,8,1,6,3]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,8,1,6,3]=>[1,7,6,2,5,8,3,4]=>[8,2,3,7,4,1,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,8,4,5,1]=>[1,7,5,8,2,6,4,3]=>[8,2,4,1,7,3,5,6]=>[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,8,4,5,1]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,8,3,6,1]=>[1,7,6,3,5,8,2,4]=>[8,2,3,6,4,1,7,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,8,3,6,1]=>[1,7,6,3,5,8,2,4]=>[8,2,3,6,4,1,7,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,4,5,2,8]=>[1,3,6,5,4,7,2,8]=>[8,6,3,4,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,7,6,2,8]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,4,6,8,7]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,1,7,3,6]=>[1,8,6,7,3,2,4,5]=>[8,1,3,2,6,7,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,2,3,6,1]=>[1,5,2,7,6,3,8,4]=>[8,4,7,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,8,3,7,1]=>[1,6,3,5,8,2,4,7]=>[8,3,6,4,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,3,1,2,7]=>[1,5,3,4,8,7,2,6]=>[8,4,6,5,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,6,3,8,5,1]=>[1,7,5,3,4,6,8,2]=>[8,2,4,6,5,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,8,7,3,1]=>[1,5,8,2,4,6,7,3]=>[8,4,1,7,5,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,8,1,7,2]=>[1,4,3,5,8,2,6,7]=>[8,5,6,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,6,1,5,3]=>[1,2,4,7,5,6,3,8]=>[8,7,5,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,4,6,5,1]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,7,6,3,1]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,2,1,6,5]=>[1,3,4,7,6,2,8,5]=>[8,6,5,2,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,7,6,3,2]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,6,2,3,4]=>[1,5,6,2,8,4,7,3]=>[8,4,3,7,1,5,2,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,5,7,1,8]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,4,6,3,8]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,6,5,1,2]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,3,6,7,4]=>[1,5,3,8,4,2,6,7]=>[8,4,6,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,4,5,8,1]=>[1,6,5,4,7,8,2,3]=>[8,3,4,5,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,5,6,1,2]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,6,3,4,8]=>[1,5,6,3,2,4,7,8]=>[8,4,3,6,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,5,7,1,3]=>[1,4,8,3,6,7,2,5]=>[8,5,1,6,3,2,7,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,7,8,2,6,5]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,8,7,2,6]=>[1,2,5,8,6,7,3,4]=>[8,7,4,1,3,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,4,3,6,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,6,4,3,7]=>[1,2,5,6,4,3,8,7]=>[8,7,4,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,4,7,8,1]=>[1,3,6,7,8,2,5,4]=>[8,6,3,2,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,2,4,8,1]=>[1,3,6,4,7,8,2,5]=>[8,6,3,5,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,6,8,4,1]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,6,8,4,1]=>[1,3,2,5,6,8,4,7]=>[8,6,7,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,2,6,8,1]=>[1,3,4,7,8,2,5,6]=>[8,6,5,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,2,6,8,1]=>[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,2,8,6,1]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,2,8,6,1]=>[1,3,4,7,6,8,2,5]=>[8,6,5,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,4,8,6,1]=>[1,3,5,4,7,6,8,2]=>[8,6,4,5,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,2,8,6,1]=>[1,3,7,6,8,2,5,4]=>[8,6,2,3,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,8,4,6,1]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,2,6,4,1]=>[1,3,7,4,8,2,5,6]=>[8,6,2,5,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,6,2,4,1]=>[1,3,7,4,8,2,5,6]=>[8,6,2,5,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,7,3,8,1]=>[1,4,6,3,5,7,8,2]=>[8,5,3,6,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,9,10,11,1]=>[1,3,4,5,6,7,8,9,10,11,2]=>[11,9,8,7,6,5,4,3,2,1,10]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,6,1,4,3,5,2,7]=>[1,8,7,2,6,5,3,4]=>[8,1,2,7,3,4,6,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,8,2,3,7]=>[1,5,8,7,3,6,2,4]=>[8,4,1,2,6,3,7,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,3,6,7]=>[1,8,7,6,3,4,2,5]=>[8,1,2,3,6,5,7,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,5,3,6,7]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,5,2,6,7]=>[1,8,7,6,2,4,3,5]=>[8,1,2,3,7,5,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,5,4,6,7]=>[1,8,7,6,4,2,3,5]=>[8,1,2,3,5,7,6,4]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,5,4,6,7]=>[1,3,8,7,6,4,2,5]=>[8,6,1,2,3,5,7,4]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,8,7,6,3]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,1,7,6,3]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,6,8,1,5]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,3,8,2,6]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,6,3,1,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,8,2,3,1,6]=>[1,4,8,6,3,5,2,7]=>[8,5,1,3,6,4,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,6,7,1,5]=>[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,2,6,5,4]=>[1,7,5,2,3,4,8,6]=>[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,4,3,1,6]=>[1,5,4,2,8,6,3,7]=>[8,4,5,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,8,6,7,3,4]=>[1,5,6,7,3,2,4,8]=>[8,4,3,2,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,6,1,4,3]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,4,5,1,3]=>[1,7,2,3,6,5,4,8]=>[8,2,7,6,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,1,5,3,8]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,4,3,8,5]=>[1,2,7,8,5,4,3,6]=>[8,7,2,1,4,5,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,4,5,3,8]=>[1,7,3,6,5,4,2,8]=>[8,2,6,3,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,2,3,4,8]=>[1,5,2,7,4,6,3,8]=>[8,4,7,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,3,4,1,7]=>[1,6,4,8,7,2,3,5]=>[8,3,5,1,2,7,6,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,1,3,2,4]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,8,2,6,7]=>[1,2,5,8,7,6,3,4]=>[8,7,4,1,2,3,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,5,8,4,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,7,4,3,1]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,7,4,1,3]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,4,2,1,6]=>[1,7,2,5,4,3,8,6]=>[8,2,7,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,6,5,7,3]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,7,4,2,1]=>[1,5,7,2,6,4,3,8]=>[8,4,2,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,7,2,8,3]=>[1,4,5,7,8,3,2,6]=>[8,5,4,2,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,6,3,7,1]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,2,6,8,5]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,2,7,4,3]=>[1,8,3,6,7,4,5,2]=>[8,1,6,3,2,5,4,7]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,2,7,4,3]=>[1,6,7,4,5,2,8,3]=>[8,3,2,5,4,7,1,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,3,7,6,1]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,4,8,6,5]=>[1,2,7,6,8,5,4,3]=>[8,7,2,3,1,4,5,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,2,6,7,5]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,8,6,2,4]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,1,4,7,6]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,1,3,7,6]=>[1,4,8,6,3,5,2,7]=>[8,5,1,3,6,4,7,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,3,5,7,6]=>[1,8,6,5,3,2,4,7]=>[8,1,3,4,6,7,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,2,8,7,1]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,5,6,4,1]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,1,5,7,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,4,3,6,5]=>[1,2,7,6,3,8,5,4]=>[8,7,2,3,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,3,2,4,7]=>[1,6,2,5,3,8,7,4]=>[8,3,7,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,3,4,6,7]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,2,5,6,7]=>[1,8,7,6,5,2,4,3]=>[8,1,2,3,4,7,5,6]=>[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,3,5,4,7]=>[1,8,7,4,2,6,5,3]=>[8,1,2,5,7,3,4,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,2,4,6,3]=>[1,7,6,4,5,2,8,3]=>[8,2,3,5,4,7,1,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,4,1,6,3]=>[1,5,4,8,3,2,7,6]=>[8,4,5,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,8,1,4,7]=>[1,2,5,8,7,4,3,6]=>[8,7,4,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,2,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,6,8,1,4,5,3,2]=>[1,7,3,8,2,6,5,4]=>[8,2,6,1,7,3,4,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,6,4,3,2]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,4,5,3,6]=>[1,2,8,6,5,4,7,3]=>[8,7,1,3,4,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,5,4,8,1]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,5,8,4,7]=>[1,2,6,8,7,4,3,5]=>[8,7,3,1,2,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,4,3,7,2]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,5,1,7,3]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,7,8,4,6]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,6,7,2,5]=>[1,8,5,6,7,2,4,3]=>[8,1,4,3,2,7,5,6]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,3,4,8,1,7]=>[1,6,8,7,2,3,5,4]=>[8,3,1,2,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,3,4,8,7,1]=>[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,4,8,1,7]=>[1,2,6,8,7,3,5,4]=>[8,7,3,1,2,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,1,7,2,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,8,7,2,6]=>[1,5,8,6,7,2,3,4]=>[8,4,1,3,2,7,6,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,8,7,2,6]=>[1,2,5,8,6,7,3,4]=>[8,7,4,1,3,2,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,4,7,6,2]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,1,7,6,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,8,1,2,7]=>[1,3,5,8,7,2,6,4]=>[8,6,4,1,2,7,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,8,7,6,1]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,8,4,1,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,1,7,8,3]=>[1,4,5,2,6,7,8,3]=>[8,5,4,7,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,8,4,1,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,7,6,4,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,4,8,6,5]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,6,4,1,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,4,1,5,8]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,1,6,4,8]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,4,2,7,5]=>[1,2,8,5,4,6,3,7]=>[8,7,1,4,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,8,5,3,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,3,6,7,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,7,4,6,3]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,1,2,5,8]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,7,2,5,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,6,1,4,7]=>[1,8,7,4,3,5,6,2]=>[8,1,2,5,6,4,3,7]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,4,6,2,8]=>[1,3,5,4,2,7,6,8]=>[8,6,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,1,5,2,3]=>[1,6,5,2,8,3,7,4]=>[8,3,4,7,1,6,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,5,1,3,2]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,5,7,1,8,3]=>[1,2,4,5,7,8,3,6]=>[8,7,5,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,7,8,6,4]=>[1,3,2,5,7,6,8,4]=>[8,6,7,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,6,5,3,7]=>[1,4,2,8,7,3,5,6]=>[8,5,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,2,4,8,5]=>[1,7,8,5,2,3,6,4]=>[8,2,1,4,7,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,2,3,7,5]=>[1,6,3,8,5,2,4,7]=>[8,3,6,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,6,8,5,2]=>[1,7,5,6,8,2,4,3]=>[8,2,4,3,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,4,6,3,8]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,7,1,4,2]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,4,6,5,7]=>[1,2,8,7,5,4,3,6]=>[8,7,1,2,4,5,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,1,3,8,2]=>[1,4,6,3,7,8,2,5]=>[8,5,3,6,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,5,8,2,4]=>[1,3,2,7,4,6,8,5]=>[8,6,7,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,8,2,1,5]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,4,7,6,1,2]=>[1,3,5,7,2,8,4,6]=>[8,6,4,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,3,8,7,2]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,1,4,6,7]=>[1,3,8,7,6,4,5,2]=>[8,6,1,2,3,5,4,7]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,2,8,6,7]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,4,2,6,7]=>[1,5,4,2,3,8,7,6]=>[8,4,5,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,4,2,7,6]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,8,6,2,3]=>[1,2,4,5,8,3,7,6]=>[8,7,5,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,3,4,1,2]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,1,4,8,3]=>[1,7,8,3,2,5,4,6]=>[8,2,1,6,7,4,5,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,8,3,7,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,8,5,2,3]=>[1,2,4,6,5,8,3,7]=>[8,7,5,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,9,6,7,8]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,1,8,9,5,6,7]=>[1,2,3,4,5,8,6,9,7]=>[9,8,7,6,5,2,4,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,8,9,10,1,6,7]=>[1,2,3,4,5,8,6,9,7,10]=>[10,9,8,7,6,3,5,2,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,5,6,3,4,1,8,7]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,5,8,3,7]=>[1,4,2,6,8,7,3,5]=>[8,5,7,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,3,8,5,1]=>[1,4,2,6,8,3,7,5]=>[8,5,7,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,7,4,1,6]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,7,4,6,1]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,8,1,2,6]=>[1,4,7,2,5,8,6,3]=>[8,5,2,7,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,1,6,4,7]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,8,3,6,2]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,4,2,7,3]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,1,5,4,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,8,3,1,4]=>[1,5,8,4,7,2,3,6]=>[8,4,1,5,2,7,6,3]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,8,3,1,4]=>[1,5,8,4,7,2,6,3]=>[8,4,1,5,2,7,3,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,8,4,6,1]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,1,4,6,2]=>[1,3,8,2,7,6,4,5]=>[8,6,1,7,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,4,2,1,7]=>[1,8,7,2,5,4,6,3]=>[8,1,2,7,4,5,3,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,1,2,5,3]=>[1,6,2,4,8,3,7,5]=>[8,3,7,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,4,6,5,3]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,7,5,6,2]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,7,4,6,5]=>[1,2,3,8,5,7,6,4]=>[8,7,6,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,4,3,5]=>[1,8,5,6,4,2,3,7]=>[8,1,4,3,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,1,7,5,6]=>[1,4,8,6,7,5,2,3]=>[8,5,1,3,2,4,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,6,3,8,2]=>[1,7,8,2,5,6,3,4]=>[8,2,1,7,4,3,6,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,3,2,4,8,7]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,2,4,8,6]=>[1,2,7,8,6,4,5,3]=>[8,7,2,1,3,5,4,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,5,1,6,8]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,2,6,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,5,4,6,8]=>[1,7,6,4,3,2,5,8]=>[8,2,3,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,5,2,3,4]=>[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,8,5,2,7]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,5,4,8,7]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,3,1,8,2]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,1,3,8,2]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,4,7,8,2]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,7,3,6,2]=>[1,5,7,6,3,2,4,8]=>[8,4,2,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,8,7,3,4]=>[1,6,7,3,5,8,4,2]=>[8,3,2,6,4,1,5,7]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,5,8,7,4]=>[1,3,6,8,4,2,5,7]=>[8,6,3,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,6,7,5,1,8]=>[1,4,6,5,7,2,3,8]=>[8,5,3,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,7,4,1,8]=>[1,6,4,5,7,2,3,8]=>[8,3,5,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,4,7,2,5]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,5,8,7,9]=>[1,4,3,2,5,6,7,8,9]=>[9,6,7,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,8,5,6,2,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,8,6,5,4]=>[1,3,7,5,8,4,2,6]=>[8,6,2,4,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,6,7,2,4]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,5,7,8,3]=>[1,6,7,8,3,4,2,5]=>[8,3,2,1,6,5,7,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,3,6,7,2]=>[1,5,3,4,2,8,6,7]=>[8,4,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,8,1,5,6]=>[1,3,7,5,8,6,2,4]=>[8,6,2,4,1,3,7,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,7,4,6,3]=>[1,5,7,6,4,2,3,8]=>[8,4,2,3,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,3,1,8,6]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,2,5,7,8]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,3,1,2,5]=>[1,7,2,4,8,5,3,6]=>[8,2,7,5,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,3,1,2,6]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,8,1,3,7]=>[1,2,5,8,7,3,6,4]=>[8,7,4,1,2,6,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,2,4,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,7,6,3,8]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,1,2,4,6]=>[1,5,2,8,6,3,7,4]=>[8,4,7,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,4,5,3,6]=>[1,2,7,3,8,6,5,4]=>[8,7,2,6,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,7,3,6,5]=>[1,4,8,5,7,6,3,2]=>[8,5,1,4,2,3,6,7]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,1,2,6,5,7]=>[1,8,7,5,2,4,3,6]=>[8,1,2,4,7,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,4,5,1,6]=>[1,3,2,8,6,5,4,7]=>[8,6,7,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,5,4,1,7]=>[1,8,7,2,6,4,3,5]=>[8,1,2,7,3,5,6,4]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,2,5,6,1]=>[1,8,2,4,7,6,5,3]=>[8,1,7,5,2,3,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,1,7,3,6]=>[1,8,6,7,3,4,5,2]=>[8,1,3,2,6,5,4,7]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,5,1,7,3]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,7,5,6,2]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,1,5,6,2]=>[1,8,2,4,7,6,5,3]=>[8,1,7,5,2,3,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,2,6,5,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,6,4,5,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,4,5,6,2]=>[1,8,2,3,7,6,5,4]=>[8,1,7,6,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,1,2,5,4]=>[1,8,4,6,2,7,5,3]=>[8,1,5,3,7,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,2,4,5,1]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,6,1,5,4]=>[1,8,4,3,2,7,5,6]=>[8,1,5,6,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,3,4,6,5]=>[1,8,5,3,7,6,4,2]=>[8,1,4,6,2,3,5,7]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,3,1,4,5]=>[1,8,5,3,7,4,6,2]=>[8,1,4,6,2,5,3,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,3,1,6,4]=>[1,5,3,2,8,4,7,6]=>[8,4,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,7,5,4,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