Identifier
- St000696: Permutations ⟶ ℤ
Values
=>
[1]=>2
[1,2]=>3
[2,1]=>1
[1,2,3]=>4
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>2
[1,2,3,4]=>5
[1,2,4,3]=>3
[1,3,2,4]=>3
[1,3,4,2]=>3
[1,4,2,3]=>3
[1,4,3,2]=>3
[2,1,3,4]=>3
[2,1,4,3]=>1
[2,3,1,4]=>3
[2,3,4,1]=>3
[2,4,1,3]=>1
[2,4,3,1]=>1
[3,1,2,4]=>3
[3,1,4,2]=>1
[3,2,1,4]=>3
[3,2,4,1]=>1
[3,4,1,2]=>3
[3,4,2,1]=>3
[4,1,2,3]=>3
[4,1,3,2]=>1
[4,2,1,3]=>1
[4,2,3,1]=>3
[4,3,1,2]=>3
[4,3,2,1]=>1
[1,2,3,4,5]=>6
[1,2,3,5,4]=>4
[1,2,4,3,5]=>4
[1,2,4,5,3]=>4
[1,2,5,3,4]=>4
[1,2,5,4,3]=>4
[1,3,2,4,5]=>4
[1,3,2,5,4]=>2
[1,3,4,2,5]=>4
[1,3,4,5,2]=>4
[1,3,5,2,4]=>2
[1,3,5,4,2]=>2
[1,4,2,3,5]=>4
[1,4,2,5,3]=>2
[1,4,3,2,5]=>4
[1,4,3,5,2]=>2
[1,4,5,2,3]=>4
[1,4,5,3,2]=>4
[1,5,2,3,4]=>4
[1,5,2,4,3]=>2
[1,5,3,2,4]=>2
[1,5,3,4,2]=>4
[1,5,4,2,3]=>4
[1,5,4,3,2]=>2
[2,1,3,4,5]=>4
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>2
[2,1,5,3,4]=>2
[2,1,5,4,3]=>2
[2,3,1,4,5]=>4
[2,3,1,5,4]=>2
[2,3,4,1,5]=>4
[2,3,4,5,1]=>4
[2,3,5,1,4]=>2
[2,3,5,4,1]=>2
[2,4,1,3,5]=>2
[2,4,1,5,3]=>2
[2,4,3,1,5]=>2
[2,4,3,5,1]=>2
[2,4,5,1,3]=>2
[2,4,5,3,1]=>2
[2,5,1,3,4]=>2
[2,5,1,4,3]=>2
[2,5,3,1,4]=>2
[2,5,3,4,1]=>2
[2,5,4,1,3]=>2
[2,5,4,3,1]=>2
[3,1,2,4,5]=>4
[3,1,2,5,4]=>2
[3,1,4,2,5]=>2
[3,1,4,5,2]=>2
[3,1,5,2,4]=>2
[3,1,5,4,2]=>2
[3,2,1,4,5]=>4
[3,2,1,5,4]=>2
[3,2,4,1,5]=>2
[3,2,4,5,1]=>2
[3,2,5,1,4]=>2
[3,2,5,4,1]=>2
[3,4,1,2,5]=>4
[3,4,1,5,2]=>2
[3,4,2,1,5]=>4
[3,4,2,5,1]=>2
[3,4,5,1,2]=>4
[3,4,5,2,1]=>4
[3,5,1,2,4]=>2
[3,5,1,4,2]=>2
[3,5,2,1,4]=>2
[3,5,2,4,1]=>2
[3,5,4,1,2]=>2
[3,5,4,2,1]=>2
[4,1,2,3,5]=>4
[4,1,2,5,3]=>2
[4,1,3,2,5]=>2
[4,1,3,5,2]=>2
[4,1,5,2,3]=>2
[4,1,5,3,2]=>2
[4,2,1,3,5]=>2
[4,2,1,5,3]=>2
[4,2,3,1,5]=>4
[4,2,3,5,1]=>2
[4,2,5,1,3]=>2
[4,2,5,3,1]=>2
[4,3,1,2,5]=>4
[4,3,1,5,2]=>2
[4,3,2,1,5]=>2
[4,3,2,5,1]=>2
[4,3,5,1,2]=>2
[4,3,5,2,1]=>2
[4,5,1,2,3]=>4
[4,5,1,3,2]=>2
[4,5,2,1,3]=>2
[4,5,2,3,1]=>4
[4,5,3,1,2]=>4
[4,5,3,2,1]=>2
[5,1,2,3,4]=>4
[5,1,2,4,3]=>2
[5,1,3,2,4]=>2
[5,1,3,4,2]=>2
[5,1,4,2,3]=>2
[5,1,4,3,2]=>2
[5,2,1,3,4]=>2
[5,2,1,4,3]=>2
[5,2,3,1,4]=>2
[5,2,3,4,1]=>4
[5,2,4,1,3]=>2
[5,2,4,3,1]=>2
[5,3,1,2,4]=>2
[5,3,1,4,2]=>2
[5,3,2,1,4]=>2
[5,3,2,4,1]=>2
[5,3,4,1,2]=>4
[5,3,4,2,1]=>2
[5,4,1,2,3]=>4
[5,4,1,3,2]=>2
[5,4,2,1,3]=>2
[5,4,2,3,1]=>2
[5,4,3,1,2]=>2
[5,4,3,2,1]=>2
[1,2,3,4,5,6]=>7
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>5
[1,2,3,5,6,4]=>5
[1,2,3,6,4,5]=>5
[1,2,3,6,5,4]=>5
[1,2,4,3,5,6]=>5
[1,2,4,3,6,5]=>3
[1,2,4,5,3,6]=>5
[1,2,4,5,6,3]=>5
[1,2,4,6,3,5]=>3
[1,2,4,6,5,3]=>3
[1,2,5,3,4,6]=>5
[1,2,5,3,6,4]=>3
[1,2,5,4,3,6]=>5
[1,2,5,4,6,3]=>3
[1,2,5,6,3,4]=>5
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>5
[1,2,6,3,5,4]=>3
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>5
[1,2,6,5,3,4]=>5
[1,2,6,5,4,3]=>3
[1,3,2,4,5,6]=>5
[1,3,2,4,6,5]=>3
[1,3,2,5,4,6]=>3
[1,3,2,5,6,4]=>3
[1,3,2,6,4,5]=>3
[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>5
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>5
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>3
[1,3,4,6,5,2]=>3
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>3
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>3
[1,3,5,6,2,4]=>3
[1,3,5,6,4,2]=>3
[1,3,6,2,4,5]=>3
[1,3,6,2,5,4]=>3
[1,3,6,4,2,5]=>3
[1,3,6,4,5,2]=>3
[1,3,6,5,2,4]=>3
[1,3,6,5,4,2]=>3
[1,4,2,3,5,6]=>5
[1,4,2,3,6,5]=>3
[1,4,2,5,3,6]=>3
[1,4,2,5,6,3]=>3
[1,4,2,6,3,5]=>3
[1,4,2,6,5,3]=>3
[1,4,3,2,5,6]=>5
[1,4,3,2,6,5]=>3
[1,4,3,5,2,6]=>3
[1,4,3,5,6,2]=>3
[1,4,3,6,2,5]=>3
[1,4,3,6,5,2]=>3
[1,4,5,2,3,6]=>5
[1,4,5,2,6,3]=>3
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>3
[1,4,5,6,2,3]=>5
[1,4,5,6,3,2]=>5
[1,4,6,2,3,5]=>3
[1,4,6,2,5,3]=>3
[1,4,6,3,2,5]=>3
[1,4,6,3,5,2]=>3
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>3
[1,5,2,3,4,6]=>5
[1,5,2,3,6,4]=>3
[1,5,2,4,3,6]=>3
[1,5,2,4,6,3]=>3
[1,5,2,6,3,4]=>3
[1,5,2,6,4,3]=>3
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>3
[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>3
[1,5,3,6,2,4]=>3
[1,5,3,6,4,2]=>3
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>3
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>3
[1,5,4,6,3,2]=>3
[1,5,6,2,3,4]=>5
[1,5,6,2,4,3]=>3
[1,5,6,3,2,4]=>3
[1,5,6,3,4,2]=>5
[1,5,6,4,2,3]=>5
[1,5,6,4,3,2]=>3
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>3
[1,6,2,4,3,5]=>3
[1,6,2,4,5,3]=>3
[1,6,2,5,3,4]=>3
[1,6,2,5,4,3]=>3
[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>3
[1,6,3,4,2,5]=>3
[1,6,3,4,5,2]=>5
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>3
[1,6,4,2,3,5]=>3
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>3
[1,6,4,5,2,3]=>5
[1,6,4,5,3,2]=>3
[1,6,5,2,3,4]=>5
[1,6,5,2,4,3]=>3
[1,6,5,3,2,4]=>3
[1,6,5,3,4,2]=>3
[1,6,5,4,2,3]=>3
[1,6,5,4,3,2]=>3
[2,1,3,4,5,6]=>5
[2,1,3,4,6,5]=>3
[2,1,3,5,4,6]=>3
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>3
[2,1,3,6,5,4]=>3
[2,1,4,3,5,6]=>3
[2,1,4,3,6,5]=>1
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>3
[2,1,4,6,3,5]=>1
[2,1,4,6,5,3]=>1
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>1
[2,1,5,4,3,6]=>3
[2,1,5,4,6,3]=>1
[2,1,5,6,3,4]=>3
[2,1,5,6,4,3]=>3
[2,1,6,3,4,5]=>3
[2,1,6,3,5,4]=>1
[2,1,6,4,3,5]=>1
[2,1,6,4,5,3]=>3
[2,1,6,5,3,4]=>3
[2,1,6,5,4,3]=>1
[2,3,1,4,5,6]=>5
[2,3,1,4,6,5]=>3
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>3
[2,3,1,6,4,5]=>3
[2,3,1,6,5,4]=>3
[2,3,4,1,5,6]=>5
[2,3,4,1,6,5]=>3
[2,3,4,5,1,6]=>5
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>3
[2,3,4,6,5,1]=>3
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>3
[2,3,5,4,1,6]=>3
[2,3,5,4,6,1]=>3
[2,3,5,6,1,4]=>3
[2,3,5,6,4,1]=>3
[2,3,6,1,4,5]=>3
[2,3,6,1,5,4]=>3
[2,3,6,4,1,5]=>3
[2,3,6,4,5,1]=>3
[2,3,6,5,1,4]=>3
[2,3,6,5,4,1]=>3
[2,4,1,3,5,6]=>3
[2,4,1,3,6,5]=>1
[2,4,1,5,3,6]=>3
[2,4,1,5,6,3]=>3
[2,4,1,6,3,5]=>1
[2,4,1,6,5,3]=>1
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>1
[2,4,3,5,1,6]=>3
[2,4,3,5,6,1]=>3
[2,4,3,6,1,5]=>1
[2,4,3,6,5,1]=>1
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>3
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>3
[2,4,5,6,3,1]=>3
[2,4,6,1,3,5]=>1
[2,4,6,1,5,3]=>1
[2,4,6,3,1,5]=>1
[2,4,6,3,5,1]=>1
