Identifier
-
Mp00223:
Permutations
—runsort⟶
Permutations
St000001: Permutations ⟶ ℤ
Values
=>
[1]=>[1]=>1
[1,2]=>[1,2]=>1
[2,1]=>[1,2]=>1
[1,2,3]=>[1,2,3]=>1
[1,3,2]=>[1,3,2]=>1
[2,1,3]=>[1,3,2]=>1
[2,3,1]=>[1,2,3]=>1
[3,1,2]=>[1,2,3]=>1
[3,2,1]=>[1,2,3]=>1
[1,2,3,4]=>[1,2,3,4]=>1
[1,2,4,3]=>[1,2,4,3]=>1
[1,3,2,4]=>[1,3,2,4]=>1
[1,3,4,2]=>[1,3,4,2]=>1
[1,4,2,3]=>[1,4,2,3]=>1
[1,4,3,2]=>[1,4,2,3]=>1
[2,1,3,4]=>[1,3,4,2]=>1
[2,1,4,3]=>[1,4,2,3]=>1
[2,3,1,4]=>[1,4,2,3]=>1
[2,3,4,1]=>[1,2,3,4]=>1
[2,4,1,3]=>[1,3,2,4]=>1
[2,4,3,1]=>[1,2,4,3]=>1
[3,1,2,4]=>[1,2,4,3]=>1
[3,1,4,2]=>[1,4,2,3]=>1
[3,2,1,4]=>[1,4,2,3]=>1
[3,2,4,1]=>[1,2,4,3]=>1
[3,4,1,2]=>[1,2,3,4]=>1
[3,4,2,1]=>[1,2,3,4]=>1
[4,1,2,3]=>[1,2,3,4]=>1
[4,1,3,2]=>[1,3,2,4]=>1
[4,2,1,3]=>[1,3,2,4]=>1
[4,2,3,1]=>[1,2,3,4]=>1
[4,3,1,2]=>[1,2,3,4]=>1
[4,3,2,1]=>[1,2,3,4]=>1
[1,2,3,4,5]=>[1,2,3,4,5]=>1
[1,2,3,5,4]=>[1,2,3,5,4]=>1
[1,2,4,3,5]=>[1,2,4,3,5]=>1
[1,2,4,5,3]=>[1,2,4,5,3]=>1
[1,2,5,3,4]=>[1,2,5,3,4]=>1
[1,2,5,4,3]=>[1,2,5,3,4]=>1
[1,3,2,4,5]=>[1,3,2,4,5]=>1
[1,3,2,5,4]=>[1,3,2,5,4]=>2
[1,3,4,2,5]=>[1,3,4,2,5]=>1
[1,3,4,5,2]=>[1,3,4,5,2]=>1
[1,3,5,2,4]=>[1,3,5,2,4]=>2
[1,3,5,4,2]=>[1,3,5,2,4]=>2
[1,4,2,3,5]=>[1,4,2,3,5]=>1
[1,4,2,5,3]=>[1,4,2,5,3]=>2
[1,4,3,2,5]=>[1,4,2,5,3]=>2
[1,4,3,5,2]=>[1,4,2,3,5]=>1
[1,4,5,2,3]=>[1,4,5,2,3]=>2
[1,4,5,3,2]=>[1,4,5,2,3]=>2
[1,5,2,3,4]=>[1,5,2,3,4]=>1
[1,5,2,4,3]=>[1,5,2,4,3]=>3
[1,5,3,2,4]=>[1,5,2,4,3]=>3
[1,5,3,4,2]=>[1,5,2,3,4]=>1
[1,5,4,2,3]=>[1,5,2,3,4]=>1
[1,5,4,3,2]=>[1,5,2,3,4]=>1
[2,1,3,4,5]=>[1,3,4,5,2]=>1
[2,1,3,5,4]=>[1,3,5,2,4]=>2
[2,1,4,3,5]=>[1,4,2,3,5]=>1
[2,1,4,5,3]=>[1,4,5,2,3]=>2
[2,1,5,3,4]=>[1,5,2,3,4]=>1
[2,1,5,4,3]=>[1,5,2,3,4]=>1
[2,3,1,4,5]=>[1,4,5,2,3]=>2
[2,3,1,5,4]=>[1,5,2,3,4]=>1
[2,3,4,1,5]=>[1,5,2,3,4]=>1
[2,3,4,5,1]=>[1,2,3,4,5]=>1
[2,3,5,1,4]=>[1,4,2,3,5]=>1
[2,3,5,4,1]=>[1,2,3,5,4]=>1
[2,4,1,3,5]=>[1,3,5,2,4]=>2
[2,4,1,5,3]=>[1,5,2,4,3]=>3
[2,4,3,1,5]=>[1,5,2,4,3]=>3
[2,4,3,5,1]=>[1,2,4,3,5]=>1
[2,4,5,1,3]=>[1,3,2,4,5]=>1
[2,4,5,3,1]=>[1,2,4,5,3]=>1
[2,5,1,3,4]=>[1,3,4,2,5]=>1
[2,5,1,4,3]=>[1,4,2,5,3]=>2
[2,5,3,1,4]=>[1,4,2,5,3]=>2
[2,5,3,4,1]=>[1,2,5,3,4]=>1
[2,5,4,1,3]=>[1,3,2,5,4]=>2
[2,5,4,3,1]=>[1,2,5,3,4]=>1
[3,1,2,4,5]=>[1,2,4,5,3]=>1
[3,1,2,5,4]=>[1,2,5,3,4]=>1
[3,1,4,2,5]=>[1,4,2,5,3]=>2
[3,1,4,5,2]=>[1,4,5,2,3]=>2
[3,1,5,2,4]=>[1,5,2,4,3]=>3
[3,1,5,4,2]=>[1,5,2,3,4]=>1
[3,2,1,4,5]=>[1,4,5,2,3]=>2
[3,2,1,5,4]=>[1,5,2,3,4]=>1
[3,2,4,1,5]=>[1,5,2,4,3]=>3
[3,2,4,5,1]=>[1,2,4,5,3]=>1
[3,2,5,1,4]=>[1,4,2,5,3]=>2
[3,2,5,4,1]=>[1,2,5,3,4]=>1
[3,4,1,2,5]=>[1,2,5,3,4]=>1
[3,4,1,5,2]=>[1,5,2,3,4]=>1
[3,4,2,1,5]=>[1,5,2,3,4]=>1
[3,4,2,5,1]=>[1,2,5,3,4]=>1
[3,4,5,1,2]=>[1,2,3,4,5]=>1
[3,4,5,2,1]=>[1,2,3,4,5]=>1
[3,5,1,2,4]=>[1,2,4,3,5]=>1
[3,5,1,4,2]=>[1,4,2,3,5]=>1
[3,5,2,1,4]=>[1,4,2,3,5]=>1
[3,5,2,4,1]=>[1,2,4,3,5]=>1
[3,5,4,1,2]=>[1,2,3,5,4]=>1
[3,5,4,2,1]=>[1,2,3,5,4]=>1
[4,1,2,3,5]=>[1,2,3,5,4]=>1
[4,1,2,5,3]=>[1,2,5,3,4]=>1
[4,1,3,2,5]=>[1,3,2,5,4]=>2
[4,1,3,5,2]=>[1,3,5,2,4]=>2
[4,1,5,2,3]=>[1,5,2,3,4]=>1
[4,1,5,3,2]=>[1,5,2,3,4]=>1
[4,2,1,3,5]=>[1,3,5,2,4]=>2
[4,2,1,5,3]=>[1,5,2,3,4]=>1
[4,2,3,1,5]=>[1,5,2,3,4]=>1
[4,2,3,5,1]=>[1,2,3,5,4]=>1
[4,2,5,1,3]=>[1,3,2,5,4]=>2
[4,2,5,3,1]=>[1,2,5,3,4]=>1
[4,3,1,2,5]=>[1,2,5,3,4]=>1
[4,3,1,5,2]=>[1,5,2,3,4]=>1
[4,3,2,1,5]=>[1,5,2,3,4]=>1
[4,3,2,5,1]=>[1,2,5,3,4]=>1
[4,3,5,1,2]=>[1,2,3,5,4]=>1
[4,3,5,2,1]=>[1,2,3,5,4]=>1
[4,5,1,2,3]=>[1,2,3,4,5]=>1
[4,5,1,3,2]=>[1,3,2,4,5]=>1
[4,5,2,1,3]=>[1,3,2,4,5]=>1
[4,5,2,3,1]=>[1,2,3,4,5]=>1
[4,5,3,1,2]=>[1,2,3,4,5]=>1
[4,5,3,2,1]=>[1,2,3,4,5]=>1
[5,1,2,3,4]=>[1,2,3,4,5]=>1
[5,1,2,4,3]=>[1,2,4,3,5]=>1
[5,1,3,2,4]=>[1,3,2,4,5]=>1
[5,1,3,4,2]=>[1,3,4,2,5]=>1
[5,1,4,2,3]=>[1,4,2,3,5]=>1
[5,1,4,3,2]=>[1,4,2,3,5]=>1
[5,2,1,3,4]=>[1,3,4,2,5]=>1
[5,2,1,4,3]=>[1,4,2,3,5]=>1
[5,2,3,1,4]=>[1,4,2,3,5]=>1
[5,2,3,4,1]=>[1,2,3,4,5]=>1
[5,2,4,1,3]=>[1,3,2,4,5]=>1
[5,2,4,3,1]=>[1,2,4,3,5]=>1
[5,3,1,2,4]=>[1,2,4,3,5]=>1
[5,3,1,4,2]=>[1,4,2,3,5]=>1
[5,3,2,1,4]=>[1,4,2,3,5]=>1
[5,3,2,4,1]=>[1,2,4,3,5]=>1
[5,3,4,1,2]=>[1,2,3,4,5]=>1
[5,3,4,2,1]=>[1,2,3,4,5]=>1
[5,4,1,2,3]=>[1,2,3,4,5]=>1
[5,4,1,3,2]=>[1,3,2,4,5]=>1
[5,4,2,1,3]=>[1,3,2,4,5]=>1
[5,4,2,3,1]=>[1,2,3,4,5]=>1
[5,4,3,1,2]=>[1,2,3,4,5]=>1
[5,4,3,2,1]=>[1,2,3,4,5]=>1
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>[1,2,3,5,6,4]=>1
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>1
[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>1
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>[1,2,4,5,3,6]=>1
[1,2,4,5,6,3]=>[1,2,4,5,6,3]=>1
[1,2,4,6,3,5]=>[1,2,4,6,3,5]=>2
[1,2,4,6,5,3]=>[1,2,4,6,3,5]=>2
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>1
[1,2,5,3,6,4]=>[1,2,5,3,6,4]=>2
[1,2,5,4,3,6]=>[1,2,5,3,6,4]=>2
[1,2,5,4,6,3]=>[1,2,5,3,4,6]=>1
[1,2,5,6,3,4]=>[1,2,5,6,3,4]=>2
[1,2,5,6,4,3]=>[1,2,5,6,3,4]=>2
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>1
[1,2,6,3,5,4]=>[1,2,6,3,5,4]=>3
[1,2,6,4,3,5]=>[1,2,6,3,5,4]=>3
[1,2,6,4,5,3]=>[1,2,6,3,4,5]=>1
[1,2,6,5,3,4]=>[1,2,6,3,4,5]=>1
[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>1
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>[1,3,2,5,6,4]=>3
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>3
[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>3
[1,3,4,2,5,6]=>[1,3,4,2,5,6]=>1
[1,3,4,2,6,5]=>[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>[1,3,4,5,2,6]=>1
[1,3,4,5,6,2]=>[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>[1,3,4,6,2,5]=>3
[1,3,4,6,5,2]=>[1,3,4,6,2,5]=>3
[1,3,5,2,4,6]=>[1,3,5,2,4,6]=>2
[1,3,5,2,6,4]=>[1,3,5,2,6,4]=>5
[1,3,5,4,2,6]=>[1,3,5,2,6,4]=>5
[1,3,5,4,6,2]=>[1,3,5,2,4,6]=>2
[1,3,5,6,2,4]=>[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>[1,3,5,6,2,4]=>5
[1,3,6,2,4,5]=>[1,3,6,2,4,5]=>3
[1,3,6,2,5,4]=>[1,3,6,2,5,4]=>11
[1,3,6,4,2,5]=>[1,3,6,2,5,4]=>11
[1,3,6,4,5,2]=>[1,3,6,2,4,5]=>3
[1,3,6,5,2,4]=>[1,3,6,2,4,5]=>3
[1,3,6,5,4,2]=>[1,3,6,2,4,5]=>3
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>1
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>3
[1,4,2,5,3,6]=>[1,4,2,5,3,6]=>2
[1,4,2,5,6,3]=>[1,4,2,5,6,3]=>3
[1,4,2,6,3,5]=>[1,4,2,6,3,5]=>5
[1,4,2,6,5,3]=>[1,4,2,6,3,5]=>5
[1,4,3,2,5,6]=>[1,4,2,5,6,3]=>3
[1,4,3,2,6,5]=>[1,4,2,6,3,5]=>5
[1,4,3,5,2,6]=>[1,4,2,6,3,5]=>5
[1,4,3,5,6,2]=>[1,4,2,3,5,6]=>1
[1,4,3,6,2,5]=>[1,4,2,5,3,6]=>2
[1,4,3,6,5,2]=>[1,4,2,3,6,5]=>3
[1,4,5,2,3,6]=>[1,4,5,2,3,6]=>2
[1,4,5,2,6,3]=>[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>[1,4,5,2,6,3]=>5
[1,4,5,3,6,2]=>[1,4,5,2,3,6]=>2
[1,4,5,6,2,3]=>[1,4,5,6,2,3]=>5
[1,4,5,6,3,2]=>[1,4,5,6,2,3]=>5
[1,4,6,2,3,5]=>[1,4,6,2,3,5]=>5
[1,4,6,2,5,3]=>[1,4,6,2,5,3]=>16
[1,4,6,3,2,5]=>[1,4,6,2,5,3]=>16
[1,4,6,3,5,2]=>[1,4,6,2,3,5]=>5
[1,4,6,5,2,3]=>[1,4,6,2,3,5]=>5
[1,4,6,5,3,2]=>[1,4,6,2,3,5]=>5
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>1
[1,5,2,3,6,4]=>[1,5,2,3,6,4]=>3
[1,5,2,4,3,6]=>[1,5,2,4,3,6]=>3
[1,5,2,4,6,3]=>[1,5,2,4,6,3]=>6
[1,5,2,6,3,4]=>[1,5,2,6,3,4]=>5
[1,5,2,6,4,3]=>[1,5,2,6,3,4]=>5
[1,5,3,2,4,6]=>[1,5,2,4,6,3]=>6
[1,5,3,2,6,4]=>[1,5,2,6,3,4]=>5
[1,5,3,4,2,6]=>[1,5,2,6,3,4]=>5
[1,5,3,4,6,2]=>[1,5,2,3,4,6]=>1
[1,5,3,6,2,4]=>[1,5,2,4,3,6]=>3
[1,5,3,6,4,2]=>[1,5,2,3,6,4]=>3
[1,5,4,2,3,6]=>[1,5,2,3,6,4]=>3
[1,5,4,2,6,3]=>[1,5,2,6,3,4]=>5
[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>5
[1,5,4,3,6,2]=>[1,5,2,3,6,4]=>3
[1,5,4,6,2,3]=>[1,5,2,3,4,6]=>1
[1,5,4,6,3,2]=>[1,5,2,3,4,6]=>1
[1,5,6,2,3,4]=>[1,5,6,2,3,4]=>5
[1,5,6,2,4,3]=>[1,5,6,2,4,3]=>21
[1,5,6,3,2,4]=>[1,5,6,2,4,3]=>21
[1,5,6,3,4,2]=>[1,5,6,2,3,4]=>5
[1,5,6,4,2,3]=>[1,5,6,2,3,4]=>5
[1,5,6,4,3,2]=>[1,5,6,2,3,4]=>5
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>1
[1,6,2,3,5,4]=>[1,6,2,3,5,4]=>4
[1,6,2,4,3,5]=>[1,6,2,4,3,5]=>4
[1,6,2,4,5,3]=>[1,6,2,4,5,3]=>10
[1,6,2,5,3,4]=>[1,6,2,5,3,4]=>9
[1,6,2,5,4,3]=>[1,6,2,5,3,4]=>9
[1,6,3,2,4,5]=>[1,6,2,4,5,3]=>10
[1,6,3,2,5,4]=>[1,6,2,5,3,4]=>9
[1,6,3,4,2,5]=>[1,6,2,5,3,4]=>9
[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>1
[1,6,3,5,2,4]=>[1,6,2,4,3,5]=>4
[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>4
[1,6,4,2,3,5]=>[1,6,2,3,5,4]=>4
[1,6,4,2,5,3]=>[1,6,2,5,3,4]=>9
[1,6,4,3,2,5]=>[1,6,2,5,3,4]=>9
[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>4
[1,6,4,5,2,3]=>[1,6,2,3,4,5]=>1
[1,6,4,5,3,2]=>[1,6,2,3,4,5]=>1
[1,6,5,2,3,4]=>[1,6,2,3,4,5]=>1
[1,6,5,2,4,3]=>[1,6,2,4,3,5]=>4
[1,6,5,3,2,4]=>[1,6,2,4,3,5]=>4
[1,6,5,3,4,2]=>[1,6,2,3,4,5]=>1
[1,6,5,4,2,3]=>[1,6,2,3,4,5]=>1
[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>1
[2,1,3,4,5,6]=>[1,3,4,5,6,2]=>1
[2,1,3,4,6,5]=>[1,3,4,6,2,5]=>3
[2,1,3,5,4,6]=>[1,3,5,2,4,6]=>2
[2,1,3,5,6,4]=>[1,3,5,6,2,4]=>5
[2,1,3,6,4,5]=>[1,3,6,2,4,5]=>3
[2,1,3,6,5,4]=>[1,3,6,2,4,5]=>3
[2,1,4,3,5,6]=>[1,4,2,3,5,6]=>1
[2,1,4,3,6,5]=>[1,4,2,3,6,5]=>3
[2,1,4,5,3,6]=>[1,4,5,2,3,6]=>2
[2,1,4,5,6,3]=>[1,4,5,6,2,3]=>5
[2,1,4,6,3,5]=>[1,4,6,2,3,5]=>5
[2,1,4,6,5,3]=>[1,4,6,2,3,5]=>5
[2,1,5,3,4,6]=>[1,5,2,3,4,6]=>1
[2,1,5,3,6,4]=>[1,5,2,3,6,4]=>3
[2,1,5,4,3,6]=>[1,5,2,3,6,4]=>3
[2,1,5,4,6,3]=>[1,5,2,3,4,6]=>1
[2,1,5,6,3,4]=>[1,5,6,2,3,4]=>5
[2,1,5,6,4,3]=>[1,5,6,2,3,4]=>5
[2,1,6,3,4,5]=>[1,6,2,3,4,5]=>1
[2,1,6,3,5,4]=>[1,6,2,3,5,4]=>4
[2,1,6,4,3,5]=>[1,6,2,3,5,4]=>4
[2,1,6,4,5,3]=>[1,6,2,3,4,5]=>1
[2,1,6,5,3,4]=>[1,6,2,3,4,5]=>1
[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>1
[2,3,1,4,5,6]=>[1,4,5,6,2,3]=>5
[2,3,1,4,6,5]=>[1,4,6,2,3,5]=>5
[2,3,1,5,4,6]=>[1,5,2,3,4,6]=>1
[2,3,1,5,6,4]=>[1,5,6,2,3,4]=>5
[2,3,1,6,4,5]=>[1,6,2,3,4,5]=>1
[2,3,1,6,5,4]=>[1,6,2,3,4,5]=>1
[2,3,4,1,5,6]=>[1,5,6,2,3,4]=>5
[2,3,4,1,6,5]=>[1,6,2,3,4,5]=>1
[2,3,4,5,1,6]=>[1,6,2,3,4,5]=>1
[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>1
[2,3,4,6,1,5]=>[1,5,2,3,4,6]=>1
[2,3,4,6,5,1]=>[1,2,3,4,6,5]=>1
[2,3,5,1,4,6]=>[1,4,6,2,3,5]=>5
[2,3,5,1,6,4]=>[1,6,2,3,5,4]=>4
[2,3,5,4,1,6]=>[1,6,2,3,5,4]=>4
[2,3,5,4,6,1]=>[1,2,3,5,4,6]=>1
[2,3,5,6,1,4]=>[1,4,2,3,5,6]=>1
[2,3,5,6,4,1]=>[1,2,3,5,6,4]=>1
[2,3,6,1,4,5]=>[1,4,5,2,3,6]=>2
[2,3,6,1,5,4]=>[1,5,2,3,6,4]=>3
[2,3,6,4,1,5]=>[1,5,2,3,6,4]=>3
[2,3,6,4,5,1]=>[1,2,3,6,4,5]=>1
[2,3,6,5,1,4]=>[1,4,2,3,6,5]=>3
[2,3,6,5,4,1]=>[1,2,3,6,4,5]=>1
[2,4,1,3,5,6]=>[1,3,5,6,2,4]=>5
[2,4,1,3,6,5]=>[1,3,6,2,4,5]=>3
[2,4,1,5,3,6]=>[1,5,2,4,3,6]=>3
[2,4,1,5,6,3]=>[1,5,6,2,4,3]=>21
[2,4,1,6,3,5]=>[1,6,2,4,3,5]=>4
[2,4,1,6,5,3]=>[1,6,2,4,3,5]=>4
[2,4,3,1,5,6]=>[1,5,6,2,4,3]=>21
[2,4,3,1,6,5]=>[1,6,2,4,3,5]=>4
[2,4,3,5,1,6]=>[1,6,2,4,3,5]=>4
[2,4,3,5,6,1]=>[1,2,4,3,5,6]=>1
[2,4,3,6,1,5]=>[1,5,2,4,3,6]=>3
[2,4,3,6,5,1]=>[1,2,4,3,6,5]=>2
[2,4,5,1,3,6]=>[1,3,6,2,4,5]=>3
[2,4,5,1,6,3]=>[1,6,2,4,5,3]=>10
[2,4,5,3,1,6]=>[1,6,2,4,5,3]=>10
[2,4,5,3,6,1]=>[1,2,4,5,3,6]=>1
[2,4,5,6,1,3]=>[1,3,2,4,5,6]=>1
[2,4,5,6,3,1]=>[1,2,4,5,6,3]=>1
[2,4,6,1,3,5]=>[1,3,5,2,4,6]=>2
[2,4,6,1,5,3]=>[1,5,2,4,6,3]=>6
[2,4,6,3,1,5]=>[1,5,2,4,6,3]=>6
[2,4,6,3,5,1]=>[1,2,4,6,3,5]=>2
[2,4,6,5,1,3]=>[1,3,2,4,6,5]=>2
[2,4,6,5,3,1]=>[1,2,4,6,3,5]=>2
[2,5,1,3,4,6]=>[1,3,4,6,2,5]=>3
[2,5,1,3,6,4]=>[1,3,6,2,5,4]=>11
[2,5,1,4,3,6]=>[1,4,2,5,3,6]=>2
[2,5,1,4,6,3]=>[1,4,6,2,5,3]=>16
[2,5,1,6,3,4]=>[1,6,2,5,3,4]=>9
[2,5,1,6,4,3]=>[1,6,2,5,3,4]=>9
[2,5,3,1,4,6]=>[1,4,6,2,5,3]=>16
[2,5,3,1,6,4]=>[1,6,2,5,3,4]=>9
[2,5,3,4,1,6]=>[1,6,2,5,3,4]=>9
[2,5,3,4,6,1]=>[1,2,5,3,4,6]=>1
[2,5,3,6,1,4]=>[1,4,2,5,3,6]=>2
[2,5,3,6,4,1]=>[1,2,5,3,6,4]=>2
[2,5,4,1,3,6]=>[1,3,6,2,5,4]=>11
[2,5,4,1,6,3]=>[1,6,2,5,3,4]=>9
[2,5,4,3,1,6]=>[1,6,2,5,3,4]=>9
[2,5,4,3,6,1]=>[1,2,5,3,6,4]=>2
[2,5,4,6,1,3]=>[1,3,2,5,4,6]=>2
[2,5,4,6,3,1]=>[1,2,5,3,4,6]=>1
[2,5,6,1,3,4]=>[1,3,4,2,5,6]=>1
[2,5,6,1,4,3]=>[1,4,2,5,6,3]=>3
[2,5,6,3,1,4]=>[1,4,2,5,6,3]=>3
[2,5,6,3,4,1]=>[1,2,5,6,3,4]=>2
[2,5,6,4,1,3]=>[1,3,2,5,6,4]=>3
[2,5,6,4,3,1]=>[1,2,5,6,3,4]=>2
[2,6,1,3,4,5]=>[1,3,4,5,2,6]=>1
[2,6,1,3,5,4]=>[1,3,5,2,6,4]=>5
[2,6,1,4,3,5]=>[1,4,2,6,3,5]=>5
[2,6,1,4,5,3]=>[1,4,5,2,6,3]=>5
[2,6,1,5,3,4]=>[1,5,2,6,3,4]=>5
[2,6,1,5,4,3]=>[1,5,2,6,3,4]=>5
[2,6,3,1,4,5]=>[1,4,5,2,6,3]=>5
[2,6,3,1,5,4]=>[1,5,2,6,3,4]=>5
[2,6,3,4,1,5]=>[1,5,2,6,3,4]=>5
[2,6,3,4,5,1]=>[1,2,6,3,4,5]=>1
[2,6,3,5,1,4]=>[1,4,2,6,3,5]=>5
[2,6,3,5,4,1]=>[1,2,6,3,5,4]=>3
[2,6,4,1,3,5]=>[1,3,5,2,6,4]=>5
[2,6,4,1,5,3]=>[1,5,2,6,3,4]=>5
[2,6,4,3,1,5]=>[1,5,2,6,3,4]=>5
[2,6,4,3,5,1]=>[1,2,6,3,5,4]=>3
[2,6,4,5,1,3]=>[1,3,2,6,4,5]=>3
[2,6,4,5,3,1]=>[1,2,6,3,4,5]=>1
[2,6,5,1,3,4]=>[1,3,4,2,6,5]=>3
[2,6,5,1,4,3]=>[1,4,2,6,3,5]=>5
[2,6,5,3,1,4]=>[1,4,2,6,3,5]=>5
[2,6,5,3,4,1]=>[1,2,6,3,4,5]=>1
[2,6,5,4,1,3]=>[1,3,2,6,4,5]=>3
[2,6,5,4,3,1]=>[1,2,6,3,4,5]=>1
[3,1,2,4,5,6]=>[1,2,4,5,6,3]=>1
[3,1,2,4,6,5]=>[1,2,4,6,3,5]=>2
[3,1,2,5,4,6]=>[1,2,5,3,4,6]=>1
[3,1,2,5,6,4]=>[1,2,5,6,3,4]=>2
[3,1,2,6,4,5]=>[1,2,6,3,4,5]=>1
[3,1,2,6,5,4]=>[1,2,6,3,4,5]=>1
[3,1,4,2,5,6]=>[1,4,2,5,6,3]=>3
[3,1,4,2,6,5]=>[1,4,2,6,3,5]=>5
[3,1,4,5,2,6]=>[1,4,5,2,6,3]=>5
[3,1,4,5,6,2]=>[1,4,5,6,2,3]=>5
[3,1,4,6,2,5]=>[1,4,6,2,5,3]=>16
[3,1,4,6,5,2]=>[1,4,6,2,3,5]=>5
[3,1,5,2,4,6]=>[1,5,2,4,6,3]=>6
[3,1,5,2,6,4]=>[1,5,2,6,3,4]=>5
[3,1,5,4,2,6]=>[1,5,2,6,3,4]=>5
[3,1,5,4,6,2]=>[1,5,2,3,4,6]=>1
[3,1,5,6,2,4]=>[1,5,6,2,4,3]=>21
[3,1,5,6,4,2]=>[1,5,6,2,3,4]=>5
[3,1,6,2,4,5]=>[1,6,2,4,5,3]=>10
[3,1,6,2,5,4]=>[1,6,2,5,3,4]=>9
[3,1,6,4,2,5]=>[1,6,2,5,3,4]=>9
[3,1,6,4,5,2]=>[1,6,2,3,4,5]=>1
[3,1,6,5,2,4]=>[1,6,2,4,3,5]=>4
[3,1,6,5,4,2]=>[1,6,2,3,4,5]=>1
[3,2,1,4,5,6]=>[1,4,5,6,2,3]=>5
[3,2,1,4,6,5]=>[1,4,6,2,3,5]=>5
[3,2,1,5,4,6]=>[1,5,2,3,4,6]=>1
[3,2,1,5,6,4]=>[1,5,6,2,3,4]=>5
[3,2,1,6,4,5]=>[1,6,2,3,4,5]=>1
[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>1
[3,2,4,1,5,6]=>[1,5,6,2,4,3]=>21
[3,2,4,1,6,5]=>[1,6,2,4,3,5]=>4
[3,2,4,5,1,6]=>[1,6,2,4,5,3]=>10
[3,2,4,5,6,1]=>[1,2,4,5,6,3]=>1
[3,2,4,6,1,5]=>[1,5,2,4,6,3]=>6
[3,2,4,6,5,1]=>[1,2,4,6,3,5]=>2
[3,2,5,1,4,6]=>[1,4,6,2,5,3]=>16
[3,2,5,1,6,4]=>[1,6,2,5,3,4]=>9
[3,2,5,4,1,6]=>[1,6,2,5,3,4]=>9
[3,2,5,4,6,1]=>[1,2,5,3,4,6]=>1
[3,2,5,6,1,4]=>[1,4,2,5,6,3]=>3
[3,2,5,6,4,1]=>[1,2,5,6,3,4]=>2
[3,2,6,1,4,5]=>[1,4,5,2,6,3]=>5
[3,2,6,1,5,4]=>[1,5,2,6,3,4]=>5
[3,2,6,4,1,5]=>[1,5,2,6,3,4]=>5
[3,2,6,4,5,1]=>[1,2,6,3,4,5]=>1
[3,2,6,5,1,4]=>[1,4,2,6,3,5]=>5
[3,2,6,5,4,1]=>[1,2,6,3,4,5]=>1
[3,4,1,2,5,6]=>[1,2,5,6,3,4]=>2
[3,4,1,2,6,5]=>[1,2,6,3,4,5]=>1
[3,4,1,5,2,6]=>[1,5,2,6,3,4]=>5
[3,4,1,5,6,2]=>[1,5,6,2,3,4]=>5
[3,4,1,6,2,5]=>[1,6,2,5,3,4]=>9
[3,4,1,6,5,2]=>[1,6,2,3,4,5]=>1
[3,4,2,1,5,6]=>[1,5,6,2,3,4]=>5
[3,4,2,1,6,5]=>[1,6,2,3,4,5]=>1
[3,4,2,5,1,6]=>[1,6,2,5,3,4]=>9
[3,4,2,5,6,1]=>[1,2,5,6,3,4]=>2
[3,4,2,6,1,5]=>[1,5,2,6,3,4]=>5
[3,4,2,6,5,1]=>[1,2,6,3,4,5]=>1
[3,4,5,1,2,6]=>[1,2,6,3,4,5]=>1
[3,4,5,1,6,2]=>[1,6,2,3,4,5]=>1
[3,4,5,2,1,6]=>[1,6,2,3,4,5]=>1
[3,4,5,2,6,1]=>[1,2,6,3,4,5]=>1
[3,4,5,6,1,2]=>[1,2,3,4,5,6]=>1
[3,4,5,6,2,1]=>[1,2,3,4,5,6]=>1
[3,4,6,1,2,5]=>[1,2,5,3,4,6]=>1
[3,4,6,1,5,2]=>[1,5,2,3,4,6]=>1
[3,4,6,2,1,5]=>[1,5,2,3,4,6]=>1
[3,4,6,2,5,1]=>[1,2,5,3,4,6]=>1
[3,4,6,5,1,2]=>[1,2,3,4,6,5]=>1
[3,4,6,5,2,1]=>[1,2,3,4,6,5]=>1
[3,5,1,2,4,6]=>[1,2,4,6,3,5]=>2
[3,5,1,2,6,4]=>[1,2,6,3,5,4]=>3
[3,5,1,4,2,6]=>[1,4,2,6,3,5]=>5
[3,5,1,4,6,2]=>[1,4,6,2,3,5]=>5
[3,5,1,6,2,4]=>[1,6,2,4,3,5]=>4
[3,5,1,6,4,2]=>[1,6,2,3,5,4]=>4
[3,5,2,1,4,6]=>[1,4,6,2,3,5]=>5
[3,5,2,1,6,4]=>[1,6,2,3,5,4]=>4
[3,5,2,4,1,6]=>[1,6,2,4,3,5]=>4
[3,5,2,4,6,1]=>[1,2,4,6,3,5]=>2
[3,5,2,6,1,4]=>[1,4,2,6,3,5]=>5
[3,5,2,6,4,1]=>[1,2,6,3,5,4]=>3
[3,5,4,1,2,6]=>[1,2,6,3,5,4]=>3
[3,5,4,1,6,2]=>[1,6,2,3,5,4]=>4
[3,5,4,2,1,6]=>[1,6,2,3,5,4]=>4
[3,5,4,2,6,1]=>[1,2,6,3,5,4]=>3
[3,5,4,6,1,2]=>[1,2,3,5,4,6]=>1
[3,5,4,6,2,1]=>[1,2,3,5,4,6]=>1
[3,5,6,1,2,4]=>[1,2,4,3,5,6]=>1
[3,5,6,1,4,2]=>[1,4,2,3,5,6]=>1
[3,5,6,2,1,4]=>[1,4,2,3,5,6]=>1
[3,5,6,2,4,1]=>[1,2,4,3,5,6]=>1
[3,5,6,4,1,2]=>[1,2,3,5,6,4]=>1
[3,5,6,4,2,1]=>[1,2,3,5,6,4]=>1
[3,6,1,2,4,5]=>[1,2,4,5,3,6]=>1
[3,6,1,2,5,4]=>[1,2,5,3,6,4]=>2
[3,6,1,4,2,5]=>[1,4,2,5,3,6]=>2
[3,6,1,4,5,2]=>[1,4,5,2,3,6]=>2
[3,6,1,5,2,4]=>[1,5,2,4,3,6]=>3
[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>3
[3,6,2,1,4,5]=>[1,4,5,2,3,6]=>2
[3,6,2,1,5,4]=>[1,5,2,3,6,4]=>3
[3,6,2,4,1,5]=>[1,5,2,4,3,6]=>3
[3,6,2,4,5,1]=>[1,2,4,5,3,6]=>1
[3,6,2,5,1,4]=>[1,4,2,5,3,6]=>2
[3,6,2,5,4,1]=>[1,2,5,3,6,4]=>2
[3,6,4,1,2,5]=>[1,2,5,3,6,4]=>2
[3,6,4,1,5,2]=>[1,5,2,3,6,4]=>3
[3,6,4,2,1,5]=>[1,5,2,3,6,4]=>3
[3,6,4,2,5,1]=>[1,2,5,3,6,4]=>2
[3,6,4,5,1,2]=>[1,2,3,6,4,5]=>1
[3,6,4,5,2,1]=>[1,2,3,6,4,5]=>1
[3,6,5,1,2,4]=>[1,2,4,3,6,5]=>2
[3,6,5,1,4,2]=>[1,4,2,3,6,5]=>3
[3,6,5,2,1,4]=>[1,4,2,3,6,5]=>3
[3,6,5,2,4,1]=>[1,2,4,3,6,5]=>2
[3,6,5,4,1,2]=>[1,2,3,6,4,5]=>1
[3,6,5,4,2,1]=>[1,2,3,6,4,5]=>1
[4,1,2,3,5,6]=>[1,2,3,5,6,4]=>1
[4,1,2,3,6,5]=>[1,2,3,6,4,5]=>1
[4,1,2,5,3,6]=>[1,2,5,3,6,4]=>2
[4,1,2,5,6,3]=>[1,2,5,6,3,4]=>2
[4,1,2,6,3,5]=>[1,2,6,3,5,4]=>3
[4,1,2,6,5,3]=>[1,2,6,3,4,5]=>1
[4,1,3,2,5,6]=>[1,3,2,5,6,4]=>3
[4,1,3,2,6,5]=>[1,3,2,6,4,5]=>3
[4,1,3,5,2,6]=>[1,3,5,2,6,4]=>5
[4,1,3,5,6,2]=>[1,3,5,6,2,4]=>5
[4,1,3,6,2,5]=>[1,3,6,2,5,4]=>11
[4,1,3,6,5,2]=>[1,3,6,2,4,5]=>3
[4,1,5,2,3,6]=>[1,5,2,3,6,4]=>3
[4,1,5,2,6,3]=>[1,5,2,6,3,4]=>5
[4,1,5,3,2,6]=>[1,5,2,6,3,4]=>5
[4,1,5,3,6,2]=>[1,5,2,3,6,4]=>3
[4,1,5,6,2,3]=>[1,5,6,2,3,4]=>5
[4,1,5,6,3,2]=>[1,5,6,2,3,4]=>5
[4,1,6,2,3,5]=>[1,6,2,3,5,4]=>4
[4,1,6,2,5,3]=>[1,6,2,5,3,4]=>9
[4,1,6,3,2,5]=>[1,6,2,5,3,4]=>9
[4,1,6,3,5,2]=>[1,6,2,3,5,4]=>4
[4,1,6,5,2,3]=>[1,6,2,3,4,5]=>1
[4,1,6,5,3,2]=>[1,6,2,3,4,5]=>1
[4,2,1,3,5,6]=>[1,3,5,6,2,4]=>5
[4,2,1,3,6,5]=>[1,3,6,2,4,5]=>3
[4,2,1,5,3,6]=>[1,5,2,3,6,4]=>3
[4,2,1,5,6,3]=>[1,5,6,2,3,4]=>5
[4,2,1,6,3,5]=>[1,6,2,3,5,4]=>4
[4,2,1,6,5,3]=>[1,6,2,3,4,5]=>1
[4,2,3,1,5,6]=>[1,5,6,2,3,4]=>5
[4,2,3,1,6,5]=>[1,6,2,3,4,5]=>1
[4,2,3,5,1,6]=>[1,6,2,3,5,4]=>4
[4,2,3,5,6,1]=>[1,2,3,5,6,4]=>1
[4,2,3,6,1,5]=>[1,5,2,3,6,4]=>3
[4,2,3,6,5,1]=>[1,2,3,6,4,5]=>1
[4,2,5,1,3,6]=>[1,3,6,2,5,4]=>11
[4,2,5,1,6,3]=>[1,6,2,5,3,4]=>9
[4,2,5,3,1,6]=>[1,6,2,5,3,4]=>9
[4,2,5,3,6,1]=>[1,2,5,3,6,4]=>2
[4,2,5,6,1,3]=>[1,3,2,5,6,4]=>3
[4,2,5,6,3,1]=>[1,2,5,6,3,4]=>2
[4,2,6,1,3,5]=>[1,3,5,2,6,4]=>5
[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>5
[4,2,6,3,1,5]=>[1,5,2,6,3,4]=>5
[4,2,6,3,5,1]=>[1,2,6,3,5,4]=>3
[4,2,6,5,1,3]=>[1,3,2,6,4,5]=>3
[4,2,6,5,3,1]=>[1,2,6,3,4,5]=>1
[4,3,1,2,5,6]=>[1,2,5,6,3,4]=>2
[4,3,1,2,6,5]=>[1,2,6,3,4,5]=>1
[4,3,1,5,2,6]=>[1,5,2,6,3,4]=>5
[4,3,1,5,6,2]=>[1,5,6,2,3,4]=>5
[4,3,1,6,2,5]=>[1,6,2,5,3,4]=>9
[4,3,1,6,5,2]=>[1,6,2,3,4,5]=>1
[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>5
[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>1
[4,3,2,5,1,6]=>[1,6,2,5,3,4]=>9
[4,3,2,5,6,1]=>[1,2,5,6,3,4]=>2
[4,3,2,6,1,5]=>[1,5,2,6,3,4]=>5
[4,3,2,6,5,1]=>[1,2,6,3,4,5]=>1
[4,3,5,1,2,6]=>[1,2,6,3,5,4]=>3
[4,3,5,1,6,2]=>[1,6,2,3,5,4]=>4
[4,3,5,2,1,6]=>[1,6,2,3,5,4]=>4
[4,3,5,2,6,1]=>[1,2,6,3,5,4]=>3
[4,3,5,6,1,2]=>[1,2,3,5,6,4]=>1
[4,3,5,6,2,1]=>[1,2,3,5,6,4]=>1
[4,3,6,1,2,5]=>[1,2,5,3,6,4]=>2
[4,3,6,1,5,2]=>[1,5,2,3,6,4]=>3
[4,3,6,2,1,5]=>[1,5,2,3,6,4]=>3
[4,3,6,2,5,1]=>[1,2,5,3,6,4]=>2
[4,3,6,5,1,2]=>[1,2,3,6,4,5]=>1
[4,3,6,5,2,1]=>[1,2,3,6,4,5]=>1
[4,5,1,2,3,6]=>[1,2,3,6,4,5]=>1
[4,5,1,2,6,3]=>[1,2,6,3,4,5]=>1
[4,5,1,3,2,6]=>[1,3,2,6,4,5]=>3
[4,5,1,3,6,2]=>[1,3,6,2,4,5]=>3
[4,5,1,6,2,3]=>[1,6,2,3,4,5]=>1
[4,5,1,6,3,2]=>[1,6,2,3,4,5]=>1
[4,5,2,1,3,6]=>[1,3,6,2,4,5]=>3
[4,5,2,1,6,3]=>[1,6,2,3,4,5]=>1
[4,5,2,3,1,6]=>[1,6,2,3,4,5]=>1
[4,5,2,3,6,1]=>[1,2,3,6,4,5]=>1
[4,5,2,6,1,3]=>[1,3,2,6,4,5]=>3
[4,5,2,6,3,1]=>[1,2,6,3,4,5]=>1
[4,5,3,1,2,6]=>[1,2,6,3,4,5]=>1
[4,5,3,1,6,2]=>[1,6,2,3,4,5]=>1
[4,5,3,2,1,6]=>[1,6,2,3,4,5]=>1
[4,5,3,2,6,1]=>[1,2,6,3,4,5]=>1
[4,5,3,6,1,2]=>[1,2,3,6,4,5]=>1
[4,5,3,6,2,1]=>[1,2,3,6,4,5]=>1
[4,5,6,1,2,3]=>[1,2,3,4,5,6]=>1
[4,5,6,1,3,2]=>[1,3,2,4,5,6]=>1
[4,5,6,2,1,3]=>[1,3,2,4,5,6]=>1
[4,5,6,2,3,1]=>[1,2,3,4,5,6]=>1
[4,5,6,3,1,2]=>[1,2,3,4,5,6]=>1
[4,5,6,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,1,2,3,5]=>[1,2,3,5,4,6]=>1
[4,6,1,2,5,3]=>[1,2,5,3,4,6]=>1
[4,6,1,3,2,5]=>[1,3,2,5,4,6]=>2
[4,6,1,3,5,2]=>[1,3,5,2,4,6]=>2
[4,6,1,5,2,3]=>[1,5,2,3,4,6]=>1
[4,6,1,5,3,2]=>[1,5,2,3,4,6]=>1
[4,6,2,1,3,5]=>[1,3,5,2,4,6]=>2
[4,6,2,1,5,3]=>[1,5,2,3,4,6]=>1
[4,6,2,3,1,5]=>[1,5,2,3,4,6]=>1
[4,6,2,3,5,1]=>[1,2,3,5,4,6]=>1
[4,6,2,5,1,3]=>[1,3,2,5,4,6]=>2
[4,6,2,5,3,1]=>[1,2,5,3,4,6]=>1
[4,6,3,1,2,5]=>[1,2,5,3,4,6]=>1
[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>1
[4,6,3,2,1,5]=>[1,5,2,3,4,6]=>1
[4,6,3,2,5,1]=>[1,2,5,3,4,6]=>1
[4,6,3,5,1,2]=>[1,2,3,5,4,6]=>1
[4,6,3,5,2,1]=>[1,2,3,5,4,6]=>1
[4,6,5,1,2,3]=>[1,2,3,4,6,5]=>1
[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>2
[4,6,5,2,1,3]=>[1,3,2,4,6,5]=>2
[4,6,5,2,3,1]=>[1,2,3,4,6,5]=>1
[4,6,5,3,1,2]=>[1,2,3,4,6,5]=>1
[4,6,5,3,2,1]=>[1,2,3,4,6,5]=>1
[5,1,2,3,4,6]=>[1,2,3,4,6,5]=>1