,5,6,2,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,6,5,1,3]=>[1,8,3,4,7,2,5,6]=>[8,1,6,5,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,4,5,1,3]=>[1,8,3,7,2,4,6,5]=>[8,1,6,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,3,6,5,1]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,3,6,5,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,4,5,2,3]=>[1,8,3,7,2,4,6,5]=>[8,1,6,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,6,4,5,3]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,3,6,5,2]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,3,7,6,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,7,1,6,5]=>[1,2,3,8,5,7,6,4]=>[8,7,6,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,2,3,5,8]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,3,8,4,5]=>[1,2,7,4,3,6,8,5]=>[8,7,2,5,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,7,6,4,5]=>[1,2,8,5,7,4,3,6]=>[8,7,1,4,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,6,2,5,4]=>[1,2,7,5,6,3,4,8]=>[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,7,4,1,6]=>[1,5,7,2,8,6,4,3]=>[8,4,2,7,1,3,5,6]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,4,8,2,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,5,2,4,6]=>[1,3,7,4,8,6,2,5]=>[8,6,2,5,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,3,7,2,1]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,5,8,4,7]=>[1,2,6,8,7,4,3,5]=>[8,7,3,1,2,5,6,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,6,3,1,7]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,6,3,7,1]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,8,6,3,7]=>[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,2,1,7,3]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,2,6,8,7]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,2,8,6,7]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,4,8,2,6,7]=>[1,2,3,5,8,7,6,4]=>[8,7,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,2,6,1,7]=>[1,3,4,8,7,2,5,6]=>[8,6,5,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,5,1,2,8,7]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,8,6,2,7]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,1,6,2,7]=>[1,3,4,8,7,2,5,6]=>[8,6,5,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,6,1,2,7]=>[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,6,2,1,7]=>[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,1,6,7,2]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,5,8,6,7]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,4,2,7,8]=>[1,3,5,4,6,2,7,8]=>[8,6,4,5,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,6,5,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,3,5,2,7]=>[1,8,7,2,3,6,5,4]=>[8,1,2,7,6,3,4,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,2,6,4,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,3,8,7,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,6,7,8,9,1]=>[1,3,5,6,7,8,9,2,4]=>[9,7,5,4,3,2,1,8,6]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,2,5,6,7,8,9,10,1]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,5,2,1,6,7,8,9,4]=>[1,3,2,5,6,7,8,9,4]=>[9,7,8,5,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,2,9,10,1]=>[1,3,5,7,2,4,6,8,9,10]=>[10,8,6,4,9,7,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,9,2,1,8]=>[1,3,5,7,2,4,6,9,8]=>[9,7,5,3,8,6,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,2,5,6,7,8,9,10,11,1]=>[1,3,2,4,5,6,7,8,9,10,11]=>[11,9,10,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,5,2,1,6,7,8,9,10,4]=>[1,3,2,5,6,7,8,9,10,4]=>[10,8,9,6,5,4,3,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,7,5,6,4,2,1,8]=>[1,3,5,4,6,2,7,8]=>[8,6,4,5,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,5,2,7,1]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,6,2,3,7,1]=>[1,4,6,3,8,2,5,7]=>[8,5,3,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,3,7,2,1]=>[1,4,5,3,8,2,6,7]=>[8,5,4,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,8,6,3,1]=>[1,4,2,5,8,3,7,6]=>[8,5,7,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,1,6,8,2]=>[1,3,4,5,2,7,8,6]=>[8,6,5,4,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,1,3,7,2]=>[1,4,5,2,6,3,8,7]=>[8,5,4,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,2,8,6,1]=>[1,3,4,5,2,7,6,8]=>[8,6,5,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,6,1,5,2]=>[1,3,8,2,7,5,6,4]=>[8,6,1,7,2,4,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,1,6,8,3]=>[1,4,2,5,3,7,8,6]=>[8,5,7,4,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,2,6,8,3]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,9,6,7,2,8,3]=>[1,2,4,9,3,5,6,7,8]=>[9,8,6,1,7,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,2,6,5,3,8,7]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,1,5,7]=>[1,8,7,5,4,3,6,2]=>[8,1,2,4,5,6,3,7]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,5,6,2,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,2,3,6,5]=>[1,2,8,5,3,7,6,4]=>[8,7,1,4,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,5,7,2,6]=>[1,4,8,6,7,2,3,5]=>[8,5,1,3,2,7,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,8,1,6,5]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,5,8,1,6]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,6,1,7,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,5,7,1,6]=>[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,3,5,6,1]=>[1,8,2,4,3,7,6,5]=>[8,1,7,5,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,6,1,5,7]=>[1,4,8,7,5,6,2,3]=>[8,5,1,2,4,3,7,6]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,4,3,6,2]=>[1,5,4,8,2,7,6,3]=>[8,4,5,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,6,2,3,1]=>[1,5,6,2,4,7,3,8]=>[8,4,3,7,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,1,5,2,7]=>[1,8,7,2,4,3,6,5]=>[8,1,2,7,5,6,3,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,5,2,4,7,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,3,4,6,8]=>[1,2,7,6,4,5,3,8]=>[8,7,2,3,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,2,7,6,3]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,7,1,6,4]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,5,1,3,4]=>[1,7,3,6,2,4,8,5]=>[8,2,6,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,1,3,7,2]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,1,6,7,5]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,2,1,4,5,6,7,8,3]=>[1,9,3,2,4,5,6,7,8]=>[9,1,7,8,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,9,3,5,6,7,8,4]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,4,3,8,1,6,5,2]=>[1,7,5,2,4,8,3,6]=>[8,2,4,7,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,5,8,1,3]=>[1,4,2,7,3,6,8,5]=>[8,5,7,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,4,5,8,1,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,6,2,5,1]=>[1,3,4,8,2,7,5,6]=>[8,6,5,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,4,2,3,6]=>[1,2,5,4,7,3,8,6]=>[8,7,4,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,5,8,6,3]=>[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,5,3,4,8]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,8,5,6,4]=>[1,2,7,6,5,8,4,3]=>[8,7,2,3,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,4,8,3,7]=>[1,2,6,8,7,3,5,4]=>[8,7,3,1,2,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,4,2,5,6]=>[1,2,7,5,4,8,6,3]=>[8,7,2,4,5,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,4,3,8,5]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,3,6,4,7]=>[1,2,5,3,8,7,4,6]=>[8,7,4,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,6,7,1,4,8]=>[1,2,5,7,4,6,3,8]=>[8,7,4,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,7,2,3,8]=>[1,6,2,4,5,7,3,8]=>[8,3,7,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,8,5,6,4]=>[1,2,3,7,6,5,8,4]=>[8,7,6,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,3,8,6,2]=>[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,1,4,5,8,6]=>[1,2,7,8,6,5,4,3]=>[8,7,2,1,3,4,5,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,7,6,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,8,7,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,9,8,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,8,6,9,7]=>[1,2,3,4,5,6,8,9,7]=>[9,8,7,6,5,4,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,1,7,5,8,6,9]=>[1,2,3,4,5,7,8,6,9]=>[9,8,7,6,5,3,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,7,6,9,8,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,4,3,1,7,6,5,2]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,5,3,4,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,7,4,5,3]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,9,1,8,2]=>[1,3,5,7,2,4,6,9,8]=>[9,7,5,3,8,6,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,8,2,7,1]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,9,2,8,1]=>[1,3,5,7,2,4,6,9,8]=>[9,7,5,3,8,6,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,1,9,8,2]=>[1,3,5,7,9,2,4,6,8]=>[9,7,5,3,1,8,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,2,1,4,5,6,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,3,4,2,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,2,1,7,3]=>[1,4,5,2,6,3,8,7]=>[8,5,4,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,2,4,5,3]=>[1,2,6,4,8,3,7,5]=>[8,7,3,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,2,4,6,1]=>[1,5,2,7,6,4,3,8]=>[8,4,7,2,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,8,6,1,3]=>[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,7,2,6,4]=>[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,5,7,3,2]=>[1,6,7,3,2,4,8,5]=>[8,3,2,6,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,1,5,8,4]=>[1,3,7,8,4,2,6,5]=>[8,6,2,1,5,7,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,2,4,6,1]=>[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,5,2,8,3]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,7,1,8,2]=>[1,4,5,7,8,2,6,3]=>[8,5,4,2,1,7,3,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,7,1,8,6]=>[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,5,7,3,2]=>[1,6,7,3,4,2,8,5]=>[8,3,2,6,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,3,7,5,4]=>[1,8,4,2,3,6,7,5]=>[8,1,5,7,6,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,4,1,7,5]=>[1,2,8,5,4,6,3,7]=>[8,7,1,4,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,3,2,6,4]=>[1,5,3,8,4,7,6,2]=>[8,4,6,1,5,2,3,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,3,6,2,1]=>[1,5,3,8,2,4,7,6]=>[8,4,6,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,7,3,6,1]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,5,2,8,1]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,8,2,7,1]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,7,4,5,1]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,7,5,6,1]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,7,4,5,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,6,7,8,9,10,1]=>[1,4,5,6,7,8,9,10,2,3]=>[10,7,6,5,4,3,2,1,9,8]=>[10,8,7,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,7,8,4,3,6,5,2]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,6,5,4,2]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,7,2,1,3]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,1,6,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,1,8,5,3]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,3,8,2,4]=>[1,2,6,8,4,7,3,5]=>[8,7,3,1,5,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,8,7,5,1]=>[1,6,7,5,8,2,4,3]=>[8,3,2,4,1,7,5,6]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,3,8,4,2,7]=>[1,6,4,3,2,5,8,7]=>[8,3,5,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,7,8,3,5]=>[1,6,8,5,7,3,4,2]=>[8,3,1,4,2,6,5,7]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,3,7,8,4,2]=>[1,6,8,2,5,7,4,3]=>[8,3,1,7,4,2,5,6]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,7,8,6,4]=>[1,5,7,6,8,4,2,3]=>[8,4,2,3,1,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,4,7,1,3]=>[1,5,4,2,6,7,3,8]=>[8,4,5,7,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,2,4,6,1]=>[1,5,2,8,3,7,6,4]=>[8,4,7,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,6,8,4,7]=>[1,5,6,8,7,4,2,3]=>[8,4,3,1,2,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,7,5,6,3,8]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,7,3,8,4]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,6,4,2,8]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,4,8,3,5]=>[1,2,6,8,5,4,3,7]=>[8,7,3,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,4,1,5,6]=>[1,3,2,7,5,4,8,6]=>[8,6,7,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,8,2,3,1]=>[1,4,5,8,2,7,3,6]=>[8,5,4,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,5,7,1,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,8,4,3,5,7]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,3,7,2,6]=>[1,5,3,4,2,8,6,7]=>[8,4,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,6,8,5,7]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,6,4,7,2]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,5,6,2,8]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,5,6,1,3]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,4,7,3,2,1]=>[1,5,7,2,8,3,6,4]=>[8,4,2,7,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,1,6,7,4]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,4,1,7,5]=>[1,8,5,4,6,2,3,7]=>[8,1,4,5,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,4,6,7,2]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,4,7,6]=>[1,8,6,4,5,2,3,7]=>[8,1,3,5,4,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,2,6,7,3]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,2,6,7,4]=>[1,8,4,3,5,2,6,7]=>[8,1,5,6,4,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,1,3,8,7]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,2,8,6,4]=>[1,7,6,8,4,5,2,3]=>[8,2,3,1,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,1,3,5,2]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,2,1,7,5]=>[1,6,2,8,5,3,4,7]=>[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,4,3,7,6]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,4,1,3,7]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,7,2,3,1]=>[1,6,2,8,3,5,7,4]=>[8,3,7,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,4,8,1,6]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,7,8,1,3,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,1,2,7,3]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,7,1,4,3]=>[1,2,5,7,4,8,3,6]=>[8,7,4,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,4,6,2,3]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,5,2,7,3]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,4,1,7,5]=>[1,8,5,4,6,2,3,7]=>[8,1,4,5,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,8,6,1,4]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,1,2,4,7,6]=>[1,3,5,2,8,6,4,7]=>[8,6,4,7,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,8,2,7,5]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,7,6,2,8,5,3,4]=>[1,2,7,3,6,5,8,4]=>[8,7,2,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,1,4,6,7]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,2,4,5,7]=>[1,2,6,4,3,8,7,5]=>[8,7,3,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,4,3,7,1]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,6,3,7,1]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,6,4,7,1]=>[1,8,2,5,6,4,3,7]=>[8,1,7,4,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,8,2,3,1]=>[1,7,3,6,2,4,5,8]=>[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,8,2,4,1]=>[1,7,4,5,8,2,3,6]=>[8,2,5,4,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,8,2,5,1]=>[1,7,5,8,2,3,6,4]=>[8,2,4,1,7,6,3,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,8,4,5,1,2]=>[1,7,2,3,6,5,4,8]=>[8,2,7,6,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,4,2,8,3]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,8,5,6,3]=>[1,2,3,7,6,5,8,4]=>[8,7,6,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,8,4,6,1]=>[1,3,7,6,4,5,8,2]=>[8,6,2,3,5,4,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,4,3,7,1]=>[1,2,5,4,6,3,8,7]=>[8,7,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,3,5,6,2]=>[1,8,2,3,4,7,6,5]=>[8,1,7,6,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,4,5,6,1]=>[1,8,2,3,7,6,5,4]=>[8,1,7,6,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,7,3,6,2]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,2,8,7,1]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,6,8,1,3]=>[1,2,5,6,8,3,7,4]=>[8,7,4,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,1,3,8,7]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,5,7,2,8]=>[1,4,3,2,6,7,5,8]=>[8,5,6,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,8,1,6,4]=>[1,3,7,6,2,4,5,8]=>[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,5,2,1,7]=>[1,4,8,7,2,3,6,5]=>[8,5,1,2,7,6,3,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,1,7,4,2]=>[1,3,5,2,6,7,4,8]=>[8,6,4,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,5,2,3,7]=>[1,4,8,7,3,6,2,5]=>[8,5,1,2,6,3,7,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,8,6,1,7]=>[1,3,4,5,8,7,2,6]=>[8,6,5,4,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,6,1,7,2]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,6,1,2,7]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,5,4,8,7]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,4,3,7,6]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,1,2,6,7,4]=>[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,7,2,3,6]=>[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,2,4,5,6]=>[1,2,8,6,4,3,7,5]=>[8,7,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,3,4,1,5]=>[1,8,5,3,2,6,4,7]=>[8,1,4,6,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,3,4,5,1]=>[1,8,2,6,4,7,5,3]=>[8,1,7,3,5,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,8,7,1,4]=>[1,5,8,4,2,6,7,3]=>[8,4,1,5,7,3,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,8,3,2,4]=>[1,5,8,4,7,2,3,6]=>[8,4,1,5,2,7,6,3]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,3,4,2,8]=>[1,5,3,6,4,7,2,8]=>[8,4,6,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,3,4,5,2]=>[1,8,2,6,4,7,5,3]=>[8,1,7,3,5,2,4,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,7,4,2,3]=>[1,6,4,2,8,3,5,7]=>[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,5,7,6,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,3,1,6,7]=>[1,4,2,8,7,6,3,5]=>[8,5,7,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,2,5,6,1]=>[1,8,2,4,3,7,6,5]=>[8,1,7,5,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,8,1,4,5]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,7,1,5,3]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,6,5,2,4]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,8,7,4,1]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,7,5,8,1]=>[1,6,5,7,8,2,4,3]=>[8,3,4,2,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,1,2,8,4]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,7,4,5,1]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,4,6,5,3]=>[1,7,5,4,8,3,2,6]=>[8,2,4,5,1,6,7,3]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,8,5,2,7]=>[1,2,4,6,5,8,7,3]=>[8,7,5,3,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,4,7,2,1]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,4,1,3,5]=>[1,8,5,4,6,2,3,7]=>[8,1,4,5,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,1,6,2,4]=>[1,8,4,5,2,3,7,6]=>[8,1,5,4,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,4,2,6,3]=>[1,8,3,7,6,2,5,4]=>[8,1,6,2,3,7,4,5]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,6,3,7,1]=>[1,4,5,6,3,2,8,7]=>[8,5,4,3,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,4,6,2,3]=>[1,8,3,5,4,7,2,6]=>[8,1,6,4,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,6,3,2,