[2,4,6,5,1,3]=>1
[2,4,6,5,3,1]=>1
[2,5,1,3,4,6]=>3
[2,5,1,3,6,4]=>1
[2,5,1,4,3,6]=>3
[2,5,1,4,6,3]=>1
[2,5,1,6,3,4]=>3
[2,5,1,6,4,3]=>3
[2,5,3,1,4,6]=>3
[2,5,3,1,6,4]=>1
[2,5,3,4,1,6]=>3
[2,5,3,4,6,1]=>3
[2,5,3,6,1,4]=>1
[2,5,3,6,4,1]=>1
[2,5,4,1,3,6]=>3
[2,5,4,1,6,3]=>1
[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>3
[2,5,4,6,1,3]=>1
[2,5,4,6,3,1]=>1
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>3
[2,5,6,3,1,4]=>3
[2,5,6,3,4,1]=>3
[2,5,6,4,1,3]=>3
[2,5,6,4,3,1]=>3
[2,6,1,3,4,5]=>3
[2,6,1,3,5,4]=>1
[2,6,1,4,3,5]=>1
[2,6,1,4,5,3]=>3
[2,6,1,5,3,4]=>3
[2,6,1,5,4,3]=>1
[2,6,3,1,4,5]=>3
[2,6,3,1,5,4]=>1
[2,6,3,4,1,5]=>3
[2,6,3,4,5,1]=>3
[2,6,3,5,1,4]=>1
[2,6,3,5,4,1]=>1
[2,6,4,1,3,5]=>1
[2,6,4,1,5,3]=>3
[2,6,4,3,1,5]=>1
[2,6,4,3,5,1]=>1
[2,6,4,5,1,3]=>3
[2,6,4,5,3,1]=>3
[2,6,5,1,3,4]=>3
[2,6,5,1,4,3]=>1
[2,6,5,3,1,4]=>3
[2,6,5,3,4,1]=>3
[2,6,5,4,1,3]=>1
[2,6,5,4,3,1]=>1
[3,1,2,4,5,6]=>5
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>3
[3,1,2,5,6,4]=>3
[3,1,2,6,4,5]=>3
[3,1,2,6,5,4]=>3
[3,1,4,2,5,6]=>3
[3,1,4,2,6,5]=>1
[3,1,4,5,2,6]=>3
[3,1,4,5,6,2]=>3
[3,1,4,6,2,5]=>1
[3,1,4,6,5,2]=>1
[3,1,5,2,4,6]=>3
[3,1,5,2,6,4]=>1
[3,1,5,4,2,6]=>3
[3,1,5,4,6,2]=>1
[3,1,5,6,2,4]=>3
[3,1,5,6,4,2]=>3
[3,1,6,2,4,5]=>3
[3,1,6,2,5,4]=>1
[3,1,6,4,2,5]=>1
[3,1,6,4,5,2]=>3
[3,1,6,5,2,4]=>3
[3,1,6,5,4,2]=>1
[3,2,1,4,5,6]=>5
[3,2,1,4,6,5]=>3
[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>3
[3,2,1,6,4,5]=>3
[3,2,1,6,5,4]=>3
[3,2,4,1,5,6]=>3
[3,2,4,1,6,5]=>1
[3,2,4,5,1,6]=>3
[3,2,4,5,6,1]=>3
[3,2,4,6,1,5]=>1
[3,2,4,6,5,1]=>1
[3,2,5,1,4,6]=>3
[3,2,5,1,6,4]=>1
[3,2,5,4,1,6]=>3
[3,2,5,4,6,1]=>1
[3,2,5,6,1,4]=>3
[3,2,5,6,4,1]=>3
[3,2,6,1,4,5]=>3
[3,2,6,1,5,4]=>1
[3,2,6,4,1,5]=>1
[3,2,6,4,5,1]=>3
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>1
[3,4,1,2,5,6]=>5
[3,4,1,2,6,5]=>3
[3,4,1,5,2,6]=>3
[3,4,1,5,6,2]=>3
[3,4,1,6,2,5]=>3
[3,4,1,6,5,2]=>3
[3,4,2,1,5,6]=>5
[3,4,2,1,6,5]=>3
[3,4,2,5,1,6]=>3
[3,4,2,5,6,1]=>3
[3,4,2,6,1,5]=>3
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>5
[3,4,5,1,6,2]=>3
[3,4,5,2,1,6]=>5
[3,4,5,2,6,1]=>3
[3,4,5,6,1,2]=>5
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>3
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>3
[3,4,6,5,1,2]=>3
[3,4,6,5,2,1]=>3
[3,5,1,2,4,6]=>3
[3,5,1,2,6,4]=>3
[3,5,1,4,2,6]=>3
[3,5,1,4,6,2]=>1
[3,5,1,6,2,4]=>1
[3,5,1,6,4,2]=>1
[3,5,2,1,4,6]=>3
[3,5,2,1,6,4]=>3
[3,5,2,4,1,6]=>3
[3,5,2,4,6,1]=>1
[3,5,2,6,1,4]=>1
[3,5,2,6,4,1]=>1
[3,5,4,1,2,6]=>3
[3,5,4,1,6,2]=>1
[3,5,4,2,1,6]=>3
[3,5,4,2,6,1]=>1
[3,5,4,6,1,2]=>3
[3,5,4,6,2,1]=>3
[3,5,6,1,2,4]=>3
[3,5,6,1,4,2]=>3
[3,5,6,2,1,4]=>3
[3,5,6,2,4,1]=>3
[3,5,6,4,1,2]=>3
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>3
[3,6,1,4,2,5]=>1
[3,6,1,4,5,2]=>3
[3,6,1,5,2,4]=>1
[3,6,1,5,4,2]=>3
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>3
[3,6,2,4,1,5]=>1
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>1
[3,6,2,5,4,1]=>3
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>1
[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>1
[3,6,4,5,1,2]=>3
[3,6,4,5,2,1]=>3
[3,6,5,1,2,4]=>3
[3,6,5,1,4,2]=>1
[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>1
[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>3
[4,1,2,3,5,6]=>5
[4,1,2,3,6,5]=>3
[4,1,2,5,3,6]=>3
[4,1,2,5,6,3]=>3
[4,1,2,6,3,5]=>3
[4,1,2,6,5,3]=>3
[4,1,3,2,5,6]=>3
[4,1,3,2,6,5]=>1
[4,1,3,5,2,6]=>3
[4,1,3,5,6,2]=>3
[4,1,3,6,2,5]=>1
[4,1,3,6,5,2]=>1
[4,1,5,2,3,6]=>3
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>3
[4,1,5,3,6,2]=>1
[4,1,5,6,2,3]=>3
[4,1,5,6,3,2]=>3
[4,1,6,2,3,5]=>3
[4,1,6,2,5,3]=>1
[4,1,6,3,2,5]=>1
[4,1,6,3,5,2]=>3
[4,1,6,5,2,3]=>3
[4,1,6,5,3,2]=>1
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>1
[4,2,1,5,3,6]=>3
[4,2,1,5,6,3]=>3
[4,2,1,6,3,5]=>1
[4,2,1,6,5,3]=>1
[4,2,3,1,5,6]=>5
[4,2,3,1,6,5]=>3
[4,2,3,5,1,6]=>3
[4,2,3,5,6,1]=>3
[4,2,3,6,1,5]=>3
[4,2,3,6,5,1]=>3
[4,2,5,1,3,6]=>3
[4,2,5,1,6,3]=>1
[4,2,5,3,1,6]=>3
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>3
[4,2,5,6,3,1]=>3
[4,2,6,1,3,5]=>1
[4,2,6,1,5,3]=>3
[4,2,6,3,1,5]=>3
[4,2,6,3,5,1]=>1
[4,2,6,5,1,3]=>1
[4,2,6,5,3,1]=>3
[4,3,1,2,5,6]=>5
[4,3,1,2,6,5]=>3
[4,3,1,5,2,6]=>3
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>3
[4,3,1,6,5,2]=>3
[4,3,2,1,5,6]=>3
[4,3,2,1,6,5]=>1
[4,3,2,5,1,6]=>3
[4,3,2,5,6,1]=>3
[4,3,2,6,1,5]=>1
[4,3,2,6,5,1]=>1
[4,3,5,1,2,6]=>3
[4,3,5,1,6,2]=>1
[4,3,5,2,1,6]=>3
[4,3,5,2,6,1]=>1
[4,3,5,6,1,2]=>3
[4,3,5,6,2,1]=>3
[4,3,6,1,2,5]=>3
[4,3,6,1,5,2]=>1
[4,3,6,2,1,5]=>1
[4,3,6,2,5,1]=>3
[4,3,6,5,1,2]=>3
[4,3,6,5,2,1]=>1
[4,5,1,2,3,6]=>5
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>3
[4,5,1,3,6,2]=>3
[4,5,1,6,2,3]=>3
[4,5,1,6,3,2]=>3
[4,5,2,1,3,6]=>3
[4,5,2,1,6,3]=>3
[4,5,2,3,1,6]=>5
[4,5,2,3,6,1]=>3
[4,5,2,6,1,3]=>3
[4,5,2,6,3,1]=>3
[4,5,3,1,2,6]=>5
[4,5,3,1,6,2]=>3
[4,5,3,2,1,6]=>3
[4,5,3,2,6,1]=>3
[4,5,3,6,1,2]=>3
[4,5,3,6,2,1]=>3
[4,5,6,1,2,3]=>5
[4,5,6,1,3,2]=>3
[4,5,6,2,1,3]=>3
[4,5,6,2,3,1]=>5
[4,5,6,3,1,2]=>5
[4,5,6,3,2,1]=>3
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>3
[4,6,1,3,2,5]=>1
[4,6,1,3,5,2]=>1
[4,6,1,5,2,3]=>3
[4,6,1,5,3,2]=>1
[4,6,2,1,3,5]=>1
[4,6,2,1,5,3]=>1
[4,6,2,3,1,5]=>3
[4,6,2,3,5,1]=>3
[4,6,2,5,1,3]=>1
[4,6,2,5,3,1]=>3
[4,6,3,1,2,5]=>3
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>1
[4,6,3,2,5,1]=>1
[4,6,3,5,1,2]=>3
[4,6,3,5,2,1]=>1
[4,6,5,1,2,3]=>3
[4,6,5,1,3,2]=>1
[4,6,5,2,1,3]=>1
[4,6,5,2,3,1]=>3
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>1
[5,1,2,3,4,6]=>5
[5,1,2,3,6,4]=>3
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>3
[5,1,2,6,3,4]=>3
[5,1,2,6,4,3]=>3
[5,1,3,2,4,6]=>3
[5,1,3,2,6,4]=>1
[5,1,3,4,2,6]=>3
[5,1,3,4,6,2]=>3
[5,1,3,6,2,4]=>1
[5,1,3,6,4,2]=>1
[5,1,4,2,3,6]=>3
[5,1,4,2,6,3]=>1
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>1
[5,1,4,6,2,3]=>3
[5,1,4,6,3,2]=>3
[5,1,6,2,3,4]=>3
[5,1,6,2,4,3]=>1
[5,1,6,3,2,4]=>1
[5,1,6,3,4,2]=>3
[5,1,6,4,2,3]=>3
[5,1,6,4,3,2]=>1
[5,2,1,3,4,6]=>3
[5,2,1,3,6,4]=>1
[5,2,1,4,3,6]=>3
[5,2,1,4,6,3]=>1
[5,2,1,6,3,4]=>3
[5,2,1,6,4,3]=>3
[5,2,3,1,4,6]=>3
[5,2,3,1,6,4]=>3
[5,2,3,4,1,6]=>5
[5,2,3,4,6,1]=>3
[5,2,3,6,1,4]=>3
[5,2,3,6,4,1]=>3
