Identifier
Mp00223:
Permutations
—runsort⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00064: Permutations —reverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Images
=>
Cc0005;cc-rep-4
[1]=>[1]=>[1]=>[1]=>[1,0]
[1,2]=>[1,2]=>[2,1]=>[2,1]=>[1,1,0,0]
[2,1]=>[1,2]=>[2,1]=>[2,1]=>[1,1,0,0]
[1,2,3]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0]
[1,3,2]=>[1,3,2]=>[2,3,1]=>[3,1,2]=>[1,1,1,0,0,0]
[2,1,3]=>[1,3,2]=>[2,3,1]=>[3,1,2]=>[1,1,1,0,0,0]
[2,3,1]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0]
[3,1,2]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0]
[3,2,1]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0]
[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[1,2,4,3]=>[1,2,4,3]=>[3,4,2,1]=>[4,3,1,2]=>[1,1,1,1,0,0,0,0]
[1,3,2,4]=>[1,3,2,4]=>[4,2,3,1]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[1,3,4,2]=>[1,3,4,2]=>[2,4,3,1]=>[4,1,3,2]=>[1,1,1,1,0,0,0,0]
[1,4,2,3]=>[1,4,2,3]=>[3,2,4,1]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[1,4,3,2]=>[1,4,2,3]=>[3,2,4,1]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[2,1,3,4]=>[1,3,4,2]=>[2,4,3,1]=>[4,1,3,2]=>[1,1,1,1,0,0,0,0]
[2,1,4,3]=>[1,4,2,3]=>[3,2,4,1]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[2,3,1,4]=>[1,4,2,3]=>[3,2,4,1]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[2,3,4,1]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[2,4,1,3]=>[1,3,2,4]=>[4,2,3,1]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[2,4,3,1]=>[1,2,4,3]=>[3,4,2,1]=>[4,3,1,2]=>[1,1,1,1,0,0,0,0]
[3,1,2,4]=>[1,2,4,3]=>[3,4,2,1]=>[4,3,1,2]=>[1,1,1,1,0,0,0,0]
[3,1,4,2]=>[1,4,2,3]=>[3,2,4,1]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[3,2,1,4]=>[1,4,2,3]=>[3,2,4,1]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[3,2,4,1]=>[1,2,4,3]=>[3,4,2,1]=>[4,3,1,2]=>[1,1,1,1,0,0,0,0]
[3,4,1,2]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[3,4,2,1]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[4,1,2,3]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[4,1,3,2]=>[1,3,2,4]=>[4,2,3,1]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[4,2,1,3]=>[1,3,2,4]=>[4,2,3,1]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[4,2,3,1]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[4,3,1,2]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[4,3,2,1]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[1,2,3,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,3,5,4]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,4,3,5]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,4,5,3]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,5,3,4]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,5,4,3]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,2,4,5]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,2,5,4]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[5,3,4,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,4,2,5]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,4,5,2]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[5,1,4,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,5,2,4]=>[1,3,5,2,4]=>[4,2,5,3,1]=>[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[1,3,5,4,2]=>[1,3,5,2,4]=>[4,2,5,3,1]=>[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,2,3,5]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,2,5,3]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,3,2,5]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,3,5,2]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,5,2,3]=>[1,4,5,2,3]=>[3,2,5,4,1]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[1,4,5,3,2]=>[1,4,5,2,3]=>[3,2,5,4,1]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,2,3,4]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,2,4,3]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,3,2,4]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,3,4,2]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,4,2,3]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,5,4,3,2]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,3,4,5]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[5,1,4,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,3,5,4]=>[1,3,5,2,4]=>[4,2,5,3,1]=>[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,4,3,5]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,4,5,3]=>[1,4,5,2,3]=>[3,2,5,4,1]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,5,3,4]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[2,1,5,4,3]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,1,4,5]=>[1,4,5,2,3]=>[3,2,5,4,1]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,1,5,4]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,4,1,5]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,4,5,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,5,1,4]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,3,5,4,1]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,1,3,5]=>[1,3,5,2,4]=>[4,2,5,3,1]=>[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,1,5,3]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,3,1,5]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,3,5,1]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,5,1,3]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,4,5,3,1]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,1,3,4]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,1,4,3]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,3,1,4]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,3,4,1]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,4,1,3]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[5,3,4,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[2,5,4,3,1]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,2,4,5]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,2,5,4]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,4,2,5]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,4,5,2]=>[1,4,5,2,3]=>[3,2,5,4,1]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,5,2,4]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[3,1,5,4,2]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,1,4,5]=>[1,4,5,2,3]=>[3,2,5,4,1]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,1,5,4]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,4,1,5]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,4,5,1]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,5,1,4]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]
[3,2,5,4,1]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,1,2,5]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,1,5,2]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,2,1,5]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,2,5,1]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,5,1,2]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,4,5,2,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,1,2,4]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,1,4,2]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,2,1,4]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,2,4,1]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,4,1,2]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[3,5,4,2,1]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,2,3,5]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,2,5,3]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,3,2,5]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[5,3,4,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,3,5,2]=>[1,3,5,2,4]=>[4,2,5,3,1]=>[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,5,2,3]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[4,1,5,3,2]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,1,3,5]=>[1,3,5,2,4]=>[4,2,5,3,1]=>[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,1,5,3]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,3,1,5]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,3,5,1]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,5,1,3]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[5,3,4,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[4,2,5,3,1]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,1,2,5]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,1,5,2]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,2,1,5]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,2,5,1]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,5,1,2]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[4,3,5,2,1]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,1,2,3]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,1,3,2]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,2,1,3]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,2,3,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,3,1,2]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[4,5,3,2,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,2,3,4]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,2,4,3]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,3,2,4]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,3,4,2]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,4,2,3]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,4,3,2]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,1,3,4]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,1,4,3]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,3,1,4]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,3,4,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,4,1,3]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,4,3,1]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,1,2,4]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,1,4,2]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,2,1,4]=>[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,2,4,1]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,4,1,2]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,4,2,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,1,2,3]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,1,3,2]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,2,1,3]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,2,3,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,3,1,2]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,3,2,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,5,6,4]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,5,3,6]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,5,6,3]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,6,3,5]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,6,5,3]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,3,6,4]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,4,3,6]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,4,6,3]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,6,3,4]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,6,4,3]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,3,5,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,4,3,5]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,4,5,3]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,5,3,4]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,5,6,4]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[6,4,5,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,2,5,6]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,2,6,5]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[6,3,5,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,5,2,6]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,5,6,2]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[6,1,5,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,6,2,5]=>[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,4,6,5,2]=>[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,2,4,6]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,2,6,4]=>[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,4,2,6]=>[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,4,6,2]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,6,2,4]=>[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,6,4,2]=>[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,2,4,5]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,2,5,4]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,4,2,5]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,4,5,2]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,5,2,4]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,5,4,2]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,5,3,6]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,5,6,3]=>[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,6,3,5]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,6,5,3]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,2,5,6]=>[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,2,6,5]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,5,2,6]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,5,6,2]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,6,2,5]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,6,5,2]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,2,3,6]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,2,6,3]=>[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,3,2,6]=>[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,3,6,2]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,6,2,3]=>[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,5,6,3,2]=>[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,2,3,5]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,2,5,3]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,3,2,5]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,3,5,2]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,5,2,3]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,5,3,2]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,3,6,4]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,4,3,6]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,4,6,3]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,6,3,4]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,6,4,3]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,2,4,6]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,2,6,4]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,4,2,6]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,4,6,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,6,2,4]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,3,6,4,2]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,2,3,6]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,2,6,3]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,3,6,2]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,6,2,3]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,6,3,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,2,3,4]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,2,4,3]=>[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,3,2,4]=>[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,3,4,2]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,4,2,3]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,6,4,3,2]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,3,5,4]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,4,3,5]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,4,5,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,5,3,4]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,5,4,3]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,2,4,5]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,2,5,4]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,4,2,5]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,5,2,4]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,2,3,5]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,2,5,3]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,3,2,5]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,5,2,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,5,3,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,2,3,4]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,2,4,3]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,3,2,4]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,3,4,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,4,2,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,4,5,6]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[6,1,5,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,4,6,5]=>[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,5,4,6]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,5,6,4]=>[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,6,4,5]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,6,5,4]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,5,6]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,6,5]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,5,3,6]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,5,6,3]=>[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,6,3,5]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,6,5,3]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,3,4,6]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,3,6,4]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,4,3,6]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,4,6,3]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,6,3,4]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,5,6,4,3]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,3,4,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,3,5,4]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,4,3,5]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,4,5,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,5,3,4]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,4,5,6]=>[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,4,6,5]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,5,4,6]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,5,6,4]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,6,4,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,6,5,4]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,1,5,6]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,1,6,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,1,6]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,6,1,5]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,6,5,1]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,1,4,6]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,1,6,4]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,4,1,6]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,4,6,1]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,6,1,4]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,5,6,4,1]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,1,4,5]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,1,5,4]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,4,1,5]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,4,5,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,5,1,4]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,5,4,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,3,5,6]=>[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,3,6,5]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,5,3,6]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,5,6,3]=>[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,6,3,5]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,6,5,3]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,1,5,6]=>[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,1,6,5]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,5,1,6]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,5,6,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,6,1,5]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,6,5,1]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,1,3,6]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,1,6,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,3,1,6]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,3,6,1]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,6,1,3]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,5,6,3,1]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,1,3,5]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,1,5,3]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,3,1,5]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,3,5,1]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,5,1,3]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,6,5,3,1]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,3,4,6]=>[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,3,6,4]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,4,3,6]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,4,6,3]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,6,3,4]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,1,6,4,3]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,1,4,6]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,1,6,4]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,4,1,6]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,4,6,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,6,1,4]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,6,4,1]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,1,3,6]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,1,6,3]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,3,1,6]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,3,6,1]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,6,1,3]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,6,3,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,1,3,4]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,1,4,3]=>[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,3,1,4]=>[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,3,4,1]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,4,1,3]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[6,4,5,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,6,4,3,1]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,3,4,5]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,3,5,4]=>[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,4,3,5]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,4,5,3]=>[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,5,3,4]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,5,4,3]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,1,4,5]=>[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,1,5,4]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,4,1,5]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,4,5,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,5,1,4]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,3,5,4,1]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,1,3,5]=>[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,1,5,3]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,3,1,5]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,3,5,1]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,5,1,3]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,4,5,3,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,1,3,4]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[6,3,5,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,1,4,3]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,3,1,4]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,3,4,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,4,1,3]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,4,3,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,4,5,6]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,4,6,5]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,5,4,6]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,5,6,4]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,6,4,5]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,6,5,4]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,2,5,6]=>[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,2,6,5]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,5,2,6]=>[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,5,6,2]=>[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,6,2,5]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,6,5,2]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,2,4,6]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,2,6,4]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,4,2,6]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,4,6,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,6,2,4]=>[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,5,6,4,2]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,2,4,5]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,2,5,4]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,4,2,5]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,4,5,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,5,2,4]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,5,4,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,4,5,6]=>[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,4,6,5]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,5,4,6]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,5,6,4]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,6,4,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,1,5,6]=>[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,1,6,5]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,5,1,6]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,5,6,1]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,6,1,5]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,4,6,5,1]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,1,4,6]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,1,6,4]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,4,1,6]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,4,6,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,6,1,4]=>[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,5,6,4,1]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,1,4,5]=>[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,1,5,4]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,4,1,5]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,4,5,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,5,1,4]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,5,4,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,2,5,6]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,2,6,5]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,5,2,6]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,5,6,2]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,6,2,5]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,6,5,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,1,5,6]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,1,6,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,5,1,6]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,5,6,1]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,6,1,5]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,6,5,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,1,2,6]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,1,6,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,2,1,6]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,2,6,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,6,1,2]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,6,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,1,2,5]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,1,5,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,2,1,5]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,2,5,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,5,1,2]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,5,2,1]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,2,4,6]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,2,6,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,4,2,6]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,4,6,2]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,6,2,4]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,6,4,2]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,1,4,6]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,1,6,4]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,4,1,6]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,4,6,1]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,6,1,4]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,6,4,1]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,1,2,6]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,1,6,2]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,2,1,6]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,2,6,1]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,6,1,2]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,6,2,1]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,1,2,4]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,1,4,2]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,2,1,4]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,2,4,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,4,1,2]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,6,4,2,1]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,2,4,5]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,2,5,4]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,4,2,5]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,4,5,2]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,5,2,4]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,1,4,5]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,1,5,4]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,4,1,5]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,4,5,1]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,5,1,4]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,5,4,1]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,1,2,5]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,1,5,2]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,2,1,5]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,2,5,1]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,5,1,2]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,4,5,2,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,1,2,4]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,1,4,2]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,2,1,4]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,2,4,1]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,4,1,2]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,4,2,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,3,5,6]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,3,6,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,5,3,6]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,5,6,3]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,6,3,5]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,6,5,3]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,5,6]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[6,4,5,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,6,5]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,5,2,6]=>[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,5,6,2]=>[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,6,2,5]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,6,5,2]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,2,3,6]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,2,6,3]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,3,2,6]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,3,6,2]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,6,2,3]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,6,3,2]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,2,3,5]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,2,5,3]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,3,2,5]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,3,5,2]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,5,2,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,5,3,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,3,5,6]=>[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,3,6,5]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,5,3,6]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,5,6,3]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,6,3,5]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,6,5,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,1,5,6]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,1,6,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,5,1,6]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,5,6,1]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,6,1,5]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,6,5,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,1,3,6]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,1,6,3]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,3,1,6]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,3,6,1]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,6,1,3]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[6,4,5,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,6,3,1]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,1,3,5]=>[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,3,1,5]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,3,5,1]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,5,1,3]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,5,3,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,2,5,6]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,2,6,5]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,5,2,6]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,5,6,2]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,6,2,5]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,1,6,5,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,5,1,6]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,5,6,1]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,6,1,5]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,6,5,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,1,2,6]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,1,6,2]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,2,1,6]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,2,6,1]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,6,1,2]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,5,6,2,1]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,1,2,5]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,1,5,2]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,2,1,5]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,2,5,1]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,5,1,2]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,5,2,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,2,3,6]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,2,6,3]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,3,2,6]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,3,6,2]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,6,2,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,1,6,3,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,1,3,6]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,1,6,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,3,1,6]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,3,6,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,6,1,3]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,2,6,3,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,1,2,6]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,1,6,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,2,1,6]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,2,6,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,6,1,2]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,3,6,2,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,1,2,3]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,1,3,2]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,2,1,3]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,2,3,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,3,1,2]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,3,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,2,3,5]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,2,5,3]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,3,2,5]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,3,5,2]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,5,2,3]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,5,3,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,1,3,5]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,1,5,3]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,3,1,5]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,3,5,1]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,5,1,3]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,2,5,3,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,1,2,5]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,2,1,5]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,2,5,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,5,1,2]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,3,5,2,1]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,1,2,3]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,2,1,3]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,2,3,1]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,3,1,2]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,5,3,2,1]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,3,4,6]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,3,6,4]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,4,3,6]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,4,6,3]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,6,3,4]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,2,6,4,3]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,2,4,6]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,2,6,4]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,4,2,6]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[6,3,5,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,4,6,2]=>[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,6,2,4]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,3,6,4,2]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,2,3,6]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,2,6,3]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,3,2,6]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,3,6,2]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,6,2,3]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,6,3,2]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,2,3,4]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,2,4,3]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,3,2,4]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,3,4,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,4,2,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,6,4,3,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,3,4,6]=>[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,3,6,4]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,4,3,6]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,4,6,3]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,6,3,4]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,6,4,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,1,4,6]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,1,6,4]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,4,6,1]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,6,1,4]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,6,4,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,1,3,6]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,1,6,3]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,3,6,1]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,6,1,3]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,6,3,1]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,1,3,4]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[6,3,5,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,1,4,3]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,3,1,4]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,3,4,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,4,3,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,2,4,6]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,2,6,4]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,4,2,6]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,4,6,2]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,6,2,4]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,1,6,4,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,1,4,6]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,1,6,4]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,4,6,1]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,6,4,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,1,2,6]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,1,6,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,2,1,6]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,2,6,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,6,1,2]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,4,6,2,1]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,1,2,4]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,1,4,2]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,2,1,4]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,2,4,1]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,4,1,2]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,6,4,2,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,2,3,6]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,2,6,3]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,3,2,6]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,3,6,2]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,6,2,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,6,3,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,1,3,6]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,1,6,3]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,3,1,6]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,3,6,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,6,1,3]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,2,6,3,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,1,2,6]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,1,6,2]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,2,6,1]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,6,1,2]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,6,2,1]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,1,2,3]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,1,3,2]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,2,3,1]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,3,1,2]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,4,6,3,2,1]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,2,3,4]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,2,4,3]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,3,2,4]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,3,4,2]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,4,2,3]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,4,3,2]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,1,3,4]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,1,4,3]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,3,1,4]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,3,4,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,4,1,3]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,2,4,3,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,1,2,4]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,1,4,2]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,2,1,4]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,2,4,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,3,4,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,1,2,3]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,1,3,2]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,2,1,3]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,2,3,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[5,6,4,3,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,3,4,5]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,3,5,4]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,4,3,5]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,4,5,3]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,5,3,4]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,5,4,3]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,4,5]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,5,4]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,4,2,5]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,4,5,2]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,5,2,4]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,5,4,2]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,2,3,5]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,2,5,3]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,3,2,5]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,3,5,2]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,5,2,3]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,5,3,2]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,2,3,4]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,2,4,3]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,3,2,4]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,3,4,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,4,2,3]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,4,3,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,3,4,5]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,3,5,4]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,4,3,5]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,4,5,3]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,5,3,4]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,5,4,3]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,1,4,5]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,1,5,4]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,4,1,5]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,5,1,4]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,1,3,5]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,1,5,3]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,3,1,5]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,5,1,3]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,5,3,1]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,1,3,4]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,1,4,3]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,3,1,4]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,3,4,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,4,1,3]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,2,4,5]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,2,5,4]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,4,2,5]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,4,5,2]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,5,2,4]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,5,4,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,1,4,5]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,1,5,4]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,4,1,5]=>[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,5,1,4]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,1,2,5]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,1,5,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,2,1,5]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,2,5,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,5,1,2]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,5,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,1,2,4]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,1,4,2]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,2,1,4]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,2,4,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,4,1,2]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,4,2,1]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,2,3,5]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,2,5,3]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,3,2,5]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,3,5,2]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,5,2,3]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,5,3,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,1,3,5]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,1,5,3]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,3,1,5]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,3,5,1]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,5,1,3]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,5,3,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,1,2,5]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,1,5,2]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,2,1,5]=>[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,5,1,2]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,5,2,1]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,1,2,3]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,1,3,2]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,2,1,3]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,3,1,2]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,3,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,2,3,4]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,2,4,3]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,3,2,4]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,3,4,2]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,4,2,3]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,4,3,2]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,1,3,4]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,1,4,3]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,3,1,4]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,3,4,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,4,1,3]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,4,3,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,1,2,4]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,1,4,2]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,2,1,4]=>[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,2,4,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,4,1,2]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,1,2,3]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,1,3,2]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,2,1,3]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,2,3,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,3,1,2]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,6,7,5]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,7,6,5]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,6,4,7]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,6,7,4]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,7,4,6]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,5,7,6,4]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,4,7,5]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,5,4,7]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,5,7,4]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,7,4,5]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,7,5,4]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,4,6,5]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,5,4,6]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,5,6,4]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,6,4,5]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,7,6,5,4]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,6,7,5]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,3,7,6,5]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,3,6,7]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,3,7,6]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,6,3,7]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,6,7,3]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,7,3,6]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,5,7,6,3]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,3,5,7]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,3,7,5]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,5,3,7]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,5,7,3]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,7,3,5]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,7,5,3]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,3,5,6]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,3,6,5]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,5,3,6]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,5,6,3]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,6,3,5]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,7,6,5,3]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,6,4,7]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,6,7,4]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,7,4,6]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,7,6,4]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,3,6,7]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,3,7,6]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,6,3,7]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,6,7,3]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,7,3,6]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,7,6,3]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,3,4,7]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,3,7,4]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,4,3,7]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,4,7,3]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,7,3,4]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,7,4,3]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,3,4,6]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,3,6,4]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,4,3,6]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,4,6,3]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,6,3,4]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,7,6,4,3]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,4,7,5]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,5,4,7]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,5,7,4]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,7,4,5]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,3,7,5,4]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,3,5,7]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,3,7,5]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,5,3,7]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,5,7,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,7,3,5]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,7,5,3]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,3,4,7]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,3,7,4]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,4,3,7]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,4,7,3]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,7,3,4]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,5,7,4,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,3,4,5]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,3,5,4]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,4,3,5]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,4,5,3]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,5,3,4]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,5,4,3]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,4,6,5]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,5,4,6]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,5,6,4]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,6,4,5]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,3,6,5,4]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,3,5,6]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,3,6,5]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,5,3,6]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,5,6,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,6,3,5]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,4,6,5,3]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,3,4,6]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,3,6,4]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,4,3,6]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,4,6,3]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,6,3,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,6,4,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,3,4,5]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,3,5,4]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,4,3,5]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,4,5,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,5,3,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,6,5,4,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,6,7,5]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,7,6,5]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,6,4,7]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,6,7,4]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,7,4,6]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,5,7,6,4]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,4,7,5]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,5,4,7]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,5,7,4]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,7,4,5]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,7,5,4]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,4,6,5]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,5,4,6]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,5,6,4]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,6,4,5]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,6,5,4]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,5,6,7]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,5,7,6]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,6,5,7]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,6,7,5]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[7,4,6,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,7,5,6]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,7,6,5]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,2,6,7]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,2,7,6]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[7,3,6,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,6,2,7]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,6,7,2]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>[7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,7,2,6]=>[1,3,4,5,7,2,6]=>[6,2,7,5,4,3,1]=>[7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,5,7,6,2]=>[1,3,4,5,7,2,6]=>[6,2,7,5,4,3,1]=>[7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,2,5,7]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,2,7,5]=>[1,3,4,6,2,7,5]=>[5,7,2,6,4,3,1]=>[7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,5,2,7]=>[1,3,4,6,2,7,5]=>[5,7,2,6,4,3,1]=>[7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,5,7,2]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,7,2,5]=>[1,3,4,6,7,2,5]=>[5,2,7,6,4,3,1]=>[7,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,6,7,5,2]=>[1,3,4,6,7,2,5]=>[5,2,7,6,4,3,1]=>[7,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,2,5,6]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,2,6,5]=>[1,3,4,7,2,6,5]=>[5,6,2,7,4,3,1]=>[7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,5,2,6]=>[1,3,4,7,2,6,5]=>[5,6,2,7,4,3,1]=>[7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,5,6,2]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,6,2,5]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,6,5,2]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,4,6,7]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,4,7,6]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,6,4,7]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,6,7,4]=>[1,3,5,2,6,7,4]=>[4,7,6,2,5,3,1]=>[7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,7,4,6]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,7,6,4]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,2,6,7]=>[1,3,5,2,6,7,4]=>[4,7,6,2,5,3,1]=>[7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,2,7,6]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,6,2,7]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,6,7,2]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,7,2,6]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,4,7,6,2]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,2,4,7]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,2,7,4]=>[1,3,5,6,2,7,4]=>[4,7,2,6,5,3,1]=>[7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,4,2,7]=>[1,3,5,6,2,7,4]=>[4,7,2,6,5,3,1]=>[7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,4,7,2]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,7,2,4]=>[1,3,5,6,7,2,4]=>[4,2,7,6,5,3,1]=>[7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,6,7,4,2]=>[1,3,5,6,7,2,4]=>[4,2,7,6,5,3,1]=>[7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,2,4,6]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,2,6,4]=>[1,3,5,7,2,6,4]=>[4,6,2,7,5,3,1]=>[7,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,4,2,6]=>[1,3,5,7,2,6,4]=>[4,6,2,7,5,3,1]=>[7,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,4,6,2]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,6,2,4]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,6,4,2]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,4,5,7]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,4,7,5]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,5,4,7]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,5,7,4]=>[1,3,6,2,5,7,4]=>[4,7,5,2,6,3,1]=>[7,4,6,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,7,4,5]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,2,7,5,4]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,2,5,7]=>[1,3,6,2,5,7,4]=>[4,7,5,2,6,3,1]=>[7,4,6,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,2,7,5]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,5,2,7]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,5,7,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,7,2,5]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,7,5,2]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,2,4,7]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,2,7,4]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,4,2,7]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,4,7,2]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,7,2,4]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,5,7,4,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,2,4,5]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,2,5,4]=>[1,3,6,7,2,5,4]=>[4,5,2,7,6,3,1]=>[7,3,6,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,4,2,5]=>[1,3,6,7,2,5,4]=>[4,5,2,7,6,3,1]=>[7,3,6,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,4,5,2]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,5,2,4]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,7,5,4,2]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,4,5,6]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,4,6,5]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,5,4,6]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,5,6,4]=>[1,3,7,2,5,6,4]=>[4,6,5,2,7,3,1]=>[7,4,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,6,4,5]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,2,6,5,4]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,2,5,6]=>[1,3,7,2,5,6,4]=>[4,6,5,2,7,3,1]=>[7,4,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,2,6,5]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,5,2,6]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,5,6,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,6,2,5]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,4,6,5,2]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,2,4,6]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,2,6,4]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,4,2,6]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,4,6,2]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,6,2,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,6,4,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,2,4,5]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,2,5,4]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,4,2,5]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,4,5,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,5,2,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,5,4,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,6,7,5]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,7,6,5]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,3,6,7]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,3,7,6]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,6,3,7]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,6,7,3]=>[1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1]=>[7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,7,3,6]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,5,7,6,3]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,3,5,7]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,3,7,5]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,5,3,7]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,5,7,3]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,7,3,5]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,6,7,5,3]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,3,5,6]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,3,6,5]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,5,3,6]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,5,6,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,6,3,5]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,6,5,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,5,6,7]=>[1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1]=>[7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,5,7,6]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,6,5,7]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,6,7,5]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,7,5,6]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,7,6,5]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,2,6,7]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,2,7,6]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,6,2,7]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,6,7,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,7,2,6]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,7,6,2]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,2,5,7]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,2,7,5]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,5,2,7]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,5,7,2]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,7,2,5]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,7,5,2]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,2,5,6]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,2,6,5]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,5,2,6]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,5,6,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,6,2,5]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,7,6,5,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,3,6,7]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,3,7,6]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,6,3,7]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,6,7,3]=>[1,4,5,2,6,7,3]=>[3,7,6,2,5,4,1]=>[7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,7,3,6]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,2,7,6,3]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,2,6,7]=>[1,4,5,2,6,7,3]=>[3,7,6,2,5,4,1]=>[7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,2,7,6]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,6,2,7]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,6,7,2]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,7,2,6]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,3,7,6,2]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,2,3,7]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,2,7,3]=>[1,4,5,6,2,7,3]=>[3,7,2,6,5,4,1]=>[7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,3,2,7]=>[1,4,5,6,2,7,3]=>[3,7,2,6,5,4,1]=>[7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,3,7,2]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,7,2,3]=>[1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,7,3,2]=>[1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,2,3,6]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,2,6,3]=>[1,4,5,7,2,6,3]=>[3,6,2,7,5,4,1]=>[7,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,3,2,6]=>[1,4,5,7,2,6,3]=>[3,6,2,7,5,4,1]=>[7,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,3,6,2]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,6,2,3]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,6,3,2]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,3,5,7]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,3,7,5]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,5,3,7]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,5,7,3]=>[1,4,6,2,5,7,3]=>[3,7,5,2,6,4,1]=>[7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,7,3,5]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,7,5,3]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,2,5,7]=>[1,4,6,2,5,7,3]=>[3,7,5,2,6,4,1]=>[7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,2,7,5]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,5,2,7]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,5,7,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,7,2,5]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,7,5,2]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,2,3,7]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,2,7,3]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,3,2,7]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,3,7,2]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,7,2,3]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,5,7,3,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,2,3,5]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,2,5,3]=>[1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1]=>[7,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,3,2,5]=>[1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1]=>[7,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,3,5,2]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,5,2,3]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,7,5,3,2]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,3,5,6]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,3,6,5]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,5,3,6]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,5,6,3]=>[1,4,7,2,5,6,3]=>[3,6,5,2,7,4,1]=>[7,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,6,3,5]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,6,5,3]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,2,5,6]=>[1,4,7,2,5,6,3]=>[3,6,5,2,7,4,1]=>[7,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,2,6,5]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,5,2,6]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,5,6,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,6,2,5]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,6,5,2]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,2,3,6]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,2,6,3]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,3,2,6]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,3,6,2]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,6,2,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,6,3,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,2,3,5]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,2,5,3]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,3,2,5]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,3,5,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,5,2,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,5,3,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,6,4,7]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,6,7,4]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,7,4,6]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,7,6,4]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,3,6,7]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,3,7,6]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,6,3,7]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,6,7,3]=>[1,5,2,4,6,7,3]=>[3,7,6,4,2,5,1]=>[7,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,7,3,6]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,7,6,3]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,3,4,7]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,3,7,4]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,4,3,7]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,4,7,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,7,3,4]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,6,7,4,3]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,3,4,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,3,6,4]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,4,3,6]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,4,6,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,6,3,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,6,4,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,4,6,7]=>[1,5,2,4,6,7,3]=>[3,7,6,4,2,5,1]=>[7,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,4,7,6]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,6,4,7]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,6,7,4]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,7,4,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,7,6,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,2,6,7]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,6,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,6,7,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,7,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,4,7,6,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,2,4,7]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,2,7,4]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,4,2,7]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,4,7,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,7,2,4]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,6,7,4,2]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,2,4,6]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,2,6,4]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,4,2,6]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,4,6,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,6,2,4]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,6,4,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,3,6,7]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,3,7,6]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,6,3,7]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,6,7,3]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,7,3,6]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,7,6,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,2,6,7]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,6,2,7]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,6,7,2]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,7,2,6]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,3,7,6,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,2,3,7]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,3,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,3,7,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,7,2,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,6,7,3,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,2,3,6]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,2,6,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,3,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,3,6,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,6,2,3]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,7,6,3,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,3,4,7]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,3,7,4]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,4,3,7]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,4,7,3]=>[1,5,6,2,4,7,3]=>[3,7,4,2,6,5,1]=>[7,4,1,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,7,3,4]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,2,7,4,3]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,2,4,7]=>[1,5,6,2,4,7,3]=>[3,7,4,2,6,5,1]=>[7,4,1,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,2,7,4]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,4,2,7]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,4,7,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,7,2,4]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,7,4,2]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,2,3,7]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,2,7,3]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,3,2,7]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,3,7,2]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,7,2,3]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,4,7,3,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,2,3,4]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,2,4,3]=>[1,5,6,7,2,4,3]=>[3,4,2,7,6,5,1]=>[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,3,2,4]=>[1,5,6,7,2,4,3]=>[3,4,2,7,6,5,1]=>[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,3,4,2]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,4,2,3]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,4,3,2]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,3,4,6]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,3,6,4]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,4,3,6]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,4,6,3]=>[1,5,7,2,4,6,3]=>[3,6,4,2,7,5,1]=>[7,4,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,6,3,4]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,2,6,4,3]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,2,4,6]=>[1,5,7,2,4,6,3]=>[3,6,4,2,7,5,1]=>[7,4,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,2,6,4]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,4,2,6]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,4,6,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,6,2,4]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,6,4,2]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,2,3,6]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,2,6,3]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,3,2,6]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,3,6,2]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,6,2,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,6,3,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,2,3,4]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,2,4,3]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,3,2,4]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,3,4,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,4,2,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,6,4,3,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,4,7,5]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,5,4,7]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,5,7,4]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,7,4,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,7,5,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,3,5,7]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,3,7,5]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,5,3,7]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,5,7,3]=>[1,6,2,4,5,7,3]=>[3,7,5,4,2,6,1]=>[7,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,7,3,5]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,4,7,5,3]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,3,4,7]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,3,7,4]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,4,3,7]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,4,7,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,7,3,4]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,5,7,4,3]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,3,4,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,3,5,4]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,4,3,5]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,4,5,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,5,3,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,7,5,4,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,4,5,7]=>[1,6,2,4,5,7,3]=>[3,7,5,4,2,6,1]=>[7,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,4,7,5]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,5,4,7]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,5,7,4]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,7,4,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,7,5,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,2,5,7]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,2,7,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,5,7,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,7,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,7,5,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,2,4,7]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,2,7,4]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,4,2,7]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,4,7,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,7,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,7,4,2]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,2,4,5]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