8]=>[1,4,5,6,3,2,7,8]=>[8,5,4,3,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,6,3,8,2]=>[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,8,3,6,5]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,6,8,4,3]=>[1,2,7,4,5,6,8,3]=>[8,7,2,5,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,7,4,6,5]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,6,1,2,8]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,6,1,7,3]=>[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,2,1,6,8]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,3,2,7,1]=>[1,4,8,2,5,3,6,7]=>[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,6,1,8,3]=>[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,9,2,1,4,5,6,7,8]=>[1,3,2,9,8,7,6,5,4]=>[9,7,8,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,6,7,2,5,8,4,1]=>[1,3,7,4,2,6,8,5]=>[8,6,2,5,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,4,8,1,2]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,8,1,6,2]=>[1,5,8,2,4,7,6,3]=>[8,4,1,7,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,4,2,1,6]=>[1,3,7,2,5,4,8,6]=>[8,6,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,2,8,1,5]=>[1,4,3,7,2,6,8,5]=>[8,5,6,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,7,8,3,1]=>[1,5,7,3,2,6,8,4]=>[8,4,2,6,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,8,4,7,1]=>[1,5,8,2,6,4,3,7]=>[8,4,1,7,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,1,6,5,2]=>[1,3,4,8,2,7,5,6]=>[8,6,5,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,8,7,3,1]=>[1,5,8,2,3,6,7,4]=>[8,4,1,7,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,9,1,3,2]=>[1,4,7,2,5,8,3,6,9]=>[9,6,3,8,5,2,7,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,2,6,7,8,1,4,3]=>[1,5,8,3,6,2,4,7]=>[8,4,1,6,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,5,3,1,6]=>[1,4,7,2,8,6,3,5]=>[8,5,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,5,8,3,7]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,1,7,8,6]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,1,7,4,2,6]=>[1,3,8,6,4,2,5,7]=>[8,6,1,3,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,7,2,3,4]=>[1,5,7,3,6,2,8,4]=>[8,4,2,6,3,7,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,5,2,4,1]=>[1,3,6,2,8,4,7,5]=>[8,6,3,7,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,7,3,6,1]=>[1,8,2,3,5,7,6,4]=>[8,1,7,6,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,3,6,5,1]=>[1,4,7,5,3,8,2,6]=>[8,5,2,4,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,1,4,5,2]=>[1,3,8,2,7,5,4,6]=>[8,6,1,7,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,8,1,5,2]=>[1,4,3,6,2,7,5,8]=>[8,5,6,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,8,7,1,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,2,8,1,3]=>[1,4,6,8,3,5,2,7]=>[8,5,3,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,6,3,2,4]=>[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,8,2,5,3]=>[1,4,7,5,8,3,6,2]=>[8,5,2,4,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,1,2,7,5]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,6,1,3,7]=>[1,2,5,6,3,8,7,4]=>[8,7,4,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,5,1,3,2]=>[1,4,6,2,7,3,8,5]=>[8,5,3,7,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,3,6,2,1]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,5,6,2,1]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,8,1,7,5]=>[1,3,4,2,6,5,8,7]=>[8,6,5,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,1,7,4,5]=>[1,3,6,7,4,2,8,5]=>[8,6,3,2,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,4,6,5,7]=>[1,3,8,7,5,4,2,6]=>[8,6,1,2,4,5,7,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,2,5,4,3]=>[1,8,3,7,4,6,5,2]=>[8,1,6,2,5,3,4,7]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,7,6,1,2]=>[1,8,2,5,7,3,4,6]=>[8,1,7,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,6,7,5,2]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,5,2,6,3]=>[1,8,3,4,7,6,2,5]=>[8,1,6,5,2,3,7,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,4,1,5,2]=>[1,3,8,2,7,5,4,6]=>[8,6,1,7,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,3,7,2,6]=>[1,5,3,8,6,7,2,4]=>[8,4,6,1,3,2,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,1,7,2,6]=>[1,8,6,7,2,4,3,5]=>[8,1,3,2,7,5,6,4]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,1,8,6,2]=>[1,7,6,8,2,4,3,5]=>[8,2,3,1,7,5,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,2,4,3,1]=>[1,5,2,6,4,7,3,8]=>[8,4,7,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,4,2,3,1]=>[1,5,4,6,2,7,3,8]=>[8,4,5,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,1,3,2,4]=>[1,6,3,7,2,8,4,5]=>[8,3,6,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,7,5,1,4]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,8,2,5,1]=>[1,4,3,6,2,7,5,8]=>[8,5,6,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,8,2,5,3]=>[1,6,2,7,5,8,3,4]=>[8,3,7,2,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,3,2,4,1]=>[1,5,3,6,2,7,4,8]=>[8,4,6,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,8,7,1,2,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,1,6,3,5]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,7,8,2,4]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,6,1,2,5]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,8,6,3,5]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,1,6,3,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,2,4,5,3]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,2,5,8,3]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,8,6,3,4]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,5,3,8,2]=>[1,4,6,3,2,7,8,5]=>[8,5,3,6,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,4,8,2,3]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,7,3,1,6]=>[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,6,2,7,5]=>[1,8,5,6,2,3,4,7]=>[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,6,8,1,3]=>[1,7,2,3,5,6,8,4]=>[8,2,7,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,8,4,1,6]=>[1,3,7,2,5,8,6,4]=>[8,6,2,7,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,4,8,6,5]=>[1,7,6,8,5,4,2,3]=>[8,2,3,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,1,7,6,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,4,5,8,3]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,1,5,3,4]=>[1,8,4,6,5,2,7,3]=>[8,1,5,3,4,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,3,4,7,1,8]=>[1,6,7,2,3,5,4,8]=>[8,3,2,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,4,1,5,8,6]=>[1,2,7,8,6,5,3,4]=>[8,7,2,1,3,4,6,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,6,7,3,4]=>[1,2,5,6,7,3,8,4]=>[8,7,4,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,4,5,1,7]=>[1,6,5,4,3,8,7,2]=>[8,3,4,5,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,8,2,1,5]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,2,8,4,6]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,6,1,7,8,3]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,5,1,6,4]=>[1,8,4,2,7,6,3,5]=>[8,1,5,7,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,4,3,6,8]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,2,5,8,7]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,4,6,8,7]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,3,5,8,6]=>[1,4,2,3,7,8,6,5]=>[8,5,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,6,2,8,7]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,6,2,8,4]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,7,5,4,1]=>[1,8,2,3,6,5,7,4]=>[8,1,7,6,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,5,3,7,1]=>[1,8,2,4,6,3,5,7]=>[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,1,8,6,3]=>[1,5,2,4,7,6,8,3]=>[8,4,7,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,6,5,3,2,8]=>[1,4,6,3,7,2,5,8]=>[8,5,3,6,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,1,8,5,4]=>[1,2,3,6,8,4,7,5]=>[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,7,6,3,2]=>[1,4,8,2,5,7,3,6]=>[8,5,1,7,4,2,6,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,7,6,3,1]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,7,5,2,8]=>[1,4,6,5,7,2,3,8]=>[8,5,3,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,7,6,2,8]=>[1,3,4,5,7,2,6,8]=>[8,6,5,4,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,4,3,6,7]=>[1,8,7,6,3,2,5,4]=>[8,1,2,3,6,7,4,5]=>[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,2,3,6,7]=>[1,5,2,8,7,6,3,4]=>[8,4,7,1,2,3,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,1,4,3,6]=>[1,2,8,6,4,7,3,5]=>[8,7,1,3,5,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,1,2,3,6]=>[1,4,5,2,8,6,3,7]=>[8,5,4,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,2,3,8,5]=>[1,7,8,5,2,6,3,4]=>[8,2,1,4,7,3,6,5]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,8,4,3,5]=>[1,6,4,7,3,2,5,8]=>[8,3,5,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,5,3,4,6]=>[1,7,4,2,8,6,3,5]=>[8,2,5,7,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,5,2,3,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,1,6,7,3]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,3,6,1,8]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,5,2,4,8]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,3,7,8,2]=>[1,5,3,4,6,7,8,2]=>[8,4,6,5,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,6,8,2,4]=>[1,7,2,3,5,6,8,4]=>[8,2,7,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,6,7,2,4]=>[1,8,4,3,5,6,7,2]=>[8,1,5,6,4,3,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,4,7,8,1]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,2,5,6,1,3]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,6,7,1,3]=>[1,2,8,3,5,6,7,4]=>[8,7,1,6,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,1,8,3,7]=>[1,4,6,8,7,3,2,5]=>[8,5,3,1,2,6,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,4,1,5,7]=>[1,6,2,8,7,5,4,3]=>[8,3,7,1,2,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,2,6,5,7]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,2,7,5,6]=>[1,2,3,8,6,7,5,4]=>[8,7,6,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,7,5,4,6]=>[1,8,6,5,7,4,2,3]=>[8,1,3,4,2,5,7,6]=>[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,9,8,7]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,9,8,7,6]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,9,10,8,7,1]=>[1,2,3,4,5,6,9,7,10,8]=>[10,9,8,7,6,5,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,8,9,7,6,5]=>[1,2,3,4,5,8,6,9,7]=>[9,8,7,6,5,2,4,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,6,1,8,2,5,4,3]=>[1,7,4,8,3,2,6,5]=>[8,2,5,1,6,7,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,7,3,5,2]=>[1,8,2,4,6,3,5,7]=>[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,1,6,3,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,2,5,3,8]=>[1,7,3,4,2,6,5,8]=>[8,2,6,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,1,6,3,7]=>[1,5,2,4,8,7,3,6]=>[8,4,7,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,3,6,1,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,8,6,2,3]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,3,2,7,1,4]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,2,4,8,1]=>[1,5,2,7,8,3,6,4]=>[8,4,7,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,8,2,7,3]=>[1,4,6,2,5,8,3,7]=>[8,5,3,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,2,4,8,5]=>[1,2,6,4,7,8,5,3]=>[8,7,3,5,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,6,2,5,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,7,2,5,8]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,7,2,4,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,8,6,7,3]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,3,7,6,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,1,6,5,3]=>[1,8,3,7,5,2,4,6]=>[8,1,6,2,4,7,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,1,5,8,2]=>[1,3,6,5,2,7,8,4]=>[8,6,3,4,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,4,2,8,3]=>[1,7,8,3,6,2,4,5]=>[8,2,1,6,3,7,5,4]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,2,3,6,5]=>[1,7,6,3,8,5,2,4]=>[8,2,3,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,7,3,5,2]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,5,7,4,2]=>[1,3,8,2,6,7,4,5]=>[8,6,1,7,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,6,7,4,5]=>[1,2,8,5,6,7,4,3]=>[8,7,1,4,3,2,5,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,1,3,7,2]=>[1,4,8,2,5,3,6,7]=>[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,2,6,7,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,1,6,5,8]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,5,6,2,8]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,1,6,7,5]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,4,6,7,3]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,8,1,4,2]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,3,6,2,8]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,1,5,4,8]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,5,4,7,3]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,4,5,2,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,5,6,2,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,3,6,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,8,4,3,1]=>[1,6,4,7,3,2,5,8]=>[8,3,5,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,4,2,1,8]=>[1,7,2,5,4,6,3,8]=>[8,2,7,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,8,4,7,1]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,7,5,2,4,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,6,7,8,9,4]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,1,5,6,7,8,9,10,4]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,3,4,7,2,1,6,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,7,6,1,8,5]=>[1,4,7,8,5,6,2,3]=>[8,5,2,1,4,3,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,5,8,7,1]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,2,6,1,7]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,8,6,2,3]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,7,3,8,2,4]=>[1,6,8,4,7,2,3,5]=>[8,3,1,5,2,7,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,6,4,3,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,7,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,7,8,6,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,7,6,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,6,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,6,4,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,6,4,7,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,7,8,6,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,7,6,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,6,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,8,5,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,5,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,5,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,6,5,7,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,7,8,6,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,7,6,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,6,4,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,6,4,7,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,8,6,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,6,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,8,5,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,5,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,5,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,7,8,9,10,6]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,8,7,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,7,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,7,8,6,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,7,6,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,6,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,8,5,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,5,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,5,7,8,9,10,6]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,4,10,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,4,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,4,8,9,10,7]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,8,9,10,6]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,7,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,7,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,7,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,7,8,6,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,7,8,6,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,7,6,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,7,6,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,7,6,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,6,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,6,8,9,7,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,6,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,5,6,7,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,6,4,8,7,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,6,4,8,7,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,6,4,7,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,6,4,7,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,6,4,7,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,7,8,6,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,7,8,6,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,7,6,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,7,6,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,7,6,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,6,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,6,8,9,7,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,6,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,5,4,6,7,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,8,5,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,8,5,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,5,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,5,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,5,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,5,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,5,8,9,7,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,5,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,6,5,7,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,7,8,9,10,6,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,7,8,9,6,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,7,8,6,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,7,6,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,8,9,10,11,12,7]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,6,5,8,7,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,6,5,8,7,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,6,5,7,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,6,5,7,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,6,5,7,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,7,8,6,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,7,8,6,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,7,6,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,7,6,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,7,6,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,8,9,7,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,7,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,6,4,8,7,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,6,4,8,7,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,6,4,7,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,6,4,7,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,6,4,7,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,8,6,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,8,6,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