[5,2,4,1,3,6]=>3
[5,2,4,1,6,3]=>3
[5,2,4,3,1,6]=>3
[5,2,4,3,6,1]=>1
[5,2,4,6,1,3]=>1
[5,2,4,6,3,1]=>1
[5,2,6,1,3,4]=>3
[5,2,6,1,4,3]=>1
[5,2,6,3,1,4]=>1
[5,2,6,3,4,1]=>3
[5,2,6,4,1,3]=>3
[5,2,6,4,3,1]=>1
[5,3,1,2,4,6]=>3
[5,3,1,2,6,4]=>3
[5,3,1,4,2,6]=>3
[5,3,1,4,6,2]=>1
[5,3,1,6,2,4]=>1
[5,3,1,6,4,2]=>1
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>1
[5,3,2,4,1,6]=>3
[5,3,2,4,6,1]=>1
[5,3,2,6,1,4]=>3
[5,3,2,6,4,1]=>3
[5,3,4,1,2,6]=>5
[5,3,4,1,6,2]=>3
[5,3,4,2,1,6]=>3
[5,3,4,2,6,1]=>3
[5,3,4,6,1,2]=>3
[5,3,4,6,2,1]=>3
[5,3,6,1,2,4]=>3
[5,3,6,1,4,2]=>1
[5,3,6,2,1,4]=>1
[5,3,6,2,4,1]=>3
[5,3,6,4,1,2]=>3
[5,3,6,4,2,1]=>1
[5,4,1,2,3,6]=>5
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>3
[5,4,1,3,6,2]=>3
[5,4,1,6,2,3]=>3
[5,4,1,6,3,2]=>3
[5,4,2,1,3,6]=>3
[5,4,2,1,6,3]=>1
[5,4,2,3,1,6]=>3
[5,4,2,3,6,1]=>3
[5,4,2,6,1,3]=>1
[5,4,2,6,3,1]=>1
[5,4,3,1,2,6]=>3
[5,4,3,1,6,2]=>1
[5,4,3,2,1,6]=>3
[5,4,3,2,6,1]=>1
[5,4,3,6,1,2]=>3
[5,4,3,6,2,1]=>3
[5,4,6,1,2,3]=>3
[5,4,6,1,3,2]=>1
[5,4,6,2,1,3]=>1
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>3
[5,4,6,3,2,1]=>1
[5,6,1,2,3,4]=>5
[5,6,1,2,4,3]=>3
[5,6,1,3,2,4]=>3
[5,6,1,3,4,2]=>3
[5,6,1,4,2,3]=>3
[5,6,1,4,3,2]=>3
[5,6,2,1,3,4]=>3
[5,6,2,1,4,3]=>3
[5,6,2,3,1,4]=>3
[5,6,2,3,4,1]=>5
[5,6,2,4,1,3]=>3
[5,6,2,4,3,1]=>3
[5,6,3,1,2,4]=>3
[5,6,3,1,4,2]=>3
[5,6,3,2,1,4]=>3
[5,6,3,2,4,1]=>3
[5,6,3,4,1,2]=>5
[5,6,3,4,2,1]=>3
[5,6,4,1,2,3]=>5
[5,6,4,1,3,2]=>3
[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>3
[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>3
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>3
[6,1,2,4,3,5]=>3
[6,1,2,4,5,3]=>3
[6,1,2,5,3,4]=>3
[6,1,2,5,4,3]=>3
[6,1,3,2,4,5]=>3
[6,1,3,2,5,4]=>1
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>1
[6,1,3,5,4,2]=>1
[6,1,4,2,3,5]=>3
[6,1,4,2,5,3]=>1
[6,1,4,3,2,5]=>3
[6,1,4,3,5,2]=>1
[6,1,4,5,2,3]=>3
[6,1,4,5,3,2]=>3
[6,1,5,2,3,4]=>3
[6,1,5,2,4,3]=>1
[6,1,5,3,2,4]=>1
[6,1,5,3,4,2]=>3
[6,1,5,4,2,3]=>3
[6,1,5,4,3,2]=>1
[6,2,1,3,4,5]=>3
[6,2,1,3,5,4]=>1
[6,2,1,4,3,5]=>1
[6,2,1,4,5,3]=>3
[6,2,1,5,3,4]=>3
[6,2,1,5,4,3]=>1
[6,2,3,1,4,5]=>3
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>3
[6,2,3,4,5,1]=>5
[6,2,3,5,1,4]=>3
[6,2,3,5,4,1]=>3
[6,2,4,1,3,5]=>1
[6,2,4,1,5,3]=>1
[6,2,4,3,1,5]=>1
[6,2,4,3,5,1]=>3
[6,2,4,5,1,3]=>3
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>3
[6,2,5,1,4,3]=>3
[6,2,5,3,1,4]=>1
[6,2,5,3,4,1]=>3
[6,2,5,4,1,3]=>1
[6,2,5,4,3,1]=>3
[6,3,1,2,4,5]=>3
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>1
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>1
[6,3,1,5,4,2]=>3
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>1
[6,3,2,4,1,5]=>1
[6,3,2,4,5,1]=>3
[6,3,2,5,1,4]=>3
[6,3,2,5,4,1]=>1
[6,3,4,1,2,5]=>3
[6,3,4,1,5,2]=>3
[6,3,4,2,1,5]=>3
[6,3,4,2,5,1]=>3
[6,3,4,5,1,2]=>5
[6,3,4,5,2,1]=>3
[6,3,5,1,2,4]=>3
[6,3,5,1,4,2]=>3
[6,3,5,2,1,4]=>1
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>3
[6,3,5,4,2,1]=>1
[6,4,1,2,3,5]=>3
[6,4,1,2,5,3]=>3
[6,4,1,3,2,5]=>1
[6,4,1,3,5,2]=>1
[6,4,1,5,2,3]=>3
[6,4,1,5,3,2]=>1
[6,4,2,1,3,5]=>1
[6,4,2,1,5,3]=>3
[6,4,2,3,1,5]=>3
[6,4,2,3,5,1]=>3
[6,4,2,5,1,3]=>3
[6,4,2,5,3,1]=>1
[6,4,3,1,2,5]=>3
[6,4,3,1,5,2]=>1
[6,4,3,2,1,5]=>1
[6,4,3,2,5,1]=>3
[6,4,3,5,1,2]=>3
[6,4,3,5,2,1]=>1
[6,4,5,1,2,3]=>5
[6,4,5,1,3,2]=>3
[6,4,5,2,1,3]=>3
[6,4,5,2,3,1]=>3
[6,4,5,3,1,2]=>3
[6,4,5,3,2,1]=>3
[6,5,1,2,3,4]=>5
[6,5,1,2,4,3]=>3
[6,5,1,3,2,4]=>3
[6,5,1,3,4,2]=>3
[6,5,1,4,2,3]=>3
[6,5,1,4,3,2]=>3
[6,5,2,1,3,4]=>3
[6,5,2,1,4,3]=>1
[6,5,2,3,1,4]=>3
[6,5,2,3,4,1]=>3
[6,5,2,4,1,3]=>1
[6,5,2,4,3,1]=>1
[6,5,3,1,2,4]=>3
[6,5,3,1,4,2]=>1
[6,5,3,2,1,4]=>3
[6,5,3,2,4,1]=>1
[6,5,3,4,1,2]=>3
[6,5,3,4,2,1]=>3
[6,5,4,1,2,3]=>3
[6,5,4,1,3,2]=>1
[6,5,4,2,1,3]=>1
[6,5,4,2,3,1]=>3
[6,5,4,3,1,2]=>3
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>8
[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>6
[1,2,3,4,6,7,5]=>6
[1,2,3,4,7,5,6]=>6
[1,2,3,4,7,6,5]=>6
[1,2,3,5,4,6,7]=>6
[1,2,3,5,4,7,6]=>4
[1,2,3,5,6,4,7]=>6
[1,2,3,5,6,7,4]=>6
[1,2,3,5,7,4,6]=>4
[1,2,3,5,7,6,4]=>4
[1,2,3,6,4,5,7]=>6
[1,2,3,6,4,7,5]=>4
[1,2,3,6,5,4,7]=>6
[1,2,3,6,5,7,4]=>4
[1,2,3,6,7,4,5]=>6
[1,2,3,6,7,5,4]=>6
[1,2,3,7,4,5,6]=>6
[1,2,3,7,4,6,5]=>4
[1,2,3,7,5,4,6]=>4
[1,2,3,7,5,6,4]=>6
[1,2,3,7,6,4,5]=>6
[1,2,3,7,6,5,4]=>4
[1,2,4,3,5,6,7]=>6
[1,2,4,3,5,7,6]=>4
[1,2,4,3,6,5,7]=>4
[1,2,4,3,6,7,5]=>4
[1,2,4,3,7,5,6]=>4
[1,2,4,3,7,6,5]=>4
[1,2,4,5,3,6,7]=>6
[1,2,4,5,3,7,6]=>4
[1,2,4,5,6,3,7]=>6
[1,2,4,5,6,7,3]=>6
[1,2,4,5,7,3,6]=>4
[1,2,4,5,7,6,3]=>4
[1,2,4,6,3,5,7]=>4
[1,2,4,6,3,7,5]=>4
[1,2,4,6,5,3,7]=>4
[1,2,4,6,5,7,3]=>4
[1,2,4,6,7,3,5]=>4
[1,2,4,6,7,5,3]=>4
[1,2,4,7,3,5,6]=>4
[1,2,4,7,3,6,5]=>4
[1,2,4,7,5,3,6]=>4
[1,2,4,7,5,6,3]=>4
[1,2,4,7,6,3,5]=>4
[1,2,4,7,6,5,3]=>4
[1,2,5,3,4,6,7]=>6
[1,2,5,3,4,7,6]=>4
[1,2,5,3,6,4,7]=>4
[1,2,5,3,6,7,4]=>4
[1,2,5,3,7,4,6]=>4
[1,2,5,3,7,6,4]=>4
[1,2,5,4,3,6,7]=>6
[1,2,5,4,3,7,6]=>4
[1,2,5,4,6,3,7]=>4
[1,2,5,4,6,7,3]=>4
[1,2,5,4,7,3,6]=>4
[1,2,5,4,7,6,3]=>4
[1,2,5,6,3,4,7]=>6
[1,2,5,6,3,7,4]=>4
[1,2,5,6,4,3,7]=>6
[1,2,5,6,4,7,3]=>4
[1,2,5,6,7,3,4]=>6
[1,2,5,6,7,4,3]=>6
[1,2,5,7,3,4,6]=>4
[1,2,5,7,3,6,4]=>4
[1,2,5,7,4,3,6]=>4
[1,2,5,7,4,6,3]=>4
[1,2,5,7,6,3,4]=>4
[1,2,5,7,6,4,3]=>4
[1,2,6,3,4,5,7]=>6
[1,2,6,3,4,7,5]=>4
[1,2,6,3,5,4,7]=>4
[1,2,6,3,5,7,4]=>4
[1,2,6,3,7,4,5]=>4
[1,2,6,3,7,5,4]=>4
[1,2,6,4,3,5,7]=>4
[1,2,6,4,3,7,5]=>4
[1,2,6,4,5,3,7]=>6
[1,2,6,4,5,7,3]=>4
[1,2,6,4,7,3,5]=>4
[1,2,6,4,7,5,3]=>4
[1,2,6,5,3,4,7]=>6
[1,2,6,5,3,7,4]=>4
[1,2,6,5,4,3,7]=>4
[1,2,6,5,4,7,3]=>4
[1,2,6,5,7,3,4]=>4
[1,2,6,5,7,4,3]=>4
[1,2,6,7,3,4,5]=>6
[1,2,6,7,3,5,4]=>4
[1,2,6,7,4,3,5]=>4
[1,2,6,7,4,5,3]=>6
[1,2,6,7,5,3,4]=>6
[1,2,6,7,5,4,3]=>4
[1,2,7,3,4,5,6]=>6
[1,2,7,3,4,6,5]=>4
[1,2,7,3,5,4,6]=>4
[1,2,7,3,5,6,4]=>4
[1,2,7,3,6,4,5]=>4
[1,2,7,3,6,5,4]=>4
[1,2,7,4,3,5,6]=>4
[1,2,7,4,3,6,5]=>4
[1,2,7,4,5,3,6]=>4
[1,2,7,4,5,6,3]=>6
[1,2,7,4,6,3,5]=>4
[1,2,7,4,6,5,3]=>4
[1,2,7,5,3,4,6]=>4
[1,2,7,5,3,6,4]=>4
[1,2,7,5,4,3,6]=>4
[1,2,7,5,4,6,3]=>4
[1,2,7,5,6,3,4]=>6
[1,2,7,5,6,4,3]=>4
[1,2,7,6,3,4,5]=>6
[1,2,7,6,3,5,4]=>4
[1,2,7,6,4,3,5]=>4
[1,2,7,6,4,5,3]=>4
[1,2,7,6,5,3,4]=>4