,2,5,4]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,4,2,5]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,4,5,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,5,2,4]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,7,5,4,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,3,5,7]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,3,7,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,5,3,7]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,5,7,3]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,7,3,5]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,2,7,5,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,2,5,7]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,2,7,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,5,2,7]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,5,7,2]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,7,2,5]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,7,5,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,2,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,2,7,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,3,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,3,7,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,7,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,7,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,2,3,5]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,2,5,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,3,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,3,5,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,5,2,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,5,3,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,3,4,7]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,3,7,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,4,3,7]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,4,7,3]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,7,3,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,7,4,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,2,4,7]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,2,7,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,4,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,4,7,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,7,2,4]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,3,7,4,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,2,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,2,7,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,3,7,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,7,2,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,7,3,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,2,3,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,2,4,3]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,3,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,3,4,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,4,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,4,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,3,4,5]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,3,5,4]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,4,3,5]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,4,5,3]=>[1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1]=>[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,5,3,4]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,2,5,4,3]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,2,4,5]=>[1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1]=>[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,2,5,4]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,4,2,5]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,4,5,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,5,2,4]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,5,4,2]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,2,3,5]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,2,5,3]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,3,2,5]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,3,5,2]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,5,3,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,2,3,4]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,2,4,3]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,3,2,4]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,3,4,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,4,3,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,4,6,5]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,5,4,6]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,5,6,4]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,6,4,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,6,5,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,3,5,6]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,3,6,5]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,5,3,6]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,5,6,3]=>[1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1]=>[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,6,3,5]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,6,5,3]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,3,4,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,3,6,4]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,4,3,6]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,4,6,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,6,3,4]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,6,4,3]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,3,4,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,3,5,4]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,4,3,5]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,4,5,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,5,3,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,5,4,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,4,5,6]=>[1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1]=>[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,4,6,5]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,5,4,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,5,6,4]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,6,4,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,6,5,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,2,5,6]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,2,6,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,5,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,6,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,6,5,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,2,4,6]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,2,6,4]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,4,2,6]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,4,6,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,6,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,6,4,2]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,2,4,5]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,2,5,4]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,4,2,5]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,4,5,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,5,2,4]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,5,4,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,3,5,6]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,3,6,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,5,3,6]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,5,6,3]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,6,3,5]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,2,6,5,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,2,5,6]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,2,6,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,5,2,6]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,5,6,2]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,6,2,5]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,6,5,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,2,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,2,6,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,3,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,3,6,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,6,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,6,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,2,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,2,5,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,3,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,3,5,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,5,2,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,5,3,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,3,4,6]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,3,6,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,4,3,6]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,4,6,3]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,6,3,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,6,4,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,2,4,6]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,2,6,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,4,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,4,6,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,6,2,4]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,6,4,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,2,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,2,6,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,3,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,3,6,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,6,2,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,6,3,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,2,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,2,4,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,3,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,4,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,6,4,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,3,4,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,3,5,4]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,4,3,5]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,4,5,3]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,5,3,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,5,4,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,2,4,5]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,2,5,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,4,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,4,5,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,5,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,5,4,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,2,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,2,5,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,3,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,3,5,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,5,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,2,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,2,4,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,3,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,3,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,4,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>[7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,5,7,6]=>[1,3,4,5,7,2,6]=>[6,2,7,5,4,3,1]=>[7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,6,5,7]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,6,7,5]=>[1,3,4,6,7,2,5]=>[5,2,7,6,4,3,1]=>[7,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,7,5,6]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,7,6,5]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,4,6,7]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,4,7,6]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,6,4,7]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,6,7,4]=>[1,3,5,6,7,2,4]=>[4,2,7,6,5,3,1]=>[7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,7,4,6]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,5,7,6,4]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,4,5,7]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,4,7,5]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,5,4,7]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,5,7,4]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,7,4,5]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,6,7,5,4]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,4,5,6]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,4,6,5]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,5,4,6]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,5,6,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,6,4,5]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,5,6,7]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,5,7,6]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,6,5,7]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,6,7,5]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,7,5,6]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,7,6,5]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,3,6,7]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,3,7,6]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,6,3,7]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,6,7,3]=>[1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,7,3,6]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,7,6,3]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,3,5,7]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,3,7,5]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,5,3,7]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,5,7,3]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,7,3,5]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,6,7,5,3]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,3,5,6]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,3,6,5]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,5,3,6]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,5,6,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,6,3,5]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,7,6,5,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,4,6,7]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,4,7,6]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,6,4,7]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,6,7,4]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,7,4,6]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,3,7,6,4]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,3,6,7]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,3,7,6]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,6,3,7]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,6,7,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,7,3,6]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,7,6,3]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,3,4,7]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,3,7,4]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,4,3,7]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,4,7,3]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,7,3,4]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,7,4,3]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,3,4,6]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,3,6,4]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,4,3,6]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,4,6,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,6,3,4]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,6,4,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,4,5,7]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,4,7,5]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,5,4,7]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,5,7,4]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,7,4,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,7,5,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,3,5,7]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,3,7,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,5,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,5,7,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,7,3,5]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,7,5,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,3,4,7]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,3,7,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,4,7,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,7,3,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,5,7,4,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,3,4,5]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,3,5,4]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,4,3,5]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,4,5,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,5,3,4]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,7,5,4,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,4,5,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,4,6,5]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,5,4,6]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,5,6,4]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,6,4,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,6,5,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,3,5,6]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,3,6,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,5,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,6,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,6,5,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,3,4,6]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,3,6,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,4,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,4,6,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,6,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,6,4,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,3,4,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,3,5,4]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,4,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,4,5,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,5,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,5,6,7]=>[1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,5,7,6]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,6,5,7]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,6,7,5]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,7,5,6]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,4,6,7]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,4,7,6]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,6,4,7]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,6,7,4]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,7,4,6]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,5,7,6,4]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,4,5,7]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,4,7,5]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,5,7,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,7,4,5]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,7,5,4]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,4,5,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,4,6,5]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,5,4,6]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,6,4,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,5,6,7]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,5,7,6]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,6,5,7]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,6,7,5]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,7,5,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,1,7,6,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,1,6,7]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,1,7,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,6,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,7,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,7,6,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,1,5,7]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,1,7,5]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,5,1,7]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,5,7,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,7,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,7,5,1]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,1,5,6]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,1,6,5]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,5,1,6]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,5,6,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,6,1,5]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,7,6,5,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,4,6,7]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,4,7,6]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,6,4,7]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,6,7,4]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,7,4,6]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,7,6,4]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,1,6,7]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,1,7,6]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,6,1,7]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,6,7,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,7,1,6]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,4,7,6,1]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,1,4,7]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,1,7,4]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,4,1,7]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,4,7,1]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,7,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,7,4,1]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,1,4,6]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,1,6,4]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,4,1,6]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,4,6,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,6,1,4]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,6,4,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,4,5,7]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,4,7,5]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,5,4,7]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,5,7,4]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,7,4,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,1,7,5,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,1,5,7]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,1,7,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,5,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,5,7,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,7,1,5]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,7,5,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,1,4,7]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,1,7,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,4,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,4,7,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,7,1,4]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,7,4,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,1,4,5]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,1,5,4]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,4,1,5]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,4,5,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,5,1,4]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,7,5,4,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,4,5,6]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,4,6,5]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,5,4,6]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,5,6,4]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,6,4,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,1,6,5,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,1,5,6]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,1,6,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,5,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,5,6,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,6,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,4,6,5,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,1,4,6]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,1,6,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,4,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,4,6,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,6,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,6,4,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,1,4,5]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,1,5,4]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,4,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,4,5,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,5,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,6,5,4,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,5,6,7]=>[1,3,5,6,7,2,4]=>[4,2,7,6,5,3,1]=>[7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,5,7,6]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,6,5,7]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,6,7,5]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,7,5,6]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,3,7,6,5]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,3,6,7]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,3,7,6]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,6,3,7]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,6,7,3]=>[1,5,6,7,2,4,3]=>[3,4,2,7,6,5,1]=>[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,7,3,6]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,5,7,6,3]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,3,5,7]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,3,7,5]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,5,3,7]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,5,7,3]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,7,3,5]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,7,5,3]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,3,5,6]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,3,6,5]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,5,3,6]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,5,6,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,6,3,5]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,7,6,5,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,5,6,7]=>[1,5,6,7,2,4,3]=>[3,4,2,7,6,5,1]=>[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,5,7,6]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,6,5,7]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,6,7,5]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,7,5,6]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,7,6,5]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,1,6,7]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,1,7,6]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,6,1,7]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,6,7,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,7,1,6]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,7,6,1]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,1,5,7]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,1,7,5]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,5,1,7]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,5,7,1]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,7,1,5]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,6,7,5,1]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,1,5,6]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,1,6,5]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,5,1,6]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,5,6,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,6,1,5]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,6,5,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,3,6,7]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,3,7,6]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,6,3,7]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,6,7,3]=>[1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1]=>[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,7,3,6]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,1,7,6,3]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,1,6,7]=>[1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1]=>[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,1,7,6]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,6,1,7]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,6,7,1]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,7,1,6]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,7,6,1]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,1,3,7]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,1,7,3]=>[1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1]=>[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,3,1,7]=>[1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1]=>[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,3,7,1]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,7,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,6,7,3,1]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,1,3,6]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,1,6,3]=>[1,6,2,4,5,7,3]=>[3,7,5,4,2,6,1]=>[7,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,3,1,6]=>[1,6,2,4,5,7,3]=>[3,7,5,4,2,6,1]=>[7,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,3,6,1]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,6,1,3]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,6,3,1]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,3,5,7]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,3,7,5]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,5,3,7]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,5,7,3]=>[1,5,7,2,4,6,3]=>[3,6,4,2,7,5,1]=>[7,4,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,7,3,5]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,1,7,5,3]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,1,5,7]=>[1,5,7,2,4,6,3]=>[3,6,4,2,7,5,1]=>[7,4,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,1,7,5]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,5,1,7]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,5,7,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,7,1,5]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,3,7,5,1]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,1,3,7]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,1,7,3]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,3,1,7]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,3,7,1]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,7,1,3]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,5,7,3,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,1,3,5]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,1,5,3]=>[1,5,2,4,6,7,3]=>[3,7,6,4,2,5,1]=>[7,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,3,1,5]=>[1,5,2,4,6,7,3]=>[3,7,6,4,2,5,1]=>[7,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,3,5,1]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,5,1,3]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,5,3,1]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,3,5,6]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,3,6,5]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,5,3,6]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,5,6,3]=>[1,5,6,2,4,7,3]=>[3,7,4,2,6,5,1]=>[7,4,1,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,6,3,5]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,6,5,3]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,1,5,6]=>[1,5,6,2,4,7,3]=>[3,7,4,2,6,5,1]=>[7,4,1,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,1,6,5]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,5,1,6]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,5,6,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,6,1,5]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,6,5,1]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,1,3,6]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,1,6,3]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,3,1,6]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,3,6,1]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,6,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,6,3,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,1,3,5]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,1,5,3]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,3,1,5]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,3,5,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,5,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,6,5,3,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,4,6,7]=>[1,3,4,6,7,2,5]=>[5,2,7,6,4,3,1]=>[7,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,4,7,6]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,6,4,7]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,6,7,4]=>[1,3,6,7,2,5,4]=>[4,5,2,7,6,3,1]=>[7,3,6,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,7,4,6]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,7,6,4]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,3,6,7]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,3,7,6]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,6,3,7]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,6,7,3]=>[1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1]=>[7,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,7,3,6]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,4,7,6,3]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,3,4,7]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,3,7,4]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,4,3,7]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,4,7,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,7,3,4]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,7,4,3]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,3,4,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,3,6,4]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,4,3,6]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,4,6,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,6,3,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,7,6,4,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,4,6,7]=>[1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1]=>[7,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,4,7,6]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,6,4,7]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,6,7,4]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,7,4,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,7,6,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,1,6,7]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,1,7,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,6,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,6,7,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,7,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,7,6,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,1,4,7]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,1,7,4]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,4,1,7]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,4,7,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,7,1,4]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,6,7,4,1]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,1,4,6]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,1,6,4]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,4,1,6]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,4,6,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,6,1,4]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,7,6,4,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,3,6,7]=>[1,3,6,7,2,5,4]=>[4,5,2,7,6,3,1]=>[7,3,6,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,3,7,6]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,6,3,7]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,6,7,3]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,7,3,6]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,7,6,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,1,6,7]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,1,7,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,6,1,7]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,6,7,1]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,7,1,6]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,7,6,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,1,3,7]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,1,7,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,3,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,3,7,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,7,1,3]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,7,3,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,1,3,6]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,1,6,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,3,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,3,6,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,6,1,3]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,6,3,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,3,4,7]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,3,7,4]=>[1,3,7,2,5,6,4]=>[4,6,5,2,7,3,1]=>[7,4,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,4,3,7]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,4,7,3]=>[1,4,7,2,5,6,3]=>[3,6,5,2,7,4,1]=>[7,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,7,3,4]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,1,7,4,3]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,1,4,7]=>[1,4,7,2,5,6,3]=>[3,6,5,2,7,4,1]=>[7,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,1,7,4]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,4,1,7]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,4,7,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,7,1,4]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,7,4,1]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,1,3,7]=>[1,3,7,2,5,6,4]=>[4,6,5,2,7,3,1]=>[7,4,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,1,7,3]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,3,1,7]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,3,7,1]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,7,1,3]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,7,3,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,1,3,4]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,1,4,3]=>[1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1]=>[7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,3,1,4]=>[1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1]=>[7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,3,4,1]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,4,1,3]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,7,4,3,1]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,3,4,6]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,3,6,4]=>[1,3,6,2,5,7,4]=>[4,7,5,2,6,3,1]=>[7,4,6,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,4,3,6]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,4,6,3]=>[1,4,6,2,5,7,3]=>[3,7,5,2,6,4,1]=>[7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,6,3,4]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,1,6,4,3]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,1,4,6]=>[1,4,6,2,5,7,3]=>[3,7,5,2,6,4,1]=>[7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,1,6,4]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,4,1,6]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,4,6,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,6,1,4]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,6,4,1]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,1,3,6]=>[1,3,6,2,5,7,4]=>[4,7,5,2,6,3,1]=>[7,4,6,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,1,6,3]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,3,1,6]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,3,6,1]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,6,1,3]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,4,6,3,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,1,3,4]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,1,4,3]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,3,1,4]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,3,4,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,4,1,3]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,4,3,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,4,5,7]=>[1,3,4,5,7,2,6]=>[6,2,7,5,4,3,1]=>[7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,4,7,5]=>[1,3,4,7,2,6,5]=>[5,6,2,7,4,3,1]=>[7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,5,4,7]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,5,7,4]=>[1,3,5,7,2,6,4]=>[4,6,2,7,5,3,1]=>[7,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,7,4,5]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,7,5,4]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,3,5,7]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,3,7,5]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,5,3,7]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,5,7,3]=>[1,4,5,7,2,6,3]=>[3,6,2,7,5,4,1]=>[7,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,7,3,5]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,7,5,3]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,3,4,7]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,3,7,4]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,4,3,7]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,4,7,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,7,3,4]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,7,4,3]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,3,4,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,3,5,4]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,4,3,5]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,4,5,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,5,3,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,7,5,4,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,4,5,7]=>[1,4,5,7,2,6,3]=>[3,6,2,7,5,4,1]=>[7,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,4,7,5]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,5,4,7]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,5,7,4]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,7,4,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,1,7,5,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,1,5,7]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,1,7,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,5,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,5,7,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,7,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,7,5,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,1,4,7]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,1,7,4]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,4,1,7]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,4,7,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,7,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,7,4,1]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,1,4,5]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,1,5,4]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,4,1,5]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,4,5,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,5,1,4]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,5,4,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,3,5,7]=>[1,3,5,7,2,6,4]=>[4,6,2,7,5,3,1]=>[7,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,3,7,5]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,5,3,7]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,5,7,3]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,7,3,5]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,7,5,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,1,5,7]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,1,7,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,5,1,7]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,5,7,1]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,7,1,5]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,3,7,5,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,1,3,7]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,1,7,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,3,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,3,7,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,7,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,7,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,1,3,5]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,1,5,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,3,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,3,5,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,5,1,3]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,7,5,3,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,3,4,7]=>[1,3,4,7,2,6,5]=>[5,6,2,7,4,3,1]=>[7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,3,7,4]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,4,3,7]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,4,7,3]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,7,3,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,7,4,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,1,4,7]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,1,7,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,4,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,4,7,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,7,1,4]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,7,4,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,1,3,7]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,1,7,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,3,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,3,7,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,7,1,3]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,7,3,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,1,3,4]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,1,4,3]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,3,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,3,4,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,4,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,7,4,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,3,4,5]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,3,5,4]=>[1,3,5,2,6,7,4]=>[4,7,6,2,5,3,1]=>[7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,4,3,5]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,4,5,3]=>[1,4,5,2,6,7,3]=>[3,7,6,2,5,4,1]=>[7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,5,3,4]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,5,4,3]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,1,4,5]=>[1,4,5,2,6,7,3]=>[3,7,6,2,5,4,1]=>[7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,1,5,4]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,4,1,5]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,4,5,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,5,1,4]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,3,5,4,1]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,1,3,5]=>[1,3,5,2,6,7,4]=>[4,7,6,2,5,3,1]=>[7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,1,5,3]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,3,1,5]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,3,5,1]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,5,1,3]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,4,5,3,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,1,3,4]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[7,4,6,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,1,4,3]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,3,1,4]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,3,4,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,4,1,3]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,4,3,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,4,5,6]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,4,6,5]=>[1,3,4,6,2,7,5]=>[5,7,2,6,4,3,1]=>[7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,5,4,6]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,5,6,4]=>[1,3,5,6,2,7,4]=>[4,7,2,6,5,3,1]=>[7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,6,4,5]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,6,5,4]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,3,5,6]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,3,6,5]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,5,3,6]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,5,6,3]=>[1,4,5,6,2,7,3]=>[3,7,2,6,5,4,1]=>[7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,6,3,5]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,6,5,3]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,3,4,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,3,6,4]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,4,3,6]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,4,6,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,6,3,4]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,6,4,3]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,3,4,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,3,5,4]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,4,3,5]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,4,5,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,5,3,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,5,4,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,4,5,6]=>[1,4,5,6,2,7,3]=>[3,7,2,6,5,4,1]=>[7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,4,6,5]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,5,4,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,5,6,4]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,6,4,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,1,6,5,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,1,5,6]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,1,6,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,5,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,5,6,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,6,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,6,5,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,1,4,6]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,1,6,4]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,4,1,6]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,4,6,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,6,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,6,4,1]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,1,4,5]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,1,5,4]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,4,1,5]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,4,5,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,5,1,4]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,5,4,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,3,5,6]=>[1,3,5,6,2,7,4]=>[4,7,2,6,5,3,1]=>[7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,3,6,5]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,5,3,6]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,5,6,3]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,6,3,5]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,6,5,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,1,5,6]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,1,6,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,5,1,6]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,5,6,1]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,6,1,5]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,6,5,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,1,3,6]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,1,6,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,3,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,3,6,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,6,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,6,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,1,3,5]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,1,5,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,3,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,3,5,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,5,1,3]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,5,3,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,3,4,6]=>[1,3,4,6,2,7,5]=>[5,7,2,6,4,3,1]=>[7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,3,6,4]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,4,3,6]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,4,6,3]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,6,3,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,6,4,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,1,4,6]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,1,6,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,4,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,4,6,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,6,1,4]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,3,6,4,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,1,3,6]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,1,6,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,3,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,3,6,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,6,1,3]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,6,3,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,1,3,4]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,1,4,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,3,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,3,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,4,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,6,4,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,3,4,5]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[7,3,6,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,3,5,4]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,4,3,5]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,4,5,3]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,5,3,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,5,4,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,1,4,5]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,1,5,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,4,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,4,5,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,5,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,5,4,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,1,3,5]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,1,5,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,3,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,3,5,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,5,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,5,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,1,3,4]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,1,4,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,3,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,3,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,4,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,5,4,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,5,7,6]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,6,5,7]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,6,7,5]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,7,5,6]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,4,7,6,5]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,4,6,7]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,4,7,6]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,6,4,7]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,6,7,4]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,7,4,6]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,7,6,4]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,4,5,7]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,4,7,5]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,5,4,7]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,5,7,4]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,7,4,5]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,6,7,5,4]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,4,5,6]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,4,6,5]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,5,4,6]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,5,6,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,6,4,5]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,7,6,5,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,5,6,7]=>[1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1]=>[7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,5,7,6]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,6,5,7]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,6,7,5]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,7,5,6]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,2,7,6,5]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,2,6,7]=>[1,4,5,2,6,7,3]=>[3,7,6,2,5,4,1]=>[7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,2,7,6]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,6,2,7]=>[1,4,5,6,2,7,3]=>[3,7,2,6,5,4,1]=>[7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,6,7,2]=>[1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,7,2,6]=>[1,4,5,7,2,6,3]=>[3,6,2,7,5,4,1]=>[7,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,5,7,6,2]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,2,5,7]=>[1,4,6,2,5,7,3]=>[3,7,5,2,6,4,1]=>[7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,2,7,5]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,5,2,7]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,5,7,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,7,2,5]=>[1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1]=>[7,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,6,7,5,2]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,2,5,6]=>[1,4,7,2,5,6,3]=>[3,6,5,2,7,4,1]=>[7,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,2,6,5]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,5,2,6]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,5,6,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,6,2,5]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,4,7,6,5,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,4,6,7]=>[1,5,2,4,6,7,3]=>[3,7,6,4,2,5,1]=>[7,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,4,7,6]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,6,4,7]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,6,7,4]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,7,4,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,7,6,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,2,6,7]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,2,7,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,6,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,6,7,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,7,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,4,7,6,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,2,4,7]=>[1,5,6,2,4,7,3]=>[3,7,4,2,6,5,1]=>[7,4,1,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,2,7,4]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,4,2,7]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,4,7,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,7,2,4]=>[1,5,6,7,2,4,3]=>[3,4,2,7,6,5,1]=>[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,6,7,4,2]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,2,4,6]=>[1,5,7,2,4,6,3]=>[3,6,4,2,7,5,1]=>[7,4,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,2,6,4]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,4,2,6]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,4,6,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,6,2,4]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,6,4,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,4,5,7]=>[1,6,2,4,5,7,3]=>[3,7,5,4,2,6,1]=>[7,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,4,7,5]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,5,4,7]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,5,7,4]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,7,4,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,2,7,5,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,2,5,7]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,2,7,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,5,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,5,7,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,7,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,7,5,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,2,4,7]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,2,7,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,4,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,4,7,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,7,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,5,7,4,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,2,4,5]=>[1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1]=>[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,2,5,4]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,4,2,5]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,4,5,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,5,2,4]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,7,5,4,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,4,5,6]=>[1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1]=>[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,4,6,5]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,5,4,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,5,6,4]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,6,4,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,6,5,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,2,5,6]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,2,6,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,5,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,5,6,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,6,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,4,6,5,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,2,4,6]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,2,6,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,4,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,4,6,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,6,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,5,6,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,2,4,5]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,2,5,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,4,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,4,5,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,5,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,6,5,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,5,6,7]=>[1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,5,7,6]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,6,5,7]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,6,7,5]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,7,5,6]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,4,6,7]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,4,7,6]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,6,4,7]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,6,7,4]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,7,4,6]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,5,7,6,4]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,4,5,7]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,4,7,5]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,5,7,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,7,4,5]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,7,5,4]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,4,5,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,4,6,5]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,5,4,6]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,6,4,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,5,6,7]=>[1,5,6,7,2,4,3]=>[3,4,2,7,6,5,1]=>[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,5,7,6]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,6,5,7]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,6,7,5]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,7,5,6]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,1,7,6,5]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,1,6,7]=>[1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1]=>[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,1,7,6]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,6,1,7]=>[1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1]=>[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,6,7,1]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,7,1,6]=>[1,6,2,4,5,7,3]=>[3,7,5,4,2,6,1]=>[7,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,7,6,1]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,1,5,7]=>[1,5,7,2,4,6,3]=>[3,6,4,2,7,5,1]=>[7,4,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,1,7,5]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,5,1,7]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,5,7,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,7,1,5]=>[1,5,2,4,6,7,3]=>[3,7,6,4,2,5,1]=>[7,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,7,5,1]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,1,5,6]=>[1,5,6,2,4,7,3]=>[3,7,4,2,6,5,1]=>[7,4,1,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,1,6,5]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,5,1,6]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,5,6,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,6,1,5]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,7,6,5,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,4,6,7]=>[1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1]=>[7,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,4,7,6]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,6,4,7]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,6,7,4]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,7,4,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,1,7,6,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,1,6,7]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,1,7,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,6,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,6,7,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,7,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,7,6,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,1,4,7]=>[1,4,7,2,5,6,3]=>[3,6,5,2,7,4,1]=>[7,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,1,7,4]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,4,1,7]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,4,7,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,7,1,4]=>[1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1]=>[7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,6,7,4,1]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,1,4,6]=>[1,4,6,2,5,7,3]=>[3,7,5,2,6,4,1]=>[7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,1,6,4]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,4,1,6]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,4,6,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,6,1,4]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,7,6,4,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,4,5,7]=>[1,4,5,7,2,6,3]=>[3,6,2,7,5,4,1]=>[7,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,4,7,5]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,5,4,7]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,5,7,4]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,7,4,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,1,7,5,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,1,5,7]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,1,7,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,5,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,5,7,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,7,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,7,5,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,1,4,7]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,1,7,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,4,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,4,7,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,7,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,5,7,4,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,1,4,5]=>[1,4,5,2,6,7,3]=>[3,7,6,2,5,4,1]=>[7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,1,5,4]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,4,1,5]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,4,5,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,5,1,4]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,7,5,4,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,4,5,6]=>[1,4,5,6,2,7,3]=>[3,7,2,6,5,4,1]=>[7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,4,6,5]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,5,4,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,5,6,4]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,6,4,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,1,6,5,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,1,5,6]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,1,6,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,5,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,5,6,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,6,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,4,6,5,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,1,4,6]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,1,6,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,4,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,4,6,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,6,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,5,6,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,1,4,5]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,1,5,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,4,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,4,5,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,5,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,5,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,5,6,7]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,5,7,6]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,6,5,7]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,6,7,5]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,7,5,6]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,2,7,6,5]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,2,6,7]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,2,7,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,6,2,7]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,6,7,2]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,7,2,6]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,5,7,6,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,2,5,7]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,2,7,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,5,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,5,7,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,7,2,5]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,6,7,5,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,2,5,6]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,2,6,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,5,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,5,6,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,6,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,6,5,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,6,5,7]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,6,7,5]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,7,5,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,1,6,7]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,1,7,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,6,1,7]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,6,7,1]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,7,1,6]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,7,6,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,1,5,7]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,1,7,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,5,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,5,7,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,7,1,5]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,7,5,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,1,5,6]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,1,6,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,5,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,5,6,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,6,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,6,5,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,2,6,7]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,2,7,6]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,6,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,6,7,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,7,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,7,6,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,1,6,7]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,1,7,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,6,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,6,7,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,7,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,2,7,6,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,1,2,7]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,1,7,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,2,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,2,7,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,7,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,7,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,1,2,6]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,1,6,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,2,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,2,6,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,6,1,2]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,6,2,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,2,5,7]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,2,7,5]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,5,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,5,7,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,7,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,1,7,5,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,1,5,7]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,1,7,5]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,5,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,5,7,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,7,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,7,5,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,1,2,7]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,1,7,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,2,1,7]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,2,7,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,7,1,2]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,7,2,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,1,2,5]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,1,5,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,2,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,2,5,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,5,1,2]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,7,5,2,1]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,2,5,6]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,2,6,5]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,5,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,5,6,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,6,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,6,5,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,1,5,6]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,1,6,5]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,5,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,5,6,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,6,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,6,5,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,1,2,6]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,1,6,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,2,1,6]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,2,6,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,6,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,5,6,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,1,2,5]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,1,5,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,2,1,5]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,2,5,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,5,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,5,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,4,6,7]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,4,7,6]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,6,4,7]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,6,7,4]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,7,4,6]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,2,7,6,4]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,2,6,7]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,2,7,6]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,6,2,7]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,6,7,2]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,7,2,6]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,7,6,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,2,4,7]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,2,7,4]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,4,2,7]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,4,7,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,7,2,4]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,6,7,4,2]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,2,4,6]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,2,6,4]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,4,2,6]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,4,6,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,6,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,7,6,4,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,4,6,7]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,4,7,6]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,6,4,7]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,6,7,4]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,7,4,6]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,1,7,6,4]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,1,6,7]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,1,7,6]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,6,1,7]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,6,7,1]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,7,1,6]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,7,6,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,1,4,7]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,1,7,4]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,4,1,7]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,4,7,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,7,1,4]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,7,4,1]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,1,4,6]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,1,6,4]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,4,1,6]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,4,6,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,6,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,6,4,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,2,6,7]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,2,7,6]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,6,2,7]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,6,7,2]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,7,2,6]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,1,7,6,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,1,6,7]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,1,7,6]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,6,1,7]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,6,7,1]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,7,1,6]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,7,6,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,1,2,7]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,1,7,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,2,1,7]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,2,7,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,7,1,2]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,6,7,2,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,1,2,6]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,1,6,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,2,1,6]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,2,6,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,6,1,2]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,7,6,2,1]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,2,4,7]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,2,7,4]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,4,2