,6,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,6,8,9,7,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,6,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,6,7,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,8,5,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,8,5,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,5,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,5,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,5,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,5,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,5,8,9,7,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,5,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,6,5,7,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,7,8,9,10,6,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,7,8,9,6,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,7,8,6,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,7,6,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,8,9,10,11,12,7]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,8,7,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,8,7,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,7,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,7,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,7,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,7,8,6,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,7,8,6,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,7,6,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,7,6,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,7,6,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,6,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,6,8,9,7,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,6,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,3,6,7,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,8,5,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,8,5,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,5,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,5,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,5,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,8,9,7,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,7,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,5,7,8,9,10,6,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,5,7,8,9,6,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,5,7,8,6,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,5,7,6,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,4,3,5,6,8,9,10,11,12,7]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,4,10,9,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,4,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,4,9,10,8,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,4,9,8,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,4,8,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,4,8,9,10,7,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,4,8,9,7,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,4,8,7,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,4,7,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,8,9,10,6,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,8,9,6,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,8,6,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,6,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,4,6,8,9,10,11,12,7]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,9,10,5,12,11]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,9,5,11,12,10]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,5,10,11,12,9]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,5,9,10,11,12,8]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,8,9,10,11,12,7]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,9,10,11,12,6]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,9,6,7,8,5,1]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,9,5,6,7,8,4,1]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,9,4,5,6,7,8,3,1]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,4,5,6,7,8,2,1]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,10,8,9,7,1]=>[1,2,3,4,5,6,10,7,8,9]=>[10,9,8,7,6,5,1,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,1,9,7,8,6,5]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,10,7,8,9,6,1]=>[1,2,3,4,5,10,6,7,8,9]=>[10,9,8,7,6,1,5,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,1,9,6,7,8,5,4]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,10,6,7,8,9,5,1]=>[1,2,3,4,10,5,6,7,8,9]=>[10,9,8,7,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,9,5,6,7,8,4,3]=>[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,10,5,6,7,8,9,4,1]=>[1,2,3,10,4,5,6,7,8,9]=>[10,9,8,1,7,6,5,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,9,4,5,6,7,8,3,2]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,4,5,6,7,8,9,3,1]=>[1,2,10,3,4,5,6,7,8,9]=>[10,9,1,8,7,6,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,4,5,6,7,8,9,2,1]=>[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,4,3,8,1,7,2,6]=>[1,5,2,4,8,6,7,3]=>[8,4,7,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,3,1,2,4,5,6,7,10,8]=>[1,9,10,8,7,6,5,4,2,3]=>[10,2,1,3,4,5,6,7,9,8]=>[10,3,2,4,5,6,7,8,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,2,3,1,6,8,4,5]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,5,6,3,7]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,6,2,3,4]=>[1,5,6,2,7,3,8,4]=>[8,4,3,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,7,3,8,5]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,8,6,3,7]=>[1,2,4,5,8,7,3,6]=>[8,7,5,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,5,7,3,6]=>[1,4,2,8,6,7,3,5]=>[8,5,7,1,3,2,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,1,6,3,7]=>[1,4,5,2,8,7,3,6]=>[8,5,4,7,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,6,4,2,8]=>[1,5,6,4,3,7,2,8]=>[8,4,3,5,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,6,1,4,8]=>[1,3,7,4,5,6,2,8]=>[8,6,2,5,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[11,2,1,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,2,3,4,5,6,7,8,9,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[7,3,4,8,5,6,2,1]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,8,4,5,2,1]=>[1,7,2,3,6,5,4,8]=>[8,2,7,6,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,6,2,8,3]=>[1,2,4,5,6,3,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,8,6,2,7]=>[1,5,8,7,2,3,4,6]=>[8,4,1,2,7,6,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,4,1,6,2]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,8,6,2,3]=>[1,7,2,4,3,5,8,6]=>[8,2,7,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,6,3,2,4]=>[1,8,4,7,2,3,5,6]=>[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,5,3,2,4]=>[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,3,7,4,2]=>[1,6,7,4,8,2,5,3]=>[8,3,2,5,1,7,4,6]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,8,6,5,2]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,7,3,2,6]=>[1,8,6,3,4,2,5,7]=>[8,1,3,6,5,7,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,1,7,6,2]=>[1,4,8,2,5,3,6,7]=>[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,1,2,5,3]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,5,6,3,4]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,7,4,3,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,7,6,1,3]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,3,5,4,2]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,6,4,3,2]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,8,5,3,6]=>[1,7,3,4,2,5,8,6]=>[8,2,6,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,4,6,8,5]=>[1,7,8,5,4,2,3,6]=>[8,2,1,4,5,7,6,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,2,1,6,4]=>[1,8,4,5,2,7,6,3]=>[8,1,5,4,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,4,2,5,7]=>[1,6,2,8,7,5,4,3]=>[8,3,7,1,2,4,5,6]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,3,6,4,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,5,3,6,8]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,2,6,8,7]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,8,2,6,7]=>[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,2,7,6,8]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,4,2,6,8]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,7,1,5,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,1,6,4,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,1,3,7,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,4,3,7,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,1,7,2,8]=>[1,3,5,2,6,7,4,8]=>[8,6,4,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,4,2,1,3]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,6,1,3,2]=>[1,8,2,7,3,5,6,4]=>[8,1,7,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,4,6,3,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,1,3,6,2]=>[1,7,6,3,4,8,2,5]=>[8,2,3,6,5,1,7,4]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,4,3,7,2]=>[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,7,3,6,1]=>[1,8,2,5,7,6,3,4]=>[8,1,7,4,2,3,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,2,4,5,7]=>[1,3,6,4,2,8,7,5]=>[8,6,3,5,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,3,2,7,4,6]=>[1,2,8,6,7,4,3,5]=>[8,7,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,2,3,5,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,7,5,4,6]=>[1,3,8,6,5,7,4,2]=>[8,6,1,3,4,2,5,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,7,3,4,5]=>[1,2,6,3,8,5,7,4]=>[8,7,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,6,8,3,2]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,7,8,5,3]=>[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,9,2,4,5,6]=>[1,2,3,7,4,8,5,9,6]=>[9,8,7,3,6,2,5,1,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,7,8,2,1,4,5,6]=>[1,3,8,6,4,2,7,5]=>[8,6,1,3,5,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,8,2,4,5]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,5,2,6,4]=>[1,3,8,4,2,7,6,5]=>[8,6,1,5,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,10,7,9,8]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,6,3,5,4,8,7,10,9]=>[1,2,3,6,4,5,7,8,9,10]=>[10,9,8,5,7,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,5,4,7,8,3,6,2]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,1,7,3,8,2]=>[1,5,7,8,2,6,3,4]=>[8,4,2,1,7,3,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,4,2,1,6]=>[1,3,8,6,2,7,4,5]=>[8,6,1,3,7,2,5,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,6,8,3,2]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,6,8,3,1]=>[1,7,3,4,5,6,8,2]=>[8,2,6,5,4,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,6,8,3,1]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,3,1,6,5]=>[1,2,4,8,5,3,7,6]=>[8,7,5,1,4,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,8,1,7,2]=>[1,5,8,2,4,6,3,7]=>[8,4,1,7,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,5,8,1,6,2]=>[1,3,4,5,8,2,7,6]=>[8,6,5,4,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,6,8,2,7]=>[1,2,4,5,6,8,7,3]=>[8,7,5,4,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,8,2,7,3]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,3,2,8,5]=>[1,4,7,8,5,3,2,6]=>[8,5,2,1,4,6,7,3]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,4,2,8,5]=>[1,2,7,8,5,4,6,3]=>[8,7,2,1,4,5,3,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,1,2,8,6]=>[1,4,5,2,7,8,6,3]=>[8,5,4,7,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,3,5,8,7]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,2,1,6,7]=>[1,4,5,2,8,7,6,3]=>[8,5,4,7,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,5,2,6,4]=>[1,8,4,2,7,6,3,5]=>[8,1,5,7,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,8,2,3,5]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,3,4,1,6]=>[1,5,3,8,6,4,2,7]=>[8,4,6,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,7,1,4,6]=>[1,5,7,4,8,6,2,3]=>[8,4,2,5,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,2,6,4,5]=>[1,8,5,2,7,4,3,6]=>[8,1,4,7,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,8,3,1,5]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,5,8,4,1]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,1,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,6,2,1,3,7,4,5]=>[1,8,5,3,2,6,7,4]=>[8,1,4,6,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,6,5,1,8]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,1,5,6,3]=>[1,4,2,8,3,7,6,5]=>[8,5,7,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,6,1,2,7]=>[1,4,8,7,2,5,6,3]=>[8,5,1,2,7,4,3,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,4,1,2,7]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,1,2,6,3]=>[1,4,5,2,8,3,7,6]=>[8,5,4,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,1,3,5,2]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,1,3,6,2]=>[1,4,5,2,8,3,7,6]=>[8,5,4,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,8,1,2,7]=>[1,4,6,2,5,8,7,3]=>[8,5,3,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,1,4,3,5]=>[1,7,3,6,4,2,8,5]=>[8,2,6,3,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,1,2,5,4]=>[1,7,5,2,8,4,3,6]=>[8,2,4,7,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,1,5,2,8]=>[1,3,6,5,2,7,4,8]=>[8,6,3,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,2,4,5,6]=>[1,8,6,4,3,2,7,5]=>[8,1,3,5,6,7,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,5,7,2,8]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,7,2,8,6]=>[1,4,5,7,8,6,2,3]=>[8,5,4,2,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,4,6,3,7]=>[1,5,4,2,3,8,7,6]=>[8,4,5,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,4,5,3,7]=>[1,6,5,4,2,8,7,3]=>[8,3,4,5,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,6,7,2,4]=>[1,3,5,6,7,2,4,8]=>[8,6,4,3,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,4,5,7,3]=>[1,6,5,4,2,8,3,7]=>[8,3,4,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,10,7,8,9]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,8,7,6,5,4,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,10,5,6,7,8,9]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,6,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,2,7,4,9,6,1,8,3]=>[1,10,3,2,5,4,7,6,9,8]=>[10,1,8,9,6,7,4,5,2,3]=>[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,5,4,8,7,3,2,6]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,6,5,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,8,7,4,3]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,5,2,3,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,5,1,7,2]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,7,1,2,8]=>[1,4,5,7,2,6,3,8]=>[8,5,4,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,8,6,1,2]=>[1,4,5,8,2,7,3,6]=>[8,5,4,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,7,1,6,2]=>[1,4,5,7,6,2,8,3]=>[8,5,4,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,6,8,1,3]=>[1,4,5,6,8,3,2,7]=>[8,5,4,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,6,7,1,3]=>[1,4,5,6,7,2,8,3]=>[8,5,4,3,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,6,5,8,3]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,6,4,8,3]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,8,3,5,4,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,3,4,2,5]=>[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,5,7,1,3]=>[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,8,2,7,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,1,4,2,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,3,4,7,2]=>[1,6,4,8,2,5,3,7]=>[8,3,5,1,7,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,6,4,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,3,4,8,2]=>[1,7,8,2,5,3,6,4]=>[8,2,1,7,4,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,6,1,8,3]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,3,8,7,4]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,8,6,4,1]=>[1,3,7,4,5,8,2,6]=>[8,6,2,5,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,8,1,7,6]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,3,8,6,1]=>[1,7,6,8,2,3,5,4]=>[8,2,3,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,2,6,7,4]=>[1,8,4,2,5,3,6,7]=>[8,1,5,7,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,3,6,8,4]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,5,2,6,4]=>[1,2,8,4,3,7,6,5]=>[8,7,1,5,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,6,5,7,1]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,5,2,1,3]=>[1,4,8,3,7,2,6,5]=>[8,5,1,6,2,7,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,8,6,5,3]=>[1,4,2,7,5,8,3,6]=>[8,5,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,8,5,1,3]=>[1,6,5,8,3,2,7,4]=>[8,3,4,1,6,7,2,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,3,5,6,1,4]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,4,6,1,5]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,8,5,2,6]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,5,4,2,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,8,2,5,6]=>[1,2,7,5,8,6,3,4]=>[8,7,2,4,1,3,6,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,4,6,2,7]=>[1,2,5,4,3,8,7,6]=>[8,7,4,5,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,2,5,7,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,7,2,3,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,7,8,6,5]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,4,8,3,2]=>[1,5,4,6,8,2,7,3]=>[8,4,5,3,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,1,3,6,2]=>[1,7,6,3,5,2,4,8]=>[8,2,3,6,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,2,5,8,7]=>[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,2,5,8,7]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,8,2,4,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,2,8,5,7]=>[1,2,4,3,6,8,7,5]=>[8,7,5,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,5,7,2,3]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,4,1,8,3]=>[1,5,4,7,8,3,6,2]=>[8,4,5,2,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,1,7,3,2]=>[1,8,2,5,3,6,7,4]=>[8,1,7,4,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,3,1,7,4]=>[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,6,3,7,2]=>[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,2,5,7,3]=>[1,8,3,4,6,5,2,7]=>[8,1,6,5,3,4,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,6,2,7,3]=>[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,1,4,3,7]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,2,1,4,5]=>[1,6,2,7,4,8,5,3]=>[8,3,7,2,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,5,4,1,8,6]=>[1,2,7,8,6,3,4,5]=>[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,4,1,8,5]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,5,3,7,6]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,5,4,8,7]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,4,7,2,6]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,4,6,2,7]=>[1,5,4,2,3,8,7,6]=>[8,4,5,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,5,7,6,2]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,7,2,8,5]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,1,8,5,4]=>[1,7,5,2,3,6,8,4]=>[8,2,4,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,8,7,4,5]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,5,4,6,3]=>[1,2,8,3,4,7,6,5]=>[8,7,1,6,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,5,7,2,4]=>[1,6,7,2,8,4,3,5]=>[8,3,2,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,2,6,8,3]=>[1,7,8,3,5,2,4,6]=>[8,2,1,6,4,7,5,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,2,7,4,9,8]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,2,7,6,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,5,6,2,7,4,9,8,10]