[1,2,7,6,5,4,3]=>4
[1,3,2,4,5,6,7]=>6
[1,3,2,4,5,7,6]=>4
[1,3,2,4,6,5,7]=>4
[1,3,2,4,6,7,5]=>4
[1,3,2,4,7,5,6]=>4
[1,3,2,4,7,6,5]=>4
[1,3,2,5,4,6,7]=>4
[1,3,2,5,4,7,6]=>2
[1,3,2,5,6,4,7]=>4
[1,3,2,5,6,7,4]=>4
[1,3,2,5,7,4,6]=>2
[1,3,2,5,7,6,4]=>2
[1,3,2,6,4,5,7]=>4
[1,3,2,6,4,7,5]=>2
[1,3,2,6,5,4,7]=>4
[1,3,2,6,5,7,4]=>2
[1,3,2,6,7,4,5]=>4
[1,3,2,6,7,5,4]=>4
[1,3,2,7,4,5,6]=>4
[1,3,2,7,4,6,5]=>2
[1,3,2,7,5,4,6]=>2
[1,3,2,7,5,6,4]=>4
[1,3,2,7,6,4,5]=>4
[1,3,2,7,6,5,4]=>2
[1,3,4,2,5,6,7]=>6
[1,3,4,2,5,7,6]=>4
[1,3,4,2,6,5,7]=>4
[1,3,4,2,6,7,5]=>4
[1,3,4,2,7,5,6]=>4
[1,3,4,2,7,6,5]=>4
[1,3,4,5,2,6,7]=>6
[1,3,4,5,2,7,6]=>4
[1,3,4,5,6,2,7]=>6
[1,3,4,5,6,7,2]=>6
[1,3,4,5,7,2,6]=>4
[1,3,4,5,7,6,2]=>4
[1,3,4,6,2,5,7]=>4
[1,3,4,6,2,7,5]=>4
[1,3,4,6,5,2,7]=>4
[1,3,4,6,5,7,2]=>4
[1,3,4,6,7,2,5]=>4
[1,3,4,6,7,5,2]=>4
[1,3,4,7,2,5,6]=>4
[1,3,4,7,2,6,5]=>4
[1,3,4,7,5,2,6]=>4
[1,3,4,7,5,6,2]=>4
[1,3,4,7,6,2,5]=>4
[1,3,4,7,6,5,2]=>4
[1,3,5,2,4,6,7]=>4
[1,3,5,2,4,7,6]=>2
[1,3,5,2,6,4,7]=>4
[1,3,5,2,6,7,4]=>4
[1,3,5,2,7,4,6]=>2
[1,3,5,2,7,6,4]=>2
[1,3,5,4,2,6,7]=>4
[1,3,5,4,2,7,6]=>2
[1,3,5,4,6,2,7]=>4
[1,3,5,4,6,7,2]=>4
[1,3,5,4,7,2,6]=>2
[1,3,5,4,7,6,2]=>2
[1,3,5,6,2,4,7]=>4
[1,3,5,6,2,7,4]=>4
[1,3,5,6,4,2,7]=>4
[1,3,5,6,4,7,2]=>4
[1,3,5,6,7,2,4]=>4
[1,3,5,6,7,4,2]=>4
[1,3,5,7,2,4,6]=>2
[1,3,5,7,2,6,4]=>2
[1,3,5,7,4,2,6]=>2
[1,3,5,7,4,6,2]=>2
[1,3,5,7,6,2,4]=>2
[1,3,5,7,6,4,2]=>2
[1,3,6,2,4,5,7]=>4
[1,3,6,2,4,7,5]=>2
[1,3,6,2,5,4,7]=>4
[1,3,6,2,5,7,4]=>2
[1,3,6,2,7,4,5]=>4
[1,3,6,2,7,5,4]=>4
[1,3,6,4,2,5,7]=>4
[1,3,6,4,2,7,5]=>2
[1,3,6,4,5,2,7]=>4
[1,3,6,4,5,7,2]=>4
[1,3,6,4,7,2,5]=>2
[1,3,6,4,7,5,2]=>2
[1,3,6,5,2,4,7]=>4
[1,3,6,5,2,7,4]=>2
[1,3,6,5,4,2,7]=>4
[1,3,6,5,4,7,2]=>4
[1,3,6,5,7,2,4]=>2
[1,3,6,5,7,4,2]=>2
[1,3,6,7,2,4,5]=>4
[1,3,6,7,2,5,4]=>4
[1,3,6,7,4,2,5]=>4
[1,3,6,7,4,5,2]=>4
[1,3,6,7,5,2,4]=>4
[1,3,6,7,5,4,2]=>4
[1,3,7,2,4,5,6]=>4
[1,3,7,2,4,6,5]=>2
[1,3,7,2,5,4,6]=>2
[1,3,7,2,5,6,4]=>4
[1,3,7,2,6,4,5]=>4
[1,3,7,2,6,5,4]=>2
[1,3,7,4,2,5,6]=>4
[1,3,7,4,2,6,5]=>2
[1,3,7,4,5,2,6]=>4
[1,3,7,4,5,6,2]=>4
[1,3,7,4,6,2,5]=>2
[1,3,7,4,6,5,2]=>2
[1,3,7,5,2,4,6]=>2
[1,3,7,5,2,6,4]=>4
[1,3,7,5,4,2,6]=>2
[1,3,7,5,4,6,2]=>2
[1,3,7,5,6,2,4]=>4
[1,3,7,5,6,4,2]=>4
[1,3,7,6,2,4,5]=>4
[1,3,7,6,2,5,4]=>2
[1,3,7,6,4,2,5]=>4
[1,3,7,6,4,5,2]=>4
[1,3,7,6,5,2,4]=>2
[1,3,7,6,5,4,2]=>2
[1,4,2,3,5,6,7]=>6
[1,4,2,3,5,7,6]=>4
[1,4,2,3,6,5,7]=>4
[1,4,2,3,6,7,5]=>4
[1,4,2,3,7,5,6]=>4
[1,4,2,3,7,6,5]=>4
[1,4,2,5,3,6,7]=>4
[1,4,2,5,3,7,6]=>2
[1,4,2,5,6,3,7]=>4
[1,4,2,5,6,7,3]=>4
[1,4,2,5,7,3,6]=>2
[1,4,2,5,7,6,3]=>2
[1,4,2,6,3,5,7]=>4
[1,4,2,6,3,7,5]=>2
[1,4,2,6,5,3,7]=>4
[1,4,2,6,5,7,3]=>2
[1,4,2,6,7,3,5]=>4
[1,4,2,6,7,5,3]=>4
[1,4,2,7,3,5,6]=>4
[1,4,2,7,3,6,5]=>2
[1,4,2,7,5,3,6]=>2
[1,4,2,7,5,6,3]=>4
[1,4,2,7,6,3,5]=>4
[1,4,2,7,6,5,3]=>2
[1,4,3,2,5,6,7]=>6
[1,4,3,2,5,7,6]=>4
[1,4,3,2,6,5,7]=>4
[1,4,3,2,6,7,5]=>4
[1,4,3,2,7,5,6]=>4
[1,4,3,2,7,6,5]=>4
[1,4,3,5,2,6,7]=>4
[1,4,3,5,2,7,6]=>2
[1,4,3,5,6,2,7]=>4
[1,4,3,5,6,7,2]=>4
[1,4,3,5,7,2,6]=>2
[1,4,3,5,7,6,2]=>2
[1,4,3,6,2,5,7]=>4
[1,4,3,6,2,7,5]=>2
[1,4,3,6,5,2,7]=>4
[1,4,3,6,5,7,2]=>2
[1,4,3,6,7,2,5]=>4
[1,4,3,6,7,5,2]=>4
[1,4,3,7,2,5,6]=>4
[1,4,3,7,2,6,5]=>2
[1,4,3,7,5,2,6]=>2
[1,4,3,7,5,6,2]=>4
[1,4,3,7,6,2,5]=>4
[1,4,3,7,6,5,2]=>2
[1,4,5,2,3,6,7]=>6
[1,4,5,2,3,7,6]=>4
[1,4,5,2,6,3,7]=>4
[1,4,5,2,6,7,3]=>4
[1,4,5,2,7,3,6]=>4
[1,4,5,2,7,6,3]=>4
[1,4,5,3,2,6,7]=>6
[1,4,5,3,2,7,6]=>4
[1,4,5,3,6,2,7]=>4
[1,4,5,3,6,7,2]=>4
[1,4,5,3,7,2,6]=>4
[1,4,5,3,7,6,2]=>4
[1,4,5,6,2,3,7]=>6
[1,4,5,6,2,7,3]=>4
[1,4,5,6,3,2,7]=>6
[1,4,5,6,3,7,2]=>4
[1,4,5,6,7,2,3]=>6
[1,4,5,6,7,3,2]=>6
[1,4,5,7,2,3,6]=>4
[1,4,5,7,2,6,3]=>4
[1,4,5,7,3,2,6]=>4
[1,4,5,7,3,6,2]=>4
[1,4,5,7,6,2,3]=>4
[1,4,5,7,6,3,2]=>4
[1,4,6,2,3,5,7]=>4
[1,4,6,2,3,7,5]=>4
[1,4,6,2,5,3,7]=>4
[1,4,6,2,5,7,3]=>2
[1,4,6,2,7,3,5]=>2
[1,4,6,2,7,5,3]=>2
[1,4,6,3,2,5,7]=>4
[1,4,6,3,2,7,5]=>4
[1,4,6,3,5,2,7]=>4
[1,4,6,3,5,7,2]=>2
[1,4,6,3,7,2,5]=>2
[1,4,6,3,7,5,2]=>2
[1,4,6,5,2,3,7]=>4
[1,4,6,5,2,7,3]=>2
[1,4,6,5,3,2,7]=>4
[1,4,6,5,3,7,2]=>2
[1,4,6,7,2,3,5]=>4
[1,4,6,7,5,3,2]=>4
[1,4,7,2,3,5,6]=>4
[1,4,7,6,5,3,2]=>4
[1,5,2,3,4,7,6]=>4
[1,5,2,7,3,4,6]=>4
[1,5,4,7,6,3,2]=>2
[1,5,6,2,7,3,4]=>4
[1,5,6,4,7,3,2]=>4
[1,5,6,7,2,3,4]=>6
[1,5,6,7,4,3,2]=>4
[1,5,7,2,3,4,6]=>4
[1,5,7,6,4,3,2]=>2
[1,6,2,3,4,7,5]=>4
[1,6,2,3,7,4,5]=>4
[1,6,2,7,3,4,5]=>4
[1,6,5,4,3,7,2]=>2
[1,6,5,4,7,3,2]=>4
[1,6,5,7,4,3,2]=>2
[1,6,7,2,3,4,5]=>6
[1,6,7,5,4,3,2]=>4
[1,7,2,3,4,5,6]=>6
[1,7,3,5,6,4,2]=>4
[1,7,3,6,5,4,2]=>4
[1,7,4,3,6,5,2]=>2
[1,7,4,5,3,6,2]=>4
[1,7,4,5,6,3,2]=>4
[1,7,4,6,5,3,2]=>2
[1,7,5,4,3,6,2]=>4
[1,7,5,4,6,3,2]=>2
[1,7,6,4,5,3,2]=>4
[1,7,6,5,4,3,2]=>2
[2,1,3,4,5,6,7]=>6
[2,1,3,4,7,5,6]=>4
[2,1,3,7,4,5,6]=>4
[2,1,6,3,4,5,7]=>4
[2,1,7,3,4,5,6]=>4
[2,1,7,6,5,4,3]=>2
[2,3,1,4,5,6,7]=>6
[2,3,4,1,5,6,7]=>6
[2,3,4,1,5,7,6]=>4
[2,3,4,5,1,6,7]=>6
[2,3,4,5,1,7,6]=>4
[2,3,4,5,6,1,7]=>6
[2,3,4,5,6,7,1]=>6
[2,3,4,5,7,1,6]=>4
[2,3,4,6,1,7,5]=>4
[2,3,4,6,7,1,5]=>4
[2,3,4,7,1,5,6]=>4
[2,3,5,6,7,1,4]=>4
[2,4,1,3,5,6,7]=>4
[2,5,1,3,4,6,7]=>4
[2,5,7,1,3,4,6]=>2
[2,6,1,3,4,5,7]=>4
[2,6,1,7,3,4,5]=>4
[2,6,5,4,3,1,7]=>2
[2,6,7,1,3,4,5]=>4
[2,7,1,3,4,5,6]=>4
[3,1,2,4,5,6,7]=>6
[3,1,2,4,5,7,6]=>4
[3,2,1,4,5,6,7]=>6
[3,2,4,5,6,7,1]=>4
[3,4,1,2,5,6,7]=>6
[3,4,2,5,6,7,1]=>4
[3,4,5,2,6,7,1]=>4
[3,4,5,6,2,7,1]=>4
[3,4,5,6,7,1,2]=>6
[3,5,6,1,2,4,7]=>4
[3,5,6,4,2,1,7]=>4
[3,6,1,2,4,5,7]=>4
[3,6,5,4,2,1,7]=>4
[4,1,2,3,5,6,7]=>6
[4,1,2,3,5,7,6]=>4
[4,1,6,2,3,5,7]=>4
[4,2,3,5,6,7,1]=>4
[4,2,5,1,3,6,7]=>4
[4,3,2,1,5,6,7]=>4
[4,3,2,5,6,7,1]=>4
[4,3,5,2,6,7,1]=>2
[4,3,6,5,2,1,7]=>2
[4,5,1,6,2,3,7]=>4
[4,5,2,3,6,7,1]=>4
[4,5,3,6,2,1,7]=>4
[4,5,6,1,2,3,7]=>6
[4,5,6,3,2,1,7]=>4
[4,6,1,2,3,5,7]=>4
[4,6,1,2,3,7,5]=>4
[4,6,5,3,2,1,7]=>2
[5,1,2,3,4,6,7]=>6
[5,1,2,3,4,7,6]=>4
[5,1,2,3,6,4,7]=>4
[5,1,2,3,6,7,4]=>4
[5,1,2,3,7,4,6]=>4
[5,1,2,6,3,4,7]=>4
[5,1,6,2,3,4,7]=>4
[5,1,6,2,3,7,4]=>2
[5,2,3,4,6,7,1]=>4
[5,2,6,7,1,3,4]=>4
[5,3,2,4,6,7,1]=>2
[5,3,2,6,1,4,7]=>4
[5,4,3,2,1,6,7]=>4
[5,4,3,2,1,7,6]=>2
[5,4,3,2,6,1,7]=>2
[5,4,3,6,2,1,7]=>4
[5,4,6,3,2,1,7]=>2
[5,6,1,2,3,4,7]=>6
[5,6,1,2,3,7,4]=>4
[5,6,3,4,1,2,7]=>6
[5,6,4,3,2,1,7]=>4
[5,6,7,1,2,3,4]=>6