,7]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,4,7,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,7,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,1,7,4,2]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,1,4,7]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,1,7,4]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,4,1,7]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,4,7,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,7,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,7,4,1]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,1,2,7]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,1,7,2]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,2,1,7]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,2,7,1]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,7,1,2]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,4,7,2,1]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,1,2,4]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,1,4,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,2,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,2,4,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,4,1,2]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,7,4,2,1]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,2,4,6]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,2,6,4]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,4,2,6]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,4,6,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,6,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,1,6,4,2]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,1,4,6]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,1,6,4]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,4,1,6]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,4,6,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,6,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,6,4,1]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,1,2,6]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,1,6,2]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,2,1,6]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,2,6,1]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,6,1,2]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,4,6,2,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,1,2,4]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,1,4,2]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,2,1,4]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,2,4,1]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,4,1,2]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,6,4,2,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,4,5,7]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,4,7,5]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,5,4,7]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,5,7,4]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,7,4,5]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,2,7,5,4]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,2,5,7]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,2,7,5]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,5,2,7]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,5,7,2]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,7,2,5]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,4,7,5,2]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,2,4,7]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,2,7,4]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,4,2,7]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,4,7,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,7,2,4]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,7,4,2]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,2,4,5]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,2,5,4]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,4,2,5]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,4,5,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,5,2,4]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,7,5,4,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,4,5,7]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,4,7,5]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,5,4,7]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,5,7,4]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,7,4,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,7,5,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,1,5,7]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,1,7,5]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,5,1,7]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,5,7,1]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,7,1,5]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,7,5,1]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,1,4,7]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,1,7,4]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,4,1,7]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,4,7,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,7,1,4]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,7,4,1]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,1,4,5]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,1,5,4]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,4,1,5]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,4,5,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,5,1,4]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,5,4,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,2,5,7]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,2,7,5]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,5,2,7]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,5,7,2]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,7,2,5]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,7,5,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,1,5,7]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,1,7,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,5,1,7]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,5,7,1]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,7,1,5]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,7,5,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,1,2,7]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,1,7,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,2,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,2,7,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,7,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,5,7,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,1,2,5]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,1,5,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,2,1,5]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,2,5,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,5,1,2]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,5,2,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,2,4,7]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,2,7,4]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,4,2,7]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,4,7,2]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,7,2,4]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,7,4,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,1,4,7]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,1,7,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,4,1,7]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,4,7,1]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,7,1,4]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,7,4,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,1,2,7]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,1,7,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,2,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,2,7,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,7,1,2]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,4,7,2,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,1,2,4]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,1,4,2]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,2,1,4]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,2,4,1]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,4,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,7,4,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,2,4,5]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,2,5,4]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,4,2,5]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,4,5,2]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,5,2,4]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,1,5,4,2]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,1,4,5]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,1,5,4]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,4,1,5]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,4,5,1]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,5,1,4]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,2,5,4,1]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,1,2,5]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,1,5,2]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,2,1,5]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,2,5,1]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,5,1,2]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,5,2,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,1,2,4]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,1,4,2]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,2,1,4]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,2,4,1]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,4,1,2]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,5,4,2,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,4,5,6]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,4,6,5]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,5,4,6]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,5,6,4]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,6,4,5]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,6,5,4]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,2,5,6]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,2,6,5]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,5,2,6]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,5,6,2]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,6,2,5]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,6,5,2]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,2,4,6]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,2,6,4]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,4,2,6]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,4,6,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,6,2,4]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,6,4,2]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,2,4,5]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,2,5,4]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,4,2,5]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,4,5,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,5,2,4]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,4,5,6]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,4,6,5]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,5,4,6]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,5,6,4]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,6,4,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,6,5,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,1,5,6]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,1,6,5]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,5,1,6]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,5,6,1]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,6,1,5]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,6,5,1]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,1,4,6]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,1,6,4]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,4,1,6]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,4,6,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,6,1,4]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,6,4,1]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,1,4,5]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,1,5,4]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,4,1,5]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,4,5,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,5,1,4]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,5,4,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,2,5,6]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,2,6,5]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,5,2,6]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,5,6,2]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,6,2,5]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,1,6,5,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,1,5,6]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,1,6,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,5,1,6]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,5,6,1]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,6,1,5]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,6,5,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,1,2,6]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,1,6,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,2,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,2,6,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,6,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,5,6,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,1,2,5]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,1,5,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,2,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,2,5,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,5,1,2]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,5,2,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,2,4,6]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,2,6,4]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,4,2,6]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,4,6,2]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,6,2,4]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,6,4,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,1,4,6]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,1,6,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,4,1,6]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,4,6,1]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,6,1,4]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,2,6,4,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,1,2,6]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,1,6,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,2,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,2,6,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,6,1,2]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,6,2,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,1,2,4]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,1,4,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,2,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,2,4,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,4,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,6,4,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,2,4,5]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,2,5,4]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,4,2,5]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,4,5,2]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,5,2,4]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,5,4,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,1,4,5]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,1,5,4]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,4,1,5]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,4,5,1]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,5,1,4]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,5,4,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,1,2,5]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,1,5,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,2,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,2,5,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,5,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,5,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,1,2,4]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,1,4,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,2,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,2,4,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,4,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,4,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,5,6,7]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,5,7,6]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,6,5,7]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,6,7,5]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,7,5,6]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,7,6,5]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,3,6,7]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,3,7,6]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,6,3,7]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,6,7,3]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,7,3,6]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,7,6,3]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,3,5,7]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,3,7,5]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,5,3,7]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,5,7,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,7,3,5]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,6,7,5,3]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,3,5,6]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,3,6,5]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,5,3,6]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,5,6,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,6,3,5]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,6,5,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,5,6,7]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,5,7,6]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,6,5,7]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,6,7,5]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,7,5,6]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,7,6,5]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,2,6,7]=>[1,3,5,2,6,7,4]=>[4,7,6,2,5,3,1]=>[7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,2,7,6]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,6,2,7]=>[1,3,5,6,2,7,4]=>[4,7,2,6,5,3,1]=>[7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,6,7,2]=>[1,3,5,6,7,2,4]=>[4,2,7,6,5,3,1]=>[7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,7,2,6]=>[1,3,5,7,2,6,4]=>[4,6,2,7,5,3,1]=>[7,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,7,6,2]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,2,5,7]=>[1,3,6,2,5,7,4]=>[4,7,5,2,6,3,1]=>[7,4,6,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,2,7,5]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,5,2,7]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,5,7,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,7,2,5]=>[1,3,6,7,2,5,4]=>[4,5,2,7,6,3,1]=>[7,3,6,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,7,5,2]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,2,5,6]=>[1,3,7,2,5,6,4]=>[4,6,5,2,7,3,1]=>[7,4,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,2,6,5]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,5,2,6]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,5,6,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,6,2,5]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,6,5,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,3,6,7]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,3,7,6]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,6,3,7]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,6,7,3]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,7,3,6]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,7,6,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,2,6,7]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,2,7,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,6,2,7]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,6,7,2]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,7,2,6]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,3,7,6,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,2,3,7]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,2,7,3]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,3,2,7]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,3,7,2]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,7,2,3]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,7,3,2]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,2,3,6]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,2,6,3]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,3,2,6]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,3,6,2]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,6,2,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,6,3,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,3,5,7]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,3,7,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,5,3,7]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,5,7,3]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,7,3,5]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,2,7,5,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,2,5,7]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,2,7,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,5,2,7]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,5,7,2]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,7,2,5]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,7,5,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,2,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,2,7,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,3,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,3,7,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,7,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,7,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,2,3,5]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,2,5,3]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,3,2,5]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,3,5,2]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,5,2,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,5,3,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,3,5,6]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,3,6,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,5,3,6]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,5,6,3]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,6,3,5]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,6,5,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,2,5,6]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,2,6,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,5,2,6]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,5,6,2]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,6,2,5]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,6,5,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,2,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,2,6,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,3,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,3,6,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,6,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,6,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,2,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,2,5,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,3,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,3,5,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,5,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,5,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,5,6,7]=>[1,3,5,6,7,2,4]=>[4,2,7,6,5,3,1]=>[7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,5,7,6]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,6,5,7]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,6,7,5]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,7,5,6]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,7,6,5]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,3,6,7]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,3,7,6]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,6,3,7]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,6,7,3]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,7,3,6]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,7,6,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,3,5,7]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,3,7,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,5,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,5,7,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,7,3,5]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,7,5,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,3,5,6]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,3,6,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,5,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,5,6,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,6,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,7,6,5,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,5,6,7]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,5,7,6]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,6,5,7]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,6,7,5]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,7,5,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,1,6,7]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,1,7,6]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,6,1,7]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,6,7,1]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,7,1,6]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,5,7,6,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,1,5,7]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,1,7,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,5,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,5,7,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,7,1,5]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,7,5,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,1,5,6]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,1,6,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,5,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,5,6,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,6,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,6,5,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,3,6,7]=>[1,3,6,7,2,5,4]=>[4,5,2,7,6,3,1]=>[7,3,6,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,3,7,6]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,6,3,7]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,6,7,3]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,7,3,6]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,7,6,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,1,6,7]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,1,7,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,6,1,7]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,6,7,1]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,7,1,6]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,3,7,6,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,1,3,7]=>[1,3,7,2,5,6,4]=>[4,6,5,2,7,3,1]=>[7,4,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,1,7,3]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,3,1,7]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,3,7,1]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,7,1,3]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,7,3,1]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,1,3,6]=>[1,3,6,2,5,7,4]=>[4,7,5,2,6,3,1]=>[7,4,6,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,1,6,3]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,3,1,6]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,3,6,1]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,6,1,3]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,6,3,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,3,5,7]=>[1,3,5,7,2,6,4]=>[4,6,2,7,5,3,1]=>[7,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,3,7,5]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,5,3,7]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,5,7,3]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,7,3,5]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,1,7,5,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,1,5,7]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,1,7,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,5,1,7]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,5,7,1]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,7,1,5]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,7,5,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,1,3,7]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,1,7,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,3,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,3,7,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,7,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,5,7,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,1,3,5]=>[1,3,5,2,6,7,4]=>[4,7,6,2,5,3,1]=>[7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,1,5,3]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,3,1,5]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,3,5,1]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,5,1,3]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,7,5,3,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,3,5,6]=>[1,3,5,6,2,7,4]=>[4,7,2,6,5,3,1]=>[7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,3,6,5]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,5,3,6]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,6,3,5]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,1,5,6]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,1,6,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,5,1,6]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,5,6,1]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,6,1,5]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,3,6,5,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,1,3,6]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,1,6,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,3,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,3,6,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,6,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,6,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,1,3,5]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,1,5,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,3,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,3,5,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,5,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,5,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,5,6,7]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,5,7,6]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,6,5,7]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,6,7,5]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,7,5,6]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,2,7,6,5]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,2,6,7]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,2,7,6]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,6,2,7]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,6,7,2]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,7,2,6]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,7,6,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,2,5,7]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,2,7,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,5,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,5,7,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,7,2,5]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,6,7,5,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,2,5,6]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,2,6,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,5,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,5,6,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,6,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,6,5,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,6,5,7]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,6,7,5]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,7,5,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,1,6,7]=>[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,1,7,6]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,6,1,7]=>[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,6,7,1]=>[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,7,1,6]=>[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,5,7,6,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,1,5,7]=>[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,1,7,5]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,5,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,5,7,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,7,1,5]=>[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,6,7,5,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,1,5,6]=>[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,1,6,5]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,5,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,5,6,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,6,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,7,6,5,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,2,6,7]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,2,7,6]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,6,2,7]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,6,7,2]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,7,2,6]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,1,7,6,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,1,6,7]=>[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,1,7,6]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,6,1,7]=>[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,6,7,1]=>[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,7,1,6]=>[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,2,7,6,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,1,2,7]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,1,7,2]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,2,1,7]=>[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,2,7,1]=>[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,7,1,2]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,7,2,1]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,1,2,6]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,1,6,2]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,2,1,6]=>[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,2,6,1]=>[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,6,1,2]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,6,2,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,2,5,7]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,2,7,5]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,5,2,7]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,5,7,2]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,7,2,5]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,1,7,5,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,1,5,7]=>[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,1,7,5]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,5,1,7]=>[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,5,7,1]=>[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,7,1,5]=>[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,7,5,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,1,2,7]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,1,7,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,2,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,2,7,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,7,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,7,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,1,2,5]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,1,5,2]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,2,1,5]=>[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,2,5,1]=>[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,5,1,2]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,5,2,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,2,5,6]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,2,6,5]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,5,2,6]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,5,6,2]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,6,2,5]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,1,6,5,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,1,5,6]=>[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,1,6,5]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,5,1,6]=>[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,5,6,1]=>[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,6,1,5]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,6,5,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,1,2,6]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,1,6,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,2,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,2,6,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,6,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,5,6,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,1,2,5]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,1,5,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,2,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,2,5,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,5,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,5,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,3,6,7]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,3,7,6]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,6,3,7]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,6,7,3]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,7,3,6]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,2,7,6,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,2,6,7]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,2,7,6]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,6,2,7]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,6,7,2]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,7,2,6]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,7,6,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,2,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,2,7,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,3,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,3,7,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,7,2,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,6,7,3,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,2,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,2,6,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,3,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,3,6,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,6,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,7,6,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,3,6,7]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,3,7,6]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,6,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,6,7,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,7,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,7,6,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,1,6,7]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,1,7,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,6,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,6,7,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,7,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,7,6,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,1,3,7]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,1,7,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,3,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,3,7,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,7,1,3]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,7,3,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,1,3,6]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,1,6,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,3,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,3,6,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,6,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,6,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,2,6,7]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,2,7,6]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,6,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,6,7,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,7,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,7,6,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,6,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,6,7,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,7,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,2,7,6,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,1,2,7]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,1,7,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,2,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,2,7,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,7,1,2]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,7,2,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,1,2,6]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,1,6,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,2,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,2,6,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,6,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,7,6,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,2,3,7]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,2,7,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,3,2,7]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,3,7,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,7,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,1,7,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,1,3,7]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,1,7,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,3,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,3,7,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,7,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,2,7,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,1,2,7]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,1,7,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,2,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,2,7,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,7,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,3,7,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,1,2,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,1,3,2]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,2,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,2,3,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,3,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,2,3,6]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,2,6,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,3,2,6]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,3,6,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,6,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,1,6,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,1,3,6]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,1,6,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,3,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,3,6,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,6,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,6,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,1,2,6]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,1,6,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,2,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,2,6,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,6,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,3,6,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,1,2,3]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,1,3,2]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,2,1,3]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,2,3,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,3,1,2]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,3,2,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,3,5,7]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,3,7,5]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,5,3,7]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,5,7,3]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,7,3,5]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,7,5,3]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,2,5,7]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,2,7,5]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,5,2,7]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,5,7,2]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,7,2,5]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,7,5,2]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,2,3,7]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,2,7,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,3,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,3,7,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,7,2,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,5,7,3,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,2,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,2,5,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,3,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,3,5,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,5,2,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,7,5,3,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,3,5,7]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,3,7,5]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,5,3,7]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,5,7,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,7,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,7,5,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,1,5,7]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,1,7,5]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,5,1,7]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,5,7,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,7,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,3,7,5,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,1,3,7]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,1,7,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,3,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,3,7,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,7,1,3]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,5,7,3,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,1,3,5]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,1,5,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,3,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,3,5,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,5,1,3]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,7,5,3,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,2,5,7]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,2,7,5]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,5,7,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,7,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,7,5,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,1,5,7]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,1,7,5]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,5,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,5,7,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,7,5,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,1,2,7]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,1,7,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,2,1,7]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,2,7,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,7,1,2]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,5,7,2,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,1,2,5]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,1,5,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,2,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,2,5,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,5,1,2]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,5,2,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,2,3,7]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,2,7,3]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,3,2,7]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,3,7,2]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,7,2,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,1,7,3,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,1,3,7]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,1,7,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,3,1,7]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,3,7,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,7,1,3]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,7,3,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,1,2,7]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,1,7,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,2,1,7]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,2,7,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,7,1,2]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,3,7,2,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,1,2,3]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,1,3,2]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,2,1,3]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,2,3,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,3,1,2]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,7,3,2,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,2,3,5]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,2,5,3]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,3,2,5]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,3,5,2]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,5,2,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,1,5,3,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,1,3,5]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,1,5,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,3,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,3,5,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,5,1,3]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,5,3,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,1,2,5]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,1,5,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,2,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,2,5,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,5,1,2]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,3,5,2,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,1,2,3]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,1,3,2]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,2,1,3]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,2,3,1]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,3,1,2]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,3,2,1]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,3,5,6]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,3,6,5]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,5,3,6]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,5,6,3]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,6,3,5]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,6,5,3]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,2,5,6]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,2,6,5]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,5,2,6]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,5,6,2]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,6,2,5]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,3,6,5,2]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,2,3,6]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,2,6,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,3,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,3,6,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,6,2,3]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,5,6,3,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,2,3,5]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,2,5,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,3,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,3,5,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,5,2,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,5,3,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,3,5,6]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,3,6,5]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,5,3,6]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,5,6,3]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,6,3,5]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,1,6,5,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,1,5,6]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,1,6,5]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,5,1,6]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,5,6,1]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,6,1,5]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,6,5,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,1,3,6]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,1,6,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,3,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,3,6,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,6,1,3]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,6,3,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,1,3,5]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,1,5,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,3,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,3,5,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,5,1,3]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,5,3,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,2,5,6]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,2,6,5]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,5,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,5,6,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,6,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,1,5,6]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,1,6,5]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,5,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,5,6,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,6,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,6,5,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,1,2,6]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,1,6,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,2,1,6]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,2,6,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,6,1,2]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,6,2,1]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,1,2,5]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,1,5,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,2,1,5]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,2,5,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,5,1,2]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,5,2,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,2,3,6]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,2,6,3]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,3,2,6]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,3,6,2]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,6,2,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,6,3,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,1,3,6]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,1,6,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,3,1,6]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,3,6,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,6,1,3]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,2,6,3,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,1,2,6]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,1,6,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,2,1,6]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,2,6,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,6,1,2]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,6,2,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,1,2,3]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,1,3,2]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,2,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,2,3,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,3,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,3,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,2,3,5]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,2,5,3]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,3,2,5]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,3,5,2]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,5,2,3]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,1,3,5]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,1,5,3]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,3,1,5]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,3,5,1]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,5,1,3]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,5,3,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,1,2,5]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,1,5,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,2,1,5]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,2,5,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,5,1,2]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,5,2,1]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,1,2,3]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,1,3,2]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,2,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,2,3,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,3,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,5,3,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,4,6,7]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,4,7,6]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,6,4,7]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,6,7,4]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,7,4,6]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,3,7,6,4]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,3,6,7]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,3,7,6]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,6,3,7]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,6,7,3]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,7,3,6]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,4,7,6,3]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,3,4,7]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,3,7,4]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,4,3,7]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,4,7,3]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,7,3,4]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,7,4,3]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,3,4,6]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,3,6,4]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,4,3,6]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,4,6,3]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,6,3,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,7,6,4,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,4,6,7]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,4,7,6]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,6,4,7]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,6,7,4]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,7,4,6]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,7,6,4]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,2,6,7]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[7,4,6,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,2,7,6]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,6,2,7]=>[1,3,4,6,2,7,5]=>[5,7,2,6,4,3,1]=>[7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,6,7,2]=>[1,3,4,6,7,2,5]=>[5,2,7,6,4,3,1]=>[7,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,7,2,6]=>[1,3,4,7,2,6,5]=>[5,6,2,7,4,3,1]=>[7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,7,6,2]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,2,4,7]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,2,7,4]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,4,2,7]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,4,7,2]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,7,2,4]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,6,7,4,2]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,2,4,6]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,2,6,4]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,4,2,6]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,4,6,2]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,6,2,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,7,6,4,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,3,6,7]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,3,7,6]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,6,3,7]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,6,7,3]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,7,3,6]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,7,6,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,2,6,7]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,2,7,6]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,6,2,7]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,6,7,2]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,7,2,6]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,7,6,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,2,3,7]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,2,7,3]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,3,2,7]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,3,7,2]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,7,2,3]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,7,3,2]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,2,3,6]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,2,6,3]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,3,2,6]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,3,6,2]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,6,2,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,7,6,3,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,3,4,7]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,3,7,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,4,3,7]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,4,7,3]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,7,3,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,2,7,4,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,2,4,7]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,2,7,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,4,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,4,7,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,7,2,4]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,7,4,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,2,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,2,7,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,3,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,3,7,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,7,2,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,7,3,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,2,3,4]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,2,4,3]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,3,2,4]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,3,4,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,4,2,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,7,4,3,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,3,4,6]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,3,6,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,4,3,6]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,4,6,3]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,6,3,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,6,4,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,2,4,6]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,2,6,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,4,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,4,6,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,6,2,4]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,6,4,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,2,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,2,6,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,3,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,3,6,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,6,2,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,6,3,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,2,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,2,4,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,3,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,3,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,4,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,4,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,4,6,7]=>[1,3,4,6,7,2,5]=>[5,2,7,6,4,3,1]=>[7,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,4,7,6]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,6,4,7]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,6,7,4]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,7,4,6]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,3,7,6,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,3,6,7]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,3,7,6]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,6,3,7]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,6,7,3]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,7,3,6]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,7,6,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,3,4,7]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,3,7,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,4,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,4,7,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,7,3,4]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,7,4,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,3,4,6]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,3,6,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,4,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,4,6,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,6,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,7,6,4,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,4,6,7]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,4,7,6]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,6,4,7]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,6,7,4]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,7,4,6]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,1,7,6,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,6,1,7]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,6,7,1]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,7,1,6]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,7,6,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,1,4,7]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,1,7,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,4,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,4,7,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,7,1,4]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,6,7,4,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,1,4,6]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,4,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,4,6,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,6,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,7,6,4,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,3,6,7]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,3,7,6]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,6,3,7]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,6,7,3]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,7,3,6]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,7,6,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,1,6,7]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,1,7,6]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,6,1,7]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,6,7,1]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,7,1,6]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,3,7,6,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,1,3,7]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,1,7,3]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,3,1,7]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,3,7,1]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,7,1,3]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,6,7,3,1]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,1,3,6]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,1,6,3]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,3,1,6]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,3,6,1]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,6,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,6,3,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,3,4,7]=>[1,3,4,7,2,6,5]=>[5,6,2,7,4,3,1]=>[7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,3,7,4]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,4,3,7]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,4,7,3]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,7,3,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,1,7,4,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,1,4,7]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,1,7,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,4,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,4,7,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,7,1,4]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,3,7,4,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,1,3,7]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,1,7,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,3,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,3,7,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,7,1,3]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,4,7,3,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,1,3,4]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[7,4,6,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,1,4,3]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,3,1,4]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,3,4,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,4,1,3]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,6,7,4,3,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,3,4,6]=>[1,3,4,6,2,7,5]=>[5,7,2,6,4,3,1]=>[7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,3,6,4]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,4,3,6]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,4,6,3]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,6,3,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,6,4,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,1,4,6]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,1,6,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,4,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,4,6,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,6,1,4]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,3,6,4,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,1,3,6]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,3,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,3,6,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,6,1,3]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,6,3,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,1,3,4]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,1,4,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,3,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,3,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,4,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,6,4,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,4,6,7]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,4,7,6]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,6,4,7]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,6,7,4]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,7,4,6]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,7,6,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,2,6,7]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,2,7,6]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,6,2,7]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,6,7,2]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,7,2,6]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,4,7,6,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,2,4,7]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,2,7,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,4,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,4,7,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,7,2,4]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,6,7,4,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,2,4,6]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,2,6,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,4,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,4,6,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,6,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,7,6,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,4,6,7]=>[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,4,7,6]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,6,4,7]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,6,7,4]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,7,4,6]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,1,7,6,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,1,6,7]=>[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,1,7,6]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,6,1,7]=>[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,6,7,1]=>[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,7,1,6]=>[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,7,6,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,1,4,7]=>[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,1,7,4]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,4,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,4,7,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,7,1,4]=>[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,6,7,4,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,1,4,6]=>[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,4,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,4,6,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,6,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,7,6,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,2,6,7]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,2,7,6]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,6,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,6,7,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,7,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,1,7,6,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,1,6,7]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,1,7,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,6,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,6,7,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,7,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,2,7,6,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,1,2,7]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,1,7,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,2,1,7]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,2,7,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,7,1,2]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,6,7,2,1]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,1,2,6]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,1,6,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,2,1,6]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,2,6,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,6,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,6,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,2,4,7]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,2,7,4]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,4,2,7]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,4,7,2]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,7,2,4]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,1,7,4,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,1,4,7]=>[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,1,7,4]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,4,1,7]=>[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,4,7,1]=>[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,7,1,4]=>[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,7,4,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,1,2,7]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,1,7,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,2,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,2,7,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,7,1,2]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,4,7,2,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,1,2,4]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,1,4,2]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,2,1,4]=>[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,2,4,1]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,4,1,2]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,7,4,2,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,2,4,6]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,2,6,4]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,4,2,6]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,4,6,2]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,6,2,4]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,1,6,4,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,1,4,6]=>[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,1,6,4]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,4,1,6]=>[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,4,6,1]=>[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,6,1,4]=>[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,6,4,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,1,2,6]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,1,6,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,2,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,2,6,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,6,1,2]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,4,6,2,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,1,2,4]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,1,4,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,2,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,2,4,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,4,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,6,4,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,3,6,7]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,3,7,6]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,6,3,7]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,6,7,3]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,7,3,6]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,7,6,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,2,6,7]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,2,7,6]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,6,2,7]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,6,7,2]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,7,2,6]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,3,7,6,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,2,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,2,7,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,3,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,3,7,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,7,2,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,6,7,3,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,2,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,2,6,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,3,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,3,6,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,6,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,7,6,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,3,6,7]=>[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,3,7,6]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,6,3,7]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,6,7,3]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