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,4,5,2,7,6,9,8,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,4,3,6,1,7,8,2]=>[1,5,2,4,6,7,8,3]=>[8,4,7,5,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,5,6,1,4]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,4,7,8,3]=>[1,5,4,6,7,8,3,2]=>[8,4,5,3,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,6,7,8,9,2]=>[1,4,3,5,6,7,8,9,2]=>[9,6,7,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,5,3,6,7,8,9,10,2]=>[1,4,3,5,6,7,8,9,10,2]=>[10,7,8,6,5,4,3,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,4,5,6,3,2,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,5,8,2,3]=>[1,4,2,7,3,6,8,5]=>[8,5,7,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,4,6,3,2]=>[1,8,2,5,4,7,3,6]=>[8,1,7,4,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,6,7,2,5]=>[1,3,8,5,6,7,2,4]=>[8,6,1,4,3,2,7,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,4,1,5,2]=>[1,3,7,5,4,8,2,6]=>[8,6,2,4,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,4,6,1,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,4,6,2,5]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,4,6,2,5]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,6,7,2,5]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,6,1,2,5]=>[1,4,3,7,2,8,5,6]=>[8,5,6,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,7,1,2,6]=>[1,5,7,2,8,6,3,4]=>[8,4,2,7,1,3,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,6,7,1,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,7,3,2,4]=>[1,2,6,3,5,7,4,8]=>[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,3,5,1,4]=>[1,7,2,3,6,5,4,8]=>[8,2,7,6,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,6,1,2,5]=>[1,4,7,2,8,5,6,3]=>[8,5,2,7,1,4,3,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,1,3,6,5]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,9,10,2,1,3]=>[1,4,7,10,3,6,9,2,5,8]=>[10,7,4,1,8,5,2,9,6,3]=>[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,7,1,4,5,6,2,8]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,5,2,7,8]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,5,6,4,8]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,5,4,7,2]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,7,2,4,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,6,4,3,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,4,3,7,2]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,4,3,1,6]=>[1,2,5,4,8,6,3,7]=>[8,7,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,3,2,7,4]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,8,5,2,4]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,6,1,2,8]=>[1,5,6,2,4,7,3,8]=>[8,4,3,7,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,2,3,8,5]=>[1,4,2,7,8,5,3,6]=>[8,5,7,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,7,8,1,3]=>[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,3,8,5,4]=>[1,2,7,5,3,6,8,4]=>[8,7,2,4,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,7,6,2,8]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,6,4,5,1]=>[1,7,5,6,4,8,2,3]=>[8,2,4,3,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,8,6,2,7]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,8,4,6,2]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,3,4,6,2]=>[1,7,6,4,5,3,2,8]=>[8,2,3,5,4,6,7,1]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,1,6,2,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,1,4,2,8]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,3,4,8,2]=>[1,2,7,8,3,5,4,6]=>[8,7,2,1,6,4,5,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,7,8,4,6]=>[1,5,7,4,2,3,6,8]=>[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,8,2,6,4]=>[1,5,8,4,7,6,2,3]=>[8,4,1,5,2,3,7,6]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,7,6,4,3]=>[1,5,7,4,2,8,3,6]=>[8,4,2,5,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,5,3,2,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,7,5,3,8]=>[1,2,4,6,5,7,3,8]=>[8,7,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,6,5,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,5,8,2,6]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,2,7,4,3,5]=>[1,2,8,5,7,3,6,4]=>[8,7,1,4,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,1,8,5,3]=>[1,7,5,2,3,6,8,4]=>[8,2,4,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,3,7,5,2]=>[1,6,7,5,3,2,4,8]=>[8,3,2,4,6,7,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,3,6,2,1]=>[1,4,7,2,5,3,8,6]=>[8,5,2,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,1,7,8,6,2]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,1,5,4,3]=>[1,6,5,2,8,3,7,4]=>[8,3,4,7,1,6,2,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,7,5,4,2]=>[1,8,2,3,6,5,7,4]=>[8,1,7,6,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,7,6,4,2]=>[1,8,2,5,7,4,3,6]=>[8,1,7,4,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,4,2,1,7]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,5,7,2,8,4]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,6,4,3,7]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,8,4,2,3]=>[1,2,6,4,5,8,3,7]=>[8,7,3,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,3,2,5,1]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,2,1,6,4]=>[1,5,2,8,4,3,7,6]=>[8,4,7,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,6,4,3,1]=>[1,5,6,4,2,8,3,7]=>[8,4,3,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,5,1,4,2]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,6,8,3,4,1]=>[1,7,4,6,3,5,8,2]=>[8,2,5,3,6,4,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,3,5,4,1]=>[1,8,2,6,5,3,7,4]=>[8,1,7,3,4,6,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,1,6,8,5]=>[1,4,3,7,8,5,2,6]=>[8,5,6,2,1,4,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,2,1,8,5]=>[1,7,8,5,2,3,6,4]=>[8,2,1,4,7,6,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,8,5,2,7]=>[1,6,5,8,7,2,4,3]=>[8,3,4,1,2,7,5,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,5,8,6,2]=>[1,7,6,8,2,4,3,5]=>[8,2,3,1,7,5,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,6,7,3,1]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,8,5,6,4]=>[1,7,6,5,8,4,2,3]=>[8,2,3,4,1,5,7,6]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,9,6,7,8]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,5,7,2,4,3,8,6]=>[1,2,5,4,3,7,8,6]=>[8,7,4,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,8,4,3,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,2,7,4,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,2,8,4,6]=>[1,5,2,7,4,3,6,8]=>[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,3,6,5,4]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,8,3,2,5,6]=>[1,2,4,8,6,3,7,5]=>[8,7,5,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,2,4,6,5]=>[1,8,5,2,7,6,4,3]=>[8,1,4,7,2,3,5,6]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,2,7,4,5]=>[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,4,1,2,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,7,2,1,4]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,4,1,2,5]=>[1,8,5,4,6,2,7,3]=>[8,1,4,5,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,5,1,4,6]=>[1,8,6,2,7,4,3,5]=>[8,1,3,7,2,5,6,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,1,7,2,8]=>[1,6,7,2,4,3,5,8]=>[8,3,2,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,3,1,5,6]=>[1,8,6,2,7,5,3,4]=>[8,1,3,7,2,4,6,5]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,1,4,8,5]=>[1,7,8,5,2,6,4,3]=>[8,2,1,4,7,3,5,6]=>[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,2,3,1,5,8]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,3,2,8,5]=>[1,4,2,7,8,5,3,6]=>[8,5,7,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,4,7,8,5,1]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,8,5,2,4]=>[1,7,2,6,5,8,4,3]=>[8,2,7,3,4,1,5,6]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,1,5,2,4]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,8,5,3,2]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,6,1,3,4]=>[1,7,3,5,6,2,4,8]=>[8,2,6,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,2,5,8,7]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,6,2,3,1]=>[1,7,3,5,6,2,4,8]=>[8,2,6,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,8,7,4,3]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,9,7,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,3,7,5,2,6,4]=>[1,2,8,4,7,6,3,5]=>[8,7,1,5,2,3,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,2,6,8,3]=>[1,7,8,3,2,4,5,6]=>[8,2,1,6,7,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,5,2,8,4]=>[1,3,6,2,4,7,8,5]=>[8,6,3,7,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,5,1,7,3]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,2,1,4,3]=>[1,8,3,7,4,5,2,6]=>[8,1,6,2,5,4,7,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,2,6,8,3]=>[1,7,8,3,4,5,2,6]=>[8,2,1,6,5,4,7,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,3,8,7,5]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,2,7,3]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,6,1,7,2]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,3,5,6,1]=>[1,2,8,3,4,7,6,5]=>[8,7,1,6,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,3,8,2,4]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,7,8,4,5]=>[1,2,6,8,5,7,4,3]=>[8,7,3,1,4,2,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,3,5,4,6]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,7,4,2,3]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,5,2,6,4]=>[1,8,4,3,2,7,6,5]=>[8,1,5,6,7,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,5,4,1,6]=>[1,3,8,6,4,2,7,5]=>[8,6,1,3,5,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,8,1,3,2]=>[1,4,5,8,2,7,3,6]=>[8,5,4,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,2,1,5,3]=>[1,4,6,2,7,5,3,8]=>[8,5,3,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,6,8,3,2]=>[1,5,6,8,2,3,4,7]=>[8,4,3,1,7,6,5,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,1,8,3,2]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,6,1,8,2]=>[1,5,6,2,3,7,8,4]=>[8,4,3,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,5,4,8,2]=>[1,3,7,8,2,6,4,5]=>[8,6,2,1,7,3,5,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,5,8,2,1]=>[1,3,4,7,2,6,8,5]=>[8,6,5,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,4,5,6,9,7]=>[1,8,9,7,6,5,4,3,2]=>[9,2,1,3,4,5,6,7,8]=>[9,3,2,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,4,7,1,5,2,8,3]=>[1,6,2,4,3,7,8,5]=>[8,3,7,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,8,7,4,3]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,8,1,9,6]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,2,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,6,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,9,1,6,8]=>[1,2,3,4,5,7,6,9,8]=>[9,8,7,6,5,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,9,6,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,6,7,9,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,5,3,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,5,6,1,7,8,9,10,4]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,1,7,2,5,8,3,6]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,6,1,7,4]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,2,8,6,3]=>[1,4,7,6,8,3,2,5]=>[8,5,2,3,1,6,7,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,6,7,4,1]=>[1,2,8,3,5,6,7,4]=>[8,7,1,6,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,6,7,4,1]=>[1,8,2,3,5,6,7,4]=>[8,1,7,6,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,5,3,1,8]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,6,8,2,5]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,4,8,7,2]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,5,4,2,6]=>[1,7,2,3,4,8,6,5]=>[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,1,6,2,4]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,2,8,7,5]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,4,3,1,8]=>[1,5,4,7,2,3,6,8]=>[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,4,3,2,7]=>[1,8,7,2,5,4,6,3]=>[8,1,2,7,4,5,3,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,2,7,1,4]=>[1,8,4,5,2,6,7,3]=>[8,1,5,4,7,3,2,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,5,1,4,6]=>[1,7,4,8,6,2,3,5]=>[8,2,5,1,3,7,6,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,2,8,5,6]=>[1,4,3,7,5,2,6,8]=>[8,5,6,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,4,7,1,6]=>[1,8,6,7,2,3,5,4]=>[8,1,3,2,7,6,4,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,7,8,5,4]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,4,2,1,7]=>[1,3,8,7,2,6,4,5]=>[8,6,1,2,7,3,5,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,5,3,1,8]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,2,8,4,1]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,7,2,3,4]=>[1,5,7,3,2,6,4,8]=>[8,4,2,6,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,2,1,4,6]=>[1,5,2,8,6,3,7,4]=>[8,4,7,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,5,6,4,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,5,8,2,6]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,5,8,3,6]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,2,3,5,6,8,7,9]=>[1,4,3,2,5,6,7,8,9]=>[9,6,7,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,6,3,5,1,7,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,7,3,4,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,3,8,5,2,7]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,2,3,6,8]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,8,2,3,7]=>[1,2,4,5,8,7,3,6]=>[8,7,5,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,7,6,2,5]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,7,2,6,8]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,6,8,3,4,1]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,2,8,5,4]=>[1,3,6,8,4,7,5,2]=>[8,6,3,1,5,2,4,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,8,4,7,2]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,3,8,4,7,2]=>[1,6,4,3,2,5,8,7]=>[8,3,5,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,5,3,2,6]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,8,4,5,2]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,6,7,3,2]=>[1,8,2,5,6,7,3,4]=>[8,1,7,4,3,2,6,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,6,8,2,1]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,5,2,6,1]=>[1,3,7,6,2,4,8,5]=>[8,6,2,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,6,5,1,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,1,5,6,8]=>[1,7,6,5,2,3,4,8]=>[8,2,3,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,8,7,1,2]=>[1,6,7,2,3,5,8,4]=>[8,3,2,7,6,4,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,3,1,7,5,8]=>[1,2,6,7,5,3,4,8]=>[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,5,6,3,2]=>[1,4,7,3,2,8,5,6]=>[8,5,2,6,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,8,4,6,3]=>[1,2,5,8,3,7,6,4]=>[8,7,4,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,3,6,4,1]=>[1,5,3,7,4,2,8,6]=>[8,4,6,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,2,3,7,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,2,6,3,4]=>[1,2,8,4,5,3,7,6]=>[8,7,1,5,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,4,5,8,2]=>[1,2,7,8,3,6,5,4]=>[8,7,2,1,6,3,4,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,5,6,2,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,6,4,2,5]=>[1,2,8,5,6,4,3,7]=>[8,7,1,4,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,8,2,6,3]=>[1,2,4,5,8,3,7,6]=>[8,7,5,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,6,3,4,8]=>[1,2,7,4,5,6,3,8]=>[8,7,2,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,8,3,4,7]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,6,3,4,7]=>[1,2,5,6,3,8,7,4]=>[8,7,4,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,7,2,6,3,8]=>[1,4,7,3,5,2,6,8]=>[8,5,2,6,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,1,3,6,4,8]=>[1,5,3,2,7,4,6,8]=>[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,2,4,1,8]=>[1,3,6,4,7,2,5,8]=>[8,6,3,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,2,3,1,8]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,8,3,2,7]=>[1,2,5,8,7,3,6,4]=>[8,7,4,1,2,6,3,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,4,8,3,7]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,8,6,2,3]=>[1,5,8,3,4,7,2,6]=>[8,4,1,6,5,2,7,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,7,8,6,4]=>[1,5,7,6,8,4,2,3]=>[8,4,2,3,1,5,7,6]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,6,1,5,2]=>[1,7,5,6,2,4,8,3]=>[8,2,4,3,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,5,8,6,2]=>[1,4,2,3,7,6,8,5]=>[8,5,7,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,3,1,7,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,7,5,8,6]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,6,1,3,5]=>[1,4,2,8,5,6,3,7]=>[8,5,7,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,1,7,3,6]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,7,3,2,5]=>[1,6,3,4,2,8,5,7]=>[8,3,6,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,2,7,5,4]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,8,3,2,5,6]=>[1,4,8,6,2,3,7,5]=>[8,5,1,3,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,3,6,2,8]=>[1,5,3,7,2,4,6,8]=>[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,3,6,4,7]=>[1,5,3,2,8,7,4,6]=>[8,4,6,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,2,6,4,7]=>[1,2,8,7,4,5,3,6]=>[8,7,1,2,5,4,6,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,4,5,1,6]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,6,7,1,3]=>[1,2,5,6,7,3,8,4]=>[8,7,4,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,5,3,4,8]=>[1,7,4,6,3,2,5,8]=>[8,2,5,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,2,3,5,1]=>[1,4,6,3,8,2,7,5]=>[8,5,3,6,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,4,8,6,5,3]=>[1,7,5,8,3,2,4,6]=>[8,2,4,1,6,7,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,4,8,1,3]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,5,7,1,4]=>[1,2,8,4,6,7,3,5]=>[8,7,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,6,5,2,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,6,8,7,4]=>[1,3,2,5,6,8,4,7]=>[8,6,7,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,8,7,5,6]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,3,7,8,6]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,5,8,3,4]=>[1,2,6,8,4,3,7,5]=>[8,7,3,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,4,3,1]=>[1,7,3,5,2,8,4,6]=>[8,2,6,4,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,2,4,1,7]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,6,2,1,3]=>[1,5,6,2,4,8,3,7]=>[8,4,3,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,7,4,6,5]=>[1,8,5,7,6,4,3,2]=>[8,1,4,2,3,5,6,7]=>[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,3,7,5,6]=>[1,4,2,3,8,6,7,5]=>[8,5,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,5,1,8,3]=>[1,4,7,8,3,6,2,5]=>[8,5,2,1,6,3,7,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,2,8,1,6]=>[1,3,7,2,5,4,6,8]=>[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,6,3,8,1,5]=>[1,2,4,6,8,5,3,7]=>[8,7,5,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,1,2,3,7]=>[1,4,5,2,6,3,8,7]=>[8,5,4,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,1,2,3,8]=>[1,4,7,3,5,2,6,8]=>[8,5,2,6,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,6,1,8,2,5]=>[1,3,7,2,4,6,8,5]=>[8,6,2,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,3,2,4,6]=>[1,7,4,5,3,8,6,2]=>[8,2,5,4,6,1,3,7]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,2,7,5,4]=>[1,8,4,3,2,6,7,5]=>[8,1,5,6,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,2,4,6,3]=>[1,8,3,7,6,4,5,2]=>[8,1,6,2,3,5,4,7]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,4,1,6,3]=