[6,1,2,3,4,5,7]=>6
[6,1,2,3,4,7,5]=>4
[6,1,2,3,7,4,5]=>4
[6,1,2,7,3,4,5]=>4
[6,2,3,4,5,7,1]=>4
[6,2,4,5,3,1,7]=>4
[6,2,5,4,3,1,7]=>4
[6,3,2,5,4,1,7]=>2
[6,3,4,2,5,1,7]=>4
[6,3,4,5,2,1,7]=>4
[6,3,5,4,2,1,7]=>2
[6,4,3,2,5,1,7]=>4
[6,4,3,2,7,1,5]=>2
[6,4,3,5,2,1,7]=>2
[6,4,7,2,5,1,3]=>2
[6,5,3,4,2,1,7]=>4
[6,5,4,3,2,1,7]=>2
[6,7,1,2,3,4,5]=>6
[6,7,4,5,1,2,3]=>6
[7,1,2,3,4,5,6]=>6
[7,2,1,3,4,5,6]=>4
[7,2,3,1,4,5,6]=>4
[7,2,3,4,1,5,6]=>4
[7,2,3,4,5,1,6]=>4
[7,3,1,2,4,5,6]=>4
[7,3,2,1,4,5,6]=>4
[7,3,2,4,1,5,6]=>2
[7,3,4,1,2,5,6]=>4
[7,4,1,2,3,5,6]=>4
[7,4,2,1,3,5,6]=>2
[7,4,5,6,1,2,3]=>6
[7,5,1,2,3,4,6]=>4
[7,5,6,1,2,3,4]=>6
[7,5,6,3,4,1,2]=>4
[7,6,1,2,3,4,5]=>6
[7,6,4,5,1,2,3]=>4
[7,6,5,1,2,3,4]=>4
[7,6,5,3,4,1,2]=>4
[7,6,5,4,1,2,3]=>4
[7,6,5,4,3,1,2]=>2
[7,6,5,4,3,2,1]=>2
[8,7,6,5,4,3,2,1]=>1
[7,6,8,5,4,3,2,1]=>1
[7,8,5,6,4,3,2,1]=>3
[7,8,6,4,5,3,2,1]=>3
[8,6,7,4,5,3,2,1]=>3
[7,6,5,4,8,3,2,1]=>1
[6,5,7,4,8,3,2,1]=>1
[7,8,6,5,3,4,2,1]=>3
[8,6,7,5,3,4,2,1]=>3
[8,7,5,6,3,4,2,1]=>3
[6,7,8,3,4,5,2,1]=>5
[7,8,6,5,4,2,3,1]=>3
[8,6,7,5,4,2,3,1]=>3
[8,7,5,6,4,2,3,1]=>3
[8,7,6,4,5,2,3,1]=>3
[8,6,5,7,3,2,4,1]=>1
[6,7,8,5,2,3,4,1]=>5
[8,5,6,7,2,3,4,1]=>5
[7,8,3,2,4,5,6,1]=>5
[7,6,5,4,3,2,8,1]=>1
[6,5,7,4,3,2,8,1]=>1
[6,5,4,3,7,2,8,1]=>1
[5,4,6,3,7,2,8,1]=>1
[3,4,5,2,6,7,8,1]=>5
[5,2,3,4,6,7,8,1]=>5
[4,3,2,5,6,7,8,1]=>5
[3,4,2,5,6,7,8,1]=>5
[4,2,3,5,6,7,8,1]=>5
[3,2,4,5,6,7,8,1]=>5
[2,3,4,5,6,7,8,1]=>7
[8,7,6,5,4,3,1,2]=>3
[7,8,6,5,4,3,1,2]=>3
[8,6,7,5,4,3,1,2]=>3
[8,7,5,6,4,3,1,2]=>3
[8,7,6,4,5,3,1,2]=>3
[8,7,6,5,3,4,1,2]=>3
[8,7,5,6,3,4,1,2]=>5
[7,8,5,6,3,4,1,2]=>5
[5,6,7,8,3,4,1,2]=>7
[7,8,3,4,5,6,1,2]=>7
[3,4,5,6,7,8,1,2]=>7
[8,7,6,5,4,2,1,3]=>1
[7,6,8,5,4,2,1,3]=>1
[8,7,6,5,4,1,2,3]=>3
[6,7,8,5,4,1,2,3]=>5
[8,5,6,7,4,1,2,3]=>5
[8,7,6,4,5,1,2,3]=>5
[8,6,7,4,5,1,2,3]=>5
[8,7,4,5,6,1,2,3]=>5
[7,8,4,5,6,1,2,3]=>7
[7,6,5,8,3,2,1,4]=>3
[7,5,6,8,2,3,1,4]=>3
[6,7,5,8,3,1,2,4]=>3
[6,5,7,8,2,1,3,4]=>3
[8,7,6,5,1,2,3,4]=>5
[8,7,5,6,1,2,3,4]=>5
[7,8,5,6,1,2,3,4]=>7
[8,5,6,7,1,2,3,4]=>7
[5,6,7,8,1,2,3,4]=>7
[8,7,6,4,3,2,1,5]=>1
[8,7,6,4,2,1,3,5]=>1
[8,7,6,1,2,3,4,5]=>5
[8,6,7,1,2,3,4,5]=>7
[6,7,8,1,2,3,4,5]=>7
[7,8,5,4,2,1,3,6]=>3
[7,8,5,4,1,2,3,6]=>5
[8,7,1,2,3,4,5,6]=>7
[7,8,1,2,3,4,5,6]=>7
[8,6,5,4,3,2,1,7]=>1
[8,6,5,4,3,1,2,7]=>3
[8,5,6,3,4,1,2,7]=>5
[8,6,5,4,2,1,3,7]=>1
[8,6,4,3,2,1,5,7]=>1
[8,6,4,2,1,3,5,7]=>1
[8,2,3,4,1,5,6,7]=>5
[8,4,1,2,3,5,6,7]=>5
[8,3,2,1,4,5,6,7]=>5
[8,2,3,1,4,5,6,7]=>5
[8,3,1,2,4,5,6,7]=>5
[8,2,1,3,4,5,6,7]=>5
[8,1,2,3,4,5,6,7]=>7
[7,6,5,4,3,2,1,8]=>3
[6,7,5,4,3,2,1,8]=>3
[6,5,7,4,3,2,1,8]=>3
[5,6,7,4,3,2,1,8]=>5
[7,6,4,5,3,2,1,8]=>3
[6,5,4,7,3,2,1,8]=>3
[7,5,6,3,4,2,1,8]=>5
[7,6,4,3,5,2,1,8]=>3
[7,6,3,4,5,2,1,8]=>5
[7,5,4,3,6,2,1,8]=>3
[6,7,5,4,2,3,1,8]=>5
[6,5,7,3,2,4,1,8]=>3
[5,6,7,2,3,4,1,8]=>7
[2,3,4,5,6,7,1,8]=>7
[5,6,7,1,2,3,4,8]=>7
[6,7,1,2,3,4,5,8]=>7
[7,1,2,3,4,5,6,8]=>7
[6,5,4,3,2,1,7,8]=>3
[2,3,4,5,6,1,7,8]=>7
[5,6,3,4,1,2,7,8]=>7
[4,5,6,1,2,3,7,8]=>7
[6,1,2,3,4,5,7,8]=>7
[5,4,3,2,1,6,7,8]=>5
[2,3,4,5,1,6,7,8]=>7
[5,1,2,3,4,6,7,8]=>7
[4,3,2,1,5,6,7,8]=>5
[3,4,1,2,5,6,7,8]=>7
[3,2,1,4,5,6,7,8]=>7
[2,1,3,4,5,6,7,8]=>7
[1,2,3,4,5,6,7,8]=>9
[6,5,8,7,4,3,2,1]=>1
[3,5,8,7,6,4,2,1]=>3
[4,3,6,5,8,7,2,1]=>1
[2,6,8,7,5,4,3,1]=>1
[2,3,5,6,8,7,4,1]=>3
[3,2,6,5,4,8,7,1]=>1
[4,3,6,5,7,2,8,1]=>1
[3,2,6,5,7,4,8,1]=>1
[4,3,5,2,7,6,8,1]=>1
[3,2,5,4,7,6,8,1]=>1
[1,8,7,6,5,4,3,2]=>3
[1,7,8,6,5,4,3,2]=>3
[1,6,8,7,5,4,3,2]=>3
[1,7,6,8,5,4,3,2]=>3
[1,6,7,8,5,4,3,2]=>5
[1,5,8,7,6,4,3,2]=>3
[1,7,6,5,8,4,3,2]=>3
[1,3,5,7,8,6,4,2]=>3
[1,4,3,8,7,6,5,2]=>3
[1,6,5,4,3,8,7,2]=>3
[1,4,3,6,5,8,7,2]=>3
[2,1,8,7,6,5,4,3]=>1
[2,1,6,5,7,4,8,3]=>1
[2,1,5,4,7,6,8,3]=>1
[1,2,6,7,8,5,4,3]=>5
[3,2,1,8,7,6,5,4]=>3
[3,2,1,6,5,8,7,4]=>3
[1,2,3,5,6,7,8,4]=>7
[4,3,2,1,8,7,6,5]=>1
[3,4,2,1,7,8,6,5]=>5
[2,4,3,1,6,8,7,5]=>1
[2,4,3,1,7,6,8,5]=>1
[3,2,4,1,6,8,7,5]=>1
[3,2,4,1,7,6,8,5]=>1
[2,3,4,1,6,7,8,5]=>5
[2,1,4,3,8,7,6,5]=>1
[2,1,4,3,6,8,7,5]=>1
[2,1,4,3,7,6,8,5]=>1
[5,4,3,2,1,8,7,6]=>3
[3,2,5,4,1,8,7,6]=>3
[3,2,1,4,5,8,7,6]=>5
[2,3,1,4,5,7,8,6]=>5
[6,5,4,3,2,1,8,7]=>1
[4,3,5,2,6,1,8,7]=>1
[3,2,5,4,6,1,8,7]=>1
[2,3,4,5,6,1,8,7]=>5
[2,1,6,5,4,3,8,7]=>1
[2,1,4,6,5,3,8,7]=>1
[2,1,5,4,6,3,8,7]=>1
[4,3,2,1,6,5,8,7]=>1
[2,4,3,1,6,5,8,7]=>1
[3,2,4,1,6,5,8,7]=>1
[2,1,4,3,6,5,8,7]=>1
[2,1,3,4,5,6,8,7]=>5
[1,2,3,4,5,6,8,7]=>7
[5,7,6,4,3,2,1,8]=>3
[4,7,6,5,3,2,1,8]=>3
[3,2,7,6,5,4,1,8]=>3
[5,4,3,2,7,6,1,8]=>3
[3,2,5,4,7,6,1,8]=>3
[1,4,3,2,7,6,5,8]=>5
[1,3,4,2,6,7,5,8]=>5
[1,3,2,5,4,7,6,8]=>3
[1,2,3,5,4,7,6,8]=>5
[1,3,2,4,5,7,6,8]=>5
[1,2,3,4,5,7,6,8]=>7
[1,2,4,3,6,5,7,8]=>5
[1,3,2,5,4,6,7,8]=>5
[1,2,3,5,4,6,7,8]=>7
[1,3,2,4,5,6,7,8]=>7
[1,8,4,7,6,5,3,2]=>3
[1,8,5,4,7,6,3,2]=>3
[1,8,7,4,5,6,3,2]=>5
[1,8,7,4,6,5,3,2]=>3
[1,8,6,5,4,7,3,2]=>3
[1,8,7,5,4,6,3,2]=>3
[1,8,7,5,6,4,3,2]=>3
[2,1,4,5,8,6,7,3]=>3
[2,1,8,5,4,7,6,3]=>1
[2,3,4,8,5,6,7,1]=>5
[2,3,6,4,5,1,8,7]=>3
[2,3,7,4,5,6,8,1]=>5
[2,8,4,3,5,7,6,1]=>1
[4,2,3,1,8,6,7,5]=>5
[8,2,7,4,6,5,3,1]=>3
[4,3,2,7,5,6,8,1]=>3
[4,3,2,8,5,7,6,1]=>1
[6,3,2,5,4,1,8,7]=>1
[8,3,2,5,4,7,6,1]=>1
[8,3,2,7,6,5,4,1]=>1
[8,3,7,4,6,5,2,1]=>1
[7,3,6,5,4,2,1,8]=>3
[7,4,3,6,5,2,1,8]=>3
[7,6,3,5,4,2,1,8]=>3
[8,5,4,3,2,7,6,1]=>1
[8,7,4,3,6,5,2,1]=>1
[2,4,6,8,1,3,5,7]=>1
[2,4,6,1,7,3,8,5]=>3
[2,1,4,3,7,5,8,6]=>1
[2,4,1,3,7,5,8,6]=>1
[2,1,4,3,7,8,5,6]=>3
[2,4,7,8,1,3,5,6]=>3
[2,1,4,3,8,5,6,7]=>3
[2,4,5,6,7,1,8,3]=>5
[2,1,5,3,6,4,8,7]=>1
[2,1,5,6,3,4,8,7]=>3
[2,5,6,8,1,3,4,7]=>3
[2,1,5,3,7,4,8,6]=>1
[2,5,1,7,3,4,8,6]=>3
[2,1,5,7,3,8,4,6]=>1
[2,5,7,8,1,3,4,6]=>3
[2,3,5,6,1,7,8,4]=>5
[2,1,6,3,7,4,8,5]=>1
[2,6,7,1,3,4,8,5]=>3
[2,1,6,7,8,3,4,5]=>5
[2,6,7,8,1,3,4,5]=>5
[2,1,6,3,4,7,8,5]=>3
[2,1,6,3,4,5,8,7]=>3
[2,6,1,3,4,5,7,8]=>5
[2,7,8,1,3,4,5,6]=>5
[2,7,1,3,4,5,6,8]=>5
[2,3,4,5,7,8,1,6]=>5
[2,1,8,3,4,5,6,7]=>5
[2,8,1,3,4,5,6,7]=>5
[2,1,3,8,4,5,6,7]=>5
[2,3,4,5,6,8,1,7]=>5
[3,1,4,2,6,5,8,7]=>1
[3,4,1,2,6,5,8,7]=>3
[3,1,4,2,6,8,5,7]=>1
[3,4,6,8,1,2,5,7]=>3
[3,1,4,2,7,5,8,6]=>1
[3,4,1,2,7,8,5,6]=>5
[3,4,7,8,1,2,5,6]=>5
[3,1,5,2,6,4,8,7]=>1
[3,5,1,6,2,4,8,7]=>1
[3,1,5,6,2,8,4,7]=>3
[3,5,6,8,1,2,4,7]=>3
[3,1,5,2,7,4,8,6]=>1
[3,5,1,7,2,8,4,6]=>1
[3,5,7,8,1,2,4,6]=>3