,7,3,6]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,1,7,6,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,1,6,7]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,1,7,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,6,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,6,7,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,7,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,7,6,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,1,3,7]=>[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,1,7,3]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,3,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,3,7,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,7,1,3]=>[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,7,3,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,1,3,6]=>[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,1,6,3]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,3,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,3,6,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,6,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,6,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,2,6,7]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,2,7,6]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,6,2,7]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,6,7,2]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,7,2,6]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,7,6,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,6,1,7]=>[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,6,7,1]=>[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,7,1,6]=>[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,7,6,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,1,2,7]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,1,7,2]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,2,1,7]=>[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,2,7,1]=>[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,7,1,2]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,6,7,2,1]=>[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,1,2,6]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,1,6,2]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,2,1,6]=>[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,2,6,1]=>[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,6,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,6,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,2,3,7]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,2,7,3]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,3,2,7]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,3,7,2]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,7,2,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,1,7,3,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,1,3,7]=>[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,1,7,3]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,3,1,7]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,3,7,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,7,1,3]=>[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,2,7,3,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,1,2,7]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,1,7,2]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,2,1,7]=>[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,2,7,1]=>[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,7,1,2]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,7,2,1]=>[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,1,2,3]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,1,3,2]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,2,1,3]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,2,3,1]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,3,1,2]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,7,3,2,1]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,2,3,6]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,2,6,3]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,3,2,6]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,3,6,2]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,6,2,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,6,3,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,1,3,6]=>[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,3,1,6]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,3,6,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,6,1,3]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,6,3,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,1,2,6]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,1,6,2]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,2,1,6]=>[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,2,6,1]=>[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,6,1,2]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,6,2,1]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,1,2,3]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,1,3,2]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,2,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,2,3,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,3,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,6,3,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,3,4,7]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,3,7,4]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,4,3,7]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,4,7,3]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,7,3,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,7,4,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,2,4,7]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,2,7,4]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,4,2,7]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,4,7,2]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,7,2,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,3,7,4,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,2,3,7]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,2,7,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,3,2,7]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,3,7,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,7,2,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,7,3,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,2,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,2,4,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,3,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,3,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,4,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,7,4,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,3,4,7]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,3,7,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,4,3,7]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,4,7,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,7,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,7,4,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,1,4,7]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,1,7,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,4,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,4,7,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,7,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,7,4,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,1,3,7]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,1,7,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,3,1,7]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,3,7,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,7,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,7,3,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,1,3,4]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,1,4,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,3,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,3,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,4,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,7,4,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,2,4,7]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,2,7,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,4,2,7]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,4,7,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,7,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,7,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,1,4,7]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,1,7,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,4,1,7]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,4,7,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,7,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,2,7,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,1,2,7]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,1,7,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,2,7,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,7,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,7,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,1,2,4]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,1,4,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,2,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,2,4,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,4,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,7,4,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,2,3,7]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,2,7,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,3,2,7]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,3,7,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,7,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,7,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,1,3,7]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,1,7,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,3,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,3,7,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,7,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,2,7,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,1,2,7]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,1,7,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,2,7,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,7,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,7,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,1,2,3]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,1,3,2]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,2,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,2,3,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,3,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,3,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,2,4,3]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,3,2,4]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,3,4,2]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,4,2,3]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,4,3,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,1,3,4]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,1,4,3]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,3,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,3,4,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,4,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,2,4,3,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,1,2,4]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,1,4,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,2,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,2,4,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,4,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,4,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,1,3,2]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,2,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,2,3,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,3,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,3,4,6]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,3,6,4]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,4,3,6]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,4,6,3]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,6,3,4]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,6,4,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,2,4,6]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,2,6,4]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,4,2,6]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,4,6,2]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,6,2,4]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,3,6,4,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,2,3,6]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,2,6,3]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,3,2,6]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,3,6,2]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,6,2,3]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,4,6,3,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,2,3,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,2,4,3]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,3,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,3,4,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,4,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,4,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,3,4,6]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,3,6,4]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,4,3,6]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,4,6,3]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,6,3,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,6,4,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,1,4,6]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,1,6,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,4,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,4,6,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,6,1,4]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,3,6,4,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,1,3,6]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,1,6,3]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,3,1,6]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,3,6,1]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,6,1,3]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,4,6,3,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,1,3,4]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,1,4,3]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,3,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,3,4,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,4,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,6,4,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,2,4,6]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,2,6,4]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,4,2,6]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,4,6,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,6,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,6,4,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,1,4,6]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,1,6,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,4,1,6]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,4,6,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,6,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,6,4,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,1,2,6]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,1,6,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,2,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,2,6,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,6,1,2]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,6,2,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,1,2,4]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,1,4,2]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,2,1,4]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,2,4,1]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,4,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,4,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,2,3,6]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,2,6,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,3,2,6]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,3,6,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,6,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,6,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,1,3,6]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,1,6,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,3,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,3,6,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,6,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,2,6,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,1,2,6]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,1,6,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,2,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,2,6,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,6,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,6,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,1,2,3]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,1,3,2]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,2,1,3]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,2,3,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,3,1,2]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,6,3,2,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,2,3,4]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,2,4,3]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,3,2,4]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,3,4,2]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,4,2,3]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,4,3,2]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,1,3,4]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,1,4,3]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,3,1,4]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,3,4,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,4,1,3]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,4,3,1]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,1,2,4]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,1,4,2]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,2,1,4]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,2,4,1]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,4,1,2]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,4,2,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,1,2,3]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,1,3,2]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,2,1,3]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,2,3,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,3,1,2]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,3,2,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,4,5,7]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,4,7,5]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,5,4,7]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,5,7,4]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,7,4,5]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,7,5,4]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,3,5,7]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,3,7,5]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,5,3,7]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,5,7,3]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,7,3,5]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,4,7,5,3]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,3,4,7]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,3,7,4]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,4,3,7]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,4,7,3]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,7,3,4]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,5,7,4,3]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,3,4,5]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,3,5,4]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,4,3,5]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,4,5,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,5,3,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,5,4,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,4,5,7]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,4,7,5]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,5,4,7]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,5,7,4]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,7,4,5]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,2,7,5,4]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,2,5,7]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,2,7,5]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,5,2,7]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[7,3,6,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,5,7,2]=>[1,3,4,5,7,2,6]=>[6,2,7,5,4,3,1]=>[7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,7,2,5]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,7,5,2]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,2,4,7]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,2,7,4]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,4,2,7]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,4,7,2]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,7,2,4]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,7,4,2]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,2,4,5]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,2,5,4]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,4,2,5]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,4,5,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,5,2,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,5,4,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,3,5,7]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,3,7,5]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,5,3,7]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,5,7,3]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,7,3,5]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,2,7,5,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,2,5,7]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,2,7,5]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,5,2,7]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,5,7,2]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,7,2,5]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,3,7,5,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,2,3,7]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,2,7,3]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,3,2,7]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,3,7,2]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,7,2,3]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,7,3,2]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,2,3,5]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,2,5,3]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,3,2,5]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,3,5,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,5,2,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,5,3,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,3,4,7]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,3,7,4]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,4,3,7]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,4,7,3]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,7,3,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,7,4,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,2,4,7]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,2,7,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,4,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,4,7,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,7,2,4]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,3,7,4,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,2,3,7]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,2,7,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,3,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,3,7,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,7,2,3]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,4,7,3,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,2,3,4]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,2,4,3]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,3,2,4]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,3,4,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,4,2,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,4,3,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,3,4,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,3,5,4]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,4,3,5]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,4,5,3]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,5,3,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,5,4,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,2,4,5]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,2,5,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,4,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,4,5,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,5,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,3,5,4,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,2,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,2,5,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,3,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,3,5,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,5,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,5,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,2,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,2,4,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,3,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,3,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,4,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,4,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,4,5,7]=>[1,3,4,5,7,2,6]=>[6,2,7,5,4,3,1]=>[7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,4,7,5]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,5,4,7]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,5,7,4]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,7,4,5]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,3,7,5,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,3,5,7]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,3,7,5]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,5,3,7]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,5,7,3]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,7,3,5]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,4,7,5,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,3,4,7]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,3,7,4]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,4,3,7]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,4,7,3]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,7,3,4]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,7,4,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,3,4,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,3,5,4]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,4,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,4,5,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,5,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,5,4,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,4,5,7]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,4,7,5]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,5,4,7]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,5,7,4]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,7,4,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,7,5,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,1,5,7]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,1,7,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,5,7,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,4,7,5,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,1,4,7]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,1,7,4]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,4,1,7]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,4,7,1]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,7,1,4]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,5,7,4,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,1,4,5]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,1,5,4]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,4,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,4,5,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,5,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,7,5,4,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,3,5,7]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,3,7,5]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,5,3,7]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,5,7,3]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,7,3,5]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,1,7,5,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,1,5,7]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,1,7,5]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,5,1,7]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,5,7,1]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,7,1,5]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,7,5,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,1,3,7]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,1,7,3]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,3,1,7]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,3,7,1]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,7,1,3]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,5,7,3,1]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,1,3,5]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,1,5,3]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,3,1,5]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,3,5,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,5,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,7,5,3,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,3,4,7]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,3,7,4]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,4,3,7]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,4,7,3]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,7,3,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,7,4,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,1,4,7]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,1,7,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,4,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,4,7,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,7,1,4]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,3,7,4,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,1,3,7]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,1,7,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,3,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,3,7,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,7,1,3]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,4,7,3,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,1,3,4]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,1,4,3]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,3,1,4]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,3,4,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,4,1,3]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,7,4,3,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,3,4,5]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[7,3,6,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,3,5,4]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,4,3,5]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,4,5,3]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,5,3,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,5,4,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,1,4,5]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,1,5,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,4,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,4,5,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,5,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,3,5,4,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,1,3,5]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,1,5,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,3,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,3,5,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,5,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,5,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,1,3,4]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,1,4,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,3,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,3,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,4,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,5,4,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,4,5,7]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,4,7,5]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,5,4,7]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,5,7,4]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,7,4,5]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,2,7,5,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,2,5,7]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,2,7,5]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,5,2,7]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,5,7,2]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,7,2,5]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,7,5,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,2,4,7]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,2,7,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,4,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,4,7,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,7,2,4]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,5,7,4,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,2,4,5]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,2,5,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,4,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,4,5,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,5,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,5,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,4,5,7]=>[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,4,7,5]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,5,4,7]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,5,7,4]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,7,4,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,7,5,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,1,5,7]=>[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,1,7,5]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,5,1,7]=>[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,5,7,1]=>[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,7,1,5]=>[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,4,7,5,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,1,4,7]=>[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,1,7,4]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,4,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,4,7,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,7,1,4]=>[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,5,7,4,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,1,4,5]=>[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,1,5,4]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,4,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,4,5,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,5,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,7,5,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,2,5,7]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,2,7,5]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,5,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,5,7,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,7,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,1,7,5,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,1,5,7]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,1,7,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,5,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,5,7,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,7,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,2,7,5,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,1,2,7]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,1,7,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,2,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,2,7,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,7,1,2]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,5,7,2,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,1,2,5]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,1,5,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,2,1,5]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,2,5,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,5,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,5,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,2,4,7]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,2,7,4]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,4,2,7]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,4,7,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,7,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,7,4,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,1,4,7]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,1,7,4]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,4,1,7]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,4,7,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,7,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,7,4,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,1,2,7]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,1,7,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,2,1,7]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,2,7,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,7,1,2]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,7,2,1]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,1,2,4]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,1,4,2]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,2,1,4]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,2,4,1]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,4,1,2]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,7,4,2,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,2,4,5]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,2,5,4]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,4,2,5]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,4,5,2]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,5,2,4]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,1,5,4,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,1,4,5]=>[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,1,5,4]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,4,1,5]=>[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,4,5,1]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,5,1,4]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,2,5,4,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,1,2,5]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,1,5,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,2,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,2,5,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,5,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,5,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,1,2,4]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,1,4,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,2,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,2,4,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,4,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,4,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,3,5,7]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,3,7,5]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,5,3,7]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,5,7,3]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,7,3,5]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,7,5,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,2,5,7]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,2,7,5]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,5,2,7]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,5,7,2]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,7,2,5]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,7,5,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,2,3,7]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,2,7,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,3,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,3,7,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,7,2,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,5,7,3,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,2,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,2,5,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,3,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,3,5,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,5,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,5,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,3,5,7]=>[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,3,7,5]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,5,3,7]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,5,7,3]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,7,3,5]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,7,5,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,1,5,7]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,1,7,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,5,1,7]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,5,7,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,7,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,7,5,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,1,3,7]=>[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,1,7,3]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,3,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,3,7,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,7,1,3]=>[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,7,3,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,1,3,5]=>[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,1,5,3]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,3,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,3,5,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,5,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,5,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,2,5,7]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,2,7,5]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,5,7,2]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,7,2,5]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,7,5,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,1,5,7]=>[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,1,7,5]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,5,1,7]=>[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,5,7,1]=>[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,2,7,5,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,1,2,7]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,1,7,2]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,2,1,7]=>[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,2,7,1]=>[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,7,1,2]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,5,7,2,1]=>[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,1,2,5]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,1,5,2]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,2,1,5]=>[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,2,5,1]=>[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,5,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,7,5,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,2,3,7]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,2,7,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,3,2,7]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,3,7,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,7,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,7,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,1,3,7]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,1,7,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,3,7,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,7,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,2,7,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,1,2,7]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,1,7,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,2,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,2,7,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,7,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,7,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,1,2,3]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,1,3,2]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,2,1,3]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,2,3,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,3,1,2]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,7,3,2,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,2,3,5]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,2,5,3]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,3,2,5]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,3,5,2]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,5,2,3]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,5,3,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,1,3,5]=>[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,1,5,3]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,3,1,5]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,3,5,1]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,5,1,3]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,5,3,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,1,2,5]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,1,5,2]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,2,1,5]=>[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,2,5,1]=>[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,5,1,2]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,5,2,1]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,1,2,3]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,1,3,2]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,2,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,2,3,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,3,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,5,3,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,3,4,7]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,3,7,4]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,4,3,7]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,4,7,3]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,7,3,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,7,4,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,2,4,7]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,2,7,4]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,4,2,7]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,4,7,2]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,7,2,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,7,4,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,2,3,7]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,2,7,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,3,2,7]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,3,7,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,7,2,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,4,7,3,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,2,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,2,4,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,3,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,3,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,4,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,4,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,3,4,7]=>[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,3,7,4]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,4,3,7]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,4,7,3]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,7,3,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,1,7,4,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,1,4,7]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,1,7,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,4,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,4,7,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,7,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,7,4,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,1,3,7]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,1,7,3]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,3,1,7]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,3,7,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,7,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,7,3,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,1,3,4]=>[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,1,4,3]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,3,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,3,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,4,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,4,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,2,4,7]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,2,7,4]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,4,2,7]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,4,7,2]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,7,2,4]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,1,7,4,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,1,4,7]=>[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,1,7,4]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,4,1,7]=>[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,4,7,1]=>[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,7,1,4]=>[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,2,7,4,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,1,2,7]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,1,7,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,2,7,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,7,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,4,7,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,1,2,4]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,1,4,2]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,2,1,4]=>[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,2,4,1]=>[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,4,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,3,7,4,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,2,3,7]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,2,7,3]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,3,2,7]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,3,7,2]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,7,2,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,1,7,3,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,1,3,7]=>[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,1,7,3]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,3,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,3,7,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,7,1,3]=>[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,7,3,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,1,2,7]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,1,7,2]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,2,7,1]=>[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,7,1,2]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,7,2,1]=>[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,1,2,3]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,1,3,2]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,2,1,3]=>[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,2,3,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,3,1,2]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,7,3,2,1]=>[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,2,3,4]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,2,4,3]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,3,2,4]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,3,4,2]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,4,2,3]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,1,4,3,2]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,1,3,4]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,1,4,3]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,3,1,4]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,3,4,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,4,1,3]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,4,3,1]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,1,2,4]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,1,4,2]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,2,1,4]=>[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,2,4,1]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,4,1,2]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,3,4,2,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,1,2,3]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,1,3,2]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,2,1,3]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,2,3,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,3,1,2]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,3,2,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,3,5,4]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,4,3,5]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,4,5,3]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,5,3,4]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,5,4,3]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,2,4,5]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,2,5,4]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,4,2,5]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,4,5,2]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,5,2,4]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,5,4,2]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,2,3,5]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,2,5,3]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,3,2,5]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,3,5,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,5,2,3]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,5,3,2]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,2,3,4]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,2,4,3]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,3,2,4]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,3,4,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,4,2,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,4,3,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,3,4,5]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,3,5,4]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,4,3,5]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,4,5,3]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,5,3,4]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,1,5,4,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,1,4,5]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,1,5,4]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,4,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,4,5,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,5,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,5,4,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,1,3,5]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,1,5,3]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,3,1,5]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,3,5,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,5,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,5,3,1]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,1,3,4]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,1,4,3]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,3,1,4]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,3,4,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,4,1,3]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,4,3,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,2,4,5]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,2,5,4]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,4,2,5]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,4,5,2]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,5,2,4]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,1,5,4,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,1,4,5]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,1,5,4]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,4,1,5]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,4,5,1]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,5,1,4]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,2,5,4,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,1,2,5]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,1,5,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,2,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,2,5,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,1,2,4]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,1,4,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,2,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,2,4,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,4,1,2]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,3,5,4,2,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,2,3,5]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,2,5,3]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,3,2,5]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,3,5,2]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,5,2,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,1,5,3,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,1,3,5]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,1,5,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,3,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,3,5,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,5,1,3]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,2,5,3,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,1,2,5]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,1,5,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,2,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,2,5,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,5,1,2]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,3,5,2,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,1,3,2]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,2,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,2,3,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,3,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,4,5,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,2,3,4]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,2,4,3]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,3,2,4]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,3,4,2]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,4,2,3]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,4,3,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,1,3,4]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,1,4,3]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,3,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,4,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,4,3,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,1,2,4]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,1,4,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,2,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,2,4,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,4,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,3,4,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,1,2,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,1,3,2]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,2,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,2,3,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,4,6,5]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,5,4,6]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,5,6,4]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,6,4,5]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,6,5,4]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,3,5,6]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,3,6,5]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,5,3,6]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,5,6,3]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,6,3,5]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,6,5,3]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,3,4,6]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,3,6,4]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,4,3,6]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,4,6,3]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,6,3,4]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,6,4,3]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,3,4,5]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,3,5,4]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,4,3,5]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,4,5,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,5,3,4]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,5,4,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,4,5,6]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,4,6,5]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,5,4,6]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,5,6,4]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,6,4,5]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,6,5,4]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,2,5,6]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,2,6,5]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,5,2,6]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,5,6,2]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,6,2,5]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,6,5,2]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,2,4,6]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,2,6,4]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,4,2,6]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,4,6,2]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,6,2,4]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,6,4,2]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,2,4,5]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,2,5,4]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,4,2,5]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,4,5,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,5,2,4]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,5,4,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,3,5,6]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,3,6,5]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,5,3,6]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,5,6,3]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,6,3,5]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,6,5,3]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,2,5,6]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,2,6,5]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,5,2,6]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,5,6,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,6,2,5]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,6,5,2]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,2,3,6]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,2,6,3]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,3,2,6]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,3,6,2]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,6,2,3]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,6,3,2]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,2,3,5]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,2,5,3]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,3,2,5]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,3,5,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,5,2,3]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,5,3,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,3,4,6]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,3,6,4]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,4,3,6]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,4,6,3]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,6,3,4]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,6,4,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,2,4,6]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,2,6,4]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,4,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,4,6,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,6,2,4]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,6,4,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,2,3,6]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,2,6,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,3,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,3,6,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,6,2,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,6,3,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,2,3,4]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,2,4,3]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,3,2,4]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,3,4,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,4,2,3]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,4,3,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,3,4,5]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,3,5,4]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,4,3,5]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,4,5,3]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,5,3,4]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,5,4,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,2,4,5]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,2,5,4]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,4,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,4,5,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,5,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,5,4,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,2,3,5]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,2,5,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,3,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,3,5,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,5,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,5,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,2,3,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,2,4,3]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,3,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,3,4,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,4,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,4,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,4,5,6]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,4,6,5]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,5,4,6]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,5,6,4]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,6,4,5]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,6,5,4]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,3,5,6]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,3,6,5]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,5,3,6]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,5,6,3]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,6,3,5]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,6,5,3]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,3,4,6]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,3,6,4]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,4,3,6]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,4,6,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,6,3,4]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,6,4,3]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,3,4,5]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,3,5,4]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,4,3,5]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,4,5,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,5,3,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,5,4,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,4,5,6]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,4,6,5]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,5,4,6]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,5,6,4]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,6,4,5]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,6,5,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,1,5,6]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,1,6,5]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,5,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,6,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,1,4,6]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,1,6,4]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,4,1,6]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,4,6,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,6,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,6,4,1]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,1,4,5]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,1,5,4]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,4,1,5]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,4,5,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,5,1,4]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,5,4,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,3,5,6]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,3,6,5]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,5,3,6]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,5,6,3]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,6,3,5]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,6,5,3]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,1,5,6]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,1,6,5]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,5,1,6]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,5,6,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,6,1,5]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,6,5,1]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,1,3,6]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,1,6,3]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,3,1,6]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,3,6,1]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,6,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,6,3,1]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,1,3,5]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,1,5,3]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,3,1,5]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,3,5,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,5,1,3]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,5,3,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,3,4,6]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,3,6,4]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,4,3,6]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,4,6,3]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,6,3,4]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,6,4,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,1,4,6]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,1,6,4]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,4,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,4,6,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,6,1,4]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,6,4,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,1,3,6]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,1,6,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,3,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,3,6,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,6,1,3]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,6,3,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,1,3,4]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,1,4,3]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,3,1,4]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,3,4,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,4,1,3]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,4,3,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,3,4,5]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,3,5,4]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,4,3,5]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,4,5,3]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,5,3,4]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,5,4,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,1,4,5]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,1,5,4]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,4,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,4,5,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,5,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,5,4,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,1,3,5]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,1,5,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,3,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,3,5,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,5,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,5,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,1,3,4]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,1,4,3]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,3,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,3,4,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,4,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,4,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,4,5,6]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,4,6,5]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,5,4,6]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,5,6,4]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,6,4,5]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,6,5,4]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,2,5,6]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,2,6,5]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,5,2,6]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,5,6,2]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,6,2,5]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,6,5,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,2,4,6]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,2,6,4]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,4,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,4,6,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,6,2,4]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,6,4,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,2,4,5]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,2,5,4]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,4,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,4,5,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,5,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,5,4,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,4,5,6]=>[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,4,6,5]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,5,4,6]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,5,6,4]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,6,4,5]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,6,5,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,1,5,6]=>[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,1,6,5]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,5,1,6]=>[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,5,6,1]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,6,1,5]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,6,5,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,1,4,6]=>[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,1,6,4]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,4,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,4,6,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,6,1,4]=>[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,6,4,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,1,4,5]=>[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,1,5,4]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,4,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,4,5,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,5,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,5,4,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,2,5,6]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,2,6,5]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,5,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,5,6,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,6,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,6,5,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,1,5,6]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,1,6,5]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,5,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,5,6,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,6,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,6,5,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,1,2,6]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,1,6,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,2,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,2,6,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,6,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,6,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,1,2,5]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,1,5,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,2,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,2,5,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,5,1,2]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,5,2,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,2,4,6]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,2,6,4]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,4,2,6]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,4,6,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,6,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,6,4,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,1,4,6]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,1,6,4]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,4,1,6]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,4,6,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,6,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,6,4,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,1,2,6]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,1,6,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,2,1,6]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,2,6,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,6,1,2]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,6,2,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,1,2,4]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,1,4,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,2,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,2,4,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,4,1,2]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,4,2,1]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,2,4,5]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,2,5,4]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,4,2,5]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,4,5,2]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,5,2,4]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,5,4,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,1,4,5]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,1,5,4]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,4,1,5]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,4,5,1]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,5,1,4]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,5,4,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,1,2,5]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,1,5,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,2,1,5]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,2,5,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,5,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,5,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,1,2,4]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,1,4,2]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,2,1,4]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,2,4,1]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,4,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,4,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,3,5,6]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