[5,1,2,3,6,4]=>[1,2,3,6,4,5]=>1
[5,1,2,4,3,6]=>[1,2,4,3,6,5]=>2
[5,1,2,4,6,3]=>[1,2,4,6,3,5]=>2
[5,1,2,6,3,4]=>[1,2,6,3,4,5]=>1
[5,1,2,6,4,3]=>[1,2,6,3,4,5]=>1
[5,1,3,2,4,6]=>[1,3,2,4,6,5]=>2
[5,1,3,2,6,4]=>[1,3,2,6,4,5]=>3
[5,1,3,4,2,6]=>[1,3,4,2,6,5]=>3
[5,1,3,4,6,2]=>[1,3,4,6,2,5]=>3
[5,1,3,6,2,4]=>[1,3,6,2,4,5]=>3
[5,1,3,6,4,2]=>[1,3,6,2,4,5]=>3
[5,1,4,2,3,6]=>[1,4,2,3,6,5]=>3
[5,1,4,2,6,3]=>[1,4,2,6,3,5]=>5
[5,1,4,3,2,6]=>[1,4,2,6,3,5]=>5
[5,1,4,3,6,2]=>[1,4,2,3,6,5]=>3
[5,1,4,6,2,3]=>[1,4,6,2,3,5]=>5
[5,1,4,6,3,2]=>[1,4,6,2,3,5]=>5
[5,1,6,2,3,4]=>[1,6,2,3,4,5]=>1
[5,1,6,2,4,3]=>[1,6,2,4,3,5]=>4
[5,1,6,3,2,4]=>[1,6,2,4,3,5]=>4
[5,1,6,3,4,2]=>[1,6,2,3,4,5]=>1
[5,1,6,4,2,3]=>[1,6,2,3,4,5]=>1
[5,1,6,4,3,2]=>[1,6,2,3,4,5]=>1
[5,2,1,3,4,6]=>[1,3,4,6,2,5]=>3
[5,2,1,3,6,4]=>[1,3,6,2,4,5]=>3
[5,2,1,4,3,6]=>[1,4,2,3,6,5]=>3
[5,2,1,4,6,3]=>[1,4,6,2,3,5]=>5
[5,2,1,6,3,4]=>[1,6,2,3,4,5]=>1
[5,2,1,6,4,3]=>[1,6,2,3,4,5]=>1
[5,2,3,1,4,6]=>[1,4,6,2,3,5]=>5
[5,2,3,1,6,4]=>[1,6,2,3,4,5]=>1
[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>1
[5,2,3,4,6,1]=>[1,2,3,4,6,5]=>1
[5,2,3,6,1,4]=>[1,4,2,3,6,5]=>3
[5,2,3,6,4,1]=>[1,2,3,6,4,5]=>1
[5,2,4,1,3,6]=>[1,3,6,2,4,5]=>3
[5,2,4,1,6,3]=>[1,6,2,4,3,5]=>4
[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>4
[5,2,4,3,6,1]=>[1,2,4,3,6,5]=>2
[5,2,4,6,1,3]=>[1,3,2,4,6,5]=>2
[5,2,4,6,3,1]=>[1,2,4,6,3,5]=>2
[5,2,6,1,3,4]=>[1,3,4,2,6,5]=>3
[5,2,6,1,4,3]=>[1,4,2,6,3,5]=>5
[5,2,6,3,1,4]=>[1,4,2,6,3,5]=>5
[5,2,6,3,4,1]=>[1,2,6,3,4,5]=>1
[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>3
[5,2,6,4,3,1]=>[1,2,6,3,4,5]=>1
[5,3,1,2,4,6]=>[1,2,4,6,3,5]=>2
[5,3,1,2,6,4]=>[1,2,6,3,4,5]=>1
[5,3,1,4,2,6]=>[1,4,2,6,3,5]=>5
[5,3,1,4,6,2]=>[1,4,6,2,3,5]=>5
[5,3,1,6,2,4]=>[1,6,2,4,3,5]=>4
[5,3,1,6,4,2]=>[1,6,2,3,4,5]=>1
[5,3,2,1,4,6]=>[1,4,6,2,3,5]=>5
[5,3,2,1,6,4]=>[1,6,2,3,4,5]=>1
[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>4
[5,3,2,4,6,1]=>[1,2,4,6,3,5]=>2
[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>5
[5,3,2,6,4,1]=>[1,2,6,3,4,5]=>1
[5,3,4,1,2,6]=>[1,2,6,3,4,5]=>1
[5,3,4,1,6,2]=>[1,6,2,3,4,5]=>1
[5,3,4,2,1,6]=>[1,6,2,3,4,5]=>1
[5,3,4,2,6,1]=>[1,2,6,3,4,5]=>1
[5,3,4,6,1,2]=>[1,2,3,4,6,5]=>1
[5,3,4,6,2,1]=>[1,2,3,4,6,5]=>1
[5,3,6,1,2,4]=>[1,2,4,3,6,5]=>2
[5,3,6,1,4,2]=>[1,4,2,3,6,5]=>3
[5,3,6,2,1,4]=>[1,4,2,3,6,5]=>3
[5,3,6,2,4,1]=>[1,2,4,3,6,5]=>2
[5,3,6,4,1,2]=>[1,2,3,6,4,5]=>1
[5,3,6,4,2,1]=>[1,2,3,6,4,5]=>1
[5,4,1,2,3,6]=>[1,2,3,6,4,5]=>1
[5,4,1,2,6,3]=>[1,2,6,3,4,5]=>1
[5,4,1,3,2,6]=>[1,3,2,6,4,5]=>3
[5,4,1,3,6,2]=>[1,3,6,2,4,5]=>3
[5,4,1,6,2,3]=>[1,6,2,3,4,5]=>1
[5,4,1,6,3,2]=>[1,6,2,3,4,5]=>1
[5,4,2,1,3,6]=>[1,3,6,2,4,5]=>3
[5,4,2,1,6,3]=>[1,6,2,3,4,5]=>1
[5,4,2,3,1,6]=>[1,6,2,3,4,5]=>1
[5,4,2,3,6,1]=>[1,2,3,6,4,5]=>1
[5,4,2,6,1,3]=>[1,3,2,6,4,5]=>3
[5,4,2,6,3,1]=>[1,2,6,3,4,5]=>1
[5,4,3,1,2,6]=>[1,2,6,3,4,5]=>1
[5,4,3,1,6,2]=>[1,6,2,3,4,5]=>1
[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>1
[5,4,3,2,6,1]=>[1,2,6,3,4,5]=>1
[5,4,3,6,1,2]=>[1,2,3,6,4,5]=>1
[5,4,3,6,2,1]=>[1,2,3,6,4,5]=>1
[5,4,6,1,2,3]=>[1,2,3,4,6,5]=>1
[5,4,6,1,3,2]=>[1,3,2,4,6,5]=>2
[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>2
[5,4,6,2,3,1]=>[1,2,3,4,6,5]=>1
[5,4,6,3,1,2]=>[1,2,3,4,6,5]=>1
[5,4,6,3,2,1]=>[1,2,3,4,6,5]=>1
[5,6,1,2,3,4]=>[1,2,3,4,5,6]=>1
[5,6,1,2,4,3]=>[1,2,4,3,5,6]=>1
[5,6,1,3,2,4]=>[1,3,2,4,5,6]=>1
[5,6,1,3,4,2]=>[1,3,4,2,5,6]=>1
[5,6,1,4,2,3]=>[1,4,2,3,5,6]=>1
[5,6,1,4,3,2]=>[1,4,2,3,5,6]=>1
[5,6,2,1,3,4]=>[1,3,4,2,5,6]=>1
[5,6,2,1,4,3]=>[1,4,2,3,5,6]=>1
[5,6,2,3,1,4]=>[1,4,2,3,5,6]=>1
[5,6,2,3,4,1]=>[1,2,3,4,5,6]=>1
[5,6,2,4,1,3]=>[1,3,2,4,5,6]=>1
[5,6,2,4,3,1]=>[1,2,4,3,5,6]=>1
[5,6,3,1,2,4]=>[1,2,4,3,5,6]=>1
[5,6,3,1,4,2]=>[1,4,2,3,5,6]=>1
[5,6,3,2,1,4]=>[1,4,2,3,5,6]=>1
[5,6,3,2,4,1]=>[1,2,4,3,5,6]=>1
[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[5,6,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,6,4,1,2,3]=>[1,2,3,4,5,6]=>1
[5,6,4,1,3,2]=>[1,3,2,4,5,6]=>1
[5,6,4,2,1,3]=>[1,3,2,4,5,6]=>1
[5,6,4,2,3,1]=>[1,2,3,4,5,6]=>1
[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[5,6,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,1,2,3,4,5]=>[1,2,3,4,5,6]=>1
[6,1,2,3,5,4]=>[1,2,3,5,4,6]=>1
[6,1,2,4,3,5]=>[1,2,4,3,5,6]=>1
[6,1,2,4,5,3]=>[1,2,4,5,3,6]=>1
[6,1,2,5,3,4]=>[1,2,5,3,4,6]=>1
[6,1,2,5,4,3]=>[1,2,5,3,4,6]=>1
[6,1,3,2,4,5]=>[1,3,2,4,5,6]=>1
[6,1,3,2,5,4]=>[1,3,2,5,4,6]=>2
[6,1,3,4,2,5]=>[1,3,4,2,5,6]=>1
[6,1,3,4,5,2]=>[1,3,4,5,2,6]=>1
[6,1,3,5,2,4]=>[1,3,5,2,4,6]=>2
[6,1,3,5,4,2]=>[1,3,5,2,4,6]=>2
[6,1,4,2,3,5]=>[1,4,2,3,5,6]=>1
[6,1,4,2,5,3]=>[1,4,2,5,3,6]=>2
[6,1,4,3,2,5]=>[1,4,2,5,3,6]=>2
[6,1,4,3,5,2]=>[1,4,2,3,5,6]=>1
[6,1,4,5,2,3]=>[1,4,5,2,3,6]=>2
[6,1,4,5,3,2]=>[1,4,5,2,3,6]=>2
[6,1,5,2,3,4]=>[1,5,2,3,4,6]=>1
[6,1,5,2,4,3]=>[1,5,2,4,3,6]=>3
[6,1,5,3,2,4]=>[1,5,2,4,3,6]=>3
[6,1,5,3,4,2]=>[1,5,2,3,4,6]=>1
[6,1,5,4,2,3]=>[1,5,2,3,4,6]=>1
[6,1,5,4,3,2]=>[1,5,2,3,4,6]=>1
[6,2,1,3,4,5]=>[1,3,4,5,2,6]=>1
[6,2,1,3,5,4]=>[1,3,5,2,4,6]=>2
[6,2,1,4,3,5]=>[1,4,2,3,5,6]=>1
[6,2,1,4,5,3]=>[1,4,5,2,3,6]=>2
[6,2,1,5,3,4]=>[1,5,2,3,4,6]=>1
[6,2,1,5,4,3]=>[1,5,2,3,4,6]=>1
[6,2,3,1,4,5]=>[1,4,5,2,3,6]=>2
[6,2,3,1,5,4]=>[1,5,2,3,4,6]=>1
[6,2,3,4,1,5]=>[1,5,2,3,4,6]=>1
[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[6,2,3,5,1,4]=>[1,4,2,3,5,6]=>1
[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>1
[6,2,4,1,3,5]=>[1,3,5,2,4,6]=>2
[6,2,4,1,5,3]=>[1,5,2,4,3,6]=>3
[6,2,4,3,1,5]=>[1,5,2,4,3,6]=>3
[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>1
[6,2,4,5,1,3]=>[1,3,2,4,5,6]=>1
[6,2,4,5,3,1]=>[1,2,4,5,3,6]=>1
[6,2,5,1,3,4]=>[1,3,4,2,5,6]=>1
[6,2,5,1,4,3]=>[1,4,2,5,3,6]=>2
[6,2,5,3,1,4]=>[1,4,2,5,3,6]=>2
[6,2,5,3,4,1]=>[1,2,5,3,4,6]=>1
[6,2,5,4,1,3]=>[1,3,2,5,4,6]=>2
[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>1
[6,3,1,2,4,5]=>[1,2,4,5,3,6]=>1
[6,3,1,2,5,4]=>[1,2,5,3,4,6]=>1
[6,3,1,4,2,5]=>[1,4,2,5,3,6]=>2
[6,3,1,4,5,2]=>[1,4,5,2,3,6]=>2
[6,3,1,5,2,4]=>[1,5,2,4,3,6]=>3
[6,3,1,5,4,2]=>[1,5,2,3,4,6]=>1
[6,3,2,1,4,5]=>[1,4,5,2,3,6]=>2
[6,3,2,1,5,4]=>[1,5,2,3,4,6]=>1
[6,3,2,4,1,5]=>[1,5,2,4,3,6]=>3
[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>1
[6,3,2,5,1,4]=>[1,4,2,5,3,6]=>2
[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>1
[6,3,4,1,2,5]=>[1,2,5,3,4,6]=>1
[6,3,4,1,5,2]=>[1,5,2,3,4,6]=>1
[6,3,4,2,1,5]=>[1,5,2,3,4,6]=>1
[6,3,4,2,5,1]=>[1,2,5,3,4,6]=>1
[6,3,4,5,1,2]=>[1,2,3,4,5,6]=>1
[6,3,4,5,2,1]=>[1,2,3,4,5,6]=>1
[6,3,5,1,2,4]=>[1,2,4,3,5,6]=>1
[6,3,5,1,4,2]=>[1,4,2,3,5,6]=>1
[6,3,5,2,1,4]=>[1,4,2,3,5,6]=>1
[6,3,5,2,4,1]=>[1,2,4,3,5,6]=>1
[6,3,5,4,1,2]=>[1,2,3,5,4,6]=>1
[6,3,5,4,2,1]=>[1,2,3,5,4,6]=>1
[6,4,1,2,3,5]=>[1,2,3,5,4,6]=>1
[6,4,1,2,5,3]=>[1,2,5,3,4,6]=>1
[6,4,1,3,2,5]=>[1,3,2,5,4,6]=>2
[6,4,1,3,5,2]=>[1,3,5,2,4,6]=>2
[6,4,1,5,2,3]=>[1,5,2,3,4,6]=>1
[6,4,1,5,3,2]=>[1,5,2,3,4,6]=>1
[6,4,2,1,3,5]=>[1,3,5,2,4,6]=>2
[6,4,2,1,5,3]=>[1,5,2,3,4,6]=>1
[6,4,2,3,1,5]=>[1,5,2,3,4,6]=>1
[6,4,2,3,5,1]=>[1,2,3,5,4,6]=>1
[6,4,2,5,1,3]=>[1,3,2,5,4,6]=>2
[6,4,2,5,3,1]=>[1,2,5,3,4,6]=>1
[6,4,3,1,2,5]=>[1,2,5,3,4,6]=>1
[6,4,3,1,5,2]=>[1,5,2,3,4,6]=>1
[6,4,3,2,1,5]=>[1,5,2,3,4,6]=>1
[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>1
[6,4,3,5,1,2]=>[1,2,3,5,4,6]=>1
[6,4,3,5,2,1]=>[1,2,3,5,4,6]=>1
[6,4,5,1,2,3]=>[1,2,3,4,5,6]=>1
[6,4,5,1,3,2]=>[1,3,2,4,5,6]=>1
[6,4,5,2,1,3]=>[1,3,2,4,5,6]=>1
[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[6,4,5,3,1,2]=>[1,2,3,4,5,6]=>1
[6,4,5,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,1,2,3,4]=>[1,2,3,4,5,6]=>1
[6,5,1,2,4,3]=>[1,2,4,3,5,6]=>1
[6,5,1,3,2,4]=>[1,3,2,4,5,6]=>1
[6,5,1,3,4,2]=>[1,3,4,2,5,6]=>1
[6,5,1,4,2,3]=>[1,4,2,3,5,6]=>1
[6,5,1,4,3,2]=>[1,4,2,3,5,6]=>1
[6,5,2,1,3,4]=>[1,3,4,2,5,6]=>1
[6,5,2,1,4,3]=>[1,4,2,3,5,6]=>1
[6,5,2,3,1,4]=>[1,4,2,3,5,6]=>1
[6,5,2,3,4,1]=>[1,2,3,4,5,6]=>1
[6,5,2,4,1,3]=>[1,3,2,4,5,6]=>1
[6,5,2,4,3,1]=>[1,2,4,3,5,6]=>1
[6,5,3,1,2,4]=>[1,2,4,3,5,6]=>1
[6,5,3,1,4,2]=>[1,4,2,3,5,6]=>1
[6,5,3,2,1,4]=>[1,4,2,3,5,6]=>1
[6,5,3,2,4,1]=>[1,2,4,3,5,6]=>1
[6,5,3,4,1,2]=>[1,2,3,4,5,6]=>1
[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,5,4,1,2,3]=>[1,2,3,4,5,6]=>1
[6,5,4,1,3,2]=>[1,3,2,4,5,6]=>1
[6,5,4,2,1,3]=>[1,3,2,4,5,6]=>1
[6,5,4,2,3,1]=>[1,2,3,4,5,6]=>1
[6,5,4,3,1,2]=>[1,2,3,4,5,6]=>1
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>1
[1,2,3,6,4,7,5]=>[1,2,3,6,4,7,5]=>2
[1,2,3,6,5,4,7]=>[1,2,3,6,4,7,5]=>2
[1,2,6,3,4,7,5]=>[1,2,6,3,4,7,5]=>3
[1,2,6,4,7,5,3]=>[1,2,6,3,4,7,5]=>3
[1,2,6,5,3,4,7]=>[1,2,6,3,4,7,5]=>3
[1,2,6,5,4,7,3]=>[1,2,6,3,4,7,5]=>3
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>1
[1,3,7,2,4,5,6]=>[1,3,7,2,4,5,6]=>4
[1,3,7,4,5,6,2]=>[1,3,7,2,4,5,6]=>4
[1,3,7,5,6,2,4]=>[1,3,7,2,4,5,6]=>4
[1,3,7,5,6,4,2]=>[1,3,7,2,4,5,6]=>4
[1,3,7,6,2,4,5]=>[1,3,7,2,4,5,6]=>4
[1,3,7,6,4,5,2]=>[1,3,7,2,4,5,6]=>4
[1,3,7,6,5,2,4]=>[1,3,7,2,4,5,6]=>4
[1,3,7,6,5,4,2]=>[1,3,7,2,4,5,6]=>4
[1,4,6,7,2,3,5]=>[1,4,6,7,2,3,5]=>42
[1,4,6,7,3,5,2]=>[1,4,6,7,2,3,5]=>42
[1,4,6,7,5,2,3]=>[1,4,6,7,2,3,5]=>42
[1,4,6,7,5,3,2]=>[1,4,6,7,2,3,5]=>42
[1,4,7,2,3,5,6]=>[1,4,7,2,3,5,6]=>9
[1,4,7,3,5,6,2]=>[1,4,7,2,3,5,6]=>9
[1,4,7,5,6,2,3]=>[1,4,7,2,3,5,6]=>9
[1,4,7,5,6,3,2]=>[1,4,7,2,3,5,6]=>9
[1,4,7,6,2,3,5]=>[1,4,7,2,3,5,6]=>9
[1,4,7,6,3,5,2]=>[1,4,7,2,3,5,6]=>9
[1,4,7,6,5,2,3]=>[1,4,7,2,3,5,6]=>9
[1,4,7,6,5,3,2]=>[1,4,7,2,3,5,6]=>9
[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>4
[1,5,2,7,3,4,6]=>[1,5,2,7,3,4,6]=>14
[1,5,2,7,4,6,3]=>[1,5,2,7,3,4,6]=>14
[1,5,2,7,6,3,4]=>[1,5,2,7,3,4,6]=>14
[1,5,2,7,6,4,3]=>[1,5,2,7,3,4,6]=>14
[1,5,3,2,7,4,6]=>[1,5,2,7,3,4,6]=>14
[1,5,3,2,7,6,4]=>[1,5,2,7,3,4,6]=>14
[1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6]=>14
[1,5,3,4,6,2,7]=>[1,5,2,7,3,4,6]=>14
[1,5,3,4,7,6,2]=>[1,5,2,3,4,7,6]=>4
[1,5,4,2,7,6,3]=>[1,5,2,7,3,4,6]=>14
[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>14
[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>14
[1,5,4,6,3,2,7]=>[1,5,2,7,3,4,6]=>14
[1,5,4,7,6,2,3]=>[1,5,2,3,4,7,6]=>4
[1,5,4,7,6,3,2]=>[1,5,2,3,4,7,6]=>4
[1,5,6,2,7,3,4]=>[1,5,6,2,7,3,4]=>42
[1,5,6,2,7,4,3]=>[1,5,6,2,7,3,4]=>42
[1,5,6,3,2,7,4]=>[1,5,6,2,7,3,4]=>42
[1,5,6,3,4,2,7]=>[1,5,6,2,7,3,4]=>42
[1,5,6,4,2,7,3]=>[1,5,6,2,7,3,4]=>42
[1,5,6,4,3,2,7]=>[1,5,6,2,7,3,4]=>42
[1,5,6,7,2,3,4]=>[1,5,6,7,2,3,4]=>42
[1,5,6,7,3,4,2]=>[1,5,6,7,2,3,4]=>42
[1,5,6,7,4,2,3]=>[1,5,6,7,2,3,4]=>42
[1,5,6,7,4,3,2]=>[1,5,6,7,2,3,4]=>42
[1,5,7,2,3,4,6]=>[1,5,7,2,3,4,6]=>14
[1,5,7,3,4,6,2]=>[1,5,7,2,3,4,6]=>14
[1,5,7,4,6,2,3]=>[1,5,7,2,3,4,6]=>14
[1,5,7,4,6,3,2]=>[1,5,7,2,3,4,6]=>14
[1,5,7,6,2,3,4]=>[1,5,7,2,3,4,6]=>14
[1,5,7,6,3,4,2]=>[1,5,7,2,3,4,6]=>14
[1,5,7,6,4,2,3]=>[1,5,7,2,3,4,6]=>14
[1,5,7,6,4,3,2]=>[1,5,7,2,3,4,6]=>14
[1,6,2,3,4,7,5]=>[1,6,2,3,4,7,5]=>4
[1,6,2,3,7,4,5]=>[1,6,2,3,7,4,5]=>9
[1,6,2,3,7,5,4]=>[1,6,2,3,7,4,5]=>9
[1,6,2,7,3,4,5]=>[1,6,2,7,3,4,5]=>14
[1,6,2,7,4,5,3]=>[1,6,2,7,3,4,5]=>14
[1,6,2,7,5,3,4]=>[1,6,2,7,3,4,5]=>14
[1,6,2,7,5,4,3]=>[1,6,2,7,3,4,5]=>14
[1,6,3,2,7,4,5]=>[1,6,2,7,3,4,5]=>14
[1,6,3,2,7,5,4]=>[1,6,2,7,3,4,5]=>14
[1,6,3,4,2,7,5]=>[1,6,2,7,3,4,5]=>14
[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>14
[1,6,3,4,7,5,2]=>[1,6,2,3,4,7,5]=>4
[1,6,3,7,4,5,2]=>[1,6,2,3,7,4,5]=>9
[1,6,3,7,5,4,2]=>[1,6,2,3,7,4,5]=>9
[1,6,4,2,3,7,5]=>[1,6,2,3,7,4,5]=>9
[1,6,4,2,7,5,3]=>[1,6,2,7,3,4,5]=>14
[1,6,4,3,2,7,5]=>[1,6,2,7,3,4,5]=>14
[1,6,4,3,7,5,2]=>[1,6,2,3,7,4,5]=>9
[1,6,4,5,2,3,7]=>[1,6,2,3,7,4,5]=>9
[1,6,4,5,2,7,3]=>[1,6,2,7,3,4,5]=>14
[1,6,4,5,3,2,7]=>[1,6,2,7,3,4,5]=>14
[1,6,4,5,3,7,2]=>[1,6,2,3,7,4,5]=>9
[1,6,4,7,5,2,3]=>[1,6,2,3,4,7,5]=>4
[1,6,4,7,5,3,2]=>[1,6,2,3,4,7,5]=>4
[1,6,5,2,3,4,7]=>[1,6,2,3,4,7,5]=>4
[1,6,5,2,3,7,4]=>[1,6,2,3,7,4,5]=>9
[1,6,5,2,7,3,4]=>[1,6,2,7,3,4,5]=>14
[1,6,5,2,7,4,3]=>[1,6,2,7,3,4,5]=>14
[1,6,5,3,2,7,4]=>[1,6,2,7,3,4,5]=>14
[1,6,5,3,4,2,7]=>[1,6,2,7,3,4,5]=>14
[1,6,5,3,4,7,2]=>[1,6,2,3,4,7,5]=>4
[1,6,5,3,7,4,2]=>[1,6,2,3,7,4,5]=>9
[1,6,5,4,2,3,7]=>[1,6,2,3,7,4,5]=>9
[1,6,5,4,2,7,3]=>[1,6,2,7,3,4,5]=>14
[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>14
[1,6,5,4,3,7,2]=>[1,6,2,3,7,4,5]=>9
[1,6,5,4,7,2,3]=>[1,6,2,3,4,7,5]=>4
[1,6,5,4,7,3,2]=>[1,6,2,3,4,7,5]=>4
[1,6,7,2,3,4,5]=>[1,6,7,2,3,4,5]=>14
[1,6,7,3,4,5,2]=>[1,6,7,2,3,4,5]=>14
[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>14
[1,6,7,4,5,3,2]=>[1,6,7,2,3,4,5]=>14
[1,6,7,5,2,3,4]=>[1,6,7,2,3,4,5]=>14
[1,6,7,5,3,4,2]=>[1,6,7,2,3,4,5]=>14
[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>14
[1,6,7,5,4,3,2]=>[1,6,7,2,3,4,5]=>14
[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>1
[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>1
[1,7,4,5,6,2,3]=>[1,7,2,3,4,5,6]=>1
[1,7,4,5,6,3,2]=>[1,7,2,3,4,5,6]=>1
[1,7,5,6,2,3,4]=>[1,7,2,3,4,5,6]=>1
[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>1
[1,7,5,6,4,2,3]=>[1,7,2,3,4,5,6]=>1
[1,7,5,6,4,3,2]=>[1,7,2,3,4,5,6]=>1
[1,7,6,2,3,4,5]=>[1,7,2,3,4,5,6]=>1
[1,7,6,3,4,5,2]=>[1,7,2,3,4,5,6]=>1
[1,7,6,4,5,2,3]=>[1,7,2,3,4,5,6]=>1
[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>1
[1,7,6,5,2,3,4]=>[1,7,2,3,4,5,6]=>1
[1,7,6,5,3,4,2]=>[1,7,2,3,4,5,6]=>1
[1,7,6,5,4,2,3]=>[1,7,2,3,4,5,6]=>1
[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>1
[2,1,3,7,4,5,6]=>[1,3,7,2,4,5,6]=>4
[2,1,3,7,5,6,4]=>[1,3,7,2,4,5,6]=>4
[2,1,3,7,6,4,5]=>[1,3,7,2,4,5,6]=>4
[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>4
[2,1,4,6,7,3,5]=>[1,4,6,7,2,3,5]=>42
[2,1,4,6,7,5,3]=>[1,4,6,7,2,3,5]=>42
[2,1,4,7,3,5,6]=>[1,4,7,2,3,5,6]=>9
[2,1,4,7,5,6,3]=>[1,4,7,2,3,5,6]=>9
[2,1,4,7,6,3,5]=>[1,4,7,2,3,5,6]=>9
[2,1,4,7,6,5,3]=>[1,4,7,2,3,5,6]=>9
[2,1,5,3,4,7,6]=>[1,5,2,3,4,7,6]=>4
[2,1,5,4,7,6,3]=>[1,5,2,3,4,7,6]=>4
[2,1,5,6,7,3,4]=>[1,5,6,7,2,3,4]=>42
[2,1,5,6,7,4,3]=>[1,5,6,7,2,3,4]=>42
[2,1,5,7,3,4,6]=>[1,5,7,2,3,4,6]=>14
[2,1,5,7,4,6,3]=>[1,5,7,2,3,4,6]=>14
[2,1,5,7,6,3,4]=>[1,5,7,2,3,4,6]=>14
[2,1,5,7,6,4,3]=>[1,5,7,2,3,4,6]=>14
[2,1,6,3,4,7,5]=>[1,6,2,3,4,7,5]=>4
[2,1,6,3,7,4,5]=>[1,6,2,3,7,4,5]=>9
[2,1,6,3,7,5,4]=>[1,6,2,3,7,4,5]=>9
[2,1,6,4,3,7,5]=>[1,6,2,3,7,4,5]=>9
[2,1,6,4,5,3,7]=>[1,6,2,3,7,4,5]=>9
[2,1,6,4,7,5,3]=>[1,6,2,3,4,7,5]=>4
[2,1,6,5,3,4,7]=>[1,6,2,3,4,7,5]=>4
[2,1,6,5,3,7,4]=>[1,6,2,3,7,4,5]=>9
[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>9
[2,1,6,5,4,7,3]=>[1,6,2,3,4,7,5]=>4
[2,1,6,7,3,4,5]=>[1,6,7,2,3,4,5]=>14
[2,1,6,7,4,5,3]=>[1,6,7,2,3,4,5]=>14
[2,1,6,7,5,3,4]=>[1,6,7,2,3,4,5]=>14
[2,1,6,7,5,4,3]=>[1,6,7,2,3,4,5]=>14
[2,1,7,3,4,5,6]=>[1,7,2,3,4,5,6]=>1
[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>1
[2,1,7,5,6,3,4]=>[1,7,2,3,4,5,6]=>1
[2,1,7,5,6,4,3]=>[1,7,2,3,4,5,6]=>1
[2,1,7,6,3,4,5]=>[1,7,2,3,4,5,6]=>1
[2,1,7,6,4,5,3]=>[1,7,2,3,4,5,6]=>1
[2,1,7,6,5,3,4]=>[1,7,2,3,4,5,6]=>1
[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>1
[2,3,1,4,6,7,5]=>[1,4,6,7,2,3,5]=>42
[2,3,1,4,7,5,6]=>[1,4,7,2,3,5,6]=>9
[2,3,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>9
[2,3,1,5,4,7,6]=>[1,5,2,3,4,7,6]=>4
[2,3,1,5,6,7,4]=>[1,5,6,7,2,3,4]=>42
[2,3,1,5,7,4,6]=>[1,5,7,2,3,4,6]=>14
[2,3,1,5,7,6,4]=>[1,5,7,2,3,4,6]=>14
[2,3,1,6,4,7,5]=>[1,6,2,3,4,7,5]=>4
[2,3,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>4
[2,3,1,6,7,4,5]=>[1,6,7,2,3,4,5]=>14
[2,3,1,6,7,5,4]=>[1,6,7,2,3,4,5]=>14
[2,3,1,7,4,5,6]=>[1,7,2,3,4,5,6]=>1
[2,3,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>1
[2,3,1,7,6,4,5]=>[1,7,2,3,4,5,6]=>1
[2,3,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>1
[2,3,4,1,5,6,7]=>[1,5,6,7,2,3,4]=>42
[2,3,4,1,5,7,6]=>[1,5,7,2,3,4,6]=>14
[2,3,4,1,6,7,5]=>[1,6,7,2,3,4,5]=>14
[2,3,4,1,7,5,6]=>[1,7,2,3,4,5,6]=>1
[2,3,4,1,7,6,5]=>[1,7,2,3,4,5,6]=>1
[2,3,4,5,1,6,7]=>[1,6,7,2,3,4,5]=>14
[2,3,4,5,1,7,6]=>[1,7,2,3,4,5,6]=>1
[2,3,4,5,6,1,7]=>[1,7,2,3,4,5,6]=>1
[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>1
[2,3,4,5,7,6,1]=>[1,2,3,4,5,7,6]=>1
[2,3,4,6,1,5,7]=>[1,5,7,2,3,4,6]=>14
[2,3,4,6,5,7,1]=>[1,2,3,4,6,5,7]=>1
[2,3,4,7,1,6,5]=>[1,6,2,3,4,7,5]=>4
[2,3,4,7,5,1,6]=>[1,6,2,3,4,7,5]=>4
[2,3,4,7,6,1,5]=>[1,5,2,3,4,7,6]=>4
[2,3,5,1,4,6,7]=>[1,4,6,7,2,3,5]=>42
[2,3,5,1,4,7,6]=>[1,4,7,2,3,5,6]=>9
[2,3,5,6,1,4,7]=>[1,4,7,2,3,5,6]=>9
[2,3,6,4,7,5,1]=>[1,2,3,6,4,7,5]=>2
[2,3,6,5,4,7,1]=>[1,2,3,6,4,7,5]=>2
[2,3,7,1,6,4,5]=>[1,6,2,3,7,4,5]=>9
[2,3,7,1,6,5,4]=>[1,6,2,3,7,4,5]=>9
[2,3,7,4,1,6,5]=>[1,6,2,3,7,4,5]=>9
[2,3,7,4,5,1,6]=>[1,6,2,3,7,4,5]=>9
[2,3,7,5,1,6,4]=>[1,6,2,3,7,4,5]=>9
[2,3,7,5,4,1,6]=>[1,6,2,3,7,4,5]=>9
[2,4,1,3,7,5,6]=>[1,3,7,2,4,5,6]=>4
[2,4,1,3,7,6,5]=>[1,3,7,2,4,5,6]=>4
[2,4,5,1,3,7,6]=>[1,3,7,2,4,5,6]=>4
[2,4,5,6,1,3,7]=>[1,3,7,2,4,5,6]=>4
[2,4,5,6,7,1,3]=>[1,3,2,4,5,6,7]=>1
[2,6,3,4,7,5,1]=>[1,2,6,3,4,7,5]=>3
[2,6,4,7,5,3,1]=>[1,2,6,3,4,7,5]=>3
[2,6,5,3,4,7,1]=>[1,2,6,3,4,7,5]=>3
[2,6,5,4,7,3,1]=>[1,2,6,3,4,7,5]=>3
[2,7,1,5,3,4,6]=>[1,5,2,7,3,4,6]=>14
[2,7,1,5,4,6,3]=>[1,5,2,7,3,4,6]=>14
[2,7,1,5,6,3,4]=>[1,5,6,2,7,3,4]=>42
[2,7,1,5,6,4,3]=>[1,5,6,2,7,3,4]=>42
[2,7,1,6,3,4,5]=>[1,6,2,7,3,4,5]=>14
[2,7,1,6,4,5,3]=>[1,6,2,7,3,4,5]=>14
[2,7,1,6,5,3,4]=>[1,6,2,7,3,4,5]=>14
[2,7,1,6,5,4,3]=>[1,6,2,7,3,4,5]=>14
[2,7,3,1,5,4,6]=>[1,5,2,7,3,4,6]=>14
[2,7,3,1,5,6,4]=>[1,5,6,2,7,3,4]=>42
[2,7,3,1,6,4,5]=>[1,6,2,7,3,4,5]=>14
[2,7,3,1,6,5,4]=>[1,6,2,7,3,4,5]=>14
[2,7,3,4,1,5,6]=>[1,5,6,2,7,3,4]=>42
[2,7,3,4,1,6,5]=>[1,6,2,7,3,4,5]=>14
[2,7,3,4,5,1,6]=>[1,6,2,7,3,4,5]=>14
[2,7,3,4,6,1,5]=>[1,5,2,7,3,4,6]=>14
[2,7,4,1,5,6,3]=>[1,5,6,2,7,3,4]=>42
[2,7,4,1,6,5,3]=>[1,6,2,7,3,4,5]=>14
[2,7,4,3,1,5,6]=>[1,5,6,2,7,3,4]=>42
[2,7,4,3,1,6,5]=>[1,6,2,7,3,4,5]=>14
[2,7,4,5,1,6,3]=>[1,6,2,7,3,4,5]=>14
[2,7,4,5,3,1,6]=>[1,6,2,7,3,4,5]=>14
[2,7,4,6,1,5,3]=>[1,5,2,7,3,4,6]=>14
[2,7,4,6,3,1,5]=>[1,5,2,7,3,4,6]=>14
[2,7,5,1,6,3,4]=>[1,6,2,7,3,4,5]=>14
[2,7,5,1,6,4,3]=>[1,6,2,7,3,4,5]=>14
[2,7,5,3,1,6,4]=>[1,6,2,7,3,4,5]=>14
[2,7,5,3,4,1,6]=>[1,6,2,7,3,4,5]=>14
[2,7,5,4,1,6,3]=>[1,6,2,7,3,4,5]=>14
[2,7,5,4,3,1,6]=>[1,6,2,7,3,4,5]=>14
[2,7,6,1,5,3,4]=>[1,5,2,7,3,4,6]=>14
[2,7,6,1,5,4,3]=>[1,5,2,7,3,4,6]=>14
[2,7,6,3,1,5,4]=>[1,5,2,7,3,4,6]=>14
[2,7,6,3,4,1,5]=>[1,5,2,7,3,4,6]=>14
[2,7,6,4,1,5,3]=>[1,5,2,7,3,4,6]=>14
[2,7,6,4,3,1,5]=>[1,5,2,7,3,4,6]=>14
[3,1,2,6,4,7,5]=>[1,2,6,3,4,7,5]=>3
[3,1,2,6,5,4,7]=>[1,2,6,3,4,7,5]=>3
[3,1,4,6,7,5,2]=>[1,4,6,7,2,3,5]=>42
[3,1,4,7,5,6,2]=>[1,4,7,2,3,5,6]=>9
[3,1,4,7,6,5,2]=>[1,4,7,2,3,5,6]=>9
[3,1,5,2,7,4,6]=>[1,5,2,7,3,4,6]=>14
[3,1,5,2,7,6,4]=>[1,5,2,7,3,4,6]=>14
[3,1,5,4,2,7,6]=>[1,5,2,7,3,4,6]=>14
[3,1,5,4,6,2,7]=>[1,5,2,7,3,4,6]=>14
[3,1,5,4,7,6,2]=>[1,5,2,3,4,7,6]=>4
[3,1,5,6,2,7,4]=>[1,5,6,2,7,3,4]=>42
[3,1,5,6,4,2,7]=>[1,5,6,2,7,3,4]=>42
[3,1,5,6,7,4,2]=>[1,5,6,7,2,3,4]=>42
[3,1,5,7,4,6,2]=>[1,5,7,2,3,4,6]=>14
[3,1,5,7,6,4,2]=>[1,5,7,2,3,4,6]=>14
[3,1,6,2,7,4,5]=>[1,6,2,7,3,4,5]=>14
[3,1,6,2,7,5,4]=>[1,6,2,7,3,4,5]=>14
[3,1,6,4,2,7,5]=>[1,6,2,7,3,4,5]=>14
[3,1,6,4,5,2,7]=>[1,6,2,7,3,4,5]=>14
[3,1,6,4,7,5,2]=>[1,6,2,3,4,7,5]=>4
[3,1,6,5,2,7,4]=>[1,6,2,7,3,4,5]=>14
[3,1,6,5,4,2,7]=>[1,6,2,7,3,4,5]=>14
[3,1,6,5,4,7,2]=>[1,6,2,3,4,7,5]=>4
[3,1,6,7,4,5,2]=>[1,6,7,2,3,4,5]=>14
[3,1,6,7,5,4,2]=>[1,6,7,2,3,4,5]=>14
[3,1,7,4,5,6,2]=>[1,7,2,3,4,5,6]=>1
[3,1,7,5,6,4,2]=>[1,7,2,3,4,5,6]=>1
[3,1,7,6,4,5,2]=>[1,7,2,3,4,5,6]=>1
[3,1,7,6,5,4,2]=>[1,7,2,3,4,5,6]=>1
[3,2,1,4,6,7,5]=>[1,4,6,7,2,3,5]=>42
[3,2,1,4,7,5,6]=>[1,4,7,2,3,5,6]=>9
[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>9
[3,2,1,5,4,7,6]=>[1,5,2,3,4,7,6]=>4
[3,2,1,5,6,7,4]=>[1,5,6,7,2,3,4]=>42
[3,2,1,5,7,4,6]=>[1,5,7,2,3,4,6]=>14
[3,2,1,5,7,6,4]=>[1,5,7,2,3,4,6]=>14
[3,2,1,6,4,7,5]=>[1,6,2,3,4,7,5]=>4
[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>4
[3,2,1,6,7,4,5]=>[1,6,7,2,3,4,5]=>14
[3,2,1,6,7,5,4]=>[1,6,7,2,3,4,5]=>14
[3,2,1,7,4,5,6]=>[1,7,2,3,4,5,6]=>1
[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>1
[3,2,1,7,6,4,5]=>[1,7,2,3,4,5,6]=>1
[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>1
[3,2,6,4,7,5,1]=>[1,2,6,3,4,7,5]=>3
[3,2,6,5,4,7,1]=>[1,2,6,3,4,7,5]=>3
[3,2,7,1,5,4,6]=>[1,5,2,7,3,4,6]=>14
[3,2,7,1,5,6,4]=>[1,5,6,2,7,3,4]=>42
[3,2,7,1,6,4,5]=>[1,6,2,7,3,4,5]=>14
[3,2,7,1,6,5,4]=>[1,6,2,7,3,4,5]=>14
[3,2,7,4,1,5,6]=>[1,5,6,2,7,3,4]=>42
[3,2,7,4,1,6,5]=>[1,6,2,7,3,4,5]=>14
[3,2,7,4,5,1,6]=>[1,6,2,7,3,4,5]=>14
[3,2,7,4,6,1,5]=>[1,5,2,7,3,4,6]=>14
[3,2,7,5,1,6,4]=>[1,6,2,7,3,4,5]=>14
[3,2,7,5,4,1,6]=>[1,6,2,7,3,4,5]=>14
[3,2,7,6,1,5,4]=>[1,5,2,7,3,4,6]=>14
[3,2,7,6,4,1,5]=>[1,5,2,7,3,4,6]=>14
[3,4,1,5,2,7,6]=>[1,5,2,7,3,4,6]=>14
[3,4,1,5,6,2,7]=>[1,5,6,2,7,3,4]=>42
[3,4,1,5,6,7,2]=>[1,5,6,7,2,3,4]=>42
[3,4,1,5,7,6,2]=>[1,5,7,2,3,4,6]=>14
[3,4,1,6,2,7,5]=>[1,6,2,7,3,4,5]=>14
[3,4,1,6,5,2,7]=>[1,6,2,7,3,4,5]=>14