[1,3,2,5,4,8,6,7]=>3
[1,3,5,8,2,4,6,7]=>3
[1,3,5,6,2,7,4,8]=>5
[3,1,6,2,7,4,8,5]=>1
[3,6,7,1,2,8,4,5]=>5
[3,6,1,7,8,2,4,5]=>3
[3,6,7,8,1,2,4,5]=>5
[1,3,2,6,4,7,5,8]=>3
[3,1,2,6,7,4,8,5]=>3
[1,3,2,6,4,8,5,7]=>3
[1,3,2,6,4,5,7,8]=>5
[1,3,2,7,4,8,5,6]=>3
[1,3,2,7,4,5,6,8]=>5
[1,3,2,8,4,5,6,7]=>5
[3,1,2,4,5,8,6,7]=>5
[1,3,2,4,5,8,6,7]=>5
[4,1,5,2,6,3,8,7]=>1
[4,5,6,1,2,3,8,7]=>5
[4,1,5,6,8,2,3,7]=>3
[4,5,6,8,1,2,3,7]=>5
[4,1,5,2,7,3,8,6]=>1
[4,1,5,2,7,8,3,6]=>3
[4,5,7,1,2,8,3,6]=>3
[4,5,1,7,8,2,3,6]=>5
[4,5,7,8,1,2,3,6]=>5
[1,4,2,5,3,7,6,8]=>3
[1,4,2,5,3,8,6,7]=>3
[1,4,2,5,3,6,7,8]=>5
[1,4,5,6,7,2,3,8]=>7
[4,1,6,2,7,3,8,5]=>1
[4,6,7,1,8,2,3,5]=>3
[4,6,7,8,1,2,3,5]=>5
[1,4,2,6,3,7,5,8]=>3
[1,4,2,6,7,8,3,5]=>5
[1,4,2,6,3,8,5,7]=>3
[4,1,2,3,6,5,8,7]=>3
[1,4,2,6,3,5,7,8]=>5
[1,4,2,7,3,8,5,6]=>3
[4,7,1,2,3,5,6,8]=>5
[1,4,2,7,3,5,6,8]=>5
[1,4,2,3,7,5,6,8]=>5
[1,4,2,3,5,7,6,8]=>5
[1,4,2,8,3,5,6,7]=>5
[4,1,2,3,8,5,6,7]=>5
[1,4,2,3,5,8,6,7]=>5
[1,4,2,3,5,6,7,8]=>7
[5,1,6,2,7,3,8,4]=>1
[1,5,2,6,3,7,4,8]=>3
[1,5,2,6,3,8,4,7]=>3
[1,5,2,6,3,4,7,8]=>5
[1,2,5,6,3,4,7,8]=>7
[1,5,2,7,3,8,4,6]=>3
[5,7,1,2,3,4,6,8]=>5
[1,5,2,7,3,4,6,8]=>5
[1,5,2,3,4,7,6,8]=>5
[5,1,2,8,3,4,6,7]=>5
[1,5,2,8,3,4,6,7]=>5
[1,5,8,2,3,4,6,7]=>5
[1,5,2,3,4,8,6,7]=>5
[1,2,3,5,4,8,6,7]=>5
[5,1,2,3,4,6,8,7]=>5
[1,5,2,3,4,6,7,8]=>7
[1,6,2,7,3,8,4,5]=>3
[1,6,7,8,2,3,4,5]=>7
[6,7,1,2,3,4,8,5]=>5
[6,1,7,2,3,4,5,8]=>5
[6,1,2,7,3,4,5,8]=>5
[1,6,2,7,3,4,5,8]=>5
[1,6,7,2,3,4,5,8]=>7
[1,6,2,3,4,7,5,8]=>5
[1,2,3,6,4,7,5,8]=>5
[6,1,8,2,3,4,5,7]=>5
[1,6,2,8,3,4,5,7]=>5
[1,6,8,2,3,4,5,7]=>5
[1,6,2,3,4,8,5,7]=>5
[1,2,3,6,4,8,5,7]=>5
[6,1,2,3,4,5,8,7]=>5
[1,6,2,3,4,5,7,8]=>7
[1,2,3,6,4,5,7,8]=>7
[1,7,2,8,3,4,5,6]=>5
[1,7,8,2,3,4,5,6]=>7
[1,7,2,3,8,4,5,6]=>5
[7,1,2,3,4,8,5,6]=>5
[1,7,2,3,4,8,5,6]=>5
[1,2,3,7,4,8,5,6]=>5
[7,1,2,3,4,5,8,6]=>5
[1,7,2,3,4,5,8,6]=>5
[1,2,7,3,4,5,8,6]=>5
[1,7,2,3,4,5,6,8]=>7
[1,2,3,7,4,5,6,8]=>7
[1,8,2,3,4,5,6,7]=>7
[1,2,3,8,4,5,6,7]=>7
[1,2,3,4,5,8,6,7]=>7
[5,3,2,6,1,4,8,7]=>3
[7,3,2,5,4,8,1,6]=>3
[8,4,5,2,3,7,6,1]=>3
[7,4,5,2,3,8,1,6]=>5
[6,4,5,2,3,1,8,7]=>3
[5,4,6,2,1,3,8,7]=>1
[3,6,1,5,4,2,8,7]=>3
[4,6,5,1,3,2,8,7]=>1
[5,6,4,3,1,2,8,7]=>3
[7,5,4,3,2,8,1,6]=>3
[8,6,4,3,7,2,5,1]=>3
[7,6,4,3,8,2,1,5]=>1
[6,7,4,3,8,1,2,5]=>5
[5,7,4,3,1,8,2,6]=>1
[4,7,5,1,3,8,2,6]=>1
[3,7,1,5,4,8,2,6]=>1
[2,1,7,5,4,8,3,6]=>3
[3,8,1,5,4,7,6,2]=>3
[4,8,5,1,3,7,6,2]=>1
[5,8,4,3,1,7,6,2]=>3
[6,8,4,3,7,1,5,2]=>1
[7,8,4,3,6,5,1,2]=>3
[6,8,5,7,3,1,4,2]=>1
[5,8,6,7,1,3,4,2]=>3
[4,8,6,1,7,3,5,2]=>1
[3,8,1,6,7,4,5,2]=>5
[2,1,8,6,7,4,5,3]=>3
[2,1,7,6,8,4,3,5]=>1
[3,7,1,6,8,4,2,5]=>1
[4,7,6,1,8,3,2,5]=>1
[5,7,6,8,1,3,2,4]=>3
[5,4,7,2,1,8,3,6]=>3
[6,4,7,2,8,1,3,5]=>3
[7,4,6,2,8,3,1,5]=>1
[8,4,6,2,7,3,5,1]=>1
[8,3,2,6,7,4,5,1]=>3
[7,3,2,6,8,4,1,5]=>1
[6,3,2,7,8,1,4,5]=>5
[5,3,2,7,1,8,4,6]=>1
[4,3,2,1,7,8,5,6]=>3
[3,4,1,2,8,7,6,5]=>3
[5,3,2,8,1,7,6,4]=>3
[6,3,2,8,7,1,5,4]=>1
[7,3,2,8,6,5,1,4]=>3
[8,4,7,2,6,5,3,1]=>3
[7,4,8,2,6,5,1,3]=>1
[6,4,8,2,7,1,5,3]=>1
[5,4,8,2,1,7,6,3]=>1
[4,5,8,1,2,7,6,3]=>5
[3,5,1,8,2,7,6,4]=>1
[2,1,5,8,3,7,6,4]=>3
[2,1,6,8,7,3,5,4]=>1
[3,6,1,8,7,2,5,4]=>3
[4,6,8,1,7,2,5,3]=>3
[5,6,8,7,1,2,4,3]=>3
[6,5,8,7,2,1,4,3]=>1
[7,5,8,6,2,4,1,3]=>1
[8,5,7,6,2,4,3,1]=>1
[5,7,8,6,1,4,2,3]=>3
[4,7,8,1,6,5,2,3]=>5
[3,7,1,8,6,5,2,4]=>1
[2,1,7,8,6,5,3,4]=>3
[3,8,1,7,6,5,4,2]=>3
[4,8,7,1,6,5,3,2]=>1
[5,8,7,6,1,4,3,2]=>3
[6,8,7,5,4,1,3,2]=>1
[4,2,5,1,3,6,7,8]=>5
[5,2,6,7,1,3,4,8]=>5
[3,2,7,8,1,4,5,6]=>5
[5,3,2,6,1,4,7,8]=>5
[7,4,3,8,1,2,5,6]=>5
[4,7,3,6,8,1,2,5]=>3
[6,7,3,4,8,1,2,5]=>5
[5,4,2,7,8,1,3,6]=>3
[6,4,7,2,5,1,3,8]=>3
[6,4,3,2,7,1,5,8]=>3
[5,4,3,2,8,1,6,7]=>3
[7,5,3,8,2,6,1,4]=>3
[8,5,4,7,2,6,1,3]=>1
[8,5,4,7,3,6,1,2]=>3
[8,1,2,7,6,3,4,5]=>5
[8,1,4,2,6,3,5,7]=>3
[8,3,1,2,4,7,5,6]=>3
[8,3,1,5,6,2,4,7]=>3
[6,3,8,1,2,7,4,5]=>5
[7,8,4,1,6,2,3,5]=>3
[8,3,4,1,6,7,2,5]=>3
[2,7,6,5,1,3,8,4]=>1
[8,3,6,5,1,7,2,4]=>1
[4,6,7,3,8,5,1,2]=>3
[3,5,2,7,1,8,6,4]=>1
[4,6,7,2,8,1,5,3]=>3
[5,6,7,8,2,1,4,3]=>5
[6,5,8,7,3,4,1,2]=>3
[3,6,7,4,5,8,1,2]=>5
[2,6,7,4,5,1,8,3]=>3
[1,6,7,4,5,2,3,8]=>7
[1,5,4,7,6,2,3,8]=>5
[2,5,4,7,6,1,8,3]=>1
[3,5,4,7,6,8,1,2]=>3
[4,5,3,7,8,6,1,2]=>5
[5,4,3,8,7,6,1,2]=>3
[6,4,8,3,7,5,1,2]=>5
[6,3,8,4,5,7,1,2]=>3
[5,3,4,8,6,7,1,2]=>5
[4,3,5,6,8,7,1,2]=>3
[3,2,5,6,1,8,7,4]=>3
[4,2,5,6,8,1,7,3]=>3
[5,2,4,8,6,1,7,3]=>1
[6,2,8,4,5,1,7,3]=>5
[7,8,2,4,5,1,6,3]=>3
[7,8,1,4,5,2,3,6]=>5
[6,1,8,4,5,2,3,7]=>3
[5,1,4,8,6,2,3,7]=>3
[4,1,3,2,8,6,5,7]=>1
[5,1,3,8,2,6,4,7]=>1
[6,1,8,3,2,5,4,7]=>1
[7,8,1,3,2,5,4,6]=>3
[7,8,2,3,1,5,6,4]=>5
[6,2,8,3,1,5,7,4]=>1
[5,2,3,8,1,6,7,4]=>5
[6,3,8,2,1,7,5,4]=>1
[7,8,3,2,1,6,5,4]=>3
[7,8,4,2,6,1,5,3]=>5
[5,4,2,8,7,1,6,3]=>1
[4,5,2,7,8,1,6,3]=>5
[2,5,3,7,1,6,8,4]=>1
[1,5,3,7,2,6,4,8]=>5
[1,6,7,3,2,5,4,8]=>5
[2,6,7,3,1,5,8,4]=>3
[3,6,7,2,1,8,5,4]=>5
[7,8,5,6,2,1,4,3]=>3
[6,5,8,7,1,2,3,4]=>5
[5,4,1,8,7,2,3,6]=>5
[6,4,8,1,7,2,3,5]=>3
[7,8,3,1,2,6,4,5]=>5
[5,3,1,8,2,7,4,6]=>1
[4,3,1,2,8,7,5,6]=>5
[4,2,1,3,8,5,7,6]=>1
[5,2,1,8,3,4,7,6]=>3
[6,2,8,1,3,4,7,5]=>3
[7,8,2,1,3,4,6,5]=>3
[6,3,1,5,2,4,8,7]=>1
[2,1,8,5,3,7,4,6]=>1
[8,2,6,1,4,3,7,5]=>1
[4,7,1,5,8,3,2,6]=>1
[8,6,1,3,4,2,5,7]=>3
[8,1,2,4,5,6,3,7]=>5
[8,2,5,1,3,6,4,7]=>1
[4,1,5,3,7,2,8,6]=>1
[5,2,7,1,3,8,4,6]=>1
[5,3,1,7,8,2,4,6]=>3
[1,7,3,4,2,5,8,6]=>3
[4,7,2,1,3,5,8,6]=>1
[4,5,2,3,7,6,1,8]=>5
[6,4,3,7,2,5,1,8]=>5
[8,4,3,6,5,1,2,7]=>3
[1,5,6,3,4,8,7,2]=>5
[4,6,2,7,3,5,1,8]=>3
[3,2,6,7,4,5,1,8]=>5
[4,7,2,6,5,3,1,8]=>5
[5,7,6,2,4,3,1,8]=>3
[1,7,5,4,8,3,6,2]=>5
[8,7,5,4,1,3,2,6]=>3
[6,8,5,4,2,1,3,7]=>1
[5,8,6,2,4,1,3,7]=>3
[4,8,2,6,5,1,3,7]=>1
[3,2,8,6,5,1,4,7]=>3
[4,1,2,6,5,8,7,3]=>3
[5,1,6,2,4,8,7,3]=>1
[6,1,5,4,2,8,7,3]=>3
[7,1,5,4,8,2,6,3]=>1
[8,1,5,4,7,6,2,3]=>3
[1,8,6,7,4,5,3,2]=>5
[8,1,6,7,4,5,2,3]=>5
[7,1,6,8,4,2,5,3]=>3
[6,1,7,8,2,4,5,3]=>3
[5,1,7,2,8,4,6,3]=>3
[4,1,2,7,8,5,6,3]=>5
[3,2,1,7,8,5,6,4]=>5
[3,2,8,7,1,5,4,6]=>3
[4,8,2,7,1,5,3,6]=>1
[5,8,7,2,1,4,3,6]=>3
[6,8,7,1,2,4,3,5]=>3
[7,8,6,1,4,2,3,5]=>5
[8,7,6,1,4,3,2,5]=>3
[1,7,6,8,4,3,5,2]=>3
[1,6,7,8,3,4,5,2]=>7
[8,6,7,1,3,4,2,5]=>5
[7,6,8,1,3,2,4,5]=>3
[5,7,8,2,1,3,4,6]=>3
[4,7,2,8,1,3,5,6]=>3
[3,2,6,8,4,1,5,7]=>1
[4,6,2,8,3,1,5,7]=>3
[5,6,8,2,3,1,4,7]=>3