>[1,8,3,7,6,2,4,5]=>[8,1,6,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,7,3,5,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,7,1,6,3]=>[1,4,5,7,6,2,3,8]=>[8,5,4,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,5,3,2,1]=>[1,6,3,7,2,8,4,5]=>[8,3,6,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,4,8,3,1]=>[1,5,4,7,3,6,8,2]=>[8,4,5,2,6,3,1,7]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,7,3,2,4]=>[1,6,3,8,4,2,5,7]=>[8,3,6,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,5,2,3,7]=>[1,6,2,4,3,8,7,5]=>[8,3,7,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,6,3,5,8]=>[1,7,5,6,3,4,2,8]=>[8,2,4,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,6,5,8,7,9]=>[1,4,3,2,5,6,7,8,9]=>[9,6,7,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,6,1,5,3,4,8,7]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,4,2,6,1]=>[1,3,7,6,2,8,4,5]=>[8,6,2,3,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,3,6,4,1]=>[1,5,3,8,2,7,4,6]=>[8,4,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,1,4,5,6]=>[1,2,8,6,4,3,7,5]=>[8,7,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,2,3,1,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,2,3]=>[10,1,2,3,4,5,6,7,9,8]=>[10,2,3,4,5,6,7,8,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,8,6,7,5,4,2,1]=>[1,3,6,4,7,2,8,5]=>[8,6,3,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,4,6,2,3]=>[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,3,1,2,5]=>[1,8,5,3,7,2,4,6]=>[8,1,4,6,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,3,2,8,1]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,1,5,7,2]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,5,6,8,2]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,4,2,1,8,5]=>[1,6,2,7,8,5,3,4]=>[8,3,7,2,1,4,6,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,2,4,8,7]=>[1,3,6,4,5,2,7,8]=>[8,6,3,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,3,2,7,6]=>[1,5,3,4,2,8,6,7]=>[8,4,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,6,1,8,2]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,6,3,8,7]=>[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,6,7,3,8]=>[1,4,2,5,6,7,3,8]=>[8,5,7,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,4,3,8,7]=>[1,2,5,4,6,3,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,5,7,2,3]=>[1,4,2,6,7,3,8,5]=>[8,5,7,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,4,8,7,5]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,7,5,6,3]=>[1,4,2,8,3,5,7,6]=>[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,8,7,5,2]=>[1,2,6,7,5,8,3,4]=>[8,7,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,2,5,8,6,1]=>[1,3,7,6,8,2,4,5]=>[8,6,2,3,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,6,1,4,5]=>[1,3,7,4,2,8,5,6]=>[8,6,2,5,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,2,7,1,3]=>[1,5,2,6,7,3,8,4]=>[8,4,7,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,1,2,5,7]=>[1,4,6,2,3,8,7,5]=>[8,5,3,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,7,1,3,2]=>[1,4,5,7,3,6,2,8]=>[8,5,4,2,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,4,1,3,2]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,3,6,5,1]=>[1,8,2,7,5,3,4,6]=>[8,1,7,2,4,6,5,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,7,6,5,1]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,3,1,6,8]=>[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,4,5,8,2]=>[1,7,8,2,6,5,4,3]=>[8,2,1,7,3,4,5,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,6,2,1,8,5]=>[1,3,4,6,2,7,8,5]=>[8,6,5,3,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,8,6,2,3]=>[1,5,8,3,2,4,7,6]=>[8,4,1,6,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,2,3,7,6]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,9,7,8]=>[1,3,2,4,5,6,7,9,8]=>[9,7,8,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,8,3,4,6,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,3,5,4,6]=>[1,8,6,5,3,2,4,7]=>[8,1,3,4,6,7,5,2]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,6,3,4,8]=>[1,5,6,3,2,7,4,8]=>[8,4,3,6,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,6,3,4,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,2,3,6,8]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,3,6,5,7]=>[1,4,2,8,7,5,3,6]=>[8,5,7,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,4,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,5,6,4,2,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,6,4,7,8,9,5]=>[1,2,3,4,6,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,6,7,2,8,5,9]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,3,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,4,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,5,3,6,7,4,8,9,10]=>[1,2,3,5,6,7,4,8,9,10]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,5,6,4,2,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,4,6,7,2,8,5,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,2,3,8,7,1,4,5]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,4,7,5,1]=>[1,8,2,3,4,6,7,5]=>[8,1,7,6,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,2,6,8,7]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,1,3,2,8]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,2,7,8,4]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,1,8,3,5]=>[1,6,8,5,2,7,3,4]=>[8,3,1,4,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,3,2,7,8,4]=>[1,5,2,3,6,7,8,4]=>[8,4,7,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,4,7,3,8]=>[1,5,4,6,7,3,2,8]=>[8,4,5,3,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,2,7,8,3]=>[1,5,2,4,6,7,8,3]=>[8,4,7,5,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,5,4,1,3,8]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,4,2,8,6]=>[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,4,5,3,1]=>[1,7,3,8,2,6,5,4]=>[8,2,6,1,7,3,4,5]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,5,1,3,7]=>[1,4,6,2,3,8,7,5]=>[8,5,3,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,4,7,1,2,6]=>[1,3,5,7,2,8,6,4]=>[8,6,4,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,6,2,7,5]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,4,8,7,1,5]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,5,7,4,8,1]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,6,8,5,3]=>[1,7,5,6,8,3,4,2]=>[8,2,4,3,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,3,8,5,1]=>[1,6,8,2,4,3,7,5]=>[8,3,1,7,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,5,7,4,2,3]=>[1,6,4,5,7,2,3,8]=>[8,3,5,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,6,5,8,2]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,5,4,2,8,3]=>[1,7,8,3,2,6,4,5]=>[8,2,1,6,7,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,7,2,4,3]=>[1,5,7,4,8,3,6,2]=>[8,4,2,5,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,8,7,4,1]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,6,7,2,3,1]=>[1,4,6,2,5,7,3,8]=>[8,5,3,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,1,2,8,3]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,2,1,8,3]=>[1,4,7,8,3,5,2,6]=>[8,5,2,1,6,4,7,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,10,6,7,1,9,8,5]=>[1,2,3,4,10,5,6,7,8,9]=>[10,9,8,7,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,2,4,3,6,1,8,5]=>[1,7,8,5,6,2,3,4]=>[8,2,1,4,3,7,6,5]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,8,6,1,5]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,4,2,8,5]=>[1,6,2,3,7,8,5,4]=>[8,3,7,6,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,1,8,2,7]=>[1,4,5,2,6,8,7,3]=>[8,5,4,7,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,2,3,4,1]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,8,2,5,1]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,2,1,7,3]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,8,6,3,1]=>[1,2,4,5,8,3,7,6]=>[8,7,5,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,7,4,8,1]=>[1,2,5,7,8,3,6,4]=>[8,7,4,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,7,4,8,1]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,5,4,8,2]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,7,4,3,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,8,5,3,6]=>[1,7,3,4,2,5,8,6]=>[8,2,6,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,5,3,8,2,7]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,5,6,4,2]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,6,3,4,2]=>[1,5,6,3,8,2,4,7]=>[8,4,3,6,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,3,6,4,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,1,5,6,4]=>[1,8,4,3,2,7,6,5]=>[8,1,5,6,7,2,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,6,4,5,3]=>[1,8,3,2,7,5,6,4]=>[8,1,6,7,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,6,2,5,3]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,4,3,5,2]=>[1,8,2,7,5,4,6,3]=>[8,1,7,2,4,5,3,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,3,6,5,2]=>[1,8,2,4,7,5,3,6]=>[8,1,7,5,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,8,2,5,4]=>[1,2,7,5,8,4,6,3]=>[8,7,2,4,1,5,3,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,6,7,4,1]=>[1,3,5,6,7,4,2,8]=>[8,6,4,3,2,5,7,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,2,6,1,7]=>[1,4,5,2,3,8,7,6]=>[8,5,4,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,5,2,1,8]=>[1,3,4,7,2,6,5,8]=>[8,6,5,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,2,6,8,3]=>[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,5,3,1,4]=>[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,6,3,1,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,5,1,7,2]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,4,1,7,2]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,1,3,6,2]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,1,2,5,6]=>[1,8,6,2,4,3,7,5]=>[8,1,3,7,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,6,4,2]=>[1,8,2,7,4,5,3,6]=>[8,1,7,2,5,4,6,3]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,6,1,7,5]=>[1,4,2,8,5,6,3,7]=>[8,5,7,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,6,1,5,2,8]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,6,1,8,2]=>[1,7,8,2,5,6,3,4]=>[8,2,1,7,4,3,6,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,3,1,2,7]=>[1,4,5,3,8,7,2,6]=>[8,5,4,6,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,3,7,2,1]=>[1,5,3,8,2,6,7,4]=>[8,4,6,1,7,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,2,1,6,3]=>[1,7,6,2,5,3,8,4]=>[8,2,3,7,4,6,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,6,2,5,3]=>[1,2,4,7,5,6,3,8]=>[8,7,5,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,5,3,8,6]=>[1,7,8,6,3,4,2,5]=>[8,2,1,3,6,5,7,4]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,1,7,2,6]=>[1,8,6,7,2,5,3,4]=>[8,1,3,2,7,4,6,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,1,2,7,4]=>[1,8,4,3,5,2,6,7]=>[8,1,5,6,4,7,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,3,8,4,1]=>[1,5,3,7,4,2,6,8]=>[8,4,6,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,5,7,3,1]=>[1,8,2,4,6,7,3,5]=>[8,1,7,5,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,8,5,6,3]=>[1,2,7,6,5,8,3,4]=>[8,7,2,3,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,4,6,8,5]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,3,1,2,6,7]=>[1,4,3,5,2,8,7,6]=>[8,5,6,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,7,2,6,8]=>[1,2,5,7,6,3,4,8]=>[8,7,4,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,1,3,8,5]=>[1,6,3,7,8,5,2,4]=>[8,3,6,2,1,4,7,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,2,4,8,5]=>[1,6,4,2,7,8,5,3]=>[8,3,5,7,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,7,6,2,5,4]=>[1,3,8,4,7,5,6,2]=>[8,6,1,5,2,4,3,7]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,7,2,5,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,1,8,4,7]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,6,8,3,5,1]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,1,5,4,2]=>[1,3,6,5,2,7,4,8]=>[8,6,3,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,8,4,2,3]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,5,1,4,2]=>[1,3,6,2,7,4,8,5]=>[8,6,3,7,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,6,2,4,5]=>[1,7,4,8,5,6,2,3]=>[8,2,5,1,4,3,7,6]=>[8,4,6,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,6,5,3,4]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,6,8,9,1]=>[1,2,3,4,5,7,8,9,6]=>[9,8,7,6,5,3,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,8,6,9,1]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,8,7,6,9,1]=>[1,2,3,4,5,8,9,6,7]=>[9,8,7,6,5,2,1,4,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,9,8,6,1]=>[1,2,3,4,5,7,8,6,9]=>[9,8,7,6,5,3,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,5,6,4,7,8,9,10,1]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,1,5,2,6,4,7,3]=>[1,8,3,5,6,4,2,7]=>[8,1,6,4,3,5,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,1,2,3,8]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,7,6,2,1,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,7,2,6,3]=>[1,4,5,7,6,2,3,8]=>[8,5,4,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,7,5,6,3]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,4,3,5,1]=>[1,7,5,4,2,6,3,8]=>[8,2,4,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,8,1,6,2]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,1,4,2,8,5]=>[1,7,8,5,4,2,3,6]=>[8,2,1,4,5,7,6,3]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,4,5,1,3]=>[1,8,3,2,7,4,6,5]=>[8,1,6,7,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,9,5,6,8]=>[1,2,3,4,5,7,6,9,8]=>[9,8,7,6,5,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,9,5,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,8,5,6,9,7]=>[1,2,3,4,5,8,9,7,6]=>[9,8,7,6,5,2,1,3,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,7,8,5,9,6]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,6,4,8,3,5,1,7]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,3,2,7,6]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,6,7,1,2]=>[1,3,8,2,5,6,7,4]=>[8,6,1,7,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,5,7,3,6]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,8,2,5,6]=>[1,7,5,8,6,2,3,4]=>[8,2,4,1,3,7,6,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,8,2,4,7]=>[1,5,8,7,4,2,6,3]=>[8,4,1,2,5,7,3,6]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,1,8,4,2]=>[1,7,4,5,2,3,6,8]=>[8,2,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,6,4,8,3]=>[1,7,8,3,5,6,4,2]=>[8,2,1,6,4,3,5,7]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,6,4,8,3]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,4,6,3,2]=>[1,2,5,4,8,3,7,6]=>[8,7,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,7,6,3,2]=>[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,6,4,7,3]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,1,5,6,4]=>[1,3,2,7,6,5,4,8]=>[8,6,7,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,3,6,5,4]=>[1,8,4,2,7,5,3,6]=>[8,1,5,7,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,6,4,8,2]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,1,6,5,3]=>[1,8,3,4,2,7,5,6]=>[8,1,6,5,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,7,1,6,4]=>[1,3,2,5,7,6,4,8]=>[8,6,7,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,5,4,1,8,2]=>[1,3,6,2,7,8,4,5]=>[8,6,3,7,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,1,8,7,2]=>[1,4,3,5,2,6,8,7]=>[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,3,1,5,2]=>[1,8,2,6,3,7,5,4]=>[8,1,7,3,6,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,5,3,2,6]=>[1,4,8,6,3,2,7,5]=>[8,5,1,3,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,4,3,5,2]=>[1,8,2,6,3,7,5,4]=>[8,1,7,3,6,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,1,3,5,4]=>[1,8,4,2,6,3,7,5]=>[8,1,5,7,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,7,6,2,8]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,7,1,3,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,1,6,2,8]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,1,8,2,5]=>[1,6,8,5,2,4,7,3]=>[8,3,1,4,7,5,2,6]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,6,4,5,8]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,6,3,4,8]=>[1,5,6,3,2,4,7,8]=>[8,4,3,6,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,2,4,3,8]=>[1,5,2,6,4,7,3,8]=>[8,4,7,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,1,3,4,8]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,5,6,4,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,4,1,7,8]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,5,4,7,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,4,2,7,8,3]=>[1,6,7,8,3,5,2,4]=>[8,3,2,1,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,5,2,7,8,3]=>[1,4,5,2,6,7,8,3]=>[8,5,4,7,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,1,3,7,4]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,5,7,4,2]=>[1,3,6,7,4,2,8,5]=>[8,6,3,2,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,4,2,5,7]=>[1,8,7,5,4,3,6,2]=>[8,1,2,4,5,6,3,7]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,7,3,2,8]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,7,2,8,3]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,4,8,3,2]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,3,2,4,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,1,5,3,4]=>[1,7,3,8,4,2,6,5]=>[8,2,6,1,5,7,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,1,3,7,4]=>[1,8,4,5,2,6,3,7]=>[8,1,5,4,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,4,1,8,3]=>[1,5,4,6,2,7,8,3]=>[8,4,5,3,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,4,7,3,5]=>[1,8,5,4,6,7,3,2]=>[8,1,4,5,3,2,6,7]=>[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,5,2,7,4]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,8,5,6,4,1]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,7,4,6,3]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,4,7,2,3]=>[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,3,2,6,4]=>[1,5,3,2,7,6,4,8]=>[8,4,6,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,6,4,7,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,3,7,1,6]=>[1,8,6,7,2,3,5,4]=>[8,1,3,2,7,6,4,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,7,6,2,1]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,4,7,2,6]=>[1,8,6,7,2,3,5,4]=>[8,1,3,2,7,6,4,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,4,3,7,2]=>[1,2,5,4,6,3,8,7]=>[8,7,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,4,2,1,7,3]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,6,2,7,3]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,7,1,8,5]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,7,8,5,1]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,5,3,8,4]=>[1,2,7,8,4,3,6,5]=>[8,7,2,1,5,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,2,5,3,1]=>[1,7,3,6,5,2,8,4]=>[8,2,6,3,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,7,1,3,2]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,8,3,2,5]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,6,7,9,1]=>[1,2,3,4,5,8,9,6,7]=>[9,8,7,6,5,2,1,4,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,9,6,8,7,1]=>[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,4,5,2,6,7,8,1]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,4,3,8,7,2,5,1]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,1,3,8,6]=>[1,5,2,4,3,7,8,6]=>[8,4,7,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,7,1,8,3]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,8,2,1,3]=>[1,4,5,8,3,7,2,6]=>[8,5,4,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,6,4,1,8,3]=>[1,2,5,4,6,3,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,2,7,8,3]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,7,8,6,4]=>[1,2,3,5,7,6,8,4]=>[8,7,6,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