[3,4,1,6,7,5,2]=>[1,6,7,2,3,4,5]=>14
[3,4,1,7,5,6,2]=>[1,7,2,3,4,5,6]=>1
[3,4,1,7,6,5,2]=>[1,7,2,3,4,5,6]=>1
[3,4,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>42
[3,4,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>14
[3,4,2,1,6,7,5]=>[1,6,7,2,3,4,5]=>14
[3,4,2,1,7,5,6]=>[1,7,2,3,4,5,6]=>1
[3,4,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>1
[3,4,2,7,1,5,6]=>[1,5,6,2,7,3,4]=>42
[3,4,2,7,1,6,5]=>[1,6,2,7,3,4,5]=>14
[3,4,2,7,5,1,6]=>[1,6,2,7,3,4,5]=>14
[3,4,2,7,6,1,5]=>[1,5,2,7,3,4,6]=>14
[3,4,5,1,6,2,7]=>[1,6,2,7,3,4,5]=>14
[3,4,5,1,6,7,2]=>[1,6,7,2,3,4,5]=>14
[3,4,5,1,7,6,2]=>[1,7,2,3,4,5,6]=>1
[3,4,5,2,1,6,7]=>[1,6,7,2,3,4,5]=>14
[3,4,5,2,1,7,6]=>[1,7,2,3,4,5,6]=>1
[3,4,5,2,7,1,6]=>[1,6,2,7,3,4,5]=>14
[3,4,5,6,1,7,2]=>[1,7,2,3,4,5,6]=>1
[3,4,5,6,2,1,7]=>[1,7,2,3,4,5,6]=>1
[3,4,5,6,7,1,2]=>[1,2,3,4,5,6,7]=>1
[3,4,5,6,7,2,1]=>[1,2,3,4,5,6,7]=>1
[3,4,5,7,6,1,2]=>[1,2,3,4,5,7,6]=>1
[3,4,5,7,6,2,1]=>[1,2,3,4,5,7,6]=>1
[3,4,6,1,5,2,7]=>[1,5,2,7,3,4,6]=>14
[3,4,6,1,5,7,2]=>[1,5,7,2,3,4,6]=>14
[3,4,6,2,1,5,7]=>[1,5,7,2,3,4,6]=>14
[3,4,6,2,7,1,5]=>[1,5,2,7,3,4,6]=>14
[3,4,6,5,7,1,2]=>[1,2,3,4,6,5,7]=>1
[3,4,6,5,7,2,1]=>[1,2,3,4,6,5,7]=>1
[3,4,7,1,2,6,5]=>[1,2,6,3,4,7,5]=>3
[3,4,7,1,6,5,2]=>[1,6,2,3,4,7,5]=>4
[3,4,7,2,1,6,5]=>[1,6,2,3,4,7,5]=>4
[3,4,7,2,6,5,1]=>[1,2,6,3,4,7,5]=>3
[3,4,7,5,1,2,6]=>[1,2,6,3,4,7,5]=>3
[3,4,7,5,1,6,2]=>[1,6,2,3,4,7,5]=>4
[3,4,7,5,2,1,6]=>[1,6,2,3,4,7,5]=>4
[3,4,7,5,2,6,1]=>[1,2,6,3,4,7,5]=>3
[3,4,7,6,1,5,2]=>[1,5,2,3,4,7,6]=>4
[3,4,7,6,2,1,5]=>[1,5,2,3,4,7,6]=>4
[3,5,1,4,6,7,2]=>[1,4,6,7,2,3,5]=>42
[3,5,1,4,7,6,2]=>[1,4,7,2,3,5,6]=>9
[3,5,2,1,4,6,7]=>[1,4,6,7,2,3,5]=>42
[3,5,2,1,4,7,6]=>[1,4,7,2,3,5,6]=>9
[3,5,6,1,4,7,2]=>[1,4,7,2,3,5,6]=>9
[3,5,6,2,1,4,7]=>[1,4,7,2,3,5,6]=>9
[3,6,4,7,5,1,2]=>[1,2,3,6,4,7,5]=>2
[3,6,4,7,5,2,1]=>[1,2,3,6,4,7,5]=>2
[3,6,5,4,7,1,2]=>[1,2,3,6,4,7,5]=>2
[3,6,5,4,7,2,1]=>[1,2,3,6,4,7,5]=>2
[3,7,1,6,4,5,2]=>[1,6,2,3,7,4,5]=>9
[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>9
[3,7,2,1,6,4,5]=>[1,6,2,3,7,4,5]=>9
[3,7,2,1,6,5,4]=>[1,6,2,3,7,4,5]=>9
[3,7,4,1,6,5,2]=>[1,6,2,3,7,4,5]=>9
[3,7,4,2,1,6,5]=>[1,6,2,3,7,4,5]=>9
[3,7,4,5,1,6,2]=>[1,6,2,3,7,4,5]=>9
[3,7,4,5,2,1,6]=>[1,6,2,3,7,4,5]=>9
[3,7,5,1,6,4,2]=>[1,6,2,3,7,4,5]=>9
[3,7,5,2,1,6,4]=>[1,6,2,3,7,4,5]=>9
[3,7,5,4,1,6,2]=>[1,6,2,3,7,4,5]=>9
[3,7,5,4,2,1,6]=>[1,6,2,3,7,4,5]=>9
[4,1,3,7,5,6,2]=>[1,3,7,2,4,5,6]=>4
[4,1,3,7,6,5,2]=>[1,3,7,2,4,5,6]=>4
[4,1,5,2,7,6,3]=>[1,5,2,7,3,4,6]=>14
[4,1,5,3,2,7,6]=>[1,5,2,7,3,4,6]=>14
[4,1,5,6,2,7,3]=>[1,5,6,2,7,3,4]=>42
[4,1,5,6,3,2,7]=>[1,5,6,2,7,3,4]=>42
[4,1,5,6,7,2,3]=>[1,5,6,7,2,3,4]=>42
[4,1,5,6,7,3,2]=>[1,5,6,7,2,3,4]=>42
[4,1,5,7,6,2,3]=>[1,5,7,2,3,4,6]=>14
[4,1,5,7,6,3,2]=>[1,5,7,2,3,4,6]=>14
[4,1,6,2,3,7,5]=>[1,6,2,3,7,4,5]=>9
[4,1,6,2,7,5,3]=>[1,6,2,7,3,4,5]=>14
[4,1,6,3,2,7,5]=>[1,6,2,7,3,4,5]=>14
[4,1,6,3,7,5,2]=>[1,6,2,3,7,4,5]=>9
[4,1,6,5,2,3,7]=>[1,6,2,3,7,4,5]=>9
[4,1,6,5,2,7,3]=>[1,6,2,7,3,4,5]=>14
[4,1,6,5,3,2,7]=>[1,6,2,7,3,4,5]=>14
[4,1,6,5,3,7,2]=>[1,6,2,3,7,4,5]=>9
[4,1,6,7,5,2,3]=>[1,6,7,2,3,4,5]=>14
[4,1,6,7,5,3,2]=>[1,6,7,2,3,4,5]=>14
[4,1,7,5,6,2,3]=>[1,7,2,3,4,5,6]=>1
[4,1,7,5,6,3,2]=>[1,7,2,3,4,5,6]=>1
[4,1,7,6,5,2,3]=>[1,7,2,3,4,5,6]=>1
[4,1,7,6,5,3,2]=>[1,7,2,3,4,5,6]=>1
[4,2,1,3,7,5,6]=>[1,3,7,2,4,5,6]=>4
[4,2,1,3,7,6,5]=>[1,3,7,2,4,5,6]=>4
[4,2,1,5,6,7,3]=>[1,5,6,7,2,3,4]=>42
[4,2,1,5,7,6,3]=>[1,5,7,2,3,4,6]=>14
[4,2,1,6,3,7,5]=>[1,6,2,3,7,4,5]=>9
[4,2,1,6,5,3,7]=>[1,6,2,3,7,4,5]=>9
[4,2,1,6,7,5,3]=>[1,6,7,2,3,4,5]=>14
[4,2,1,7,5,6,3]=>[1,7,2,3,4,5,6]=>1
[4,2,1,7,6,5,3]=>[1,7,2,3,4,5,6]=>1
[4,2,3,1,5,6,7]=>[1,5,6,7,2,3,4]=>42
[4,2,3,1,5,7,6]=>[1,5,7,2,3,4,6]=>14
[4,2,3,1,6,7,5]=>[1,6,7,2,3,4,5]=>14
[4,2,3,1,7,5,6]=>[1,7,2,3,4,5,6]=>1
[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>1
[4,2,3,7,1,6,5]=>[1,6,2,3,7,4,5]=>9
[4,2,3,7,5,1,6]=>[1,6,2,3,7,4,5]=>9
[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>42
[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>14
[4,2,7,3,1,5,6]=>[1,5,6,2,7,3,4]=>42
[4,2,7,3,1,6,5]=>[1,6,2,7,3,4,5]=>14
[4,2,7,5,1,6,3]=>[1,6,2,7,3,4,5]=>14
[4,2,7,5,3,1,6]=>[1,6,2,7,3,4,5]=>14
[4,2,7,6,1,5,3]=>[1,5,2,7,3,4,6]=>14
[4,2,7,6,3,1,5]=>[1,5,2,7,3,4,6]=>14
[4,3,1,5,2,7,6]=>[1,5,2,7,3,4,6]=>14
[4,3,1,5,6,2,7]=>[1,5,6,2,7,3,4]=>42
[4,3,1,5,6,7,2]=>[1,5,6,7,2,3,4]=>42
[4,3,1,5,7,6,2]=>[1,5,7,2,3,4,6]=>14
[4,3,1,6,2,7,5]=>[1,6,2,7,3,4,5]=>14
[4,3,1,6,5,2,7]=>[1,6,2,7,3,4,5]=>14
[4,3,1,6,7,5,2]=>[1,6,7,2,3,4,5]=>14
[4,3,1,7,5,6,2]=>[1,7,2,3,4,5,6]=>1
[4,3,1,7,6,5,2]=>[1,7,2,3,4,5,6]=>1
[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>42
[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>14
[4,3,2,1,6,7,5]=>[1,6,7,2,3,4,5]=>14
[4,3,2,1,7,5,6]=>[1,7,2,3,4,5,6]=>1
[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>1
[4,3,2,7,1,5,6]=>[1,5,6,2,7,3,4]=>42
[4,3,2,7,1,6,5]=>[1,6,2,7,3,4,5]=>14
[4,3,2,7,5,1,6]=>[1,6,2,7,3,4,5]=>14
[4,3,2,7,6,1,5]=>[1,5,2,7,3,4,6]=>14
[4,3,7,1,6,5,2]=>[1,6,2,3,7,4,5]=>9
[4,3,7,2,1,6,5]=>[1,6,2,3,7,4,5]=>9
[4,3,7,5,1,6,2]=>[1,6,2,3,7,4,5]=>9
[4,3,7,5,2,1,6]=>[1,6,2,3,7,4,5]=>9
[4,5,1,3,7,6,2]=>[1,3,7,2,4,5,6]=>4
[4,5,1,6,2,3,7]=>[1,6,2,3,7,4,5]=>9
[4,5,1,6,2,7,3]=>[1,6,2,7,3,4,5]=>14
[4,5,1,6,3,2,7]=>[1,6,2,7,3,4,5]=>14
[4,5,1,6,3,7,2]=>[1,6,2,3,7,4,5]=>9
[4,5,1,6,7,2,3]=>[1,6,7,2,3,4,5]=>14
[4,5,1,6,7,3,2]=>[1,6,7,2,3,4,5]=>14
[4,5,1,7,6,2,3]=>[1,7,2,3,4,5,6]=>1
[4,5,1,7,6,3,2]=>[1,7,2,3,4,5,6]=>1
[4,5,2,1,3,7,6]=>[1,3,7,2,4,5,6]=>4
[4,5,2,1,6,3,7]=>[1,6,2,3,7,4,5]=>9
[4,5,2,1,6,7,3]=>[1,6,7,2,3,4,5]=>14
[4,5,2,1,7,6,3]=>[1,7,2,3,4,5,6]=>1
[4,5,2,3,1,6,7]=>[1,6,7,2,3,4,5]=>14
[4,5,2,3,1,7,6]=>[1,7,2,3,4,5,6]=>1
[4,5,2,3,7,1,6]=>[1,6,2,3,7,4,5]=>9
[4,5,2,7,1,6,3]=>[1,6,2,7,3,4,5]=>14
[4,5,2,7,3,1,6]=>[1,6,2,7,3,4,5]=>14
[4,5,3,1,6,2,7]=>[1,6,2,7,3,4,5]=>14
[4,5,3,1,6,7,2]=>[1,6,7,2,3,4,5]=>14
[4,5,3,1,7,6,2]=>[1,7,2,3,4,5,6]=>1
[4,5,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>14
[4,5,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>1
[4,5,3,2,7,1,6]=>[1,6,2,7,3,4,5]=>14
[4,5,3,7,1,6,2]=>[1,6,2,3,7,4,5]=>9
[4,5,3,7,2,1,6]=>[1,6,2,3,7,4,5]=>9
[4,5,6,1,3,7,2]=>[1,3,7,2,4,5,6]=>4
[4,5,6,1,7,2,3]=>[1,7,2,3,4,5,6]=>1
[4,5,6,1,7,3,2]=>[1,7,2,3,4,5,6]=>1
[4,5,6,2,1,3,7]=>[1,3,7,2,4,5,6]=>4
[4,5,6,2,1,7,3]=>[1,7,2,3,4,5,6]=>1
[4,5,6,2,3,1,7]=>[1,7,2,3,4,5,6]=>1
[4,5,6,3,1,7,2]=>[1,7,2,3,4,5,6]=>1
[4,5,6,3,2,1,7]=>[1,7,2,3,4,5,6]=>1
[4,5,6,7,1,2,3]=>[1,2,3,4,5,6,7]=>1
[4,5,6,7,1,3,2]=>[1,3,2,4,5,6,7]=>1
[4,5,6,7,2,1,3]=>[1,3,2,4,5,6,7]=>1
[4,5,6,7,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,5,6,7,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,5,6,7,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,6,1,2,3]=>[1,2,3,4,5,7,6]=>1
[4,5,7,6,2,3,1]=>[1,2,3,4,5,7,6]=>1
[4,5,7,6,3,1,2]=>[1,2,3,4,5,7,6]=>1
[4,5,7,6,3,2,1]=>[1,2,3,4,5,7,6]=>1
[4,6,1,5,2,7,3]=>[1,5,2,7,3,4,6]=>14
[4,6,1,5,3,2,7]=>[1,5,2,7,3,4,6]=>14
[4,6,1,5,7,2,3]=>[1,5,7,2,3,4,6]=>14
[4,6,1,5,7,3,2]=>[1,5,7,2,3,4,6]=>14
[4,6,2,1,5,7,3]=>[1,5,7,2,3,4,6]=>14
[4,6,2,3,1,5,7]=>[1,5,7,2,3,4,6]=>14
[4,6,2,7,1,5,3]=>[1,5,2,7,3,4,6]=>14
[4,6,2,7,3,1,5]=>[1,5,2,7,3,4,6]=>14
[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>14
[4,6,3,1,5,7,2]=>[1,5,7,2,3,4,6]=>14
[4,6,3,2,1,5,7]=>[1,5,7,2,3,4,6]=>14
[4,6,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>14
[4,6,5,7,1,2,3]=>[1,2,3,4,6,5,7]=>1
[4,6,5,7,2,3,1]=>[1,2,3,4,6,5,7]=>1
[4,6,5,7,3,1,2]=>[1,2,3,4,6,5,7]=>1
[4,6,5,7,3,2,1]=>[1,2,3,4,6,5,7]=>1
[4,7,1,2,3,6,5]=>[1,2,3,6,4,7,5]=>2
[4,7,1,2,6,5,3]=>[1,2,6,3,4,7,5]=>3
[4,7,1,6,5,2,3]=>[1,6,2,3,4,7,5]=>4
[4,7,1,6,5,3,2]=>[1,6,2,3,4,7,5]=>4
[4,7,2,1,6,5,3]=>[1,6,2,3,4,7,5]=>4
[4,7,2,3,1,6,5]=>[1,6,2,3,4,7,5]=>4
[4,7,2,3,6,5,1]=>[1,2,3,6,4,7,5]=>2
[4,7,2,6,5,3,1]=>[1,2,6,3,4,7,5]=>3
[4,7,3,1,2,6,5]=>[1,2,6,3,4,7,5]=>3
[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>4
[4,7,3,2,1,6,5]=>[1,6,2,3,4,7,5]=>4
[4,7,3,2,6,5,1]=>[1,2,6,3,4,7,5]=>3
[4,7,3,6,5,1,2]=>[1,2,3,6,4,7,5]=>2
[4,7,3,6,5,2,1]=>[1,2,3,6,4,7,5]=>2
[4,7,5,1,2,3,6]=>[1,2,3,6,4,7,5]=>2
[4,7,5,1,2,6,3]=>[1,2,6,3,4,7,5]=>3
[4,7,5,1,6,2,3]=>[1,6,2,3,4,7,5]=>4
[4,7,5,1,6,3,2]=>[1,6,2,3,4,7,5]=>4
[4,7,5,2,1,6,3]=>[1,6,2,3,4,7,5]=>4
[4,7,5,2,3,1,6]=>[1,6,2,3,4,7,5]=>4
[4,7,5,2,3,6,1]=>[1,2,3,6,4,7,5]=>2
[4,7,5,2,6,3,1]=>[1,2,6,3,4,7,5]=>3
[4,7,5,3,1,2,6]=>[1,2,6,3,4,7,5]=>3
[4,7,5,3,1,6,2]=>[1,6,2,3,4,7,5]=>4
[4,7,5,3,2,1,6]=>[1,6,2,3,4,7,5]=>4
[4,7,5,3,2,6,1]=>[1,2,6,3,4,7,5]=>3
[4,7,5,3,6,1,2]=>[1,2,3,6,4,7,5]=>2
[4,7,5,3,6,2,1]=>[1,2,3,6,4,7,5]=>2
[4,7,6,1,5,2,3]=>[1,5,2,3,4,7,6]=>4
[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>4
[4,7,6,2,1,5,3]=>[1,5,2,3,4,7,6]=>4
[4,7,6,2,3,1,5]=>[1,5,2,3,4,7,6]=>4
[4,7,6,3,1,5,2]=>[1,5,2,3,4,7,6]=>4
[4,7,6,3,2,1,5]=>[1,5,2,3,4,7,6]=>4
[5,1,2,3,6,4,7]=>[1,2,3,6,4,7,5]=>2
[5,1,2,6,3,4,7]=>[1,2,6,3,4,7,5]=>3
[5,1,2,6,4,7,3]=>[1,2,6,3,4,7,5]=>3
[5,1,3,7,6,2,4]=>[1,3,7,2,4,5,6]=>4
[5,1,3,7,6,4,2]=>[1,3,7,2,4,5,6]=>4
[5,1,4,6,7,2,3]=>[1,4,6,7,2,3,5]=>42
[5,1,4,6,7,3,2]=>[1,4,6,7,2,3,5]=>42
[5,1,4,7,6,2,3]=>[1,4,7,2,3,5,6]=>9
[5,1,4,7,6,3,2]=>[1,4,7,2,3,5,6]=>9
[5,1,6,2,3,4,7]=>[1,6,2,3,4,7,5]=>4
[5,1,6,2,3,7,4]=>[1,6,2,3,7,4,5]=>9
[5,1,6,2,7,3,4]=>[1,6,2,7,3,4,5]=>14
[5,1,6,2,7,4,3]=>[1,6,2,7,3,4,5]=>14
[5,1,6,3,2,7,4]=>[1,6,2,7,3,4,5]=>14
[5,1,6,3,4,2,7]=>[1,6,2,7,3,4,5]=>14
[5,1,6,3,4,7,2]=>[1,6,2,3,4,7,5]=>4
[5,1,6,3,7,4,2]=>[1,6,2,3,7,4,5]=>9
[5,1,6,4,2,3,7]=>[1,6,2,3,7,4,5]=>9
[5,1,6,4,2,7,3]=>[1,6,2,7,3,4,5]=>14
[5,1,6,4,3,2,7]=>[1,6,2,7,3,4,5]=>14
[5,1,6,4,3,7,2]=>[1,6,2,3,7,4,5]=>9
[5,1,6,4,7,2,3]=>[1,6,2,3,4,7,5]=>4
[5,1,6,4,7,3,2]=>[1,6,2,3,4,7,5]=>4
[5,1,6,7,2,3,4]=>[1,6,7,2,3,4,5]=>14
[5,1,6,7,3,4,2]=>[1,6,7,2,3,4,5]=>14
[5,1,6,7,4,2,3]=>[1,6,7,2,3,4,5]=>14
[5,1,6,7,4,3,2]=>[1,6,7,2,3,4,5]=>14
[5,1,7,6,2,3,4]=>[1,7,2,3,4,5,6]=>1
[5,1,7,6,3,4,2]=>[1,7,2,3,4,5,6]=>1
[5,1,7,6,4,2,3]=>[1,7,2,3,4,5,6]=>1
[5,1,7,6,4,3,2]=>[1,7,2,3,4,5,6]=>1
[5,2,1,3,7,6,4]=>[1,3,7,2,4,5,6]=>4
[5,2,1,4,6,7,3]=>[1,4,6,7,2,3,5]=>42
[5,2,1,4,7,6,3]=>[1,4,7,2,3,5,6]=>9
[5,2,1,6,3,4,7]=>[1,6,2,3,4,7,5]=>4
[5,2,1,6,3,7,4]=>[1,6,2,3,7,4,5]=>9
[5,2,1,6,4,3,7]=>[1,6,2,3,7,4,5]=>9
[5,2,1,6,4,7,3]=>[1,6,2,3,4,7,5]=>4
[5,2,1,6,7,3,4]=>[1,6,7,2,3,4,5]=>14
[5,2,1,6,7,4,3]=>[1,6,7,2,3,4,5]=>14
[5,2,1,7,6,3,4]=>[1,7,2,3,4,5,6]=>1
[5,2,1,7,6,4,3]=>[1,7,2,3,4,5,6]=>1
[5,2,3,1,4,6,7]=>[1,4,6,7,2,3,5]=>42
[5,2,3,1,4,7,6]=>[1,4,7,2,3,5,6]=>9
[5,2,3,1,6,4,7]=>[1,6,2,3,4,7,5]=>4
[5,2,3,1,6,7,4]=>[1,6,7,2,3,4,5]=>14
[5,2,3,1,7,6,4]=>[1,7,2,3,4,5,6]=>1
[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>14
[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>1
[5,2,3,4,7,1,6]=>[1,6,2,3,4,7,5]=>4
[5,2,3,6,4,7,1]=>[1,2,3,6,4,7,5]=>2
[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>9
[5,2,3,7,4,1,6]=>[1,6,2,3,7,4,5]=>9
[5,2,4,1,3,7,6]=>[1,3,7,2,4,5,6]=>4
[5,2,6,3,4,7,1]=>[1,2,6,3,4,7,5]=>3
[5,2,6,4,7,3,1]=>[1,2,6,3,4,7,5]=>3
[5,2,7,1,6,3,4]=>[1,6,2,7,3,4,5]=>14
[5,2,7,1,6,4,3]=>[1,6,2,7,3,4,5]=>14
[5,2,7,3,1,6,4]=>[1,6,2,7,3,4,5]=>14
[5,2,7,3,4,1,6]=>[1,6,2,7,3,4,5]=>14
[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>14
[5,2,7,4,3,1,6]=>[1,6,2,7,3,4,5]=>14
[5,3,1,2,6,4,7]=>[1,2,6,3,4,7,5]=>3
[5,3,1,4,6,7,2]=>[1,4,6,7,2,3,5]=>42
[5,3,1,4,7,6,2]=>[1,4,7,2,3,5,6]=>9
[5,3,1,6,2,7,4]=>[1,6,2,7,3,4,5]=>14
[5,3,1,6,4,2,7]=>[1,6,2,7,3,4,5]=>14
[5,3,1,6,4,7,2]=>[1,6,2,3,4,7,5]=>4
[5,3,1,6,7,4,2]=>[1,6,7,2,3,4,5]=>14
[5,3,1,7,6,4,2]=>[1,7,2,3,4,5,6]=>1
[5,3,2,1,4,6,7]=>[1,4,6,7,2,3,5]=>42
[5,3,2,1,4,7,6]=>[1,4,7,2,3,5,6]=>9
[5,3,2,1,6,4,7]=>[1,6,2,3,4,7,5]=>4
[5,3,2,1,6,7,4]=>[1,6,7,2,3,4,5]=>14
[5,3,2,1,7,6,4]=>[1,7,2,3,4,5,6]=>1
[5,3,2,6,4,7,1]=>[1,2,6,3,4,7,5]=>3
[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>14
[5,3,2,7,4,1,6]=>[1,6,2,7,3,4,5]=>14
[5,3,4,1,6,2,7]=>[1,6,2,7,3,4,5]=>14
[5,3,4,1,6,7,2]=>[1,6,7,2,3,4,5]=>14
[5,3,4,1,7,6,2]=>[1,7,2,3,4,5,6]=>1
[5,3,4,2,1,6,7]=>[1,6,7,2,3,4,5]=>14
[5,3,4,2,1,7,6]=>[1,7,2,3,4,5,6]=>1
[5,3,4,2,7,1,6]=>[1,6,2,7,3,4,5]=>14
[5,3,4,7,1,2,6]=>[1,2,6,3,4,7,5]=>3
[5,3,4,7,1,6,2]=>[1,6,2,3,4,7,5]=>4
[5,3,4,7,2,1,6]=>[1,6,2,3,4,7,5]=>4
[5,3,4,7,2,6,1]=>[1,2,6,3,4,7,5]=>3
[5,3,6,4,7,1,2]=>[1,2,3,6,4,7,5]=>2
[5,3,6,4,7,2,1]=>[1,2,3,6,4,7,5]=>2
[5,3,7,1,6,4,2]=>[1,6,2,3,7,4,5]=>9
[5,3,7,2,1,6,4]=>[1,6,2,3,7,4,5]=>9
[5,3,7,4,1,6,2]=>[1,6,2,3,7,4,5]=>9
[5,3,7,4,2,1,6]=>[1,6,2,3,7,4,5]=>9
[5,4,1,3,7,6,2]=>[1,3,7,2,4,5,6]=>4
[5,4,1,6,2,3,7]=>[1,6,2,3,7,4,5]=>9
[5,4,1,6,2,7,3]=>[1,6,2,7,3,4,5]=>14
[5,4,1,6,3,2,7]=>[1,6,2,7,3,4,5]=>14
[5,4,1,6,3,7,2]=>[1,6,2,3,7,4,5]=>9
[5,4,1,6,7,2,3]=>[1,6,7,2,3,4,5]=>14
[5,4,1,6,7,3,2]=>[1,6,7,2,3,4,5]=>14
[5,4,1,7,6,2,3]=>[1,7,2,3,4,5,6]=>1
[5,4,1,7,6,3,2]=>[1,7,2,3,4,5,6]=>1
[5,4,2,1,3,7,6]=>[1,3,7,2,4,5,6]=>4
[5,4,2,1,6,3,7]=>[1,6,2,3,7,4,5]=>9
[5,4,2,1,6,7,3]=>[1,6,7,2,3,4,5]=>14
[5,4,2,1,7,6,3]=>[1,7,2,3,4,5,6]=>1
[5,4,2,3,1,6,7]=>[1,6,7,2,3,4,5]=>14
[5,4,2,3,1,7,6]=>[1,7,2,3,4,5,6]=>1
[5,4,2,3,7,1,6]=>[1,6,2,3,7,4,5]=>9
[5,4,2,7,1,6,3]=>[1,6,2,7,3,4,5]=>14
[5,4,2,7,3,1,6]=>[1,6,2,7,3,4,5]=>14
[5,4,3,1,6,2,7]=>[1,6,2,7,3,4,5]=>14
[5,4,3,1,6,7,2]=>[1,6,7,2,3,4,5]=>14
[5,4,3,1,7,6,2]=>[1,7,2,3,4,5,6]=>1
[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>14
[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>1
[5,4,3,2,7,1,6]=>[1,6,2,7,3,4,5]=>14
[5,4,3,7,1,6,2]=>[1,6,2,3,7,4,5]=>9
[5,4,3,7,2,1,6]=>[1,6,2,3,7,4,5]=>9
[5,4,7,1,2,3,6]=>[1,2,3,6,4,7,5]=>2
[5,4,7,1,2,6,3]=>[1,2,6,3,4,7,5]=>3
[5,4,7,1,6,2,3]=>[1,6,2,3,4,7,5]=>4
[5,4,7,1,6,3,2]=>[1,6,2,3,4,7,5]=>4
[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>4
[5,4,7,2,3,1,6]=>[1,6,2,3,4,7,5]=>4
[5,4,7,2,3,6,1]=>[1,2,3,6,4,7,5]=>2
[5,4,7,2,6,3,1]=>[1,2,6,3,4,7,5]=>3
[5,4,7,3,1,2,6]=>[1,2,6,3,4,7,5]=>3
[5,4,7,3,1,6,2]=>[1,6,2,3,4,7,5]=>4
[5,4,7,3,2,1,6]=>[1,6,2,3,4,7,5]=>4
[5,4,7,3,2,6,1]=>[1,2,6,3,4,7,5]=>3
[5,4,7,3,6,1,2]=>[1,2,3,6,4,7,5]=>2
[5,4,7,3,6,2,1]=>[1,2,3,6,4,7,5]=>2
[5,6,1,3,7,2,4]=>[1,3,7,2,4,5,6]=>4
[5,6,1,3,7,4,2]=>[1,3,7,2,4,5,6]=>4
[5,6,1,4,7,2,3]=>[1,4,7,2,3,5,6]=>9
[5,6,1,4,7,3,2]=>[1,4,7,2,3,5,6]=>9
[5,6,1,7,2,3,4]=>[1,7,2,3,4,5,6]=>1
[5,6,1,7,3,4,2]=>[1,7,2,3,4,5,6]=>1
[5,6,1,7,4,2,3]=>[1,7,2,3,4,5,6]=>1
[5,6,1,7,4,3,2]=>[1,7,2,3,4,5,6]=>1
[5,6,2,1,3,7,4]=>[1,3,7,2,4,5,6]=>4
[5,6,2,1,4,7,3]=>[1,4,7,2,3,5,6]=>9
[5,6,2,1,7,3,4]=>[1,7,2,3,4,5,6]=>1
[5,6,2,1,7,4,3]=>[1,7,2,3,4,5,6]=>1
[5,6,2,3,1,4,7]=>[1,4,7,2,3,5,6]=>9
[5,6,2,3,1,7,4]=>[1,7,2,3,4,5,6]=>1
[5,6,2,3,4,1,7]=>[1,7,2,3,4,5,6]=>1
[5,6,2,4,1,3,7]=>[1,3,7,2,4,5,6]=>4
[5,6,3,1,4,7,2]=>[1,4,7,2,3,5,6]=>9
[5,6,3,1,7,4,2]=>[1,7,2,3,4,5,6]=>1
[5,6,3,2,1,4,7]=>[1,4,7,2,3,5,6]=>9
[5,6,3,2,1,7,4]=>[1,7,2,3,4,5,6]=>1
[5,6,3,4,1,7,2]=>[1,7,2,3,4,5,6]=>1
[5,6,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>1
[5,6,4,1,3,7,2]=>[1,3,7,2,4,5,6]=>4
[5,6,4,1,7,2,3]=>[1,7,2,3,4,5,6]=>1
[5,6,4,1,7,3,2]=>[1,7,2,3,4,5,6]=>1
[5,6,4,2,1,3,7]=>[1,3,7,2,4,5,6]=>4
[5,6,4,2,1,7,3]=>[1,7,2,3,4,5,6]=>1
[5,6,4,2,3,1,7]=>[1,7,2,3,4,5,6]=>1
[5,6,4,3,1,7,2]=>[1,7,2,3,4,5,6]=>1
[5,6,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>1
[5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7]=>1
[5,6,7,1,3,2,4]=>[1,3,2,4,5,6,7]=>1
[5,6,7,2,3,4,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,2,4,1,3]=>[1,3,2,4,5,6,7]=>1
[5,6,7,3,4,1,2]=>[1,2,3,4,5,6,7]=>1
[5,6,7,3,4,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,1,3,2]=>[1,3,2,4,5,6,7]=>1
[5,6,7,4,2,1,3]=>[1,3,2,4,5,6,7]=>1
[5,6,7,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,1,2,3,4,6]=>[1,2,3,4,6,5,7]=>1
[5,7,2,3,4,6,1]=>[1,2,3,4,6,5,7]=>1
[5,7,3,4,6,1,2]=>[1,2,3,4,6,5,7]=>1
[5,7,3,4,6,2,1]=>[1,2,3,4,6,5,7]=>1
[5,7,4,6,1,2,3]=>[1,2,3,4,6,5,7]=>1
[5,7,4,6,2,3,1]=>[1,2,3,4,6,5,7]=>1
[5,7,4,6,3,1,2]=>[1,2,3,4,6,5,7]=>1
[5,7,4,6,3,2,1]=>[1,2,3,4,6,5,7]=>1
[5,7,6,1,2,3,4]=>[1,2,3,4,5,7,6]=>1
[5,7,6,2,3,4,1]=>[1,2,3,4,5,7,6]=>1
[5,7,6,3,4,1,2]=>[1,2,3,4,5,7,6]=>1
[5,7,6,3,4,2,1]=>[1,2,3,4,5,7,6]=>1
[5,7,6,4,1,2,3]=>[1,2,3,4,5,7,6]=>1
[5,7,6,4,2,3,1]=>[1,2,3,4,5,7,6]=>1
[5,7,6,4,3,1,2]=>[1,2,3,4,5,7,6]=>1
[5,7,6,4,3,2,1]=>[1,2,3,4,5,7,6]=>1
[6,1,2,3,4,5,7]=>[1,2,3,4,5,7,6]=>1
[6,1,3,7,2,4,5]=>[1,3,7,2,4,5,6]=>4
[6,1,3,7,4,5,2]=>[1,3,7,2,4,5,6]=>4
[6,1,3,7,5,2,4]=>[1,3,7,2,4,5,6]=>4
[6,1,3,7,5,4,2]=>[1,3,7,2,4,5,6]=>4
[6,1,4,7,2,3,5]=>[1,4,7,2,3,5,6]=>9
[6,1,4,7,3,5,2]=>[1,4,7,2,3,5,6]=>9
[6,1,4,7,5,2,3]=>[1,4,7,2,3,5,6]=>9
[6,1,4,7,5,3,2]=>[1,4,7,2,3,5,6]=>9
[6,1,5,2,3,4,7]=>[1,5,2,3,4,7,6]=>4
[6,1,5,2,7,3,4]=>[1,5,2,7,3,4,6]=>14
[6,1,5,2,7,4,3]=>[1,5,2,7,3,4,6]=>14
[6,1,5,3,2,7,4]=>[1,5,2,7,3,4,6]=>14
[6,1,5,3,4,2,7]=>[1,5,2,7,3,4,6]=>14
[6,1,5,3,4,7,2]=>[1,5,2,3,4,7,6]=>4
[6,1,5,4,2,7,3]=>[1,5,2,7,3,4,6]=>14
[6,1,5,4,3,2,7]=>[1,5,2,7,3,4,6]=>14
[6,1,5,4,7,2,3]=>[1,5,2,3,4,7,6]=>4
[6,1,5,4,7,3,2]=>[1,5,2,3,4,7,6]=>4
[6,1,5,7,2,3,4]=>[1,5,7,2,3,4,6]=>14
[6,1,5,7,3,4,2]=>[1,5,7,2,3,4,6]=>14
[6,1,5,7,4,2,3]=>[1,5,7,2,3,4,6]=>14
[6,1,5,7,4,3,2]=>[1,5,7,2,3,4,6]=>14
[6,1,7,2,3,4,5]=>[1,7,2,3,4,5,6]=>1
[6,1,7,3,4,5,2]=>[1,7,2,3,4,5,6]=>1
[6,1,7,4,5,2,3]=>[1,7,2,3,4,5,6]=>1
[6,1,7,4,5,3,2]=>[1,7,2,3,4,5,6]=>1
[6,1,7,5,2,3,4]=>[1,7,2,3,4,5,6]=>1
[6,1,7,5,3,4,2]=>[1,7,2,3,4,5,6]=>1
[6,1,7,5,4,2,3]=>[1,7,2,3,4,5,6]=>1
[6,1,7,5,4,3,2]=>[1,7,2,3,4,5,6]=>1
[6,2,1,3,7,4,5]=>[1,3,7,2,4,5,6]=>4
[6,2,1,3,7,5,4]=>[1,3,7,2,4,5,6]=>4
[6,2,1,4,7,3,5]=>[1,4,7,2,3,5,6]=>9
[6,2,1,4,7,5,3]=>[1,4,7,2,3,5,6]=>9
[6,2,1,5,3,4,7]=>[1,5,2,3,4,7,6]=>4
[6,2,1,5,4,7,3]=>[1,5,2,3,4,7,6]=>4
[6,2,1,5,7,3,4]=>[1,5,7,2,3,4,6]=>14
[6,2,1,5,7,4,3]=>[1,5,7,2,3,4,6]=>14
[6,2,1,7,3,4,5]=>[1,7,2,3,4,5,6]=>1
[6,2,1,7,4,5,3]=>[1,7,2,3,4,5,6]=>1
[6,2,1,7,5,3,4]=>[1,7,2,3,4,5,6]=>1
[6,2,1,7,5,4,3]=>[1,7,2,3,4,5,6]=>1
[6,2,3,1,4,7,5]=>[1,4,7,2,3,5,6]=>9
[6,2,3,1,5,4,7]=>[1,5,2,3,4,7,6]=>4
[6,2,3,1,5,7,4]=>[1,5,7,2,3,4,6]=>14
[6,2,3,1,7,4,5]=>[1,7,2,3,4,5,6]=>1
[6,2,3,1,7,5,4]=>[1,7,2,3,4,5,6]=>1
[6,2,3,4,1,5,7]=>[1,5,7,2,3,4,6]=>14
[6,2,3,4,1,7,5]=>[1,7,2,3,4,5,6]=>1
[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>1
[6,2,3,4,5,7,1]=>[1,2,3,4,5,7,6]=>1
[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>4
[6,2,3,5,1,4,7]=>[1,4,7,2,3,5,6]=>9
[6,2,4,1,3,7,5]=>[1,3,7,2,4,5,6]=>4
[6,2,4,5,1,3,7]=>[1,3,7,2,4,5,6]=>4
[6,2,7,1,5,3,4]=>[1,5,2,7,3,4,6]=>14
[6,2,7,1,5,4,3]=>[1,5,2,7,3,4,6]=>14
[6,2,7,3,1,5,4]=>[1,5,2,7,3,4,6]=>14
[6,2,7,3,4,1,5]=>[1,5,2,7,3,4,6]=>14
[6,2,7,4,1,5,3]=>[1,5,2,7,3,4,6]=>14
[6,2,7,4,3,1,5]=>[1,5,2,7,3,4,6]=>14
[6,3,1,4,7,5,2]=>[1,4,7,2,3,5,6]=>9
[6,3,1,5,2,7,4]=>[1,5,2,7,3,4,6]=>14
[6,3,1,5,4,2,7]=>[1,5,2,7,3,4,6]=>14
[6,3,1,5,4,7,2]=>[1,5,2,3,4,7,6]=>4
[6,3,1,5,7,4,2]=>[1,5,7,2,3,4,6]=>14
[6,3,1,7,4,5,2]=>[1,7,2,3,4,5,6]=>1
[6,3,1,7,5,4,2]=>[1,7,2,3,4,5,6]=>1
[6,3,2,1,4,7,5]=>[1,4,7,2,3,5,6]=>9
[6,3,2,1,5,4,7]=>[1,5,2,3,4,7,6]=>4
[6,3,2,1,5,7,4]=>[1,5,7,2,3,4,6]=>14
[6,3,2,1,7,4,5]=>[1,7,2,3,4,5,6]=>1
[6,3,2,1,7,5,4]=>[1,7,2,3,4,5,6]=>1
[6,3,2,7,1,5,4]=>[1,5,2,7,3,4,6]=>14
[6,3,2,7,4,1,5]=>[1,5,2,7,3,4,6]=>14
[6,3,4,1,5,2,7]=>[1,5,2,7,3,4,6]=>14
[6,3,4,1,5,7,2]=>[1,5,7,2,3,4,6]=>14
[6,3,4,1,7,5,2]=>[1,7,2,3,4,5,6]=>1
[6,3,4,2,1,5,7]=>[1,5,7,2,3,4,6]=>14
[6,3,4,2,1,7,5]=>[1,7,2,3,4,5,6]=>1
[6,3,4,2,7,1,5]=>[1,5,2,7,3,4,6]=>14
[6,3,4,5,1,7,2]=>[1,7,2,3,4,5,6]=>1
[6,3,4,5,2,1,7]=>[1,7,2,3,4,5,6]=>1
[6,3,4,5,7,1,2]=>[1,2,3,4,5,7,6]=>1
[6,3,4,5,7,2,1]=>[1,2,3,4,5,7,6]=>1
[6,3,4,7,1,5,2]=>[1,5,2,3,4,7,6]=>4
[6,3,4,7,2,1,5]=>[1,5,2,3,4,7,6]=>4
[6,3,5,1,4,7,2]=>[1,4,7,2,3,5,6]=>9
[6,3,5,2,1,4,7]=>[1,4,7,2,3,5,6]=>9
[6,4,1,3,7,5,2]=>[1,3,7,2,4,5,6]=>4
[6,4,1,5,2,7,3]=>[1,5,2,7,3,4,6]=>14
[6,4,1,5,3,2,7]=>[1,5,2,7,3,4,6]=>14
[6,4,1,5,7,2,3]=>[1,5,7,2,3,4,6]=>14
[6,4,1,5,7,3,2]=>[1,5,7,2,3,4,6]=>14
[6,4,1,7,5,2,3]=>[1,7,2,3,4,5,6]=>1
[6,4,1,7,5,3,2]=>[1,7,2,3,4,5,6]=>1
[6,4,2,1,3,7,5]=>[1,3,7,2,4,5,6]=>4
[6,4,2,1,5,7,3]=>[1,5,7,2,3,4,6]=>14
[6,4,2,1,7,5,3]=>[1,7,2,3,4,5,6]=>1
[6,4,2,3,1,5,7]=>[1,5,7,2,3,4,6]=>14
[6,4,2,3,1,7,5]=>[1,7,2,3,4,5,6]=>1
[6,4,2,7,1,5,3]=>[1,5,2,7,3,4,6]=>14
[6,4,2,7,3,1,5]=>[1,5,2,7,3,4,6]=>14
[6,4,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>14
[6,4,3,1,5,7,2]=>[1,5,7,2,3,4,6]=>14
[6,4,3,1,7,5,2]=>[1,7,2,3,4,5,6]=>1
[6,4,3,2,1,5,7]=>[1,5,7,2,3,4,6]=>14
[6,4,3,2,1,7,5]=>[1,7,2,3,4,5,6]=>1
[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>14
[6,4,5,1,3,7,2]=>[1,3,7,2,4,5,6]=>4
[6,4,5,1,7,2,3]=>[1,7,2,3,4,5,6]=>1
[6,4,5,1,7,3,2]=>[1,7,2,3,4,5,6]=>1
[6,4,5,2,1,3,7]=>[1,3,7,2,4,5,6]=>4
[6,4,5,2,1,7,3]=>[1,7,2,3,4,5,6]=>1
[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>1
[6,4,5,3,1,7,2]=>[1,7,2,3,4,5,6]=>1
[6,4,5,3,2,1,7]=>[1,7,2,3,4,5,6]=>1