[6,5,8,3,2,1,4,7]=>3
[7,5,8,3,1,2,4,6]=>3
[8,5,7,3,1,4,2,6]=>1
[1,5,7,3,8,4,6,2]=>3
[1,4,3,7,8,5,6,2]=>5
[8,4,3,7,1,5,2,6]=>3
[6,4,3,8,2,1,5,7]=>1
[4,5,2,3,8,1,6,7]=>5
[3,2,5,4,8,1,6,7]=>3
[4,5,2,3,1,8,7,6]=>5
[6,4,3,1,2,8,7,5]=>3
[7,4,3,1,8,2,6,5]=>1
[8,4,3,1,7,6,2,5]=>3
[1,5,8,3,7,6,4,2]=>5
[8,5,1,3,7,6,2,4]=>3
[7,5,1,3,8,2,6,4]=>1
[6,5,1,3,2,8,7,4]=>3
[5,6,1,2,3,8,7,4]=>5
[4,6,2,1,3,8,7,5]=>1
[3,2,6,1,4,8,7,5]=>3
[3,2,7,1,8,4,6,5]=>1
[4,7,2,1,8,3,6,5]=>3
[5,7,1,2,8,3,6,4]=>3
[6,7,1,8,2,3,5,4]=>3
[7,6,1,8,3,2,5,4]=>3
[8,6,1,7,3,5,2,4]=>1
[1,6,8,7,3,5,4,2]=>3
[1,7,8,6,5,3,4,2]=>5
[8,7,1,6,5,3,2,4]=>3
[7,8,1,6,5,2,3,4]=>5
[6,8,1,7,2,5,3,4]=>3
[5,8,1,2,7,6,3,4]=>5
[4,8,2,1,7,6,3,5]=>1
[3,2,8,1,7,6,4,5]=>3
[4,1,2,8,7,6,5,3]=>3
[5,1,8,2,7,6,4,3]=>1
[6,1,8,7,2,5,4,3]=>3
[7,1,8,6,5,2,4,3]=>1
[8,1,7,6,5,4,2,3]=>3
[1,4,3,8,7,5,6,2]=>3
[4,1,2,8,7,5,6,3]=>3
[3,2,5,1,6,4,8,7]=>1
[3,2,5,4,7,1,8,6]=>1
[4,2,5,3,7,6,8,1]=>1
[4,2,5,3,7,1,8,6]=>1
[4,2,5,3,6,1,8,7]=>1
[4,2,5,1,6,3,8,7]=>1
[3,1,5,4,6,2,8,7]=>1
[4,1,5,3,6,2,8,7]=>1
[4,3,5,1,6,2,8,7]=>1
[4,3,5,2,7,1,8,6]=>1
[4,3,6,2,7,5,8,1]=>1
[4,3,6,2,7,1,8,5]=>1
[4,3,6,1,7,2,8,5]=>1
[4,3,5,1,7,2,8,6]=>1
[3,1,5,4,7,2,8,6]=>1
[2,1,5,4,7,3,8,6]=>1
[3,1,5,4,7,6,8,2]=>1
[4,1,5,3,7,6,8,2]=>1
[4,3,5,1,7,6,8,2]=>1
[4,3,6,1,7,5,8,2]=>1
[4,3,6,5,7,1,8,2]=>1
[5,3,6,4,7,2,8,1]=>1
[5,3,6,4,7,1,8,2]=>1
[5,3,6,1,7,4,8,2]=>1
[5,1,6,3,7,4,8,2]=>1
[4,1,6,3,7,5,8,2]=>1
[3,1,6,4,7,5,8,2]=>1
[2,1,6,4,7,5,8,3]=>1
[2,1,6,4,7,3,8,5]=>1
[3,1,6,4,7,2,8,5]=>1
[4,1,6,3,7,2,8,5]=>1
[5,1,6,3,7,2,8,4]=>1
[5,3,6,1,7,2,8,4]=>1
[5,3,6,2,7,1,8,4]=>1
[5,3,6,2,7,4,8,1]=>1
[5,2,6,3,7,4,8,1]=>1
[5,2,6,3,7,1,8,4]=>1
[5,2,6,1,7,3,8,4]=>1
[4,2,5,1,7,3,8,6]=>1
[4,2,6,1,7,3,8,5]=>1
[4,2,6,3,7,1,8,5]=>1
[4,2,6,3,7,5,8,1]=>1
[3,2,6,4,7,5,8,1]=>1
[3,2,6,4,7,1,8,5]=>1
[3,2,6,1,7,4,8,5]=>1
[3,2,5,1,7,4,8,6]=>1
[3,2,4,1,7,5,8,6]=>1
[3,1,4,2,7,6,8,5]=>1
[3,2,5,1,7,6,8,4]=>1
[3,2,6,1,7,5,8,4]=>1
[3,2,6,5,7,1,8,4]=>1
[4,2,6,5,7,3,8,1]=>1
[4,2,6,5,7,1,8,3]=>1
[4,2,6,1,7,5,8,3]=>1
[4,2,5,1,7,6,8,3]=>1
[4,1,5,2,7,6,8,3]=>1
[3,1,5,2,7,6,8,4]=>1
[2,1,5,3,7,6,8,4]=>1
[2,1,6,3,7,5,8,4]=>1
[3,1,6,2,7,5,8,4]=>1
[4,1,6,2,7,5,8,3]=>1
[5,1,6,2,7,4,8,3]=>1
[5,2,6,1,7,4,8,3]=>1
[5,2,6,4,7,1,8,3]=>1
[5,2,6,4,7,3,8,1]=>1
[5,4,6,2,7,3,8,1]=>1
[5,4,6,2,7,1,8,3]=>1
[5,4,6,1,7,2,8,3]=>1
[5,1,6,4,7,2,8,3]=>1
[4,1,6,5,7,2,8,3]=>1
[3,1,6,5,7,2,8,4]=>1
[2,1,6,5,7,3,8,4]=>1
[3,1,6,5,7,4,8,2]=>1
[4,1,6,5,7,3,8,2]=>1
[5,1,6,4,7,3,8,2]=>1
[5,4,6,1,7,3,8,2]=>1
[5,4,6,3,7,1,8,2]=>1
[8,3,5,2,1,6,4,7]=>3
[8,6,3,5,2,4,1,7]=>1
[3,7,5,2,4,1,8,6]=>1
[8,3,7,5,2,4,6,1]=>1
[8,2,4,5,7,3,6,1]=>3
[2,4,5,7,3,1,8,6]=>3
[8,2,4,6,5,3,1,7]=>1
[8,2,5,4,6,1,3,7]=>1
[8,6,3,5,1,4,2,7]=>3
[8,6,1,4,5,3,2,7]=>3
[8,1,5,6,4,3,2,7]=>3
[5,7,4,3,2,1,8,6]=>3
[8,5,7,4,3,2,6,1]=>1
[4,6,8,3,2,7,5,1]=>1
[4,7,6,3,2,8,1,5]=>1
[1,4,6,7,3,2,8,5]=>5
[5,4,7,3,1,8,2,6]=>1
[1,7,4,5,3,2,8,6]=>3
[3,7,5,1,4,2,8,6]=>1
[5,7,4,2,1,3,8,6]=>3
[8,5,7,4,2,1,6,3]=>1
[8,3,7,5,1,4,6,2]=>3
[8,4,1,7,5,3,6,2]=>3
[4,6,3,8,7,1,5,2]=>3
[1,7,4,8,6,3,5,2]=>3
[8,4,7,6,3,5,2,1]=>1
[3,6,5,8,7,4,1,2]=>3
[3,1,5,8,6,7,4,2]=>3
[4,8,1,6,7,3,5,2]=>3
[3,6,4,1,8,7,5,2]=>1
[8,2,6,1,4,7,5,3]=>3
[2,7,6,8,1,4,3,5]=>1
[3,7,1,6,4,8,2,5]=>3
[1,7,3,5,6,8,2,4]=>3
[1,3,6,7,5,8,2,4]=>3
[3,7,6,5,8,2,1,4]=>3
[3,6,8,5,7,2,4,1]=>1
[2,3,5,7,6,8,1,4]=>3
[2,1,6,5,7,8,3,4]=>3
[4,2,7,6,8,3,1,5]=>3
[4,2,6,8,7,3,5,1]=>1
[3,8,2,4,6,7,5,1]=>3
[3,7,2,6,4,8,1,5]=>3
[3,2,6,1,4,7,8,5]=>3
[5,3,7,2,1,8,4,6]=>3
[4,7,3,2,1,5,8,6]=>1
[8,7,6,1,3,4,2,5]=>3
[8,5,7,3,2,1,6,4]=>3
[8,3,6,7,2,1,5,4]=>3
[3,7,8,6,2,1,5,4]=>3
[8,7,6,3,5,2,4,1]=>1
[2,7,4,8,1,6,5,3]=>1
[4,6,8,2,1,7,5,3]=>1
[8,4,1,5,7,2,6,3]=>3
[8,5,3,7,1,6,2,4]=>3
[8,5,7,2,1,3,6,4]=>3
[8,2,6,7,1,3,5,4]=>3
[8,3,6,1,7,5,2,4]=>1
[4,6,1,8,7,2,5,3]=>3
[8,1,2,5,6,7,4,3]=>5
[8,2,6,5,7,4,1,3]=>1
[2,1,7,8,5,6,4,3]=>3
[8,2,5,7,6,4,3,1]=>3
[2,7,6,8,5,4,1,3]=>1
[1,7,2,5,8,6,4,3]=>3
[1,7,4,8,2,6,5,3]=>3
[3,7,8,1,6,5,2,4]=>3
[2,7,8,6,1,3,5,4]=>3
[8,7,6,3,5,1,4,2]=>3
[8,4,7,6,5,1,3,2]=>3
[8,7,1,5,6,4,3,2]=>3
[8,1,6,7,5,4,3,2]=>3
[5,4,3,6,1,2,8,7]=>3
[2,7,6,4,5,8,1,3]=>3
[5,7,3,6,1,8,2,4]=>1
[2,1,7,6,5,8,3,4]=>3
[6,4,3,5,8,1,7,2]=>1
[7,3,5,4,8,6,1,2]=>3
[5,4,3,2,7,1,8,6]=>1
[4,3,6,2,8,7,5,1]=>3
[4,3,7,6,2,1,8,5]=>1
[6,4,3,1,7,2,8,5]=>1
[4,3,7,1,8,6,5,2]=>1
[5,3,8,7,6,4,2,1]=>1
[7,5,3,1,8,6,4,2]=>3
[1,8,6,5,3,7,4,2]=>3
[6,1,7,5,3,2,8,4]=>1
[7,6,5,3,2,1,8,4]=>1
[6,5,3,2,8,7,4,1]=>1
[5,2,6,3,8,7,4,1]=>3
[5,2,7,6,3,1,8,4]=>3
[6,5,2,1,7,3,8,4]=>1
[5,2,7,1,8,6,4,3]=>1
[6,2,8,7,5,4,3,1]=>3
[7,6,2,1,8,5,4,3]=>1
[6,1,7,2,8,5,4,3]=>1
[7,1,8,6,5,4,3,2]=>1
[4,5,2,6,3,1,8,7]=>3
[6,5,2,1,4,3,8,7]=>1
[6,5,2,7,4,8,3,1]=>1
[8,5,2,7,4,1,6,3]=>3
[8,3,7,5,2,1,6,4]=>3
[6,3,7,5,2,8,4,1]=>1
[3,1,6,5,4,2,8,7]=>1
[5,6,3,2,4,1,8,7]=>3
[3,6,2,4,1,5,8,7]=>1
[2,6,1,3,5,4,8,7]=>1
[6,7,2,3,4,8,5,1]=>5
[8,7,2,3,4,1,6,5]=>3
[5,1,7,3,8,4,6,2]=>3
[2,5,7,3,8,6,4,1]=>1
[7,6,1,3,5,8,4,2]=>3
[3,6,7,4,1,8,5,2]=>3
[5,6,3,7,4,8,1,2]=>3
[2,1,6,7,4,8,5,3]=>3
[2,1,8,7,4,3,6,5]=>1
[5,8,3,7,4,2,6,1]=>1
[3,8,7,4,1,2,6,5]=>3
[7,8,1,3,5,2,6,4]=>3
[5,8,7,3,2,6,1,4]=>3
[2,8,6,3,1,5,7,4]=>1
[8,1,6,3,2,5,4,7]=>3
[2,8,4,1,6,3,7,5]=>1
[4,8,1,2,7,6,3,5]=>3
[3,8,4,2,5,7,1,6]=>1
[6,8,3,5,2,7,4,1]=>1
[2,1,5,3,8,7,6,4]=>1
[6,5,3,2,8,7,1,4]=>3
[7,5,2,4,8,1,6,3]=>3
[3,4,2,8,5,7,6,1]=>3
[2,4,1,8,7,6,5,3]=>1
[8,4,2,1,7,5,3,6]=>1
[4,3,1,8,6,7,5,2]=>3
[3,1,4,8,6,5,7,2]=>1
[7,1,6,5,4,8,2,3]=>3
[3,7,5,6,8,4,2,1]=>3
[5,7,1,6,8,2,4,3]=>1
[8,6,2,5,1,7,4,3]=>3
[5,6,2,1,8,7,3,4]=>3
[4,6,2,5,8,3,7,1]=>1
[7,5,2,6,3,8,1,4]=>1
[4,1,2,3,6,8,7,5]=>3
[2,4,3,1,8,5,6,7]=>3
[7,5,2,8,3,4,6,1]=>3
[5,6,2,8,4,3,1,7]=>3
[4,7,2,8,1,5,3,6]=>1
[8,7,2,1,4,5,6,3]=>3
[3,6,8,7,1,5,4,2]=>3
[5,7,8,6,3,4,1,2]=>5
[7,1,8,5,4,3,6,2]=>3
[2,7,8,4,5,3,6,1]=>3
[5,7,3,8,1,4,6,2]=>1
[2,1,7,8,5,4,6,3]=>3
[2,1,5,8,4,6,3,7]=>1
[6,5,3,8,4,1,2,7]=>3
[7,5,8,4,3,6,2,1]=>1
[2,4,8,3,5,6,1,7]=>3
[4,1,8,3,6,5,2,7]=>1
[3,4,8,1,7,2,5,6]=>3
[8,4,1,3,7,2,6,5]=>1
[3,1,8,2,4,7,6,5]=>3
[2,3,8,1,4,6,7,5]=>3
[4,3,8,2,5,1,7,6]=>3
[6,3,8,4,2,5,7,1]=>1
[7,4,3,8,2,5,1,6]=>3
[2,1,4,8,3,5,7,6]=>1
[6,8,2,4,3,5,1,7]=>3
[4,8,2,3,5,1,6,7]=>3
[3,8,2,1,4,6,5,7]=>3
[2,8,1,3,4,5,7,6]=>3