,3,6,5]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,5,3,6]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,5,6,3]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,6,3,5]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,6,5,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,2,5,6]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,2,6,5]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,5,2,6]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,5,6,2]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,6,2,5]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,6,5,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,2,3,6]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,2,6,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,3,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,3,6,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,6,2,3]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,6,3,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,2,3,5]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,2,5,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,3,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,3,5,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,5,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,5,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,3,5,6]=>[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,3,6,5]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,5,3,6]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,5,6,3]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,6,3,5]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,6,5,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,1,5,6]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,1,6,5]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,5,1,6]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,5,6,1]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,6,1,5]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,6,5,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,1,3,6]=>[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,1,6,3]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,3,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,3,6,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,6,1,3]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,6,3,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,1,3,5]=>[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,1,5,3]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,3,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,3,5,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,5,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,5,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,2,5,6]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,2,6,5]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,5,2,6]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,5,6,2]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,6,2,5]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,6,5,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,1,5,6]=>[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,1,6,5]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,5,1,6]=>[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,5,6,1]=>[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,6,1,5]=>[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,6,5,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,1,2,6]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,1,6,2]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,2,1,6]=>[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,2,6,1]=>[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,6,1,2]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,6,2,1]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,1,2,5]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,1,5,2]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,2,1,5]=>[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,2,5,1]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,5,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,5,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,2,3,6]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,2,6,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,3,2,6]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,3,6,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,6,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,6,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,1,3,6]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,1,6,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,3,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,3,6,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,6,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,6,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,1,2,6]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,1,6,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,2,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,2,6,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,6,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,6,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,1,3,2]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,2,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,2,3,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,3,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,2,3,5]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,2,5,3]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,3,2,5]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,3,5,2]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,5,2,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,5,3,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,1,3,5]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,1,5,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,3,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,3,5,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,5,1,3]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,5,3,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,1,2,5]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,1,5,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,2,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,2,5,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,5,1,2]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,5,2,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,1,2,3]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,1,3,2]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,2,1,3]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,2,3,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,3,1,2]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,3,2,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,3,4,6]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,3,6,4]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,4,3,6]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,4,6,3]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,6,3,4]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,6,4,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,2,4,6]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,2,6,4]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,4,2,6]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,4,6,2]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,6,2,4]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,6,4,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,2,3,6]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,2,6,3]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,3,2,6]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,3,6,2]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,6,2,3]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,6,3,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,2,3,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,2,4,3]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,3,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,3,4,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,4,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,4,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,3,4,6]=>[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,3,6,4]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,4,3,6]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,4,6,3]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,6,3,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,6,4,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,1,4,6]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,1,6,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,4,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,4,6,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,6,1,4]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,6,4,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,1,3,6]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,1,6,3]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,3,1,6]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,3,6,1]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,6,1,3]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,6,3,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,1,3,4]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,1,4,3]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,3,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,3,4,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,4,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,4,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,2,4,6]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,2,6,4]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,4,2,6]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,4,6,2]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,6,2,4]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,6,4,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,1,4,6]=>[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,1,6,4]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,4,1,6]=>[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,4,6,1]=>[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,6,1,4]=>[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,6,4,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,1,2,6]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,1,6,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,2,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,2,6,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,6,1,2]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,6,2,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,1,2,4]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,1,4,2]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,2,1,4]=>[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,2,4,1]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,4,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,4,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,2,3,6]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,2,6,3]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,3,2,6]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,3,6,2]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,6,2,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,6,3,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,1,3,6]=>[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,1,6,3]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,3,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,3,6,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,6,1,3]=>[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,6,3,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,1,2,6]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,1,6,2]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,2,1,6]=>[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,2,6,1]=>[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,6,1,2]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,6,2,1]=>[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,1,2,3]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,1,3,2]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,2,1,3]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,2,3,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,3,1,2]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,3,2,1]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,2,4,3]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,3,2,4]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,3,4,2]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,4,2,3]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,4,3,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,1,3,4]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,1,4,3]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,3,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,3,4,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,4,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,4,3,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,1,2,4]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,1,4,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,2,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,2,4,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,4,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,1,2,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,1,3,2]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,2,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,3,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,3,5,4]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,4,3,5]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,4,5,3]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,5,3,4]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,5,4,3]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,2,4,5]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,2,5,4]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,4,2,5]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,4,5,2]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,5,2,4]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,5,4,2]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,2,3,5]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,2,5,3]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,3,2,5]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,3,5,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,5,2,3]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,5,3,2]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,2,3,4]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,2,4,3]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,3,2,4]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,3,4,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,4,2,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,4,3,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,3,4,5]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,3,5,4]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,4,3,5]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,4,5,3]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,5,3,4]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,5,4,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,1,4,5]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,1,5,4]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,4,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,4,5,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,5,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,5,4,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,1,3,5]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,1,5,3]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,3,1,5]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,3,5,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,5,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,5,3,1]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,1,3,4]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,1,4,3]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,3,1,4]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,3,4,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,4,1,3]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,4,3,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,2,4,5]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,2,5,4]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,4,2,5]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,4,5,2]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,5,2,4]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,5,4,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,1,4,5]=>[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,1,5,4]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,4,1,5]=>[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,4,5,1]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,5,1,4]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,5,4,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,1,2,5]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,1,5,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,2,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,2,5,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,1,2,4]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,1,4,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,2,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,2,4,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,4,1,2]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,4,2,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,2,3,5]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,2,5,3]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,3,2,5]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,3,5,2]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,5,2,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,5,3,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,1,3,5]=>[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,1,5,3]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,3,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,3,5,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,5,1,3]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,5,3,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,1,2,5]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,1,5,2]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,2,1,5]=>[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,2,5,1]=>[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,5,1,2]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,5,2,1]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,1,3,2]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,2,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,2,3,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,3,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,2,4,3]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,3,2,4]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,3,4,2]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,4,2,3]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,4,3,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,1,3,4]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,1,4,3]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,3,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,4,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,4,3,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,1,2,4]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,1,4,2]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,2,1,4]=>[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,2,4,1]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,4,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,1,3,2]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,2,1,3]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,4,3,2,1]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,5,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,8,3,2,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,8,3,2,1]=>[1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,8,3,2,1]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,8,3,2,1]=>[1,2,3,4,6,8,5,7]=>[7,5,8,6,4,3,2,1]=>[8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,8,3,2,1]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,5,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,3,6,2,1]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,8,2,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,3,8,2,1]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,3,8,2,1]=>[1,2,3,8,4,6,7,5]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,8,2,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,4,8,2,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,5,8,2,1]=>[1,2,3,5,8,4,6,7]=>[7,6,4,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,5,8,2,1]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,7,8,2,1]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,7,8,2,1]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,2,3,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,2,3,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,2,3,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,2,4,1]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,3,2,4,1]=>[1,2,4,3,5,7,6,8]=>[8,6,7,5,3,4,2,1]=>[8,7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,2,4,1]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,4,5,6,1]=>[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,2,8,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,3,2,8,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,3,2,8,1]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,3,2,8,1]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,2,8,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,7,2,8,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,7,2,8,1]=>[1,2,8,3,7,4,6,5]=>[5,6,4,7,3,8,2,1]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,2,3,8,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,2,3,8,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,2,3,8,1]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,3,8,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,2,4,8,1]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,3,4,8,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,4,5,8,1]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,6,7,8,1]=>[1,2,6,7,8,3,4,5]=>[5,4,3,8,7,6,2,1]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,6,7,8,1]=>[1,2,6,7,8,3,4,5]=>[5,4,3,8,7,6,2,1]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,6,7,8,1]=>[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,6,7,8,1]=>[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,6,7,8,1]=>[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,6,7,8,1]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,1]=>[1,2,4,5,6,7,8,3]=>[3,8,7,6,5,4,2,1]=>[8,7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,4,3,1,2]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,3,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,5,3,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,3,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,3,4,1,2]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,3,4,1,2]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,4,6,1,2]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,6,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,7,1,2]=>[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,7,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,3,8,1,2]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,3,8,1,2]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,3,8,1,2]=>[1,2,3,8,4,6,7,5]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,7,8,1,2]=>[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,7,8,1,2]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,7,8,1,2]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,1,2]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,2,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,2,1,3]=>[1,3,2,4,5,6,8,7]=>[7,8,6,5,4,2,3,1]=>[8,6,7,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,2,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,2,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,4,1,2,3]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,8,1,2,3]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,8,1,2,3]=>[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,1,2,3]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,2,1,4]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,2,1,4]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,2,1,4]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,3,1,4]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,3,1,4]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,2,3,1,4]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,3,1,4]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,1,2,4]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,1,2,4]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,3,1,2,4]=>[1,2,4,3,5,8,6,7]=>[7,6,8,5,3,4,2,1]=>[8,7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,3,1,2,4]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,1,2,4]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,1,2,3,4]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,3,2,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,3,2,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,4,2,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,2,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,2,3,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,3,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,2,4,1,5]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,4,1,5]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,3,4,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,3,4,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,3,1,2,5]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,3,1,2,5]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,4,1,2,5]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,1,2,5]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,2,1,3,5]=>[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>[8,5,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,1,3,5]=>[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>[8,5,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,2,1,4,5]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,1,4,5]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,3,1,4,5]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,3,1,4,5]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,1,2,4,5]=>[1,2,4,5,3,6,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,1,2,4,5]=>[1,2,4,5,3,6,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,1,3,4,5]=>[1,3,4,5,2,6,7,8]=>[8,7,6,2,5,4,3,1]=>[8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,1,3,4,5]=>[1,3,4,5,2,6,7,8]=>[8,7,6,2,5,4,3,1]=>[8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,2,3,4,5]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,2,1,6]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,2,3,1,6]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,2,5,1,6]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,2,1,3,6]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,1,3,4,6]=>[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>[8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,2,1,3,4,6]=>[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>[8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,3,4,6]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,2,3,4,6]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,2,1,5,6]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,2,1,5,6]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,4,1,5,6]=>[1,5,6,2,4,3,7,8]=>[8,7,3,4,2,6,5,1]=>[8,5,3,4,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,4,1,5,6]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,1,2,5,6]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,3,5,6]=>[1,3,5,6,2,4,7,8]=>[8,7,4,2,6,5,3,1]=>[8,4,7,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,1,4,5,6]=>[1,4,5,6,2,3,7,8]=>[8,7,3,2,6,5,4,1]=>[8,4,3,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,4,5,6]=>[1,4,5,6,2,3,7,8]=>[8,7,3,2,6,5,4,1]=>[8,4,3,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,3,4,5,6]=>[1,3,4,5,6,2,7,8]=>[8,7,2,6,5,4,3,1]=>[8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,3,2,1,7]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,1,2,7]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,4,1,2,7]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,1,2,7]=>[1,2,7,3,5,6,4,8]=>[8,4,6,5,3,7,2,1]=>[8,7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,1,2,7]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,1,3,7]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,1,2,3,7]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,2,3,4,7]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,2,3,4,7]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,2,1,5,7]=>[1,5,7,2,3,4,6,8]=>[8,6,4,3,2,7,5,1]=>[8,5,4,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,2,1,5,7]=>[1,5,7,2,3,4,6,8]=>[8,6,4,3,2,7,5,1]=>[8,5,4,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,4,7,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,1,5,6,7]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,3,5,6,7]=>[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,4,5,6,7]=>[1,4,5,6,7,2,3,8]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,4,5,6,7]=>[1,4,5,6,7,2,3,8]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,4,5,6,7]=>[1,3,4,5,6,7,2,8]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,3,2,1,8]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,3,2,1,8]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,3,4,2,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,4,2,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,5,2,1,8]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,5,2,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,6,2,1,8]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,2,3,1,8]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,2,4,1,8]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,2,4,1,8]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,3,4,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,2,3,4,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,2,3,4,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,3,4,1,8]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,3,4,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,3,6,1,8]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,2,7,1,8]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,2,7,1,8]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,6,7,1,8]=>[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,1,8]=>[1,8,2,4,5,6,7,3]=>[3,7,6,5,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,8]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,1,2,8]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,3,1,2,8]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,3,1,2,8]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,1,2,8]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,2,1,3,8]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,2,1,3,8]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,1,3,8]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,1,2,3,8]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,1,2,3,8]=>[1,2,3,8,4,6,7,5]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,1,2,4,8]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,1,3,4,8]=>[1,3,4,8,2,5,6,7]=>[7,6,5,2,8,4,3,1]=>[8,4,7,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,2,3,4,8]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,2,3,4,8]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,2,3,4,8]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,1,2,3,4,8]=>[1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,2,3,4,8]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,2,1,5,8]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,1,2,5,8]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,3,4,5,8]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,2,4,6,8]=>[1,2,4,6,8,3,5,7]=>[7,5,3,8,6,4,2,1]=>[8,7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,3,4,6,8]=>[1,2,3,4,6,8,5,7]=>[7,5,8,6,4,3,2,1]=>[8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,5,6,8]=>[1,5,6,8,2,3,4,7]=>[7,4,3,2,8,6,5,1]=>[8,4,3,2,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,4,5,6,8]=>[1,2,4,5,6,8,3,7]=>[7,3,8,6,5,4,2,1]=>[8,7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,4,5,6,8]=>[1,3,4,5,6,8,2,7]=>[7,2,8,6,5,4,3,1]=>[8,2,7,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,1,7,8]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,6,1,7,8]=>[1,7,8,2,6,3,4,5]=>[5,4,3,6,2,8,7,1]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,6,1,7,8]=>[1,7,8,2,6,3,4,5]=>[5,4,3,6,2,8,7,1]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,6,1,7,8]=>[1,7,8,2,3,5,6,4]=>[4,6,5,3,2,8,7,1]=>[8,5,4,1,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,7,8]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,1,2,7,8]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,1,2,7,8]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,1,2,7,8]=>[1,2,7,8,3,6,4,5]=>[5,4,6,3,8,7,2,1]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,1,3,7,8]=>[1,3,7,8,2,4,6,5]=>[5,6,4,2,8,7,3,1]=>[8,4,7,3,1,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,2,3,7,8]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,1,4,7,8]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,5,7,8]=>[1,5,7,8,2,3,4,6]=>[6,4,3,2,8,7,5,1]=>[8,4,3,2,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,2,5,7,8]=>[1,2,5,7,8,3,4,6]=>[6,4,3,8,7,5,2,1]=>[8,7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,4,5,7,8]=>[1,4,5,7,8,2,3,6]=>[6,3,2,8,7,5,4,1]=>[8,3,2,7,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,5,7,8]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,4,6,7,8]=>[1,2,4,6,7,8,3,5]=>[5,3,8,7,6,4,2,1]=>[8,7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,4,6,7,8]=>[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,6,7,8]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,5,6,7,8]=>[1,5,6,7,8,2,4,3]=>[3,4,2,8,7,6,5,1]=>[8,3,1,2,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,6,7,8]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,5,6,7,8]=>[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,6,7,8]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,5,6,7,8]=>[1,4,5,6,7,8,2,3]=>[3,2,8,7,6,5,4,1]=>[8,2,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7,8]=>[1,2,4,5,6,7,8,3]=>[3,8,7,6,5,4,2,1]=>[8,7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,2]=>[2,8,7,6,5,4,3,1]=>[8,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,5,3,2,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,8,3,2,1]=>[1,2,3,4,7,5,8,6]=>[6,8,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,5,4,2,1]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,6,4,2,1]=>[1,2,3,5,8,4,6,7]=>[7,6,4,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,4,2,1]=>[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>[8,7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,4,2,1]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,6,5,2,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,7,6,2,1]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,3,8,2,1]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,5,4,3,1]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,7,5,4,3,1]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,4,3,1]=>[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,6,5,3,1]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,7,5,3,1]=>[1,2,4,6,8,3,5,7]=>[7,5,3,8,6,4,2,1]=>[8,7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,4,8,3,1]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,8,7,4,1]=>[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>[8,7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,7,8,4,1]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,7,6,5,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,7,6,5,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,7,6,5,1]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,8,7,6,5,1]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,7,6,5,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,8,7,6,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,7,8,6,1]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,5,7,8,6,1]=>[1,2,5,7,8,3,4,6]=>[6,4,3,8,7,5,2,1]=>[8,7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,2,8,7,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,4,8,7,1]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,5,8,7,1]=>[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>[8,7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,6,8,7,1]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,6,8,7,1]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,7,1]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,7,2,8,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,6,3,8,1]=>[1,2,5,3,8,4,7,6]=>[6,7,4,8,3,5,2,1]=>[8,7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,5,7,4,8,1]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,7,6,5,8,1]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,7,6,5,8,1]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,7,6,5,8,1]=>[1,2,4,3,7,5,8,6]=>[6,8,5,7,3,4,2,1]=>[8,7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,6,5,8,1]=>[1,2,3,4,7,5,8,6]=>[6,8,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,7,6,8,1]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,7,6,8,1]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,7,6,8,1]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,6,8,1]=>[1,2,5,3,4,7,6,8]=>[8,6,7,4,3,5,2,1]=>[8,7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,7,6,8,1]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,7,6,8,1]=>[1,2,4,5,7,3,6,8]=>[8,6,3,7,5,4,2,1]=>[8,7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,6,5,7,8,1]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,3,6,7,8,1]=>[1,2,5,3,6,7,8,4]=>[4,8,7,6,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,5,4,3,2]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,5,4,3,2]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,5,4,3,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,5,4,3,2]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,6,4,3,2]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,8,4,3,2]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,8,4,3,2]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,6,5,3,2]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,8,6,5,3,2]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,7,8,6,4,2]=>[1,3,5,7,8,2,4,6]=>[6,4,2,8,7,5,3,1]=>[8,3,7,2,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,5,7,8,4,2]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,7,8,4,2]=>[1,3,5,6,7,8,2,4]=>[4,2,8,7,6,5,3,1]=>[8,2,7,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,7,6,5,2]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,8,6,5,2]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,6,8,5,2]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,7,6,5,2]=>[1,3,4,8,2,5,6,7]=>[7,6,5,2,8,4,3,1]=>[8,4,7,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,7,8,6,2]=>[1,3,4,5,7,8,2,6]=>[6,2,8,7,5,4,3,1]=>[8,2,7,6,5,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,3,8,7,2]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,3,8,7,2]=>[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>[8,5,4,2,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,5,8,7,2]=>[1,4,2,3,6,5,8,7]=>[7,8,5,6,3,2,4,1]=>[8,6,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,8,7,2]=>[1,3,4,5,6,8,2,7]=>[7,2,8,6,5,4,3,1]=>[8,2,7,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,3,6,7,8,2]=>[1,5,2,3,6,7,8,4]=>[4,8,7,6,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,6,7,8,2]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,5,6,7,8,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,2]=>[1,3,4,5,6,7,8,2]=>[2,8,7,6,5,4,3,1]=>[8,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,5,4,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,5,4,3]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,8,7,4,3]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,5,8,4,3]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,5,8,4,3]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,7,8,4,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,7,8,4,3]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,7,6,5,3]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,8,6,5,3]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,8,7,6,3]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,7,8,6,3]=>[1,4,5,7,8,2,3,6]=>[6,3,2,8,7,5,4,1]=>[8,3,2,7,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,5,8,7,3]=>[1,4,6,2,3,5,8,7]=>[7,8,5,3,2,6,4,1]=>[8,5,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,7,6,8,3]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,6,7,8,3]=>[1,4,5,6,7,8,2,3]=>[3,2,8,7,6,5,4,1]=>[8,2,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,8,5,4,3]=>[1,2,6,7,8,3,4,5]=>[5,4,3,8,7,6,2,1]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,7,8,4,3]=>[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,7,6,5,3]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,8,6,5,3]=>[1,2,4,7,8,3,5,6]=>[6,5,3,8,7,4,2,1]=>[8,7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,7,8,5,3]=>[1,2,4,6,7,8,3,5]=>[5,3,8,7,6,4,2,1]=>[8,7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,4,7,8,3]=>[1,2,6,3,4,7,8,5]=>[5,8,7,4,3,6,2,1]=>[8,7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,4,7,8,3]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,6,7,8,3]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,6,7,8,3]=>[1,2,4,5,6,7,8,3]=>[3,8,7,6,5,4,2,1]=>[8,7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,7,6,5,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,8,6,5,4]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,8,7,5,4]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,6,8,5,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,7,8,5,4]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,8,7,6,4]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,7,8,6,4]=>[1,5,7,8,2,3,4,6]=>[6,4,3,2,8,7,5,1]=>[8,4,3,2,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,5,8,7,4]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,6,8,7,4]=>[1,5,6,8,2,3,4,7]=>[7,4,3,2,8,6,5,1]=>[8,4,3,2,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,6,5,8,4]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,7,5,8,4]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,7,6,8,4]=>[1,5,7,2,3,4,6,8]=>[8,6,4,3,2,7,5,1]=>[8,5,4,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,5,7,8,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,6,7,8,4]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,7,6,5,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,7,6,5,4]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,7,6,5,4]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,7,6,5,4]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,8,6,5,4]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,8,7,5,4]=>[1,2,3,6,8,4,5,7]=>[7,5,4,8,6,3,2,1]=>[8,7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,6,8,5,4]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,8,7,6,4]=>[1,2,3,5,8,4,6,7]=>[7,6,4,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,6,8,7,4]=>[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>[8,7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,6,5,8,4]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,7,5,8,4]=>[1,2,3,6,7,4,5,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,7,6,8,4]=>[1,2,3,5,7,4,6,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,5,7,8,4]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,4]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,7,6,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,8,6,5]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,8,7,5]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,8,7,6,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,7,8,6,5]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,6,8,7,5]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,8,7,6,5]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,6,8,7,5]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,7,6,8,5]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,7,6,5]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,6,8,7,5]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,7,6,8,5]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,7,6,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,8,6,5]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,8,7,5]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,7,6,8,5]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,6,7,8,5]=>[1,4,2,6,7,8,3,5]=>[5,3,8,7,6,2,4,1]=>[8,6,2,7,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,8,7,6,5]=>[1,3,4,2,8,5,6,7]=>[7,6,5,8,2,4,3,1]=>[8,5,7,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,7,6,8,5]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,5,7,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,6,7,8,5]=>[1,3,4,2,6,7,8,5]=>[5,8,7,6,2,4,3,1]=>[8,5,7,6,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,7,6,5]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,7,8,6,5]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,8,7,5]=>[1,4,2,3,6,8,5,7]=>[7,5,8,6,3,2,4,1]=>[8,6,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,7,6,8,5]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,7,8,5]=>[1,4,2,3,6,7,8,5]=>[5,8,7,6,3,2,4,1]=>[8,6,5,7,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,7,6,8,5]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,6,7,8,5]=>[1,2,4,3,6,7,8,5]=>[5,8,7,6,3,4,2,1]=>[8,7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,8,7,6,5]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,7,8,6,5]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,6,7,8,5]=>[1,4,6,7,8,2,3,5]=>[5,3,2,8,7,6,4,1]=>[8,3,2,7,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,8,7,6,5]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,6,7,8,5]=>[1,4,6,7,8,2,3,5]=>[5,3,2,8,7,6,4,1]=>[8,3,2,7,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>[8,6,7,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,7,6,8,5]=>[1,3,2,4,7,5,6,8]=>[8,6,5,7,4,2,3,1]=>[8,6,7,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,6,7,8,5]=>[1,3,2,4,6,7,8,5]=>[5,8,7,6,4,2,3,1]=>[8,6,7,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,8,7,6,5]=>[1,3,4,8,2,5,6,7]=>[7,6,5,2,8,4,3,1]=>[8,4,7,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,7,8,6,5]=>[1,3,4,7,8,2,5,6]=>[6,5,2,8,7,4,3,1]=>[8,3,7,6,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,6,7,8,5]=>[1,3,4,6,7,8,2,5]=>[5,2,8,7,6,4,3,1]=>[8,2,7,6,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,8,6,5]=>[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,6,8,5]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,5]=>[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,7,8,6]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,1,8,7,6]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,1,8,7,6]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,4,1,8,7,6]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,5,1,8,7,6]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,8,7,6]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,7,8,6]=>[1,5,7,8,2,3,4,6]=>[6,4,3,2,8,7,5,1]=>[8,4,3,2,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,5,7,8,6]=>[1,5,7,8,2,4,3,6]=>[6,3,4,2,8,7,5,1]=>[8,4,2,3,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,8,7,6]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,7,8,6]=>[1,5,7,8,2,3,4,6]=>[6,4,3,2,8,7,5,1]=>[8,4,3,2,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,5,8,7,6]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,5,7,8,6]=>[1,4,5,7,8,2,3,6]=>[6,3,2,8,7,5,4,1]=>[8,3,2,7,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,1,8,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,2,1,8,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,2,1,8,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,2,1,8,7]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,2,1,8,7]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,2,1,8,7]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,2,1,8,7]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,4,1,8,7]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,6,1,8,7]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,3,2,8,7]=>[1,5,6,2,8,3,4,7]=>[7,4,3,8,2,6,5,1]=>[8,5,3,2,7,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,4,3,8,7]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,4,3,8,7]=>[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>[8,5,4,2,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,5,3,8,7]=>[1,4,6,2,3,8,5,7]=>[7,5,8,3,2,6,4,1]=>[8,5,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,6,3,8,7]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,6,3,8,7]=>[1,4,5,6,2,3,8,7]=>[7,8,3,2,6,5,4,1]=>[8,4,3,7,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,5,8,7]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,6,5,8,7]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,8,7]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[7,8,5,6,3,2,4,1]=>[8,6,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,6,8,7]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,6,8,7]=>[1,5,6,8,2,3,4,7]=>[7,4,3,2,8,6,5,1]=>[8,4,3,2,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,5,6,8,7]=>[1,5,6,8,2,4,3,7]=>[7,3,4,2,8,6,5,1]=>[8,4,2,3,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,6,8,7]=>[1,5,6,8,2,3,4,7]=>[7,4,3,2,8,6,5,1]=>[8,4,3,2,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,8,7]=>[1,3,4,5,6,8,2,7]=>[7,2,8,6,5,4,3,1]=>[8,2,7,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,3,2,1,8]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,5,3,2,1,8]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,6,5,2,1,8]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,5,4,1,8]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,5,4,1,8]=>[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,7,6,1,8]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,7,6,1,8]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,7,6,1,8]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,6,1,8]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,6,7,1,8]=>[1,8,2,6,7,3,5,4]=>[4,5,3,7,6,2,8,1]=>[8,6,3,1,2,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,7,5,2,8]=>[1,3,4,6,7,2,8,5]=>[5,8,2,7,6,4,3,1]=>[8,3,7,6,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,7,6,2,8]=>[1,3,4,5,7,2,8,6]=>[6,8,2,7,5,4,3,1]=>[8,3,7,6,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,5,4,3,8]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,6,7,4,8]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,6,5,8]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,7,5,8]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,6,7,5,8]=>[1,6,7,2,4,3,5,8]=>[8,5,3,4,2,7,6,1]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,6,5,8]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,7,5,8]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,7,6,5,8]=>[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>[8,6,4,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,6,7,5,8]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,7,6,8]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,5,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,7,6,8]=>[1,5,7,2,3,4,6,8]=>[8,6,4,3,2,7,5,1]=>[8,5,4,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,7,6,8]=>[1,5,7,2,3,4,6,8]=>[8,6,4,3,2,7,5,1]=>[8,5,4,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,5,3,7,8]=>[1,2,4,6,3,7,8,5]=>[5,8,7,3,6,4,2,1]=>[8,7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,5,7,8]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,5,7,8]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,1,6,7,8]=>[1,6,7,8,2,5,3,4]=>[4,3,5,2,8,7,6,1]=>[8,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,6,7,5]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,8,6,7,4]=>[1,2,3,5,8,4,6,7]=>[7,6,4,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,5,6,8,4]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,5,6,7,4]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,5,7,6,4]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,6,5,7,4]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,6,7,5,4]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,8,6,7,3]=>[1,2,4,5,8,3,6,7]=>[7,6,3,8,5,4,2,1]=>[8,7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,5,7,8,3]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,4,6,7,3]=>[1,2,8,3,4,6,7,5]=>[5,7,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,5,6,2,8]=>[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>[8,5,7,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,6,7,4,2]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,6,7,8,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,3,5,6,7,2]=>[1,8,2,3,5,6,7,4]=>[4,7,6,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,6,5,3,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,3,6,7,2]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,7,6,3,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,5,6,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,6,5,3,2]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,4,7,3,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,4,6,3,2]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,6,4,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,6,7,5]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,8,6,7,3]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,5,3,8,7]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,6,5,8,3]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,4,7,6,3]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,6,4,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,6,7,5,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,6,7,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,5,6,7,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,5,7,6,1]=>[1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,5,7,1]=>[1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,7,5,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,4,5,1,8,7]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,4,5,6,8,1]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,5,6,7,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,4,7,6,1]=>[1,2,8,3,5,4,7,6]=>[6,7,4,5,3,8,2,1]=>[8,7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,8,6,7,4]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,5,6,4,8]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,5,6,8,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,5,6,7,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,5,7,6,4]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,6,5,7,4]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,6,7,5,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,6,7,5]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,4,6,5,8,1]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,4,6,1,8]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,6,5,8,7]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,6,7,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,7,6,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,5,1,8,7,6]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,7,5,6,8,1]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,7,6,5,8,1]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,7,6,5,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,6,5,1,8]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,5,4,1,8]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,1,7,6,8]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,1,8,7,6]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,7,6,8,1]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,6,5,8,1]=>[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>[8,7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,6,5,3,1]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,6,7,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,7,5,6,8,1]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,5,7,6,1]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,1,6,8,7]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,4,1,8,7,6]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,4,7,6,1]=>[1,2,5,3,4,7,6,8]=>[8,6,7,4,3,5,2,1]=>[8,7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,5,4,1]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,1,7,8,6]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,4,2,1,8]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,8,6,7,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,5,2,1,8]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,2,1,8,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,4,2,1,8]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,4,6,2,1]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,5,4,2,1]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,7,6,1]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,5,2,1]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,6,5,8,7]=>[1,3,6,2,4,5,8,7]=>[7,8,5,4,2,6,3,1]=>[8,5,7,4,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,3,5,8,7]=>[1,4,6,2,3,5,8,7]=>[7,8,5,3,2,6,4,1]=>[8,5,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,3,5,8,7]=>[1,3,5,8,2,4,6,7]=>[7,6,4,2,8,5,3,1]=>[8,4,7,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,8,5,7]=>[1,4,2,3,6,8,5,7]=>[7,5,8,6,3,2,4,1]=>[8,6,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,6,8,5,7]=>[1,3,6,8,2,4,5,7]=>[7,5,4,2,8,6,3,1]=>[8,4,7,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,3,8,5,7]=>[1,4,6,2,3,8,5,7]=>[7,5,8,3,2,6,4,1]=>[8,5,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,3,8,5,7]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,8,3,5,7]=>[1,4,6,8,2,3,5,7]=>[7,5,3,2,8,6,4,1]=>[8,4,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,8,3,5,7]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,1,8,3,5,7]=>[1,8,2,4,6,3,5,7]=>[7,5,3,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,4,7,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,6,7,8,5]=>[1,3,6,7,8,2,4,5]=>[5,4,2,8,7,6,3,1]=>[8,3,7,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,7,5,8,6]=>[1,3,7,2,4,5,8,6]=>[6,8,5,4,2,7,3,1]=>[8,5,7,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,3,5,8,6]=>[1,3,5,8,2,4,7,6]=>[6,7,4,2,8,5,3,1]=>[8,4,7,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,7,8,5,6]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,1,3,8,5,6]=>[1,3,8,2,4,7,5,6]=>[6,5,7,4,2,8,3,1]=>[8,5,7,4,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,1,3,5,6]=>[1,3,5,6,2,4,7,8]=>[8,7,4,2,6,5,3,1]=>[8,4,7,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>[8,6,7,3,4,2,5,1]=>[8,6,4,5,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,7,3,8,6]=>[1,4,5,7,2,3,8,6]=>[6,8,3,2,7,5,4,1]=>[8,4,3,7,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,8,5,6,7]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,5,8,3,6,7]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,6,8,7]=>[1,5,2,4,3,6,8,7]=>[7,8,6,3,4,2,5,1]=>[8,6,4,5,7,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,3,7,8]=>[1,5,6,2,4,3,7,8]=>[8,7,3,4,2,6,5,1]=>[8,5,3,4,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,7,8,3]=>[1,5,6,7,8,2,4,3]=>[3,4,2,8,7,6,5,1]=>[8,3,1,2,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,7,1,8,3]=>[1,8,2,4,5,6,7,3]=>[3,7,6,5,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,7,8,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,3,4,8,7]=>[1,5,6,2,3,4,8,7]=>[7,8,4,3,2,6,5,1]=>[8,5,4,3,7,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,6,7,8,3,4]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,7,8,3,4]=>[1,6,7,8,2,5,3,4]=>[4,3,5,2,8,7,6,1]=>[8,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,1,7,8,3,4]=>[1,7,8,2,5,6,3,4]=>[4,3,6,5,2,8,7,1]=>[8,5,2,1,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,1,3,4]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,7,8,4,6]=>[1,3,7,8,2,5,4,6]=>[6,4,5,2,8,7,3,1]=>[8,4,7,2,3,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,8,3,4,6]=>[1,5,7,8,2,3,4,6]=>[6,4,3,2,8,7,5,1]=>[8,4,3,2,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,1,8,3,4,6]=>[1,8,2,5,7,3,4,6]=>[6,4,3,7,5,2,8,1]=>[8,6,3,2,5,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,1,3,4,6]=>[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>[8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,6,7,8,4]=>[1,6,7,8,2,3,5,4]=>[4,5,3,2,8,7,6,1]=>[8,4,3,1,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,1,7,8,4]=>[1,7,8,2,3,5,6,4]=>[4,6,5,3,2,8,7,1]=>[8,5,4,1,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,6,7,8,1,4]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,7,8,4,5]=>[1,6,2,3,7,8,4,5]=>[5,4,8,7,3,2,6,1]=>[8,6,5,2,1,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,3,4,5]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,8,1,3,4,5]=>[1,3,4,5,2,6,7,8]=>[8,7,6,2,5,4,3,1]=>[8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,4,7,5,8]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,6,7,8,4,5]=>[1,3,6,7,8,2,4,5]=>[5,4,2,8,7,6,3,1]=>[8,3,7,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,7,8,4,5]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,7,8,4,5]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,6,8,4,5,7]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,8,4,5,7]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,1,4,5,8,7]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,6,8,5,7]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,4,5,7,8]=>[1,3,4,5,7,8,2,6]=>[6,2,8,7,5,4,3,1]=>[8,2,7,6,5,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,1,7,5,8]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,6,7,8,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,3,4,5,6]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,3,4,5,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,3,4,5,6]=>[1,3,4,5,6,2,7,8]=>[8,7,2,6,5,4,3,1]=>[8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,7,4,8,5,6]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,1,4,8,5,6]=>[1,4,8,2,3,7,5,6]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,1,4,5,6]=>[1,4,5,6,2,3,7,8]=>[8,7,3,2,6,5,4,1]=>[8,4,3,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,7,8,5,6]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,8,5,6]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,1,8,5,6]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,4,5,6,8]=>[1,3,4,5,6,8,2,7]=>[7,2,8,6,5,4,3,1]=>[8,2,7,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,7,5,6,8]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,1,8,6]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,7,8,1,6]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,5,6,7]=>[1,3,4,5,6,7,2,8]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,4,5,6,7]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,4,8,5,6,7]=>[1,3,4,8,2,5,6,7]=>[7,6,5,2,8,4,3,1]=>[8,4,7,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,4,8,5,6,7]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,5,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,1,5,6,7]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,5,8,6,7]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,1,8,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,1,6,7]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,1,7]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,6,5,8,7]=>[1,4,2,6,3,5,8,7]=>[7,8,5,3,6,2,4,1]=>[8,6,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,6,8,5,7]=>[1,4,2,6,8,3,5,7]=>[7,5,3,8,6,2,4,1]=>[8,6,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,6,8,5,7]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,8,2,5,7]=>[1,4,6,8,2,5,7,3]=>[3,7,5,2,8,6,4,1]=>[8,4,1,7,3,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,1,2,5,7]=>[1,2,5,7,3,4,6,8]=>[8,6,4,3,7,5,2,1]=>[8,7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,2,7,5,8]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,1,2,5,8]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,6,7,8,5]=>[1,4,2,6,7,8,3,5]=>[5,3,8,7,6,2,4,1]=>[8,6,2,7,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,6,7,8,5]=>[1,2,6,7,8,3,4,5]=>[5,4,3,8,7,6,2,1]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,1,2,8,5]=>[1,2,8,3,4,6,7,5]=>[5,7,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,7,8,2,5]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,7,5,8,6]=>[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>[8,6,4,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,7,8,5,6]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,1,2,5,6]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,7,1,2,8,6]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,8,5,6,7]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,8,2,6,7]=>[1,5,8,2,6,7,3,4]=>[4,3,7,6,2,8,5,1]=>[8,5,2,1,7,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,5,6,7,8]=>[1,4,2,5,6,7,8,3]=>[3,8,7,6,5,2,4,1]=>[8,6,1,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,2]=>[1,4,5,6,7,8,2,3]=>[3,2,8,7,6,5,4,1]=>[8,2,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,6,7,8,2]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,1,8,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,6,4,8,7]=>[1,5,2,6,3,4,8,7]=>[7,8,4,3,6,2,5,1]=>[8,6,4,3,7,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,2,4,8,7]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,2,4,8,7]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,6,8,4,7]=>[1,2,6,8,3,5,4,7]=>[7,4,5,3,8,6,2,1]=>[8,7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,2,8,4,7]=>[1,5,6,2,8,3,4,7]=>[7,4,3,8,2,6,5,1]=>[8,5,3,2,7,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,8,2,4,7]=>[1,8,2,4,7,3,5,6]=>[6,5,3,7,4,2,8,1]=>[8,6,3,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,1,2,4,7]=>[1,2,4,7,3,5,6,8]=>[8,6,5,3,7,4,2,1]=>[8,7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,2,4,8]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,2,8,4]=>[1,7,2,8,3,5,6,4]=>[4,6,5,3,8,2,7,1]=>[8,6,4,1,3,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,1,2,4]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,7,4,8,6]=>[1,5,2,7,3,4,8,6]=>[6,8,4,3,7,2,5,1]=>[8,6,4,3,7,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,2,4,8,6]=>[1,5,7,2,4,8,3,6]=>[6,3,8,4,2,7,5,1]=>[8,5,2,4,7,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,7,2,8,4,6]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,2,8,4,6]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,8,2,4,6]=>[1,7,8,2,4,6,3,5]=>[5,3,6,4,2,8,7,1]=>[8,5,2,4,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,1,2,4,6]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,7,4,6,8]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,7,4,8,6]=>[1,3,5,2,7,4,8,6]=>[6,8,4,7,2,5,3,1]=>[8,5,7,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,5,8,4,6,7]=>[1,3,2,5,8,4,6,7]=>[7,6,4,8,5,2,3,1]=>[8,6,7,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,2,4,6,7]=>[1,3,5,8,2,4,6,7]=>[7,6,4,2,8,5,3,1]=>[8,4,7,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,6,7,4,8]=>[1,3,5,2,6,7,4,8]=>[8,4,7,6,2,5,3,1]=>[8,5,7,2,6,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,2,7,4,8]=>[1,3,5,6,2,7,4,8]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,6,7,8,2,4]=>[1,3,5,6,7,8,2,4]=>[4,2,8,7,6,5,3,1]=>[8,2,7,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,2,4,8,5]=>[1,7,2,4,8,3,6,5]=>[5,6,3,8,4,2,7,1]=>[8,6,3,5,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,2,8,4,5]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,8,2,4,5]=>[1,7,8,2,4,5,3,6]=>[6,3,5,4,2,8,7,1]=>[8,5,2,4,3,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,1,2,4,5]=>[1,2,4,5,3,6,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,7,2,4,5,8]=>[1,6,7,2,4,5,8,3]=>[3,8,5,4,2,7,6,1]=>[8,5,1,4,3,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,4,7,5,8]=>[1,3,2,6,4,7,5,8]=>[8,5,7,4,6,2,3,1]=>[8,6,7,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,4,7,8,5]=>[1,3,6,2,4,7,8,5]=>[5,8,7,4,2,6,3,1]=>[8,5,7,4,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,2,7,8,4,5]=>[1,3,6,2,7,8,4,5]=>[5,4,8,7,2,6,3,1]=>[8,5,7,2,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,2,4,5,7]=>[1,6,8,2,4,5,7,3]=>[3,7,5,4,2,8,6,1]=>[8,5,1,4,3,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,4,5,7,8]=>[1,6,2,4,5,7,8,3]=>[3,8,7,5,4,2,6,1]=>[8,6,1,5,4,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,6,7,8,5]=>[1,2,4,6,7,8,3,5]=>[5,3,8,7,6,4,2,1]=>[8,7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,6,7,2,8,5]=>[1,3,4,6,7,2,8,5]=>[5,8,2,7,6,4,3,1]=>[8,3,7,6,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,8,4,5,6]=>[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>[8,5,7,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,2,4,5,6,8]=>[1,2,4,5,6,8,3,7]=>[7,3,8,6,5,4,2,1]=>[8,7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,7,8,2,6]=>[1,3,4,5,7,8,2,6]=>[6,2,8,7,5,4,3,1]=>[8,2,7,6,5,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,4,5,6,7]=>[1,8,2,4,5,6,7,3]=>[3,7,6,5,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,8,5,6,7]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>[8,6,7,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]=>[7,6,5,8,2,4,3,1]=>[8,5,7,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,5,8,6,7]=>[1,2,4,5,8,3,6,7]=>[7,6,3,8,5,4,2,1]=>[8,7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>[7,6,8,5,4,2,3,1]=>[8,6,7,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,6,3,8,7]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,6,3,8,7]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,6,8,3,7]=>[1,5,2,6,8,3,7,4]=>[4,7,3,8,6,2,5,1]=>[8,6,3,1,7,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,2,8,3,7]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,8,2,3,7]=>[1,5,6,8,2,3,7,4]=>[4,7,3,2,8,6,5,1]=>[8,4,3,1,7,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,1,2,3,7]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,2,7,3,8]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,7,2,3,8]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,2,8,3]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,7,8,2,3]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,8,2,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,2,3,8,6]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,7,2,8,3,6]=>[1,5,7,2,8,3,6,4]=>[4,6,3,8,2,7,5,1]=>[8,5,3,1,7,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,2,8,3,6]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,2,8,3,6]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,8,2,3,6]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,7,3,6,8]=>[1,2,7,3,6,8,4,5]=>[5,4,8,6,3,7,2,1]=>[8,7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>[8,6,7,3,5,2,4,1]=>[8,6,4,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,7,3,6,8]=>[1,2,5,7,3,6,8,4]=>[4,8,6,3,7,5,2,1]=>[8,7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,7,3,8,6]=>[1,4,2,5,7,3,8,6]=>[6,8,3,7,5,2,4,1]=>[8,6,3,7,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,7,3,8,6]=>[1,4,5,2,7,3,8,6]=>[6,8,3,7,2,5,4,1]=>[8,5,3,7,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,7,2,3,8,6]=>[1,4,5,7,2,3,8,6]=>[6,8,3,2,7,5,4,1]=>[8,4,3,7,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,7,8,3,6]=>[1,4,2,5,7,8,3,6]=>[6,3,8,7,5,2,4,1]=>[8,6,2,7,5,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>[8,6,4,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,8,3,6,7]=>[1,4,2,5,8,3,6,7]=>[7,6,3,8,5,2,4,1]=>[8,6,3,7,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,6,3,8,7]=>[1,2,5,6,3,8,4,7]=>[7,4,8,3,6,5,2,1]=>[8,7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,6,3,7,8]=>[1,4,5,2,6,3,7,8]=>[8,7,3,6,2,5,4,1]=>[8,5,3,7,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,6,7,3,8]=>[1,4,2,5,6,7,3,8]=>[8,3,7,6,5,2,4,1]=>[8,6,2,7,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,2,3,8]=>[1,4,5,6,7,2,3,8]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,6,7,8,3]=>[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,5,6,7,8,3]=>[1,4,2,5,6,7,8,3]=>[3,8,7,6,5,2,4,1]=>[8,6,1,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,6,7,8,3]=>[1,4,5,2,6,7,8,3]=>[3,8,7,6,2,5,4,1]=>[8,5,1,7,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,8,2,3]=>[1,4,5,6,7,8,2,3]=>[3,2,8,7,6,5,4,1]=>[8,2,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,7,3,8,5]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,2,3,5]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,7,2,3,5,8]=>[1,7,2,3,5,8,4,6]=>[6,4,8,5,3,2,7,1]=>[8,6,5,2,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,3,7,5,8]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,3,7,8,5]=>[1,6,2,3,7,8,4,5]=>[5,4,8,7,3,2,6,1]=>[8,6,5,2,1,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,7,3,8,5]=>[1,2,6,7,3,8,4,5]=>[5,4,8,3,7,6,2,1]=>[8,7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,7,3,8,5]=>[1,4,6,2,7,3,8,5]=>[5,8,3,7,2,6,4,1]=>[8,5,3,7,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,7,8,3,5]=>[1,4,2,6,7,8,3,5]=>[5,3,8,7,6,2,4,1]=>[8,6,2,7,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,7,8,3,5]=>[1,4,6,2,7,8,3,5]=>[5,3,8,7,2,6,4,1]=>[8,5,2,7,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,2,8,3,5]=>[1,4,6,7,2,8,3,5]=>[5,3,8,2,7,6,4,1]=>[8,4,2,7,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,2,8,3,5,7]=>[1,6,2,8,3,5,7,4]=>[4,7,5,3,8,2,6,1]=>[8,6,4,1,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,2,3,5,7]=>[1,8,2,3,5,7,4,6]=>[6,4,7,5,3,2,8,1]=>[8,6,5,2,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,3,8,5,7]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,3,8,5,7]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,8,5,7]=>[1,2,3,6,8,4,5,7]=>[7,5,4,8,6,3,2,1]=>[8,7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,5,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,7,5,8]=>[1,2,3,6,7,4,5,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,6,7,8,5]=>[1,4,2,3,6,7,8,5]=>[5,8,7,6,3,2,4,1]=>[8,6,5,7,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,6,7,8,3,5]=>[1,2,4,6,7,8,3,5]=>[5,3,8,7,6,4,2,1]=>[8,7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,8,3,5,6]=>[1,7,2,8,3,5,6,4]=>[4,6,5,3,8,2,7,1]=>[8,6,4,1,3,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,8,2,3,5,6]=>[1,7,8,2,3,5,6,4]=>[4,6,5,3,2,8,7,1]=>[8,5,4,1,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,8,3,5,6]=>[1,2,7,8,3,5,6,4]=>[4,6,5,3,8,7,2,1]=>[8,7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,8,3,5,6]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,8,2,3,5,6]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,5,8,6]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,8,5,6]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,2,3,5,6,8]=>[1,7,2,3,5,6,8,4]=>[4,8,6,5,3,2,7,1]=>[8,6,5,1,4,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,3,5,6,8]=>[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>[8,7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,3,5,6,8]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,5,6,8]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,7,6,8]=>[1,2,3,5,7,4,6,8]=>[8,6,4,7,5,3,2,1]=>[8,7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,5,7,3,8,6]=>[1,2,4,5,7,3,8,6]=>[6,8,3,7,5,4,2,1]=>[8,7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,3,5,6,7]=>[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,5,6,7]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,8,6,7]=>[1,2,3,5,8,4,6,7]=>[7,6,4,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,6,8,7]=>[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>[8,7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,7,3,8,4]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,7,8,3,4]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,7,4,8]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,3,7,8,4]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,7,8,2,3,4]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,2,3,4,7]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,3,8,4,7]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,8,4,7]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,3,8,4,7]=>[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>[8,5,4,2,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,4,7,8]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,6,4,7,8]=>[1,5,2,3,6,4,7,8]=>[8,7,4,6,3,2,5,1]=>[8,6,5,3,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,6,4,7,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,3,4,7,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,6,7,4,8]=>[1,2,5,3,6,7,4,8]=>[8,4,7,6,3,5,2,1]=>[8,7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,6,7,8,4]=>[1,5,2,3,6,7,8,4]=>[4,8,7,6,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,6,7,8,4]=>[1,2,5,3,6,7,8,4]=>[4,8,7,6,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,3,7,8,4]=>[1,2,5,6,3,7,8,4]=>[4,8,7,3,6,5,2,1]=>[8,7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,7,3,8,4]=>[1,2,5,6,7,3,8,4]=>[4,8,3,7,6,5,2,1]=>[8,7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,7,8,3,4]=>[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,2,3,4,6]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,8,3,4,6]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,3,4,8,6]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,3,4,6,8]=>[1,2,3,4,6,8,5,7]=>[7,5,8,6,4,3,2,1]=>[8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,3,4,6,8]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,7,4,6,8]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,8,3,4,6,7]=>[1,2,8,3,4,6,7,5]=>[5,7,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,3,4,6,7]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,3,4,6,7]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,8,4,6,7]=>[1,2,3,8,4,6,7,5]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,4,6,8,7]=>[1,2,3,4,6,8,5,7]=>[7,5,8,6,4,3,2,1]=>[8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,2,3,4,5]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,3,8,4,5]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,8,3,4,5]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,2,3,4,5]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,3,4,8,5]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,7,8,4,5]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,3,4,5,8]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,7,3,4,5,8]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,2,3,4,5,8]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,7,4,5,8]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,4,7,5,8]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,7,5,8]=>[1,2,3,6,4,7,5,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,7,8,5]=>[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,4,7,8,5]=>[1,2,6,3,4,7,8,5]=>[5,8,7,4,3,6,2,1]=>[8,7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,7,8,5]=>[1,2,3,6,4,7,8,5]=>[5,8,7,4,6,3,2,1]=>[8,7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,7,4,8,5]=>[1,2,3,6,7,4,8,5]=>[5,8,4,7,6,3,2,1]=>[8,7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,3,4,5,7]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,3,4,5,7]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,3,4,5,7]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,4,8,5,7]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,8,5,7]=>[1,2,3,6,4,8,5,7]=>[7,5,8,4,6,3,2,1]=>[8,7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,5,8,7]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,3,4,5,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,3,4,5,6]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,3,4,5,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,3,4,5,6]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,8,4,5,6]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,8,5,6]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,8,5,6]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,4,8,5,6]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,8,6]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,5,8,6]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,4,5,8,6]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,4,5,8,6]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,5,8,6]=>[6,8,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,8,5,6]=>[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,4,8,7]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,7,6,1]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,3,8,1,6]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,3,1,8,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,3,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,2,5,1]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,2,1,5]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,3,8,2,6]=>[1,3,8,2,6,4,7,5]=>[5,7,4,6,2,8,3,1]=>[8,5,7,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,4,8,2,6]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,4,7,6,2]=>[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>[8,6,5,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,3,7,6,2]=>[1,3,7,2,4,8,5,6]=>[6,5,8,4,2,7,3,1]=>[8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,1,7,6,2]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,7,1,5,2]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,6,5,1,2]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,3,1,4,2]=>[1,4,2,3,5,7,6,8]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,1,3,4,2]=>[1,3,4,2,5,8,6,7]=>[7,6,8,5,2,4,3,1]=>[8,5,7,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,7,4,5,2]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