[6,4,5,7,1,2,3]=>[1,2,3,4,5,7,6]=>1
[6,4,5,7,2,3,1]=>[1,2,3,4,5,7,6]=>1
[6,4,5,7,3,1,2]=>[1,2,3,4,5,7,6]=>1
[6,4,5,7,3,2,1]=>[1,2,3,4,5,7,6]=>1
[6,4,7,1,5,2,3]=>[1,5,2,3,4,7,6]=>4
[6,4,7,1,5,3,2]=>[1,5,2,3,4,7,6]=>4
[6,4,7,2,1,5,3]=>[1,5,2,3,4,7,6]=>4
[6,4,7,2,3,1,5]=>[1,5,2,3,4,7,6]=>4
[6,4,7,3,1,5,2]=>[1,5,2,3,4,7,6]=>4
[6,4,7,3,2,1,5]=>[1,5,2,3,4,7,6]=>4
[6,5,1,3,7,2,4]=>[1,3,7,2,4,5,6]=>4
[6,5,1,3,7,4,2]=>[1,3,7,2,4,5,6]=>4
[6,5,1,4,7,2,3]=>[1,4,7,2,3,5,6]=>9
[6,5,1,4,7,3,2]=>[1,4,7,2,3,5,6]=>9
[6,5,1,7,2,3,4]=>[1,7,2,3,4,5,6]=>1
[6,5,1,7,3,4,2]=>[1,7,2,3,4,5,6]=>1
[6,5,1,7,4,2,3]=>[1,7,2,3,4,5,6]=>1
[6,5,1,7,4,3,2]=>[1,7,2,3,4,5,6]=>1
[6,5,2,1,3,7,4]=>[1,3,7,2,4,5,6]=>4
[6,5,2,1,4,7,3]=>[1,4,7,2,3,5,6]=>9
[6,5,2,1,7,3,4]=>[1,7,2,3,4,5,6]=>1
[6,5,2,1,7,4,3]=>[1,7,2,3,4,5,6]=>1
[6,5,2,3,1,4,7]=>[1,4,7,2,3,5,6]=>9
[6,5,2,3,1,7,4]=>[1,7,2,3,4,5,6]=>1
[6,5,2,3,4,1,7]=>[1,7,2,3,4,5,6]=>1
[6,5,2,4,1,3,7]=>[1,3,7,2,4,5,6]=>4
[6,5,3,1,4,7,2]=>[1,4,7,2,3,5,6]=>9
[6,5,3,1,7,4,2]=>[1,7,2,3,4,5,6]=>1
[6,5,3,2,1,4,7]=>[1,4,7,2,3,5,6]=>9
[6,5,3,2,1,7,4]=>[1,7,2,3,4,5,6]=>1
[6,5,3,4,1,7,2]=>[1,7,2,3,4,5,6]=>1
[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>1
[6,5,4,1,3,7,2]=>[1,3,7,2,4,5,6]=>4
[6,5,4,1,7,2,3]=>[1,7,2,3,4,5,6]=>1
[6,5,4,1,7,3,2]=>[1,7,2,3,4,5,6]=>1
[6,5,4,2,1,3,7]=>[1,3,7,2,4,5,6]=>4
[6,5,4,2,1,7,3]=>[1,7,2,3,4,5,6]=>1
[6,5,4,2,3,1,7]=>[1,7,2,3,4,5,6]=>1
[6,5,4,3,1,7,2]=>[1,7,2,3,4,5,6]=>1
[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>1
[6,5,7,1,2,3,4]=>[1,2,3,4,5,7,6]=>1
[6,5,7,2,3,4,1]=>[1,2,3,4,5,7,6]=>1
[6,5,7,3,4,1,2]=>[1,2,3,4,5,7,6]=>1
[6,5,7,3,4,2,1]=>[1,2,3,4,5,7,6]=>1
[6,5,7,4,1,2,3]=>[1,2,3,4,5,7,6]=>1
[6,5,7,4,2,3,1]=>[1,2,3,4,5,7,6]=>1
[6,5,7,4,3,1,2]=>[1,2,3,4,5,7,6]=>1
[6,5,7,4,3,2,1]=>[1,2,3,4,5,7,6]=>1
[6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7]=>1
[6,7,1,3,2,4,5]=>[1,3,2,4,5,6,7]=>1
[6,7,2,3,4,5,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,4,5,1,3]=>[1,3,2,4,5,6,7]=>1
[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[6,7,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,1,3,2]=>[1,3,2,4,5,6,7]=>1
[6,7,4,5,2,1,3]=>[1,3,2,4,5,6,7]=>1
[6,7,4,5,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,3,1,2]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,1,2,3,4]=>[1,2,3,4,5,6,7]=>1
[6,7,5,1,3,2,4]=>[1,3,2,4,5,6,7]=>1
[6,7,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,2,4,1,3]=>[1,3,2,4,5,6,7]=>1
[6,7,5,3,4,1,2]=>[1,2,3,4,5,6,7]=>1
[6,7,5,3,4,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,1,3,2]=>[1,3,2,4,5,6,7]=>1
[6,7,5,4,2,1,3]=>[1,3,2,4,5,6,7]=>1
[6,7,5,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7]=>1
[7,1,2,3,4,6,5]=>[1,2,3,4,6,5,7]=>1
[7,1,3,2,4,5,6]=>[1,3,2,4,5,6,7]=>1
[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>1
[7,2,4,5,6,1,3]=>[1,3,2,4,5,6,7]=>1
[7,3,4,5,6,1,2]=>[1,2,3,4,5,6,7]=>1
[7,3,4,5,6,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,6,5,1,2]=>[1,2,3,4,6,5,7]=>1
[7,3,4,6,5,2,1]=>[1,2,3,4,6,5,7]=>1
[7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7]=>1
[7,4,5,6,1,3,2]=>[1,3,2,4,5,6,7]=>1
[7,4,5,6,2,1,3]=>[1,3,2,4,5,6,7]=>1
[7,4,5,6,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,6,3,1,2]=>[1,2,3,4,5,6,7]=>1
[7,4,5,6,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,5,1,2,3]=>[1,2,3,4,6,5,7]=>1
[7,4,6,5,2,3,1]=>[1,2,3,4,6,5,7]=>1
[7,4,6,5,3,1,2]=>[1,2,3,4,6,5,7]=>1
[7,4,6,5,3,2,1]=>[1,2,3,4,6,5,7]=>1
[7,5,1,2,3,4,6]=>[1,2,3,4,6,5,7]=>1
[7,5,2,3,4,6,1]=>[1,2,3,4,6,5,7]=>1
[7,5,3,4,6,1,2]=>[1,2,3,4,6,5,7]=>1
[7,5,3,4,6,2,1]=>[1,2,3,4,6,5,7]=>1
[7,5,4,6,1,2,3]=>[1,2,3,4,6,5,7]=>1
[7,5,4,6,2,3,1]=>[1,2,3,4,6,5,7]=>1
[7,5,4,6,3,1,2]=>[1,2,3,4,6,5,7]=>1
[7,5,4,6,3,2,1]=>[1,2,3,4,6,5,7]=>1
[7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7]=>1
[7,5,6,1,3,2,4]=>[1,3,2,4,5,6,7]=>1
[7,5,6,2,3,4,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,2,4,1,3]=>[1,3,2,4,5,6,7]=>1
[7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7]=>1
[7,5,6,3,4,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,1,3,2]=>[1,3,2,4,5,6,7]=>1
[7,5,6,4,2,1,3]=>[1,3,2,4,5,6,7]=>1
[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7]=>1
[7,6,1,3,2,4,5]=>[1,3,2,4,5,6,7]=>1
[7,6,2,3,4,5,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,4,5,1,3]=>[1,3,2,4,5,6,7]=>1
[7,6,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,1,3,2]=>[1,3,2,4,5,6,7]=>1
[7,6,4,5,2,1,3]=>[1,3,2,4,5,6,7]=>1
[7,6,4,5,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,3,1,2]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7]=>1
[7,6,5,1,3,2,4]=>[1,3,2,4,5,6,7]=>1
[7,6,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,2,4,1,3]=>[1,3,2,4,5,6,7]=>1
[7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7]=>1
[7,6,5,3,4,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,1,3,2]=>[1,3,2,4,5,6,7]=>1
[7,6,5,4,2,1,3]=>[1,3,2,4,5,6,7]=>1
[7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>1
[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>1
[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>1
[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>1
[7,8,5,6,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>1
[7,6,5,8,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>1
[7,5,6,8,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>1
[5,6,7,8,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,4,5,3,2,1]=>[1,2,3,4,5,6,7,8]=>1
[7,8,6,4,5,3,2,1]=>[1,2,3,4,5,6,7,8]=>1
[8,6,7,4,5,3,2,1]=>[1,2,3,4,5,6,7,8]=>1
[7,6,4,5,8,3,2,1]=>[1,2,3,4,5,8,6,7]=>1
[7,4,5,6,8,3,2,1]=>[1,2,3,4,5,6,8,7]=>1
[4,5,6,7,8,3,2,1]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,5,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>1
[7,8,6,5,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>1
[8,6,7,5,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>1
[8,7,5,6,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>1
[5,6,7,8,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>1
[6,7,8,3,4,5,2,1]=>[1,2,3,4,5,6,7,8]=>1
[8,7,5,4,3,6,2,1]=>[1,2,3,6,4,5,7,8]=>1
[7,6,5,4,3,8,2,1]=>[1,2,3,8,4,5,6,7]=>1
[4,5,6,7,3,8,2,1]=>[1,2,3,8,4,5,6,7]=>1
[7,6,3,4,5,8,2,1]=>[1,2,3,4,5,8,6,7]=>1
[4,3,5,6,7,8,2,1]=>[1,2,3,5,6,7,8,4]=>1
[8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>1
[7,8,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>1
[8,6,7,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>1
[8,7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>1
[5,6,7,8,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,4,5,2,3,1]=>[1,2,3,4,5,6,7,8]=>1
[8,6,7,4,5,2,3,1]=>[1,2,3,4,5,6,7,8]=>1
[4,5,6,7,8,2,3,1]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,5,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>1
[6,7,8,5,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>1
[8,5,6,7,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>1
[5,6,7,8,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>1
[7,6,5,4,2,3,8,1]=>[1,2,3,8,4,5,6,7]=>1
[6,7,4,5,2,3,8,1]=>[1,2,3,8,4,5,6,7]=>1
[4,5,6,7,2,3,8,1]=>[1,2,3,8,4,5,6,7]=>1
[6,7,2,3,4,5,8,1]=>[1,2,3,4,5,8,6,7]=>1
[4,2,3,5,6,7,8,1]=>[1,2,3,5,6,7,8,4]=>1
[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>1
[7,8,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>1
[8,6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>1
[8,7,5,6,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>1
[5,6,7,8,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,4,5,3,1,2]=>[1,2,3,4,5,6,7,8]=>1
[7,8,6,4,5,3,1,2]=>[1,2,3,4,5,6,7,8]=>1
[4,5,6,7,8,3,1,2]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>1
[8,7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>1
[7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>1
[7,6,5,8,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>1
[6,7,5,8,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>1
[7,5,6,8,3,4,1,2]=>[1,2,3,4,5,6,8,7]=>1
[5,6,7,8,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>1
[7,8,5,4,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>1
[7,8,4,5,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>1
[7,8,3,4,5,6,1,2]=>[1,2,3,4,5,6,7,8]=>1
[8,3,4,5,6,7,1,2]=>[1,2,3,4,5,6,7,8]=>1
[7,6,5,4,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>1
[5,6,7,4,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>1
[6,7,4,5,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>1
[5,6,4,7,3,8,1,2]=>[1,2,3,8,4,7,5,6]=>9
[4,5,6,7,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>1
[4,3,5,6,7,8,1,2]=>[1,2,3,5,6,7,8,4]=>1
[3,4,5,6,7,8,1,2]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,5,4,2,1,3]=>[1,3,2,4,5,6,7,8]=>1
[5,6,7,8,4,2,1,3]=>[1,3,2,4,5,6,7,8]=>1
[4,5,6,7,8,2,1,3]=>[1,3,2,4,5,6,7,8]=>1
[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>1
[6,7,8,5,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>1
[8,5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>1
[5,6,7,8,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7,8]=>1
[8,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8]=>1
[8,7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8]=>1
[7,8,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8]=>1
[6,7,4,5,8,1,2,3]=>[1,2,3,4,5,8,6,7]=>1
[4,5,6,7,8,1,2,3]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,5,3,2,1,4]=>[1,4,2,3,5,6,7,8]=>1
[7,8,5,6,3,2,1,4]=>[1,4,2,3,5,6,7,8]=>1
[7,6,5,8,3,2,1,4]=>[1,4,2,3,5,8,6,7]=>6
[5,6,7,8,3,2,1,4]=>[1,4,2,3,5,6,7,8]=>1
[8,7,6,5,2,3,1,4]=>[1,4,2,3,5,6,7,8]=>1
[7,8,5,6,2,3,1,4]=>[1,4,2,3,5,6,7,8]=>1
[6,7,5,8,2,3,1,4]=>[1,4,2,3,5,8,6,7]=>6
[5,6,7,8,2,3,1,4]=>[1,4,2,3,5,6,7,8]=>1
[8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>1
[7,8,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>1
[8,6,7,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>1
[7,6,8,5,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>1
[6,7,8,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>1
[8,7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>1
[7,8,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>1
[8,6,5,7,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>1
[8,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>1
[7,6,5,8,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>1
[6,7,5,8,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>1
[7,5,6,8,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>1
[5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>1
[8,7,6,4,3,2,1,5]=>[1,5,2,3,4,6,7,8]=>1
[6,7,8,4,3,2,1,5]=>[1,5,2,3,4,6,7,8]=>1
[8,7,6,3,4,2,1,5]=>[1,5,2,3,4,6,7,8]=>1
[6,7,8,3,4,2,1,5]=>[1,5,2,3,4,6,7,8]=>1
[8,7,6,4,2,3,1,5]=>[1,5,2,3,4,6,7,8]=>1
[6,7,8,4,2,3,1,5]=>[1,5,2,3,4,6,7,8]=>1
[8,7,6,3,2,4,1,5]=>[1,5,2,4,3,6,7,8]=>3
[6,7,8,3,2,4,1,5]=>[1,5,2,4,3,6,7,8]=>3
[8,7,6,2,3,4,1,5]=>[1,5,2,3,4,6,7,8]=>1
[6,7,8,2,3,4,1,5]=>[1,5,2,3,4,6,7,8]=>1
[8,7,6,4,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>1
[6,7,8,4,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>1
[8,7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>1
[7,8,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>1
[8,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>1
[7,6,8,1,2,3,4,5]=>[1,2,3,4,5,6,8,7]=>1
[6,7,8,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>1
[7,8,5,4,3,2,1,6]=>[1,6,2,3,4,5,7,8]=>1
[7,8,4,5,2,3,1,6]=>[1,6,2,3,4,5,7,8]=>1
[7,8,3,4,2,5,1,6]=>[1,6,2,5,3,4,7,8]=>9
[7,8,5,4,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>1
[7,8,4,5,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>1
[7,8,3,4,1,2,5,6]=>[1,2,5,6,3,4,7,8]=>2
[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8]=>1
[7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8]=>1
[8,6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6,8]=>1
[8,4,5,6,3,2,1,7]=>[1,7,2,3,4,5,6,8]=>1
[8,6,4,5,1,2,3,7]=>[1,2,3,7,4,5,6,8]=>1
[8,3,2,1,4,5,6,7]=>[1,4,5,6,7,2,3,8]=>14
[8,2,3,1,4,5,6,7]=>[1,4,5,6,7,2,3,8]=>14
[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8]=>1
[7,6,5,4,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>1
[5,6,7,4,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>1
[7,4,5,6,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>1
[5,6,4,7,1,2,3,8]=>[1,2,3,8,4,7,5,6]=>9
[4,5,6,7,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>1
[7,6,4,3,2,1,5,8]=>[1,5,8,2,3,4,6,7]=>28
[6,7,1,2,3,4,5,8]=>[1,2,3,4,5,8,6,7]=>1
[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,6,8,7]=>1
[6,5,4,3,2,1,7,8]=>[1,7,8,2,3,4,5,6]=>42
[2,3,4,5,6,1,7,8]=>[1,7,8,2,3,4,5,6]=>42
[5,4,3,2,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>462
[4,5,2,3,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>462
[5,2,3,4,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>462
[2,3,4,5,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>462
[4,1,2,3,5,6,7,8]=>[1,2,3,5,6,7,8,4]=>1
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>1
[5,8,7,6,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>1
[6,5,8,7,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>1
[3,7,6,8,5,4,2,1]=>[1,2,3,7,4,5,6,8]=>1
[3,5,6,7,8,4,2,1]=>[1,2,3,5,6,7,8,4]=>1
[3,4,5,8,7,6,2,1]=>[1,2,3,4,5,8,6,7]=>1
[2,3,5,6,7,8,4,1]=>[1,2,3,5,6,7,8,4]=>1
[2,3,4,5,6,8,7,1]=>[1,2,3,4,5,6,8,7]=>1
[4,3,2,7,6,5,8,1]=>[1,2,7,3,4,5,8,6]=>4
[3,4,2,7,6,5,8,1]=>[1,2,7,3,4,5,8,6]=>4
[2,3,5,4,7,6,8,1]=>[1,2,3,5,4,7,6,8]=>2
[2,4,3,6,5,7,8,1]=>[1,2,4,3,6,5,7,8]=>2
[1,7,8,6,5,4,3,2]=>[1,7,8,2,3,4,5,6]=>42
[1,6,8,7,5,4,3,2]=>[1,6,8,2,3,4,5,7]=>42
[1,7,6,8,5,4,3,2]=>[1,7,2,3,4,5,6,8]=>1
[1,6,7,8,5,4,3,2]=>[1,6,7,8,2,3,4,5]=>462
[1,5,8,7,6,4,3,2]=>[1,5,8,2,3,4,6,7]=>28
[1,7,6,5,8,4,3,2]=>[1,7,2,3,4,5,8,6]=>5
[1,4,3,7,6,8,5,2]=>[1,4,2,3,7,5,6,8]=>6
[1,4,3,5,6,7,8,2]=>[1,4,2,3,5,6,7,8]=>1
[2,1,6,7,8,5,4,3]=>[1,6,7,8,2,3,4,5]=>462
[2,1,7,6,5,8,4,3]=>[1,7,2,3,4,5,8,6]=>5
[2,1,6,7,5,8,4,3]=>[1,6,7,2,3,4,5,8]=>14
[2,1,6,5,7,8,4,3]=>[1,6,2,3,4,5,7,8]=>1
[2,1,6,5,7,4,8,3]=>[1,6,2,3,4,8,5,7]=>14
[2,1,5,4,7,6,8,3]=>[1,5,2,3,4,7,6,8]=>4
[1,2,5,6,4,7,8,3]=>[1,2,5,6,3,4,7,8]=>2
[3,2,1,7,8,6,5,4]=>[1,7,8,2,3,4,5,6]=>42
[3,2,1,6,8,7,5,4]=>[1,6,8,2,3,4,5,7]=>42
[3,2,1,7,6,8,5,4]=>[1,7,2,3,4,5,6,8]=>1
[3,2,1,6,7,8,5,4]=>[1,6,7,8,2,3,4,5]=>462
[3,2,1,5,8,7,6,4]=>[1,5,8,2,3,4,6,7]=>28
[3,2,1,7,6,5,8,4]=>[1,7,2,3,4,5,8,6]=>5
[3,2,1,6,7,5,8,4]=>[1,6,7,2,3,4,5,8]=>14
[3,2,1,6,5,7,8,4]=>[1,6,2,3,4,5,7,8]=>1
[1,3,2,8,7,6,5,4]=>[1,3,2,8,4,5,6,7]=>5
[1,2,3,8,7,6,5,4]=>[1,2,3,8,4,5,6,7]=>1
[1,2,3,7,6,8,5,4]=>[1,2,3,7,4,5,6,8]=>1
[1,2,3,6,5,7,8,4]=>[1,2,3,6,4,5,7,8]=>1
[1,2,3,5,6,7,8,4]=>[1,2,3,5,6,7,8,4]=>1
[4,3,2,1,7,8,6,5]=>[1,7,8,2,3,4,5,6]=>42
[4,3,2,1,6,8,7,5]=>[1,6,8,2,3,4,5,7]=>42
[4,3,2,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>1
[4,3,2,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>462
[3,4,2,1,7,8,6,5]=>[1,7,8,2,3,4,5,6]=>42
[3,4,2,1,6,8,7,5]=>[1,6,8,2,3,4,5,7]=>42
[3,4,2,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>1
[3,4,2,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>462
[2,4,3,1,7,6,8,5]=>[1,7,2,4,3,5,6,8]=>5
[3,2,4,1,7,6,8,5]=>[1,7,2,4,3,5,6,8]=>5
[2,3,4,1,7,8,6,5]=>[1,7,8,2,3,4,5,6]=>42
[2,3,4,1,6,8,7,5]=>[1,6,8,2,3,4,5,7]=>42
[2,3,4,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>1
[2,3,4,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>462
[1,4,3,2,8,7,6,5]=>[1,4,2,8,3,5,6,7]=>14
[1,4,3,2,7,6,8,5]=>[1,4,2,7,3,5,6,8]=>9
[1,4,3,2,6,7,8,5]=>[1,4,2,6,7,8,3,5]=>84
[2,1,4,3,7,6,8,5]=>[1,4,2,3,7,5,6,8]=>6
[5,4,3,2,1,7,8,6]=>[1,7,8,2,3,4,5,6]=>42
[4,3,2,1,5,8,7,6]=>[1,5,8,2,3,4,6,7]=>28
[2,3,4,1,5,8,7,6]=>[1,5,8,2,3,4,6,7]=>28
[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,6,7]=>1
[5,4,3,2,1,6,8,7]=>[1,6,8,2,3,4,5,7]=>42
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>1
[4,3,2,1,7,6,5,8]=>[1,7,2,3,4,5,8,6]=>5
[4,3,2,1,6,7,5,8]=>[1,6,7,2,3,4,5,8]=>14
[2,3,4,1,7,6,5,8]=>[1,7,2,3,4,5,8,6]=>5
[2,3,4,1,6,7,5,8]=>[1,6,7,2,3,4,5,8]=>14
[1,3,4,2,6,7,5,8]=>[1,3,4,2,6,7,5,8]=>6
[5,4,3,2,1,7,6,8]=>[1,7,2,3,4,5,6,8]=>1
[3,2,1,5,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>4
[2,3,1,5,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>4
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>6
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>2
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>2
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>1
[4,3,2,1,6,5,7,8]=>[1,6,2,3,4,5,7,8]=>1
[3,2,4,1,6,5,7,8]=>[1,6,2,4,3,5,7,8]=>4
[2,3,4,1,6,5,7,8]=>[1,6,2,3,4,5,7,8]=>1
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>2
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>2
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>1
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>1
[1,2,3,7,5,6,8,4]=>[1,2,3,7,4,5,6,8]=>1
[1,2,3,8,5,6,7,4]=>[1,2,3,8,4,5,6,7]=>1
[1,2,3,8,6,7,5,4]=>[1,2,3,8,4,5,6,7]=>1
[1,5,3,4,6,7,8,2]=>[1,5,2,3,4,6,7,8]=>1
[2,1,7,4,6,5,8,3]=>[1,7,2,3,4,6,5,8]=>5
[2,3,7,4,5,6,8,1]=>[1,2,3,7,4,5,6,8]=>1
[3,2,1,5,8,6,7,4]=>[1,5,8,2,3,4,6,7]=>28
[3,2,1,7,5,6,4,8]=>[1,7,2,3,4,8,5,6]=>14
[3,2,1,7,5,6,8,4]=>[1,7,2,3,4,5,6,8]=>1
[4,2,3,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>462
[4,2,3,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>1
[4,2,3,7,5,6,8,1]=>[1,2,3,7,4,5,6,8]=>1
[4,2,3,8,7,6,5,1]=>[1,2,3,8,4,5,6,7]=>1
[5,2,4,3,1,7,6,8]=>[1,7,2,4,3,5,6,8]=>5
[5,3,4,2,1,7,8,6]=>[1,7,8,2,3,4,5,6]=>42
[8,3,7,4,6,5,2,1]=>[1,2,3,7,4,6,5,8]=>3
[8,7,3,5,4,6,2,1]=>[1,2,3,5,4,6,7,8]=>1
[8,7,3,6,5,4,2,1]=>[1,2,3,6,4,5,7,8]=>1
[8,7,4,3,6,5,2,1]=>[1,2,3,6,4,5,7,8]=>1
[2,4,6,1,3,5,8,7]=>[1,3,5,8,2,4,6,7]=>35
[2,4,1,6,3,8,5,7]=>[1,6,2,4,3,8,5,7]=>78
[2,4,1,6,3,7,5,8]=>[1,6,2,4,3,7,5,8]=>19
[2,4,1,5,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>15
[2,4,1,5,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>45
[2,4,1,5,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>3
[2,4,5,6,7,8,1,3]=>[1,3,2,4,5,6,7,8]=>1
[2,3,5,6,7,8,1,4]=>[1,4,2,3,5,6,7,8]=>1
[2,6,1,7,3,8,4,5]=>[1,7,2,6,3,8,4,5]=>450
[2,1,6,7,8,3,4,5]=>[1,6,7,8,2,3,4,5]=>462
[2,3,1,6,4,7,5,8]=>[1,6,2,3,4,7,5,8]=>4
[2,3,1,6,7,8,4,5]=>[1,6,7,8,2,3,4,5]=>462
[2,1,6,3,4,8,5,7]=>[1,6,2,3,4,8,5,7]=>14
[2,3,1,6,4,8,5,7]=>[1,6,2,3,4,8,5,7]=>14
[2,3,1,6,8,4,5,7]=>[1,6,8,2,3,4,5,7]=>42
[2,3,4,1,6,8,5,7]=>[1,6,8,2,3,4,5,7]=>42
[2,3,4,6,1,7,5,8]=>[1,7,2,3,4,6,5,8]=>5
[2,3,4,6,7,8,1,5]=>[1,5,2,3,4,6,7,8]=>1
[2,1,7,8,3,4,5,6]=>[1,7,8,2,3,4,5,6]=>42
[2,3,1,7,4,8,5,6]=>[1,7,2,3,4,8,5,6]=>14
[2,3,4,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>5
[2,3,4,1,7,8,5,6]=>[1,7,8,2,3,4,5,6]=>42
[2,3,4,1,7,5,6,8]=>[1,7,2,3,4,5,6,8]=>1
[2,3,4,5,7,8,1,6]=>[1,6,2,3,4,5,7,8]=>1
[2,3,4,1,5,8,6,7]=>[1,5,8,2,3,4,6,7]=>28
[2,3,4,5,8,1,6,7]=>[1,6,7,2,3,4,5,8]=>14
[2,3,4,5,6,8,1,7]=>[1,7,2,3,4,5,6,8]=>1
[3,1,4,2,6,7,8,5]=>[1,4,2,6,7,8,3,5]=>84
[3,4,7,8,1,2,5,6]=>[1,2,5,6,3,4,7,8]=>2
[3,1,4,2,8,5,6,7]=>[1,4,2,8,3,5,6,7]=>14
[3,5,1,7,2,8,4,6]=>[1,7,2,8,3,5,4,6]=>288
[3,1,5,2,7,4,6,8]=>[1,5,2,7,3,4,6,8]=>14
[3,1,5,2,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>28
[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>12
[1,3,5,8,2,4,6,7]=>[1,3,5,8,2,4,6,7]=>35
[1,3,5,6,2,7,4,8]=>[1,3,5,6,2,7,4,8]=>14
[3,6,1,7,2,8,4,5]=>[1,7,2,8,3,6,4,5]=>990
[3,1,6,2,7,4,5,8]=>[1,6,2,7,3,4,5,8]=>14
[1,3,2,6,4,7,5,8]=>[1,3,2,6,4,7,5,8]=>8
[3,1,6,2,8,4,5,7]=>[1,6,2,8,3,4,5,7]=>42
[1,3,2,6,4,8,5,7]=>[1,3,2,6,4,8,5,7]=>25
[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>3
[1,3,2,7,4,8,5,6]=>[1,3,2,7,4,8,5,6]=>30
[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>4
[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>5
[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>3
[4,1,5,2,6,3,8,7]=>[1,5,2,6,3,8,4,7]=>77
[4,5,6,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>1
[4,5,1,6,2,8,3,7]=>[1,6,2,8,3,7,4,5]=>702
[4,5,6,8,1,2,3,7]=>[1,2,3,7,4,5,6,8]=>1
[4,5,1,6,2,7,3,8]=>[1,6,2,7,3,8,4,5]=>168
[4,5,6,1,7,2,3,8]=>[1,7,2,3,8,4,5,6]=>28
[4,1,5,2,7,3,8,6]=>[1,5,2,7,3,8,4,6]=>168
[4,5,1,7,2,3,8,6]=>[1,7,2,3,8,4,5,6]=>28
[4,5,1,7,2,8,3,6]=>[1,7,2,8,3,6,4,5]=>990
[4,5,7,8,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>1
[1,4,2,5,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>8
[1,4,2,5,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>20
[1,4,2,5,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>2
[1,4,5,6,7,2,3,8]=>[1,4,5,6,7,2,3,8]=>14
[4,1,6,2,7,3,8,5]=>[1,6,2,7,3,8,4,5]=>168
[4,6,7,8,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>1
[4,6,1,2,3,7,5,8]=>[1,2,3,7,4,6,5,8]=>3
[1,4,2,6,3,7,5,8]=>[1,4,2,6,3,7,5,8]=>16
[1,4,2,6,7,8,3,5]=>[1,4,2,6,7,8,3,5]=>84