,1,2,7,6]=>[1,4,5,2,8,6,3,7]=>[8,5,4,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,4,1,7,2,6]=>[1,3,5,2,8,6,7,4]=>[8,6,4,7,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,2,6,7,4]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,1,7,4,6]=>[1,2,8,6,7,4,3,5]=>[8,7,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,4,8,3,5]=>[1,7,3,2,4,6,8,5]=>[8,2,6,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,7,5,8,4,6]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,7,1,8,3]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,1,4,6,5]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,8,6,7,9]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,7,6,3,8,4,5,1]=>[1,2,7,5,8,3,6,4]=>[8,7,2,4,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,3,1,7,5]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,5,1,8,6]=>[1,4,3,2,7,8,6,5]=>[8,5,6,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,3,7,5,8]=>[1,6,7,5,3,2,4,8]=>[8,3,2,4,6,7,5,1]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,6,1,8,4]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,8,7,1,3]=>[1,5,8,3,4,2,6,7]=>[8,4,1,6,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,6,1,8,3]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,6,2,8,3]=>[1,5,6,2,4,3,7,8]=>[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,2,3,8,5]=>[1,6,3,7,8,5,2,4]=>[8,3,6,2,1,4,7,5]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,3,8,4,5,2]=>[1,6,4,3,7,5,8,2]=>[8,3,5,6,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,6,4,7,5]=>[1,8,5,6,4,2,3,7]=>[8,1,4,3,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,3,4,6,5]=>[1,2,8,5,3,7,6,4]=>[8,7,1,4,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,5,6,4,7]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,4,6,8,5]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,6,2,7,5]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,7,4,5,1]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,6,3,8,4,1]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,8,6,3,4]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,6,8,2,3]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,2,6,3,5]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,7,4,1,8]=>[1,6,4,5,7,2,3,8]=>[8,3,5,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,3,7,8,4]=>[1,6,7,8,4,5,3,2]=>[8,3,2,1,5,4,6,7]=>[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,1,3,6,7]=>[1,5,2,8,7,6,3,4]=>[8,4,7,1,2,3,6,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,5,1,8,6,3]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,8,5,6,4]=>[1,2,3,7,6,5,8,4]=>[8,7,6,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,8,7,4,2]=>[1,3,5,8,2,6,7,4]=>[8,6,4,1,7,3,2,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,5,4,3,6]=>[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,5,1,7,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,4,8,6,2]=>[1,3,5,4,7,6,8,2]=>[8,6,4,5,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,6,8,2,5,3]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,1,5,3,8]=>[1,7,3,6,5,2,4,8]=>[8,2,6,3,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,8,3,7,4]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,1,4,2,8]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,6,7,4,2]=>[1,5,6,7,4,2,8,3]=>[8,4,3,2,5,7,1,6]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,8,5,2,3]=>[1,4,6,5,8,3,2,7]=>[8,5,3,4,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,6,4,2,3]=>[1,5,6,4,2,8,3,7]=>[8,4,3,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,2,5,4,6]=>[1,2,7,4,8,6,5,3]=>[8,7,2,5,1,3,4,6]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,6,7,5,2]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,6,7,4,2]=>[1,5,6,7,4,8,2,3]=>[8,4,3,2,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,4,2,8,3]=>[1,5,4,6,2,7,8,3]=>[8,4,5,3,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,6,5,8,4,3]=>[1,2,7,4,6,8,3,5]=>[8,7,2,5,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,7,5,4,8]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,8,6,5,3]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,1,3,2,8]=>[1,6,3,5,2,7,4,8]=>[8,3,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,4,3,5,8]=>[1,6,3,7,5,4,2,8]=>[8,3,6,2,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,5,1,4,8]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,7,1,3,5]=>[1,2,6,3,8,5,7,4]=>[8,7,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,8,2,3,5,7]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,4,1,7,3]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,3,5,8,6,2]=>[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,5,1,6,4]=>[1,3,8,4,2,7,6,5]=>[8,6,1,5,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,3,2,7,5]=>[1,8,5,3,2,6,4,7]=>[8,1,4,6,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,1,2,5,4]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,6,7,2,3,4]=>[1,5,7,3,8,4,6,2]=>[8,4,2,6,1,5,3,7]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,8,2,3,4]=>[1,5,8,4,6,2,7,3]=>[8,4,1,5,3,7,2,6]=>[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,1,7,3,5]=>[1,6,7,3,4,2,8,5]=>[8,3,2,6,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,1,7,4,5]=>[1,6,7,4,8,5,2,3]=>[8,3,2,5,1,4,7,6]=>[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,7,8,5,2]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,3,7,1,2]=>[1,6,7,2,8,3,5,4]=>[8,3,2,7,1,6,4,5]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,3,1,2,6]=>[1,5,3,4,8,6,2,7]=>[8,4,6,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,1,4,7,3]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,5,2,3,8]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,2,3,8,7]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,8,6,2,3]=>[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,4,6,2,1]=>[1,8,2,5,4,3,7,6]=>[8,1,7,4,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,2,4,7,3,1]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,5,7,3,1]=>[1,4,2,8,3,6,7,5]=>[8,5,7,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,5,3,2,8]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,3,2,7,4,8]=>[1,2,6,7,4,3,5,8]=>[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,3,2,6,8]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,3,2,8,6]=>[1,2,7,8,6,3,5,4]=>[8,7,2,1,3,6,4,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,8,2,4,3]=>[1,5,8,3,6,2,7,4]=>[8,4,1,6,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,7,2,3,1]=>[1,4,5,7,3,6,2,8]=>[8,5,4,2,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,2,6,1,7]=>[1,3,8,7,2,5,4,6]=>[8,6,1,2,7,4,5,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,5,9,8,6]=>[1,2,3,4,5,7,9,6,8]=>[9,8,7,6,5,3,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,6,4,9,8,7,5]=>[1,2,3,4,6,9,5,7,8]=>[9,8,7,6,4,1,5,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,6,10,9,7]=>[1,2,3,4,5,6,8,10,7,9]=>[10,9,8,7,6,5,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,3,1,6,2,5,8,7]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,7,8,2,6]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,4,8,3,5,6]=>[1,7,5,8,6,3,2,4]=>[8,2,4,1,3,6,7,5]=>[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,5,7,4,2]=>[1,8,2,6,7,4,3,5]=>[8,1,7,3,2,5,6,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,2,3,4,6]=>[1,7,4,8,6,3,5,2]=>[8,2,5,1,3,6,4,7]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,1,4,2,7]=>[1,3,8,7,2,6,4,5]=>[8,6,1,2,7,3,5,4]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,1,6,8,3,7]=>[1,5,6,8,7,3,4,2]=>[8,4,3,1,2,6,5,7]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,9,6,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,5,7,4,9,6,8]=>[1,2,3,4,5,7,9,8,6]=>[9,8,7,6,5,3,1,2,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,5,7,9,4,6,8]=>[1,2,3,4,5,7,6,9,8]=>[9,8,7,6,5,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,3,7,5,8,6,9]=>[1,2,3,4,5,7,8,6,9]=>[9,8,7,6,5,3,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,10,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,7,1,2,5,6,3,8]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,6,2,8,5]=>[1,7,8,5,6,2,3,4]=>[8,2,1,4,3,7,6,5]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,5,6,3,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,6,8,7,2]=>[1,5,6,8,2,4,3,7]=>[8,4,3,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,1,6,3,2]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,5,7,6,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,7,6,1,9]=>[1,2,3,4,5,8,6,7,9]=>[9,8,7,6,5,2,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,9,8,7,2]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,9,7,6]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,8,9,6,7,5]=>[1,2,3,4,5,8,7,6,9]=>[9,8,7,6,5,2,3,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,7,8,5,6,3]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,7,4,2,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,7,4,3,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,5,2,6,3]=>[1,8,3,7,6,2,4,5]=>[8,1,6,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,7,5,4,1]=>[1,8,2,3,6,5,7,4]=>[8,1,7,6,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,7,6,4,1]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,4,3,6,2]=>[1,8,2,5,4,3,7,6]=>[8,1,7,4,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,8,7,3,4]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,1,3,6,5]=>[1,2,8,5,3,7,6,4]=>[8,7,1,4,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,7,6,4,5]=>[1,8,5,7,4,2,3,6]=>[8,1,4,2,5,7,6,3]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,1,6,4,5]=>[1,8,5,2,7,4,3,6]=>[8,1,4,7,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,3,1,4,6]=>[1,7,4,8,6,2,3,5]=>[8,2,5,1,3,7,6,4]=>[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,1,7,4,5]=>[1,6,7,4,3,2,8,5]=>[8,3,2,5,6,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,3,1,4,6]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,7,1,6,4]=>[1,5,7,6,2,3,4,8]=>[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,1,3,5,2]=>[1,8,2,6,3,7,5,4]=>[8,1,7,3,6,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,5,2,8,7]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,5,1,8,7]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,6,5,7,1]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,5,2,7,1]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,6,1,7,5]=>[1,2,4,8,5,6,3,7]=>[8,7,5,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,5,4,7,1]=>[1,2,6,4,8,3,5,7]=>[8,7,3,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,5,3,7,1]=>[1,6,3,4,2,8,5,7]=>[8,3,6,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,5,2,7,1]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,5,3,7,2]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,1,11,10]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,9,7,3,8]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,5,4,6,1,2,8,7]=>[1,3,4,6,2,5,7,8]=>[8,6,5,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,7,8,9,10,11,2]=>[1,3,2,4,5,6,7,8,9,10,11]=>[11,9,10,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,9,11,2,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,10,9,8,7,6,5,4,3,1,2]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,10,8,3,9]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,8,7,6,5,4,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,7,9,6,3,8]=>[1,2,3,4,5,7,6,9,8]=>[9,8,7,6,5,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,3,5,6,1,8,2,4]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,9,6,8,7,4]=>[1,2,3,5,9,4,6,7,8]=>[9,8,7,5,1,6,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,6,7,2,3,5,8,1]=>[1,4,2,6,5,3,7,8]=>[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,7,2,3,1]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,9,8,5,6,7]=>[1,2,3,4,5,9,7,6,8]=>[9,8,7,6,5,1,3,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,9,8,6,7]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,9,6,8,7]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,4,9,8,5,6,7]=>[1,2,3,4,5,9,7,6,8]=>[9,8,7,6,5,1,3,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,2,4,6,8,1,5,3]=>[1,7,5,8,3,4,6,2]=>[8,2,4,1,6,5,3,7]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,1,7,4,5]=>[1,3,2,8,5,4,6,7]=>[8,6,7,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,3,2,7,4]=>[1,8,4,2,5,3,6,7]=>[8,1,5,7,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,2,6,1,4]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,2,3,1,6]=>[1,4,7,2,5,3,8,6]=>[8,5,2,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,3,7,5,1]=>[1,8,2,3,6,7,5,4]=>[8,1,7,6,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,7,4,5,2]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,7,4,5,1]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,7,4,5,2]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,6,2,4,8]=>[1,5,6,2,7,4,3,8]=>[8,4,3,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,3,6,8,1]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,2,5,8,6]=>[1,4,3,2,7,8,6,5]=>[8,5,6,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,2,6,8,5]=>[1,4,3,2,7,8,5,6]=>[8,5,6,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,6,2,8,4]=>[1,5,6,2,7,8,4,3]=>[8,4,3,7,2,1,5,6]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,7,3,1,4]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,3,6,1,7]=>[1,4,2,8,7,3,5,6]=>[8,5,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,2,8,1,6]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,7,8,2,3]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,2,8,5,6]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,8,2,4,7]=>[1,3,5,8,7,4,2,6]=>[8,6,4,1,2,5,7,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,7,4,6,1]=>[1,8,2,5,7,6,4,3]=>[8,1,7,4,2,3,5,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,4,8,2,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,5,2,8,1]=>[1,4,3,6,2,7,8,5]=>[8,5,6,3,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,4,8,6,2]=>[1,2,7,6,8,3,5,4]=>[8,7,2,3,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,6,4,5,1]=>[1,8,2,7,5,6,4,3]=>[8,1,7,2,4,3,5,6]=>[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,7,5,2,6]=>[1,8,6,5,7,2,3,4]=>[8,1,3,4,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,4,8,7,2]=>[1,5,4,6,8,2,3,7]=>[8,4,5,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,7,2,6,1]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,1,5,4,7]=>[1,8,7,4,3,6,5,2]=>[8,1,2,5,6,3,4,7]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,6,2,4,1]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,2,5,8,1]=>[1,7,8,2,4,6,5,3]=>[8,2,1,7,5,3,4,6]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,1,6,2,5]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,4,7,2,6]=>[1,2,5,4,8,6,7,3]=>[8,7,4,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,6,5,7,4]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,1,3,6,5]=>[1,8,5,2,4,7,6,3]=>[8,1,4,7,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,6,5,8,1]=>[1,4,3,2,7,8,5,6]=>[8,5,6,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,4,7,1,5]=>[1,3,2,8,5,4,6,7]=>[8,6,7,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,6,2,4,3]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,4,8,3,2]=>[1,6,8,2,5,4,7,3]=>[8,3,1,7,4,5,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,1,4,8,2]=>[1,7,8,2,6,4,5,3]=>[8,2,1,7,3,5,4,6]=>[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,7,2,3,8]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,7,4,5,2]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,4,8,3,5]=>[1,7,3,2,4,6,8,5]=>[8,2,6,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,4,6,2,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,4,5,3,2]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,7,5,3,2]=>[1,8,2,3,6,5,7,4]=>[8,1,7,6,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,6,3,2,4]=>[1,5,6,3,2,7,4,8]=>[8,4,3,6,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,2,7,8,5]=>[1,4,2,3,6,7,8,5]=>[8,5,7,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,1,3,5,8,4]=>[1,7,8,4,2,3,6,5]=>[8,2,1,5,7,6,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,1,5,8,3,4]=>[1,6,8,4,2,3,7,5]=>[8,3,1,5,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,5,7,4,3]=>[1,8,3,6,7,4,2,5]=>[8,1,6,3,2,5,7,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,3,6,8,4]=>[1,2,7,8,4,5,3,6]=>[8,7,2,1,5,4,6,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,4,2,5,1]=>[1,6,2,8,3,7,5,4]=>[8,3,7,1,6,2,4,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,4,2,1,8]=>[1,5,4,6,2,7,3,8]=>[8,4,5,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,4,1,8,2]=>[1,5,4,6,2,7,8,3]=>[8,4,5,3,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,4,1,8,2]=>[1,3,5,4,6,2,7,8]=>[8,6,4,5,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,3,4,6,1]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,5,1,7,8,9]=>[1,2,3,6,4,5,7,8,9]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,6,4,1,5,3,7,8,9]=>[1,2,6,3,4,5,7,8,9]=>[9,8,4,7,6,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,6,4,5,1,7,8,9,10]=>[1,2,3,6,4,5,7,8,9,10]=>[10,9,8,5,7,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,2,3,5,8,1,4]=>[1,6,8,4,3,2,7,5]=>[8,3,1,5,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,5,4,6,7]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,8,2,4,1,7]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,3,2,4,5]=>[1,2,7,4,6,3,8,5]=>[8,7,2,5,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,5,1,8,6]=>[1,3,4,2,7,8,6,5]=>[8,6,5,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,2,1,3,8]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,5,4,3,1]=>[1,7,3,2,8,4,6,5]=>[8,2,6,7,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,4,2,1,6]=>[1,5,4,8,6,2,3,7]=>[8,4,5,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,8,1,5,4,2]=>[1,7,4,8,2,3,6,5]=>[8,2,5,1,7,6,3,4]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,4,6,2,7]=>[1,8,7,2,3,5,4,6]=>[8,1,2,7,6,4,5,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,8,5,6,3]=>[1,2,7,6,5,8,3,4]=>[8,7,2,3,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,7,4,6,1]=>[1,5,7,6,4,3,2,8]=>[8,4,2,3,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,5,4,6,1]=>[1,7,6,4,3,2,8,5]=>[8,2,3,5,6,7,1,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,2,6,5,7]=>[1,8,7,5,2,4,3,6]=>[8,1,2,4,7,5,6,3]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,5,4,6,1]=>[1,8,2,7,6,4,3,5]=>[8,1,7,2,3,5,6,4]=>[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,1,8,5,6,4]=>[1,2,7,6,5,8,4,3]=>[8,7,2,3,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,1,6,7,4]=>[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,7,6,4,2]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,7,1,6,2]=>[1,8,2,3,5,7,6,4]=>[8,1,7,6,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,7,8,2,3]=>[1,6,8,3,2,4,5,7]=>[8,3,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,2,5,3,6]=>[1,4,2,8,6,5,3,7]=>[8,5,7,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,1,4,3,5]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,3,8,2,4,5]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,4,2,3,5]=>[1,7,3,8,5,4,6,2]=>[8,2,6,1,4,5,3,7]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,5,8,2,6,7]=>[1,4,5,8,7,6,2,3]=>[8,5,4,1,2,3,7,6]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,4,6,3,2]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,8,3,5,2]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,6,5,3,4]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,4,2,3,8]=>[1,5,4,6,2,7,3,8]=>[8,4,5,