,4,5,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,8,4,3,5]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,1,3,2,4]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,8,3,1,5]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,7,3,5,1]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,4,1,5]=>[1,5,2,6,8,3,4,7]=>[7,4,3,8,6,2,5,1]=>[8,6,3,2,7,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,8,1,4,5]=>[1,4,5,2,7,8,3,6]=>[6,3,8,7,2,5,4,1]=>[8,5,2,7,6,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,8,4,6]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,8,5,6]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,8,7,6,5]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,7,6,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,7,1,5,4]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,7,1,5,3]=>[1,5,2,7,3,4,8,6]=>[6,8,4,3,7,2,5,1]=>[8,6,4,3,7,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,1,7,6,3]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,2,7,6,3]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,2,7,6,4]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,7,3,5,4]=>[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,7,2,5,3]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,1,2,4,3]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>[7,6,8,5,4,2,3,1]=>[8,6,7,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,2,4,3,1]=>[1,2,4,3,5,7,6,8]=>[8,6,7,5,3,4,2,1]=>[8,7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,4,2,3]=>[1,4,2,3,5,7,8,6]=>[6,8,7,5,3,2,4,1]=>[8,6,5,7,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,6,5,3,4]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,6,5,4,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,4,1,3,2]=>[1,3,2,4,5,6,8,7]=>[7,8,6,5,4,2,3,1]=>[8,6,7,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,1,10,9]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,7,6,5,4,9,8,3]=>[1,10,2,3,4,9,5,6,7,8]=>[8,7,6,5,9,4,3,2,10,1]=>[10,8,7,6,4,3,2,1,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,3,2,1,10,7,6,9,8,5]=>[1,10,2,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,2,1,3,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,4,3,2,1,10,9,8,7]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,5,4,9,8,7,6,3]=>[1,10,2,3,4,9,5,6,7,8]=>[8,7,6,5,9,4,3,2,10,1]=>[10,8,7,6,4,3,2,1,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,3,2,1,10,9,8,7,6,5]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,9,8,7,6,5,4,3]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,6,1,4,5,7,8]=>[1,4,5,7,8,2,6,3]=>[3,6,2,8,7,5,4,1]=>[8,3,1,7,6,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,2,4,7,8]=>[1,2,4,7,8,3,5,6]=>[6,5,3,8,7,4,2,1]=>[8,7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,2,4,6,8]=>[1,2,4,6,8,3,5,7]=>[7,5,3,8,6,4,2,1]=>[8,7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,3,4,5,7]=>[1,3,4,5,7,2,8,6]=>[6,8,2,7,5,4,3,1]=>[8,3,7,6,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,2,3,4,7]=>[1,2,3,4,7,5,8,6]=>[6,8,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,2,3,4,6]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,2,4,6,7]=>[1,2,4,6,7,3,5,8]=>[8,5,3,7,6,4,2,1]=>[8,7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,2,4,5,6]=>[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,3,4,6]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,7,1,3,4,8]=>[1,3,4,8,2,5,7,6]=>[6,7,5,2,8,4,3,1]=>[8,4,7,6,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,1,3,5,7]=>[1,3,5,7,2,6,8,4]=>[4,8,6,2,7,5,3,1]=>[8,4,7,1,6,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,8,1,2,5,7]=>[1,2,5,7,3,6,8,4]=>[4,8,6,3,7,5,2,1]=>[8,7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,1,3,5,7]=>[1,3,5,7,2,4,8,6]=>[6,8,4,2,7,5,3,1]=>[8,4,7,3,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,4,5,6]=>[1,4,5,6,2,7,8,3]=>[3,8,7,2,6,5,4,1]=>[8,4,1,7,6,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,1,2,5,6]=>[1,2,5,6,3,4,8,7]=>[7,8,4,3,6,5,2,1]=>[8,7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,4,7,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,1,2,4,6]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,1,3,6,8]=>[1,3,6,8,2,4,5,7]=>[7,5,4,2,8,6,3,1]=>[8,4,7,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,1,2,5,8]=>[1,2,5,8,3,6,4,7]=>[7,4,6,3,8,5,2,1]=>[8,7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,1,3,6,7]=>[1,3,6,7,2,5,4,8]=>[8,4,5,2,7,6,3,1]=>[8,4,7,2,3,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,1,3,5,7]=>[1,3,5,7,2,6,4,8]=>[8,4,6,2,7,5,3,1]=>[8,4,7,2,6,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,4,7,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,1,2,5,6]=>[1,2,5,6,3,7,4,8]=>[8,4,7,3,6,5,2,1]=>[8,7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,1,3,4,6]=>[1,3,4,6,2,7,5,8]=>[8,5,7,2,6,4,3,1]=>[8,4,7,6,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,1,2,3,6]=>[1,2,3,6,4,7,5,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,1,3,5,6]=>[1,3,5,6,2,4,7,8]=>[8,7,4,2,6,5,3,1]=>[8,4,7,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,1,2,4,6]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,1,5,7,8]=>[1,5,7,8,2,6,3,4]=>[4,3,6,2,8,7,5,1]=>[8,4,2,1,7,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,4,7,8]=>[1,4,7,8,2,6,3,5]=>[5,3,6,2,8,7,4,1]=>[8,4,2,7,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,1,3,7,8]=>[1,3,7,8,2,6,4,5]=>[5,4,6,2,8,7,3,1]=>[8,4,7,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,7,1,5,6,8]=>[1,5,6,8,2,7,3,4]=>[4,3,7,2,8,6,5,1]=>[8,4,2,1,7,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,4,6,8]=>[1,4,6,8,2,7,3,5]=>[5,3,7,2,8,6,4,1]=>[8,4,2,7,1,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,1,3,6,8]=>[1,3,6,8,2,5,4,7]=>[7,4,5,2,8,6,3,1]=>[8,4,7,2,3,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,6,1,3,5,8]=>[1,3,5,8,2,6,4,7]=>[7,4,6,2,8,5,3,1]=>[8,4,7,2,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,1,5,6,7]=>[1,5,6,7,2,8,3,4]=>[4,3,8,2,7,6,5,1]=>[8,4,2,1,7,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,4,6,7]=>[1,4,6,7,2,8,3,5]=>[5,3,8,2,7,6,4,1]=>[8,4,2,7,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,1,3,5,7]=>[1,3,5,7,2,8,4,6]=>[6,4,8,2,7,5,3,1]=>[8,4,7,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,1,3,4,7]=>[1,3,4,7,2,8,5,6]=>[6,5,8,2,7,4,3,1]=>[8,4,7,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,1,2,4,7]=>[1,2,4,7,3,8,5,6]=>[6,5,8,3,7,4,2,1]=>[8,7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,1,2,3,7]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,1,3,5,6]=>[1,3,5,6,2,8,4,7]=>[7,4,8,2,6,5,3,1]=>[8,4,7,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,1,2,5,6]=>[1,2,5,6,3,8,4,7]=>[7,4,8,3,6,5,2,1]=>[8,7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,1,3,6,7]=>[1,3,6,7,2,5,4,8]=>[8,4,5,2,7,6,3,1]=>[8,4,7,2,3,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,1,3,5,7]=>[1,3,5,7,2,6,4,8]=>[8,4,6,2,7,5,3,1]=>[8,4,7,2,6,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[8,4,7,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,1,2,3,6]=>[1,2,3,6,4,7,5,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,1,3,5,6]=>[1,3,5,6,2,4,7,8]=>[8,7,4,2,6,5,3,1]=>[8,4,7,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,2,4,6]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,1,3,4,5]=>[1,3,4,5,2,6,7,8]=>[8,7,6,2,5,4,3,1]=>[8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,1,2,4,5]=>[1,2,4,5,3,6,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,8,1,3,7]=>[1,3,7,2,4,8,5,6]=>[6,5,8,4,2,7,3,1]=>[8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,8,1,2,6]=>[1,2,6,3,5,8,4,7]=>[7,4,8,5,3,6,2,1]=>[8,7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,8,1,3,6]=>[1,3,6,2,4,8,5,7]=>[7,5,8,4,2,6,3,1]=>[8,5,7,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,7,1,2,6]=>[1,2,6,3,5,7,4,8]=>[8,4,7,5,3,6,2,1]=>[8,7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,7,1,2,3]=>[1,2,3,4,6,7,5,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,7,1,3,4]=>[1,3,4,2,5,7,6,8]=>[8,6,7,5,2,4,3,1]=>[8,5,7,6,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,6,1,3,5]=>[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>[8,5,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,8,1,5,7]=>[1,5,7,2,6,8,3,4]=>[4,3,8,6,2,7,5,1]=>[8,5,2,1,7,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,8,1,3,7]=>[1,3,7,2,6,8,4,5]=>[5,4,8,6,2,7,3,1]=>[8,5,7,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,8,1,4,7]=>[1,4,7,2,5,8,3,6]=>[6,3,8,5,2,7,4,1]=>[8,5,2,7,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,8,1,2,7]=>[1,2,7,3,5,8,4,6]=>[6,4,8,5,3,7,2,1]=>[8,7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,4,8,1,3,7]=>[1,3,7,2,4,8,5,6]=>[6,5,8,4,2,7,3,1]=>[8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,7,8,1,5,6]=>[1,5,6,2,7,8,3,4]=>[4,3,8,7,2,6,5,1]=>[8,5,2,1,7,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,8,1,3,6]=>[1,3,6,2,7,8,4,5]=>[5,4,8,7,2,6,3,1]=>[8,5,7,2,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,6,1,3,5]=>[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>[8,5,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,6,1,2,5]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,1,5,8]=>[1,5,8,2,6,3,7,4]=>[4,7,3,6,2,8,5,1]=>[8,5,3,1,7,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,5,1,4,8]=>[1,4,8,2,5,3,7,6]=>[6,7,3,5,2,8,4,1]=>[8,5,3,7,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,5,1,3,7]=>[1,3,7,2,5,4,8,6]=>[6,8,4,5,2,7,3,1]=>[8,5,7,3,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,7,1,3,5]=>[1,3,5,2,7,4,8,6]=>[6,8,4,7,2,5,3,1]=>[8,5,7,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,7,1,3,4]=>[1,3,4,2,7,5,8,6]=>[6,8,5,7,2,4,3,1]=>[8,5,7,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,4,1,3,6]=>[1,3,6,2,4,5,8,7]=>[7,8,5,4,2,6,3,1]=>[8,5,7,4,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,6,1,3,4]=>[1,3,4,2,6,5,8,7]=>[7,8,5,6,2,4,3,1]=>[8,5,7,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,6,1,2,3]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,1,4,5]=>[1,4,5,2,6,3,7,8]=>[8,7,3,6,2,5,4,1]=>[8,5,3,7,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,1,3,5]=>[1,3,5,2,6,4,7,8]=>[8,7,4,6,2,5,3,1]=>[8,5,7,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,1,2,5]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,1,3,4]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,7,1,5,8]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,7,1,4,8]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,6,1,4,8]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,8,1,6,7]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,8,1,4,7]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,8,1,4,6]=>[1,4,6,2,8,3,5,7]=>[7,5,3,8,2,6,4,1]=>[8,5,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,8,1,2,4]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,6,1,4,7]=>[1,4,7,2,6,3,5,8]=>[8,5,3,6,2,7,4,1]=>[8,5,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,7,1,4,6]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,7,1,2,4]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,1,3,5]=>[1,3,5,2,6,4,7,8]=>[8,7,4,6,2,5,3,1]=>[8,5,7,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,1,2,5]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,6,1,2,4]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,4,1,3,5]=>[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>[8,5,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,2,6,1,5]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,2,6,1,4]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,2,6,1,3]=>[1,3,2,6,4,7,5,8]=>[8,5,7,4,6,2,3,1]=>[8,6,7,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,3,6,1,2]=>[1,2,3,6,4,7,5,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,2,5,1,4]=>[1,4,2,5,3,7,6,8]=>[8,6,7,3,5,2,4,1]=>[8,6,4,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,2,5,1,3]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,3,5,1,2]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,2,4,1,3]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,3,4,1,2]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,2,5,1,4]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,2,5,1,3]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,3,5,1,2]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,2,6,1,4]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,2,6,1,4]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,2,6,1,3]=>[1,3,2,6,4,7,5,8]=>[8,5,7,4,6,2,3,1]=>[8,6,7,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,3,6,1,2]=>[1,2,3,6,4,7,5,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,2,5,1,3]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,8,1,7]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,8,7,4,6]=>[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,7,4,5]=>[1,2,3,6,7,4,5,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,6,3,8,5]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,6,3,4,7]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,7,3,4,6]=>[1,2,5,7,3,4,6,8]=>[8,6,4,3,7,5,2,1]=>[8,7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,6,3,4,5]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,5,6,3,8,4]=>[1,2,5,6,3,8,4,7]=>[7,4,8,3,6,5,2,1]=>[8,7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,8,7,3,6]=>[1,2,5,8,3,6,4,7]=>[7,4,6,3,8,5,2,1]=>[8,7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,6,4,8,5]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,6,7,4,5]=>[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,3,8,5,7]=>[1,4,2,3,8,5,7,6]=>[6,7,5,8,3,2,4,1]=>[8,6,5,7,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,3,8,4,7]=>[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>[8,6,5,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,8,3,6,7]=>[1,4,2,8,3,6,7,5]=>[5,7,6,3,8,2,4,1]=>[8,6,4,7,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,6,3,8,5]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,7,3,4,6]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,6,3,8,4]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,8,7,3,6]=>[1,4,2,8,3,6,5,7]=>[7,5,6,3,8,2,4,1]=>[8,6,4,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,6,7,8,3]=>[1,4,2,6,7,8,3,5]=>[5,3,8,7,6,2,4,1]=>[8,6,2,7,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,2,4,5,7]=>[1,8,2,4,5,7,3,6]=>[6,3,7,5,4,2,8,1]=>[8,6,2,5,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,2,7,4,5]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,2,3,6,7]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,2,3,5,6]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,2,3,4,6]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,2,7,3,6]=>[1,4,5,2,7,3,6,8]=>[8,6,3,7,2,5,4,1]=>[8,5,3,7,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,2,7,8,3]=>[1,4,5,2,7,8,3,6]=>[6,3,8,7,2,5,4,1]=>[8,5,2,7,6,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,7,2,5,6]=>[1,4,8,2,5,6,3,7]=>[7,3,6,5,2,8,4,1]=>[8,5,2,7,4,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,6,2,8,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,2,3,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,8,7,2,6]=>[1,4,5,8,2,6,3,7]=>[7,3,6,2,8,5,4,1]=>[8,4,2,7,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,6,7,2,4]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,6,7,2,3]=>[1,4,5,6,7,2,3,8]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,7,5,6]=>[1,3,4,7,2,8,5,6]=>[6,5,8,2,7,4,3,1]=>[8,4,7,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,6,3,5,7]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,4,5,8,6]=>[1,2,4,5,8,3,6,7]=>[7,6,3,8,5,4,2,1]=>[8,7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,4,7,5,6]=>[1,2,4,7,3,5,6,8]=>[8,6,5,3,7,4,2,1]=>[8,7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,6,4,5,7]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,3,4,8,5]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,3,7,4,5]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,3,5,6]=>[1,2,7,3,5,6,4,8]=>[8,4,6,5,3,7,2,1]=>[8,7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,6,3,8,5]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,7,3,4,6]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,6,3,4,5]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,6,3,8,4]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,8,7,3,6]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,6,7,8,3]=>[1,2,6,7,8,3,4,5]=>[5,4,3,8,7,6,2,1]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,2,7,8,5]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,2,4,8,5]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,2,7,4,6]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,2,7,8,4]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,2,3,8,6]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,2,3,8,5]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,2,3,4,6]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,3,4,5]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,2,3,8,4]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,2,7,3,6]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,2,7,3,5]=>[1,6,2,7,3,5,4,8]=>[8,4,5,3,7,2,6,1]=>[8,6,4,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,2,7,3,4]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,2,7,8,3]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,7,6,2,8,5]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,2,4,5]=>[1,7,2,4,5,3,6,8]=>[8,6,3,5,4,2,7,1]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,6,2,8,4]=>[1,5,6,2,8,3,4,7]=>[7,4,3,8,2,6,5,1]=>[8,5,3,2,7,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,7,2,3,6]=>[1,5,7,2,3,6,4,8]=>[8,4,6,3,2,7,5,1]=>[8,5,4,2,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,6,2,3,5]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,6,2,3,4]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,6,2,8,3]=>[1,5,6,2,8,3,4,7]=>[7,4,3,8,2,6,5,1]=>[8,5,3,2,7,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,6,8,2,7]=>[1,5,6,8,2,7,3,4]=>[4,3,7,2,8,6,5,1]=>[8,4,2,1,7,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,7,2,3]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,6,7,8,2]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,6,7,4,5]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,3,7,8,5]=>[1,3,7,8,2,6,4,5]=>[5,4,6,2,8,7,3,1]=>[8,4,7,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,3,4,8,6]=>[1,3,4,8,2,7,5,6]=>[6,5,7,2,8,4,3,1]=>[8,4,7,6,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,3,7,4,6]=>[1,3,7,2,8,4,6,5]=>[5,6,4,8,2,7,3,1]=>[8,5,7,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,3,7,4,5]=>[1,3,7,2,6,8,4,5]=>[5,4,8,6,2,7,3,1]=>[8,5,7,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,3,7,8,4]=>[1,3,7,8,2,6,4,5]=>[5,4,6,2,8,7,3,1]=>[8,4,7,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,6,3,5,7]=>[1,6,2,8,3,5,7,4]=>[4,7,5,3,8,2,6,1]=>[8,6,4,1,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,7,3,5,6]=>[1,7,2,8,3,5,6,4]=>[4,6,5,3,8,2,7,1]=>[8,6,4,1,3,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,6,3,8,5]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,6,3,4,5]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,6,3,8,4]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,6,7,3,4]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,1,6,7,8,3]=>[1,6,7,8,2,5,3,4]=>[4,3,5,2,8,7,6,1]=>[8,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,2,7,8,5]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,2,4,8,6]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,2,7,4,6]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,2,7,4,5]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,2,3,8,6]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,2,3,8,5]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,2,3,4,7]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,2,3,8,4]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,2,7,3,6]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,2,7,3,5]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,2,7,3,4]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,2,7,8,3]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,7,2,5,6]=>[1,7,2,5,6,3,4,8]=>[8,4,3,6,5,2,7,1]=>[8,6,3,2,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,6,2,4,7]=>[1,6,2,4,7,3,5,8]=>[8,5,3,7,4,2,6,1]=>[8,6,3,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,6,2,8,4]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,7,2,3,6]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,6,2,3,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,6,7,2,4]=>[1,6,7,2,4,3,5,8]=>[8,5,3,4,2,7,6,1]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,6,7,2,3]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,6,7,8,2]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,1,7,5,6]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,6,1,4,8,5]=>[1,4,8,2,3,7,5,6]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,1,7,4,6]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,1,7,4,5]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,5,1,7,8,4]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,1,3,5,7]=>[1,3,5,7,2,8,4,6]=>[6,4,8,2,7,5,3,1]=>[8,4,7,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,6,1,3,8,5]=>[1,3,8,2,7,4,6,5]=>[5,6,4,7,2,8,3,1]=>[8,5,7,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,1,3,4,7]=>[1,3,4,7,2,8,5,6]=>[6,5,8,2,7,4,3,1]=>[8,4,7,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,1,3,4,5]=>[1,3,4,5,2,7,8,6]=>[6,8,7,2,5,4,3,1]=>[8,4,7,6,5,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,1,8,3,7]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,1,7,3,6]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,1,7,3,5]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,1,7,3,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,5,1,7,8,3]=>[1,7,8,2,6,3,4,5]=>[5,4,3,6,2,8,7,1]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,1,2,4,6]=>[1,2,4,6,3,8,5,7]=>[7,5,8,3,6,4,2,1]=>[8,7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,1,2,8,4]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,1,2,8,3]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,1,8,2,7]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,1,7,2,5]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,1,7,2,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,1,7,8,2]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,7,1,5,6]=>[1,5,6,2,3,4,8,7]=>[7,8,4,3,2,6,5,1]=>[8,5,4,3,7,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,6,1,8,5]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,7,1,4,6]=>[1,4,6,2,3,8,5,7]=>[7,5,8,3,2,6,4,1]=>[8,5,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,6,1,4,5]=>[1,4,5,2,3,8,6,7]=>[7,6,8,3,2,5,4,1]=>[8,5,4,7,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,6,1,8,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,6,1,3,7]=>[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>[8,5,7,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,7,1,3,6]=>[1,3,6,2,8,4,5,7]=>[7,5,4,8,2,6,3,1]=>[8,5,7,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,6,1,3,4]=>[1,3,4,2,8,5,6,7]=>[7,6,5,8,2,4,3,1]=>[8,5,7,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,6,1,8,3]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,7,1,2,6]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,6,1,2,5]=>[1,2,5,3,4,7,6,8]=>[8,6,7,4,3,5,2,1]=>[8,7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,1,2,4]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,6,1,8,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,7,1,6]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,6,7,1,4]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,6,7,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,9,7]=>[1,2,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7,9]=>[9,7,6,8,5,4,3,2,1]=>[9,8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,8,9,6]=>[1,2,3,4,5,8,9,6,7]=>[7,6,9,8,5,4,3,2,1]=>[9,8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,2,3,9,4,5,6,7]=>[1,2,3,9,4,5,6,7,8]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,8,5,6,7,2,3,4]=>[1,8,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,9,2]=>[1,4,5,6,7,8,9,2,3]=>[3,2,9,8,7,6,5,4,1]=>[9,2,1,8,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,9,1,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,2,9]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,9,1,8]=>[1,8,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,1]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,5,2,6,1,4,8,7]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,6,4,1,8,7]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,4,8,1,6]=>[1,6,2,7,3,5,4,8]=>[8,4,5,3,7,2,6,1]=>[8,6,4,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,4,8,6,1]=>[1,2,7,3,5,4,8,6]=>[6,8,4,5,3,7,2,1]=>[8,7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,3,8,6,1]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,3,8,1,6]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,3,1,8,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,1,3,8,7]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,4,2,8,7]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,1,3,2,8,7]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,2,8,6,1]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,2,1,5]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,4,8,2,6]=>[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,7,4,8,3,6]=>[1,5,7,2,3,6,4,8]=>[8,4,6,3,2,7,5,1]=>[8,5,4,2,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,1,8,6,2]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,1,5,2]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,5,1,2]=>[1,2,3,8,4,6,7,5]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,3,8,5,2,1]=>[1,2,3,8,4,6,7,5]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,3,1,4,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,3,4,2]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,3,5,2]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,8,4,5,2]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,4,5,3]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,4,3,5]=>[1,6,7,8,2,3,5,4]=>[4,5,3,2,8,7,6,1]=>[8,4,3,1,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,1,8,3,6]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,3,1,5]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,3,5,1]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,8,4,5,1]=>[1,2,7,8,3,6,4,5]=>[5,4,6,3,8,7,2,1]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,8,1,4,5]=>[1,4,5,2,7,8,3,6]=>[6,3,8,7,2,5,4,1]=>[8,5,2,7,6,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,1,8,4,6]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,7,8,5,6]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,7,8,6,5]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,1,8,6,4]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,8,5,4,1]=>[1,2,7,8,3,6,4,5]=>[5,4,6,3,8,7,2,1]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,5,3,1]=>[1,2,8,3,4,6,7,5]=>[5,7,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,8,1,5,3]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,2,1,8,6,3]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,2,8,6,3]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,2,8,6,4]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,3,5,4]=>[1,6,7,8,2,3,5,4]=>[4,5,3,2,8,7,6,1]=>[8,4,3,1,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,2,4,3]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,1,4,3]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,2,4,3,1]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,5,2,3]=>[1,8,2,3,4,6,7,5]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,8,5,3,4]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,8,5,4,2]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,8,5,3,2]=>[1,8,2,3,4,6,7,5]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,1,4,3,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,1,3,2]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,8,4,3,2,1,10,9]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,5,6,3,2,1,9,10,8,7]=>[1,9,10,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,10,9,1]=>[10,7,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,8,7,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,5,8,1,2]=>[1,2,3,6,7,4,5,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,5,1,8,3]=>[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,5,2,3,8]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,7,6,2,3,8]=>[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>[8,6,5,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,6,8,1,2]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,8,6,1,2]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,7,6,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,7,5,1,2]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,5,7,1,2]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,6,7,1,2]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,8,7,1,2]=>[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>[8,7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,6,1,7,3]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,5,1,7,3]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,5,1,6,3]=>[1,6,2,4,5,3,7,8]=>[8,7,3,5,4,2,6,1]=>[8,6,3,5,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,5,2,3,6]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,5,2,3,7]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,6,2,3,7]=>[1,4,8,2,3,7,5,6]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,2,6,4,7]=>[1,3,8,2,6,4,7,5]=>[5,7,4,6,2,8,3,1]=>[8,5,7,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,2,5,4,6]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,1,5,6,4]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,1,5,7,4]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,1,6,7,4]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,7,5,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,6,5,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,6,1,5,3]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,8,1,6,3]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,2,6,4,8]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,1,5,8,4]=>[1,5,8,2,6,7,3,4]=>[4,3,7,6,2,8,5,1]=>[8,5,2,1,7,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,1,8,5,4]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,1,4,3]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,7,2,3,6]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,2,6,4,5]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,2,7,4,6]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,7,5,6]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,3,4,7,6]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,3,4,7,5]=>[1,3,4,7,2,8,5,6]=>[6,5,8,2,7,4,3,1]=>[8,4,7,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,3,4,6,5]=>[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>[8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,2,4,8,7]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,2,8,4,6]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,2,7,3,6]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,2,8,3,6]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,2,3,8,7]=>[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,2,3,8,7]=>[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,2,8,3,6]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,7,2,3,5]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,8,2,3,5]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,8,2,3,5]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,2,8,3,6]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,2,8,3,6]=>[1,2,8,3,6,4,7,5]=>[5,7,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,3,8,4,6]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,2,7,3,6]=>[1,2,7,3,6,4,8,5]=>[5,8,4,6,3,7,2,1]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,2,7,3,6]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,7,2,3,5]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,8,3,4,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,8,2,4,5]=>[1,6,8,2,4,5,3,7]=>[7,3,5,4,2,8,6,1]=>[8,5,2,4,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,1,8,2,3,5]=>[1,8,2,3,5,4,7,6]=>[6,7,4,5,3,2,8,1]=>[8,6,5,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,2,8,3,6]=>[1,2,8,3,6,4,7,5]=>[5,7,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,8,2,3,5]=>[1,8,2,3,5,4,7,6]=>[6,7,4,5,3,2,8,1]=>[8,6,5,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,8,2,3,5]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,2,3,5]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,8,2,4,5]=>[1,6,8,2,4,5,3,7]=>[7,3,5,4,2,8,6,1]=>[8,5,2,4,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,8,2,4,5]=>[1,7,8,2,4,5,3,6]=>[6,3,5,4,2,8,7,1]=>[8,5,2,4,3,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,7,8,5,6]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,7,5,6]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,8,7,5,6]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,2,7,3,6]=>[1,2,7,3,6,4,8,5]=>[5,8,4,6,3,7,2,1]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,2,7,3,6]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,2,7,4,6]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,7,3,4,5]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,7,2,3,5]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,2,3,4]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,6,2,4,5]=>[1,8,2,4,5,3,7,6]=>[6,7,3,5,4,2,8,1]=>[8,6,3,5,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,6,3,4,5]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,6,2,4,5]=>[1,7,2,4,5,3,8,6]=>[6,8,3,5,4,2,7,1]=>[8,6,3,5,4,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,8,5,1,2]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,5,8,1,2]=>[1,2,3,5,8,4,7,6]=>[6,7,4,8,5,3,2,1]=>[8,7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,6,1,8,3]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,6,8,1,2]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,8,6,1,2]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,5,7,1,2]=>[1,2,3,5,7,4,8,6]=>[6,8,4,7,5,3,2,1]=>[8,7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,6,7,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,8,7,1,2]=>[1,2,3,6,8,4,5,7]=>[7,5,4,8,6,3,2,1]=>[8,7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,7,1,8,3]=>[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,7,1,3,8]=>[1,3,8,2,6,7,4,5]=>[5,4,7,6,2,8,3,1]=>[8,5,7,2,1,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,7,4,8]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,6,1,7,8,4]=>[1,7,8,2,6,3,4,5]=>[5,4,3,6,2,8,7,1]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,6,1,7,3]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,5,1,6,3]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,5,1,3,6]=>[1,3,6,2,5,4,7,8]=>[8,7,4,5,2,6,3,1]=>[8,5,7,3,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,6,1,3,7]=>[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>[8,5,7,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,6,8,5,7]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,6,5,7]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,6,4,7]=>[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,5,4,7]=>[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>[8,6,5,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,5,4,6]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,5,6,4]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,6,7,4]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,8,1,6,3]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,8,6,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,1,8,5,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,8,1,5,3]=>[1,5,2,8,3,4,7,6]=>[6,7,4,3,8,2,5,1]=>[8,6,4,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,2,1,4,3]=>[1,4,2,3,5,7,8,6]=>[6,8,7,5,3,2,4,1]=>[8,6,5,7,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,2,1,3,4]=>[1,3,4,2,5,8,6,7]=>[7,6,8,5,2,4,3,1]=>[8,5,7,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,1,8,4,5]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,1,4,8,5]=>[1,4,8,2,3,7,5,6]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,1,4,8,6]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,7,1,3,6]=>[1,3,6,2,8,4,5,7]=>[7,5,4,8,2,6,3,1]=>[8,5,7,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,6,1,3,5]=>[1,3,5,2,6,4,7,8]=>[8,7,4,6,2,5,3,1]=>[8,5,7,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,6,4,5]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,7,4,5]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,7,5,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,7,5,6,8]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,5,7,6]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,1,4,7,6]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,4,6,5]=>[1,4,6,2,3,5,7,8]=>[8,7,5,3,2,6,4,1]=>[8,5,4,7,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,1,4,5,7]=>[1,4,5,7,2,3,8,6]=>[6,8,3,2,7,5,4,1]=>[8,4,3,7,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,5,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,5,8,6,7]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,2,4,3]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,6,2,5,3]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,6,2,5,3]=>[1,4,6,2,5,3,7,8]=>[8,7,3,5,2,6,4,1]=>[8,5,3,7,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,7,2,5,3]=>[1,6,8,2,5,3,4,7]=>[7,4,3,5,2,8,6,1]=>[8,5,3,2,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,2,7,5,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,2,6,5,4]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,2,6,5,4]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,6,5,1,2]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,6,1,5,3]=>[1,5,2,4,6,3,7,8]=>[8,7,3,6,4,2,5,1]=>[8,6,3,5,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,1,6,5,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,3,6,5,4]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,6,5,4]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,3,7,5,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,3,7,5,4]=>[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,8,3,7,6,4]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,3,7,6,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,3,7,5,4]=>[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>[8,5,7,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,1,7,5,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,7,1,5,3]=>[1,5,2,8,3,4,7,6]=>[6,7,4,3,8,2,5,1]=>[8,6,4,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,7,5,1,2]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,4,7,5,1,2]=>[1,2,3,6,8,4,7,5]=>[5,7,4,8,6,3,2,1]=>[8,7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,7,1,5,3]=>[1,5,2,6,8,3,4,7]=>[7,4,3,8,6,2,5,1]=>[8,6,3,2,7,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,3,7,5,4]=>[1,3,7,2,6,8,4,5]=>[5,4,8,6,2,7,3,1]=>[8,5,7,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,3,7,6,4]=>[1,2,5,8,3,7,4,6]=>[6,4,7,3,8,5,2,1]=>[8,7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,8,7,6,5]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,8,7,6,1,2]=>[1,2,3,5,4,8,6,7]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,8,7,6,1,2]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,7,1,6,3]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,1,7,6,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,8,7,6,5]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,7,6,5]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,8,7,6,5]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,8,7,6,5]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,7,6,5]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,2,7,5,4]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,2,7,6,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,7,2,6,3]=>[1,5,2,6,3,4,8,7]=>[7,8,4,3,6,2,5,1]=>[8,6,4,3,7,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,7,2,6,3]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,1,2,4,3]=>[1,2,4,3,5,8,6,7]=>[7,6,8,5,3,4,2,1]=>[8,7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,3,4,1,2]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,2,1,4,3]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,7,2,6,3]=>[1,4,5,8,2,6,3,7]=>[7,3,6,2,8,5,4,1]=>[8,4,2,7,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,8,2,7,6,4]=>[1,3,5,8,2,7,4,6]=>[6,4,7,2,8,5,3,1]=>[8,4,7,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,2,7,6,4]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,2,7,5,4]=>[1,2,7,3,6,8,4,5]=>[5,4,8,6,3,7,2,1]=>[8,7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,7,1,5,3]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,7,6,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,1,7,6,4]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,8,7,6,5]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,7,1,6,3]=>[1,6,2,5,8,3,4,7]=>[7,4,3,8,5,2,6,1]=>[8,6,3,2,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,8,7,6,1,2]=>[1,2,3,5,8,4,6,7]=>[7,6,4,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,7,6,1,2]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,8,1,7,6,4]=>[1,7,2,3,5,8,4,6]=>[6,4,8,5,3,2,7,1]=>[8,6,5,2,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,3,7,6]=>[1,4,2,5,3,7,6,8]=>[8,6,7,3,5,2,4,1]=>[8,6,4,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,5,3,8,6]=>[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>[8,6,4,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,5,3,8,7]=>[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>[8,6,4,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,6,3,8,7]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,4,3,8,7]=>[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>[8,6,4,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,4,3,8,7]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,4,3,7,6]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,4,3,7,5]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,1,4,3,8,5]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,4,3,8,6]=>[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>[8,6,4,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,5,4,7,6]=>[1,8,2,3,5,4,7,6]=>[6,7,4,5,3,2,8,1]=>[8,6,5,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,4,3,7,6]=>[1,4,2,5,3,7,6,8]=>[8,6,7,3,5,2,4,1]=>[8,6,4,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,4,3,7,5]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,8,2,6,5]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,7,2,6,5]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,7,2,6,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,8,2,6,4]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,5,3,7,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,6,3,7,4]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,6,3,7,5]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,1,5,3,8,4]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,6,3,7,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,3,7,5]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,6,4,7,5]=>[1,3,2,6,4,7,5,8]=>[8,5,7,4,6,2,3,1]=>[8,6,7,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,7,5,8,6]=>[1,3,2,7,4,5,8,6]=>[6,8,5,4,7,2,3,1]=>[8,6,7,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,8,5,7,6]=>[1,4,2,3,8,5,7,6]=>[6,7,5,8,3,2,4,1]=>[8,6,5,7,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,8,5,7,6]=>[1,4,2,8,3,5,7,6]=>[6,7,5,3,8,2,4,1]=>[8,6,4,7,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,8,4,7,6]=>[1,3,2,8,4,7,5,6]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,2,8,4,7,5]=>[1,3,2,8,4,7,5,6]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,3,2,6,5]=>[1,3,2,6,4,7,5,8]=>[8,5,7,4,6,2,3,1]=>[8,6,7,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,4,2,6,5]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,4,2,6,5]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,8,3,7,5]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,8,3,7,6]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,8,4,7,6]=>[1,5,2,8,3,4,7,6]=>[6,7,4,3,8,2,5,1]=>[8,6,4,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,8,4,7,6]=>[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>[8,6,5,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,8,4,7,5]=>[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,5,2,6,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,5,2,6,4]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,1,5,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,7,2,6,4]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,7,2,6,5]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,8,2,6,5]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,6,1,5,4]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,7,1,5,4]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,8,1,5,4]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,6,8,1,5,7]=>[1,5,7,2,6,8,3,4]=>[4,3,8,6,2,7,5,1]=>[8,5,2,1,7,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,8,1,4,7]=>[1,4,7,2,8,3,6,5]=>[5,6,3,8,2,7,4,1]=>[8,5,3,7,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,4,8,1,7]=>[1,7,2,4,8,3,6,5]=>[5,6,3,8,4,2,7,1]=>[8,6,3,5,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,2,4,1,6]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,2,4,6,1]=>[1,2,4,6,3,8,5,7]=>[7,5,8,3,6,4,2,1]=>[8,7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,8,3,6,1]=>[1,2,5,8,3,6,4,7]=>[7,4,6,3,8,5,2,1]=>[8,7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,8,3,1,6]=>[1,6,2,5,8,3,4,7]=>[7,4,3,8,5,2,6,1]=>[8,6,3,2,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,1,6,8,3,7]=>[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,1,3,4,7]=>[1,3,4,7,2,8,5,6]=>[6,5,8,2,7,4,3,1]=>[8,4,7,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,4,8,2,7]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,3,8,2,7]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,3,2,8,1,7]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,8,2,1,6]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,8,2,6,1]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,1,4,2,6]=>[1,4,2,6,3,7,8,5]=>[5,8,7,3,6,2,4,1]=>[8,6,4,7,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,1,4,6,2]=>[1,4,6,2,3,5,8,7]=>[7,8,5,3,2,6,4,1]=>[8,5,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,8,3,6,2]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,8,1,5,2]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,8,3,5,2,1]=>[1,2,3,5,4,8,6,7]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,8,4,2,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,1,8,4,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,3,8,4,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,3,8,4,2]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,8,3,5,2]=>[1,8,2,3,5,4,7,6]=>[6,7,4,5,3,2,8,1]=>[8,6,5,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,1,4,5,2]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,4,5,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,3,2,8,4]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,2,1,8,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,2,8,4,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,8,4,1]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,1,8,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,7,3,8,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,4,2,8,3,5]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,8,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,8,2,4,6]=>[1,8,2,4,6,3,5,7]=>[7,5,3,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,1,8,3,5]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,8,3,1,5]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,8,3,5,1]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,8,4,1,5]=>[1,5,2,8,3,6,7,4]=>[4,7,6,3,8,2,5,1]=>[8,6,4,1,7,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,1,8,4,5]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,2,1,4,6]=>[1,4,6,2,3,8,5,7]=>[7,5,8,3,2,6,4,1]=>[8,5,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,2,1,5,6]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,4,6,2,5]=>[1,4,6,2,5,3,7,8]=>[8,7,3,5,2,6,4,1]=>[8,5,3,7,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,2,6,1,5]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,2,6,1,4]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,8,5,1,4]=>[1,4,2,8,3,6,7,5]=>[5,7,6,3,8,2,4,1]=>[8,6,4,7,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,5,2,1,4]=>[1,4,2,3,6,7,8,5]=>[5,8,7,6,3,2,4,1]=>[8,6,5,7,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,5,2,4,1]=>[1,2,4,3,6,7,8,5]=>[5,8,7,6,3,4,2,1]=>[8,7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,2,5,3,1]=>[1,2,5,3,4,7,8,6]=>[6,8,7,4,3,5,2,1]=>[8,7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,2,1,5,3]=>[1,5,2,3,4,7,8,6]=>[6,8,7,4,3,2,5,1]=>[8,6,5,4,7,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,7,8,2,6,3]=>[1,5,7,8,2,6,3,4]=>[4,3,6,2,8,7,5,1]=>[8,4,2,1,7,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,5,1,3,4]=>[1,3,4,2,8,5,6,7]=>[7,6,5,8,2,4,3,1]=>[8,5,7,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,8,2,5,3]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,7,8,4,3]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,7,8,4,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,1,8,4,3]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,8,4,3,1]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,8,4,3,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,1,8,4,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,2,8,4,3]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,2,8,4,3]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,5,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,5,1,4,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,1,5,3,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,8,4,3,2]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,7,8,4,3,2]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,8,4,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,4,2,5,7]=>[1,3,4,2,5,7,6,8]=>[8,6,7,5,2,4,3,1]=>[8,5,7,6,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,6,4,7]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,4,1,8,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,2,4,6,1]=>[1,2,4,6,3,8,5,7]=>[7,5,8,3,6,4,2,1]=>[8,7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,8,3,6,1]=>[1,2,4,5,8,3,6,7]=>[7,6,3,8,5,4,2,1]=>[8,7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,3,7,1,8,6]=>[1,8,2,4,5,3,7,6]=>[6,7,3,5,4,2,8,1]=>[8,6,3,5,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,6,3,1,7]=>[1,7,2,4,5,6,3,8]=>[8,3,6,5,4,2,7,1]=>[8,6,2,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,6,1,3,7]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,5,6,3,7]=>[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,3,6,4,7]=>[1,3,6,2,5,4,7,8]=>[8,7,4,5,2,6,3,1]=>[8,5,7,3,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,1,4,3,7]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,4,1,2,7]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,3,2,7]=>[1,5,6,2,7,3,4,8]=>[8,4,3,7,2,6,5,1]=>[8,5,3,2,7,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,2,1,8,6]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,2,8,1,5]=>[1,5,2,8,3,6,7,4]=>[4,7,6,3,8,2,5,1]=>[8,6,4,1,7,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,7,2,8,5]=>[1,4,2,8,3,6,7,5]=>[5,7,6,3,8,2,4,1]=>[8,6,4,7,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,1,8,2,6]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,1,4,6,3]=>[1,4,6,2,3,5,8,7]=>[7,8,5,3,2,6,4,1]=>[8,5,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,4,1,6,2]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,8,1,5,2]=>[1,5,2,3,6,7,8,4]=>[4,8,7,6,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,4,1,2]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,6,7,8,4,2]=>[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,1,4,8,5,2]=>[1,4,8,2,3,6,7,5]=>[5,7,6,3,2,8,4,1]=>[8,5,4,7,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,4,8,3,5]=>[1,4,8,2,6,7,3,5]=>[5,3,7,6,2,8,4,1]=>[8,5,2,7,1,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,8,1,2,5]=>[1,2,5,3,6,7,8,4]=>[4,8,7,6,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,6,7,8,2,4]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,2,1,4]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,2,4,1]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,3,8,4,6]=>[1,3,8,2,7,4,6,5]=>[5,6,4,7,2,8,3,1]=>[8,5,7,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,8,2,4,6]=>[1,7,8,2,4,6,3,5]=>[5,3,6,4,2,8,7,1]=>[8,5,2,4,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,8,1,3,6]=>[1,3,6,2,7,8,4,5]=>[5,4,8,7,2,6,3,1]=>[8,5,7,2,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,4,8,5,1]=>[1,2,7,3,6,4,8,5]=>[5,8,4,6,3,7,2,1]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,4,8,1,5]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,3,5,8,6]=>[1,3,5,8,2,4,7,6]=>[6,7,4,2,8,5,3,1]=>[8,4,7,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,3,6,5]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,2,1,6,5]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,1,8,5,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,1,8,5,4]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,5,2,3,1]=>[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,8,1,5,3]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,8,1,5,3]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,8,6,2,1,3]=>[1,3,2,4,5,8,6,7]=>[7,6,8,5,4,2,3,1]=>[8,6,7,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,8,6,2,3]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,6,1,2,4]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,1,6,3,4]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,8,2,5,4]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,7,8,4,3]=>[1,2,6,7,8,3,4,5]=>[5,4,3,8,7,6,2,1]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,7,8,4,3,1]=>[1,2,6,7,8,3,4,5]=>[5,4,3,8,7,6,2,1]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,4,1,3]=>[1,3,2,5,6,7,8,4]=>[4,8,7,6,5,2,3,1]=>[8,6,7,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,3,8,5,4]=>[1,3,8,2,6,7,4,5]=>[5,4,7,6,2,8,3,1]=>[8,5,7,2,1,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,1,5,4,3]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,1,4,2]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,5,3,1,2]=>[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,7,6,1,8]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,5,1,2,7]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,4,8,7,2]=>[1,5,6,2,3,4,8,7]=>[7,8,4,3,2,6,5,1]=>[8,5,4,3,7,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,3,5,1,8]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,4,5,1,8]=>[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,4,3,1,8]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,1,3,2,6]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,2,1,3,7]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,2,4,1,3,7]=>[1,3,7,2,4,5,8,6]=>[6,8,5,4,2,7,3,1]=>[8,5,7,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,5,1,4,7]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,4,8,7,3]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,4,2,8,7,3]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,8,2,6,3]=>[1,5,2,6,3,4,8,7]=>[7,8,4,3,6,2,5,1]=>[8,6,4,3,7,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,7,6,2,3]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,4,5,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,4,2,5,3]=>[1,6,8,2,5,3,4,7]=>[7,4,3,5,2,8,6,1]=>[8,5,3,2,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,2,4,5,3]=>[1,7,8,2,4,5,3,6]=>[6,3,5,4,2,8,7,1]=>[8,5,2,4,3,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,8,5,6,3]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,8,5,6,4]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,1,5,4,6]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,1,5,3,6]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,1,4,3,6]=>[1,4,2,3,6,5,8,7]=>[7,8,5,6,3,2,4,1]=>[8,6,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,2,4,3,5]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,4,2,3,5]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,4,3,2,5]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,4,3,5,2]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,3,4,5,2]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,3,4,2,5]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,3,2,4,5]=>[1,3,2,4,5,6,8,7]=>[7,8,6,5,4,2,3,1]=>[8,6,7,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,3,4,6]=>[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>[8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,1,3,5,6]=>[1,3,5,6,2,8,4,7]=>[7,4,8,2,6,5,3,1]=>[8,4,7,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,4,1,5,7]=>[1,5,7,2,6,8,3,4]=>[4,3,8,6,2,7,5,1]=>[8,5,2,1,7,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,3,1,5,7]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,1,2,4,6]=>[1,2,4,6,3,5,8,7]=>[7,8,5,3,6,4,2,1]=>[8,7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,7,8,5,6,2]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,1,5,2,6]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,8,1,6,7]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,2,8,7,5]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,1,7,6,2,5]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,7,6,2,4]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,3,2,8,7,4]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,2,3,8,7,4]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,4,8,7,5]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,8,4,6,5]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,8,3,6,4]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,2,3,5,4]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,3,5,2,4]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,3,5,4,2]=>[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,5,3,4,2]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,5,2,3,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,2,5,3,4]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,7,6,3,4]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,7,6,4,5]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,7,6,5,3]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,7,6,4,3]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,5,2,4,3]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,4,2,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,4,8,7,5]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,3,8,7,6]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,3,8,7,5]=>[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,3,8,7,4]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,3,8,7,5]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,3,8,7,6]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,7,3,6,8]=>[1,2,7,3,6,8,4,5]=>[5,4,8,6,3,7,2,1]=>[8,7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,2,3,5,8]=>[1,7,2,3,5,8,4,6]=>[6,4,8,5,3,2,7,1]=>[8,6,5,2,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,2,3,5,7]=>[1,8,2,3,5,7,4,6]=>[6,4,7,5,3,2,8,1]=>[8,6,5,2,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,8,3,6,5]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,8,3,6,4]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,8,4,6,3]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,8,4,6,2]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,7,4,6,3]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,3,6,4]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,3,6,5]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,2,3,5,6]=>[1,7,2,3,5,6,4,8]=>[8,4,6,5,3,2,7,1]=>[8,6,5,2,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,2,3,5,8]=>[1,6,2,3,5,8,4,7]=>[7,4,8,5,3,2,6,1]=>[8,6,5,2,4,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,2,3,5,4]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,3,4,5,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,3,4,5,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,2,4,5,3]=>[1,6,8,2,4,5,3,7]=>[7,3,5,4,2,8,6,1]=>[8,5,2,4,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,2,3,5,4]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,8,3,6,5]=>[1,2,8,3,6,4,7,5]=>[5,7,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,8,5,6,4]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,8,7,5,6,2]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,7,5,6,3]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,7,5,6,4]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,7,4,6,5]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,6,2,4,5,8]=>[1,7,2,4,5,8,3,6]=>[6,3,8,5,4,2,7,1]=>[8,6,2,5,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,2,3,5,8]=>[1,6,2,3,5,8,4,7]=>[7,4,8,5,3,2,6,1]=>[8,6,5,2,4,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,2,3,5,6]=>[1,7,2,3,5,6,4,8]=>[8,4,6,5,3,2,7,1]=>[8,6,5,2,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,7,3,6,5]=>[1,2,7,3,6,4,8,5]=>[5,8,4,6,3,7,2,1]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,7,3,6,4]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,7,4,6,3]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,3,4,5,2]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,2,3,5,4]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,2,3,4,5]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,2,3,4,6]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,2,3,4,7]=>[1,2,3,4,7,5,8,6]=>[6,8,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,2,3,4,8]=>[1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,3,4,5,2]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,3,4,5,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,2,4,5,3]=>[1,7,2,4,5,3,6,8]=>[8,6,3,5,4,2,7,1]=>[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,3,7,6,8,1]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,6,2,8,7]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,6,2,8,7]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,7,1,8,6]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,7,5,8,1]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,7,1,8,5]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,7,2,8,5]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,7,2,8,6]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,7,2,8,6]=>[1,5,2,8,3,4,7,6]=>[6,7,4,3,8,2,5,1]=>[8,6,4,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,4,7,3,8,6]=>[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>[8,6,5,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,7,6,8,2]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,7,6,8,2]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,7,6,8,2]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,1,7,5,8,2]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,5,7,1,8,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,7,2,8,1]=>[1,2,8,3,6,4,7,5]=>[5,7,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,7,5,8,2]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,4,7,5,8,3]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,4,7,2,8,5]=>[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,7,2,8,4]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,7,1,8,4]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,7,4,8,1]=>[1,2,7,3,6,4,8,5]=>[5,8,4,6,3,7,2,1]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,7,4,8,1]=>[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>[8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,7,1,8,4]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,7,1,8,5]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,3,7,5,8,1]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,7,4,8,5]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,7,6,8,5]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,6,8,4]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,7,5,8,4]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,7,3,8,1]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,7,5,8,3]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,7,6,8,3]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,7,6,8,3]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,7,6,8,4]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,7,6,8,4]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,7,4,8,3]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,7,3,8,1]=>[1,2,7,3,8,4,6,5]=>[5,6,4,8,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,7,1,8,3]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,7,2,8,3]=>[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,7,3,8,4]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,5,7,3,8,2]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,1,7,3,8,2]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,2,4,1,7]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,7,3,6,1]=>[1,2,4,5,7,3,6,8]=>[8,6,3,7,5,4,2,1]=>[8,7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,3,1,8,6]=>[1,8,2,4,5,7,3,6]=>[6,3,7,5,4,2,8,1]=>[8,6,2,5,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,6,1,3,7]=>[1,3,7,2,5,4,6,8]=>[8,6,4,5,2,7,3,1]=>[8,5,7,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,1,4,2,7]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,5,3,2,7]=>[1,4,5,2,7,3,6,8]=>[8,6,3,7,2,5,4,1]=>[8,5,3,7,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,4,3,2,7]=>[1,5,6,2,7,3,4,8]=>[8,4,3,7,2,6,5,1]=>[8,5,3,2,7,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,2,1,8,6]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,3,2,6,1]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,2,8,1,5]=>[1,5,2,8,3,4,7,6]=>[6,7,4,3,8,2,5,1]=>[8,6,4,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,7,3,2,8,5]=>[1,4,6,7,2,8,3,5]=>[5,3,8,2,7,6,4,1]=>[8,4,2,7,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,3,2,8,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,4,2,8,6]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,2,1,6,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,1,4,6,2]=>[1,4,6,2,3,7,5,8]=>[8,5,7,3,2,6,4,1]=>[8,5,4,7,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,5,3,6,2]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,7,1,5,2]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,3,5,2,1]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,8,6,7,4,2]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,7,3,5,2]=>[1,6,7,2,3,5,4,8]=>[8,4,5,3,2,7,6,1]=>[8,5,4,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,8,7,5,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,4,7,5,3]=>[1,4,7,2,6,3,5,8]=>[8,5,3,6,2,7,4,1]=>[8,5,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,1,4,3,5]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,6,8,2,4]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,7,2,4,1]=>[1,2,4,3,6,8,5,7]=>[7,5,8,6,3,4,2,1]=>[8,7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,7,6,8,1,4]=>[1,4,2,3,5,7,6,8]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,7,8,3,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,8,3,1,5]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,7,3,5,1]=>[1,2,6,8,3,5,4,7]=>[7,4,5,3,8,6,2,1]=>[8,7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,6,7,5,1]=>[1,2,4,6,7,3,8,5]=>[5,8,3,7,6,4,2,1]=>[8,7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,4,8,1,5]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,4,7,8,5]=>[1,4,7,8,2,6,3,5]=>[5,3,6,2,8,7,4,1]=>[8,4,2,7,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,4,2,5]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,2,1,6,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,7,2,1,5,4]=>[1,5,2,3,6,7,4,8]=>[8,4,7,6,3,2,5,1]=>[8,6,5,2,7,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,2,1,5,4]=>[1,5,2,3,7,8,4,6]=>[6,4,8,7,3,2,5,1]=>[8,6,5,2,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,5,2,4,1]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,1,7,5,3]=>[1,7,2,3,4,6,8,5]=>[5,8,6,4,3,2,7,1]=>[8,6,5,4,1,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,3,6,4]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,1,3,5,4]=>[1,3,5,2,6,7,4,8]=>[8,4,7,6,2,5,3,1]=>[8,5,7,2,6,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,7,4,1,3]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,5,6,4,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,6,4,3,1]=>[1,2,5,7,3,4,6,8]=>[8,6,4,3,7,5,2,1]=>[8,7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,5,4,1,3]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,2,6,5,3]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,1,3,5,4]=>[1,3,5,2,7,8,4,6]=>[6,4,8,7,2,5,3,1]=>[8,5,7,2,6,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,5,1,4,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,1,3,2]=>[1,3,2,4,7,5,6,8]=>[8,6,5,7,4,2,3,1]=>[8,6,7,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,6,4,3,2]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,5,4,3,2]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,2,4,8,7]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,1,2,8,7]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,2,1,4,6]=>[1,4,6,2,3,7,5,8]=>[8,5,7,3,2,6,4,1]=>[8,5,4,7,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,5,1,3,6]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,1,4,8,7]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,1,2,8,7]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,5,1,2,6]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,2,6,3,5]=>[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,5,1,2,6]=>[1,2,6,3,7,8,4,5]=>[5,4,8,7,3,6,2,1]=>[8,7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,3,4,6]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,5,7,3,4]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,5,8,3,2]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,5,8,2,1]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,1,6,3,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,7,6,2,3]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,7,6,1,3]=>[1,3,2,5,8,4,7,6]=>[6,7,4,8,5,2,3,1]=>[8,6,7,3,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,5,6,7,1]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,5,6,7,2]=>[1,8,2,3,5,6,7,4]=>[4,7,6,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,5,6,7,1]=>[1,2,5,6,7,3,8,4]=>[4,8,3,7,6,5,2,1]=>[8,7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,5,6,7,2]=>[1,3,5,6,7,2,4,8]=>[8,4,2,7,6,5,3,1]=>[8,3,7,2,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,4,1,7,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,4,6,7,3]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,6,7,5]=>[1,4,8,2,3,6,7,5]=>[5,7,6,3,2,8,4,1]=>[8,5,4,7,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,2,1,7,5]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,5,6,7,4]=>[1,8,2,5,6,7,3,4]=>[4,3,7,6,5,2,8,1]=>[8,6,2,1,5,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,5,6,7,4]=>[1,5,6,7,2,3,8,4]=>[4,8,3,2,7,6,5,1]=>[8,4,3,1,7,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,5,6,7,1]=>[1,2,5,6,7,3,8,4]=>[4,8,3,7,6,5,2,1]=>[8,7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,5,6,7,1]=>[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,5,6,7,4]=>[1,5,6,7,2,3,8,4]=>[4,8,3,2,7,6,5,1]=>[8,4,3,1,7,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,5,6,7,4]=>[1,3,5,6,7,2,8,4]=>[4,8,2,7,6,5,3,1]=>[8,3,7,1,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,5,6,7,4]=>[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>[8,7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,3,6,1,5]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,4,1,7,5]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,4,6,7,5]=>[1,8,2,3,4,6,7,5]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,5,4,3,6]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,1,4,2,6]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,5,3,1,6]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,3,6,2,5]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,3,6,2,1]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,4,2,7,1]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,4,2,7,5]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,2,4,1,6]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,8,5,7,6]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,2,8,1,4]=>[1,4,2,8,3,6,5,7]=>[7,5,6,3,8,2,4,1]=>[8,6,4,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,1,2,7,4]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,6,1,7,4]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,6,2,7,1]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,7,6,2,1]=>[1,2,3,5,8,4,7,6]=>[6,7,4,8,5,3,2,1]=>[8,7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,7,6,1,3]=>[1,3,2,4,7,5,8,6]=>[6,8,5,7,4,2,3,1]=>[8,6,7,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,1,6,2,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,5,8,1,3]=>[1,3,2,7,4,5,8,6]=>[6,8,5,4,7,2,3,1]=>[8,6,7,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,5,8,2,3]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,5,8,3,4]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,3,6,7,4]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,2,1,7,4]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,6,7,3]=>[1,4,2,5,6,7,3,8]=>[8,3,7,6,5,2,4,1]=>[8,6,2,7,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,5,6,7,3]=>[1,5,6,7,2,8,3,4]=>[4,3,8,2,7,6,5,1]=>[8,4,2,1,7,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,5,6,7,2]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,5,6,7,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,5,6,7,3]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,5,6,7,3]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,5,6,7,3]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,8,6,1,3]=>[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>[8,6,7,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,8,1,7,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,8,6,7,4]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,8,1,7,2]=>[1,7,2,3,5,8,4,6]=>[6,4,8,5,3,2,7,1]=>[8,6,5,2,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,8,6,1,2]=>[1,2,3,5,4,8,6,7]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,5,6,7,2]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,5,6,7,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,5,6,7,2]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,2,8,4,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,5,8,2,1]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,4,5,8,3,1]=>[1,2,4,5,8,3,6,7]=>[7,6,3,8,5,4,2,1]=>[8,7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,8,6,3,2]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,8,6,3,1]=>[1,2,5,7,3,4,8,6]=>[6,8,4,3,7,5,2,1]=>[8,7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,1,8,4,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,5,2,1,6]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,4,8,6,2,1]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,8,6,2,3]=>[1,4,8,2,3,5,7,6]=>[6,7,5,3,2,8,4,1]=>[8,5,4,7,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,8,2,7,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,8,2,7,1]=>[1,2,7,3,5,8,4,6]=>[6,4,8,5,3,7,2,1]=>[8,7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,1,2,7,5]=>[1,2,7,3,8,4,6,5]=>[5,6,4,8,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,1,6,2,5]=>[1,6,2,5,3,7,8,4]=>[4,8,7,3,5,2,6,1]=>[8,6,4,1,5,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,8,4,7]=>[1,6,8,2,5,3,4,7]=>[7,4,3,5,2,8,6,1]=>[8,5,3,2,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,5,4,8,1,7]=>[1,7,2,5,3,6,4,8]=>[8,4,6,3,5,2,7,1]=>[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,7,1,8,6]=>[1,8,2,4,7,3,5,6]=>[6,5,3,7,4,2,8,1]=>[8,6,3,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,3,7,6,1]=>[1,2,5,8,3,7,4,6]=>[6,4,7,3,8,5,2,1]=>[8,7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,1,6,8,3,7]=>[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,4,8,2,7]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,3,8,2,7]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,7,1,8,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,8,2,7,6,1]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,2,8,7,5,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,6,2,1,8,5]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,7,2,8,5]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,8,3,2,6]=>[1,4,7,2,6,3,5,8]=>[8,5,3,6,2,7,4,1]=>[8,5,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,8,4,2,6]=>[1,3,5,8,2,6,4,7]=>[7,4,6,2,8,5,3,1]=>[8,4,7,2,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,1,4,6,2]=>[1,4,6,2,3,5,8,7]=>[7,8,5,3,2,6,4,1]=>[8,5,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,8,7,3,6,2]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,1,7,5,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,8,6,5,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,6,5,2,1]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,6,4,2,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,1,8,6,4,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,3,7,4,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,7,3,5,2]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,1,4,5,2]=>[1,4,5,2,3,6,8,7]=>[7,8,6,3,2,5,4,1]=>[8,5,4,7,6,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,7,4,5,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,8,4,2,5]=>[1,6,8,2,5,3,4,7]=>[7,4,3,5,2,8,6,1]=>[8,5,3,2,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,2,1,8,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,8,7,4,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,8,7,4,1]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,6,3,1,8,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,7,3,8,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,1,8,3,6]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,4,7,5,1]=>[1,2,4,7,3,8,5,6]=>[6,5,8,3,7,4,2,1]=>[8,7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,1,4,8,5]=>[1,4,8,2,3,6,7,5]=>[5,7,6,3,2,8,4,1]=>[8,5,4,7,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,2,1,5,6]=>[1,5,6,2,3,7,8,4]=>[4,8,7,3,2,6,5,1]=>[8,5,4,1,7,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,4,6,2,5]=>[1,4,6,2,5,3,7,8]=>[8,7,3,5,2,6,4,1]=>[8,5,3,7,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,7,1,6,4]=>[1,6,2,5,7,3,8,4]=>[4,8,3,7,5,2,6,1]=>[8,6,3,1,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,7,1,5,4]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,2,1,5,4]=>[1,5,2,3,6,4,7,8]=>[8,7,4,6,3,2,5,1]=>[8,6,5,3,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,2,5,4,1]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,6,1,3,4]=>[1,3,4,2,6,5,8,7]=>[7,8,5,6,2,4,3,1]=>[8,5,7,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,5,1,3,4]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[8,5,7,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,7,5,2,4]=>[1,7,2,4,3,6,8,5]=>[5,8,6,3,4,2,7,1]=>[8,6,4,5,1,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,1,7,4,3]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,8,6,4,3]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,6,4,3,1]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,7,5,4,3,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,1,8,5,4,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,2,8,5,4,3]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,1,5,3,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,4,3,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,5,4,3,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,7,6,1,8]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,7,3,5,1,8]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,6,3,5,1,8]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,4,5,1,8]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,3,5,1,8]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,3,4,1,8]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,4,1,5,7]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,8,3,4,6]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,7,3,4,6]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,2,3,4,5]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,2,3,4,5]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,8,4,5,6]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,3,4,6]=>[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>[8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,3,1,5,7]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,8,1,6,7]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,1,8,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,3,1,8,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,3,5,6]=>[1,7,2,3,5,6,4,8]=>[8,4,6,5,3,2,7,1]=>[8,6,5,2,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,7,3,4,6]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,3,4,6]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,3,8,4,7]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,4,8,5,7]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,8,4,5,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,2,3,4,5]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,2,3,4,5]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,2,3,4,5]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,7,3,5,6]=>[1,7,2,3,5,6,4,8]=>[8,4,6,5,3,2,7,1]=>[8,6,5,2,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,7,4,5,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,7,4,5,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,7,3,4,6]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,2,4,8,7]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,2,1,4,6]=>[1,4,6,2,3,7,5,8]=>[8,5,7,3,2,6,4,1]=>[8,5,4,7,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,1,8,4,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,1,8,3,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,4,3,8,7]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,1,2,8,7]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,6,2,8,7]=>[1,4,6,2,8,3,5,7]=>[7,5,3,8,2,6,4,1]=>[8,5,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,5,2,8,7]=>[1,4,6,2,8,3,5,7]=>[7,5,3,8,2,6,4,1]=>[8,5,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,2,6,3,5]=>[1,4,7,2,6,3,5,8]=>[8,5,3,6,2,7,4,1]=>[8,5,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,3,4,6]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,1,7,4,2]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,6,7,3,1]=>[1,2,4,6,7,3,5,8]=>[8,5,3,7,6,4,2,1]=>[8,7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,6,5,7,1,2]=>[1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,6,8,2,7