[1,4,2,6,3,8,5,7]=>[1,4,2,6,3,8,5,7]=>61
[1,4,2,6,3,5,7,8]=>[1,4,2,6,3,5,7,8]=>5
[4,1,2,3,6,5,7,8]=>[1,2,3,6,4,5,7,8]=>1
[1,4,2,7,3,8,5,6]=>[1,4,2,7,3,8,5,6]=>91
[1,4,2,7,3,5,6,8]=>[1,4,2,7,3,5,6,8]=>9
[4,1,2,3,7,5,6,8]=>[1,2,3,7,4,5,6,8]=>1
[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>6
[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>3
[1,4,2,8,3,5,6,7]=>[1,4,2,8,3,5,6,7]=>14
[4,1,2,3,8,5,6,7]=>[1,2,3,8,4,5,6,7]=>1
[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>6
[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>1
[5,1,6,2,7,3,8,4]=>[1,6,2,7,3,8,4,5]=>168
[1,5,2,6,3,7,4,8]=>[1,5,2,6,3,7,4,8]=>16
[5,6,1,2,3,8,4,7]=>[1,2,3,8,4,7,5,6]=>9
[1,5,2,6,3,8,4,7]=>[1,5,2,6,3,8,4,7]=>77
[1,5,2,6,3,4,7,8]=>[1,5,2,6,3,4,7,8]=>5
[1,2,5,6,3,4,7,8]=>[1,2,5,6,3,4,7,8]=>2
[1,5,2,7,3,8,4,6]=>[1,5,2,7,3,8,4,6]=>168
[1,5,2,7,3,4,6,8]=>[1,5,2,7,3,4,6,8]=>14
[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>4
[1,5,2,8,3,4,6,7]=>[1,5,2,8,3,4,6,7]=>28
[1,5,8,2,3,4,6,7]=>[1,5,8,2,3,4,6,7]=>28
[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>10
[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>3
[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>1
[6,1,7,8,2,3,4,5]=>[1,7,8,2,3,4,5,6]=>42
[1,6,2,7,3,8,4,5]=>[1,6,2,7,3,8,4,5]=>168
[1,6,7,8,2,3,4,5]=>[1,6,7,8,2,3,4,5]=>462
[6,1,7,2,3,4,5,8]=>[1,7,2,3,4,5,8,6]=>5
[6,1,2,7,3,4,5,8]=>[1,2,7,3,4,5,8,6]=>4
[1,6,2,7,3,4,5,8]=>[1,6,2,7,3,4,5,8]=>14
[1,6,7,2,3,4,5,8]=>[1,6,7,2,3,4,5,8]=>14
[1,6,2,3,4,7,5,8]=>[1,6,2,3,4,7,5,8]=>4
[1,2,3,6,4,7,5,8]=>[1,2,3,6,4,7,5,8]=>2
[1,6,2,8,3,4,5,7]=>[1,6,2,8,3,4,5,7]=>42
[1,6,8,2,3,4,5,7]=>[1,6,8,2,3,4,5,7]=>42
[1,6,2,3,4,8,5,7]=>[1,6,2,3,4,8,5,7]=>14
[1,2,3,6,4,8,5,7]=>[1,2,3,6,4,8,5,7]=>5
[6,1,2,3,4,5,8,7]=>[1,2,3,4,5,8,6,7]=>1
[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>1
[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>1
[1,7,2,8,3,4,5,6]=>[1,7,2,8,3,4,5,6]=>42
[1,7,8,2,3,4,5,6]=>[1,7,8,2,3,4,5,6]=>42
[1,7,2,3,8,4,5,6]=>[1,7,2,3,8,4,5,6]=>28
[1,7,2,3,4,8,5,6]=>[1,7,2,3,4,8,5,6]=>14
[1,2,3,7,4,8,5,6]=>[1,2,3,7,4,8,5,6]=>5
[7,1,2,3,4,5,8,6]=>[1,2,3,4,5,8,6,7]=>1
[1,7,2,3,4,5,8,6]=>[1,7,2,3,4,5,8,6]=>5
[1,2,7,3,4,5,8,6]=>[1,2,7,3,4,5,8,6]=>4
[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>1
[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>1
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>1
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>1
[8,4,5,2,3,7,6,1]=>[1,2,3,7,4,5,6,8]=>1
[3,6,1,5,4,2,8,7]=>[1,5,2,8,3,6,4,7]=>134
[4,6,5,1,3,2,8,7]=>[1,3,2,8,4,6,5,7]=>24
[7,5,4,3,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>42
[3,7,1,5,4,8,2,6]=>[1,5,2,6,3,7,4,8]=>16
[5,8,4,3,1,7,6,2]=>[1,7,2,3,4,5,8,6]=>5
[7,8,4,3,6,5,1,2]=>[1,2,3,6,4,5,7,8]=>1
[6,8,5,7,3,1,4,2]=>[1,4,2,3,5,7,6,8]=>3
[5,7,6,8,1,3,2,4]=>[1,3,2,4,5,7,6,8]=>2
[7,4,6,2,8,3,1,5]=>[1,5,2,8,3,4,6,7]=>28
[4,3,2,1,7,8,5,6]=>[1,7,8,2,3,4,5,6]=>42
[5,3,2,8,1,7,6,4]=>[1,7,2,8,3,4,5,6]=>42
[6,3,2,8,7,1,5,4]=>[1,5,2,8,3,4,6,7]=>28
[7,3,2,8,6,5,1,4]=>[1,4,2,8,3,5,6,7]=>14
[7,4,8,2,6,5,1,3]=>[1,3,2,6,4,8,5,7]=>25
[5,4,8,2,1,7,6,3]=>[1,7,2,3,4,8,5,6]=>14
[4,5,8,1,2,7,6,3]=>[1,2,7,3,4,5,8,6]=>4
[4,6,8,1,7,2,5,3]=>[1,7,2,5,3,4,6,8]=>14
[6,5,8,7,2,1,4,3]=>[1,4,2,3,5,8,6,7]=>6
[7,5,8,6,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>3
[2,1,7,8,6,5,3,4]=>[1,7,8,2,3,4,5,6]=>42
[3,8,1,7,6,5,4,2]=>[1,7,2,3,8,4,5,6]=>28
[4,8,7,1,6,5,3,2]=>[1,6,2,3,4,8,5,7]=>14
[5,8,7,6,1,4,3,2]=>[1,4,2,3,5,8,6,7]=>6
[6,7,8,9,10,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>1
[4,8,2,7,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>14
[5,8,4,7,1,2,3,6]=>[1,2,3,6,4,7,5,8]=>2
[6,8,5,7,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>1
[7,8,4,6,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>1
[6,5,4,8,1,2,3,7]=>[1,2,3,7,4,8,5,6]=>5
[8,4,2,7,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>14
[8,5,4,7,1,2,3,6]=>[1,2,3,6,4,7,5,8]=>2
[8,7,4,6,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>1
[8,7,5,3,6,1,2,4]=>[1,2,4,3,6,5,7,8]=>2
[4,8,3,7,2,6,1,5]=>[1,5,2,6,3,7,4,8]=>16
[5,8,3,7,2,6,1,4]=>[1,4,2,6,3,7,5,8]=>16
[5,8,4,7,2,6,1,3]=>[1,3,2,6,4,7,5,8]=>8
[5,8,4,7,3,6,1,2]=>[1,2,3,6,4,7,5,8]=>2
[6,8,3,7,2,5,1,4]=>[1,4,2,5,3,7,6,8]=>8
[6,8,4,7,2,5,1,3]=>[1,3,2,5,4,7,6,8]=>6
[6,8,4,7,3,5,1,2]=>[1,2,3,5,4,7,6,8]=>2
[6,8,5,7,2,4,1,3]=>[1,3,2,4,5,7,6,8]=>2
[6,8,5,7,3,4,1,2]=>[1,2,3,4,5,7,6,8]=>1
[7,8,3,6,2,5,1,4]=>[1,4,2,5,3,6,7,8]=>2
[7,8,4,6,2,5,1,3]=>[1,3,2,5,4,6,7,8]=>2
[7,8,4,6,3,5,1,2]=>[1,2,3,5,4,6,7,8]=>1
[7,8,5,6,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>1
[6,4,3,8,2,7,1,5]=>[1,5,2,7,3,8,4,6]=>168
[6,5,3,8,2,7,1,4]=>[1,4,2,7,3,8,5,6]=>91
[7,5,3,8,2,6,1,4]=>[1,4,2,6,3,8,5,7]=>61
[7,6,4,8,2,5,1,3]=>[1,3,2,5,4,8,6,7]=>12
[8,5,3,7,2,6,1,4]=>[1,4,2,6,3,7,5,8]=>16
[8,5,4,7,2,6,1,3]=>[1,3,2,6,4,7,5,8]=>8
[8,5,4,7,3,6,1,2]=>[1,2,3,6,4,7,5,8]=>2
[8,6,4,7,2,5,1,3]=>[1,3,2,5,4,7,6,8]=>6
[8,7,5,6,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>1
[6,5,4,3,2,8,1,7]=>[1,7,2,8,3,4,5,6]=>42
[8,5,4,3,2,7,1,6]=>[1,6,2,7,3,4,5,8]=>14
[8,7,5,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>3
[8,7,6,5,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>1
[8,1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6,8]=>1
[5,1,2,3,8,7,4,6]=>[1,2,3,8,4,6,5,7]=>4
[8,1,2,5,6,3,4,7]=>[1,2,5,6,3,4,7,8]=>2
[8,1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6,8]=>6
[8,1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6,8]=>1
[5,1,4,2,7,3,8,6]=>[1,4,2,7,3,8,5,6]=>91
[8,1,4,2,6,3,5,7]=>[1,4,2,6,3,5,7,8]=>5
[7,1,4,2,6,3,8,5]=>[1,4,2,6,3,8,5,7]=>61
[8,1,5,2,7,3,4,6]=>[1,5,2,7,3,4,6,8]=>14
[7,1,5,2,6,3,8,4]=>[1,5,2,6,3,8,4,7]=>77
[5,1,4,2,8,7,3,6]=>[1,4,2,8,3,6,5,7]=>78
[5,1,4,2,6,7,8,3]=>[1,4,2,6,7,8,3,5]=>84
[8,1,6,5,2,7,3,4]=>[1,6,2,7,3,4,5,8]=>14
[3,1,7,5,6,2,8,4]=>[1,7,2,8,3,4,5,6]=>42
[8,1,7,5,6,2,3,4]=>[1,7,2,3,4,5,6,8]=>1
[8,1,4,5,6,7,2,3]=>[1,4,5,6,7,2,3,8]=>14
[5,8,1,2,3,7,4,6]=>[1,2,3,7,4,6,5,8]=>3
[8,6,1,2,3,7,4,5]=>[1,2,3,7,4,5,6,8]=>1
[4,3,1,6,2,8,5,7]=>[1,6,2,8,3,4,5,7]=>42
[8,3,1,5,2,7,4,6]=>[1,5,2,7,3,4,6,8]=>14
[8,3,1,6,2,7,4,5]=>[1,6,2,7,3,4,5,8]=>14
[8,7,1,5,2,3,4,6]=>[1,5,2,3,4,6,7,8]=>1
[8,7,1,6,2,3,4,5]=>[1,6,2,3,4,5,7,8]=>1
[6,4,1,5,2,8,3,7]=>[1,5,2,8,3,7,4,6]=>534
[8,4,1,5,2,7,3,6]=>[1,5,2,7,3,6,4,8]=>56
[8,4,1,6,2,7,3,5]=>[1,6,2,7,3,5,4,8]=>70
[6,8,1,5,2,7,3,4]=>[1,5,2,7,3,4,6,8]=>14
[4,3,1,7,6,2,8,5]=>[1,7,2,8,3,4,5,6]=>42
[2,7,4,1,6,3,8,5]=>[1,6,2,7,3,8,4,5]=>168
[2,7,5,1,6,3,8,4]=>[1,6,2,7,3,8,4,5]=>168
[7,5,4,1,2,3,8,6]=>[1,2,3,8,4,5,6,7]=>1
[6,7,4,1,2,3,8,5]=>[1,2,3,8,4,5,6,7]=>1
[6,7,5,1,2,3,8,4]=>[1,2,3,8,4,5,6,7]=>1
[7,3,4,1,6,2,8,5]=>[1,6,2,8,3,4,5,7]=>42
[7,3,5,1,6,2,8,4]=>[1,6,2,8,3,5,4,7]=>246
[7,8,5,1,6,2,3,4]=>[1,6,2,3,4,5,7,8]=>1
[7,5,4,1,6,2,8,3]=>[1,6,2,8,3,4,5,7]=>42
[8,5,4,1,6,7,2,3]=>[1,6,7,2,3,4,5,8]=>14
[5,3,4,1,6,7,8,2]=>[1,6,7,8,2,3,4,5]=>462
[2,3,4,8,1,7,5,6]=>[1,7,2,3,4,8,5,6]=>14
[2,3,8,6,1,7,4,5]=>[1,7,2,3,8,4,5,6]=>28
[2,7,4,8,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>14
[2,8,4,5,1,7,3,6]=>[1,7,2,8,3,6,4,5]=>990
[2,8,4,6,1,7,3,5]=>[1,7,2,8,3,5,4,6]=>288
[2,8,6,5,1,7,3,4]=>[1,7,2,8,3,4,5,6]=>42
[8,3,4,5,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>28
[8,3,4,6,1,7,2,5]=>[1,7,2,5,3,4,6,8]=>14
[8,3,6,5,1,7,2,4]=>[1,7,2,4,3,6,5,8]=>29
[8,6,4,5,1,7,2,3]=>[1,7,2,3,4,5,6,8]=>1
[6,3,4,5,1,7,8,2]=>[1,7,8,2,3,4,5,6]=>42
[2,3,4,8,6,7,1,5]=>[1,5,2,3,4,8,6,7]=>10
[2,8,4,5,6,7,1,3]=>[1,3,2,8,4,5,6,7]=>5
[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8,9]=>1
[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9]=>1
[9,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9]=>1
[2,3,4,5,6,7,8,9,1]=>[1,2,3,4,5,6,7,8,9]=>1
[3,5,2,7,4,8,1,6]=>[1,6,2,7,3,5,4,8]=>70
[3,5,1,6,4,2,8,7]=>[1,6,2,8,3,5,4,7]=>246
[4,5,6,1,3,2,8,7]=>[1,3,2,8,4,5,6,7]=>5
[4,5,7,3,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>42
[3,5,1,7,4,8,2,6]=>[1,7,2,6,3,5,4,8]=>162
[5,6,7,8,3,1,4,2]=>[1,4,2,3,5,6,7,8]=>1
[2,1,6,7,8,4,5,3]=>[1,6,7,8,2,3,4,5]=>462
[5,6,7,8,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>1
[4,6,7,2,8,3,1,5]=>[1,5,2,8,3,4,6,7]=>28
[3,4,2,1,7,8,5,6]=>[1,7,8,2,3,4,5,6]=>42
[4,6,7,2,8,1,5,3]=>[1,5,2,8,3,4,6,7]=>28
[3,5,1,7,2,8,6,4]=>[1,7,2,8,3,5,4,6]=>288
[5,6,7,8,2,1,4,3]=>[1,4,2,3,5,6,7,8]=>1
[5,6,7,8,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>1
[5,6,7,8,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>1
[2,1,6,7,8,5,3,4]=>[1,6,7,8,2,3,4,5]=>462
[5,6,7,8,1,4,3,2]=>[1,4,2,3,5,6,7,8]=>1
[5,6,7,8,4,1,3,2]=>[1,3,2,4,5,6,7,8]=>1
[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>1
[6,5,8,7,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>1
[3,5,4,7,6,8,1,2]=>[1,2,3,5,4,7,6,8]=>2
[5,4,3,8,7,6,1,2]=>[1,2,3,8,4,5,6,7]=>1
[6,4,8,3,7,5,1,2]=>[1,2,3,7,4,8,5,6]=>5
[6,2,8,4,5,1,7,3]=>[1,7,2,8,3,4,5,6]=>42
[7,8,1,3,2,5,4,6]=>[1,3,2,5,4,6,7,8]=>2
[6,3,8,2,1,7,5,4]=>[1,7,2,3,8,4,5,6]=>28
[7,8,3,2,1,6,5,4]=>[1,6,2,3,4,5,7,8]=>1
[7,8,4,2,6,1,5,3]=>[1,5,2,6,3,4,7,8]=>5
[5,4,2,8,7,1,6,3]=>[1,6,2,8,3,4,5,7]=>42
[1,5,3,7,2,6,4,8]=>[1,5,2,6,3,7,4,8]=>16
[7,8,5,6,2,1,4,3]=>[1,4,2,3,5,6,7,8]=>1
[6,5,8,7,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>1
[7,3,1,5,2,8,4,6]=>[1,5,2,8,3,4,6,7]=>28
[6,4,5,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>1
[5,4,6,1,2,3,8,7]=>[1,2,3,8,4,6,5,7]=>4
[2,1,6,5,3,4,8,7]=>[1,6,2,3,4,8,5,7]=>14
[4,6,5,1,2,3,8,7]=>[1,2,3,8,4,6,5,7]=>4
[5,6,4,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>1
[6,5,4,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>1
[3,7,1,5,2,8,4,6]=>[1,5,2,8,3,7,4,6]=>534
[3,8,1,5,2,7,4,6]=>[1,5,2,7,3,8,4,6]=>168
[5,8,6,7,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>1
[2,1,7,6,8,3,4,5]=>[1,7,2,3,4,5,6,8]=>1
[5,7,6,8,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>1
[2,1,6,8,7,3,4,5]=>[1,6,8,2,3,4,5,7]=>42
[5,6,8,7,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>1
[7,5,8,6,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>1
[8,5,7,6,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>1
[2,1,7,8,6,3,4,5]=>[1,7,8,2,3,4,5,6]=>42
[5,8,7,6,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>1
[6,8,7,5,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>1
[6,4,7,3,8,5,1,2]=>[1,2,3,8,4,7,5,6]=>9
[5,4,3,7,6,8,1,2]=>[1,2,3,7,4,5,6,8]=>1
[5,4,3,8,6,7,1,2]=>[1,2,3,8,4,5,6,7]=>1
[5,4,2,8,6,1,7,3]=>[1,7,2,8,3,4,5,6]=>42
[7,8,4,2,5,1,6,3]=>[1,6,2,5,3,4,7,8]=>9
[4,3,2,1,6,8,5,7]=>[1,6,8,2,3,4,5,7]=>42
[7,8,3,2,1,5,4,6]=>[1,5,2,3,4,6,7,8]=>1
[7,8,3,2,1,6,4,5]=>[1,6,2,3,4,5,7,8]=>1
[6,3,8,2,1,7,4,5]=>[1,7,2,3,8,4,5,6]=>28
[4,3,2,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>5
[4,3,2,1,7,5,6,8]=>[1,7,2,3,4,5,6,8]=>1
[4,3,2,1,5,8,6,7]=>[1,5,8,2,3,4,6,7]=>28
[7,8,4,1,6,2,5,3]=>[1,6,2,5,3,4,7,8]=>9
[7,8,1,3,2,6,5,4]=>[1,3,2,6,4,5,7,8]=>3
[7,8,2,3,1,6,5,4]=>[1,6,2,3,4,5,7,8]=>1
[7,8,1,2,3,6,5,4]=>[1,2,3,6,4,5,7,8]=>1
[1,5,2,8,3,7,6,4]=>[1,5,2,8,3,7,4,6]=>534
[6,2,8,3,1,7,5,4]=>[1,7,2,8,3,4,5,6]=>42
[6,3,8,4,7,5,1,2]=>[1,2,3,8,4,7,5,6]=>9
[2,5,3,8,1,7,6,4]=>[1,7,2,5,3,8,4,6]=>282
[3,5,4,8,7,6,1,2]=>[1,2,3,5,4,8,6,7]=>3
[5,2,3,8,1,7,6,4]=>[1,7,2,3,8,4,5,6]=>28
[4,1,2,3,8,7,6,5]=>[1,2,3,8,4,5,6,7]=>1
[4,1,3,2,8,7,6,5]=>[1,3,2,8,4,5,6,7]=>5
[1,5,3,8,2,7,6,4]=>[1,5,2,7,3,8,4,6]=>168
[5,6,8,7,3,4,1,2]=>[1,2,3,4,5,6,8,7]=>1
[4,6,8,2,7,1,5,3]=>[1,5,2,7,3,4,6,8]=>14
[4,5,3,8,7,6,1,2]=>[1,2,3,8,4,5,6,7]=>1
[4,5,2,8,7,1,6,3]=>[1,6,2,8,3,4,5,7]=>42
[3,5,2,8,1,7,6,4]=>[1,7,2,8,3,5,4,6]=>288
[3,1,4,2,8,7,6,5]=>[1,4,2,8,3,5,6,7]=>14
[4,2,5,8,7,1,6,3]=>[1,6,2,5,8,3,4,7]=>288
[3,4,5,8,7,6,1,2]=>[1,2,3,4,5,8,6,7]=>1
[5,1,3,2,6,4,8,7]=>[1,3,2,6,4,8,5,7]=>25
[6,1,3,2,5,4,8,7]=>[1,3,2,5,4,8,6,7]=>12
[7,1,3,2,5,4,8,6]=>[1,3,2,5,4,8,6,7]=>12
[8,1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6,8]=>6
[8,1,4,2,5,3,7,6]=>[1,4,2,5,3,7,6,8]=>8
[7,1,4,2,5,3,8,6]=>[1,4,2,5,3,8,6,7]=>20
[6,1,4,2,5,3,8,7]=>[1,4,2,5,3,8,6,7]=>20
[5,1,4,2,6,3,8,7]=>[1,4,2,6,3,8,5,7]=>61
[4,1,6,2,5,3,8,7]=>[1,6,2,5,3,8,4,7]=>190
[6,2,5,1,4,3,8,7]=>[1,4,2,5,3,8,6,7]=>20
[5,2,6,1,4,3,8,7]=>[1,4,2,6,3,8,5,7]=>61
[5,2,7,1,4,3,8,6]=>[1,4,2,7,3,8,5,6]=>91
[5,2,8,1,4,3,7,6]=>[1,4,2,8,3,7,5,6]=>232
[6,2,8,1,4,3,7,5]=>[1,4,2,8,3,7,5,6]=>232
[6,2,7,1,4,3,8,5]=>[1,4,2,7,3,8,5,6]=>91
[7,2,6,1,4,3,8,5]=>[1,4,2,6,3,8,5,7]=>61
[7,2,5,1,4,3,8,6]=>[1,4,2,5,3,8,6,7]=>20
[4,1,7,2,5,3,8,6]=>[1,7,2,5,3,8,4,6]=>282
[8,2,5,1,4,3,7,6]=>[1,4,2,5,3,7,6,8]=>8
[8,2,6,1,4,3,7,5]=>[1,4,2,6,3,7,5,8]=>16
[7,1,4,3,8,2,6,5]=>[1,4,2,6,3,8,5,7]=>61
[8,1,4,3,7,2,6,5]=>[1,4,2,6,3,7,5,8]=>16
[8,1,5,3,7,2,6,4]=>[1,5,2,6,3,7,4,8]=>16
[7,1,5,3,8,2,6,4]=>[1,5,2,6,3,8,4,7]=>77
[8,2,6,1,5,3,7,4]=>[1,5,2,6,3,7,4,8]=>16
[4,1,7,2,6,3,8,5]=>[1,7,2,6,3,8,4,5]=>450
[5,1,7,2,6,3,8,4]=>[1,7,2,6,3,8,4,5]=>450
[7,2,6,1,5,3,8,4]=>[1,5,2,6,3,8,4,7]=>77
[6,2,7,1,5,3,8,4]=>[1,5,2,7,3,8,4,6]=>168
[6,2,8,1,5,3,7,4]=>[1,5,2,8,3,7,4,6]=>534
[8,1,5,2,6,3,7,4]=>[1,5,2,6,3,7,4,8]=>16
[6,1,5,2,7,3,8,4]=>[1,5,2,7,3,8,4,6]=>168
[6,1,4,2,7,3,8,5]=>[1,4,2,7,3,8,5,6]=>91
[8,1,4,2,6,3,7,5]=>[1,4,2,6,3,7,5,8]=>16
[8,1,3,2,6,4,7,5]=>[1,3,2,6,4,7,5,8]=>8
[7,1,3,2,6,4,8,5]=>[1,3,2,6,4,8,5,7]=>25
[6,1,3,2,7,4,8,5]=>[1,3,2,7,4,8,5,6]=>30
[5,1,3,2,7,4,8,6]=>[1,3,2,7,4,8,5,6]=>30
[5,1,3,2,8,4,7,6]=>[1,3,2,8,4,7,5,6]=>63
[6,1,3,2,8,4,7,5]=>[1,3,2,8,4,7,5,6]=>63
[8,4,7,1,3,2,6,5]=>[1,3,2,6,4,7,5,8]=>8
[7,4,8,1,3,2,6,5]=>[1,3,2,6,4,8,5,7]=>25
[7,3,8,1,4,2,6,5]=>[1,4,2,6,3,8,5,7]=>61
[8,3,7,1,4,2,6,5]=>[1,4,2,6,3,7,5,8]=>16
[6,1,4,2,8,3,7,5]=>[1,4,2,8,3,7,5,6]=>232
[5,1,4,2,8,3,7,6]=>[1,4,2,8,3,7,5,6]=>232
[4,1,5,2,8,3,7,6]=>[1,5,2,8,3,7,4,6]=>534
[4,1,6,2,8,3,7,5]=>[1,6,2,8,3,7,4,5]=>702
[5,1,6,2,8,3,7,4]=>[1,6,2,8,3,7,4,5]=>702
[6,1,5,2,8,3,7,4]=>[1,5,2,8,3,7,4,6]=>534
[8,3,7,1,5,2,6,4]=>[1,5,2,6,3,7,4,8]=>16
[7,3,8,1,5,2,6,4]=>[1,5,2,6,3,8,4,7]=>77
[6,2,7,3,8,1,5,4]=>[1,5,2,7,3,8,4,6]=>168
[6,2,8,3,7,1,5,4]=>[1,5,2,8,3,7,4,6]=>534
[8,3,7,2,6,1,5,4]=>[1,5,2,6,3,7,4,8]=>16
[4,1,7,3,8,2,6,5]=>[1,7,2,6,3,8,4,5]=>450
[5,1,7,3,8,2,6,4]=>[1,7,2,6,3,8,4,5]=>450
[7,3,8,2,6,1,5,4]=>[1,5,2,6,3,8,4,7]=>77
[8,2,6,3,7,1,5,4]=>[1,5,2,6,3,7,4,8]=>16
[7,2,6,3,8,1,5,4]=>[1,5,2,6,3,8,4,7]=>77
[5,7,3,8,2,4,1,6]=>[1,6,2,4,3,8,5,7]=>78
[7,4,2,5,8,3,1,6]=>[1,6,2,5,8,3,4,7]=>288
[4,5,2,6,3,8,1,7]=>[1,7,2,6,3,8,4,5]=>450
[4,5,1,6,3,8,2,7]=>[1,6,2,7,3,8,4,5]=>168
[4,5,6,3,2,8,1,7]=>[1,7,2,8,3,4,5,6]=>42
[6,7,4,8,3,2,1,5]=>[1,5,2,3,4,8,6,7]=>10
[6,7,4,8,3,1,5,2]=>[1,5,2,3,4,8,6,7]=>10
[6,7,4,8,3,5,2,1]=>[1,2,3,5,4,8,6,7]=>3
[5,6,7,3,8,4,2,1]=>[1,2,3,8,4,5,6,7]=>1
[5,6,1,7,3,8,4,2]=>[1,7,2,3,8,4,5,6]=>28
[6,7,2,8,4,5,1,3]=>[1,3,2,8,4,5,6,7]=>5
[5,6,1,7,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>42
[5,6,2,1,7,3,8,4]=>[1,7,2,3,8,4,5,6]=>28
[6,1,7,4,2,8,3,5]=>[1,7,2,8,3,5,4,6]=>288
[4,7,1,5,2,8,3,6]=>[1,5,2,8,3,6,4,7]=>134
[6,7,4,2,8,3,1,5]=>[1,5,2,8,3,4,6,7]=>28
[3,4,7,8,2,6,1,5]=>[1,5,2,6,3,4,7,8]=>5
[5,7,3,8,2,6,1,4]=>[1,4,2,6,3,8,5,7]=>61
[5,6,2,1,7,8,4,3]=>[1,7,8,2,3,4,5,6]=>42
[5,6,1,7,2,8,4,3]=>[1,7,2,8,3,4,5,6]=>42
[6,7,8,5,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>1
[6,7,8,3,5,1,4,2]=>[1,4,2,3,5,6,7,8]=>1
[4,6,7,8,1,5,3,2]=>[1,5,2,3,4,6,7,8]=>1
[5,1,6,7,8,4,3,2]=>[1,6,7,8,2,3,4,5]=>462
[5,6,1,7,8,4,3,2]=>[1,7,8,2,3,4,5,6]=>42
[8,3,2,5,1,6,4,7]=>[1,6,2,5,3,4,7,8]=>9
[8,5,3,6,2,4,1,7]=>[1,7,2,4,3,6,5,8]=>29
[8,5,6,2,1,4,3,7]=>[1,4,2,3,7,5,6,8]=>6
[4,1,5,3,7,2,8,6]=>[1,5,2,8,3,7,4,6]=>534
[3,5,6,7,8,4,1,2]=>[1,2,3,5,6,7,8,4]=>1
[1,5,3,6,7,8,2,4]=>[1,5,2,4,3,6,7,8]=>3
[3,5,6,7,8,2,1,4]=>[1,4,2,3,5,6,7,8]=>1
[3,6,2,7,4,8,1,5]=>[1,5,2,7,3,6,4,8]=>56
[7,8,3,4,2,1,6,5]=>[1,6,2,3,4,5,7,8]=>1
[2,6,4,7,8,1,5,3]=>[1,5,2,6,3,4,7,8]=>5
[7,4,5,8,6,2,1,3]=>[1,3,2,4,5,8,6,7]=>3
[7,4,1,5,8,6,2,3]=>[1,5,8,2,3,4,6,7]=>28
[6,7,8,2,1,5,4,3]=>[1,5,2,3,4,6,7,8]=>1
[8,7,5,4,1,3,2,6]=>[1,3,2,6,4,5,7,8]=>3
[6,1,5,4,2,8,7,3]=>[1,5,2,8,3,4,6,7]=>28
[8,1,5,4,7,6,2,3]=>[1,5,2,3,4,7,6,8]=>4
[8,1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5,8]=>14
[3,2,1,7,8,5,6,4]=>[1,7,8,2,3,4,5,6]=>42
[3,2,8,7,1,5,4,6]=>[1,5,2,8,3,4,6,7]=>28
[4,8,2,7,1,5,3,6]=>[1,5,2,7,3,6,4,8]=>56
[7,8,6,1,4,2,3,5]=>[1,4,2,3,5,6,7,8]=>1
[8,7,6,1,4,3,2,5]=>[1,4,2,5,3,6,7,8]=>2
[1,6,7,8,3,4,5,2]=>[1,6,7,8,2,3,4,5]=>462
[8,5,7,3,1,4,2,6]=>[1,4,2,6,3,5,7,8]=>5
[8,4,3,7,1,5,2,6]=>[1,5,2,6,3,7,4,8]=>16
[8,4,3,1,7,6,2,5]=>[1,7,2,5,3,4,6,8]=>14
[6,5,1,3,2,8,7,4]=>[1,3,2,8,4,5,6,7]=>5
[5,6,1,2,3,8,7,4]=>[1,2,3,8,4,5,6,7]=>1
[8,6,1,7,3,5,2,4]=>[1,7,2,4,3,5,6,8]=>5
[1,7,8,6,5,3,4,2]=>[1,7,8,2,3,4,5,6]=>42
[8,7,1,6,5,3,2,4]=>[1,6,2,4,3,5,7,8]=>4
[7,8,1,6,5,2,3,4]=>[1,6,2,3,4,5,7,8]=>1
[6,8,1,7,2,5,3,4]=>[1,7,2,5,3,4,6,8]=>14
[5,8,1,2,7,6,3,4]=>[1,2,7,3,4,5,8,6]=>4
[3,2,8,1,7,6,4,5]=>[1,7,2,8,3,4,5,6]=>42
[8,1,7,6,5,4,2,3]=>[1,7,2,3,4,5,6,8]=>1
[4,5,1,2,3,8,7,6]=>[1,2,3,8,4,5,6,7]=>1
[4,6,1,2,3,8,7,5]=>[1,2,3,8,4,6,5,7]=>4
[1,6,5,3,4,8,7,2]=>[1,6,2,3,4,8,5,7]=>14
[6,5,1,2,3,8,7,4]=>[1,2,3,8,4,5,6,7]=>1
[6,4,1,2,3,8,7,5]=>[1,2,3,8,4,5,6,7]=>1
[5,4,1,2,3,8,7,6]=>[1,2,3,8,4,5,6,7]=>1
[7,1,5,2,8,4,6,3]=>[1,5,2,8,3,4,6,7]=>28
[8,1,5,2,7,4,6,3]=>[1,5,2,7,3,4,6,8]=>14
[1,7,6,8,3,4,5,2]=>[1,7,2,3,4,5,6,8]=>1
[1,6,8,7,3,4,5,2]=>[1,6,8,2,3,4,5,7]=>42
[6,8,7,1,2,3,4,5]=>[1,2,3,4,5,6,8,7]=>1
[1,7,8,6,3,4,5,2]=>[1,7,8,2,3,4,5,6]=>42
[4,2,5,1,6,3,8,7]=>[1,6,2,5,3,8,4,7]=>190
[3,1,5,4,6,2,8,7]=>[1,5,2,8,3,4,6,7]=>28
[4,1,5,3,6,2,8,7]=>[1,5,2,8,3,6,4,7]=>134
[4,3,5,1,6,2,8,7]=>[1,6,2,8,3,5,4,7]=>246
[4,3,6,1,7,2,8,5]=>[1,7,2,8,3,6,4,5]=>990
[4,3,5,1,7,2,8,6]=>[1,7,2,8,3,5,4,6]=>288
[3,1,5,4,7,6,8,2]=>[1,5,2,3,4,7,6,8]=>4
[3,1,6,4,7,5,8,2]=>[1,6,2,3,4,7,5,8]=>4
[2,1,6,4,7,5,8,3]=>[1,6,2,3,4,7,5,8]=>4
[4,1,6,3,7,2,8,5]=>[1,6,2,8,3,7,4,5]=>702
[5,1,6,3,7,2,8,4]=>[1,6,2,8,3,7,4,5]=>702
[5,3,6,1,7,2,8,4]=>[1,7,2,8,3,6,4,5]=>990
[5,2,6,1,7,3,8,4]=>[1,7,2,6,3,8,4,5]=>450
[4,2,5,1,7,3,8,6]=>[1,7,2,5,3,8,4,6]=>282
[4,2,6,1,7,3,8,5]=>[1,7,2,6,3,8,4,5]=>450
[3,1,4,2,7,6,8,5]=>[1,4,2,7,3,5,6,8]=>9
[3,2,5,1,7,6,8,4]=>[1,7,2,5,3,4,6,8]=>14
[3,2,6,1,7,5,8,4]=>[1,7,2,6,3,4,5,8]=>28
[4,2,6,1,7,5,8,3]=>[1,7,2,6,3,4,5,8]=>28
[4,2,5,1,7,6,8,3]=>[1,7,2,5,3,4,6,8]=>14
[4,1,5,2,7,6,8,3]=>[1,5,2,7,3,4,6,8]=>14
[3,1,5,2,7,6,8,4]=>[1,5,2,7,3,4,6,8]=>14
[3,1,6,2,7,5,8,4]=>[1,6,2,7,3,4,5,8]=>14
[4,1,6,2,7,5,8,3]=>[1,6,2,7,3,4,5,8]=>14
[4,1,6,5,7,2,8,3]=>[1,6,2,8,3,4,5,7]=>42
[3,1,6,5,7,2,8,4]=>[1,6,2,8,3,4,5,7]=>42
[3,1,6,5,7,4,8,2]=>[1,6,2,3,4,8,5,7]=>14
[8,6,3,5,2,4,1,7]=>[1,7,2,4,3,5,6,8]=>5
[8,6,3,5,1,4,2,7]=>[1,4,2,7,3,5,6,8]=>9
[1,7,4,5,3,2,8,6]=>[1,7,2,8,3,4,5,6]=>42
[3,7,5,1,4,2,8,6]=>[1,4,2,8,3,7,5,6]=>232
[8,5,7,4,2,1,6,3]=>[1,6,2,3,4,5,7,8]=>1
[8,4,7,6,3,5,2,1]=>[1,2,3,5,4,7,6,8]=>2
[3,1,5,8,6,7,4,2]=>[1,5,8,2,3,4,6,7]=>28
[2,7,6,8,1,4,3,5]=>[1,4,2,7,3,5,6,8]=>9
[3,7,1,6,4,8,2,5]=>[1,6,2,5,3,7,4,8]=>35
[1,7,3,5,6,8,2,4]=>[1,7,2,4,3,5,6,8]=>5
[2,3,5,7,6,8,1,4]=>[1,4,2,3,5,7,6,8]=>3
[2,1,6,5,7,8,3,4]=>[1,6,2,3,4,5,7,8]=>1
[4,2,7,6,8,3,1,5]=>[1,5,2,7,3,4,6,8]=>14
[3,7,2,6,4,8,1,5]=>[1,5,2,6,3,7,4,8]=>16
[8,5,7,3,2,1,6,4]=>[1,6,2,3,4,5,7,8]=>1
[8,5,3,7,1,6,2,4]=>[1,6,2,4,3,7,5,8]=>19
[8,3,6,1,7,5,2,4]=>[1,7,2,4,3,6,5,8]=>29
[8,2,6,5,7,4,1,3]=>[1,3,2,6,4,5,7,8]=>3
[2,1,7,8,5,6,4,3]=>[1,7,8,2,3,4,5,6]=>42
[2,7,6,8,5,4,1,3]=>[1,3,2,7,4,5,6,8]=>4
[8,7,6,3,5,1,4,2]=>[1,4,2,3,5,6,7,8]=>1
[8,1,6,7,5,4,3,2]=>[1,6,7,2,3,4,5,8]=>14
[3,1,6,4,5,2,8,7]=>[1,6,2,8,3,4,5,7]=>42
[2,8,7,4,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>246
[8,1,7,4,2,6,3,5]=>[1,7,2,6,3,5,4,8]=>162
[2,1,6,8,5,7,3,4]=>[1,6,8,2,3,4,5,7]=>42
[5,6,3,8,1,7,2,4]=>[1,7,2,4,3,8,5,6]=>92
[8,5,7,4,1,6,3,2]=>[1,6,2,3,4,5,7,8]=>1
[6,5,3,8,4,1,7,2]=>[1,7,2,3,8,4,5,6]=>28
[2,1,5,8,4,6,7,3]=>[1,5,8,2,3,4,6,7]=>28
[6,4,3,8,2,1,7,5]=>[1,7,2,3,8,4,5,6]=>28
[7,3,8,4,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>77
[7,8,2,4,3,6,1,5]=>[1,5,2,4,3,6,7,8]=>3
[6,8,3,2,4,1,7,5]=>[1,7,2,4,3,5,6,8]=>5
[5,7,3,8,1,4,2,6]=>[1,4,2,6,3,8,5,7]=>61
[8,7,1,4,3,6,2,5]=>[1,4,2,5,3,6,7,8]=>2
[3,8,7,4,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>77
[5,7,8,4,3,6,2,1]=>[1,2,3,6,4,5,7,8]=>1
[8,6,3,1,4,2,7,5]=>[1,4,2,7,3,5,6,8]=>9
[7,5,3,8,2,4,1,6]=>[1,6,2,4,3,8,5,7]=>78
[7,5,3,6,2,8,1,4]=>[1,4,2,8,3,6,5,7]=>78
[5,8,3,2,6,1,7,4]=>[1,7,2,6,3,4,5,8]=>28
[8,7,5,4,1,6,2,3]=>[1,6,2,3,4,5,7,8]=>1
[2,1,7,6,5,8,3,4]=>[1,7,2,3,4,5,8,6]=>5
[7,8,5,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>3
[6,5,3,2,8,1,7,4]=>[1,7,2,8,3,4,5,6]=>42
[7,3,5,4,8,6,1,2]=>[1,2,3,5,4,8,6,7]=>3
[5,1,7,4,8,6,3,2]=>[1,7,2,3,4,8,5,6]=>14
[3,7,5,4,8,6,2,1]=>[1,2,3,7,4,8,5,6]=>5