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,5,1,6,3]=>[1,4,7,6,2,8,3,5]=>[8,5,2,3,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,1,4,2,6,7]=>[1,3,5,4,2,8,7,6]=>[8,6,4,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,5,3,8,4]=>[1,2,7,8,4,3,6,5]=>[8,7,2,1,5,6,3,4]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,4,3,8,6]=>[1,2,7,8,6,3,5,4]=>[8,7,2,1,3,6,4,5]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,4,3,6,7]=>[1,2,8,7,6,3,5,4]=>[8,7,1,2,3,6,4,5]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,7,4,6,9,8]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,6,3,5,4,8,2,1]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,10,4,5,6,7,8,9,3,2]=>[1,2,10,3,4,5,6,7,8,9]=>[10,9,1,8,7,6,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,1,2,5,7,6,8,4]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,2,6,8,4]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,5,1,6,8]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,3,5,1,7]=>[1,8,7,2,6,5,3,4]=>[8,1,2,7,3,4,6,5]=>[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,7,3,5,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,8,4,5,1,3]=>[1,7,2,6,5,4,8,3]=>[8,2,7,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,7,3,2,4]=>[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,6,3,5,2]=>[1,2,4,7,5,6,3,8]=>[8,7,5,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,5,6,9,8]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,7,6,1,8,4,5]=>[1,2,3,7,4,6,8,5]=>[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,1,3,7,6]=>[1,5,2,8,6,3,4,7]=>[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,2,3,1,8]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,3,8,7,1,4]=>[1,6,7,2,3,5,8,4]=>[8,3,2,7,6,4,1,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,8,7,1,2]=>[1,6,7,2,4,3,5,8]=>[8,3,2,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,2,3,1,6]=>[1,8,6,3,7,2,4,5]=>[8,1,3,6,2,7,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,5,3,1,6]=>[1,8,6,3,7,2,4,5]=>[8,1,3,6,2,7,5,4]=>[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,5,3,1,6]=>[1,8,6,3,4,7,2,5]=>[8,1,3,6,5,2,7,4]=>[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,3,8,7,1,2]=>[1,4,3,5,8,2,6,7]=>[8,5,6,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,5,3,1,2]=>[1,6,3,7,2,8,4,5]=>[8,3,6,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,5,3,1,6]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,7,2,1,3]=>[1,6,2,5,7,3,8,4]=>[8,3,7,4,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,5,7,1,3]=>[1,4,2,8,3,6,7,5]=>[8,5,7,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,5,7,3,4]=>[1,8,4,2,3,6,7,5]=>[8,1,5,7,6,3,2,4]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,4,7,3,5]=>[1,6,7,3,2,8,5,4]=>[8,3,2,6,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,2,7,4,6]=>[1,8,6,7,4,3,5,2]=>[8,1,3,2,5,6,4,7]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,5,6,8,9,3]=>[1,2,3,7,8,9,4,5,6]=>[9,8,7,3,2,1,6,5,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,7,8,5,6,9]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,8,9,5,6,7]=>[1,2,3,4,5,8,6,9,7]=>[9,8,7,6,5,2,4,1,3]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,5,1,3,8,7,2,6]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,6,1,8,3,5]=>[1,2,4,6,8,5,3,7]=>[8,7,5,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,9,3,4,5,6]=>[1,2,3,7,4,8,5,9,6]=>[9,8,7,3,6,2,5,1,4]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,4,5,8,6,3,2,1]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,8,5,7,4]=>[1,2,6,5,8,4,3,7]=>[8,7,3,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,6,8,2,5]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,7,3,4,5]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,5,7,4,3,2]=>[1,2,6,4,5,7,3,8]=>[8,7,3,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,4,7,6,5]=>[1,3,2,8,5,4,6,7]=>[8,6,7,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,3,6,8,2]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,4,6,5,7]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,6,2,5,7]=>[1,3,8,7,5,6,2,4]=>[8,6,1,2,4,3,7,5]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,3,5,8,1,6]=>[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,4,5,6,2,7]=>[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,8,6,3,5]=>[1,7,3,4,2,5,8,6]=>[8,2,6,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,4,8,1,6,5]=>[1,2,3,7,6,4,5,8]=>[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,5,1,7,2]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,4,5,1]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,1,6,8,3]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,7,3,5,1]=>[1,8,2,4,6,3,5,7]=>[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,6,3,4,1]=>[1,2,8,3,5,6,4,7]=>[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,3,1,4,8]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,3,1,7,5]=>[1,8,5,3,4,6,2,7]=>[8,1,4,6,5,3,7,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,6,8,9,4,7]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,2,4,8,7,3,1]=>[1,5,8,2,6,7,3,4]=>[8,4,1,7,3,2,6,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,3,7,4,1]=>[1,8,2,5,3,6,7,4]=>[8,1,7,4,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,5,6,2,3]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,9,1,3,4,2]=>[1,5,9,2,6,3,7,4,8]=>[9,5,1,8,4,7,3,6,2]=>[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,9,1,3,4,5,2]=>[1,6,3,8,5,2,7,4,9]=>[9,4,7,2,5,8,3,6,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,9,1,4,5,3,2]=>[1,6,4,9,2,7,5,3,8]=>[9,4,6,1,8,3,5,7,2]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,7,8,9,10,1,3,4,2]=>[1,5,9,4,8,3,7,2,6,10]=>[10,6,2,7,3,8,4,9,5,1]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,3,1,2,5,4,7,6]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,7,4,2,6]=>[1,8,6,4,3,5,7,2]=>[8,1,3,5,6,4,2,7]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,8,3,5,4]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,6,7,3,5]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,5,7,3,4]=>[1,8,4,6,7,3,2,5]=>[8,1,5,3,2,6,7,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,5,8,3,4]=>[1,7,3,2,4,6,8,5]=>[8,2,6,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,5,6,2,1]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,2,6,8,4]=>[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,1,6,8,4]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,3,4,8,5]=>[1,6,4,2,7,8,5,3]=>[8,3,5,7,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,9,6,8,1]=>[1,2,3,4,5,7,6,9,8]=>[9,8,7,6,5,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,5,6,8,4,7,1]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,3,6,7,1]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,6,2,5,7]=>[1,8,7,5,6,2,3,4]=>[8,1,2,4,3,7,6,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,6,4,3,2]=>[1,8,2,3,5,6,4,7]=>[8,1,7,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,6,7,2,1]=>[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,6,7,2,1]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,5,6,4,1]=>[1,3,7,4,8,2,5,6]=>[8,6,2,5,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,5,6,2,1]=>[1,4,8,2,7,3,5,6]=>[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,5,6,3,2]=>[1,7,3,4,8,2,5,6]=>[8,2,6,5,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,6,4,5,2]=>[1,2,7,5,6,4,8,3]=>[8,7,2,4,3,5,1,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,6,7,5,1]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,7,4,5,2]=>[1,2,6,4,8,3,5,7]=>[8,7,3,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,7,6,2,3]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,8,4,6,7]=>[1,5,8,7,6,4,3,2]=>[8,4,1,2,3,5,6,7]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,8,2,6,7]=>[1,2,4,5,8,7,6,3]=>[8,7,5,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,6,4,5,7]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,5,8,2,7]=>[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,3,8,2,4,7]=>[1,6,2,5,8,7,4,3]=>[8,3,7,4,1,2,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,6,2,5,7]=>[1,2,4,8,7,5,6,3]=>[8,7,5,1,2,4,3,6]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,6,2,5,7]=>[1,4,8,7,5,6,2,3]=>[8,5,1,2,4,3,7,6]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,6,3,8,2]=>[1,7,8,2,3,5,6,4]=>[8,2,1,7,6,4,3,5]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,1,8,4,2]=>[1,3,6,8,2,5,4,7]=>[8,6,3,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,8,6,7,1]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,4,8,5,2]=>[1,3,6,8,2,7,5,4]=>[8,6,3,1,7,2,4,5]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,6,1,5,4]=>[1,2,7,5,6,3,8,4]=>[8,7,2,4,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,6,2,5,4]=>[1,2,7,5,6,3,8,4]=>[8,7,2,4,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,5,8,1,6,2]=>[1,7,6,2,4,5,8,3]=>[8,2,3,7,5,4,1,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,1,8,5,2]=>[1,7,5,2,3,6,8,4]=>[8,2,4,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,6,1,5,2]=>[1,7,5,6,2,8,3,4]=>[8,2,4,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,3,8,5,2]=>[1,7,5,3,6,8,2,4]=>[8,2,4,6,3,1,7,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,1,5,2,6]=>[1,8,6,5,2,7,3,4]=>[8,1,3,4,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,3,8,5,1]=>[1,7,5,3,6,8,2,4]=>[8,2,4,6,3,1,7,5]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,3,8,2,6]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,7,3,2,6]=>[1,4,2,5,7,3,8,6]=>[8,5,7,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,9,7]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,7,8,9,6]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,6,3,1,4,7,8,5]=>[1,2,6,7,8,5,4,3]=>[8,7,3,2,1,4,5,6]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,9,10,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,7,3,4,1,8,5,6]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,7,8,9,10,6]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,1,5,6,7,8,9,10,4]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,6,4,5,1,3,7,2]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,3,6,1,2]=>[1,7,2,4,5,3,8,6]=>[8,2,7,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,7,1,2,6]=>[1,4,8,6,2,5,7,3]=>[8,5,1,3,7,4,2,6]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,6,1,2,3]=>[1,8,3,4,7,2,5,6]=>[8,1,6,5,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,4,3,1,6]=>[1,7,2,5,4,3,8,6]=>[8,2,7,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,4,1,7,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,4,1,8,3,7]=>[1,6,8,7,3,2,5,4]=>[8,3,1,2,6,7,4,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,1,3,8,6]=>[1,5,2,7,8,6,3,4]=>[8,4,7,2,1,3,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,4,1,8,3,7]=>[1,6,8,7,3,5,2,4]=>[8,3,1,2,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,5,8,1,7]=>[1,4,3,6,8,7,2,5]=>[8,5,6,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,8,5,10,7,1,9]=>[1,4,3,6,5,8,7,10,9,2]=>[10,7,8,5,6,3,4,1,2,9]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,4,2,6,8,5,3,1]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,6,3,1,7]=>[1,8,7,2,5,6,3,4]=>[8,1,2,7,4,3,6,5]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,8,5,6,3]=>[1,7,6,5,8,3,2,4]=>[8,2,3,4,1,6,7,5]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,5,2,3,7]=>[1,6,2,4,8,7,3,5]=>[8,3,7,5,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,3,5,2,7]=>[1,8,7,2,4,6,5,3]=>[8,1,2,7,5,3,4,6]=>[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,5,7,4,1]=>[1,8,2,6,7,4,3,5]=>[8,1,7,3,2,5,6,4]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,7,3,4,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,4,6,3]=>[1,8,3,2,5,7,6,4]=>[8,1,6,7,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,4,8,2,3]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,2,1,4,8]=>[1,5,2,7,4,6,3,8]=>[8,4,7,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,9,7,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,4,5,6,9,7,8]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,5,7,3,6,8,2]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,6,8,2,3]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,7,4,5,2]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,10,5,6,7,8,9,2,1]=>[1,4,5,6,7,8,9,2,3,10]=>[10,7,6,5,4,3,2,9,8,1]=>[10,9,7,6,5,4,3,8,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,7,1,3,5,6,8,2]=>[1,4,3,2,7,8,5,6]=>[8,5,6,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,6,4,1,8]=>[1,5,6,4,7,2,3,8]=>[8,4,3,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,1,8,6,4]=>[1,5,2,7,6,8,4,3]=>[8,4,7,2,3,1,5,6]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,2,1,8,4]=>[1,5,2,7,8,4,3,6]=>[8,4,7,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,4,1,8,6]=>[1,3,7,8,6,2,4,5]=>[8,6,2,1,3,7,5,4]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,4,2,6,8]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,1,8,6,2]=>[1,5,2,3,7,6,8,4]=>[8,4,7,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,8,3,2,4]=>[1,7,2,5,8,4,6,3]=>[8,2,7,4,1,5,3,6]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,2,4,8,6]=>[1,7,8,6,4,3,5,2]=>[8,2,1,3,5,6,4,7]=>[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,2,1,5,4]=>[1,6,2,8,4,3,7,5]=>[8,3,7,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,2,4,1,5]=>[1,3,8,5,2,6,4,7]=>[8,6,1,4,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,2,1,8,4]=>[1,5,2,7,8,4,6,3]=>[8,4,7,2,1,5,3,6]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,4,8,1,7]=>[1,3,5,4,2,6,8,7]=>[8,6,4,5,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,2,4,7,5]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,6,4,2,3]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,5,4,3,7]=>[1,6,4,2,8,7,3,5]=>[8,3,5,7,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,5,8,4,7]=>[1,6,8,7,4,2,3,5]=>[8,3,1,2,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,7,8,4,1]=>[1,6,8,2,3,5,7,4]=>[8,3,1,7,6,4,2,5]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,5,1,8,2]=>[1,3,6,2,4,7,8,5]=>[8,6,3,7,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,5,6,8,3]=>[1,7,8,3,2,4,5,6]=>[8,2,1,6,7,5,4,3]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,7,1,5,3]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,7,1,4,2]=>[1,6,2,5,7,4,3,8]=>[8,3,7,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,10,6,7,8,9,1,5]=>[1,2,3,4,10,5,6,7,8,9]=>[10,9,8,7,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,10,5,6,7,8,9,1,4]=>[1,2,3,10,4,5,6,7,8,9]=>[10,9,8,1,7,6,5,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,5,2,4,7,6,8,3]=>[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,7,6,9,8,3]=>[1,2,3,5,7,9,4,6,8]=>[9,8,7,5,3,1,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,2,6,5,8,7,10,9,3]=>[1,2,4,6,8,10,3,5,7,9]=>[10,9,7,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,5,4,7,1,8,3,6]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,3,8,2,6]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,3,5,4,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,6,3,5,7]=>[1,8,7,5,6,3,2,4]=>[8,1,2,4,3,6,7,5]=>[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,5,6,1,2]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,7,4,5,2]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,3,7,1,8,4]=>[1,2,6,3,5,7,8,4]=>[8,7,3,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,3,6,4,8,2]=>[1,5,6,4,3,2,7,8]=>[8,4,3,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,1,7,3,6]=>[1,8,6,7,3,5,2,4]=>[8,1,3,2,6,4,7,5]=>[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,4,2,3,5]=>[1,8,5,4,6,2,3,7]=>[8,1,4,5,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,7,4,5,2]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,2,8,6,1]=>[1,5,2,7,6,8,3,4]=>[8,4,7,2,3,1,6,5]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,2,7,6,1]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,2,4,7,1]=>[1,3,6,4,8,2,5,7]=>[8,6,3,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,6,8,5,1]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,3,2,5,1]=>[1,6,2,4,7,5,3,8]=>[8,3,7,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,7,4,3,1]=>[1,5,7,3,2,6,4,8]=>[8,4,2,6,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,7,4,5,1]=>[1,6,4,3,8,2,5,7]=>[8,3,5,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,4,2,8,1]=>[1,3,5,4,6,2,7,8]=>[8,6,4,5,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,6,1,4,7]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,5,6,2,7]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,2,3,6,1]=>[1,4,7,6,3,8,2,5]=>[8,5,2,3,6,1,7,4]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,4,2,5,3]=>[1,7,5,4,2,8,3,6]=>[8,2,4,5,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,2,7,1,4]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,6,4,2,7,8]=>[1,5,4,6,2,3,7,8]=>[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,6,7,2,5]=>[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,2,6,3,4]=>[1,7,3,5,2,8,4,6]=>[8,2,6,4,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,8,7,3,2]=>[1,6,7,3,5,8,2,4]=>[8,3,2,6,4,1,7,5]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,7,3,5,4]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,3,4,5,6,2,8,7,1]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,2,5,6,7,8,4,1]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,6,1,4,3,5,2]=>[1,7,5,4,2,8,3,6]=>[8,2,4,5,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,5,7,1,8]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,7,3,4,8,2]=>[1,2,6,4,7,8,3,5]=>[8,7,3,5,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,5,9,6,7]=>[1,2,3,4,5,8,6,7,9]=>[9,8,7,6,5,2,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,8,6,5,7,9]=>[1,2,3,4,5,8,7,6,9]=>[9,8,7,6,5,2,3,4,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,6,5,1,7,4,3]=>[1,8,3,6,7,4,5,2]=>[8,1,6,3,2,5,4,7]=>[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,2,5,8,3]=>[1,7,8,3,4,2,6,5]=>[8,2,1,6,5,7,3,4]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,3,2,4,8]=>[1,5,3,7,4,2,6,8]=>[8,4,6,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,9,3,5,6,7,8]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,7,6,8,2,5,4,3]=>[1,2,7,4,8,3,6,5]=>[8,7,2,5,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,1,8,2,3]=>[1,4,7,2,6,8,3,5]=>[8,5,2,7,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,8,4,2,1]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,8,5,3,1]=>[1,7,3,6,5,8,2,4]=>[8,2,6,3,4,1,7,5]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,2,5,8,7]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,2,3,8,4]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,6,2,5,8]=>[1,2,4,7,5,6,3,8]=>[8,7,5,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,6,8,5,2]=>[1,2,3,7,5,6,8,4]=>[8,7,6,2,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,6,8,1,5,2]=>[1,3,4,6,2,7,5,8]=>[8,6,5,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,7,6,2,5]=>[1,4,2,8,5,7,3,6]=>[8,5,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,5,3,4,1,8]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,7,5,6,8,3]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,8,3,5,1,6]=>[1,7,2,3,4,8,6,5]=>[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,3,8,7,2]=>[1,5,3,2,6,8,4,7]=>[8,4,6,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,4,3,1,7,2]=>[1,5,3,6,2,8,4,7]=>[8,4,6,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
Map
Demazure product with inverse
Description
This map sends a permutation π to π−1⋆π where ⋆ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
searching the database
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