,3]=>[1,4,6,8,2,7,3,5]=>[5,3,7,2,8,6,4,1]=>[8,4,2,7,1,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,8,5,7,2]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,8,6,5,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,5,8,6,2]=>[1,3,5,8,2,4,6,7]=>[7,6,4,2,8,5,3,1]=>[8,4,7,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,1,7,3,2]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,7,6,5]=>[1,4,8,2,3,7,5,6]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,2,1,6,5]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,5,7,6,4]=>[1,2,5,7,3,4,6,8]=>[8,6,4,3,7,5,2,1]=>[8,7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,7,6,5,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,6,7,5,4]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,8,5,1]=>[1,2,6,8,3,7,4,5]=>[5,4,7,3,8,6,2,1]=>[8,7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,8,5,6,1]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,7,5,6,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,6,5,7,4]=>[1,3,6,2,8,4,5,7]=>[7,5,4,8,2,6,3,1]=>[8,5,7,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,4,3,1,6]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,3,4,2,5]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,2,6,1]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,2,1,6,5]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,5,7,6]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,7,4,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,4,7,1,3]=>[1,3,2,8,4,7,5,6]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,5,7,2,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,5,7,3,4]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,2,1,8,4]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,5,6,8,3]=>[1,4,2,5,6,8,3,7]=>[7,3,8,6,5,2,4,1]=>[8,6,2,7,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,8,7,3,5]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,8,6,7,3]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,5,8,7,3]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,6,8,1,4]=>[1,4,2,6,8,3,5,7]=>[7,5,3,8,6,2,4,1]=>[8,6,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,6,1,8,2]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,5,7,8,2]=>[1,5,7,8,2,3,4,6]=>[6,4,3,2,8,7,5,1]=>[8,4,3,2,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,7,6,8,2]=>[1,5,7,2,3,4,6,8]=>[8,6,4,3,2,7,5,1]=>[8,5,4,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,6,8,7,2]=>[1,4,5,6,8,2,3,7]=>[7,3,2,8,6,5,4,1]=>[8,3,2,7,6,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,4,3,8,7]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,4,8,3,1]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,8,4,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,4,1,8,7]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,3,5,4,8,7]=>[1,3,5,2,6,4,8,7]=>[7,8,4,6,2,5,3,1]=>[8,5,7,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,4,8,5,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,4,1,6,5]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,8,4,6,2]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,3,8,6,4,1]=>[1,2,5,7,3,8,4,6]=>[6,4,8,3,7,5,2,1]=>[8,7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,5,8,4,2]=>[1,3,5,8,2,4,6,7]=>[7,6,4,2,8,5,3,1]=>[8,4,7,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,1,8,5,2]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,4,8,1,2]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,7,4,8,5,3]=>[1,6,7,2,3,4,8,5]=>[5,8,4,3,2,7,6,1]=>[8,5,4,3,1,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,4,3,6,5]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,4,2,6,1]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,1,2,6,5]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,5,2,6,4]=>[1,3,5,2,6,4,7,8]=>[8,7,4,6,2,5,3,1]=>[8,5,7,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,2,6,1,4]=>[1,4,2,6,3,5,8,7]=>[7,8,5,3,6,2,4,1]=>[8,6,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,1,5,7,4]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,2,5,4,7]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,7,6,3,5]=>[1,2,7,3,5,4,8,6]=>[6,8,4,5,3,7,2,1]=>[8,7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,2,5,7,1,6]=>[1,6,2,5,7,3,8,4]=>[4,8,3,7,5,2,6,1]=>[8,6,3,1,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,2,7,4,1]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,8,7,6,4]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,8,1,6,3]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,5,7,6,1]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,7,6,5,3]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,5,3,6]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,6,7,5,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,6,5,7,2]=>[1,4,8,2,3,5,7,6]=>[6,7,5,3,2,8,4,1]=>[8,5,4,7,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,8,4,2,1]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,8,2,4,3]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,1,7,4,3]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,8,7,3,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,8,3,7,1]=>[1,2,5,8,3,7,4,6]=>[6,4,7,3,8,5,2,1]=>[8,7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,3,8,1,4]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,8,7,5]=>[1,2,3,6,8,4,5,7]=>[7,5,4,8,6,3,2,1]=>[8,7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,1,8,5,6,7]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,4,3,1,7]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,4,5,6,3]=>[1,4,5,6,2,3,7,8]=>[8,7,3,2,6,5,4,1]=>[8,4,3,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,3,4,1,2]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,4,3,6,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,5,3,6,1]=>[1,2,7,8,3,6,4,5]=>[5,4,6,3,8,7,2,1]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,1,4,6,2]=>[1,4,6,2,3,8,5,7]=>[7,5,8,3,2,6,4,1]=>[8,5,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,4,1,2,7]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,5,6,1,7]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,6,5,2,7]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,7,2,5,6]=>[1,7,2,5,6,3,4,8]=>[8,4,3,6,5,2,7,1]=>[8,6,3,2,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,7,2,6,5]=>[1,3,7,2,6,4,5,8]=>[8,5,4,6,2,7,3,1]=>[8,5,7,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,4,7,6,5]=>[1,8,2,4,7,3,5,6]=>[6,5,3,7,4,2,8,1]=>[8,6,3,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,4,6,7,5]=>[1,4,6,7,2,3,8,5]=>[5,8,3,2,7,6,4,1]=>[8,4,3,7,1,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,2,5,7,1]=>[1,2,5,7,3,8,4,6]=>[6,4,8,3,7,5,2,1]=>[8,7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,5,7,6]=>[1,4,8,2,3,5,7,6]=>[6,7,5,3,2,8,4,1]=>[8,5,4,7,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,3,5,1,7]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,5,1,6,7]=>[1,6,7,2,3,5,4,8]=>[8,4,5,3,2,7,6,1]=>[8,5,4,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,4,6,5,7]=>[1,4,6,2,3,8,5,7]=>[7,5,8,3,2,6,4,1]=>[8,5,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,5,7,6]=>[1,3,4,5,7,2,8,6]=>[6,8,2,7,5,4,3,1]=>[8,3,7,6,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,7,4,3,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,1,4,2,8]=>[1,4,2,8,3,5,7,6]=>[6,7,5,3,8,2,4,1]=>[8,6,4,7,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,4,1,6,8]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,4,1,7,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,4,1,6,7]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,6,1,7,4]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,7,4,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,4,7,1,6]=>[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,3,4,6,7,1]=>[1,2,8,3,4,6,7,5]=>[5,7,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,4,6,1,8]=>[1,8,2,4,6,3,5,7]=>[7,5,3,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,3,1,4,8]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,3,1,7,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,3,1,4,7]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,2,4,6,3,1]=>[1,2,4,6,3,5,8,7]=>[7,8,5,3,6,4,2,1]=>[8,7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,1,3,7,4]=>[1,3,7,2,4,5,8,6]=>[6,8,5,4,2,7,3,1]=>[8,5,7,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,1,4,8,2]=>[1,4,8,2,3,5,7,6]=>[6,7,5,3,2,8,4,1]=>[8,5,4,7,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,4,1,8,6]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,4,6,8,1]=>[1,2,4,6,8,3,5,7]=>[7,5,3,8,6,4,2,1]=>[8,7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,3,1,8,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,3,1,7,8]=>[1,7,8,2,6,3,4,5]=>[5,4,3,6,2,8,7,1]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,6,8,5]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,3,4,8,1]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,4,3,8,2]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,6,4,8,7,3]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,7,3,4,2]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,3,7,4,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,7,5,6]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,6,5,7]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,6,7,5]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,6,5,8]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,8,5,7,6]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,4,3,5,2]=>[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,4,5,7,3]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,3,1,7,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,4,3,7,1]=>[1,2,4,3,7,5,8,6]=>[6,8,5,7,3,4,2,1]=>[8,7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,3,7,1,4]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,3,4,1,8]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,4,3,2,8]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,7,3,2,4]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,4,3,2,5]=>[1,6,8,2,5,3,4,7]=>[7,4,3,5,2,8,6,1]=>[8,5,3,2,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,3,4,2,1]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,6,5,7,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,6,2,7,5]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,6,2,7,5]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,6,5,2,7]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,8,3,2,5]=>[1,6,7,8,2,5,3,4]=>[4,3,5,2,8,7,6,1]=>[8,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,3,7,1,8]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,3,8,1,6]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,4,8,7,1]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,4,8,1,7]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,6,8,4,1,2]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,8,1,7,4]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,8,4,7,3]=>[1,2,5,8,3,4,7,6]=>[6,7,4,3,8,5,2,1]=>[8,7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,8,3,4,2]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,3,8,4,1]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,5,8,7,6]=>[1,2,3,5,8,4,6,7]=>[7,6,4,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,7,8,6,5]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,7,3,8,6,1]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,7,8,3,5,2]=>[1,6,7,8,2,3,5,4]=>[4,5,3,2,8,7,6,1]=>[8,4,3,1,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,8,5,7,3]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,5,6,8,7,3]=>[1,2,5,6,8,3,4,7]=>[7,4,3,8,6,5,2,1]=>[8,7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,3,7,8,1]=>[1,2,6,3,7,8,4,5]=>[5,4,8,7,3,6,2,1]=>[8,7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,4,3,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,5,3,6]=>[1,5,2,3,6,4,7,8]=>[8,7,4,6,3,2,5,1]=>[8,6,5,3,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,6,5,3,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,5,7,3,8]=>[1,2,5,7,3,8,4,6]=>[6,4,8,3,7,5,2,1]=>[8,7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,5,7,3,6]=>[1,5,7,2,4,8,3,6]=>[6,3,8,4,2,7,5,1]=>[8,5,2,4,7,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,7,2,5,8]=>[1,4,7,2,5,8,3,6]=>[6,3,8,5,2,7,4,1]=>[8,5,2,7,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,1,6,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,2,3,6,5]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,5,4,1,2]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,5,3,4,6]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,4,1,3,5]=>[1,3,5,2,6,4,7,8]=>[8,7,4,6,2,5,3,1]=>[8,5,7,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,5,4,3,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,5,4,3,8]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,4,3,6]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,6,4,7,5]=>[1,3,8,2,6,4,7,5]=>[5,7,4,6,2,8,3,1]=>[8,5,7,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,7,4,1,8]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,8,7,4,3]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,4,2,7,5]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,5,3,8,7]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,5,8,1,2]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,5,6,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,6,4,2,8,5]=>[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>[8,5,7,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,6,8,4,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,6,4,5,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,3,6,4,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,2,4,7,3]=>[1,5,6,8,2,4,7,3]=>[3,7,4,2,8,6,5,1]=>[8,4,1,3,7,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,7,3,5,8]=>[1,4,7,2,6,3,5,8]=>[8,5,3,6,2,7,4,1]=>[8,5,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,3,8,4,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,4,7,3,6]=>[1,4,7,2,8,3,6,5]=>[5,6,3,8,2,7,4,1]=>[8,5,3,7,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,8,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,1,8,3,2]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,2,7,3,4]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,3,1,8,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,2,3,8,6]=>[1,4,2,3,8,5,7,6]=>[6,7,5,8,3,2,4,1]=>[8,6,5,7,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,3,8,1,2]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,8,7,1,2]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,7,6,8,3]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,7,8,3,5]=>[1,6,2,4,7,8,3,5]=>[5,3,8,7,4,2,6,1]=>[8,6,2,5,1,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,1,6,3,8]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,8,5,3,7]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,5,6,3,7]=>[1,5,6,2,3,7,4,8]=>[8,4,7,3,2,6,5,1]=>[8,5,4,2,7,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,5,3,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,8,2,6,5]=>[1,4,7,8,2,6,3,5]=>[5,3,6,2,8,7,4,1]=>[8,4,2,7,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,5,6,8,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,6,3,8,5]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,6,8,1,2]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,3,5,7,1,2]=>[1,2,3,5,7,4,8,6]=>[6,8,4,7,5,3,2,1]=>[8,7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,2,1,6,4]=>[1,6,2,3,7,8,4,5]=>[5,4,8,7,3,2,6,1]=>[8,6,5,2,1,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,5,2,4,3]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,5,1,4,2]=>[1,4,2,3,6,7,8,5]=>[5,8,7,6,3,2,4,1]=>[8,6,5,7,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,5,2,1,4]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,1,2,4,6]=>[1,2,4,6,3,7,8,5]=>[5,8,7,3,6,4,2,1]=>[8,7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,6,4,2,5,8]=>[1,6,2,5,8,3,7,4]=>[4,7,3,8,5,2,6,1]=>[8,6,3,1,5,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,2,3,5,7]=>[1,8,2,3,5,7,4,6]=>[6,4,7,5,3,2,8,1]=>[8,6,5,2,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,5,4,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,5,3,4,8]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,5,1,4,3,6]=>[1,4,2,8,3,6,5,7]=>[7,5,6,3,8,2,4,1]=>[8,6,4,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,5,1,3,4]=>[1,3,4,2,8,5,6,7]=>[7,6,5,8,2,4,3,1]=>[8,5,7,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,7,4,8,5]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,2,5,8,6]=>[1,2,5,8,3,7,4,6]=>[6,4,7,3,8,5,2,1]=>[8,7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,1,4,8,5]=>[1,4,8,2,7,3,6,5]=>[5,6,3,7,2,8,4,1]=>[8,5,3,7,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,1,2,8,5]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,2,3,8,6]=>[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>[8,6,5,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,3,8,1,5]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,3,7,1,5]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,8,1,2,5]=>[1,2,5,3,8,4,7,6]=>[6,7,4,8,3,5,2,1]=>[8,7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,3,8,1,6]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,4,8,2,5]=>[1,4,8,2,5,3,7,6]=>[6,7,3,5,2,8,4,1]=>[8,5,3,7,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,2,8,1,3]=>[1,3,2,8,4,7,5,6]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,3,7,1,4]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,2,7,4,5]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,7,1,2,5]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,7,1,2,4]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,1,2,4,6]=>[1,2,4,6,3,8,5,7]=>[7,5,8,3,6,4,2,1]=>[8,7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,1,3,4,6]=>[1,3,4,6,2,8,5,7]=>[7,5,8,2,6,4,3,1]=>[8,4,7,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,7,1,3,5]=>[1,3,5,2,7,4,8,6]=>[6,8,4,7,2,5,3,1]=>[8,5,7,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,6,1,2,4]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,8,1,2,4]=>[1,2,4,3,7,5,8,6]=>[6,8,5,7,3,4,2,1]=>[8,7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,8,1,3,5]=>[1,3,5,2,7,4,8,6]=>[6,8,4,7,2,5,3,1]=>[8,5,7,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,8,1,3,6]=>[1,3,6,2,5,7,4,8]=>[8,4,7,5,2,6,3,1]=>[8,5,7,2,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,1,4,8,2,6]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,4,8,1,6]=>[1,6,2,4,8,3,7,5]=>[5,7,3,8,4,2,6,1]=>[8,6,3,5,1,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,1,2,5]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,7,2,3,5]=>[1,6,7,2,3,5,4,8]=>[8,4,5,3,2,7,6,1]=>[8,5,4,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,8,2,3,5]=>[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,7,8,2,3,6]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,7,8,3,4]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,7,8,1,2]=>[1,2,3,6,4,7,8,5]=>[5,8,7,4,6,3,2,1]=>[8,7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,8,5,1,2]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,8,6,3,4]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,1,6,2,4]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,6,2,3,5]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,5,2,3,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,5,2,3,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,2,5,1,3]=>[1,3,2,5,4,7,8,6]=>[6,8,7,4,5,2,3,1]=>[8,6,7,4,5,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,5,1,2,4]=>[1,2,4,3,7,8,5,6]=>[6,5,8,7,3,4,2,1]=>[8,7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,7,1,4,5]=>[1,4,5,2,7,3,6,8]=>[8,6,3,7,2,5,4,1]=>[8,5,3,7,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,1,3,5,6]=>[1,3,5,6,2,4,8,7]=>[7,8,4,2,6,5,3,1]=>[8,4,7,3,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,1,2,5,6]=>[1,2,5,6,3,8,4,7]=>[7,4,8,3,6,5,2,1]=>[8,7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,1,2,4,6]=>[1,2,4,6,3,8,5,7]=>[7,5,8,3,6,4,2,1]=>[8,7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,1,2,3,5]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,1,2,3,6]=>[1,2,3,6,4,8,5,7]=>[7,5,8,4,6,3,2,1]=>[8,7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,1,2,4,6]=>[1,2,4,6,3,5,8,7]=>[7,8,5,3,6,4,2,1]=>[8,7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,7,1,3,5]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,5,7,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,6,2,3,5]=>[1,8,2,3,5,4,7,6]=>[6,7,4,5,3,2,8,1]=>[8,6,5,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,4,1,2,3]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,5,1,2,3]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,6,2,3,4]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,1,2,3,5]=>[1,2,3,5,4,8,6,7]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,2,1,6,4]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,5,1,6,2]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,4,5,8,2,3]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,5,3,6,4]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,1,2,6,4]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,5,3,2,6]=>[1,4,5,2,6,3,7,8]=>[8,7,3,6,2,5,4,1]=>[8,5,3,7,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,1,6,5,3]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,8,6,3,2]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,8,4,7,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,2,5,7,4]=>[1,2,5,7,3,4,6,8]=>[8,6,4,3,7,5,2,1]=>[8,7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,1,6,5,2]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,1,9]=>[1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,8,9,1,7]=>[1,7,2,3,4,5,6,8,9]=>[9,8,6,5,4,3,2,7,1]=>[9,7,6,5,4,3,8,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,5,6,7,8,9,1,3]=>[1,3,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,3,1]=>[9,7,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,1,2]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,1]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,1,10]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,8,9]=>[1,8,9,2,3,4,5,6,7]=>[7,6,5,4,3,2,9,8,1]=>[9,6,5,4,3,2,1,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,10,1,9]=>[1,9,2,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,9,7,8]=>[1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,9,10,1,8]=>[1,8,2,3,4,5,6,7,9,10]=>[10,9,7,6,5,4,3,2,8,1]=>[10,8,7,6,5,4,3,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,1,8,9,6,7]=>[1,8,9,2,3,4,5,6,7]=>[7,6,5,4,3,2,9,8,1]=>[9,6,5,4,3,2,1,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,6,7,8,9,4,5]=>[1,6,7,8,9,2,3,4,5]=>[5,4,3,2,9,8,7,6,1]=>[9,4,3,2,1,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,6,7,8,9,10,1,5]=>[1,5,2,3,4,6,7,8,9,10]=>[10,9,8,7,6,4,3,2,5,1]=>[10,8,7,6,9,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,4,5,6,7,8,9,2,3]=>[1,4,5,6,7,8,9,2,3]=>[3,2,9,8,7,6,5,4,1]=>[9,2,1,8,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,5,6,7,8,9,10,1,3]=>[1,3,2,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,2,3,1]=>[10,8,9,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,10,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,6,4,5,7,2,8,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,2,4,8,1]=>[1,2,4,8,3,6,5,7]=>[7,5,6,3,8,4,2,1]=>[8,7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,7,1,5]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,4,5,8,1]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,4,5,8,1]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,3,6,8,1]=>[1,2,5,7,3,6,8,4]=>[4,8,6,3,7,5,2,1]=>[8,7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,2,3,8,1]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,2,4,8,1]=>[1,2,4,8,3,5,6,7]=>[7,6,5,3,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,4,5,8,1]=>[1,2,4,5,8,3,7,6]=>[6,7,3,8,5,4,2,1]=>[8,7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,4,5,8,1]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,3,7,1,4]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,7,3,4,6]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,8,3,4,6]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,1,8,4,7]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,5,1,8,3,7]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,7,3,4,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,7,2,4,5]=>[1,8,2,4,5,3,7,6]=>[6,7,3,5,4,2,8,1]=>[8,6,3,5,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,3,4,5,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,3,4,5,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,7,2,4,5]=>[1,7,2,4,5,3,8,6]=>[6,8,3,5,4,2,7,1]=>[8,6,3,5,4,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,7,2,3,6]=>[1,5,7,2,3,6,4,8]=>[8,4,6,3,2,7,5,1]=>[8,5,4,2,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,8,2,3,6]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,2,4,5,6]=>[1,7,2,4,5,6,3,8]=>[8,3,6,5,4,2,7,1]=>[8,6,2,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,1,8,3,6]=>[1,8,2,5,7,3,6,4]=>[4,6,3,7,5,2,8,1]=>[8,6,3,1,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,1,8,4,5]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,2,8,4,5]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,7,3,4,5]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,8,2,4,6]=>[1,5,8,2,4,6,3,7]=>[7,3,6,4,2,8,5,1]=>[8,5,2,4,7,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,5,8,4,6,7]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,6,8,2,7]=>[1,3,6,8,2,7,4,5]=>[5,4,7,2,8,6,3,1]=>[8,4,7,2,1,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,6,8,2,7]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,8,7,1,2]=>[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,8,7,1,2]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,7,1,4,6]=>[1,4,6,2,8,3,5,7]=>[7,5,3,8,2,6,4,1]=>[8,5,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,7,2,4,6]=>[1,8,2,4,6,3,5,7]=>[7,5,3,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,6,1,2,4]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,7,2,4,5]=>[1,8,2,4,5,3,7,6]=>[6,7,3,5,4,2,8,1]=>[8,6,3,5,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,7,2,4,5]=>[1,7,2,4,5,3,8,6]=>[6,8,3,5,4,2,7,1]=>[8,6,3,5,4,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,3,5,1,4]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,4,6,1,5]=>[1,5,2,4,6,3,7,8]=>[8,7,3,6,4,2,5,1]=>[8,6,3,5,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>[8,6,4,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,8,2,6,1,3]=>[1,3,2,6,4,7,8,5]=>[5,8,7,4,6,2,3,1]=>[8,6,7,4,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,6,2,4,5]=>[1,6,2,4,5,3,7,8]=>[8,7,3,5,4,2,6,1]=>[8,6,3,5,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,1,4,5,6]=>[1,4,5,6,2,3,8,7]=>[7,8,3,2,6,5,4,1]=>[8,4,3,7,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,3,4,5,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,1,3,4,5]=>[1,3,4,5,2,7,6,8]=>[8,6,7,2,5,4,3,1]=>[8,4,7,6,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,3,4,5,6]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,2,4,5,6]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,6,2,4,5]=>[1,7,8,2,4,5,3,6]=>[6,3,5,4,2,8,7,1]=>[8,5,2,4,3,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,6,1,2,3]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,5,1,2,4]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,5,1,3,4]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,7,2,4,6]=>[1,5,2,4,6,3,7,8]=>[8,7,3,6,4,2,5,1]=>[8,6,3,5,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,6,2,4,8]=>[1,3,6,2,4,8,5,7]=>[7,5,8,4,2,6,3,1]=>[8,5,7,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,6,2,4,1]=>[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>[8,7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,2,6,5,1]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,7,5,6]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,7,6,5]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,6,7,2,3]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,6,2,7,4]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,5,7,6]=>[1,4,2,5,7,3,6,8]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,5,6,7]=>[1,4,2,5,6,7,3,8]=>[8,3,7,6,5,2,4,1]=>[8,6,2,7,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,2,5,6,1]=>[1,2,5,6,3,4,8,7]=>[7,8,4,3,6,5,2,1]=>[8,7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,2,5,7,1]=>[1,2,5,7,3,8,4,6]=>[6,4,8,3,7,5,2,1]=>[8,7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,2,5,8,7]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,2,5,8,6]=>[1,3,2,5,8,4,6,7]=>[7,6,4,8,5,2,3,1]=>[8,6,7,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,6,2,8,4]=>[1,3,6,2,8,4,5,7]=>[7,5,4,8,2,6,3,1]=>[8,5,7,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,6,8,2,3]=>[1,4,6,8,2,3,5,7]=>[7,5,3,2,8,6,4,1]=>[8,4,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,6,2,1,4]=>[1,4,2,3,6,5,8,7]=>[7,8,5,6,3,2,4,1]=>[8,6,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,2,6,1,5]=>[1,5,2,6,3,4,8,7]=>[7,8,4,3,6,2,5,1]=>[8,6,4,3,7,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,2,5,8,1]=>[1,2,5,8,3,7,4,6]=>[6,4,7,3,8,5,2,1]=>[8,7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,8,6,1,7]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,7,2,1,4]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,7,1,2,3]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,7,8,2,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,7,2,8,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,2,7,8,5]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,1,8,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,8,2,7,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,8,7,2,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,8,6,2,3]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,2,8,6,5]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,2,8,5,6]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,2,8,5,7]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,2,7,5,8]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,2,7,5,1]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,7,2,4,1]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,7,2,4,8]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,8,2,4,7]=>[1,8,2,4,7,3,5,6]=>[6,5,3,7,4,2,8,1]=>[8,6,3,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,4,5,2,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,4,5,2,3]=>[1,4,5,2,3,6,8,7]=>[7,8,6,3,2,5,4,1]=>[8,5,4,7,6,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,3,2,5,4]=>[1,3,2,5,4,6,8,7]=>[7,8,6,4,5,2,3,1]=>[8,6,7,4,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,8,2,4,1]=>[1,2,4,3,7,8,5,6]=>[6,5,8,7,3,4,2,1]=>[8,7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,2,8,5,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,3,2,1,5,6]=>[1,5,6,2,3,4,8,7]=>[7,8,4,3,2,6,5,1]=>[8,5,4,3,7,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,1,6,2,3]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,1,7,2,3]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,1,2,7,4]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,8,1,7,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,7,2,1,8,5]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,1,2,8,4]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,1,8,2,3]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,8,2,1,4]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,7,8,1,6]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,3,4,8,7]=>[1,3,4,8,2,5,6,7]=>[7,6,5,2,8,4,3,1]=>[8,4,7,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,2,1,4,6]=>[1,4,6,2,3,7,8,5]=>[5,8,7,3,2,6,4,1]=>[8,5,4,7,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,5,8,3,4]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,4,3,5,6]=>[1,7,8,2,3,5,6,4]=>[4,6,5,3,2,8,7,1]=>[8,5,4,1,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,1,5,6,2]=>[1,5,6,2,3,7,4,8]=>[8,4,7,3,2,6,5,1]=>[8,5,4,2,7,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,5,4,6,3]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,2,4,5,7]=>[1,8,2,4,5,7,3,6]=>[6,3,7,5,4,2,8,1]=>[8,6,2,5,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,7,6,2,5]=>[1,3,7,2,5,4,6,8]=>[8,6,4,5,2,7,3,1]=>[8,5,7,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,2,1,6,3]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,8,3,4,2]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,8,7,4,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,1,3,6,5]=>[1,3,6,2,8,4,7,5]=>[5,7,4,8,2,6,3,1]=>[8,5,7,3,1,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,4,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,3,4,7,8]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,3,4,6,8]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,6,3,4,5,8]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,3,5,4,6]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,3,5,4,6]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,3,5,4,7]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,3,6,5,7]=>[1,4,2,8,3,6,5,7]=>[7,5,6,3,8,2,4,1]=>[8,6,4,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,4,6,5,7]=>[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,3,6,4,8]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,3,5,4,8]=>[1,6,2,7,3,5,4,8]=>[8,4,5,3,7,2,6,1]=>[8,6,4,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,6,3,5,4,8]=>[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,3,5,4,7]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,5,3,6,4,8]=>[1,7,2,5,3,6,4,8]=>[8,4,6,3,5,2,7,1]=>[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>[8,6,7,3,4,2,5,1]=>[8,6,4,5,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,6,5,7]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,4,6,5,8]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,7,5,6]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,3,8,5,7]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,3,7,4,5]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,4,7,5,6]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,4,7,5,6]=>[1,3,2,8,4,7,5,6]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,3,7,5,6]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,3,6,4,5]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,3,6,4,5]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,5,1,7,2]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,5,1,2,7]=>[1,2,7,3,8,4,6,5]=>[5,6,4,8,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,4,1,2,7]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,4,1,7,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,5,3,1,8]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,2,4,3,1,8]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,3,1,7,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,3,1,2,7]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,6,2,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,6,3,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,3,6,2]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,2,1,7,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,4,1,7,3]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,5,1,3,7]=>[1,3,7,2,8,4,6,5]=>[5,6,4,8,2,7,3,1]=>[8,5,7,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,2,4,1,3,7]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,2,1,3,7]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,3,2,6]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,2,6,3]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,5,2,3,4]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,5,2,4,3]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,5,3,2,4]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,5,2,4]=>[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>[8,5,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,6,3,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,6,4,5]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,6,5,4]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,1,6,5,3]=>[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,6,4,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,5,4,2]=>[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>[8,5,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,5,4,3,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,5,4,2,3]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,5,2,3]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,5,3,2]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,3,5,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,4,5,2]=>[1,3,4,5,2,6,7,8]=>[8,7,6,2,5,4,3,1]=>[8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,4,6,3]=>[1,4,6,2,3,5,7,8]=>[8,7,5,3,2,6,4,1]=>[8,5,4,7,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,1,5,6,3]=>[1,5,6,2,8,3,4,7]=>[7,4,3,8,2,6,5,1]=>[8,5,3,2,7,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,5,6,4]=>[1,5,6,2,7,8,3,4]=>[4,3,8,7,2,6,5,1]=>[8,5,2,1,7,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,3,2,1,7,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,4,6,2]=>[1,4,6,2,3,5,7,8]=>[8,7,5,3,2,6,4,1]=>[8,5,4,7,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,6,4,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,1,5,6,2]=>[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>[8,5,4,2,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,2,1,7,5]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,8,1,7,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,8,1,7,6]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,8,1,6,7]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,1,5,2,6]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,1,2,5,6]=>[1,2,5,6,3,8,4,7]=>[7,4,8,3,6,5,2,1]=>[8,7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,2,4,6]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[8,7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,1,2,6,4]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,5,4,6]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,4,2,5]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,3,2,5]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,2,5,3]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,4,2,3,5]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,5,3,4]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,5,4,3]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,4,5,3]=>[1,2,4,5,3,6,7,8]=>[8,7,6,3,5,4,2,1]=>[8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,2,5,4]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,1,3,6,4]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,1,4,6,5]=>[1,4,6,2,7,8,3,5]=>[5,3,8,7,2,6,4,1]=>[8,5,2,7,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,3,2,4,5]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,4,3,5]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,1,2,3,5,4]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,4,2,6,8]=>[1,3,7,2,6,8,4,5]=>[5,4,8,6,2,7,3,1]=>[8,5,7,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,3,1,7,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,6,1,7,3]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,7,3,1,4]=>[1,4,2,8,3,5,7,6]=>[6,7,5,3,8,2,4,1]=>[8,6,4,7,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,5,6,1,7]=>[1,7,2,8,3,5,6,4]=>[4,6,5,3,8,2,7,1]=>[8,6,4,1,3,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,5,6,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,5,2,4,8]=>[1,6,2,4,8,3,7,5]=>[5,7,3,8,4,2,6,1]=>[8,6,3,5,1,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,5,1,7,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,5,1,4,7]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,5,6,3,1]=>[1,2,5,6,3,4,8,7]=>[7,8,4,3,6,5,2,1]=>[8,7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,2,1,3,6]=>[1,3,6,2,4,8,5,7]=>[7,5,8,4,2,6,3,1]=>[8,5,7,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,5,1,3,7,2]=>[1,3,7,2,4,8,5,6]=>[6,5,8,4,2,7,3,1]=>[8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,1,8,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,1,2,8,6]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,5,6,8,2]=>[1,5,6,8,2,3,7,4]=>[4,7,3,2,8,6,5,1]=>[8,4,3,1,7,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,7,5,2,8,4]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,7,6,8,5]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,4,1,8,3]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,6,4,7,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,7,2,4,3]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,2,7,4,1]=>[1,2,7,3,5,8,4,6]=>[6,4,8,5,3,7,2,1]=>[8,7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,2,3,7,1]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,3,7,1,4]=>[1,4,2,5,8,3,7,6]=>[6,7,3,8,5,2,4,1]=>[8,6,3,7,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,7,6,3,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,1,7,5]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,8,6,5,1,7]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,5,8,6,1,4]=>[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>[8,6,4,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,7,8,6,1,5]=>[1,5,2,4,7,8,3,6]=>[6,3,8,7,4,2,5,1]=>[8,6,2,5,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,1,8,7,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,4,8,2,7]=>[1,4,8,2,7,3,6,5]=>[5,6,3,7,2,8,4,1]=>[8,5,3,7,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,8,4,2,1]=>[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>[8,7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,8,2,7,4]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,8,3,4,1]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,3,8,4,2]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,2,7,8,6,5]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,2,8,6,3]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,7,8,2,5,1]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,6,8,5,7,2]=>[1,4,6,8,2,3,5,7]=>[7,5,3,2,8,6,4,1]=>[8,4,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,7,1,8,2]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,1,7,8,3]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,3,6,5,8]=>[1,4,2,3,6,5,8,7]=>[7,8,5,6,3,2,4,1]=>[8,6,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,6,5,8]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,2,3,7,6]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,6,2,4,8]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,5,6,3,4,8]=>[1,5,6,2,3,4,8,7]=>[7,8,4,3,2,6,5,1]=>[8,5,4,3,7,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,5,4,3,8]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,3,2,7,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,3,1,8,2]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,1,3,8,2]=>[1,3,8,2,4,7,5,6]=>[6,5,7,4,2,8,3,1]=>[8,5,7,4,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,7,5,4,8,3]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,5,4,7,6]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,5,4,7,6]=>[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>[8,6,5,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,1,3,7,6]=>[1,3,7,2,4,8,5,6]=>[6,5,8,4,2,7,3,1]=>[8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,3,7,1,5]=>[1,5,2,6,8,3,7,4]=>[4,7,3,8,6,2,5,1]=>[8,6,3,1,7,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,3,6,5,1]=>[1,2,7,8,3,6,4,5]=>[5,4,6,3,8,7,2,1]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,3,6,5,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,6,3,4,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,6,3,4,1]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,7,3,1,4]=>[1,4,2,6,8,3,5,7]=>[7,5,3,8,6,2,4,1]=>[8,6,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,1,3,4]=>[1,3,4,2,5,8,6,7]=>[7,6,8,5,2,4,3,1]=>[8,5,7,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,1,7,3,5]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,6,7,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,7,6,8,4,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,6,8,4,2]=>[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,1,8,3,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,6,8,1,3,2]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,5,8,3,1,2]=>[1,2,3,4,6,7,5,8]=>[8,5,7,6,4,3,2,1]=>[8,7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,7,3,2,4]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,7,2,3,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,8,2,3,1]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,7,8,2,1,3]=>[1,3,2,4,6,5,7,8]=>[8,7,5,6,4,2,3,1]=>[8,6,7,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,7,1,8,2,3]=>[1,8,2,3,4,6,7,5]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,7,8,3,4]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,7,2,8,4]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,7,1,2,8,3]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,7,2,1,8,3]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,2,8,1,3]=>[1,3,2,8,4,7,5,6]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,2,7,3,5]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,6,7,4,5]=>[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,6,8,4,1]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,7,8,1,4]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,2,7,1,8,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,7,8,5]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,4,3,7,8,5]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,3,8,7,6]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,2,8,7,6]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,8,7,1,5]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,7,6,5,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,2,6,5,1]=>[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>[8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,2,7,1,5]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,1,2,7,6]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,1,8,2,7,6]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,8,7,3,5]=>[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,1,7,2,5]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,1,2,4]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,7,2,1,4]=>[1,4,2,3,6,5,8,7]=>[7,8,5,6,3,2,4,1]=>[8,6,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,6,2,4,1]=>[1,2,4,3,7,5,8,6]=>[6,8,5,7,3,4,2,1]=>[8,7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,6,2,4,3]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,5,4,2,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,8,6,1,4,2]=>[1,4,2,3,5,7,8,6]=>[6,8,7,5,3,2,4,1]=>[8,6,5,7,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,8,6,5,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,7,6,5,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,1,6,5,3]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,6,1,4,3]=>[1,4,2,5,8,3,6,7]=>[7,6,3,8,5,2,4,1]=>[8,6,3,7,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,12,5,4,11,8,7,10,9,6,3]=>[1,12,2,3,4,11,5,6,7,10,8,9]=>[9,8,10,7,6,5,11,4,3,2,12,1]=>[12,10,9,8,6,5,4,2,1,3,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,12,5,4,11,10,9,8,7,6,3]=>[1,12,2,3,4,11,5,6,7,8,9,10]=>[10,9,8,7,6,5,11,4,3,2,12,1]=>[12,10,9,8,6,5,4,3,2,1,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,12,7,6,5,4,11,10,9,8,3]=>[1,12,2,3,4,11,5,6,7,8,9,10]=>[10,9,8,7,6,5,11,4,3,2,12,1]=>[12,10,9,8,6,5,4,3,2,1,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,12,9,8,7,6,5,4,11,10,3]=>[1,12,2,3,4,11,5,6,7,8,9,10]=>[10,9,8,7,6,5,11,4,3,2,12,1]=>[12,10,9,8,6,5,4,3,2,1,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,12,11,10,9,8,7,6,5,4,3]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,12,1]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,3,2,1,12,7,6,11,10,9,8,5]=>[1,12,2,3,4,5,6,11,7,8,9,10]=>[10,9,8,7,11,6,5,4,3,2,12,1]=>[12,10,9,8,7,6,4,3,2,1,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,3,2,1,12,9,8,7,6,11,10,5]=>[1,12,2,3,4,5,6,11,7,8,9,10]=>[10,9,8,7,11,6,5,4,3,2,12,1]=>[12,10,9,8,7,6,4,3,2,1,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,3,2,1,12,11,10,9,8,7,6,5]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,12,1]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,5,4,3,2,1,12,9,8,11,10,7]=>[1,12,2,3,4,5,6,7,8,11,9,10]=>[10,9,11,8,7,6,5,4,3,2,12,1]=>[12,10,9,8,7,6,5,4,2,1,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,5,4,3,2,1,12,11,10,9,8,7]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,12,1]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,1,12,11,10,9]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,12,1]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,2,1,12,11]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,12,1]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[7,4,6,1,8,3,5,2]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,7,4,6,2]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,7,5,6,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,7,5,6,2]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,7,5,8,3]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,7,5,8,3]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,6,8,4,3]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,1,7,5,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,5,1,8,4,2]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,8,3,4,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,5,7,1,8,2]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,1,8,3,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,8,4,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,7,5,3,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,3,1,8,4,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,6,7,5,3]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,6,7,5,3]=>[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,7,6,8,4]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,7,6,8,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,1,7,6,8,4]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,6,7,5,3]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,5,8,2,3]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,7,5,8,3]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,6,8,4,3]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,7,6,8,4]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,7,6,8,4]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,7,6,8,5]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,2,7,6,8,4]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,8,2,3,4]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,5,8,3,4]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,5,1,7,6,8,4]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,8,4,2,3]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,7,5,2,3]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,7,6,8,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,7,6,8,4]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,7,6,8,4]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,5,7,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,1,5,8,3,4]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,7,1,5,3]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,7,4,8,3]=>[1,5,2,7,3,4,8,6]=>[6,8,4,3,7,2,5,1]=>[8,6,4,3,7,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,5,8,3,1,4]=>[1,4,2,5,8,3,6,7]=>[7,6,3,8,5,2,4,1]=>[8,6,3,7,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,6,2,1,4]=>[1,4,2,3,5,7,6,8]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,7,6,2,4]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,3,7,6,8,4]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,3,7,6,8,4]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,7,5,8,3]=>[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>[8,6,4,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,5,7,1,4]=>[1,4,2,5,7,3,6,8]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,7,6,1,4]=>[1,4,2,5,7,3,6,8]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,7,6,8,4]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,7,6,8,5]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,7,6,8,5]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,7,6,8,5]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,7,6,8,5]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,7,6,8,4]=>[1,3,7,2,5,4,6,8]=>[8,6,4,5,2,7,3,1]=>[8,5,7,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,5,7,6,1,4]=>[1,4,2,8,3,5,7,6]=>[6,7,5,3,8,2,4,1]=>[8,6,4,7,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,5,7,1,4]=>[1,4,2,3,5,7,6,8]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,5,8,2,4]=>[1,3,5,8,2,4,6,7]=>[7,6,4,2,8,5,3,1]=>[8,4,7,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,6,1,2,4]=>[1,2,4,3,5,7,6,8]=>[8,6,7,5,3,4,2,1]=>[8,7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,7,6,8,4]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,4,7,6,8,5]=>[1,2,4,7,3,5,6,8]=>[8,6,5,3,7,4,2,1]=>[8,7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,8,9,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,9,4,5,6,1,2,3,7]=>[1,2,3,7,4,5,6,8,9,10]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,8,10,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,10,5,6,8,1,2,3,4]=>[1,2,3,4,5,6,8,7,10,9]=>[9,10,7,8,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,6,2,7,4]=>[1,3,5,6,2,7,4,8]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,2,6,7,5]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,4,5,6,1]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,4,5,7,1]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,4,5,8,7]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,2,6,8,5]=>[1,4,2,6,8,3,5,7]=>[7,5,3,8,6,2,4,1]=>[8,6,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,6,8,2,3]=>[1,5,6,8,2,3,4,7]=>[7,4,3,2,8,6,5,1]=>[8,4,3,2,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,5,6,1,2,3]=>[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,6,2,1,4]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,2,6,1,5]=>[1,5,2,6,3,7,8,4]=>[4,8,7,3,6,2,5,1]=>[8,6,4,1,7,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,4,5,1,6]=>[1,6,2,4,5,3,7,8]=>[8,7,3,5,4,2,6,1]=>[8,6,3,5,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,4,5,1,7]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,7,4,5,8,1]=>[1,2,3,6,7,4,5,8]=>[8,5,4,7,6,3,2,1]=>[8,7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,8,6,1,7]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,8,7,1,6]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,8,7,1,2,3]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,7,8,2,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,3,8,5,6]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,3,7,5,8]=>[1,3,7,2,4,5,8,6]=>[6,8,5,4,2,7,3,1]=>[8,5,7,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,7,5,1]=>[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>[8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,8,3,4,7]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,7,8,3,4,1]=>[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,7,3,8,5,1]=>[1,2,4,6,7,3,8,5]=>[5,8,3,7,6,4,2,1]=>[8,7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,7,3,1,5,8]=>[1,5,8,2,6,7,3,4]=>[4,3,7,6,2,8,5,1]=>[8,5,2,1,7,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,2,3,1,5,6]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,1,7,2,3]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,1,2,7,4]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,6,7,2,1,8,5]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,2,8,1,5]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,7,8,1,6]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,8,6,4,3]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,6,5,2,3]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,5,3,2,4]=>[1,5,2,4,3,6,8,7]=>[7,8,6,3,4,2,5,1]=>[8,6,4,5,7,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,5,1,2,4]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,6,5,2,4]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,6,1,5,3]=>[1,5,2,8,3,4,7,6]=>[6,7,4,3,8,2,5,1]=>[8,6,4,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,4,8,6,5,2]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,1,8,6,5,3]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,2,3,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,6,3,4]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,1,3,5,4]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,5,7,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,5,3,1,4]=>[1,4,2,5,3,6,8,7]=>[7,8,6,3,5,2,4,1]=>[8,6,4,7,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,7,4,5,2]=>[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,4,7,5,2]=>[1,6,8,2,3,4,7,5]=>[5,7,4,3,2,8,6,1]=>[8,5,4,3,1,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,1,7,5,3]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,3,5,1,4]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,7,3,5,4]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,6,3,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,3,6,4]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,1,4,3,5]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,3,1,6,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,3,4,6,2]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,5,4,6,2]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,7,1,6,3]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,4,3,1,5]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,4,3,5]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,4,2,3,5]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,3,2,5]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,2,1,6,3]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,5,4,3,6,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,3,7,5,2]=>[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,2,5,1,4]=>[1,4,2,5,3,6,8,7]=>[7,8,6,3,5,2,4,1]=>[8,6,4,7,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,3,2,5,4]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,3,2,6,4]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,1,2,6,4]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,7,2,6,3]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,1,6,2,3]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,5,7,4,3]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,1,2,6,3]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,7,2,6,3]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,7,2,6,4]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,1,2,6,4]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,7,2,5,4]=>[1,3,7,2,5,4,6,8]=>[8,6,4,5,2,7,3,1]=>[8,5,7,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,4,5,3,6,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,1,4,2,5]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,2,4,5]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,4,5,6,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,7,1,6,3]=>[1,6,2,4,5,7,3,8]=>[8,3,7,5,4,2,6,1]=>[8,6,2,5,4,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,4,2,8,7]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,2,7,6,4]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,7,3,6]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,7,6,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,1,3,8,7]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,3,1,8,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,1,3,2,8,7]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,2,7,6,3]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,3,2,5]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,5,3,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,3,7,6,2]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,1,7,6,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,7,6,4]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,3,7,6,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,7,4,6]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,3,7,2,6]=>[1,3,7,2,6,4,5,8]=>[8,5,4,6,2,7,3,1]=>[8,5,7,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,5,2,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,2,5,3]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,1,4,3]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,2,1,5]=>[1,5,2,3,6,4,7,8]=>[8,7,4,6,3,2,5,1]=>[8,6,5,3,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,4,1,5]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,4,3,5]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,4,5,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,4,5,1]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,2,5,1]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,4,3,1]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,3,7,6,1]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,5,3,1]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,3,5,1]=>[1,2,6,3,5,4,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,3,1,5]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,4,2,5]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,4,5,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,5,4,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,4,7,6,2]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,4,7,2,6]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,5,2,4]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,2,5,4]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,1,5,3]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,5,1,3]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,4,7,1,6]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,5,1,4]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,5,1,2]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,1,4,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,3,4,2]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,4,3,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,1,3,2]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,1,5,2]=>[1,5,2,3,6,4,7,8]=>[8,7,4,6,3,2,5,1]=>[8,6,5,3,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,1,5,4]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,3,5,4]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,1,4,5]=>[1,4,5,2,7,3,6,8]=>[8,6,3,7,2,5,4,1]=>[8,5,3,7,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,2,4,3]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,8,4,6,2]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,8,5,6,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,1,8,7,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,7,4,3,8]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,1,8,6,5,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,1,8,4,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,8,5,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,8,7,5,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,7,5,3,8]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,7,6,4,8]=>[1,5,2,7,3,4,8,6]=>[6,8,4,3,7,2,5,1]=>[8,6,4,3,7,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,8,7,6,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,1,7,8,6,4]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,7,8,5,3]=>[1,7,8,2,6,3,4,5]=>[5,4,3,6,2,8,7,1]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,1,7,8,4,3]=>[1,7,8,2,6,3,4,5]=>[5,4,3,6,2,8,7,1]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,6,8,2,3]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,8,4,3,7]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,8,5,3,7]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,6,5,7]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,8,3,4,7]=>[1,2,5,8,3,4,7,6]=>[6,7,4,3,8,5,2,1]=>[8,7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,8,2,5,6]=>[1,3,4,8,2,5,6,7]=>[7,6,5,2,8,4,3,1]=>[8,4,7,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,8,2,3,4]=>[1,5,6,8,2,3,4,7]=>[7,4,3,2,8,6,5,1]=>[8,4,3,2,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,7,8,3,4]=>[1,5,7,8,2,6,3,4]=>[4,3,6,2,8,7,5,1]=>[8,4,2,1,7,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,8,5,2,3]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,8,6,7,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,6,8,7,4]=>[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,7,3,4,8]=>[1,6,2,5,7,3,4,8]=>[8,4,3,7,5,2,6,1]=>[8,6,3,2,5,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,8,7,3,4]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,8,5,7,3]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,4,8,7,3,5]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,7,3,5,8]=>[1,6,2,4,7,3,5,8]=>[8,5,3,7,4,2,6,1]=>[8,6,3,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,8,7,5,6]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,4,7,8,3,5]=>[1,4,7,8,2,6,3,5]=>[5,3,6,2,8,7,4,1]=>[8,4,2,7,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,6,8,2,3,5]=>[1,4,6,8,2,3,5,7]=>[7,5,3,2,8,6,4,1]=>[8,4,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,8,2,4,6]=>[1,3,5,8,2,4,6,7]=>[7,6,4,2,8,5,3,1]=>[8,4,7,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,3,1,8,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,5,2,4,1]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,4,1,8,6]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,4,1,8,7]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,1,6,3,8,7]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,3,5,2,8,7]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,5,2,8,7]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,4,1,8,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,6,7,3,4,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,7,3,4,1]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,4,1,8,5]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,5,2,8,6]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,5,2,8,6]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,5,2,8,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,5,3,8,6]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,7,4,5,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,7,3,5,2]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,4,1,5,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,4,1,6,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,7,3,4,1]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,7,3,6,2]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,7,4,6,2]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,4,6,3]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,6,3,8,5]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,6,2,8,5]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,6,2,8,4]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,5,1,8,4]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,7,3,5,1]=>[1,2,8,3,5,4,7,6]=>[6,7,4,5,3,8,2,1]=>[8,7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,2,5,1]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[8,7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,6,2,4,1]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,6,2,3,1]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,3,1,8,5]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,7,4,8,5]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,7,4,8,6]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,8,5,7,4]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,3,1,7,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,6,2,3,1]=>[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,6,2,4,1]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,4,1,7,3]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,1,8,6,7,3]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,8,6,7,3]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,2,8,6,7,4]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,8,5,7,4]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,2,8,4,7,3]=>[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,5,1,7,3]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,8,4,5,1]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,6,2,7,3]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,6,2,7,3]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,6,2,7,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,6,3,7,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,8,5,6,3]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,8,5,6,2]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,8,5,6,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,5,1,6,2]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,7,3,6,2]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,8,4,5,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,3,4,2]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,6,2,5,4]=>[1,3,6,2,5,4,7,8]=>[8,7,4,5,2,6,3,1]=>[8,5,7,3,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,7,2,5,8]=>[1,4,7,2,5,8,3,6]=>[6,3,8,5,2,7,4,1]=>[8,5,2,7,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,2,5,7,3,8]=>[1,2,5,7,3,8,4,6]=>[6,4,8,3,7,5,2,1]=>[8,7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,5,7,3,6]=>[1,4,8,2,5,7,3,6]=>[6,3,7,5,2,8,4,1]=>[8,5,2,7,4,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,5,6,1,3]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,4,6,3,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,6,3,4,5]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,3,1,6,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,3,2,7,6]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,3,2,7,8]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,7,1,5]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,4,7,6,3]=>[1,4,7,2,5,8,3,6]=>[6,3,8,5,2,7,4,1]=>[8,5,2,7,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,7,6,1,2]=>[1,2,3,5,8,4,7,6]=>[6,7,4,8,5,3,2,1]=>[8,7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,7,3,8,5]=>[1,6,2,4,7,3,8,5]=>[5,8,3,7,4,2,6,1]=>[8,6,3,5,1,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,4,7,8,3]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,3,6,8,2]=>[1,3,6,8,2,4,7,5]=>[5,7,4,2,8,6,3,1]=>[8,4,7,3,1,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,2,1,8,4]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,2,4,8,3]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,4,5,8,7]=>[1,2,4,5,8,3,6,7]=>[7,6,3,8,5,4,2,1]=>[8,7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,2,5,3,8,6]=>[1,4,7,2,5,3,8,6]=>[6,8,3,5,2,7,4,1]=>[8,5,3,7,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,3,5,1,2]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,4,2,5,7]=>[1,8,2,5,7,3,6,4]=>[4,6,3,7,5,2,8,1]=>[8,6,3,1,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,5,8,2,4,3]=>[1,6,7,2,4,3,5,8]=>[8,5,3,4,2,7,6,1]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,7,8,1,4,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,6,8,1,3,4]=>[1,3,4,2,5,7,6,8]=>[8,6,7,5,2,4,3,1]=>[8,5,7,6,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,8,4,1,3]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,4,5,3,7]=>[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,5,3,4,6]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,8,5,4,1,2]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,6,7,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,4,6,7,2]=>[1,8,2,3,4,6,7,5]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,5,6,1,7]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,6,1,7,5]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,5,2,6,8]=>[1,5,2,6,8,3,4,7]=>[7,4,3,8,6,2,5,1]=>[8,6,3,2,7,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,1,2,6,5]=>[1,2,6,3,7,8,4,5]=>[5,4,8,7,3,6,2,1]=>[8,7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,6,2,5,7]=>[1,8,2,5,7,3,6,4]=>[4,6,3,7,5,2,8,1]=>[8,6,3,1,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,3,2,1,4]=>[1,4,2,3,5,7,8,6]=>[6,8,7,5,3,2,4,1]=>[8,6,5,7,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,1,3,4,2]=>[1,3,4,2,5,8,6,7]=>[7,6,8,5,2,4,3,1]=>[8,5,7,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,8,2,5,7]=>[1,6,2,5,7,3,8,4]=>[4,8,3,7,5,2,6,1]=>[8,6,3,1,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,4,8,2,6,5]=>[1,3,4,8,2,6,5,7]=>[7,5,6,2,8,4,3,1]=>[8,4,7,6,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,1,2,7,8]=>[1,2,7,8,3,6,4,5]=>[5,4,6,3,8,7,2,1]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,1,7,8,6,3]=>[1,7,8,2,4,5,3,6]=>[6,3,5,4,2,8,7,1]=>[8,5,2,4,3,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,4,5,8,1,7]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,8,3,7,5]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,8,5,1,2]=>[1,2,3,6,4,8,5,7]=>[7,5,8,4,6,3,2,1]=>[8,7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,8,3,5,6]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,3,8,4,2]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,7,1,8,4,3]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,1,4,8]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,4,2,8,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,4,1,8,3,2]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,2,8,3,4]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,4,8,3,6]=>[1,7,2,4,8,3,6,5]=>[5,6,3,8,4,2,7,1]=>[8,6,3,5,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,8,3,4,7]=>[1,5,2,8,3,4,7,6]=>[6,7,4,3,8,2,5,1]=>[8,6,4,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,3,8,4,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,4,2,3,8,7]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,4,2,8,6]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,5,3,2,8,4]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,4,1,2,8,3]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,3,1,8,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,3,1,6,8]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,5,3,6,8]=>[1,4,2,5,3,6,8,7]=>[7,8,6,3,5,2,4,1]=>[8,6,4,7,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,2,5,7,3]=>[1,4,2,5,7,3,6,8]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,5,7,3,8]=>[1,6,2,5,7,3,8,4]=>[4,8,3,7,5,2,6,1]=>[8,6,3,1,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,7,5,4,2]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,6,4,2,8]=>[1,3,5,6,2,8,4,7]=>[7,4,8,2,6,5,3,1]=>[8,4,7,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,1,5,2,8]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,5,3,6,8]=>[1,5,2,4,3,6,8,7]=>[7,8,6,3,4,2,5,1]=>[8,6,4,5,7,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,4,1,6,8]=>[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,3,4,7,5]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,3,6,7,4]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,3,7,6,4,1]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,3,7,4,5]=>[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>[8,5,7,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,5,4,7,1]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,2,4,7,5]=>[1,2,4,7,3,5,6,8]=>[8,6,5,3,7,4,2,1]=>[8,7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,5,7,1,4,8]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,8,5,6,3]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,6,8,5,1,3]=>[1,3,2,4,7,5,6,8]=>[8,6,5,7,4,2,3,1]=>[8,6,7,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,8,1,4,6,3]=>[1,4,6,2,5,7,8,3]=>[3,8,7,5,2,6,4,1]=>[8,5,1,7,4,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,4,1,6,2,8]=>[1,6,2,8,3,5,7,4]=>[4,7,5,3,8,2,6,1]=>[8,6,4,1,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,8,6,7,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,8,6,3,7,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,5,3,7,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,7,6,3,1]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,5,8,6,3]=>[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>[8,6,4,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,6,7,5,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,6,2,4,1]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,6,2,1,3]=>[1,3,2,4,7,5,8,6]=>[6,8,5,7,4,2,3,1]=>[8,6,7,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,7,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>[8,6,4,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,6,7,2,4]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,6,4,2,8,3]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,1,6,2,3]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,2,7,3,5]=>[1,2,7,3,5,4,8,6]=>[6,8,4,5,3,7,2,1]=>[8,7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,2,3,7,4]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,4,3,7,1]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,1,2,7,4]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,7,6,3,8]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,6,8,7,3]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,7,5,1,4,8]=>[1,4,8,2,7,3,6,5]=>[5,6,3,7,2,8,4,1]=>[8,5,3,7,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,7,3,5,8]=>[1,7,2,6,3,5,8,4]=>[4,8,5,3,6,2,7,1]=>[8,6,4,1,3,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,2,7,5,8]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,7,6,2,8]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,1,6,3,8]=>[1,6,2,5,7,3,8,4]=>[4,8,3,7,5,2,6,1]=>[8,6,3,1,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,5,6,2,8]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,5,8,7,1,2]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,8,6,7,2]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,6,8,7,2]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,8,6,4,3]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,3,8,6,4]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,3,8,6,5]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,5,2,3,8]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,5,2,4,8]=>[1,3,7,2,4,8,5,6]=>[6,5,8,4,2,7,3,1]=>[8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,8,5,4,7]=>[1,2,6,8,3,4,7,5]=>[5,7,4,3,8,6,2,1]=>[8,7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,4,8,6,5]=>[1,3,7,2,4,8,5,6]=>[6,5,8,4,2,7,3,1]=>[8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,1,8,6,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,5,8,6,3]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,3,7,4,6]=>[1,3,7,2,8,4,6,5]=>[5,6,4,8,2,7,3,1]=>[8,5,7,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,3,4,7,5]=>[1,6,8,2,3,4,7,5]=>[5,7,4,3,2,8,6,1]=>[8,5,4,3,1,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,1,5,7,4]=>[1,5,7,2,6,8,3,4]=>[4,3,8,6,2,7,5,1]=>[8,5,2,1,7,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,1,5,7,3]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,5,1,8,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,5,8,1,4]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,6,8,1,4]=>[1,4,2,7,3,6,8,5]=>[5,8,6,3,7,2,4,1]=>[8,6,4,7,1,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,6,1,8,2]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,6,1,7,2]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,1,6,7,3]=>[1,6,7,2,4,3,5,8]=>[8,5,3,4,2,7,6,1]=>[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,1,6,7,4]=>[1,6,7,2,3,5,4,8]=>[8,4,5,3,2,7,6,1]=>[8,5,4,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,6,7,1,5]=>[1,5,2,8,3,6,7,4]=>[4,7,6,3,8,2,5,1]=>[8,6,4,1,7,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,7,3,5,6]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,6,2,5,7]=>[1,3,6,2,5,7,4,8]=>[8,4,7,5,2,6,3,1]=>[8,5,7,2,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,7,2,5,6]=>[1,7,2,5,6,3,4,8]=>[8,4,3,6,5,2,7,1]=>[8,6,3,2,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,7,1,6,3]=>[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,3,1,6,2]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,1,7,5,2]=>[1,7,2,3,4,6,8,5]=>[5,8,6,4,3,2,7,1]=>[8,6,5,4,1,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,2,4,7,5]=>[1,8,2,4,7,3,5,6]=>[6,5,3,7,4,2,8,1]=>[8,6,3,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,6,2,3,8]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,2,6,3,7]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,2,7,3,6]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,1,7,4,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,2,6,3,7]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,8,5,1,4]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,3,1,6,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,8,1,6,3]=>[1,6,2,5,8,3,4,7]=>[7,4,3,8,5,2,6,1]=>[8,6,3,2,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,6,2,5,7]=>[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>[8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,6,7,1,5]=>[1,5,2,4,6,7,3,8]=>[8,3,7,6,4,2,5,1]=>[8,6,2,5,7,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,6,1,7,2]=>[1,7,2,3,5,6,4,8]=>[8,4,6,5,3,2,7,1]=>[8,6,5,2,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,7,8,1,4]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,4,1,2,5]=>[1,2,5,3,4,6,8,7]=>[7,8,6,4,3,5,2,1]=>[8,7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,1,5,3,2]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,2,5,3,1]=>[1,2,5,3,4,7,6,8]=>[8,6,7,4,3,5,2,1]=>[8,7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,2,6,3,1]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,6,1,2,4]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,5,1,2,6]=>[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>[8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,5,1,2,7]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,6,1,2,4]=>[1,2,4,3,5,8,6,7]=>[7,6,8,5,3,4,2,1]=>[8,7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,6,1,2,3]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,7,1,6,3,2]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,7,6,4,1]=>[1,2,7,3,5,8,4,6]=>[6,4,8,5,3,7,2,1]=>[8,7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,1,7,6,4,2]=>[1,7,2,3,5,8,4,6]=>[6,4,8,5,3,2,7,1]=>[8,6,5,2,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,1,6,3,4]=>[1,6,2,5,8,3,4,7]=>[7,4,3,8,5,2,6,1]=>[8,6,3,2,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,1,6,3,5]=>[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,1,5,3,7]=>[1,5,2,4,6,3,7,8]=>[8,7,3,6,4,2,5,1]=>[8,6,3,5,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,2,5,3,7]=>[1,4,6,2,5,3,7,8]=>[8,7,3,5,2,6,4,1]=>[8,5,3,7,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,2,6,3,5]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,7,6,4,3]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,3,7,6,4,1]=>[1,2,5,8,3,7,4,6]=>[6,4,7,3,8,5,2,1]=>[8,7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,7,5,4,6]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,6,5,4,7]=>[1,3,2,6,4,7,5,8]=>[8,5,7,4,6,2,3,1]=>[8,6,7,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,6,5,4,7]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,7,6,4,5]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,7,6,5,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,7,6,5,