[3,6,2,5,4,8,1,7]=>[1,7,2,5,3,6,4,8]=>64
[4,2,6,5,3,8,1,7]=>[1,7,2,6,3,8,4,5]=>450
[4,6,1,5,3,8,2,7]=>[1,5,2,7,3,8,4,6]=>168
[5,1,6,4,3,8,2,7]=>[1,6,2,7,3,8,4,5]=>168
[6,4,3,1,7,2,8,5]=>[1,7,2,8,3,4,5,6]=>42
[2,8,5,7,4,6,1,3]=>[1,3,2,8,4,6,5,7]=>24
[6,4,3,8,1,7,5,2]=>[1,7,2,3,8,4,5,6]=>28
[4,8,3,7,6,5,2,1]=>[1,2,3,7,4,8,5,6]=>5
[5,3,8,7,6,4,2,1]=>[1,2,3,8,4,5,6,7]=>1
[6,2,8,7,4,5,1,3]=>[1,3,2,8,4,5,6,7]=>5
[5,7,1,6,3,2,8,4]=>[1,6,2,8,3,4,5,7]=>42
[6,1,7,5,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>42
[6,5,2,1,7,3,8,4]=>[1,7,2,3,8,4,5,6]=>28
[8,3,6,2,7,1,5,4]=>[1,5,2,7,3,6,4,8]=>56
[5,8,3,7,1,6,2,4]=>[1,6,2,4,3,7,5,8]=>19
[6,5,2,8,1,7,4,3]=>[1,7,2,8,3,4,5,6]=>42
[5,8,2,7,6,4,3,1]=>[1,2,7,3,4,5,8,6]=>4
[6,1,7,2,8,5,4,3]=>[1,7,2,8,3,4,5,6]=>42
[7,8,3,1,6,5,2,4]=>[1,6,2,4,3,5,7,8]=>4
[8,7,4,6,1,5,3,2]=>[1,5,2,3,4,6,7,8]=>1
[8,5,7,1,6,4,3,2]=>[1,6,2,3,4,5,7,8]=>1
[6,8,1,7,5,4,3,2]=>[1,7,2,3,4,5,6,8]=>1
[3,2,1,6,4,8,5,7]=>[1,6,2,3,4,8,5,7]=>14
[7,1,5,2,8,3,4,6]=>[1,5,2,8,3,4,6,7]=>28
[8,1,6,7,2,3,4,5]=>[1,6,7,2,3,4,5,8]=>14
[7,1,6,8,2,3,4,5]=>[1,6,8,2,3,4,5,7]=>42
[3,2,1,7,8,4,5,6]=>[1,7,8,2,3,4,5,6]=>42
[1,7,6,8,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>1
[1,4,2,8,7,3,5,6]=>[1,4,2,8,3,5,6,7]=>14
[6,5,1,2,3,8,4,7]=>[1,2,3,8,4,7,5,6]=>9
[8,6,1,7,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>1
[1,6,8,7,2,3,4,5]=>[1,6,8,2,3,4,5,7]=>42
[1,7,8,6,2,3,4,5]=>[1,7,8,2,3,4,5,6]=>42
[7,8,1,6,2,3,4,5]=>[1,6,2,3,4,5,7,8]=>1
[6,8,1,7,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>1
[3,2,8,1,7,4,5,6]=>[1,7,2,8,3,4,5,6]=>42
[8,1,7,6,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>1
[2,6,1,5,4,3,8,7]=>[1,5,2,6,3,8,4,7]=>77
[7,5,4,8,1,6,3,2]=>[1,6,2,3,4,8,5,7]=>14
[7,4,1,3,5,8,6,2]=>[1,3,5,8,2,4,6,7]=>35
[6,5,8,4,1,7,3,2]=>[1,7,2,3,4,5,8,6]=>5
[4,7,2,3,8,5,6,1]=>[1,2,3,8,4,7,5,6]=>9
[3,8,2,1,7,5,6,4]=>[1,7,2,3,8,4,5,6]=>28
[8,7,1,6,3,4,2,5]=>[1,6,2,5,3,4,7,8]=>9
[3,8,6,7,2,4,1,5]=>[1,5,2,4,3,8,6,7]=>45
[8,3,6,1,4,2,7,5]=>[1,4,2,7,3,6,5,8]=>40
[8,3,5,6,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>9
[5,6,2,8,7,4,1,3]=>[1,3,2,8,4,5,6,7]=>5
[7,8,5,6,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>1
[2,8,6,5,4,7,1,3]=>[1,3,2,8,4,7,5,6]=>63
[8,1,6,4,5,7,2,3]=>[1,6,2,3,4,5,7,8]=>1
[5,8,3,6,1,7,2,4]=>[1,7,2,4,3,6,5,8]=>29
[2,7,4,1,6,5,8,3]=>[1,6,2,7,3,4,5,8]=>14
[6,4,2,1,5,8,7,3]=>[1,5,8,2,3,4,6,7]=>28
[8,5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5,8]=>14
[3,1,6,5,4,2,8,7]=>[1,6,2,8,3,4,5,7]=>42
[8,7,2,3,4,1,6,5]=>[1,6,2,3,4,5,7,8]=>1
[7,6,1,3,5,8,4,2]=>[1,3,5,8,2,4,6,7]=>35
[5,6,3,7,4,8,1,2]=>[1,2,3,7,4,8,5,6]=>5
[8,1,6,3,2,5,4,7]=>[1,6,2,5,3,4,7,8]=>9
[2,8,4,1,6,3,7,5]=>[1,6,2,8,3,7,4,5]=>702
[6,5,3,2,8,7,1,4]=>[1,4,2,8,3,5,6,7]=>14
[7,1,6,5,4,8,2,3]=>[1,6,2,3,4,8,5,7]=>14
[3,7,5,6,8,4,2,1]=>[1,2,3,7,4,5,6,8]=>1
[8,6,2,5,1,7,4,3]=>[1,7,2,5,3,4,6,8]=>14
[7,5,2,6,3,8,1,4]=>[1,4,2,6,3,8,5,7]=>61
[5,6,2,8,4,3,1,7]=>[1,7,2,8,3,4,5,6]=>42
[4,7,2,8,1,5,3,6]=>[1,5,2,8,3,6,4,7]=>134
[4,3,8,2,5,1,7,6]=>[1,7,2,5,3,8,4,6]=>282
[7,4,3,8,2,5,1,6]=>[1,6,2,5,3,8,4,7]=>190
[6,8,2,4,3,5,1,7]=>[1,7,2,4,3,5,6,8]=>5
[2,8,4,1,6,5,3,7]=>[1,6,2,8,3,7,4,5]=>702
[2,8,4,1,6,5,7,3]=>[1,6,2,8,3,4,5,7]=>42
[2,8,7,6,1,4,3,5]=>[1,4,2,8,3,5,6,7]=>14
[7,5,8,6,1,4,2,3]=>[1,4,2,3,5,8,6,7]=>6
[2,8,5,3,4,1,7,6]=>[1,7,2,8,3,4,5,6]=>42
[2,8,5,3,6,1,7,4]=>[1,7,2,8,3,6,4,5]=>990
[2,8,5,6,7,4,1,3]=>[1,3,2,8,4,5,6,7]=>5
[6,5,2,8,3,1,7,4]=>[1,7,2,8,3,4,5,6]=>42
[7,5,8,6,1,4,3,2]=>[1,4,2,3,5,8,6,7]=>6
[4,1,2,3,7,6,8,5]=>[1,2,3,7,4,5,6,8]=>1
[5,1,6,8,7,3,4,2]=>[1,6,8,2,3,4,5,7]=>42
[4,1,2,3,8,7,5,6]=>[1,2,3,8,4,5,6,7]=>1
[4,1,2,3,8,6,7,5]=>[1,2,3,8,4,5,6,7]=>1
[5,6,8,2,3,1,7,4]=>[1,7,2,3,4,5,6,8]=>1
[7,5,2,8,3,4,1,6]=>[1,6,2,8,3,4,5,7]=>42
[6,5,2,8,3,7,1,4]=>[1,4,2,8,3,7,5,6]=>232
[4,1,6,5,7,3,2,8]=>[1,6,2,8,3,4,5,7]=>42
[4,5,2,7,3,8,1,6]=>[1,6,2,7,3,8,4,5]=>168
[3,7,5,6,8,4,1,2]=>[1,2,3,7,4,5,6,8]=>1
[3,6,5,2,8,1,7,4]=>[1,7,2,8,3,6,4,5]=>990
[7,8,5,6,1,4,3,2]=>[1,4,2,3,5,6,7,8]=>1
[7,8,2,1,6,5,3,4]=>[1,6,2,3,4,5,7,8]=>1
[7,8,3,4,5,1,6,2]=>[1,6,2,3,4,5,7,8]=>1
[7,8,4,1,2,3,6,5]=>[1,2,3,6,4,5,7,8]=>1
[7,8,3,6,5,4,1,2]=>[1,2,3,6,4,5,7,8]=>1
[7,8,2,1,5,3,4,6]=>[1,5,2,3,4,6,7,8]=>1
[7,8,1,6,5,4,3,2]=>[1,6,2,3,4,5,7,8]=>1
[6,2,1,7,5,4,3,8]=>[1,7,2,3,8,4,5,6]=>28
[4,3,8,7,5,6,1,2]=>[1,2,3,8,4,5,6,7]=>1
[2,1,7,5,6,8,4,3]=>[1,7,2,3,4,5,6,8]=>1
[3,7,2,8,6,4,1,5]=>[1,5,2,8,3,7,4,6]=>534
[3,8,1,7,6,4,5,2]=>[1,7,2,3,8,4,5,6]=>28
[2,7,5,8,3,6,1,4]=>[1,4,2,7,3,6,5,8]=>40
[5,6,7,3,8,4,1,2]=>[1,2,3,8,4,5,6,7]=>1
[4,5,6,7,2,8,1,3]=>[1,3,2,8,4,5,6,7]=>5
[1,6,5,8,3,2,7,4]=>[1,6,2,7,3,4,5,8]=>14
[5,1,6,3,4,2,8,7]=>[1,6,2,8,3,4,5,7]=>42
[6,3,4,5,8,7,1,2]=>[1,2,3,4,5,8,6,7]=>1
[5,1,4,2,7,6,8,3]=>[1,4,2,7,3,5,6,8]=>9
[5,7,2,4,1,6,3,8]=>[1,6,2,4,3,8,5,7]=>78
[6,1,4,2,8,5,3,7]=>[1,4,2,8,3,7,5,6]=>232
[6,7,5,8,1,4,3,2]=>[1,4,2,3,5,8,6,7]=>6
[5,8,7,6,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>1
[5,8,7,6,2,3,1,4]=>[1,4,2,3,5,8,6,7]=>6
[4,1,7,2,6,5,3,8]=>[1,7,2,6,3,8,4,5]=>450
[3,1,7,4,5,6,8,2]=>[1,7,2,3,4,5,6,8]=>1
[4,2,7,1,6,3,8,5]=>[1,6,2,7,3,8,4,5]=>168
[4,3,7,5,6,8,1,2]=>[1,2,3,7,4,5,6,8]=>1
[3,8,6,5,2,4,1,7]=>[1,7,2,4,3,8,5,6]=>92
[5,2,8,7,1,6,4,3]=>[1,6,2,8,3,4,5,7]=>42
[3,7,6,8,5,2,1,4]=>[1,4,2,3,7,5,6,8]=>6
[3,8,7,6,5,4,1,2]=>[1,2,3,8,4,5,6,7]=>1
[2,1,7,6,5,3,4,8]=>[1,7,2,3,4,8,5,6]=>14
[2,8,1,6,4,5,3,7]=>[1,6,2,8,3,7,4,5]=>702
[2,8,7,5,1,4,3,6]=>[1,4,2,8,3,6,5,7]=>78
[8,5,3,6,1,7,2,4]=>[1,7,2,4,3,6,5,8]=>29
[6,4,7,5,2,8,1,3]=>[1,3,2,8,4,7,5,6]=>63
[7,4,8,5,2,6,1,3]=>[1,3,2,6,4,8,5,7]=>25
[5,8,2,6,3,7,1,4]=>[1,4,2,6,3,7,5,8]=>16
[6,3,7,4,8,5,1,2]=>[1,2,3,7,4,8,5,6]=>5
[7,5,3,8,1,6,2,4]=>[1,6,2,4,3,8,5,7]=>78
[8,6,1,7,5,2,3,4]=>[1,7,2,3,4,5,6,8]=>1
[5,7,2,8,1,6,3,4]=>[1,6,2,8,3,4,5,7]=>42
[8,4,7,6,1,2,3,5]=>[1,2,3,5,4,7,6,8]=>2
[5,4,8,7,1,2,3,6]=>[1,2,3,6,4,8,5,7]=>5
[7,5,8,6,4,1,2,3]=>[1,2,3,4,5,8,6,7]=>1
[4,8,7,6,1,2,3,5]=>[1,2,3,5,4,8,6,7]=>3
[5,6,3,1,4,2,8,7]=>[1,4,2,8,3,5,6,7]=>14
[8,7,1,4,2,6,5,3]=>[1,4,2,6,3,5,7,8]=>5
[3,4,5,6,7,8,9,1,2]=>[1,2,3,4,5,6,7,8,9]=>1
[2,3,4,5,6,7,8,9,10,1]=>[1,2,3,4,5,6,7,8,9,10]=>1
[3,4,5,6,7,8,9,10,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>1
[8,5,3,6,2,7,1,4]=>[1,4,2,7,3,6,5,8]=>40
[8,2,6,3,4,7,1,5]=>[1,5,2,6,3,4,7,8]=>5
[6,2,7,3,4,5,8,1]=>[1,2,7,3,4,5,8,6]=>4
[5,4,7,6,2,3,8,1]=>[1,2,3,8,4,7,5,6]=>9
[2,7,6,3,4,5,8,1]=>[1,2,7,3,4,5,8,6]=>4
[8,6,5,2,3,7,1,4]=>[1,4,2,3,7,5,6,8]=>6
[8,5,2,1,7,3,4,6]=>[1,7,2,3,4,6,5,8]=>5
[1,6,3,2,8,4,5,7]=>[1,6,2,8,3,4,5,7]=>42
[5,4,8,6,2,7,1,3]=>[1,3,2,7,4,8,5,6]=>30
[6,8,3,5,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>9
[6,8,2,1,7,3,4,5]=>[1,7,2,3,4,5,6,8]=>1
[2,8,1,7,3,4,5,6]=>[1,7,2,8,3,4,5,6]=>42
[8,2,6,1,7,3,4,5]=>[1,7,2,6,3,4,5,8]=>28
[3,2,1,5,8,4,6,7]=>[1,5,8,2,3,4,6,7]=>28
[1,5,3,4,6,8,2,7]=>[1,5,2,7,3,4,6,8]=>14
[5,4,6,3,8,7,1,2]=>[1,2,3,8,4,6,5,7]=>4
[6,7,3,8,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>20
[8,1,4,3,2,6,5,7]=>[1,4,2,6,3,5,7,8]=>5
[8,1,4,3,2,7,5,6]=>[1,4,2,7,3,5,6,8]=>9
[8,1,4,3,2,7,6,5]=>[1,4,2,7,3,5,6,8]=>9
[8,1,5,4,6,7,2,3]=>[1,5,2,3,4,6,7,8]=>1
[8,1,5,3,6,2,7,4]=>[1,5,2,7,3,6,4,8]=>56
[6,4,3,8,2,5,1,7]=>[1,7,2,5,3,8,4,6]=>282
[5,4,3,2,8,6,1,7]=>[1,7,2,8,3,4,5,6]=>42
[5,4,3,2,8,7,1,6]=>[1,6,2,8,3,4,5,7]=>42
[6,5,4,1,7,8,2,3]=>[1,7,8,2,3,4,5,6]=>42
[6,5,3,1,7,2,8,4]=>[1,7,2,8,3,4,5,6]=>42
[7,4,1,3,2,8,6,5]=>[1,3,2,8,4,5,6,7]=>5
[7,4,1,3,2,8,5,6]=>[1,3,2,8,4,5,6,7]=>5
[6,4,3,1,2,7,5,8]=>[1,2,7,3,4,5,8,6]=>4
[7,4,8,3,2,1,6,5]=>[1,6,2,3,4,8,5,7]=>14
[6,5,4,8,1,7,2,3]=>[1,7,2,3,4,8,5,6]=>14
[5,4,3,2,8,1,7,6]=>[1,7,2,8,3,4,5,6]=>42
[6,4,3,7,2,8,1,5]=>[1,5,2,8,3,7,4,6]=>534
[7,5,1,6,8,3,4,2]=>[1,6,8,2,3,4,5,7]=>42
[1,7,2,4,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>5
[1,6,2,4,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>4
[1,5,2,4,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>3
[1,6,2,5,3,4,7,8]=>[1,6,2,5,3,4,7,8]=>9
[1,7,2,5,3,4,6,8]=>[1,7,2,5,3,4,6,8]=>14
[1,7,2,6,3,4,5,8]=>[1,7,2,6,3,4,5,8]=>28
[1,7,2,8,3,5,4,6]=>[1,7,2,8,3,5,4,6]=>288
[1,6,2,8,3,5,4,7]=>[1,6,2,8,3,5,4,7]=>246
[1,5,2,8,3,6,4,7]=>[1,5,2,8,3,6,4,7]=>134
[1,4,2,8,3,6,5,7]=>[1,4,2,8,3,6,5,7]=>78
[1,3,2,8,4,6,5,7]=>[1,3,2,8,4,6,5,7]=>24
[1,2,3,8,4,6,5,7]=>[1,2,3,8,4,6,5,7]=>4
[1,2,3,7,4,6,5,8]=>[1,2,3,7,4,6,5,8]=>3
[1,3,2,7,4,6,5,8]=>[1,3,2,7,4,6,5,8]=>15
[1,4,2,7,3,6,5,8]=>[1,4,2,7,3,6,5,8]=>40
[1,5,2,7,3,6,4,8]=>[1,5,2,7,3,6,4,8]=>56
[1,6,2,7,3,5,4,8]=>[1,6,2,7,3,5,4,8]=>70
[1,7,2,6,3,5,4,8]=>[1,7,2,6,3,5,4,8]=>162
[1,7,2,5,3,6,4,8]=>[1,7,2,5,3,6,4,8]=>64
[1,6,2,5,3,7,4,8]=>[1,6,2,5,3,7,4,8]=>35
[1,5,2,4,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>15
[1,6,2,4,3,7,5,8]=>[1,6,2,4,3,7,5,8]=>19
[1,7,2,4,3,6,5,8]=>[1,7,2,4,3,6,5,8]=>29
[1,7,2,3,4,6,5,8]=>[1,7,2,3,4,6,5,8]=>5
[1,7,2,4,3,8,5,6]=>[1,7,2,4,3,8,5,6]=>92
[1,6,2,4,3,8,5,7]=>[1,6,2,4,3,8,5,7]=>78
[1,5,2,4,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>45
[1,6,2,5,3,8,4,7]=>[1,6,2,5,3,8,4,7]=>190
[1,7,2,5,3,8,4,6]=>[1,7,2,5,3,8,4,6]=>282
[1,7,2,6,3,8,4,5]=>[1,7,2,6,3,8,4,5]=>450
[1,2,3,8,4,7,5,6]=>[1,2,3,8,4,7,5,6]=>9
[1,3,2,8,4,7,5,6]=>[1,3,2,8,4,7,5,6]=>63
[1,4,2,8,3,7,5,6]=>[1,4,2,8,3,7,5,6]=>232
[1,5,2,8,3,7,4,6]=>[1,5,2,8,3,7,4,6]=>534
[1,6,2,8,3,7,4,5]=>[1,6,2,8,3,7,4,5]=>702
[1,7,2,8,3,6,4,5]=>[1,7,2,8,3,6,4,5]=>990
[5,6,8,3,4,1,7,2]=>[1,7,2,3,4,5,6,8]=>1
[5,6,8,4,3,1,7,2]=>[1,7,2,3,4,5,6,8]=>1
[5,7,8,4,1,6,2,3]=>[1,6,2,3,4,5,7,8]=>1
[5,7,8,4,1,6,3,2]=>[1,6,2,3,4,5,7,8]=>1
[5,6,8,4,2,1,7,3]=>[1,7,2,3,4,5,6,8]=>1
[5,6,8,2,4,1,7,3]=>[1,7,2,4,3,5,6,8]=>5
[5,7,8,4,1,3,2,6]=>[1,3,2,6,4,5,7,8]=>3
[5,7,8,4,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>1
[6,7,8,1,5,2,3,4]=>[1,5,2,3,4,6,7,8]=>1
[6,7,8,1,5,2,4,3]=>[1,5,2,4,3,6,7,8]=>3
[6,7,8,1,5,3,2,4]=>[1,5,2,4,3,6,7,8]=>3
[5,7,8,2,1,6,3,4]=>[1,6,2,3,4,5,7,8]=>1
[4,7,2,8,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>246
[5,7,8,2,1,6,4,3]=>[1,6,2,3,4,5,7,8]=>1
[6,7,8,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>1
[6,7,8,1,5,4,3,2]=>[1,5,2,3,4,6,7,8]=>1
[6,7,8,1,5,4,2,3]=>[1,5,2,3,4,6,7,8]=>1
[6,7,8,1,4,3,5,2]=>[1,4,2,3,5,6,7,8]=>1
[5,6,8,3,2,1,7,4]=>[1,7,2,3,4,5,6,8]=>1
[5,7,8,3,1,6,4,2]=>[1,6,2,3,4,5,7,8]=>1
[5,7,8,3,1,6,2,4]=>[1,6,2,4,3,5,7,8]=>4
[4,7,3,8,1,6,2,5]=>[1,6,2,5,3,8,4,7]=>190
[4,5,3,2,8,1,7,6]=>[1,7,2,8,3,4,5,6]=>42
[4,5,2,3,8,1,7,6]=>[1,7,2,3,8,4,5,6]=>28
[4,7,3,8,1,5,2,6]=>[1,5,2,6,3,8,4,7]=>77
[5,7,8,3,1,4,2,6]=>[1,4,2,6,3,5,7,8]=>5
[6,7,8,1,4,3,2,5]=>[1,4,2,5,3,6,7,8]=>2
[6,7,8,1,4,2,5,3]=>[1,4,2,5,3,6,7,8]=>2
[6,7,8,1,4,2,3,5]=>[1,4,2,3,5,6,7,8]=>1
[6,7,8,1,3,2,5,4]=>[1,3,2,5,4,6,7,8]=>2
[6,7,8,1,3,2,4,5]=>[1,3,2,4,5,6,7,8]=>1
[6,7,8,1,2,3,5,4]=>[1,2,3,5,4,6,7,8]=>1
[7,2,8,5,1,6,4,3]=>[1,6,2,8,3,4,5,7]=>42
[7,2,8,5,4,1,6,3]=>[1,6,2,8,3,4,5,7]=>42
[2,8,5,4,3,1,7,6]=>[1,7,2,8,3,4,5,6]=>42
[2,8,4,5,6,1,7,3]=>[1,7,2,8,3,4,5,6]=>42
[2,8,4,5,3,7,1,6]=>[1,6,2,8,3,7,4,5]=>702
[7,2,8,4,5,6,1,3]=>[1,3,2,8,4,5,6,7]=>5
[6,2,3,8,5,1,7,4]=>[1,7,2,3,8,4,5,6]=>28
[3,6,1,7,5,2,8,4]=>[1,7,2,8,3,6,4,5]=>990
[3,4,2,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>5
[1,6,5,7,3,4,2,8]=>[1,6,2,8,3,4,5,7]=>42
[1,5,2,7,4,6,3,8]=>[1,5,2,7,3,8,4,6]=>168
[2,3,4,8,6,1,7,5]=>[1,7,2,3,4,8,5,6]=>14
[2,3,4,8,6,5,1,7]=>[1,7,2,3,4,8,5,6]=>14
[1,5,4,6,2,7,3,8]=>[1,5,2,7,3,8,4,6]=>168
[2,7,6,5,8,3,4,1]=>[1,2,7,3,4,5,8,6]=>4
[7,3,6,1,5,4,2,8]=>[1,5,2,8,3,6,4,7]=>134
[7,4,6,5,1,3,2,8]=>[1,3,2,8,4,6,5,7]=>24
[6,2,1,7,5,4,8,3]=>[1,7,2,3,4,8,5,6]=>14
[5,2,1,7,6,8,4,3]=>[1,7,2,3,4,5,6,8]=>1
[4,5,7,6,8,1,3,2]=>[1,3,2,4,5,7,6,8]=>2
[5,2,1,6,7,8,3,4]=>[1,6,7,8,2,3,4,5]=>462
[6,3,5,1,7,2,8,4]=>[1,7,2,8,3,5,4,6]=>288
[5,6,4,7,2,8,1,3]=>[1,3,2,8,4,7,5,6]=>63
[6,4,3,2,1,7,8,5]=>[1,7,8,2,3,4,5,6]=>42
[4,6,3,2,8,7,1,5]=>[1,5,2,8,3,4,6,7]=>28
[3,6,4,8,2,7,1,5]=>[1,5,2,7,3,6,4,8]=>56
[3,4,5,8,1,2,7,6]=>[1,2,7,3,4,5,8,6]=>4
[3,4,6,8,1,7,2,5]=>[1,7,2,5,3,4,6,8]=>14
[4,2,1,7,8,6,5,3]=>[1,7,8,2,3,4,5,6]=>42
[2,3,8,1,7,6,5,4]=>[1,7,2,3,8,4,5,6]=>28
[8,3,4,1,7,5,6,2]=>[1,7,2,3,4,5,6,8]=>1
[4,8,3,1,7,5,6,2]=>[1,7,2,3,4,8,5,6]=>14
[4,6,2,1,7,5,8,3]=>[1,7,2,3,4,6,5,8]=>5
[7,5,2,1,6,8,4,3]=>[1,6,8,2,3,4,5,7]=>42
[6,8,4,3,1,7,5,2]=>[1,7,2,3,4,5,6,8]=>1
[6,8,4,1,7,5,3,2]=>[1,7,2,3,4,5,6,8]=>1
[8,4,2,1,6,7,5,3]=>[1,6,7,2,3,4,5,8]=>14
[1,5,3,2,7,6,8,4]=>[1,5,2,7,3,4,6,8]=>14
[5,3,2,1,7,6,8,4]=>[1,7,2,3,4,5,6,8]=>1
[2,5,3,1,7,6,8,4]=>[1,7,2,5,3,4,6,8]=>14
[4,7,1,6,5,8,2,3]=>[1,6,2,3,4,7,5,8]=>4
[4,8,2,6,5,7,1,3]=>[1,3,2,6,4,8,5,7]=>25
[6,7,1,5,8,2,3,4]=>[1,5,8,2,3,4,6,7]=>28
[7,5,1,6,8,4,2,3]=>[1,6,8,2,3,4,5,7]=>42
[8,4,1,6,7,5,2,3]=>[1,6,7,2,3,4,5,8]=>14
[5,2,3,1,7,6,8,4]=>[1,7,2,3,4,5,6,8]=>1
[7,6,2,1,5,8,3,4]=>[1,5,8,2,3,4,6,7]=>28
[8,2,6,4,7,1,5,3]=>[1,5,2,6,3,4,7,8]=>5
[8,3,5,7,6,2,1,4]=>[1,4,2,3,5,7,6,8]=>3
[8,2,6,5,7,1,4,3]=>[1,4,2,6,3,5,7,8]=>5
[5,1,3,2,7,6,8,4]=>[1,3,2,7,4,5,6,8]=>4
[4,1,3,2,7,6,8,5]=>[1,3,2,7,4,5,6,8]=>4
[1,4,2,3,7,6,8,5]=>[1,4,2,3,7,5,6,8]=>6
[6,8,2,3,5,7,1,4]=>[1,4,2,3,5,7,6,8]=>3
[6,7,1,3,5,8,2,4]=>[1,3,5,8,2,4,6,7]=>35
[5,1,2,3,7,6,8,4]=>[1,2,3,7,4,5,6,8]=>1
[10,8,9,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>1
[9,8,10,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,10,9]=>1
[8,1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7,8]=>2
[8,1,3,5,6,2,7,4]=>[1,3,5,6,2,7,4,8]=>14
[8,1,3,4,2,6,7,5]=>[1,3,4,2,6,7,5,8]=>6
[8,1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6,8]=>2
[3,6,2,8,4,5,1,7]=>[1,7,2,8,3,6,4,5]=>990
[3,5,4,2,8,7,1,6]=>[1,6,2,8,3,5,4,7]=>246
[6,4,5,1,7,8,2,3]=>[1,7,8,2,3,4,5,6]=>42
[7,4,1,2,3,8,5,6]=>[1,2,3,8,4,5,6,7]=>1
[5,6,4,8,1,7,2,3]=>[1,7,2,3,4,8,5,6]=>14
[3,4,6,7,2,8,1,5]=>[1,5,2,8,3,4,6,7]=>28
[7,8,1,6,3,5,2,4]=>[1,6,2,4,3,5,7,8]=>4
[1,7,3,4,8,6,5,2]=>[1,7,2,3,4,8,5,6]=>14
[8,5,7,1,6,2,3,4]=>[1,6,2,3,4,5,7,8]=>1
[8,5,7,2,1,6,3,4]=>[1,6,2,3,4,5,7,8]=>1
[8,5,7,1,2,3,6,4]=>[1,2,3,6,4,5,7,8]=>1
[8,7,6,2,1,4,3,5]=>[1,4,2,3,5,6,7,8]=>1
[8,5,7,2,3,1,6,4]=>[1,6,2,3,4,5,7,8]=>1
[5,8,4,2,7,1,6,3]=>[1,6,2,7,3,4,5,8]=>14
[8,2,5,4,7,1,6,3]=>[1,6,2,5,3,4,7,8]=>9
[8,5,2,7,3,1,6,4]=>[1,6,2,7,3,4,5,8]=>14
[8,7,6,2,4,3,1,5]=>[1,5,2,4,3,6,7,8]=>3
[8,7,6,1,4,2,3,5]=>[1,4,2,3,5,6,7,8]=>1
[8,7,6,4,1,3,2,5]=>[1,3,2,5,4,6,7,8]=>2
[5,8,4,7,2,1,6,3]=>[1,6,2,3,4,7,5,8]=>4
[6,8,1,7,3,2,5,4]=>[1,7,2,5,3,4,6,8]=>14
[8,5,7,3,1,6,2,4]=>[1,6,2,4,3,5,7,8]=>4
[8,5,7,1,3,2,6,4]=>[1,3,2,6,4,5,7,8]=>3
[5,8,4,1,7,2,6,3]=>[1,7,2,6,3,4,5,8]=>28
[5,8,4,7,1,6,2,3]=>[1,6,2,3,4,7,5,8]=>4
[4,8,5,7,1,6,2,3]=>[1,6,2,3,4,8,5,7]=>14
[8,5,3,1,7,2,6,4]=>[1,7,2,6,3,4,5,8]=>28
[4,8,5,7,2,1,6,3]=>[1,6,2,3,4,8,5,7]=>14
[8,7,6,3,1,4,2,5]=>[1,4,2,5,3,6,7,8]=>2
[8,7,6,1,3,2,4,5]=>[1,3,2,4,5,6,7,8]=>1
[8,5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5,8]=>14
[6,3,1,5,4,2,8,7]=>[1,5,2,8,3,4,6,7]=>28
[8,3,1,5,2,7,6,4]=>[1,5,2,7,3,4,6,8]=>14
[8,5,4,2,1,7,6,3]=>[1,7,2,3,4,5,6,8]=>1
[6,5,4,1,3,2,8,7]=>[1,3,2,8,4,5,6,7]=>5
[8,7,4,1,6,3,2,5]=>[1,6,2,5,3,4,7,8]=>9
[8,7,4,1,6,5,3,2]=>[1,6,2,3,4,5,7,8]=>1
[8,5,4,3,1,7,6,2]=>[1,7,2,3,4,5,6,8]=>1
[8,3,2,5,1,7,6,4]=>[1,7,2,5,3,4,6,8]=>14
[8,3,2,5,1,7,4,6]=>[1,7,2,5,3,4,6,8]=>14
[8,5,4,3,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>28
[8,7,4,1,6,5,2,3]=>[1,6,2,3,4,5,7,8]=>1
[8,7,4,1,6,2,5,3]=>[1,6,2,5,3,4,7,8]=>9
[8,7,6,5,2,1,4,3]=>[1,4,2,3,5,6,7,8]=>1
[8,3,2,7,6,4,1,5]=>[1,5,2,7,3,4,6,8]=>14
[8,5,4,2,3,7,6,1]=>[1,2,3,7,4,5,6,8]=>1
[8,7,4,2,6,3,1,5]=>[1,5,2,6,3,4,7,8]=>5
[8,3,1,7,6,4,2,5]=>[1,7,2,5,3,4,6,8]=>14
[8,3,1,7,6,4,5,2]=>[1,7,2,3,4,5,6,8]=>1
[8,3,1,7,6,5,4,2]=>[1,7,2,3,4,5,6,8]=>1
[8,3,1,5,4,7,6,2]=>[1,5,2,3,4,7,6,8]=>4
[8,3,1,5,4,7,2,6]=>[1,5,2,6,3,4,7,8]=>5
[8,3,1,7,6,5,2,4]=>[1,7,2,4,3,5,6,8]=>5
[8,3,1,7,6,2,5,4]=>[1,7,2,5,3,4,6,8]=>14
[8,7,4,2,6,1,5,3]=>[1,5,2,6,3,4,7,8]=>5
[8,7,4,2,6,5,1,3]=>[1,3,2,6,4,5,7,8]=>3
[8,3,2,5,4,7,1,6]=>[1,6,2,5,3,4,7,8]=>9
[8,3,2,7,6,5,1,4]=>[1,4,2,7,3,5,6,8]=>9
[8,7,4,3,6,5,1,2]=>[1,2,3,6,4,5,7,8]=>1
[8,7,6,5,3,1,4,2]=>[1,4,2,3,5,6,7,8]=>1
[8,7,6,5,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>1
[8,7,6,5,1,4,3,2]=>[1,4,2,3,5,6,7,8]=>1
[8,7,6,5,4,1,3,2]=>[1,3,2,4,5,6,7,8]=>1
[8,3,2,7,6,1,5,4]=>[1,5,2,7,3,4,6,8]=>14
[8,7,6,5,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>1
[1,6,5,2,7,4,3,8]=>[1,6,2,7,3,8,4,5]=>168
[1,6,4,2,7,5,3,8]=>[1,6,2,7,3,8,4,5]=>168
[4,5,7,1,6,8,2,3]=>[1,6,8,2,3,4,5,7]=>42
[7,4,1,6,8,5,2,3]=>[1,6,8,2,3,4,5,7]=>42
[6,2,1,5,8,7,3,4]=>[1,5,8,2,3,4,6,7]=>28
[7,1,3,5,8,2,4,6]=>[1,3,5,8,2,4,6,7]=>35
[5,2,3,1,6,4,8,7]=>[1,6,2,3,4,8,5,7]=>14
[5,2,4,1,6,3,8,7]=>[1,6,2,4,3,8,5,7]=>78
[4,1,6,3,5,2,8,7]=>[1,6,2,8,3,5,4,7]=>246
[6,3,4,1,5,2,8,7]=>[1,5,2,8,3,4,6,7]=>28
[7,3,4,1,5,2,8,6]=>[1,5,2,8,3,4,6,7]=>28
[4,1,7,3,5,2,8,6]=>[1,7,2,8,3,5,4,6]=>288
[3,1,7,4,5,2,8,6]=>[1,7,2,8,3,4,5,6]=>42
[2,1,7,4,5,3,8,6]=>[1,7,2,3,8,4,5,6]=>28
[8,6,7,3,4,1,5,2]=>[1,5,2,3,4,6,7,8]=>1
[8,5,7,3,4,1,6,2]=>[1,6,2,3,4,5,7,8]=>1
[4,1,7,3,6,2,8,5]=>[1,7,2,8,3,6,4,5]=>990
[5,1,7,3,6,2,8,4]=>[1,7,2,8,3,6,4,5]=>990
[6,2,5,1,7,3,8,4]=>[1,7,2,5,3,8,4,6]=>282
[5,2,4,1,7,3,8,6]=>[1,7,2,4,3,8,5,6]=>92
[6,2,4,1,7,3,8,5]=>[1,7,2,4,3,8,5,6]=>92
[8,5,7,3,6,2,4,1]=>[1,2,4,3,6,5,7,8]=>2
[6,2,3,1,7,4,8,5]=>[1,7,2,3,4,8,5,6]=>14
[5,2,3,1,7,4,8,6]=>[1,7,2,3,4,8,5,6]=>14
[4,2,3,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>5
[3,1,4,2,8,6,7,5]=>[1,4,2,8,3,5,6,7]=>14
[8,5,6,2,3,1,7,4]=>[1,7,2,3,4,5,6,8]=>1
[8,5,6,2,4,1,7,3]=>[1,7,2,4,3,5,6,8]=>5
[4,1,5,2,8,6,7,3]=>[1,5,2,8,3,4,6,7]=>28
[3,1,5,2,8,6,7,4]=>[1,5,2,8,3,4,6,7]=>28
[3,1,6,2,8,5,7,4]=>[1,6,2,8,3,4,5,7]=>42
[4,1,6,2,8,5,7,3]=>[1,6,2,8,3,4,5,7]=>42
[8,4,6,2,5,1,7,3]=>[1,7,2,5,3,4,6,8]=>14
[8,4,5,1,6,2,7,3]=>[1,6,2,7,3,4,5,8]=>14
[2,1,7,4,8,5,6,3]=>[1,7,2,3,4,8,5,6]=>14
[3,1,7,4,8,5,6,2]=>[1,7,2,3,4,8,5,6]=>14
[4,1,7,3,8,5,6,2]=>[1,7,2,3,8,4,5,6]=>28
[7,8,2,4,5,6,1,3]=>[1,3,2,4,5,6,7,8]=>1
[7,8,1,5,4,6,3,2]=>[1,5,2,3,4,6,7,8]=>1
[7,8,2,1,6,3,4,5]=>[1,6,2,3,4,5,7,8]=>1
[7,8,5,1,4,2,6,3]=>[1,4,2,6,3,5,7,8]=>5
[7,8,4,5,3,1,6,2]=>[1,6,2,3,4,5,7,8]=>1
[2,6,4,8,3,7,1,5]=>[1,5,2,6,3,7,4,8]=>16
[4,6,7,8,3,5,1,2]=>[1,2,3,5,4,6,7,8]=>1
[3,5,6,7,8,1,4,2]=>[1,4,2,3,5,6,7,8]=>1
[5,2,7,6,1,4,3,8]=>[1,4,2,7,3,8,5,6]=>91
[2,7,5,6,8,4,1,3]=>[1,3,2,7,4,5,6,8]=>4
[3,7,6,8,5,4,1,2]=>[1,2,3,7,4,5,6,8]=>1
[4,3,8,5,6,7,1,2]=>[1,2,3,8,4,5,6,7]=>1
[4,2,8,1,6,3,7,5]=>[1,6,2,8,3,7,4,5]=>702
[3,2,8,4,5,6,1,7]=>[1,7,2,8,3,4,5,6]=>42
[3,4,2,8,6,1,7,5]=>[1,7,2,8,3,4,5,6]=>42
[1,7,3,8,5,2,6,4]=>[1,7,2,6,3,8,4,5]=>450
[2,6,3,4,5,8,1,7]=>[1,7,2,6,3,4,5,8]=>28
[7,3,6,4,8,5,1,2]=>[1,2,3,6,4,8,5,7]=>5
[5,6,7,4,2,8,1,3]=>[1,3,2,8,4,5,6,7]=>5
[6,7,1,5,2,8,3,4]=>[1,5,2,8,3,4,6,7]=>28
[6,7,5,3,8,4,1,2]=>[1,2,3,8,4,5,6,7]=>1
[7,1,5,3,4,2,8,6]=>[1,5,2,8,3,4,6,7]=>28
[7,6,1,5,3,2,8,4]=>[1,5,2,8,3,4,6,7]=>28
[1,6,3,7,5,4,2,8]=>[1,6,2,8,3,7,4,5]=>702
[7,3,1,6,4,5,2,8]=>[1,6,2,8,3,4,5,7]=>42
[7,4,6,3,1,5,2,8]=>[1,5,2,8,3,4,6,7]=>28
[6,8,2,3,5,4,7,1]=>[1,2,3,5,4,7,6,8]=>2
[6,3,8,7,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>20
[6,8,5,1,2,3,7,4]=>[1,2,3,7,4,5,6,8]=>1
[4,5,3,1,7,6,2,8]=>[1,7,2,8,3,4,5,6]=>42
[4,5,3,1,6,8,7,2]=>[1,6,8,2,3,4,5,7]=>42
[2,1,7,5,8,6,4,3]=>[1,7,2,3,4,5,8,6]=>5
[6,4,1,7,5,2,3,8]=>[1,7,2,3,8,4,5,6]=>28
[2,6,3,7,5,8,1,4]=>[1,4,2,6,3,7,5,8]=>16
[5,7,4,6,2,8,1,3]=>[1,3,2,8,4,6,5,7]=>24
[5,8,4,7,3,1,6,2]=>[1,6,2,3,4,7,5,8]=>4
[6,3,8,2,7,1,5,4]=>[1,5,2,7,3,8,4,6]=>168
[1,6,2,8,5,3,7,4]=>[1,6,2,8,3,7,4,5]=>702
[6,8,5,3,1,7,4,2]=>[1,7,2,3,4,5,6,8]=>1
[1,6,3,7,2,8,4,5]=>[1,6,2,8,3,7,4,5]=>702
[4,5,7,8,3,1,6,2]=>[1,6,2,3,4,5,7,8]=>1
[4,7,2,5,8,1,6,3]=>[1,6,2,5,8,3,4,7]=>288
[3,5,6,8,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>9
[6,8,4,7,1,5,3,2]=>[1,5,2,3,4,7,6,8]=>4
[5,4,8,7,1,6,3,2]=>[1,6,2,3,4,8,5,7]=>14
[4,5,8,7,6,1,2,3]=>[1,2,3,4,5,8,6,7]=>1
[2,5,8,7,1,6,3,4]=>[1,6,2,5,8,3,4,7]=>288
[2,8,4,7,1,5,3,6]=>[1,5,2,8,3,6,4,7]=>134
[1,4,2,8,7,6,5,3]=>[1,4,2,8,3,5,6,7]=>14
[8,1,3,2,6,5,4,7]=>[1,3,2,6,4,7,5,8]=>8
[8,2,3,1,6,5,4,7]=>[1,6,2,3,4,7,5,8]=>4
[2,3,8,1,7,6,4,5]=>[1,7,2,3,8,4,5,6]=>28
[8,3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5,8]=>4
[8,4,2,6,1,5,3,7]=>[1,5,2,6,3,7,4,8]=>16
[4,2,8,7,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>246
[5,2,8,7,1,6,3,4]=>[1,6,2,8,3,4,5,7]=>42
[5,2,8,1,7,6,4,3]=>[1,7,2,8,3,4,5,6]=>42
[5,3,8,1,7,6,4,2]=>[1,7,2,3,8,4,5,6]=>28
[6,8,3,1,7,5,4,2]=>[1,7,2,3,4,5,6,8]=>1
[6,8,2,1,7,5,4,3]=>[1,7,2,3,4,5,6,8]=>1
[6,8,2,7,1,5,3,4]=>[1,5,2,7,3,4,6,8]=>14
[6,8,2,3,7,5,4,1]=>[1,2,3,7,4,5,6,8]=>1
[4,8,1,7,2,5,3,6]=>[1,7,2,5,3,6,4,8]=>64
[8,4,1,6,2,5,3,7]=>[1,6,2,5,3,7,4,8]=>35
[8,1,2,3,6,5,4,7]=>[1,2,3,6,4,7,5,8]=>2
[3,1,6,2,5,8,4,7]=>[1,6,2,5,8,3,4,7]=>288
[1,4,2,6,5,8,3,7]=>[1,4,2,6,3,7,5,8]=>16
[1,5,2,6,4,8,3,7]=>[1,5,2,6,3,7,4,8]=>16
[7,1,5,4,2,8,3,6]=>[1,5,2,8,3,6,4,7]=>134
[1,6,4,2,8,3,7,5]=>[1,6,2,8,3,7,4,5]=>702
[1,4,2,8,3,7,6,5]=>[1,4,2,8,3,7,5,6]=>232
[1,5,2,8,6,3,7,4]=>[1,5,2,8,3,7,4,6]=>534
[1,6,4,2,8,7,3,5]=>[1,6,2,8,3,5,4,7]=>246
[7,3,1,6,2,8,4,5]=>[1,6,2,8,3,4,5,7]=>42
[1,7,6,4,2,8,3,5]=>[1,7,2,8,3,5,4,6]=>288
[1,7,5,2,6,3,8,4]=>[1,7,2,6,3,8,4,5]=>450
[1,6,2,7,5,3,8,4]=>[1,6,2,7,3,8,4,5]=>168
[1,5,2,6,3,8,7,4]=>[1,5,2,6,3,8,4,7]=>77
[1,5,2,7,6,3,8,4]=>[1,5,2,7,3,8,4,6]=>168
[1,6,5,2,7,3,8,4]=>[1,6,2,7,3,8,4,5]=>168
[1,4,2,8,7,3,6,5]=>[1,4,2,8,3,6,5,7]=>78
[1,7,4,2,8,3,6,5]=>[1,7,2,8,3,6,4,5]=>990
[8,1,5,4,2,7,3,6]=>[1,5,2,7,3,6,4,8]=>56
[8,6,2,1,7,3,4,5]=>[1,7,2,3,4,5,6,8]=>1
[1,5,2,7,3,8,6,4]=>[1,5,2,7,3,8,4,6]=>168
[1,6,2,7,3,8,5,4]=>[1,6,2,7,3,8,4,5]=>168
[1,7,2,8,5,3,6,4]=>[1,7,2,8,3,6,4,5]=>990
[1,7,4,2,8,6,3,5]=>[1,7,2,8,3,5,4,6]=>288
[1,4,2,8,7,6,3,5]=>[1,4,2,8,3,5,6,7]=>14
[8,1,7,6,3,4,5,2]=>[1,7,2,3,4,5,6,8]=>1
[5,7,1,6,2,4,3,8]=>[1,6,2,4,3,8,5,7]=>78
[6,4,1,5,2,7,3,8]=>[1,5,2,7,3,8,4,6]=>168
[7,4,1,5,2,6,3,8]=>[1,5,2,6,3,8,4,7]=>77
[8,4,5,7,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>1
[5,8,7,6,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>3
[5,4,8,6,3,1,7,2]=>[1,7,2,3,4,8,5,6]=>14
[5,8,1,6,2,4,3,7]=>[1,6,2,4,3,7,5,8]=>19
[8,4,1,5,2,6,3,7]=>[1,5,2,6,3,7,4,8]=>16
[2,3,8,5,6,1,7,4]=>[1,7,2,3,8,4,5,6]=>28
[8,4,5,6,3,1,7,2]=>[1,7,2,3,4,5,6,8]=>1
[7,3,5,6,2,8,1,4]=>[1,4,2,8,3,5,6,7]=>14
[8,7,5,6,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>1
[2,7,6,8,4,3,1,5]=>[1,5,2,7,3,4,6,8]=>14
[7,8,1,6,3,4,2,5]=>[1,6,2,5,3,4,7,8]=>9
[2,3,8,6,4,1,7,5]=>[1,7,2,3,8,4,5,6]=>28
[2,8,6,7,4,3,1,5]=>[1,5,2,8,3,4,6,7]=>28
[8,3,5,7,2,4,1,6]=>[1,6,2,4,3,5,7,8]=>4
[2,8,6,1,7,3,4,5]=>[1,7,2,8,3,4,5,6]=>42
[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>1
[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>1
[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>1
[8,5,6,3,4,1,7,2]=>[1,7,2,3,4,5,6,8]=>1
[8,6,5,4,3,1,7,2]=>[1,7,2,3,4,5,6,8]=>1
[1,7,6,5,4,2,3,8]=>[1,7,2,3,8,4,5,6]=>28
[8,7,5,4,1,6,3,2]=>[1,6,2,3,4,5,7,8]=>1
[6,8,5,4,2,1,7,3]=>[1,7,2,3,4,5,6,8]=>1
[3,2,8,6,5,1,7,4]=>[1,7,2,8,3,4,5,6]=>42
[3,2,1,7,6,4,5,8]=>[1,7,2,3,4,5,8,6]=>5
[7,1,6,5,2,4,3,8]=>[1,6,2,4,3,8,5,7]=>78
[1,2,7,6,3,4,5,8]=>[1,2,7,3,4,5,8,6]=>4
[8,1,7,2,6,3,5,4]=>[1,7,2,6,3,5,4,8]=>162
[3,2,8,7,1,6,5,4]=>[1,6,2,8,3,4,5,7]=>42
[7,8,6,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>1
[8,7,6,1,5,4,3,2]=>[1,5,2,3,4,6,7,8]=>1
[6,5,8,3,2,1,7,4]=>[1,7,2,3,4,5,8,6]=>5
[8,5,7,3,1,6,4,2]=>[1,6,2,3,4,5,7,8]=>1
[1,5,4,8,2,7,3,6]=>[1,5,2,7,3,6,4,8]=>56
[8,5,1,4,2,3,7,6]=>[1,4,2,3,7,5,6,8]=>6
[7,5,1,4,2,6,3,8]=>[1,4,2,6,3,8,5,7]=>61
[3,2,6,1,5,4,7,8]=>[1,5,2,6,3,4,7,8]=>5
[5,7,1,3,2,6,4,8]=>[1,3,2,6,4,8,5,7]=>25
[8,7,1,2,3,6,5,4]=>[1,2,3,6,4,5,7,8]=>1
[8,1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6,8]=>1
[2,5,6,3,4,7,8,1]=>[1,2,5,6,3,4,7,8]=>2
[8,1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7,8]=>2
[3,4,1,6,7,8,5,2]=>[1,6,7,8,2,3,4,5]=>462
[4,3,1,7,6,8,5,2]=>[1,7,2,3,4,5,6,8]=>1
[6,7,3,1,5,8,4,2]=>[1,5,8,2,3,4,6,7]=>28
[6,7,2,8,1,5,3,4]=>[1,5,2,8,3,4,6,7]=>28
[6,7,8,2,1,4,3,5]=>[1,4,2,3,5,6,7,8]=>1
[5,1,7,3,4,8,6,2]=>[1,7,2,3,4,8,5,6]=>14
[5,2,7,4,8,6,1,3]=>[1,3,2,7,4,8,5,6]=>30
[5,1,6,4,2,8,7,3]=>[1,6,2,8,3,4,5,7]=>42
[5,6,1,3,2,8,7,4]=>[1,3,2,8,4,5,6,7]=>5
[5,7,3,2,8,1,6,4]=>[1,6,2,8,3,4,5,7]=>42
[5,1,7,4,8,6,2,3]=>[1,7,2,3,4,8,5,6]=>14
[6,7,3,8,1,5,2,4]=>[1,5,2,4,3,8,6,7]=>45
[6,7,8,3,1,4,2,5]=>[1,4,2,5,3,6,7,8]=>2
[6,1,7,8,4,5,2,3]=>[1,7,8,2,3,4,5,6]=>42
[1,6,7,8,4,5,3,2]=>[1,6,7,8,2,3,4,5]=>462
[6,7,2,8,3,1,5,4]=>[1,5,2,8,3,4,6,7]=>28
[6,7,2,8,3,5,1,4]=>[1,4,2,8,3,5,6,7]=>14
[4,2,1,7,8,5,6,3]=>[1,7,8,2,3,4,5,6]=>42
[6,7,2,8,5,3,1,4]=>[1,4,2,8,3,5,6,7]=>14
[5,1,7,2,8,6,4,3]=>[1,7,2,8,3,4,5,6]=>42
[6,7,8,2,4,3,1,5]=>[1,5,2,4,3,6,7,8]=>3
[1,6,7,8,5,3,4,2]=>[1,6,7,8,2,3,4,5]=>462
[6,1,7,8,5,4,2,3]=>[1,7,8,2,3,4,5,6]=>42
[6,7,8,4,1,3,2,5]=>[1,3,2,5,4,6,7,8]=>2
[6,3,4,5,8,7,2,1]=>[1,2,3,4,5,8,6,7]=>1
[3,6,4,8,5,7,1,2]=>[1,2,3,6,4,8,5,7]=>5
[6,3,8,4,2,7,1,5]=>[1,5,2,7,3,8,4,6]=>168
[4,3,8,5,6,7,2,1]=>[1,2,3,8,4,5,6,7]=>1
[6,3,7,5,2,8,1,4]=>[1,4,2,8,3,7,5,6]=>232
[6,5,2,7,4,8,1,3]=>[1,3,2,7,4,8,5,6]=>30
[6,4,1,5,3,8,2,7]=>[1,5,2,7,3,8,4,6]=>168
[8,5,4,1,7,2,6,3]=>[1,7,2,6,3,4,5,8]=>28
[6,5,8,4,2,7,3,1]=>[1,2,7,3,4,5,8,6]=>4
[6,8,3,1,7,2,5,4]=>[1,7,2,5,3,4,6,8]=>14
[8,7,1,6,2,5,4,3]=>[1,6,2,5,3,4,7,8]=>9
[7,8,1,6,3,2,5,4]=>[1,6,2,5,3,4,7,8]=>9
[3,8,6,1,7,4,5,2]=>[1,7,2,3,8,4,5,6]=>28
[5,1,7,6,8,3,2,4]=>[1,7,2,4,3,5,6,8]=>5
[1,7,3,8,4,5,2,6]=>[1,7,2,6,3,8,4,5]=>450
[8,6,1,7,4,2,5,3]=>[1,7,2,5,3,4,6,8]=>14
[8,2,6,1,7,3,5,4]=>[1,7,2,6,3,5,4,8]=>162
[2,3,8,7,4,5,6,1]=>[1,2,3,8,4,5,6,7]=>1
[8,1,7,6,5,2,4,3]=>[1,7,2,4,3,5,6,8]=>5
[5,1,6,8,7,4,2,3]=>[1,6,8,2,3,4,5,7]=>42
[3,8,7,6,4,5,2,1]=>[1,2,3,8,4,5,6,7]=>1
[5,8,6,7,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>1
[4,8,6,7,3,5,1,2]=>[1,2,3,5,4,8,6,7]=>3
[3,8,6,7,4,5,1,2]=>[1,2,3,8,4,5,6,7]=>1
[2,8,6,7,4,5,1,3]=>[1,3,2,8,4,5,6,7]=>5
[3,8,5,7,4,6,1,2]=>[1,2,3,8,4,6,5,7]=>4
[4,8,5,7,3,6,1,2]=>[1,2,3,6,4,8,5,7]=>5
[7,8,3,6,4,5,1,2]=>[1,2,3,6,4,5,7,8]=>1
[6,8,3,7,4,5,1,2]=>[1,2,3,7,4,5,6,8]=>1
[5,8,3,7,4,6,1,2]=>[1,2,3,7,4,6,5,8]=>3
[3,7,4,8,5,6,1,2]=>[1,2,3,7,4,8,5,6]=>5
[4,7,3,8,5,6,1,2]=>[1,2,3,8,4,7,5,6]=>9
[4,7,2,8,5,6,1,3]=>[1,3,2,8,4,7,5,6]=>63
[3,7,2,8,5,6,1,4]=>[1,4,2,8,3,7,5,6]=>232
[2,7,3,8,5,6,1,4]=>[1,4,2,7,3,8,5,6]=>91
[2,7,4,8,5,6,1,3]=>[1,3,2,7,4,8,5,6]=>30
[5,8,2,7,4,6,1,3]=>[1,3,2,7,4,6,5,8]=>15
[6,8,2,7,4,5,1,3]=>[1,3,2,7,4,5,6,8]=>4
[7,8,2,6,4,5,1,3]=>[1,3,2,6,4,5,7,8]=>3
[7,8,1,6,4,5,2,3]=>[1,6,2,3,4,5,7,8]=>1
[6,8,1,7,4,5,2,3]=>[1,7,2,3,4,5,6,8]=>1
[5,8,1,7,4,6,2,3]=>[1,7,2,3,4,6,5,8]=>5
[1,7,4,8,5,6,2,3]=>[1,7,2,3,4,8,5,6]=>14
[1,7,3,8,5,6,2,4]=>[1,7,2,4,3,8,5,6]=>92
[2,8,5,6,1,7,3,4]=>[1,7,2,8,3,4,5,6]=>42
[1,7,3,8,4,6,2,5]=>[1,7,2,5,3,8,4,6]=>282
[4,8,1,7,3,6,2,5]=>[1,7,2,5,3,6,4,8]=>64
[5,8,1,7,3,6,2,4]=>[1,7,2,4,3,6,5,8]=>29
[6,8,1,7,3,5,2,4]=>[1,7,2,4,3,5,6,8]=>5
[7,8,2,6,3,5,1,4]=>[1,4,2,6,3,5,7,8]=>5
[6,8,2,7,3,5,1,4]=>[1,4,2,7,3,5,6,8]=>9
[5,8,2,7,3,6,1,4]=>[1,4,2,7,3,6,5,8]=>40
[4,8,2,7,3,6,1,5]=>[1,5,2,7,3,6,4,8]=>56
[2,7,3,8,4,6,1,5]=>[1,5,2,7,3,8,4,6]=>168
[3,7,2,8,4,6,1,5]=>[1,5,2,8,3,7,4,6]=>534
[2,8,4,7,3,6,1,5]=>[1,5,2,8,3,6,4,7]=>134
[3,8,4,7,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>77
[4,8,5,7,2,6,1,3]=>[1,3,2,6,4,8,5,7]=>25
[3,8,5,7,2,6,1,4]=>[1,4,2,6,3,8,5,7]=>61
[2,8,5,7,3,6,1,4]=>[1,4,2,8,3,6,5,7]=>78
[2,8,6,7,3,5,1,4]=>[1,4,2,8,3,5,6,7]=>14
[3,8,6,7,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>20
[4,8,6,7,2,5,1,3]=>[1,3,2,5,4,8,6,7]=>12
[5,8,6,7,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>3
[6,8,5,7,1,4,2,3]=>[1,4,2,3,5,7,6,8]=>3
[5,8,6,7,1,4,2,3]=>[1,4,2,3,5,8,6,7]=>6
[4,8,6,7,1,5,2,3]=>[1,5,2,3,4,8,6,7]=>10
[3,8,6,7,1,5,2,4]=>[1,5,2,4,3,8,6,7]=>45
[1,5,2,8,6,7,3,4]=>[1,5,2,8,3,4,6,7]=>28
[1,6,2,8,5,7,3,4]=>[1,6,2,8,3,4,5,7]=>42
[3,8,5,7,1,6,2,4]=>[1,6,2,4,3,8,5,7]=>78
[6,8,4,7,1,5,2,3]=>[1,5,2,3,4,7,6,8]=>4
[7,8,4,6,1,5,2,3]=>[1,5,2,3,4,6,7,8]=>1
[7,8,3,6,1,5,2,4]=>[1,5,2,4,3,6,7,8]=>3
[6,8,3,7,1,5,2,4]=>[1,5,2,4,3,7,6,8]=>15
[4,8,3,7,1,6,2,5]=>[1,6,2,5,3,7,4,8]=>35
[3,8,4,7,1,6,2,5]=>[1,6,2,5,3,8,4,7]=>190
[1,6,2,8,4,7,3,5]=>[1,6,2,8,3,5,4,7]=>246
[3,7,1,6,2,8,4,5]=>[1,6,2,8,3,7,4,5]=>702
[4,8,1,6,2,7,3,5]=>[1,6,2,7,3,5,4,8]=>70
[5,8,1,6,2,7,3,4]=>[1,6,2,7,3,4,5,8]=>14
[7,8,1,5,2,6,3,4]=>[1,5,2,6,3,4,7,8]=>5
[7,8,2,5,1,6,3,4]=>[1,6,2,5,3,4,7,8]=>9
[6,8,2,5,1,7,3,4]=>[1,7,2,5,3,4,6,8]=>14
[5,8,2,6,1,7,3,4]=>[1,7,2,6,3,4,5,8]=>28
[4,8,2,6,1,7,3,5]=>[1,7,2,6,3,5,4,8]=>162
[1,7,3,6,2,8,4,5]=>[1,7,2,8,3,6,4,5]=>990
[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>1
[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>1
[6,7,4,8,3,5,1,2]=>[1,2,3,5,4,8,6,7]=>3
[6,7,4,5,2,8,1,3]=>[1,3,2,8,4,5,6,7]=>5
[5,7,4,6,3,8,1,2]=>[1,2,3,8,4,6,5,7]=>4
[5,7,4,8,3,6,1,2]=>[1,2,3,6,4,8,5,7]=>5
[6,8,4,5,3,7,1,2]=>[1,2,3,7,4,5,6,8]=>1
[5,8,4,6,3,7,1,2]=>[1,2,3,7,4,6,5,8]=>3
[5,6,4,8,3,7,1,2]=>[1,2,3,7,4,8,5,6]=>5
[5,6,3,7,2,8,1,4]=>[1,4,2,8,3,7,5,6]=>232
[5,6,3,8,2,7,1,4]=>[1,4,2,7,3,8,5,6]=>91
[5,6,4,8,2,7,1,3]=>[1,3,2,7,4,8,5,6]=>30
[5,8,4,6,2,7,1,3]=>[1,3,2,7,4,6,5,8]=>15
[6,8,4,5,2,7,1,3]=>[1,3,2,7,4,5,6,8]=>4
[7,8,4,5,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>3
[6,8,4,5,2,3,1,7]=>[1,7,2,3,4,5,6,8]=>1
[5,8,4,6,2,3,1,7]=>[1,7,2,3,4,6,5,8]=>5
[5,6,4,8,2,3,1,7]=>[1,7,2,3,4,8,5,6]=>14
[5,6,3,8,2,4,1,7]=>[1,7,2,4,3,8,5,6]=>92
[5,6,3,4,2,8,1,7]=>[1,7,2,8,3,4,5,6]=>42
[4,6,3,5,2,8,1,7]=>[1,7,2,8,3,5,4,6]=>288
[4,6,3,8,2,5,1,7]=>[1,7,2,5,3,8,4,6]=>282
[4,8,3,6,2,5,1,7]=>[1,7,2,5,3,6,4,8]=>64
[5,8,3,6,2,4,1,7]=>[1,7,2,4,3,6,5,8]=>29
[6,8,3,5,2,4,1,7]=>[1,7,2,4,3,5,6,8]=>5
[7,8,3,5,2,4,1,6]=>[1,6,2,4,3,5,7,8]=>4
[7,8,3,5,2,6,1,4]=>[1,4,2,6,3,5,7,8]=>5
[5,8,3,6,2,7,1,4]=>[1,4,2,7,3,6,5,8]=>40
[4,8,3,6,2,7,1,5]=>[1,5,2,7,3,6,4,8]=>56
[4,6,3,8,2,7,1,5]=>[1,5,2,7,3,8,4,6]=>168
[4,6,3,7,2,8,1,5]=>[1,5,2,8,3,7,4,6]=>534
[4,7,3,6,2,8,1,5]=>[1,5,2,8,3,6,4,7]=>134
[4,7,3,8,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>77
[5,7,4,8,2,6,1,3]=>[1,3,2,6,4,8,5,7]=>25
[5,7,3,6,2,8,1,4]=>[1,4,2,8,3,6,5,7]=>78
[6,7,3,5,2,8,1,4]=>[1,4,2,8,3,5,6,7]=>14
[6,7,4,8,2,5,1,3]=>[1,3,2,5,4,8,6,7]=>12
[6,7,5,8,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>3
[6,8,5,7,2,3,1,4]=>[1,4,2,3,5,7,6,8]=>3
[6,7,4,8,2,3,1,5]=>[1,5,2,3,4,8,6,7]=>10
[6,7,3,8,2,4,1,5]=>[1,5,2,4,3,8,6,7]=>45
[6,7,3,4,2,8,1,5]=>[1,5,2,8,3,4,6,7]=>28
[5,7,3,4,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>42
[5,7,4,8,2,3,1,6]=>[1,6,2,3,4,8,5,7]=>14
[5,8,4,7,2,3,1,6]=>[1,6,2,3,4,7,5,8]=>4
[6,8,4,7,2,3,1,5]=>[1,5,2,3,4,7,6,8]=>4
[7,8,4,6,2,3,1,5]=>[1,5,2,3,4,6,7,8]=>1
[7,8,3,6,2,4,1,5]=>[1,5,2,4,3,6,7,8]=>3
[6,8,3,7,2,4,1,5]=>[1,5,2,4,3,7,6,8]=>15
[5,8,3,7,2,4,1,6]=>[1,6,2,4,3,7,5,8]=>19
[4,8,3,7,2,5,1,6]=>[1,6,2,5,3,7,4,8]=>35
[4,7,3,8,2,5,1,6]=>[1,6,2,5,3,8,4,7]=>190
[4,7,3,5,2,8,1,6]=>[1,6,2,8,3,5,4,7]=>246
[4,5,3,7,2,8,1,6]=>[1,6,2,8,3,7,4,5]=>702
[4,5,3,8,2,7,1,6]=>[1,6,2,7,3,8,4,5]=>168
[4,8,3,5,2,7,1,6]=>[1,6,2,7,3,5,4,8]=>70
[5,8,3,4,2,7,1,6]=>[1,6,2,7,3,4,5,8]=>14
[6,8,3,4,2,7,1,5]=>[1,5,2,7,3,4,6,8]=>14
[7,8,3,4,2,6,1,5]=>[1,5,2,6,3,4,7,8]=>5
[6,8,3,4,2,5,1,7]=>[1,7,2,5,3,4,6,8]=>14
[5,8,3,4,2,6,1,7]=>[1,7,2,6,3,4,5,8]=>28
[4,8,3,5,2,6,1,7]=>[1,7,2,6,3,5,4,8]=>162
[4,5,3,8,2,6,1,7]=>[1,7,2,6,3,8,4,5]=>450
[4,5,3,6,2,8,1,7]=>[1,7,2,8,3,6,4,5]=>990
[4,8,5,2,1,7,6,3]=>[1,7,2,3,4,8,5,6]=>14
[5,4,6,1,3,2,8,7]=>[1,3,2,8,4,6,5,7]=>24
[4,6,8,1,7,3,2,5]=>[1,7,2,5,3,4,6,8]=>14
[7,4,8,1,6,5,3,2]=>[1,6,2,3,4,8,5,7]=>14
[8,4,5,3,1,7,6,2]=>[1,7,2,3,4,5,6,8]=>1
[6,4,8,1,7,5,2,3]=>[1,7,2,3,4,8,5,6]=>14
[8,5,7,6,4,2,1,3]=>[1,3,2,4,5,7,6,8]=>2
[6,3,2,8,7,4,1,5]=>[1,5,2,8,3,4,6,7]=>28
[2,1,7,8,6,4,5,3]=>[1,7,8,2,3,4,5,6]=>42
[5,8,7,6,3,2,1,4]=>[1,4,2,3,5,8,6,7]=>6
[6,7,4,2,8,1,5,3]=>[1,5,2,8,3,4,6,7]=>28
[6,8,4,2,7,5,1,3]=>[1,3,2,7,4,5,6,8]=>4
[8,6,4,3,7,5,1,2]=>[1,2,3,7,4,5,6,8]=>1
[7,6,5,8,1,4,3,2]=>[1,4,2,3,5,8,6,7]=>6
[8,6,5,7,4,1,3,2]=>[1,3,2,4,5,7,6,8]=>2
[5,2,8,7,4,6,1,3]=>[1,3,2,8,4,6,5,7]=>24
[1,6,2,5,4,7,3,8]=>[1,6,2,5,3,8,4,7]=>190
[7,1,5,3,4,8,6,2]=>[1,5,2,3,4,8,6,7]=>10
[8,5,2,1,4,3,7,6]=>[1,4,2,3,7,5,6,8]=>6
[8,5,6,4,2,1,7,3]=>[1,7,2,3,4,5,6,8]=>1
[7,2,5,8,3,1,6,4]=>[1,6,2,5,8,3,4,7]=>288
[8,7,2,6,3,4,1,5]=>[1,5,2,6,3,4,7,8]=>5
[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>1
[8,9,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>1
[8,7,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8]=>1
[9,10,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>1
[7,8,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,10,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,10,9]=>1
[8,6,7,9,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8]=>1
[1,7,3,2,8,6,4,5]=>[1,7,2,8,3,4,5,6]=>42
[8,2,5,1,7,3,4,6]=>[1,7,2,5,3,4,6,8]=>14
[6,2,8,3,5,1,7,4]=>[1,7,2,8,3,5,4,6]=>288
[7,8,2,1,4,3,5,6]=>[1,4,2,3,5,6,7,8]=>1
[5,7,2,3,1,6,8,4]=>[1,6,8,2,3,4,5,7]=>42
[8,2,5,4,6,7,1,3]=>[1,3,2,5,4,6,7,8]=>2
[8,2,6,4,3,1,7,5]=>[1,7,2,6,3,4,5,8]=>28
[8,2,7,4,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>14
[1,7,5,4,2,6,3,8]=>[1,7,2,6,3,8,4,5]=>450
[1,7,4,5,3,8,6,2]=>[1,7,2,3,8,4,5,6]=>28
[8,6,3,2,4,1,7,5]=>[1,7,2,4,3,5,6,8]=>5
[6,2,3,4,1,7,8,5]=>[1,7,8,2,3,4,5,6]=>42
[4,1,5,2,8,7,3,6]=>[1,5,2,8,3,6,4,7]=>134
[8,3,1,6,2,5,4,7]=>[1,6,2,5,3,4,7,8]=>9
[1,7,5,4,2,8,3,6]=>[1,7,2,8,3,6,4,5]=>990
[1,7,4,5,2,8,3,6]=>[1,7,2,8,3,6,4,5]=>990
[1,4,2,8,6,7,3,5]=>[1,4,2,8,3,5,6,7]=>14
[2,1,7,6,3,4,8,5]=>[1,7,2,3,4,8,5,6]=>14
[1,4,2,7,6,8,3,5]=>[1,4,2,7,3,5,6,8]=>9
[1,4,2,7,3,8,6,5]=>[1,4,2,7,3,8,5,6]=>91
[3,1,7,2,8,6,4,5]=>[1,7,2,8,3,4,5,6]=>42
[1,2,3,8,7,5,6,4]=>[1,2,3,8,4,5,6,7]=>1
[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8,9,10]=>1
[5,7,8,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>3
[6,7,8,4,2,5,1,3]=>[1,3,2,5,4,6,7,8]=>2
[6,7,8,3,2,1,5,4]=>[1,5,2,3,4,6,7,8]=>1
[5,7,8,3,2,1,6,4]=>[1,6,2,3,4,5,7,8]=>1
[3,6,4,8,2,5,1,7]=>[1,7,2,5,3,6,4,8]=>64
[8,4,3,2,1,6,5,7]=>[1,6,2,3,4,5,7,8]=>1
[6,4,3,2,1,7,5,8]=>[1,7,2,3,4,5,8,6]=>5
[3,5,4,2,8,6,1,7]=>[1,7,2,8,3,5,4,6]=>288
[8,4,3,2,1,7,5,6]=>[1,7,2,3,4,5,6,8]=>1
[8,4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6,8]=>1
[5,6,3,8,2,1,7,4]=>[1,7,2,3,8,4,5,6]=>28
[7,5,3,2,8,1,6,4]=>[1,6,2,8,3,4,5,7]=>42
[8,5,4,2,7,6,1,3]=>[1,3,2,7,4,5,6,8]=>4
[7,5,4,2,8,6,1,3]=>[1,3,2,8,4,5,6,7]=>5
[6,5,4,2,8,7,1,3]=>[1,3,2,8,4,5,6,7]=>5
[8,5,3,2,6,1,7,4]=>[1,7,2,6,3,4,5,8]=>28
[3,6,4,7,2,8,1,5]=>[1,5,2,8,3,6,4,7]=>134
[7,4,3,2,1,6,8,5]=>[1,6,8,2,3,4,5,7]=>42
[8,4,3,2,1,6,7,5]=>[1,6,7,2,3,4,5,8]=>14
[7,4,3,2,1,5,8,6]=>[1,5,8,2,3,4,6,7]=>28
[6,4,3,2,1,5,8,7]=>[1,5,8,2,3,4,6,7]=>28
[2,1,7,8,5,6,3,4]=>[1,7,8,2,3,4,5,6]=>42
[6,8,3,7,5,1,4,2]=>[1,4,2,3,7,5,6,8]=>6
[5,7,3,8,1,6,2,4]=>[1,6,2,4,3,8,5,7]=>78
[3,5,2,4,1,7,6,8]=>[1,7,2,4,3,5,6,8]=>5
[3,1,5,4,2,8,6,7]=>[1,5,2,8,3,4,6,7]=>28
[3,5,1,4,2,7,6,8]=>[1,4,2,7,3,5,6,8]=>9
[5,3,1,4,2,7,6,8]=>[1,4,2,7,3,5,6,8]=>9
[6,3,4,1,2,7,5,8]=>[1,2,7,3,4,5,8,6]=>4
[4,6,7,2,3,1,5,8]=>[1,5,8,2,3,4,6,7]=>28
[6,4,5,1,7,2,3,8]=>[1,7,2,3,8,4,5,6]=>28
[2,4,1,5,3,8,7,6]=>[1,5,2,4,3,8,6,7]=>45
[3,4,5,8,2,1,7,6]=>[1,7,2,3,4,5,8,6]=>5
[3,4,5,2,8,1,7,6]=>[1,7,2,8,3,4,5,6]=>42
[3,4,6,2,1,7,5,8]=>[1,7,2,3,4,6,5,8]=>5
[3,4,6,2,8,7,1,5]=>[1,5,2,8,3,4,6,7]=>28
[3,4,6,8,2,7,1,5]=>[1,5,2,7,3,4,6,8]=>14
[4,5,6,7,8,1,3,2]=>[1,3,2,4,5,6,7,8]=>1
[4,5,6,7,1,3,2,8]=>[1,3,2,8,4,5,6,7]=>5
[8,2,5,3,7,1,6,4]=>[1,6,2,5,3,7,4,8]=>35
[8,2,4,3,7,1,6,5]=>[1,6,2,4,3,7,5,8]=>19
[5,8,2,4,3,7,1,6]=>[1,6,2,4,3,7,5,8]=>19
[3,2,5,1,7,4,6,8]=>[1,7,2,5,3,4,6,8]=>14
[5,8,6,1,7,3,4,2]=>[1,7,2,3,4,5,8,6]=>5
[3,2,5,1,6,4,7,8]=>[1,6,2,5,3,4,7,8]=>9
[3,8,6,5,1,7,4,2]=>[1,7,2,3,8,4,5,6]=>28
[6,5,1,7,8,4,2,3]=>[1,7,8,2,3,4,5,6]=>42
[3,2,4,1,7,5,6,8]=>[1,7,2,4,3,5,6,8]=>5
[6,5,1,7,4,2,3,8]=>[1,7,2,3,8,4,5,6]=>28
[8,5,6,1,7,3,4,2]=>[1,7,2,3,4,5,6,8]=>1
[8,5,1,6,7,4,2,3]=>[1,6,7,2,3,4,5,8]=>14
[7,8,5,1,6,4,2,3]=>[1,6,2,3,4,5,7,8]=>1
[3,8,5,1,7,6,4,2]=>[1,7,2,3,8,4,5,6]=>28
[8,7,5,1,6,4,2,3]=>[1,6,2,3,4,5,7,8]=>1
[4,2,6,1,7,5,3,8]=>[1,7,2,6,3,8,4,5]=>450
[6,4,3,8,5,1,7,2]=>[1,7,2,3,8,4,5,6]=>28
[2,5,4,6,1,7,3,8]=>[1,7,2,5,3,8,4,6]=>282
[2,5,4,6,8,1,7,3]=>[1,7,2,5,3,4,6,8]=>14
[2,4,1,7,5,3,8,6]=>[1,7,2,4,3,8,5,6]=>92
[3,5,2,8,1,6,4,7]=>[1,6,2,8,3,5,4,7]=>246
[6,5,2,1,7,8,4,3]=>[1,7,8,2,3,4,5,6]=>42
[2,1,7,5,3,8,6,4]=>[1,7,2,3,8,4,5,6]=>28
[2,4,1,7,3,8,6,5]=>[1,7,2,4,3,8,5,6]=>92
[3,5,2,8,1,7,4,6]=>[1,7,2,8,3,5,4,6]=>288
[6,2,3,1,5,4,8,7]=>[1,5,2,3,4,8,6,7]=>10
[8,4,5,2,3,1,7,6]=>[1,7,2,3,4,5,6,8]=>1
[8,2,5,3,4,1,7,6]=>[1,7,2,5,3,4,6,8]=>14
[6,1,5,2,4,3,8,7]=>[1,5,2,4,3,8,6,7]=>45
[6,4,5,1,3,2,8,7]=>[1,3,2,8,4,5,6,7]=>5
[6,1,5,3,4,2,8,7]=>[1,5,2,8,3,4,6,7]=>28
[6,3,5,1,4,2,8,7]=>[1,4,2,8,3,5,6,7]=>14
[8,3,5,2,4,1,7,6]=>[1,7,2,4,3,5,6,8]=>5
[8,3,7,2,4,1,6,5]=>[1,6,2,4,3,7,5,8]=>19
[8,3,5,1,4,2,7,6]=>[1,4,2,7,3,5,6,8]=>9
[8,1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6,8]=>14
[8,4,5,1,3,2,7,6]=>[1,3,2,7,4,5,6,8]=>4
[8,6,7,4,5,1,3,2]=>[1,3,2,4,5,6,7,8]=>1
[8,6,7,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>1
[8,6,7,3,5,1,4,2]=>[1,4,2,3,5,6,7,8]=>1
[8,3,7,5,6,1,4,2]=>[1,4,2,3,7,5,6,8]=>6
[8,1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6,8]=>1
[8,1,7,3,4,2,6,5]=>[1,7,2,6,3,4,5,8]=>28
[8,1,7,3,6,2,5,4]=>[1,7,2,5,3,6,4,8]=>64
[8,3,7,1,6,2,5,4]=>[1,6,2,5,3,7,4,8]=>35
[8,2,7,3,6,1,5,4]=>[1,5,2,7,3,6,4,8]=>56
[8,2,7,1,6,3,5,4]=>[1,6,2,7,3,5,4,8]=>70
[8,1,7,2,4,3,6,5]=>[1,7,2,4,3,6,5,8]=>29
[8,1,3,2,7,4,6,5]=>[1,3,2,7,4,6,5,8]=>15
[8,1,5,2,4,3,7,6]=>[1,5,2,4,3,7,6,8]=>15
[8,2,7,1,4,3,6,5]=>[1,4,2,7,3,6,5,8]=>40
[8,2,7,3,4,1,6,5]=>[1,6,2,7,3,4,5,8]=>14
[8,4,7,2,3,1,6,5]=>[1,6,2,3,4,7,5,8]=>4
[8,2,3,1,7,4,6,5]=>[1,7,2,3,4,6,5,8]=>5
[8,2,3,1,5,4,7,6]=>[1,5,2,3,4,7,6,8]=>4
[4,1,3,2,8,6,7,5]=>[1,3,2,8,4,5,6,7]=>5
[8,6,7,2,3,1,5,4]=>[1,5,2,3,4,6,7,8]=>1
[8,2,3,1,7,5,6,4]=>[1,7,2,3,4,5,6,8]=>1
[8,5,7,2,6,1,4,3]=>[1,4,2,6,3,5,7,8]=>5
[8,2,7,5,6,1,4,3]=>[1,4,2,7,3,5,6,8]=>9
[8,6,7,2,5,1,4,3]=>[1,4,2,5,3,6,7,8]=>2
[8,6,7,1,5,2,4,3]=>[1,5,2,4,3,6,7,8]=>3
[8,6,7,1,3,2,5,4]=>[1,3,2,5,4,6,7,8]=>2
[8,1,3,2,7,5,6,4]=>[1,3,2,7,4,5,6,8]=>4
[8,1,7,5,6,2,4,3]=>[1,7,2,4,3,5,6,8]=>5
[8,1,7,2,6,4,5,3]=>[1,7,2,6,3,4,5,8]=>28
[8,2,7,1,6,4,5,3]=>[1,6,2,7,3,4,5,8]=>14
[8,2,7,4,6,1,5,3]=>[1,5,2,7,3,4,6,8]=>14
[8,4,7,2,6,1,5,3]=>[1,5,2,6,3,4,7,8]=>5
[8,4,7,1,6,2,5,3]=>[1,6,2,5,3,4,7,8]=>9
[8,1,7,4,6,2,5,3]=>[1,7,2,5,3,4,6,8]=>14
[8,5,7,1,6,2,4,3]=>[1,6,2,4,3,5,7,8]=>4
[8,5,7,1,6,3,4,2]=>[1,6,2,3,4,5,7,8]=>1
[4,5,8,6,3,2,7,1]=>[1,2,7,3,4,5,8,6]=>4
[6,7,2,8,4,1,5,3]=>[1,5,2,8,3,4,6,7]=>28
[3,1,6,8,4,5,7,2]=>[1,6,8,2,3,4,5,7]=>42
[2,8,3,7,1,6,5,4]=>[1,6,2,8,3,7,4,5]=>702
[5,2,8,7,3,6,1,4]=>[1,4,2,8,3,6,5,7]=>78
[6,2,8,5,4,3,1,7]=>[1,7,2,8,3,4,5,6]=>42
[6,4,8,5,2,3,1,7]=>[1,7,2,3,4,8,5,6]=>14
[1,7,5,8,3,4,6,2]=>[1,7,2,3,4,6,5,8]=>5
[5,6,8,1,4,3,2,7]=>[1,4,2,7,3,5,6,8]=>9
[7,5,8,6,3,4,2,1]=>[1,2,3,4,5,8,6,7]=>1
[5,6,8,4,1,3,2,7]=>[1,3,2,7,4,5,6,8]=>4
[4,6,8,1,5,3,2,7]=>[1,5,2,7,3,4,6,8]=>14
[5,7,8,4,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>1
[2,8,7,4,1,6,5,3]=>[1,6,2,8,3,4,5,7]=>42
[6,5,8,4,2,3,1,7]=>[1,7,2,3,4,5,8,6]=>5
[4,1,3,2,8,5,6,7]=>[1,3,2,8,4,5,6,7]=>5
[1,4,3,2,8,5,6,7]=>[1,4,2,8,3,5,6,7]=>14
[6,2,8,4,5,3,1,7]=>[1,7,2,8,3,4,5,6]=>42
[7,2,3,8,5,4,6,1]=>[1,2,3,8,4,6,5,7]=>4
[2,8,1,5,4,7,3,6]=>[1,5,2,8,3,6,4,7]=>134
[2,8,1,4,3,7,6,5]=>[1,4,2,8,3,7,5,6]=>232
[3,6,4,8,1,7,2,5]=>[1,7,2,5,3,6,4,8]=>64
[7,6,1,4,2,8,3,5]=>[1,4,2,8,3,5,6,7]=>14
[7,1,6,2,8,4,3,5]=>[1,6,2,8,3,5,4,7]=>246
[6,7,1,4,2,8,3,5]=>[1,4,2,8,3,5,6,7]=>14
[1,7,2,8,4,5,3,6]=>[1,7,2,8,3,6,4,5]=>990
[2,8,1,7,3,5,4,6]=>[1,7,2,8,3,5,4,6]=>288
[4,2,8,1,7,3,6,5]=>[1,7,2,8,3,6,4,5]=>990
[2,8,1,7,4,3,6,5]=>[1,7,2,8,3,6,4,5]=>990
[8,6,1,4,2,7,3,5]=>[1,4,2,7,3,5,6,8]=>9
[8,1,6,2,7,4,3,5]=>[1,6,2,7,3,5,4,8]=>70
[3,7,4,8,1,6,2,5]=>[1,6,2,5,3,7,4,8]=>35
[4,2,8,1,7,6,3,5]=>[1,7,2,8,3,5,4,6]=>288
[2,8,1,7,6,4,3,5]=>[1,7,2,8,3,5,4,6]=>288
[7,8,3,4,1,5,2,6]=>[1,5,2,6,3,4,7,8]=>5
[7,8,3,4,1,6,2,5]=>[1,6,2,5,3,4,7,8]=>9
[6,8,3,4,1,7,2,5]=>[1,7,2,5,3,4,6,8]=>14
[5,8,3,4,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>28
[5,8,3,4,1,6,2,7]=>[1,6,2,7,3,4,5,8]=>14
[6,8,3,4,1,5,2,7]=>[1,5,2,7,3,4,6,8]=>14
[6,7,3,4,1,5,2,8]=>[1,5,2,8,3,4,6,7]=>28
[5,7,3,4,1,6,2,8]=>[1,6,2,8,3,4,5,7]=>42
[5,6,2,8,3,4,1,7]=>[1,7,2,8,3,4,5,6]=>42
[4,6,2,8,3,5,1,7]=>[1,7,2,8,3,5,4,6]=>288
[4,7,3,5,1,6,2,8]=>[1,6,2,8,3,5,4,7]=>246
[4,8,3,5,1,6,2,7]=>[1,6,2,7,3,5,4,8]=>70
[4,8,3,5,1,7,2,6]=>[1,7,2,6,3,5,4,8]=>162
[5,6,2,3,1,7,4,8]=>[1,7,2,3,4,8,5,6]=>14
[5,6,2,4,1,7,3,8]=>[1,7,2,4,3,8,5,6]=>92
[4,6,2,5,1,7,3,8]=>[1,7,2,5,3,8,4,6]=>282
[4,5,1,7,3,8,2,6]=>[1,7,2,6,3,8,4,5]=>450
[4,6,2,7,3,8,1,5]=>[1,5,2,7,3,8,4,6]=>168
[5,6,2,7,3,8,1,4]=>[1,4,2,7,3,8,5,6]=>91
[5,6,2,7,4,8,1,3]=>[1,3,2,7,4,8,5,6]=>30
[5,6,3,8,4,7,1,2]=>[1,2,3,8,4,7,5,6]=>9
[5,6,2,8,4,7,1,3]=>[1,3,2,8,4,7,5,6]=>63
[5,6,2,8,3,7,1,4]=>[1,4,2,8,3,7,5,6]=>232
[4,6,2,8,3,7,1,5]=>[1,5,2,8,3,7,4,6]=>534
[4,5,1,7,3,6,2,8]=>[1,7,2,8,3,6,4,5]=>990
[8,7,3,5,2,4,1,6]=>[1,6,2,4,3,5,7,8]=>4
[2,8,7,4,3,6,1,5]=>[1,5,2,8,3,6,4,7]=>134
[8,1,7,4,3,6,2,5]=>[1,7,2,5,3,6,4,8]=>64
[8,7,3,5,1,4,2,6]=>[1,4,2,6,3,5,7,8]=>5
[2,1,6,8,5,7,4,3]=>[1,6,8,2,3,4,5,7]=>42
[3,8,7,4,1,6,2,5]=>[1,6,2,5,3,8,4,7]=>190
[8,7,1,4,2,6,3,5]=>[1,4,2,6,3,5,7,8]=>5
[8,7,2,4,1,6,3,5]=>[1,6,2,4,3,5,7,8]=>4