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,8,7,6,5,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,7,5,4,6]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,1,5,3,7]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,7,6,4,3]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,7,6,4,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,7,6,4,1]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,7,5,4,1]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,7,5,4,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,7,5,4,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,1,5,3,4]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,1,4,3,5]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,2,4,3,7]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,2,4,3,6]=>[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>[8,7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,7,5,4,3]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,7,5,4,1]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,7,6,4,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,7,6,4,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,2,6,3,5]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,2,5,3,6]=>[1,7,2,5,3,6,4,8]=>[8,4,6,3,5,2,7,1]=>[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,7,5,4,6]=>[1,2,7,3,8,4,6,5]=>[5,6,4,8,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,7,6,4,5]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,7,6,5,4]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,7,6,5,2]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,8,7,6,5,2]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,6,4,5]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,7,5,4,6]=>[1,3,7,2,8,4,6,5]=>[5,6,4,8,2,7,3,1]=>[8,5,7,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,6,5,4,7]=>[1,3,6,2,4,7,5,8]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,5,4,7]=>[1,2,3,6,4,7,5,8]=>[8,5,7,4,6,3,2,1]=>[8,7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,7,6,4,5]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,6,8,2,5,7]=>[1,4,2,5,7,3,6,8]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,2,5,8,4,7]=>[1,6,2,5,8,3,4,7]=>[7,4,3,8,5,2,6,1]=>[8,6,3,2,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,8,2,4,7,6]=>[1,8,2,4,7,3,5,6]=>[6,5,3,7,4,2,8,1]=>[8,6,3,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,2,8,3,7,6]=>[1,4,5,2,8,3,7,6]=>[6,7,3,8,2,5,4,1]=>[8,5,3,7,6,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,5,8,3,7]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,6,8,3,7]=>[1,5,2,6,8,3,7,4]=>[4,7,3,8,6,2,5,1]=>[8,6,3,1,7,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,5,8,2,4,7]=>[1,6,2,4,7,3,5,8]=>[8,5,3,7,4,2,6,1]=>[8,6,3,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,5,8,3,7]=>[1,6,2,5,8,3,7,4]=>[4,7,3,8,5,2,6,1]=>[8,6,3,1,5,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,4,8,3,7]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,4,8,3,7]=>[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>[8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,4,7,3,8,6]=>[1,2,5,3,8,4,7,6]=>[6,7,4,8,3,5,2,1]=>[8,7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,6,3,8,7,5]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,2,8,3,6]=>[1,4,7,2,8,3,6,5]=>[5,6,3,8,2,7,4,1]=>[8,5,3,7,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,3,7,6,5]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,5,3,7,4]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,8,7,3,5]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,7,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,1,8,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,2,8,3,5]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,5,3,8,4]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,5,3,8,4]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,3,8,7,4]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,6,3,8,7,4]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,7,3,8,4]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,2,8,3,6]=>[1,5,7,2,8,3,6,4]=>[4,6,3,8,2,7,5,1]=>[8,5,3,1,7,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,6,3,7,5]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,2,4,7,5]=>[1,8,2,4,7,3,5,6]=>[6,5,3,7,4,2,8,1]=>[8,6,3,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,8,2,5,6]=>[1,8,2,5,6,3,7,4]=>[4,7,3,6,5,2,8,1]=>[8,6,3,1,5,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,4,7,5]=>[1,6,2,4,7,3,5,8]=>[8,5,3,7,4,2,6,1]=>[8,6,3,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,2,4,6,5]=>[1,8,2,4,6,3,5,7]=>[7,5,3,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,2,4,6,5]=>[1,8,2,4,6,3,5,7]=>[7,5,3,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,7,3,6,5]=>[1,4,2,8,3,6,5,7]=>[7,5,6,3,8,2,4,1]=>[8,6,4,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,8,3,6,5]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,2,7,3,6]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,2,7,3,6]=>[1,4,8,2,7,3,6,5]=>[5,6,3,7,2,8,4,1]=>[8,5,3,7,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,7,3,4,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,2,7,3,5]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,6,3,7,4]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,3,7,6,4]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,8,7,5,4]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,3,8,5,4]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,3,8,5,4]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,5,3,6,4]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,8,6,3,5]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,8,6,3,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,5,3,6,4]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,3,7,5,4]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,8,6,5,4]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,6,5,8,2]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,7,6,2,4,3]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,3,4,5,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,2,4,1,3]=>[1,3,2,4,5,7,8,6]=>[6,8,7,5,4,2,3,1]=>[8,6,7,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,6,2,4,3,8]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,3,8,7,2]=>[1,4,5,2,3,8,6,7]=>[7,6,8,3,2,5,4,1]=>[8,5,4,7,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,3,7,8,2]=>[1,4,5,2,3,7,8,6]=>[6,8,7,3,2,5,4,1]=>[8,5,4,7,6,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,3,5,7,2]=>[1,4,8,2,3,5,7,6]=>[6,7,5,3,2,8,4,1]=>[8,5,4,7,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,3,4,5,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,3,8,6,2]=>[1,4,5,2,3,8,6,7]=>[7,6,8,3,2,5,4,1]=>[8,5,4,7,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,3,6,8,2]=>[1,4,5,2,3,6,8,7]=>[7,8,6,3,2,5,4,1]=>[8,5,4,7,6,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,3,6,7,2]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,2,6,3,8]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,7,2,1,4,8]=>[1,4,8,2,3,5,7,6]=>[6,7,5,3,2,8,4,1]=>[8,5,4,7,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,2,1,7,4]=>[1,7,2,3,5,8,4,6]=>[6,4,8,5,3,2,7,1]=>[8,6,5,2,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,7,2,1,8,4]=>[1,8,2,3,5,7,4,6]=>[6,4,7,5,3,2,8,1]=>[8,6,5,2,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,7,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,3,7,2,1]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,6,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>[7,6,8,5,4,2,3,1]=>[8,6,7,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,3,1,7,2]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,2,3,7,6]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,2,6,3,7]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,6,5,7]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,6,1,7,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,6,3,1,8,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,3,1,7,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,2,1,6,4]=>[1,6,2,3,5,8,4,7]=>[7,4,8,5,3,2,6,1]=>[8,6,5,2,4,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,2,1,4,8]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,1,3,4,8]=>[1,3,4,8,2,7,5,6]=>[6,5,7,2,8,4,3,1]=>[8,4,7,6,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,1,3,5,4]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>[8,5,7,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,8,3,1,4]=>[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>[8,6,4,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,4,3,1,5]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,8,3,4,5]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,4,3,5,8]=>[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>[8,6,4,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,2,8,4,6]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,2,3,7,6]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,3,4,2,5]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,3,2,7,5]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,4,1,7,5]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,4,3,1,5]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,7,5,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,7,3,4,5]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,4,5,7,6]=>[1,4,5,7,2,3,8,6]=>[6,8,3,2,7,5,4,1]=>[8,4,3,7,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,4,3,5,7]=>[1,4,2,8,3,5,7,6]=>[6,7,5,3,8,2,4,1]=>[8,6,4,7,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,2]=>[2,9,8,7,6,5,4,3,1]=>[9,1,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,8,9,10]=>[1,3,4,5,6,7,8,9,10,2]=>[2,10,9,8,7,6,5,4,3,1]=>[10,1,9,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,6,7,10,8]=>[1,2,3,4,5,6,7,10,8,9]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,2,3,4,5,6,9,7]=>[1,8,2,3,4,5,6,9,7]=>[7,9,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,1,8,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,6,9,8]=>[1,2,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,9,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,8,1,3,4,5,6,7,9]=>[1,3,4,5,6,7,9,2,8]=>[8,2,9,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,1,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,2,10]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,2]=>[2,11,10,9,8,7,6,5,4,3,1]=>[11,1,10,9,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,4,3,6,5,1,7,2]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,4,1,7,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,1,7,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,4,2,3,8]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,2,7,3,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,1,6,3,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,1,3,6,2]=>[1,3,6,2,4,5,7,8]=>[8,7,5,4,2,6,3,1]=>[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,2,1,7,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,5,1,7,3]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,5,1,7,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,6,4,5,8]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,7,6,2,5,8]=>[1,3,7,2,5,8,4,6]=>[6,4,8,5,2,7,3,1]=>[8,5,7,2,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,6,2,4,8]=>[1,7,2,4,8,3,6,5]=>[5,6,3,8,4,2,7,1]=>[8,6,3,5,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,5,3,2,4,8]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,5,2,4,3,8]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,3,4,5,8]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,7,4,5,6]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,3,5,4]=>[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,6,4,3,5]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,4,7,3,5]=>[1,8,2,4,7,3,5,6]=>[6,5,3,7,4,2,8,1]=>[8,6,3,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,2,7,4,6]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,8,4,7,5,6]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,1,6,4,3]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,5,4,3,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,5,6,3,4]=>[1,7,8,2,5,6,3,4]=>[4,3,6,5,2,8,7,1]=>[8,5,2,1,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,4,5,3,2]=>[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,4,3,5,2]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,3,2,1,7,4]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,3,1,4,6,2]=>[1,4,6,2,3,5,8,7]=>[7,8,5,3,2,6,4,1]=>[8,5,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,1,6,4,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,2,7,3,6]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,1,5,6,2]=>[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>[8,5,4,2,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,5,2,7,8]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,1,2,5,7,6]=>[1,2,5,7,3,4,6,8]=>[8,6,4,3,7,5,2,1]=>[8,7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,3,6,7,8]=>[1,5,2,3,6,7,8,4]=>[4,8,7,6,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,2,3,7,6]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,2,6,3,8]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,4,3,2,7,8]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,4,2,7,8]=>[1,3,4,2,7,8,5,6]=>[6,5,8,7,2,4,3,1]=>[8,5,7,6,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,5,3,7,8]=>[1,5,2,3,7,8,4,6]=>[6,4,8,7,3,2,5,1]=>[8,6,5,2,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,5,4,7,8]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,4,6,5,8]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,1,3,6,5,8]=>[1,3,6,2,4,7,5,8]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,5,3,7,4]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,6,4,5,8]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,3,6,5,4]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,4,3,7,5]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,3,2,4,7,6]=>[1,3,2,4,7,5,8,6]=>[6,8,5,7,4,2,3,1]=>[8,6,7,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,3,5,7,6]=>[1,3,5,7,2,4,8,6]=>[6,8,4,2,7,5,3,1]=>[8,4,7,3,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,1,4,5,7,6]=>[1,4,5,7,2,8,3,6]=>[6,3,8,2,7,5,4,1]=>[8,4,2,7,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,5,6,7,8]=>[1,3,2,5,6,7,8,4]=>[4,8,7,6,5,2,3,1]=>[8,6,7,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,3,6,7,8]=>[1,2,4,3,6,7,8,5]=>[5,8,7,6,3,4,2,1]=>[8,7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,4,6,5,8]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,1,2,4]=>[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,1,8,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,8,1,2,3]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,6,1,2,4]=>[1,2,4,3,7,8,5,6]=>[6,5,8,7,3,4,2,1]=>[8,7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,7,1,2,6]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,8,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,4,8,1]=>[1,2,7,3,5,6,4,8]=>[8,4,6,5,3,7,2,1]=>[8,7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,8,4,2]=>[1,7,8,2,3,5,6,4]=>[4,6,5,3,2,8,7,1]=>[8,5,4,1,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,1,6,3,7]=>[1,6,2,4,5,3,7,8]=>[8,7,3,5,4,2,6,1]=>[8,6,3,5,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,2,3,7,5]=>[1,4,8,2,3,7,5,6]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,2,3,7,4]=>[1,5,6,8,2,3,7,4]=>[4,7,3,2,8,6,5,1]=>[8,4,3,1,7,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,2,8,4,7,3]=>[1,5,6,2,8,3,4,7]=>[7,4,3,8,2,6,5,1]=>[8,5,3,2,7,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,4,7,8,1]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,8,5,7,3]=>[1,4,2,6,8,3,5,7]=>[7,5,3,8,6,2,4,1]=>[8,6,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,5,6,4,7]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,5,7,4,6]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,8,7,5,3]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,7,8,5,2]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,7,6,8,5,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,1,6,3,4]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,6,4,8,1]=>[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>[8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,5,8,4,2]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,1,8,5,4,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,1,5,3,4]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,1,4,3,5]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,8,4,5,3]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,4,8,5,2]=>[1,3,4,8,2,5,6,7]=>[7,6,5,2,8,4,3,1]=>[8,4,7,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,4,8,6,2]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,2,3,6,4]=>[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,2,3,6,5]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,7,4,5,6]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,7,5,8,6,2]=>[1,3,7,2,4,5,8,6]=>[6,8,5,4,2,7,3,1]=>[8,5,7,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,5,7,8,6,2]=>[1,4,5,7,8,2,3,6]=>[6,3,2,8,7,5,4,1]=>[8,3,2,7,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,4,7,6,5]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,4,6,5,7]=>[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>[8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,5,7,6]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,4,6,7,5]=>[1,2,8,3,4,6,7,5]=>[5,7,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,6,5,8,7,3]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,4,8,7,3]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,8,6,1,4]=>[1,4,2,3,8,5,7,6]=>[6,7,5,8,3,2,4,1]=>[8,6,5,7,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,8,1,6,4]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,1,8,7,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,3,8,7,4]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,2,8,7,4]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,2,8,7,4]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,1,8,7,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,8,6,1,4]=>[1,4,2,8,3,5,7,6]=>[6,7,5,3,8,2,4,1]=>[8,6,4,7,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,2,1,5,4]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,8,2,6,3]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,8,3,6,2]=>[1,5,7,2,3,6,4,8]=>[8,4,6,3,2,7,5,1]=>[8,5,4,2,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,8,6,2,3]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,8,6,2,4]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,2,1,4]=>[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,1,4,2,5]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,3,5,2,4]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,4,5,2,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,4,5,3,2]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,4,3,5,2]=>[1,6,7,8,2,3,5,4]=>[4,5,3,2,8,7,6,1]=>[8,4,3,1,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,4,2,5,3]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,1,8,3,6,4]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,3,1,5,4]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,4,1,5,3]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,1,4,5,3]=>[1,4,5,2,7,8,3,6]=>[6,3,8,7,2,5,4,1]=>[8,5,2,7,6,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,1,8,4,6,3]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,7,8,5,6,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,7,8,6,5,3]=>[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,1,5,4,3]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,5,1,4,3]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,1,8,6,3,4]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,8,6,3,4]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,2,8,6,4,3]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,3,5,4,2]=>[1,6,7,8,2,3,5,4]=>[4,5,3,2,8,7,6,1]=>[8,4,3,1,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,2,5,4,3]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,4,1,3,5]=>[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>[8,5,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,4,3,1,5]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,5,2,3,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,8,5,3,4,2]=>[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,5,4,2,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,5,3,2,4]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,1,3,2,5]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,2,7,4,1]=>[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,8,7,2,1]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,4,8,7,3,2]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,5,7,1,2]=>[1,2,3,6,4,8,5,7]=>[7,5,8,4,6,3,2,1]=>[8,7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,6,3,7,2]=>[1,4,8,2,3,7,5,6]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,8,6,5,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,1,4,2,5]=>[1,4,2,5,3,6,8,7]=>[7,8,6,3,5,2,4,1]=>[8,6,4,7,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,6,8,2,4]=>[1,6,8,2,4,3,7,5]=>[5,7,3,4,2,8,6,1]=>[8,5,3,4,1,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,6,7,2,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,8,7,5,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,8,1,4]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,8,3,2,6]=>[1,4,8,2,6,3,5,7]=>[7,5,3,6,2,8,4,1]=>[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,5,1,4,6,2]=>[1,4,6,2,3,5,7,8]=>[8,7,5,3,2,6,4,1]=>[8,5,4,7,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,3,7,2,1]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,2,8,5,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,4,5,3]=>[1,6,2,4,5,3,7,8]=>[8,7,3,5,4,2,6,1]=>[8,6,3,5,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,1,4,5,2]=>[1,4,5,2,3,8,6,7]=>[7,6,8,3,2,5,4,1]=>[8,5,4,7,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,1,2,6]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,1,5,6,2]=>[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>[8,5,4,2,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,2,5,7,4]=>[1,2,5,7,3,6,4,8]=>[8,4,6,3,7,5,2,1]=>[8,7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,8,7,3,2,4]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,3,6,8,1]=>[1,2,7,3,6,8,4,5]=>[5,4,8,6,3,7,2,1]=>[8,7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,6,4,2,8,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,4,3,5,8,1]=>[1,2,7,3,5,8,4,6]=>[6,4,8,5,3,7,2,1]=>[8,7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,4,2,8,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,4,5,2,8,1]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,5,3,4,8,1]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,1,8,2,7]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,7,3,1]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,7,2,6,3]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,2,8,3,4,7]=>[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,2,1,8,3,6]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,1,8,2,7]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,2,7,3,1]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,5,7,4,1]=>[1,2,5,7,3,8,4,6]=>[6,4,8,3,7,5,2,1]=>[8,7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,2,6,4,1]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,7,2,5,4]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,6,4,3,1]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,5,4,3]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,3,2,5,4]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,3,5,6,4]=>[1,7,2,8,3,5,6,4]=>[4,6,5,3,8,2,7,1]=>[8,6,4,1,3,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,7,4,5,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,7,3,6,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,6,8,3,2,4]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,8,4,2,6]=>[1,5,8,2,6,3,7,4]=>[4,7,3,6,2,8,5,1]=>[8,5,3,1,7,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,4,2,5,3]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,3,4,6,5]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,3,5,4,6]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,1,8,4,3,5]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,7,3,5,4]=>[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,8,3,6,7]=>[1,5,8,2,3,6,7,4]=>[4,7,6,3,2,8,5,1]=>[8,5,4,1,7,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,1,8,3,6]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,6,8,3,2,1]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,2,7,3,1]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,7,3,4,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,7,4,2,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,5,3,2,1]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,7,2,6,3]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,2,6,4,1]=>[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,7,3,4,1]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,6,3,5,1]=>[1,2,8,3,5,4,7,6]=>[6,7,4,5,3,8,2,1]=>[8,7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,4,5,6,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,4,3,5,1]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,5,6,3,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,3,5,4,1]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,2,4,3]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,5,3,2,4]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,6,3,4,5]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,8,7,4,2,3]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,5,3,2,1]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,5,4,3,1]=>[1,2,5,3,4,6,8,7]=>[7,8,6,4,3,5,2,1]=>[8,7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,4,5,2,1]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,6,5,3,4,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,5,4,2,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,3,5,1,2]=>[1,2,3,5,4,8,6,7]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,4,5,1,2]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,7,4,5,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,4,5,2,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,4,6,2,3]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,4,6,1,2]=>[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,3,6,1,2]=>[1,2,3,6,4,8,5,7]=>[7,5,8,4,6,3,2,1]=>[8,7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,4,5,1,2]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,4,5,1,2]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,8,5,6,1,2]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,5,6,1,2]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,5,6,1,3]=>[1,3,2,8,4,7,5,6]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,5,6,2,3]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,5,6,1,4]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,4,5,1,3]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,4,5,1,3]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,4,5,2,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,4,5,2,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,4,6,2,3]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,5,6,2,3]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,1,7,3,4]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,2,7,3,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,3,6,2,5]=>[1,7,2,5,3,6,4,8]=>[8,4,6,3,5,2,7,1]=>[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,3,5,2,4]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,3,5,1,4]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,3,6,1,5]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,2,6,1,4]=>[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,3,6,1,4]=>[1,4,2,8,3,6,5,7]=>[7,5,6,3,8,2,4,1]=>[8,6,4,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,3,5,2,4]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>[8,6,4,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>[7,6,8,5,4,2,3,1]=>[8,6,7,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,1,4,2,3]=>[1,4,2,3,5,7,6,8]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,6,7,3,4]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,7,1,6,2,4]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,1,5,2,3]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,1,5,2,3]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,1,5,2,4]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,1,5,2,4]=>[1,5,2,4,3,7,6,8]=>[8,6,7,3,4,2,5,1]=>[8,6,4,5,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,4,7,3,5]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,4,7,3,5]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,1,8,4,5]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,2,7,3,5]=>[1,6,2,7,3,5,4,8]=>[8,4,5,3,7,2,6,1]=>[8,6,4,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,2,6,3,4]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,5,1,6,3,4]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,5,1,7,3,4]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,1,7,3,4]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,6,1,7,3,5]=>[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,2,8,4,5]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,6,1,8,4,5]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,8,9,7]=>[7,9,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,7,8,9,6]=>[6,9,8,7,5,4,3,2,1]=>[9,8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,6,7,8,9,5]=>[5,9,8,7,6,4,3,2,1]=>[9,8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,9,4]=>[1,2,3,5,6,7,8,9,4]=>[4,9,8,7,6,5,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,7,8,9,3]=>[1,2,4,5,6,7,8,9,3]=>[3,9,8,7,6,5,4,2,1]=>[9,8,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,9,2]=>[1,3,4,5,6,7,8,9,2]=>[2,9,8,7,6,5,4,3,1]=>[9,1,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,9,10,8]=>[8,10,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,8,6,7,9]=>[9,7,6,8,5,4,3,2,1]=>[9,8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,8,9,10,7]=>[7,10,9,8,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,7,5,6,8,9]=>[9,8,6,5,7,4,3,2,1]=>[9,8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,7,8,9,10,6]=>[6,10,9,8,7,5,4,3,2,1]=>[10,9,8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,6,5,7,8,9,4]=>[1,2,3,6,4,5,7,8,9]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,6,7,8,9,10,5]=>[5,10,9,8,7,6,4,3,2,1]=>[10,9,8,7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,5,6,7,8,9,10,4]=>[4,10,9,8,7,6,5,3,2,1]=>[10,9,8,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,4,5,6,7,8,9,10,3]=>[1,2,4,5,6,7,8,9,10,3]=>[3,10,9,8,7,6,5,4,2,1]=>[10,9,1,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,9,1]=>[1,2,4,5,6,7,8,9,3]=>[3,9,8,7,6,5,4,2,1]=>[9,8,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,9,10,2]=>[1,3,4,5,6,7,8,9,10,2]=>[2,10,9,8,7,6,5,4,3,1]=>[10,1,9,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,4,8,3,5,1,2]=>[1,2,3,5,4,8,6,7]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,5,2,8,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,2,3,1,8]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,3,8,1,2]=>[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,8,3,6,1,2]=>[1,2,3,6,4,8,5,7]=>[7,5,8,4,6,3,2,1]=>[8,7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,3,7,1,2]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,3,7,1,2]=>[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,2,8,1,4]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,2,7,1,3]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,5,2,3,1,7]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,6,2,3,1,7]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,2,3,1,7]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,2,8,1,7]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,2,7,1,8]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,2,8,1,7]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,2,5,1,7]=>[1,7,2,5,3,6,4,8]=>[8,4,6,3,5,2,7,1]=>[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,2,4,1,7]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,2,7,1,5]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,6,2,8,1,4]=>[1,4,2,8,3,6,5,7]=>[7,5,6,3,8,2,4,1]=>[8,6,4,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,5,2,4,1,8]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>[7,6,8,5,4,2,3,1]=>[8,6,7,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,2,3,1,4]=>[1,4,2,3,5,7,6,8]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,4,2,8,1,5]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,2,3,1,6]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,2,3,1,5]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,6,2,3,1,5]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,2,4,1,5]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,2,4,1,5]=>[1,5,2,4,3,7,6,8]=>[8,6,7,3,4,2,5,1]=>[8,6,4,5,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,2,8,1,6]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,2,6,1,8]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,2,6,1,8]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,2,7,1,6]=>[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,2,7,1,6]=>[1,6,2,7,3,5,4,8]=>[8,4,5,3,7,2,6,1]=>[8,6,4,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,2,7,1,5]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,2,6,1,5]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,2,5,1,7]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,2,6,1,7]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,2,6,1,7]=>[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,2,8,1,7]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,1,7,6,3]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,3,1,8,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,3,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,7,3,2,5]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,3,7,6,2]=>[1,3,7,2,4,8,5,6]=>[6,5,8,4,2,7,3,1]=>[8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,1,7,6,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,3,8,2,6]=>[1,3,8,2,6,4,7,5]=>[5,7,4,6,2,8,3,1]=>[8,5,7,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,7,5,2,3]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,2,1,3,4]=>[1,3,4,2,5,6,8,7]=>[7,8,6,5,2,4,3,1]=>[8,5,7,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,4,2,1,3]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,2,1,5]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,7,4,1,5]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,7,4,3,5]=>[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,6,4,5,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,6,4,5,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,2,4,3,1]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,2,3,1,4]=>[1,4,2,3,5,7,8,6]=>[6,8,7,5,3,2,4,1]=>[8,6,5,7,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,3,2,4,1]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,3,7,6,1]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,6,5,3,1]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,7,3,1,5]=>[1,5,2,7,3,4,8,6]=>[6,8,4,3,7,2,5,1]=>[8,6,4,3,7,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,8,6,4,5,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,8,1,5,3]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,7,5,1,3]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,5,3,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,5,1,2]=>[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,3,1,2,4]=>[1,2,4,3,5,8,6,7]=>[7,6,8,5,3,4,2,1]=>[8,7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,1,3,4,2]=>[1,3,4,2,5,8,6,7]=>[7,6,8,5,2,4,3,1]=>[8,5,7,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,4,1,3,2]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,1,5,2]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,1,5,4]=>[1,5,2,6,8,3,4,7]=>[7,4,3,8,6,2,5,1]=>[8,6,3,2,7,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,8,3,5,4]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,1,4,2,3]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,1,2,4,3]=>[1,2,4,3,5,7,8,6]=>[6,8,7,5,3,4,2,1]=>[8,7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,5,4,8,3,1]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,4,7,6,2]=>[1,3,5,2,4,7,6,8]=>[8,6,7,4,2,5,3,1]=>[8,5,7,4,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,4,3,8,7,2]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,4,5,7,2]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,5,6,8,2]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,5,6,7,2]=>[1,3,4,5,6,7,2,8]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,5,6,3,8]=>[1,7,2,4,5,6,3,8]=>[8,3,6,5,4,2,7,1]=>[8,6,2,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,5,1,8,4]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,4,3,7,6]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,4,1,3,7]=>[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>[8,5,7,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,4,8,3,7]=>[1,4,8,2,3,7,5,6]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,3,5,4,7,8]=>[1,2,6,3,5,4,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,2,8,6,5,7]=>[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,6,8,5,7]=>[1,2,6,8,3,4,5,7]=>[7,5,4,3,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,3,2,4,7]=>[1,6,2,4,7,3,5,8]=>[8,5,3,7,4,2,6,1]=>[8,6,3,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,2,1,5,4]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,2,1,7,3]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,3,1,6,4]=>[1,6,2,5,8,3,4,7]=>[7,4,3,8,5,2,6,1]=>[8,6,3,2,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,6,3,2,4,8]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,8,5,7,4]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,8,6,4,5]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,2,4,6,8]=>[1,5,7,2,4,6,8,3]=>[3,8,6,4,2,7,5,1]=>[8,5,1,4,7,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,3,1,8,4,6]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,1,3,7,6]=>[1,3,7,2,4,5,8,6]=>[6,8,5,4,2,7,3,1]=>[8,5,7,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,3,4,1,5]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,4,2,7,5]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,8,7,5,6]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,7,2,4,5]=>[1,3,7,2,4,5,6,8]=>[8,6,5,4,2,7,3,1]=>[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,6,4,7,5]=>[1,3,6,2,8,4,7,5]=>[5,7,4,8,2,6,3,1]=>[8,5,7,3,1,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,4,1,5,7]=>[1,5,7,2,3,4,6,8]=>[8,6,4,3,2,7,5,1]=>[8,5,4,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,6,9,5,4,3,2,1]=>[1,2,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,6,5,9,4,3,2,1]=>[1,2,3,4,5,9,6,7,8]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,9,3,2,1]=>[1,2,3,4,9,5,6,7,8]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,9,2,1]=>[1,2,3,9,4,5,6,7,8]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,9,1]=>[1,2,9,3,4,5,6,7,8]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,1,9]=>[1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,10,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,6,7,9,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,10,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,10,8,9]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,5,6,9,4,3,2,1]=>[1,2,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,10,5,4,3,2,1]=>[1,2,3,4,5,6,10,7,8,9]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,6,4,5,9,3,2,1]=>[1,2,3,4,5,9,6,7,8]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,10,4,3,2,1]=>[1,2,3,4,5,10,6,7,8,9]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,3,4,9,2,1]=>[1,2,3,4,9,5,6,7,8]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,10,3,2,1]=>[1,2,3,4,10,5,6,7,8,9]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,2,3,9,1]=>[1,2,3,9,4,5,6,7,8]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,3,10,2,1]=>[1,2,3,10,4,5,6,7,8,9]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,1,2,9]=>[1,2,9,3,4,5,6,7,8]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,3,2,10,1]=>[1,2,10,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,3,2,1,10]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,4,2,7,8,6,3,5]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,8,5,3,7]=>[1,6,2,4,8,3,7,5]=>[5,7,3,8,4,2,6,1]=>[8,6,3,5,1,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,4,7,5,3,8]=>[1,6,2,4,7,3,8,5]=>[5,8,3,7,4,2,6,1]=>[8,6,3,5,1,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,2,8,6,4,5]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,8,6,1,3]=>[1,3,2,5,7,8,4,6]=>[6,4,8,7,5,2,3,1]=>[8,6,7,2,5,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,8,5,6,4]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,7,3,4,6]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,3,4,7,5]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,3,5,1,7,4]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,5,7,1,3]=>[1,3,2,4,8,5,7,6]=>[6,7,5,8,4,2,3,1]=>[8,6,7,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,8,5,7,2]=>[1,3,6,2,4,8,5,7]=>[7,5,8,4,2,6,3,1]=>[8,5,7,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,7,5,8,2]=>[1,3,6,2,4,7,5,8]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,7,5,8,1,3]=>[1,3,2,4,7,5,8,6]=>[6,8,5,7,4,2,3,1]=>[8,6,7,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,4,3,5,6]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,2,3,1,8,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,3,1,6,8,4]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,3,4,6,8,2]=>[1,7,2,3,4,6,8,5]=>[5,8,6,4,3,2,7,1]=>[8,6,5,4,1,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,6,7,1,3]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,3,1,7,5]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,3,5,6,7]=>[1,2,8,3,5,6,7,4]=>[4,7,6,5,3,8,2,1]=>[8,7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,3,5,6,8]=>[1,7,2,3,5,6,8,4]=>[4,8,6,5,3,2,7,1]=>[8,6,5,1,4,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,3,2,5,7]=>[1,3,2,5,7,4,6,8]=>[8,6,4,7,5,2,3,1]=>[8,6,7,3,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,2,4,7,5]=>[1,6,2,4,7,3,8,5]=>[5,8,3,7,4,2,6,1]=>[8,6,3,5,1,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,1,2,7,4,6]=>[1,2,7,3,8,4,6,5]=>[5,6,4,8,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,1,2,6,4,8]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,4,6,3,7]=>[1,5,8,2,4,6,3,7]=>[7,3,6,4,2,8,5,1]=>[8,5,2,4,7,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,2,7,3,6]=>[1,5,8,2,7,3,6,4]=>[4,6,3,7,2,8,5,1]=>[8,5,3,1,7,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,8,3,7,5]=>[1,4,6,2,8,3,7,5]=>[5,7,3,8,2,6,4,1]=>[8,5,3,7,1,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,2,8,4,7]=>[1,2,8,3,6,4,7,5]=>[5,7,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,2,7,8,4,5]=>[1,6,2,7,8,3,4,5]=>[5,4,3,8,7,2,6,1]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,3,8,6,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,2,5,8,7]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,2,7,5,8]=>[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>[8,6,4,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,4,5,6,7]=>[1,8,2,4,5,6,7,3]=>[3,7,6,5,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,4,1,7,5]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,7,8,1,3]=>[1,3,2,5,6,7,8,4]=>[4,8,7,6,5,2,3,1]=>[8,6,7,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,6,7,1,8,4]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,1,7,8,5]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,1,4,5,8,6]=>[1,4,5,8,2,3,6,7]=>[7,6,3,2,8,5,4,1]=>[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,3,2,5,7]=>[1,4,2,5,7,3,6,8]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,5,2,4,7]=>[1,6,2,4,7,3,5,8]=>[8,5,3,7,4,2,6,1]=>[8,6,3,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,8,2,4,6]=>[1,8,2,4,6,3,7,5]=>[5,7,3,6,4,2,8,1]=>[8,6,3,5,1,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,4,6,3,7]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,5,4,7]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,4,5,3,7]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,6,4,3,7]=>[1,2,5,6,3,7,4,8]=>[8,4,7,3,6,5,2,1]=>[8,7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,5,4,3,7]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,2,8,3,6]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,2,7,3,6]=>[1,4,8,2,7,3,6,5]=>[5,6,3,7,2,8,4,1]=>[8,5,3,7,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,2,7,3,5]=>[1,4,6,8,2,7,3,5]=>[5,3,7,2,8,6,4,1]=>[8,4,2,7,1,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,6,2,8,3,5]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,7,2,8,3,6]=>[1,4,7,2,8,3,6,5]=>[5,6,3,8,2,7,4,1]=>[8,5,3,7,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,2,8,3,6]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,2,8,4,6]=>[1,2,8,3,7,4,6,5]=>[5,6,4,7,3,8,2,1]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,1,3,4,6]=>[1,3,4,6,2,8,5,7]=>[7,5,8,2,6,4,3,1]=>[8,4,7,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,1,3,4,6]=>[1,3,4,6,2,8,5,7]=>[7,5,8,2,6,4,3,1]=>[8,4,7,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,2,7,3,6]=>[1,5,8,2,7,3,6,4]=>[4,6,3,7,2,8,5,1]=>[8,5,3,1,7,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,2,8,7,3,5]=>[1,4,6,2,8,3,5,7]=>[7,5,3,8,2,6,4,1]=>[8,5,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,4,8,7,5]=>[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,6,3,4,8,5]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,8,5,7,4]=>[1,2,3,6,8,4,5,7]=>[7,5,4,8,6,3,2,1]=>[8,7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,6,8,3,5]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,8,7,3,5]=>[1,4,2,6,8,3,5,7]=>[7,5,3,8,6,2,4,1]=>[8,6,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,4,6,7,5]=>[1,2,8,3,4,6,7,5]=>[5,7,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,6,4,8,5]=>[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,1,8,2,4,6]=>[1,8,2,4,6,3,7,5]=>[5,7,3,6,4,2,8,1]=>[8,6,3,5,1,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,1,3,5,6]=>[1,3,5,6,2,4,8,7]=>[7,8,4,2,6,5,3,1]=>[8,4,7,3,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,2,6,4,5]=>[1,7,8,2,6,3,4,5]=>[5,4,3,6,2,8,7,1]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,3,4,7,6]=>[1,3,4,7,2,8,5,6]=>[6,5,8,2,7,4,3,1]=>[8,4,7,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,3,4,7,5]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,8,3,7,5]=>[1,4,2,6,8,3,7,5]=>[5,7,3,8,6,2,4,1]=>[8,6,3,7,1,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,8,5,6,4]=>[1,2,3,7,8,4,5,6]=>[6,5,4,8,7,3,2,1]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,7,5,8,6,4]=>[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,2,8,6,4,5]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,8,7,5,6,4]=>[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,10,5,6,7,8]=>[1,2,3,4,10,5,6,7,8,9]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,10,2,3,4,5,6,7,8]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,9,10,7]=>[1,2,3,4,5,6,9,10,7,8]=>[8,7,10,9,6,5,4,3,2,1]=>[10,9,8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,9,10,1,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,2,9,10]=>[10,9,2,8,7,6,5,4,3,1]=>[10,3,9,8,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11,10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[4,7,8,5,6,2,1,3]=>[1,3,2,4,7,8,5,6]=>[6,5,8,7,4,2,3,1]=>[8,6,7,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,5,1,3]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,2,1,5,4]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,2,1,5,4]=>[1,5,2,3,8,4,6,7]=>[7,6,4,8,3,2,5,1]=>[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,1,5,4]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,2,1,6,4]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,3,5,6,1]=>[1,2,7,8,3,5,6,4]=>[4,6,5,3,8,7,2,1]=>[8,7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,2,5,1,6]=>[1,6,2,5,3,7,8,4]=>[4,8,7,3,5,2,6,1]=>[8,6,4,1,5,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,2,1,5,6]=>[1,5,6,2,3,4,7,8]=>[8,7,4,3,2,6,5,1]=>[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,2,1,4,6]=>[1,4,6,2,3,5,7,8]=>[8,7,5,3,2,6,4,1]=>[8,5,4,7,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,2,1,4,5]=>[1,4,5,2,3,8,6,7]=>[7,6,8,3,2,5,4,1]=>[8,5,4,7,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,2,5,1,7]=>[1,7,2,5,3,6,4,8]=>[8,4,6,3,5,2,7,1]=>[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,5,7,1]=>[1,2,6,3,5,7,4,8]=>[8,4,7,5,3,6,2,1]=>[8,7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,3,5,8,1]=>[1,2,6,3,5,8,4,7]=>[7,4,8,5,3,6,2,1]=>[8,7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,2,1,4,8]=>[1,4,8,2,3,7,5,6]=>[6,5,7,3,2,8,4,1]=>[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,6,5,7]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,7,5,8]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,8,6,1,7]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,8,5,7]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,8,5,6]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,7,5,6]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,8,6,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,8,7,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,2,1,7,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,7,6,1,3]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,8,6,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,8,7,1,3]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,5,7,8,3,4,1]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,6,1,7,4]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,2,1,8,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,2,7,1,8,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,6,8,5]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,6,7,5]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6,8]=>[8,6,4,3,2,7,5,1]=>[8,5,4,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,5,8,6]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,5,8,7]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,6,8,1,7]=>[1,7,2,6,8,3,5,4]=>[4,5,3,8,6,2,7,1]=>[8,6,3,1,2,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,2,6,4,1]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,2,6,3,1]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,5,6,3,4]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,5,1,4,2]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,8,1,6,2,4]=>[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,8,5,1,7]=>[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,1,7,6,8]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,7,3,6,8]=>[1,5,7,2,3,6,8,4]=>[4,8,6,3,2,7,5,1]=>[8,5,4,1,7,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,3,7,1,6,8]=>[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,3,1,6,7]=>[1,6,7,2,5,8,3,4]=>[4,3,8,5,2,7,6,1]=>[8,5,2,1,4,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,5,4,2,8,6,7]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,3,8,2,6,7]=>[1,5,2,6,7,3,8,4]=>[4,8,3,7,6,2,5,1]=>[8,6,3,1,7,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,8,3,2,6,7]=>[1,5,8,2,6,7,3,4]=>[4,3,7,6,2,8,5,1]=>[8,5,2,1,7,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,5,2,1,6,7]=>[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,2,1,6,8]=>[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,5,1,7,8]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,3,2,5,8]=>[1,3,2,5,8,4,6,7]=>[7,6,4,8,5,2,3,1]=>[8,6,7,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,7,2,6,8]=>[1,3,7,2,6,8,4,5]=>[5,4,8,6,2,7,3,1]=>[8,5,7,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,2,7,6,8]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,3,7,8,6]=>[1,4,2,5,3,7,8,6]=>[6,8,7,3,5,2,4,1]=>[8,6,4,7,5,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,4,3,7,8,6]=>[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,2,7,6,8]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,7,2,6,8]=>[1,5,7,2,6,8,3,4]=>[4,3,8,6,2,7,5,1]=>[8,5,2,1,7,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,1,5,2,7,8]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,1,2,7,8]=>[1,2,7,8,3,6,4,5]=>[5,4,6,3,8,7,2,1]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,2,7,5,8]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,2,7,5,8]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,1,4,7,8]=>[1,4,7,8,2,3,6,5]=>[5,6,3,2,8,7,4,1]=>[8,4,3,7,1,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,1,3,4,8]=>[1,3,4,8,2,7,5,6]=>[6,5,7,2,8,4,3,1]=>[8,4,7,6,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,3,1,5,8]=>[1,5,8,2,3,4,6,7]=>[7,6,4,3,2,8,5,1]=>[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,7,3,5,8]=>[1,7,2,3,5,8,4,6]=>[6,4,8,5,3,2,7,1]=>[8,6,5,2,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,1,4,7,5,8]=>[1,4,7,2,6,3,5,8]=>[8,5,3,6,2,7,4,1]=>[8,5,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,7,4,6,1,8]=>[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,4,8,5,1,6]=>[1,6,2,4,8,3,7,5]=>[5,7,3,8,4,2,6,1]=>[8,6,3,5,1,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,6,3,8,5]=>[1,4,6,2,3,8,5,7]=>[7,5,8,3,2,6,4,1]=>[8,5,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,5,7,4,8]=>[1,5,7,2,3,6,4,8]=>[8,4,6,3,2,7,5,1]=>[8,5,4,2,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,5,3,7,8]=>[1,5,2,3,7,8,4,6]=>[6,4,8,7,3,2,5,1]=>[8,6,5,2,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,5,3,7,8]=>[1,5,2,6,3,7,8,4]=>[4,8,7,3,6,2,5,1]=>[8,6,4,1,7,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,6,2,3,8]=>[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>[8,5,4,2,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,2,6,4,8]=>[1,5,2,6,3,4,8,7]=>[7,8,4,3,6,2,5,1]=>[8,6,4,3,7,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,3,7,8,4]=>[1,3,7,8,2,5,4,6]=>[6,4,5,2,8,7,3,1]=>[8,4,7,2,3,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,2,7,4,8]=>[1,2,7,3,5,4,8,6]=>[6,8,4,5,3,7,2,1]=>[8,7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,7,2,3,8]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,1,3,7,8]=>[1,3,7,8,2,6,4,5]=>[5,4,6,2,8,7,3,1]=>[8,4,7,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,1,7,2,3,8]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,1,2,7,4,8]=>[1,2,7,3,6,4,8,5]=>[5,8,4,6,3,7,2,1]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,4,7,8,3]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,4,7,2,8]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,5,4,7,6]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,2,8,7,6]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,1,8,2,7,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,5,3,2,7,6]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,3,1,7,6]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,2,1,7,6]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,2,8,1,7,6]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,1,7,5,8]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,1,4,8]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,1,8,4]=>[1,8,2,7,3,5,6,4]=>[4,6,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,8,1,4]=>[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,2,8,7,1,5]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,2,7,1,5]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,3,7,1,5]=>[1,5,2,4,8,3,7,6]=>[6,7,3,8,4,2,5,1]=>[8,6,3,5,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,8,4,1]=>[1,2,7,8,3,5,6,4]=>[4,6,5,3,8,7,2,1]=>[8,7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,7,4,1,8]=>[1,8,2,7,3,5,6,4]=>[4,6,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,8,3,1]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,2,4,1]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,3,4,1]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,7,3,4,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,7,3,2,4]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,3,1,4]=>[1,4,2,5,8,3,6,7]=>[7,6,3,8,5,2,4,1]=>[8,6,3,7,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,2,1,4]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,2,1,8,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,8,7,3,5]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,6,7,4,5]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,2,6,7,5,4]=>[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,6,7,8,4,3]=>[1,6,7,8,2,5,3,4]=>[4,3,5,2,8,7,6,1]=>[8,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,4,2,8]=>[1,7,2,8,3,5,6,4]=>[4,6,5,3,8,2,7,1]=>[8,6,4,1,3,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,1,7,4,8,2]=>[1,7,2,3,5,6,4,8]=>[8,4,6,5,3,2,7,1]=>[8,6,5,2,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,1,8,7,5,2]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,1,7,5,2]=>[1,7,2,3,4,6,8,5]=>[5,8,6,4,3,2,7,1]=>[8,6,5,4,1,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,1,7,5,3]=>[1,7,2,4,8,3,5,6]=>[6,5,3,8,4,2,7,1]=>[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,2,7,5,3]=>[1,8,2,7,3,4,6,5]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,7,2,4,3]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,1,4,3]=>[1,4,2,5,8,3,6,7]=>[7,6,3,8,5,2,4,1]=>[8,6,3,7,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,1,4,2]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,8,1,3,2]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,3,8,2]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,1,3,2,8]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,7,3,1,8,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,7,4,1,2]=>[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>[8,7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,4,1,3]=>[1,3,2,5,8,4,6,7]=>[7,6,4,8,5,2,3,1]=>[8,6,7,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,7,4,2,3]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,7,4,3,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,6,7,4,3,1]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,1,8,3,7]=>[1,8,2,5,6,3,7,4]=>[4,7,3,6,5,2,8,1]=>[8,6,3,1,5,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,7,3,2,4,8]=>[1,5,7,2,4,8,3,6]=>[6,3,8,4,2,7,5,1]=>[8,5,2,4,7,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,3,2,4,7]=>[1,5,8,2,4,7,3,6]=>[6,3,7,4,2,8,5,1]=>[8,5,2,4,7,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,7,1,8,2]=>[1,8,2,3,5,6,7,4]=>[4,7,6,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,6,8,2,4]=>[1,5,6,8,2,4,3,7]=>[7,3,4,2,8,6,5,1]=>[8,4,2,3,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,8,2,4,6]=>[1,5,8,2,4,6,3,7]=>[7,3,6,4,2,8,5,1]=>[8,5,2,4,7,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,6,1,5,8]=>[1,5,8,2,4,6,3,7]=>[7,3,6,4,2,8,5,1]=>[8,5,2,4,7,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,4,6,8]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,8,4,6]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,4,6,1,5]=>[1,5,2,4,6,3,7,8]=>[8,7,3,6,4,2,5,1]=>[8,6,3,5,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,7,8,3,2,4]=>[1,5,7,8,2,4,3,6]=>[6,3,4,2,8,7,5,1]=>[8,4,2,3,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,6,1,7,8,3]=>[1,7,8,2,5,6,3,4]=>[4,3,6,5,2,8,7,1]=>[8,5,2,1,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,8,3,4,2]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,7,3,4,2]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,4,6,1,5]=>[1,5,2,4,6,3,7,8]=>[8,7,3,6,4,2,5,1]=>[8,6,3,5,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,4,7,8]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,7,5,6]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,8,7,4]=>[1,6,8,2,5,3,4,7]=>[7,4,3,5,2,8,6,1]=>[8,5,3,2,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,1,7,4,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,5,1,8,4,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,8,4,2,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,7,8,4]=>[1,6,7,8,2,5,3,4]=>[4,3,5,2,8,7,6,1]=>[8,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,5,6,7]=>[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,7,5,6,8]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,6,8,5,7]=>[1,6,8,2,4,3,5,7]=>[7,5,3,4,2,8,6,1]=>[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,5,7,6]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,7,4,2,3,8]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,4,2,3,7]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,8,3,7,5]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,8,3,7,4]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,3,5,2]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,8,5,1,6]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,4,2,3,8]=>[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,7,3,4,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,7,4,2,3]=>[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,1,8,6,5,7]=>[1,8,2,4,3,5,7,6]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,7,8,6,4]=>[1,7,8,2,5,3,4,6]=>[6,4,3,5,2,8,7,1]=>[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,6,4,2,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,1,7,6,4,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,8,6,4,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,6,4,2,3]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,1,8,4,2]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,1,6,3,8]=>[1,6,2,5,7,3,8,4]=>[4,8,3,7,5,2,6,1]=>[8,6,3,1,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,1,8,6,2]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,5,1,7,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,6,1,7,2]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,7,1,8,2]=>[1,8,2,3,6,7,4,5]=>[5,4,7,6,3,2,8,1]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,8,1,6,7,4]=>[1,6,7,2,5,8,3,4]=>[4,3,8,5,2,7,6,1]=>[8,5,2,1,4,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,6,8,1,7,3]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,4,1,6,7,3]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,1,8,5,7,3]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,8,5,3,7]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,1,6,3,7]=>[1,6,2,5,8,3,7,4]=>[4,7,3,8,5,2,6,1]=>[8,6,3,1,5,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,1,6,4,7]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,6,8,5,4,7]=>[1,6,8,2,3,4,7,5]=>[5,7,4,3,2,8,6,1]=>[8,5,4,3,1,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,5,4,8,6]=>[1,5,2,7,3,4,8,6]=>[6,8,4,3,7,2,5,1]=>[8,6,4,3,7,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,5,8,6,4]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,6,7,1,5]=>[1,5,2,6,7,3,4,8]=>[8,4,3,7,6,2,5,1]=>[8,6,3,2,7,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,6,7,1,5]=>[1,5,2,6,7,3,8,4]=>[4,8,3,7,6,2,5,1]=>[8,6,3,1,7,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,7,1,5,8]=>[1,5,8,2,6,7,3,4]=>[4,3,7,6,2,8,5,1]=>[8,5,2,1,7,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,8,1,5]=>[1,5,2,6,8,3,7,4]=>[4,7,3,8,6,2,5,1]=>[8,6,3,1,7,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,2,6,1,5]=>[1,5,2,6,3,7,8,4]=>[4,8,7,3,6,2,5,1]=>[8,6,4,1,7,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,8,1,6,3]=>[1,6,2,5,7,3,4,8]=>[8,4,3,7,5,2,6,1]=>[8,6,3,2,5,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,8,1,6,4]=>[1,6,2,5,7,8,3,4]=>[4,3,8,7,5,2,6,1]=>[8,6,2,1,5,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,1,6,4,8]=>[1,6,2,5,7,3,4,8]=>[8,4,3,7,5,2,6,1]=>[8,6,3,2,5,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,1,5,4,8]=>[1,5,2,7,3,4,8,6]=>[6,8,4,3,7,2,5,1]=>[8,6,4,3,7,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,1,5,8,4]=>[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,8,1,5,4]=>[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,7,8,5,3]=>[1,7,8,2,6,3,4,5]=>[5,4,3,6,2,8,7,1]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,7,8,4,3]=>[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,3,8,6,4]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,5,3,7,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,7,1,4,8,5]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,1,4,7,8,5]=>[1,4,7,8,2,3,5,6]=>[6,5,3,2,8,7,4,1]=>[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,1,7,4,6,8]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,1,7,3,6]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,4,8,6,5]=>[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,1,7,4,6]=>[1,7,2,3,5,8,4,6]=>[6,4,8,5,3,2,7,1]=>[8,6,5,2,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,2,1,5,6]=>[1,5,6,2,3,7,4,8]=>[8,4,7,3,2,6,5,1]=>[8,5,4,2,7,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,1,5,6,8]=>[1,5,6,8,2,3,7,4]=>[4,7,3,2,8,6,5,1]=>[8,4,3,1,7,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,7,1,5,6]=>[1,5,6,2,7,3,4,8]=>[8,4,3,7,2,6,5,1]=>[8,5,3,2,7,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,8,1,7,4,6]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,1,4,7,5]=>[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,8,4,6,7]=>[1,8,2,3,4,6,7,5]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,1,5,6,7]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,2,1,5,6,7]=>[1,5,6,7,2,3,8,4]=>[4,8,3,2,7,6,5,1]=>[8,4,3,1,7,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,6,5,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,6,4,5,3,2,1,9]=>[1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,9,8,7,5,6,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,8,7,6,5,4,3,2]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,2,1,11]=>[1,11,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,8,7,5,6,4,3,2,1,10]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,10,9,8,6,7,5,4,3,2]=>[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,4,5,2,3,1,7,6]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,3,4,1]=>[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,4,1,7,6]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,3,2,8,7]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,3,4,2,8,7]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,4,1,7,6]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,2,4,1]=>[1,2,4,3,7,5,6,8]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,4,2,7,6]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,3,2,7,6]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,5,3,7,6]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,1,3,2]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,5,1,4,2]=>[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,1,4,2]=>[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,2,5,1]=>[1,2,5,3,7,4,6,8]=>[8,6,4,7,3,5,2,1]=>[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,1,5,2]=>[1,5,2,3,7,4,6,8]=>[8,6,4,7,3,2,5,1]=>[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,6,4,5,2]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,6,1,3,2]=>[1,3,2,4,7,5,6,8]=>[8,6,5,7,4,2,3,1]=>[8,6,7,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,7,5,6,3]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,4,2,6,5]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,6,2,5,4]=>[1,7,2,5,3,6,4,8]=>[8,4,6,3,5,2,7,1]=>[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,4,5,1]=>[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,6,4,5,1]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,6,1,5,4]=>[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,3,5,4]=>[1,6,2,7,3,5,4,8]=>[8,4,5,3,7,2,6,1]=>[8,6,4,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,4,3,7,6]=>[1,5,2,4,3,7,6,8]=>[8,6,7,3,4,2,5,1]=>[8,6,4,5,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,6,3,4,1]=>[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,6,2,3,1]=>[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,3,1,6,5]=>[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,7,4,6,5]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,5,4,7,6]=>[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,5,7,6]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,8,6,7,5]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,3,1,5,4]=>[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,7,5,6,4]=>[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,6,3,4,1]=>[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,6,1,4,3]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,1,4,3]=>[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,2,4,3]=>[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,3,2,5,4]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,3,5,4]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,5,6,4]=>[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,7,5,6,4]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,2,4,3]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,4,5,3]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,6,1,5,3]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,6,3,5,1]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,3,5,1]=>[1,2,6,3,5,4,7,8]=>[8,7,4,5,3,6,2,1]=>[8,7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,1,5,3]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,6,2,5,3]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,2,5,3]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,3,6,4]=>[1,8,2,3,6,4,5,7]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,6,1,3,2]=>[1,3,2,4,6,5,7,8]=>[8,7,5,6,4,2,3,1]=>[8,6,7,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,3,4,2]=>[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,3,5,2]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,1,5,2]=>[1,5,2,3,6,4,7,8]=>[8,7,4,6,3,2,5,1]=>[8,6,5,3,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,6,1,7,5]=>[1,7,2,4,8,3,6,5]=>[5,6,3,8,4,2,7,1]=>[8,6,3,5,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,3,2,7,4]=>[1,3,2,7,4,5,8,6]=>[6,8,5,4,7,2,3,1]=>[8,6,7,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,6,3,2,7,1]=>[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,7,3,1,2,4]=>[1,2,4,3,5,8,6,7]=>[7,6,8,5,3,4,2,1]=>[8,7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,4,1,5,3]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,4,5,7,1]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,1,5,7,3]=>[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,4,5,7,2]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,4,5,7,2]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,4,5,7,1]=>[1,2,3,6,8,4,5,7]=>[7,5,4,8,6,3,2,1]=>[8,7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,8,4,1,5,2]=>[1,5,2,3,7,8,4,6]=>[6,4,8,7,3,2,5,1]=>[8,6,5,2,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,4,6,5,2]=>[1,3,7,8,2,4,6,5]=>[5,6,4,2,8,7,3,1]=>[8,4,7,3,1,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,2,4,6,3]=>[1,5,7,8,2,4,6,3]=>[3,6,4,2,8,7,5,1]=>[8,4,1,3,7,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,2,4,6,3]=>[1,7,8,2,4,6,3,5]=>[5,3,6,4,2,8,7,1]=>[8,5,2,4,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,8,4,2,5,1]=>[1,2,5,3,6,7,8,4]=>[4,8,7,6,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,3,2,1,4]=>[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,3,6,1,4]=>[1,4,2,8,3,6,5,7]=>[7,5,6,3,8,2,4,1]=>[8,6,4,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,8,4,6,5,3]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,1,4,6,3]=>[1,4,6,2,7,8,3,5]=>[5,3,8,7,2,6,4,1]=>[8,5,2,7,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,3,8,5,6,7]=>[1,3,8,2,4,5,6,7]=>[7,6,5,4,2,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,3,4,6,1]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,4,3,1,7]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,3,1,6,7]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,5,2,3,1,7]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,2,4,6,1]=>[1,2,4,6,3,5,8,7]=>[7,8,5,3,6,4,2,1]=>[8,7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,8,5,6,7]=>[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,1,8,5,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,4,3,5,1]=>[1,2,7,3,5,4,6,8]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,3,4,6,2]=>[1,8,2,3,4,6,5,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,8,1,4,6,2]=>[1,4,6,2,3,7,5,8]=>[8,5,7,3,2,6,4,1]=>[8,5,4,7,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,3,4,6,2]=>[1,7,2,3,4,6,5,8]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,1,3,2,7]=>[1,3,2,7,4,6,8,5]=>[5,8,6,4,7,2,3,1]=>[8,6,7,4,1,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,4,3,2,7]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,3,4,2,1]=>[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,6,5,1,7]=>[1,7,2,4,8,3,6,5]=>[5,6,3,8,4,2,7,1]=>[8,6,3,5,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,5,6,2,7]=>[1,8,2,7,3,5,6,4]=>[4,6,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,4,1,3,2,7]=>[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,1,5,3,2,7]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,8,5,4,6,2]=>[1,7,2,3,8,4,6,5]=>[5,6,4,8,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,8,4,6,5,1]=>[1,2,7,3,8,4,6,5]=>[5,6,4,8,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,4,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,3,1,6,7]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,2,3,1,7]=>[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,8,5,6,7]=>[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,5,1,6,7]=>[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,5,3,1,7]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,8,5,4,6,1]=>[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,5,6,7]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,4,8,5,6,7]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,4,8,6,7]=>[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>[8,6,7,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,3,4,7,6]=>[1,5,2,8,3,4,7,6]=>[6,7,4,3,8,2,5,1]=>[8,6,4,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,5,3,7,6]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,5,3,6,7]=>[1,4,2,8,3,6,7,5]=>[5,7,6,3,8,2,4,1]=>[8,6,4,7,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,5,3,6,7]=>[1,8,2,5,3,6,7,4]=>[4,7,6,3,5,2,8,1]=>[8,6,4,1,5,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,2,4,6,7]=>[1,5,2,4,6,7,3,8]=>[8,3,7,6,4,2,5,1]=>[8,6,2,5,7,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,2,4,6,7]=>[1,5,2,4,6,7,3,8]=>[8,3,7,6,4,2,5,1]=>[8,6,2,5,7,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,8,2,6,7]=>[1,4,8,2,6,7,3,5]=>[5,3,7,6,2,8,4,1]=>[8,5,2,7,1,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,4,3,6,7]=>[1,5,2,8,3,6,7,4]=>[4,7,6,3,8,2,5,1]=>[8,6,4,1,7,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,4,8,5,3,6]=>[1,2,7,3,6,4,8,5]=>[5,8,4,6,3,7,2,1]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,7,4,8,3,6]=>[1,2,7,3,6,4,8,5]=>[5,8,4,6,3,7,2,1]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,4,7,2,6]=>[1,4,7,2,6,3,5,8]=>[8,5,3,6,2,7,4,1]=>[8,5,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,5,7,4,3,6]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,7,5,3,6]=>[1,2,4,8,3,6,5,7]=>[7,5,6,3,8,4,2,1]=>[8,7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,3,7,6,5]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,7,4,3,5]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,8,7,3,5]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,1,7,2,5]=>[1,7,2,5,3,6,4,8]=>[8,4,6,3,5,2,7,1]=>[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,8,4,3,5]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,4,8,2,5]=>[1,4,8,2,5,3,7,6]=>[6,7,3,5,2,8,4,1]=>[8,5,3,7,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,1,5,2,4,6]=>[1,5,2,4,6,3,7,8]=>[8,7,3,6,4,2,5,1]=>[8,6,3,5,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,4,5,3,6]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,4,3,7,5]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,8,3,7,5]=>[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,2,4,8,5]=>[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>[8,6,7,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,2,4,8,5]=>[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>[8,6,7,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,3,5,8,4,6]=>[1,2,7,3,5,8,4,6]=>[6,4,8,5,3,7,2,1]=>[8,7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,5,8,3,4,6]=>[1,2,7,3,4,6,5,8]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,7,3,4,6]=>[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,8,3,7,4,6]=>[1,2,5,8,3,7,4,6]=>[6,4,7,3,8,5,2,1]=>[8,7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,3,5,4,6]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,2,4,7,5]=>[1,3,2,4,7,5,6,8]=>[8,6,5,7,4,2,3,1]=>[8,6,7,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,7,3,6,5]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,4,3,6,5]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,4,3,6,5]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,7,5,3,6]=>[1,2,8,3,6,4,7,5]=>[5,7,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,4,5,3,6]=>[1,2,8,3,6,4,5,7]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,5,2,4,6]=>[1,5,2,4,6,3,7,8]=>[8,7,3,6,4,2,5,1]=>[8,6,3,5,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,4,7,2,5]=>[1,4,7,2,5,3,8,6]=>[6,8,3,5,2,7,4,1]=>[8,5,3,7,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,2,7,3,5]=>[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,7,4,3,5]=>[1,6,2,7,3,5,4,8]=>[8,4,5,3,7,2,6,1]=>[8,6,4,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,6,4,3,5]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,8,6,3,5]=>[1,2,8,3,5,4,6,7]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,7,6,3,5]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,6,4,3,5]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,1,5,2,6]=>[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,1,6,2,5]=>[1,6,2,5,3,4,7,8]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,1,7,2,5]=>[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,1,5,2,7]=>[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,4,1,5,2,8]=>[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,3,4,1,7]=>[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,3,4,1,8]=>[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,3,5,1,7]=>[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,1,6,2,8]=>[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,1,6,2,7]=>[1,6,2,7,3,5,4,8]=>[8,4,5,3,7,2,6,1]=>[8,6,4,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,5,1,7,2,6]=>[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,5,1,8,2,6]=>[1,8,2,6,3,5,4,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,3,1,7,4,8]=>[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,3,7,2,6]=>[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,4,7,1,2]=>[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,4,7,1,3]=>[1,3,2,8,4,7,5,6]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,3,7,1,4]=>[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,7,3,6,2,8]=>[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,3,6,2,7]=>[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,2,1,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,2,9]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,2,1,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,2,10]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,2,3,5,6,7,8,9,1]=>[1,2,3,5,6,7,8,9,4]=>[4,9,8,7,6,5,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,9,10,1]=>[1,2,4,5,6,7,8,9,10,3]=>[3,10,9,8,7,6,5,4,2,1]=>[10,9,1,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,11,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,5,3,2,1,4,8,7]=>[1,4,8,2,3,5,6,7]=>[7,6,5,3,2,8,4,1]=>[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,2,1,8,7]=>[1,8,2,3,5,4,6,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,5,7,3,1]=>[1,2,4,5,7,3,6,8]=>[8,6,3,7,5,4,2,1]=>[8,7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,5,3,1,6]=>[1,6,2,4,5,3,7,8]=>[8,7,3,5,4,2,6,1]=>[8,6,3,5,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,5,7,2,1]=>[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,3,6,2,5]=>[1,7,2,5,3,6,4,8]=>[8,4,6,3,5,2,7,1]=>[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,5,7,4,3]=>[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,1,7,4,2]=>[1,7,2,3,5,4,6,8]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,7,6,3,2]=>[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,7,6,3,1]=>[1,2,5,8,3,4,7,6]=>[6,7,4,3,8,5,2,1]=>[8,7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,5,6,7,2]=>[1,5,6,7,2,3,8,4]=>[4,8,3,2,7,6,5,1]=>[8,4,3,1,7,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,5,6,7,2]=>[1,3,5,6,7,2,4,8]=>[8,4,2,7,6,5,3,1]=>[8,3,7,2,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,1,6,3,2]=>[1,6,2,3,4,5,8,7]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,1,2,7,5]=>[1,2,7,3,6,4,8,5]=>[5,8,4,6,3,7,2,1]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,5,6,7,4]=>[1,2,5,6,7,3,8,4]=>[4,8,3,7,6,5,2,1]=>[8,7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,2,4,7,5]=>[1,2,4,7,3,5,6,8]=>[8,6,5,3,7,4,2,1]=>[8,7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,5,2,3,6]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,5,1,3,6]=>[1,3,6,2,8,4,5,7]=>[7,5,4,8,2,6,3,1]=>[8,5,7,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,2,1,4,6]=>[1,4,6,2,3,5,7,8]=>[8,7,5,3,2,6,4,1]=>[8,5,4,7,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,2,1,7,4]=>[1,7,2,3,6,4,5,8]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,5,7,2,3]=>[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,5,1,7,2,4]=>[1,7,2,4,3,5,6,8]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,3,6,7,4]=>[1,5,8,2,3,6,7,4]=>[4,7,6,3,2,8,5,1]=>[8,5,4,1,7,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,1,2,7,4]=>[1,2,7,3,6,4,5,8]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,5,6,7,3]=>[1,8,2,5,6,7,3,4]=>[4,3,7,6,5,2,8,1]=>[8,6,2,1,5,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,5,6,7,3]=>[1,5,6,7,2,4,8,3]=>[3,8,4,2,7,6,5,1]=>[8,4,1,3,7,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,5,6,7,3]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,6,1,7,2]=>[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,5,6,7,2]=>[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,10,1,3,5,7,9]=>[1,3,5,7,9,2,4,6,8,10]=>[10,8,6,4,2,9,7,5,3,1]=>[10,5,9,4,8,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,6,8,9,10,1,3,4,5,7]=>[1,3,4,5,7,2,6,8,9,10]=>[10,9,8,6,2,7,5,4,3,1]=>[10,5,9,8,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,7,8,9,10,1,2,3,5,6]=>[1,2,3,5,6,4,7,8,9,10]=>[10,9,8,7,4,6,5,3,2,1]=>[10,9,8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,7,8,9,10,1,2,3,4,6]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,10,11,12,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4