[6,8,3,5,1,7,2,4]=>[1,7,2,4,3,5,6,8]=>5
[5,8,3,1,6,2,7,4]=>[1,6,2,7,3,4,5,8]=>14
[4,5,3,8,6,1,7,2]=>[1,7,2,3,8,4,5,6]=>28
[6,7,2,3,5,4,8,1]=>[1,2,3,5,4,8,6,7]=>3
[8,3,4,7,6,1,5,2]=>[1,5,2,3,4,7,6,8]=>4
[6,7,1,3,5,8,4,2]=>[1,3,5,8,2,4,6,7]=>35
[8,1,3,2,7,6,5,4]=>[1,3,2,7,4,5,6,8]=>4
[2,8,3,1,7,6,5,4]=>[1,7,2,8,3,4,5,6]=>42
[3,8,2,1,7,6,5,4]=>[1,7,2,3,8,4,5,6]=>28
[8,2,3,1,7,6,5,4]=>[1,7,2,3,4,5,6,8]=>1
[8,3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6,8]=>1
[3,4,1,7,6,8,5,2]=>[1,7,2,3,4,5,6,8]=>1
[8,4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5,8]=>14
[8,5,7,2,1,6,4,3]=>[1,6,2,3,4,5,7,8]=>1
[6,7,4,5,8,1,3,2]=>[1,3,2,4,5,8,6,7]=>3
[8,4,1,7,2,6,5,3]=>[1,7,2,6,3,4,5,8]=>28
[3,4,8,7,6,1,5,2]=>[1,5,2,3,4,8,6,7]=>10
[6,7,2,8,1,5,4,3]=>[1,5,2,8,3,4,6,7]=>28
[4,2,8,7,1,6,5,3]=>[1,6,2,8,3,4,5,7]=>42
[3,2,8,1,7,6,5,4]=>[1,7,2,8,3,4,5,6]=>42
[8,1,2,3,7,6,5,4]=>[1,2,3,7,4,5,6,8]=>1
[7,3,1,4,2,8,6,5]=>[1,4,2,8,3,5,6,7]=>14
[2,7,1,4,3,8,6,5]=>[1,4,2,7,3,8,5,6]=>91
[3,7,1,4,2,8,6,5]=>[1,4,2,8,3,7,5,6]=>232
[4,7,1,3,2,8,6,5]=>[1,3,2,8,4,7,5,6]=>63
[4,7,1,2,3,8,6,5]=>[1,2,3,8,4,7,5,6]=>9
[8,1,5,2,7,3,6,4]=>[1,5,2,7,3,6,4,8]=>56
[8,1,4,2,3,7,6,5]=>[1,4,2,3,7,5,6,8]=>6
[7,4,1,2,3,8,6,5]=>[1,2,3,8,4,5,6,7]=>1
[2,4,3,6,5,8,1,7]=>[1,7,2,4,3,6,5,8]=>29
[2,4,1,6,5,3,8,7]=>[1,6,2,4,3,8,5,7]=>78
[4,2,6,5,8,1,7,3]=>[1,7,2,6,3,4,5,8]=>28
[4,2,6,5,8,3,1,7]=>[1,7,2,6,3,4,5,8]=>28
[2,4,1,6,5,8,3,7]=>[1,6,2,4,3,7,5,8]=>19
[2,6,4,3,8,7,1,5]=>[1,5,2,6,3,8,4,7]=>77
[4,6,5,2,8,7,1,3]=>[1,3,2,8,4,6,5,7]=>24
[2,4,1,6,3,8,7,5]=>[1,6,2,4,3,8,5,7]=>78
[4,6,2,8,5,7,1,3]=>[1,3,2,8,4,6,5,7]=>24
[2,1,6,4,8,7,5,3]=>[1,6,2,3,4,8,5,7]=>14
[2,6,4,8,1,7,3,5]=>[1,7,2,6,3,5,4,8]=>162
[6,4,2,8,7,5,1,3]=>[1,3,2,8,4,5,6,7]=>5
[1,6,4,7,3,8,2,5]=>[1,6,2,5,3,8,4,7]=>190
[4,3,1,7,5,8,2,6]=>[1,7,2,6,3,4,5,8]=>28
[5,8,2,1,7,3,4,6]=>[1,7,2,3,4,6,5,8]=>5
[1,5,3,2,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>28
[8,3,2,1,5,4,6,7]=>[1,5,2,3,4,6,7,8]=>1
[8,3,2,1,6,4,5,7]=>[1,6,2,3,4,5,7,8]=>1
[8,4,2,5,1,6,3,7]=>[1,6,2,5,3,7,4,8]=>35
[4,8,2,5,1,7,3,6]=>[1,7,2,5,3,6,4,8]=>64
[3,2,1,7,5,8,6,4]=>[1,7,2,3,4,5,8,6]=>5
[4,2,8,6,1,7,3,5]=>[1,7,2,8,3,5,4,6]=>288
[3,8,2,1,7,4,5,6]=>[1,7,2,3,8,4,5,6]=>28
[3,2,1,6,8,5,7,4]=>[1,6,8,2,3,4,5,7]=>42
[5,3,6,4,8,7,1,2]=>[1,2,3,6,4,8,5,7]=>5
[6,3,7,5,4,8,1,2]=>[1,2,3,7,4,8,5,6]=>5
[7,3,8,5,4,6,1,2]=>[1,2,3,8,4,6,5,7]=>4
[3,8,7,5,4,6,1,2]=>[1,2,3,8,4,6,5,7]=>4
[4,5,6,3,8,7,1,2]=>[1,2,3,8,4,5,6,7]=>1
[6,8,3,5,4,7,1,2]=>[1,2,3,5,4,7,6,8]=>2
[7,6,3,5,4,8,1,2]=>[1,2,3,5,4,8,6,7]=>3
[6,2,1,5,4,8,7,3]=>[1,5,2,3,4,8,6,7]=>10
[4,1,6,2,8,7,5,3]=>[1,6,2,8,3,4,5,7]=>42
[7,8,3,1,4,2,6,5]=>[1,4,2,6,3,5,7,8]=>5
[7,5,1,6,4,3,2,8]=>[1,6,2,8,3,4,5,7]=>42
[5,8,1,6,4,3,2,7]=>[1,6,2,7,3,4,5,8]=>14
[7,8,4,1,5,3,2,6]=>[1,5,2,6,3,4,7,8]=>5
[7,8,5,1,6,3,2,4]=>[1,6,2,4,3,5,7,8]=>4
[6,8,1,7,4,3,2,5]=>[1,7,2,5,3,4,6,8]=>14
[5,6,1,7,4,3,2,8]=>[1,7,2,8,3,4,5,6]=>42
[5,1,7,6,4,3,2,8]=>[1,7,2,8,3,4,5,6]=>42
[2,1,7,5,6,3,8,4]=>[1,7,2,3,8,4,5,6]=>28
[7,8,1,6,5,3,2,4]=>[1,6,2,4,3,5,7,8]=>4
[2,8,1,5,4,6,7,3]=>[1,5,2,8,3,4,6,7]=>28
[4,1,7,5,2,3,8,6]=>[1,7,2,3,8,4,5,6]=>28
[2,8,3,5,4,1,7,6]=>[1,7,2,8,3,5,4,6]=>288
[4,2,6,3,8,1,7,5]=>[1,7,2,6,3,8,4,5]=>450
[7,8,2,3,4,1,6,5]=>[1,6,2,3,4,5,7,8]=>1
[3,1,6,4,7,8,2,5]=>[1,6,2,5,3,4,7,8]=>9
[7,8,4,6,1,3,2,5]=>[1,3,2,5,4,6,7,8]=>2
[7,8,5,4,1,3,2,6]=>[1,3,2,6,4,5,7,8]=>3
[1,6,5,8,4,3,2,7]=>[1,6,2,7,3,4,5,8]=>14
[6,8,5,1,4,3,2,7]=>[1,4,2,7,3,5,6,8]=>9
[7,6,5,1,4,3,2,8]=>[1,4,2,8,3,5,6,7]=>14
[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9]=>1
[7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9]=>1
[6,7,8,9,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>1
[9,6,7,8,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>1
[8,9,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>1
[9,5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>1
[8,9,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>1
[9,7,8,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>1
[7,8,9,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>1
[9,7,8,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>1
[8,9,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>1
[9,7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7,8,9]=>1
[9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9]=>1
[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8,9,10]=>1
[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9,10]=>1
[7,8,9,10,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>1
[9,10,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,6,7,8,9,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>1
[9,10,6,7,8,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,6,7,8,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,8,9,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>1
[9,10,5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>1
[8,9,10,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>1
[9,10,7,8,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,7,8,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,7,8,9,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>1
[9,10,7,8,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,7,8,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,8,9,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>1
[9,10,7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>1
[5,3,6,4,1,7,2,8]=>[1,7,2,8,3,6,4,5]=>990
[2,7,5,4,1,6,3,8]=>[1,6,2,7,3,8,4,5]=>168
[7,5,4,6,2,8,1,3]=>[1,3,2,8,4,6,5,7]=>24
[1,7,5,4,3,8,6,2]=>[1,7,2,3,8,4,5,6]=>28
[8,5,6,3,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>9
[2,5,4,1,6,3,8,7]=>[1,6,2,5,3,8,4,7]=>190
[7,3,2,8,5,1,6,4]=>[1,6,2,8,3,4,5,7]=>42
[8,4,6,3,2,1,7,5]=>[1,7,2,3,4,6,5,8]=>5
[8,6,4,3,2,1,7,5]=>[1,7,2,3,4,5,6,8]=>1
[7,8,4,3,2,1,6,5]=>[1,6,2,3,4,5,7,8]=>1
[5,7,3,2,1,6,8,4]=>[1,6,8,2,3,4,5,7]=>42
[5,7,3,2,1,6,4,8]=>[1,6,2,3,4,8,5,7]=>14
[6,7,8,3,5,2,1,4]=>[1,4,2,3,5,6,7,8]=>1
[3,2,6,1,7,4,5,8]=>[1,7,2,6,3,4,5,8]=>28
[1,7,9,8,6,5,4,3,2]=>[1,7,9,2,3,4,5,6,8]=>132
[7,8,3,5,4,6,1,2]=>[1,2,3,5,4,6,7,8]=>1
[5,4,1,6,3,2,8,7]=>[1,6,2,8,3,4,5,7]=>42
[5,7,1,6,2,8,3,4]=>[1,6,2,8,3,4,5,7]=>42
[5,7,1,6,2,8,4,3]=>[1,6,2,8,3,4,5,7]=>42
[2,1,7,6,3,8,5,4]=>[1,7,2,3,8,4,5,6]=>28
[2,1,7,6,3,8,4,5]=>[1,7,2,3,8,4,5,6]=>28
[2,3,4,8,7,6,1,5]=>[1,5,2,3,4,8,6,7]=>10
[2,3,4,8,5,7,1,6]=>[1,6,2,3,4,8,5,7]=>14
[2,3,4,8,7,5,1,6]=>[1,6,2,3,4,8,5,7]=>14
[2,7,6,5,4,8,1,3]=>[1,3,2,7,4,8,5,6]=>30
[6,4,1,5,8,7,2,3]=>[1,5,8,2,3,4,6,7]=>28
[6,4,1,5,8,7,3,2]=>[1,5,8,2,3,4,6,7]=>28
[5,7,1,6,3,8,2,4]=>[1,6,2,4,3,8,5,7]=>78
[2,7,6,4,5,8,3,1]=>[1,2,7,3,4,5,8,6]=>4
[7,3,5,4,8,6,2,1]=>[1,2,3,5,4,8,6,7]=>3
[2,3,4,8,5,6,1,7]=>[1,7,2,3,4,8,5,6]=>14
[2,3,4,8,7,1,6,5]=>[1,6,2,3,4,8,5,7]=>14
[2,3,4,8,1,7,6,5]=>[1,7,2,3,4,8,5,6]=>14
[2,3,4,8,5,1,7,6]=>[1,7,2,3,4,8,5,6]=>14
[2,3,4,8,1,6,5,7]=>[1,6,2,3,4,8,5,7]=>14
[7,8,2,6,1,5,3,4]=>[1,5,2,6,3,4,7,8]=>5
[7,8,1,6,2,5,3,4]=>[1,6,2,5,3,4,7,8]=>9
[5,8,1,7,2,6,3,4]=>[1,7,2,6,3,4,5,8]=>28
[5,8,2,7,1,6,3,4]=>[1,6,2,7,3,4,5,8]=>14
[2,8,6,7,1,5,3,4]=>[1,5,2,8,3,4,6,7]=>28
[2,8,5,7,1,6,3,4]=>[1,6,2,8,3,4,5,7]=>42
[2,8,1,7,5,6,3,4]=>[1,7,2,8,3,4,5,6]=>42
[2,8,1,7,4,6,3,5]=>[1,7,2,8,3,5,4,6]=>288
[2,8,4,7,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>246
[4,8,2,7,1,6,3,5]=>[1,6,2,7,3,5,4,8]=>70
[4,8,1,7,2,6,3,5]=>[1,7,2,6,3,5,4,8]=>162
[4,8,1,7,5,6,2,3]=>[1,7,2,3,4,8,5,6]=>14
[3,8,1,7,5,6,2,4]=>[1,7,2,4,3,8,5,6]=>92
[3,8,1,7,4,6,2,5]=>[1,7,2,5,3,8,4,6]=>282
[3,8,1,7,2,6,4,5]=>[1,7,2,6,3,8,4,5]=>450
[3,8,2,7,1,6,4,5]=>[1,6,2,7,3,8,4,5]=>168
[3,8,2,7,4,6,1,5]=>[1,5,2,7,3,8,4,6]=>168
[3,8,2,7,5,6,1,4]=>[1,4,2,7,3,8,5,6]=>91
[4,8,2,7,5,6,1,3]=>[1,3,2,7,4,8,5,6]=>30
[4,8,3,7,5,6,1,2]=>[1,2,3,7,4,8,5,6]=>5
[3,8,4,7,5,6,1,2]=>[1,2,3,8,4,7,5,6]=>9
[2,8,4,7,5,6,1,3]=>[1,3,2,8,4,7,5,6]=>63
[2,8,3,7,5,6,1,4]=>[1,4,2,8,3,7,5,6]=>232
[2,8,3,7,4,6,1,5]=>[1,5,2,8,3,7,4,6]=>534
[2,8,3,7,1,6,4,5]=>[1,6,2,8,3,7,4,5]=>702
[2,8,1,7,3,6,4,5]=>[1,7,2,8,3,6,4,5]=>990
[7,5,2,8,6,4,1,3]=>[1,3,2,8,4,5,6,7]=>5
[7,4,8,6,1,5,2,3]=>[1,5,2,3,4,8,6,7]=>10
[6,8,1,7,4,2,5,3]=>[1,7,2,5,3,4,6,8]=>14
[7,3,8,6,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>20
[7,2,8,4,1,5,3,6]=>[1,5,2,8,3,6,4,7]=>134
[7,2,8,3,5,1,6,4]=>[1,6,2,8,3,5,4,7]=>246
[7,2,8,3,4,6,1,5]=>[1,5,2,8,3,4,6,7]=>28
[3,1,5,4,7,8,2,6]=>[1,5,2,6,3,4,7,8]=>5
[6,3,8,2,5,1,7,4]=>[1,7,2,5,3,8,4,6]=>282
[5,8,1,4,2,6,3,7]=>[1,4,2,6,3,7,5,8]=>16
[5,8,4,1,2,7,6,3]=>[1,2,7,3,4,5,8,6]=>4
[6,5,3,1,4,2,8,7]=>[1,4,2,8,3,5,6,7]=>14
[5,2,6,4,1,7,3,8]=>[1,7,2,6,3,8,4,5]=>450
[4,5,1,7,2,6,3,8]=>[1,7,2,6,3,8,4,5]=>450
[3,4,5,8,2,7,1,6]=>[1,6,2,7,3,4,5,8]=>14
[4,1,6,5,8,3,2,7]=>[1,6,2,7,3,4,5,8]=>14
[2,7,1,5,4,3,8,6]=>[1,5,2,7,3,8,4,6]=>168
[8,5,6,7,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>1
[8,4,6,1,7,3,2,5]=>[1,7,2,5,3,4,6,8]=>14
[2,7,6,1,4,3,8,5]=>[1,4,2,7,3,8,5,6]=>91
[6,7,8,5,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>1
[5,7,6,8,2,3,4,1]=>[1,2,3,4,5,7,6,8]=>1
[5,7,3,8,4,6,2,1]=>[1,2,3,8,4,6,5,7]=>4
[8,7,3,5,1,6,2,4]=>[1,6,2,4,3,5,7,8]=>4
[5,7,6,8,4,1,2,3]=>[1,2,3,4,5,7,6,8]=>1
[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,7,9,8]=>1
[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,8,10,9]=>1
[10,1,2,3,4,5,6,7,8,9,11]=>[1,2,3,4,5,6,7,8,9,11,10]=>1
[1,7,9,2,3,4,5,6,8]=>[1,7,9,2,3,4,5,6,8]=>132
[3,6,4,8,7,5,1,2]=>[1,2,3,6,4,8,5,7]=>5
[5,6,4,3,8,7,1,2]=>[1,2,3,8,4,5,6,7]=>1
[7,3,8,4,5,6,1,2]=>[1,2,3,8,4,5,6,7]=>1
[1,6,5,4,2,8,7,3]=>[1,6,2,8,3,4,5,7]=>42
[7,8,1,4,2,6,5,3]=>[1,4,2,6,3,5,7,8]=>5
[7,4,5,3,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>42
[5,8,3,6,1,4,2,7]=>[1,4,2,7,3,6,5,8]=>40
[1,6,3,8,5,7,2,4]=>[1,6,2,4,3,8,5,7]=>78
[2,6,4,1,7,5,8,3]=>[1,7,2,6,3,4,5,8]=>28
[7,6,5,8,1,4,2,3]=>[1,4,2,3,5,8,6,7]=>6
[5,8,6,7,3,2,1,4]=>[1,4,2,3,5,8,6,7]=>6
[1,6,4,3,7,2,8,5]=>[1,6,2,8,3,7,4,5]=>702
[4,1,6,3,8,2,7,5]=>[1,6,2,7,3,8,4,5]=>168
[3,2,6,4,7,8,1,5]=>[1,5,2,6,3,4,7,8]=>5
[2,8,5,7,4,3,1,6]=>[1,6,2,8,3,4,5,7]=>42
[7,2,5,8,3,4,1,6]=>[1,6,2,5,8,3,4,7]=>288
[6,5,3,8,2,1,7,4]=>[1,7,2,3,8,4,5,6]=>28
[2,6,4,5,3,8,1,7]=>[1,7,2,6,3,8,4,5]=>450
[5,6,8,4,2,3,1,7]=>[1,7,2,3,4,5,6,8]=>1
[6,7,5,8,2,1,4,3]=>[1,4,2,3,5,8,6,7]=>6
[1,7,5,8,2,6,4,3]=>[1,7,2,6,3,4,5,8]=>28
[5,1,7,6,8,4,2,3]=>[1,7,2,3,4,5,6,8]=>1
[7,2,5,8,1,6,4,3]=>[1,6,2,5,8,3,4,7]=>288
[5,2,8,6,1,7,3,4]=>[1,7,2,8,3,4,5,6]=>42
[8,5,2,6,3,7,1,4]=>[1,4,2,6,3,7,5,8]=>16
[8,1,6,5,7,3,2,4]=>[1,6,2,4,3,5,7,8]=>4
[5,8,1,6,3,7,2,4]=>[1,6,2,4,3,7,5,8]=>19
[1,7,6,5,4,2,8,3]=>[1,7,2,8,3,4,5,6]=>42
[1,7,6,4,5,2,8,3]=>[1,7,2,8,3,4,5,6]=>42
[3,8,1,6,5,7,2,4]=>[1,6,2,4,3,8,5,7]=>78
[7,8,5,4,1,6,2,3]=>[1,6,2,3,4,5,7,8]=>1
[8,3,2,6,5,7,1,4]=>[1,4,2,6,3,5,7,8]=>5
[6,8,3,4,5,7,1,2]=>[1,2,3,4,5,7,6,8]=>1
[7,3,8,6,4,5,1,2]=>[1,2,3,8,4,5,6,7]=>1
[1,2,7,6,5,8,3,4]=>[1,2,7,3,4,5,8,6]=>4
[4,8,2,6,1,5,3,7]=>[1,5,2,6,3,7,4,8]=>16
[7,8,1,2,5,6,3,4]=>[1,2,5,6,3,4,7,8]=>2
[3,1,6,4,7,2,5,8]=>[1,6,2,5,8,3,4,7]=>288
[2,8,3,4,5,1,7,6]=>[1,7,2,8,3,4,5,6]=>42
[4,2,8,3,1,7,5,6]=>[1,7,2,8,3,4,5,6]=>42
[5,3,7,4,1,6,2,8]=>[1,6,2,8,3,7,4,5]=>702
[3,4,6,1,5,8,7,2]=>[1,5,8,2,3,4,6,7]=>28
[5,8,1,6,3,4,7,2]=>[1,6,2,3,4,7,5,8]=>4
[6,8,1,7,5,2,3,4]=>[1,7,2,3,4,5,6,8]=>1
[5,6,1,7,4,8,2,3]=>[1,7,2,3,4,8,5,6]=>14
[3,1,7,5,6,4,8,2]=>[1,7,2,3,4,8,5,6]=>14
[5,1,7,6,4,8,3,2]=>[1,7,2,3,4,8,5,6]=>14
[6,1,7,8,5,3,4,2]=>[1,7,8,2,3,4,5,6]=>42
[1,6,4,7,5,8,2,3]=>[1,6,2,3,4,7,5,8]=>4
[1,7,6,5,4,8,2,3]=>[1,7,2,3,4,8,5,6]=>14
[8,1,6,5,7,2,4,3]=>[1,6,2,4,3,5,7,8]=>4
[6,1,7,5,3,8,2,4]=>[1,7,2,4,3,8,5,6]=>92
[2,1,7,5,6,8,3,4]=>[1,7,2,3,4,5,6,8]=>1
[5,4,1,7,6,8,2,3]=>[1,7,2,3,4,5,6,8]=>1
[3,8,4,1,7,2,6,5]=>[1,7,2,6,3,8,4,5]=>450
[6,5,1,4,3,8,2,7]=>[1,4,2,7,3,8,5,6]=>91
[1,6,2,5,8,3,4,7]=>[1,6,2,5,8,3,4,7]=>288
[3,7,6,8,4,5,2,1]=>[1,2,3,7,4,5,6,8]=>1
[1,7,6,8,5,4,2,3]=>[1,7,2,3,4,5,6,8]=>1
[7,3,8,5,4,6,2,1]=>[1,2,3,8,4,6,5,7]=>4
[5,4,3,8,6,7,2,1]=>[1,2,3,8,4,5,6,7]=>1
[6,1,5,8,7,4,2,3]=>[1,5,8,2,3,4,6,7]=>28
[5,8,6,7,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>1
[6,2,1,4,3,5,8,7]=>[1,4,2,3,5,8,6,7]=>6
[6,2,4,1,3,5,8,7]=>[1,3,5,8,2,4,6,7]=>35
[4,6,2,1,3,5,8,7]=>[1,3,5,8,2,4,6,7]=>35
[6,4,2,1,3,5,8,7]=>[1,3,5,8,2,4,6,7]=>35
[2,6,1,4,3,8,5,7]=>[1,4,2,6,3,8,5,7]=>61
[2,8,1,4,3,6,5,7]=>[1,4,2,8,3,6,5,7]=>78
[6,8,2,1,4,3,5,7]=>[1,4,2,3,5,7,6,8]=>3
[8,6,2,1,4,3,5,7]=>[1,4,2,3,5,7,6,8]=>3
[8,2,4,1,6,3,5,7]=>[1,6,2,4,3,5,7,8]=>4
[8,2,6,1,4,3,5,7]=>[1,4,2,6,3,5,7,8]=>5
[5,2,4,3,8,1,7,6]=>[1,7,2,4,3,8,5,6]=>92
[6,2,4,1,5,3,8,7]=>[1,5,2,4,3,8,6,7]=>45
[4,3,6,1,5,2,8,7]=>[1,5,2,8,3,6,4,7]=>134
[4,3,5,2,8,1,7,6]=>[1,7,2,8,3,5,4,6]=>288
[4,3,8,2,6,1,7,5]=>[1,7,2,6,3,8,4,5]=>450
[4,3,8,1,7,2,6,5]=>[1,7,2,6,3,8,4,5]=>450
[4,3,8,1,5,2,7,6]=>[1,5,2,7,3,8,4,6]=>168
[5,4,8,1,3,2,7,6]=>[1,3,2,7,4,8,5,6]=>30
[5,1,7,6,8,3,4,2]=>[1,7,2,3,4,5,6,8]=>1
[8,4,6,1,3,2,7,5]=>[1,3,2,7,4,6,5,8]=>15
[8,1,6,3,4,2,7,5]=>[1,6,2,7,3,4,5,8]=>14
[8,1,6,3,7,2,5,4]=>[1,6,2,5,3,7,4,8]=>35
[8,3,5,1,7,2,6,4]=>[1,7,2,6,3,5,4,8]=>162
[8,3,5,2,6,1,7,4]=>[1,7,2,6,3,5,4,8]=>162
[8,2,6,3,5,1,7,4]=>[1,7,2,6,3,5,4,8]=>162
[8,2,7,1,5,3,6,4]=>[1,5,2,7,3,6,4,8]=>56
[8,2,4,1,5,3,7,6]=>[1,5,2,4,3,7,6,8]=>15
[8,2,4,1,7,3,6,5]=>[1,7,2,4,3,6,5,8]=>29
[8,2,4,3,6,1,7,5]=>[1,7,2,4,3,6,5,8]=>29
[3,2,7,6,8,1,5,4]=>[1,5,2,7,3,4,6,8]=>14
[3,2,6,5,8,1,7,4]=>[1,7,2,6,3,4,5,8]=>28
[2,1,7,3,8,5,6,4]=>[1,7,2,3,8,4,5,6]=>28
[7,1,3,2,8,5,6,4]=>[1,3,2,8,4,5,6,7]=>5
[7,2,8,1,5,4,6,3]=>[1,5,2,8,3,4,6,7]=>28
[2,8,3,1,5,4,6,7]=>[1,5,2,8,3,4,6,7]=>28
[1,7,4,3,8,5,2,6]=>[1,7,2,6,3,8,4,5]=>450
[3,8,4,7,6,5,2,1]=>[1,2,3,8,4,7,5,6]=>9
[6,4,8,7,1,5,2,3]=>[1,5,2,3,4,8,6,7]=>10
[1,7,5,6,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>42
[7,8,2,6,3,1,5,4]=>[1,5,2,6,3,4,7,8]=>5
[8,1,6,2,7,4,5,3]=>[1,6,2,7,3,4,5,8]=>14
[7,8,1,6,4,2,5,3]=>[1,6,2,5,3,4,7,8]=>9
[7,8,6,1,5,3,2,4]=>[1,5,2,4,3,6,7,8]=>3
[7,3,8,6,1,5,2,4]=>[1,5,2,4,3,8,6,7]=>45
[8,7,6,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>1
[8,7,1,6,4,5,3,2]=>[1,6,2,3,4,5,7,8]=>1
[8,1,7,5,6,4,3,2]=>[1,7,2,3,4,5,6,8]=>1
[8,5,2,7,4,3,1,6]=>[1,6,2,7,3,4,5,8]=>14
[8,3,4,5,7,2,1,6]=>[1,6,2,3,4,5,7,8]=>1
[5,7,4,6,3,8,2,1]=>[1,2,3,8,4,6,5,7]=>4
[2,8,4,6,3,7,1,5]=>[1,5,2,8,3,7,4,6]=>534
[8,5,3,7,1,4,2,6]=>[1,4,2,6,3,7,5,8]=>16
[3,8,6,4,1,7,2,5]=>[1,7,2,5,3,8,4,6]=>282
[5,7,6,8,4,2,3,1]=>[1,2,3,4,5,7,6,8]=>1
[5,3,6,2,8,7,1,4]=>[1,4,2,8,3,6,5,7]=>78
[6,1,7,4,5,8,2,3]=>[1,7,2,3,4,5,8,6]=>5
[2,1,6,7,5,8,3,4]=>[1,6,7,2,3,4,5,8]=>14
[3,8,2,7,1,6,5,4]=>[1,6,2,7,3,8,4,5]=>168
[3,8,2,7,6,1,5,4]=>[1,5,2,7,3,8,4,6]=>168
[3,8,2,7,6,5,1,4]=>[1,4,2,7,3,8,5,6]=>91
[4,8,7,2,6,5,1,3]=>[1,3,2,6,4,8,5,7]=>25
[4,8,7,2,1,6,5,3]=>[1,6,2,3,4,8,5,7]=>14
[4,8,7,3,1,6,5,2]=>[1,6,2,3,4,8,5,7]=>14
[4,8,7,3,2,1,6,5]=>[1,6,2,3,4,8,5,7]=>14
[4,8,7,3,6,5,1,2]=>[1,2,3,6,4,8,5,7]=>5
[4,8,7,3,6,5,2,1]=>[1,2,3,6,4,8,5,7]=>5
[5,8,7,6,3,4,2,1]=>[1,2,3,4,5,8,6,7]=>1
[5,8,7,6,3,1,4,2]=>[1,4,2,3,5,8,6,7]=>6
[5,8,7,6,2,1,4,3]=>[1,4,2,3,5,8,6,7]=>6
[5,8,7,6,4,2,3,1]=>[1,2,3,4,5,8,6,7]=>1
[5,8,7,6,4,2,1,3]=>[1,3,2,4,5,8,6,7]=>3
[5,8,7,6,4,1,3,2]=>[1,3,2,4,5,8,6,7]=>3
[5,8,7,6,4,3,1,2]=>[1,2,3,4,5,8,6,7]=>1
[7,3,5,1,6,4,2,8]=>[1,6,2,8,3,5,4,7]=>246
[7,4,5,6,1,3,2,8]=>[1,3,2,8,4,5,6,7]=>5
[3,2,1,6,7,8,4,5]=>[1,6,7,8,2,3,4,5]=>462
[5,2,1,6,7,8,4,3]=>[1,6,7,8,2,3,4,5]=>462
[6,3,4,2,1,7,8,5]=>[1,7,8,2,3,4,5,6]=>42
[4,2,1,6,7,8,5,3]=>[1,6,7,8,2,3,4,5]=>462
[1,4,3,7,6,8,2,5]=>[1,4,2,5,3,7,6,8]=>8
[1,4,3,7,5,8,2,6]=>[1,4,2,6,3,7,5,8]=>16
[1,4,3,7,2,6,5,8]=>[1,4,2,6,3,7,5,8]=>16
[1,5,3,7,4,8,2,6]=>[1,5,2,6,3,7,4,8]=>16
[1,3,2,6,5,8,4,7]=>[1,3,2,6,4,7,5,8]=>8
[1,5,4,8,2,6,3,7]=>[1,5,2,6,3,7,4,8]=>16
[1,5,4,8,3,7,2,6]=>[1,5,2,6,3,7,4,8]=>16
[1,2,3,6,5,8,4,7]=>[1,2,3,6,4,7,5,8]=>2
[6,8,2,4,5,7,1,3]=>[1,3,2,4,5,7,6,8]=>2
[5,8,3,1,6,4,7,2]=>[1,6,2,3,4,7,5,8]=>4
[7,2,8,4,1,6,5,3]=>[1,6,2,8,3,4,5,7]=>42
[7,2,8,3,6,5,1,4]=>[1,4,2,8,3,6,5,7]=>78
[7,2,8,3,6,1,5,4]=>[1,5,2,8,3,6,4,7]=>134
[5,1,2,3,8,4,7,6]=>[1,2,3,8,4,7,5,6]=>9
[3,1,6,4,2,8,5,7]=>[1,6,2,8,3,4,5,7]=>42
[2,6,3,8,7,1,5,4]=>[1,5,2,6,3,8,4,7]=>77
[2,5,3,8,1,7,4,6]=>[1,7,2,5,3,8,4,6]=>282
[4,8,1,2,3,7,6,5]=>[1,2,3,7,4,8,5,6]=>5
[5,3,1,6,4,2,8,7]=>[1,6,2,8,3,4,5,7]=>42
[5,1,6,2,8,7,4,3]=>[1,6,2,8,3,4,5,7]=>42
[3,6,2,8,7,5,1,4]=>[1,4,2,8,3,6,5,7]=>78
[7,8,1,5,4,2,6,3]=>[1,5,2,6,3,4,7,8]=>5
[7,8,2,5,4,6,1,3]=>[1,3,2,5,4,6,7,8]=>2
[6,4,2,1,7,3,8,5]=>[1,7,2,3,8,4,5,6]=>28
[1,7,6,5,3,8,4,2]=>[1,7,2,3,8,4,5,6]=>28
[2,7,6,5,3,8,1,4]=>[1,4,2,7,3,8,5,6]=>91
[3,7,6,4,8,5,1,2]=>[1,2,3,7,4,8,5,6]=>5
[4,7,6,5,2,8,1,3]=>[1,3,2,8,4,7,5,6]=>63
[1,7,6,5,2,8,3,4]=>[1,7,2,8,3,4,5,6]=>42
[1,7,6,5,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>42
[4,7,6,8,3,5,1,2]=>[1,2,3,5,4,7,6,8]=>2
[2,7,6,5,1,4,3,8]=>[1,4,2,7,3,8,5,6]=>91
[6,3,2,1,7,4,8,5]=>[1,7,2,3,4,8,5,6]=>14
[7,3,1,5,4,2,8,6]=>[1,5,2,8,3,4,6,7]=>28
[8,4,1,5,2,7,6,3]=>[1,5,2,7,3,4,6,8]=>14
[8,5,3,2,1,7,6,4]=>[1,7,2,3,4,5,6,8]=>1
[5,7,4,3,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>42
[2,7,3,6,4,8,1,5]=>[1,5,2,7,3,6,4,8]=>56
[6,2,7,5,3,8,1,4]=>[1,4,2,7,3,8,5,6]=>91
[5,8,1,6,2,7,4,3]=>[1,6,2,7,3,4,5,8]=>14
[5,8,3,2,7,1,6,4]=>[1,6,2,7,3,4,5,8]=>14
[8,7,3,1,6,5,4,2]=>[1,6,2,3,4,5,7,8]=>1
[8,7,2,6,1,5,4,3]=>[1,5,2,6,3,4,7,8]=>5
[3,8,6,1,7,2,5,4]=>[1,7,2,5,3,8,4,6]=>282
[7,2,8,5,6,1,4,3]=>[1,4,2,8,3,5,6,7]=>14
[3,6,5,8,1,4,2,7]=>[1,4,2,7,3,6,5,8]=>40
[6,5,4,8,3,2,1,7]=>[1,7,2,3,4,8,5,6]=>14
[6,5,2,1,7,8,3,4]=>[1,7,8,2,3,4,5,6]=>42
[6,3,7,4,8,5,2,1]=>[1,2,3,7,4,8,5,6]=>5
[6,5,3,8,7,4,1,2]=>[1,2,3,8,4,5,6,7]=>1
[8,5,3,7,6,4,2,1]=>[1,2,3,7,4,5,6,8]=>1
[5,4,8,1,7,6,2,3]=>[1,7,2,3,4,8,5,6]=>14
[5,2,8,1,7,3,6,4]=>[1,7,2,8,3,6,4,5]=>990
[6,4,8,2,1,7,5,3]=>[1,7,2,3,4,8,5,6]=>14
[8,2,7,6,5,1,4,3]=>[1,4,2,7,3,5,6,8]=>9
[4,7,3,8,6,5,1,2]=>[1,2,3,8,4,7,5,6]=>9
[7,5,8,6,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>1
[2,8,7,6,5,4,1,3]=>[1,3,2,8,4,5,6,7]=>5
[3,7,5,8,2,4,1,6]=>[1,6,2,4,3,7,5,8]=>19
[3,8,5,7,2,4,1,6]=>[1,6,2,4,3,8,5,7]=>78
[7,5,3,8,1,4,2,6]=>[1,4,2,6,3,8,5,7]=>61
[2,1,5,8,7,3,4,6]=>[1,5,8,2,3,4,6,7]=>28
[7,1,2,3,8,6,5,4]=>[1,2,3,8,4,5,6,7]=>1
[6,8,1,4,3,7,2,5]=>[1,4,2,5,3,7,6,8]=>8
[8,7,3,2,4,1,6,5]=>[1,6,2,4,3,5,7,8]=>4
[2,1,7,3,4,8,6,5]=>[1,7,2,3,4,8,5,6]=>14
[7,8,3,2,4,1,6,5]=>[1,6,2,4,3,5,7,8]=>4
[6,7,1,4,3,8,2,5]=>[1,4,2,5,3,8,6,7]=>20
[7,1,2,3,8,5,6,4]=>[1,2,3,8,4,5,6,7]=>1
[8,1,2,3,7,5,6,4]=>[1,2,3,7,4,5,6,8]=>1
[8,1,2,3,6,5,7,4]=>[1,2,3,6,4,5,7,8]=>1
[7,8,2,6,3,4,1,5]=>[1,5,2,6,3,4,7,8]=>5
[6,8,2,7,3,4,1,5]=>[1,5,2,7,3,4,6,8]=>14
[6,7,2,8,3,4,1,5]=>[1,5,2,8,3,4,6,7]=>28
[3,8,7,1,4,2,6,5]=>[1,4,2,6,3,8,5,7]=>61
[3,5,7,8,2,4,1,6]=>[1,6,2,4,3,5,7,8]=>4
[8,1,7,5,4,3,2,6]=>[1,7,2,6,3,4,5,8]=>28
[8,1,7,4,5,3,2,6]=>[1,7,2,6,3,4,5,8]=>28
[5,8,3,7,1,4,2,6]=>[1,4,2,6,3,7,5,8]=>16
[8,7,2,4,3,6,1,5]=>[1,5,2,4,3,6,7,8]=>3
[6,1,2,3,8,7,4,5]=>[1,2,3,8,4,5,6,7]=>1
[5,1,2,3,8,7,6,4]=>[1,2,3,8,4,5,6,7]=>1
[5,1,2,3,8,6,7,4]=>[1,2,3,8,4,5,6,7]=>1
[8,6,2,4,3,1,7,5]=>[1,7,2,4,3,5,6,8]=>5
[2,1,6,3,4,8,7,5]=>[1,6,2,3,4,8,5,7]=>14
[1,6,3,8,5,4,2,7]=>[1,6,2,7,3,8,4,5]=>168
[7,3,1,6,5,4,2,8]=>[1,6,2,8,3,4,5,7]=>42
[7,1,2,3,6,5,4,8]=>[1,2,3,6,4,8,5,7]=>5
[5,8,2,7,6,3,4,1]=>[1,2,7,3,4,5,8,6]=>4
[6,2,8,1,7,3,5,4]=>[1,7,2,8,3,5,4,6]=>288
[2,5,3,8,7,1,6,4]=>[1,6,2,5,3,8,4,7]=>190
[5,3,8,4,1,7,6,2]=>[1,7,2,3,8,4,5,6]=>28
[4,3,8,7,6,5,1,2]=>[1,2,3,8,4,5,6,7]=>1
[1,5,3,8,7,6,2,4]=>[1,5,2,4,3,8,6,7]=>45
[4,5,8,1,7,2,6,3]=>[1,7,2,6,3,4,5,8]=>28
[4,5,8,3,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>28
[3,2,5,8,7,1,6,4]=>[1,6,2,5,8,3,4,7]=>288
[3,4,8,7,6,2,1,5]=>[1,5,2,3,4,8,6,7]=>10
[4,5,8,3,1,7,6,2]=>[1,7,2,3,4,5,8,6]=>5
[2,1,3,5,8,7,4,6]=>[1,3,5,8,2,4,6,7]=>35
[1,2,7,5,8,6,4,3]=>[1,2,7,3,4,5,8,6]=>4
[6,8,3,4,1,7,5,2]=>[1,7,2,3,4,5,6,8]=>1
[8,5,7,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>3
[8,5,4,7,1,6,2,3]=>[1,6,2,3,4,7,5,8]=>4
[1,6,5,8,2,7,4,3]=>[1,6,2,7,3,4,5,8]=>14
[8,5,6,3,1,7,4,2]=>[1,7,2,3,4,5,6,8]=>1
[5,6,2,8,1,7,4,3]=>[1,7,2,8,3,4,5,6]=>42
[8,3,5,7,1,6,2,4]=>[1,6,2,4,3,5,7,8]=>4
[6,3,8,2,7,5,1,4]=>[1,4,2,7,3,8,5,6]=>91
[6,8,4,2,7,1,5,3]=>[1,5,2,7,3,4,6,8]=>14
[8,6,4,7,3,1,5,2]=>[1,5,2,3,4,7,6,8]=>4
[8,4,5,7,3,1,6,2]=>[1,6,2,3,4,5,7,8]=>1
[8,3,4,7,2,6,1,5]=>[1,5,2,6,3,4,7,8]=>5
[2,8,4,5,7,1,6,3]=>[1,6,2,8,3,4,5,7]=>42
[8,7,3,4,5,1,6,2]=>[1,6,2,3,4,5,7,8]=>1
[8,7,4,5,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>3
[8,7,2,3,4,6,1,5]=>[1,5,2,3,4,6,7,8]=>1
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Description
The number of reduced words for a permutation.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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