[7,1,6,8,4,3,2,5]=>3
[7,1,6,5,8,3,2,4]=>1
[3,7,6,1,4,8,2,5]=>1
[2,7,8,4,1,6,5,3]=>3
[3,6,4,5,7,2,8,1]=>3
[1,8,2,7,3,4,5,6]=>5
[3,2,1,5,8,4,6,7]=>3
[5,4,3,2,1,8,6,7]=>3
[1,8,2,4,3,5,6,7]=>5
[1,7,2,4,3,5,6,8]=>5
[1,6,2,4,3,5,7,8]=>5
[1,5,2,4,3,6,7,8]=>5
[1,6,2,5,3,4,7,8]=>5
[1,7,2,5,3,4,6,8]=>5
[1,8,2,5,3,4,6,7]=>5
[1,8,2,6,3,4,5,7]=>5
[1,7,2,6,3,4,5,8]=>5
[1,8,2,7,3,5,4,6]=>3
[1,7,2,8,3,5,4,6]=>3
[1,6,2,8,3,5,4,7]=>3
[1,5,2,8,3,6,4,7]=>3
[1,4,2,8,3,6,5,7]=>3
[1,3,2,8,4,6,5,7]=>3
[1,2,3,8,4,6,5,7]=>5
[1,2,3,7,4,6,5,8]=>5
[1,3,2,7,4,6,5,8]=>3
[1,4,2,7,3,6,5,8]=>3
[1,5,2,7,3,6,4,8]=>3
[1,6,2,7,3,5,4,8]=>3
[1,7,2,6,3,5,4,8]=>3
[1,8,2,6,3,5,4,7]=>3
[1,8,2,5,3,6,4,7]=>3
[1,7,2,5,3,6,4,8]=>3
[1,6,2,5,3,7,4,8]=>3
[1,5,2,4,3,7,6,8]=>3
[1,6,2,4,3,7,5,8]=>3
[1,7,2,4,3,6,5,8]=>3
[1,8,2,4,3,6,5,7]=>3
[1,8,2,3,4,6,5,7]=>5
[1,7,2,3,4,6,5,8]=>5
[1,8,2,3,4,7,5,6]=>5
[1,8,2,4,3,7,5,6]=>3
[1,7,2,4,3,8,5,6]=>3
[1,6,2,4,3,8,5,7]=>3
[1,5,2,4,3,8,6,7]=>3
[1,6,2,5,3,8,4,7]=>3
[1,7,2,5,3,8,4,6]=>3
[1,8,2,5,3,7,4,6]=>3
[1,8,2,6,3,7,4,5]=>3
[1,7,2,6,3,8,4,5]=>3
[1,2,3,8,4,7,5,6]=>5
[1,3,2,8,4,7,5,6]=>3
[1,4,2,8,3,7,5,6]=>3
[1,5,2,8,3,7,4,6]=>3
[1,6,2,8,3,7,4,5]=>3
[1,7,2,8,3,6,4,5]=>3
[1,8,2,7,3,6,4,5]=>3
[6,7,8,1,4,3,2,5]=>5
[2,8,4,1,6,7,5,3]=>3
[4,8,5,7,1,6,2,3]=>3
[8,7,6,5,2,1,4,3]=>1
[8,3,1,5,4,7,2,6]=>1
[8,7,6,5,1,4,2,3]=>3
[7,5,1,3,8,4,2,6]=>1
[7,6,1,4,8,3,2,5]=>3
[7,1,3,5,8,2,4,6]=>1
[7,5,3,6,4,2,8,1]=>1
[8,2,6,3,4,7,5,1]=>3
[7,2,6,3,5,4,8,1]=>1
[6,2,7,4,3,5,8,1]=>1
[3,7,6,4,5,2,8,1]=>3
[2,7,6,5,3,4,8,1]=>3
[8,6,5,4,2,7,3,1]=>1
[6,5,8,4,2,7,3,1]=>1
[1,8,6,3,7,5,2,4]=>3
[8,7,5,2,6,4,3,1]=>1
[8,7,1,6,2,5,4,3]=>3
[1,7,2,8,5,3,4,6]=>3
[7,6,1,8,4,3,2,5]=>3
[8,6,1,7,4,2,5,3]=>1
[8,1,2,7,3,4,6,5]=>3
[7,1,2,8,3,5,4,6]=>3
[8,2,6,1,7,3,5,4]=>1
[4,7,5,6,8,3,2,1]=>3
[8,6,4,7,5,3,2,1]=>1
[5,4,8,1,7,2,6,3]=>1
[2,3,8,7,4,5,6,1]=>5
[7,2,8,6,4,3,5,1]=>1
[8,2,7,6,3,5,4,1]=>3
[8,1,7,6,5,2,4,3]=>1
[7,1,8,6,5,3,2,4]=>1
[1,2,8,7,6,3,4,5]=>5
[3,8,7,6,4,5,2,1]=>3
[2,8,7,6,5,3,4,1]=>3
[1,8,7,6,5,4,2,3]=>3
[3,8,6,7,1,5,2,4]=>3
[5,4,7,1,3,8,2,6]=>1
[5,6,2,1,4,8,3,7]=>3
[2,1,8,4,7,5,6,3]=>3
[4,1,3,2,8,5,6,7]=>3
[3,2,1,4,8,5,6,7]=>5
[1,8,4,2,5,3,6,7]=>3
[8,1,5,3,2,4,6,7]=>3
[3,8,1,5,2,4,6,7]=>3
[1,6,7,2,8,4,3,5]=>3
[6,7,1,4,2,8,3,5]=>3
[6,3,7,1,4,8,2,5]=>1
[3,7,8,1,5,2,4,6]=>3
[7,1,2,8,5,3,4,6]=>3
[1,7,2,8,4,5,3,6]=>3
[1,2,7,5,8,3,4,6]=>5
[2,8,1,7,4,3,6,5]=>1
[4,2,6,5,8,3,7,1]=>1
[5,2,4,7,3,6,8,1]=>1
[5,1,2,4,8,3,6,7]=>3
[4,3,6,1,5,8,2,7]=>1
[2,6,1,4,5,8,3,7]=>3
[2,5,3,4,1,8,6,7]=>3
[4,3,5,2,1,8,6,7]=>3
[3,1,6,7,5,8,2,4]=>3
[2,8,1,7,5,6,3,4]=>3
[5,3,6,8,4,7,2,1]=>1
[3,7,2,5,4,8,6,1]=>1
[8,4,2,5,7,3,6,1]=>1
[4,7,2,5,8,3,6,1]=>1
[5,2,6,8,4,3,7,1]=>1
[3,1,6,5,4,8,2,7]=>1
[4,1,6,5,8,3,2,7]=>1
[5,1,6,8,4,3,2,7]=>1
[8,5,4,7,6,3,2,1]=>1
[5,7,1,8,4,3,2,6]=>1
[2,7,1,5,4,3,8,6]=>1
[8,2,1,5,4,3,7,6]=>1
[8,4,1,5,7,3,2,6]=>1
[8,5,6,7,1,3,2,4]=>5
[8,4,6,1,7,3,2,5]=>1
[8,3,6,1,4,7,2,5]=>1
[2,7,6,1,4,3,8,5]=>1
[6,7,8,5,1,3,2,4]=>5
[5,7,6,8,2,3,4,1]=>5
[5,7,2,8,4,3,6,1]=>1
[6,7,8,2,4,3,5,1]=>5
[4,7,6,2,8,3,5,1]=>1
[8,3,6,2,4,7,5,1]=>1
[3,7,6,2,4,8,5,1]=>1
[5,7,3,8,4,6,2,1]=>1
[4,7,3,5,8,6,2,1]=>1
[8,7,2,1,4,3,6,5]=>1
[8,7,3,1,4,6,2,5]=>1
[8,7,6,3,2,5,4,1]=>1
[8,7,3,5,1,6,2,4]=>1
[8,7,2,5,1,3,6,4]=>1
[8,2,6,5,1,3,7,4]=>1
[8,4,6,5,7,1,2,3]=>5
[5,7,6,8,4,1,2,3]=>5
[4,7,6,5,8,1,2,3]=>5
[3,7,6,5,1,8,2,4]=>1
[2,6,5,7,3,4,8,1]=>3
[1,6,4,7,5,8,2,3]=>3
[8,5,3,6,2,7,4,1]=>1
[1,3,7,4,6,8,2,5]=>3
[4,7,5,6,3,2,8,1]=>3
[1,7,6,5,4,8,2,3]=>3
[8,1,6,5,7,2,4,3]=>1
[1,2,7,6,8,3,4,5]=>5
[6,1,7,5,3,8,2,4]=>1
[2,1,7,5,6,8,3,4]=>3
[5,4,1,7,6,8,2,3]=>3
[4,8,5,6,2,7,3,1]=>3
[3,8,6,4,2,7,5,1]=>1
[7,8,5,2,4,6,3,1]=>3
[2,8,6,3,7,4,5,1]=>3
[7,8,1,6,2,4,5,3]=>3
[6,8,1,4,7,2,5,3]=>1
[3,8,4,1,7,2,6,5]=>1
[5,4,7,1,8,3,2,6]=>1
[3,7,4,1,8,5,2,6]=>1
[6,7,1,4,8,3,2,5]=>3
[2,7,1,8,4,5,3,6]=>3
[6,1,2,8,4,3,5,7]=>3
[6,5,1,4,3,8,2,7]=>3
[1,6,2,5,8,3,4,7]=>3
[8,5,1,3,7,2,6,4]=>3
[8,4,2,1,7,3,6,5]=>3
[7,4,2,1,8,5,3,6]=>1
[1,5,4,2,8,3,6,7]=>5
[6,4,3,1,5,8,2,7]=>1
[3,7,6,8,4,5,2,1]=>3
[2,7,6,8,5,3,4,1]=>3
[1,7,6,8,5,4,2,3]=>3
[1,4,8,6,7,5,2,3]=>5
[2,4,8,6,7,3,5,1]=>3
[7,3,8,5,4,6,2,1]=>1
[3,4,8,5,6,7,2,1]=>5
[6,3,5,8,4,7,2,1]=>1
[5,4,3,8,6,7,2,1]=>3
[5,4,2,8,7,3,6,1]=>3
[6,2,5,8,7,3,4,1]=>3
[3,2,8,5,7,4,6,1]=>1
[1,3,8,7,5,6,2,4]=>3
[2,1,8,7,4,6,3,5]=>1
[3,1,8,5,7,6,2,4]=>3
[6,1,5,8,7,4,2,3]=>3
[5,4,1,8,7,6,2,3]=>3
[5,8,6,7,4,3,2,1]=>3
[4,8,7,5,6,3,2,1]=>3
[2,8,3,1,5,4,6,7]=>3
[2,5,3,4,7,1,8,6]=>3
[2,4,8,3,5,7,6,1]=>1
[4,2,5,3,1,8,6,7]=>3
[4,2,1,8,5,3,6,7]=>3
[5,4,1,3,8,2,6,7]=>3
[5,1,4,8,3,2,6,7]=>3
[1,5,8,4,3,2,6,7]=>3
[1,8,5,4,3,2,6,7]=>3
[1,7,4,3,8,5,2,6]=>3
[1,5,7,3,8,4,2,6]=>3
[5,1,4,7,8,3,2,6]=>3
[4,8,1,5,7,3,6,2]=>1
[8,1,5,3,7,4,6,2]=>1
[3,8,4,7,6,5,2,1]=>3
[1,6,8,5,3,7,4,2]=>3
[6,8,1,7,4,3,5,2]=>1
[6,4,8,1,7,3,5,2]=>1
[6,4,8,7,1,5,2,3]=>3
[7,6,4,1,3,8,2,5]=>1
[1,7,5,6,3,2,8,4]=>3
[4,2,1,7,8,5,3,6]=>3
[2,7,4,6,3,1,8,5]=>3
[2,6,8,4,3,7,5,1]=>1
[6,2,4,8,3,7,5,1]=>3
[7,2,6,3,4,1,8,5]=>3
[2,6,7,3,1,4,8,5]=>3
[2,7,1,8,3,5,4,6]=>3
[2,1,7,3,5,8,4,6]=>1
[8,7,1,3,6,2,4,5]=>3
[8,2,1,7,3,5,6,4]=>3
[7,8,2,6,3,1,5,4]=>3
[8,7,2,6,3,5,4,1]=>1
[1,2,8,7,4,5,6,3]=>5
[8,3,7,1,5,6,2,4]=>3
[8,6,1,2,7,5,3,4]=>3
[8,1,6,2,7,4,5,3]=>3
[1,8,5,2,6,7,4,3]=>3
[5,2,1,8,6,7,4,3]=>3
[2,8,5,7,6,4,3,1]=>1
[1,7,8,5,2,6,4,3]=>3
[7,8,1,6,4,2,5,3]=>3
[7,8,6,1,5,3,2,4]=>3
[7,3,8,6,1,5,2,4]=>3
[8,7,6,1,5,3,4,2]=>3
[8,7,1,6,4,5,3,2]=>3
[8,1,7,5,6,4,3,2]=>3
[1,8,6,7,5,4,3,2]=>3
[9,1,2,3,4,5,6,7,8]=>8
[8,1,2,3,4,5,6,9,7]=>6
[2,9,1,3,4,5,6,7,8]=>6
[9,3,1,2,4,5,6,7,8]=>6
[8,9,1,2,3,4,5,6,7]=>8
[9,7,8,1,2,3,4,5,6]=>8
[2,3,4,5,6,7,9,1,8]=>6
[2,3,4,5,6,7,8,9,1]=>8
[2,3,4,5,6,7,8,1,9]=>8
[2,3,4,5,6,7,1,8,9]=>8
[1,2,3,4,5,6,7,9,8]=>8
[2,1,3,4,5,6,7,8,9]=>8
[1,8,2,3,4,5,6,9,7]=>6
[7,1,2,3,4,5,6,9,8]=>6
[2,1,9,3,4,5,6,7,8]=>6
[2,8,1,3,4,5,6,7,9]=>6
[1,2,3,4,5,6,7,8,9]=>10
[3,2,4,5,6,7,8,9,1]=>6
[9,8,7,6,5,4,3,2,1]=>2
[8,7,6,5,4,3,2,1,9]=>2
[1,9,8,7,6,5,4,3,2]=>2
[8,7,6,4,5,3,2,1,9]=>4
[1,9,8,7,5,6,4,3,2]=>4
[8,7,5,4,6,3,2,1,9]=>2
[8,7,4,6,5,3,2,1,9]=>2
[1,9,8,6,5,7,4,3,2]=>2
[1,9,8,5,7,6,4,3,2]=>2
[9,2,1,3,4,5,6,7,8]=>6
[9,2,3,1,4,5,6,7,8]=>6
[4,2,3,5,6,7,8,9,1]=>6
[3,4,2,5,6,7,8,9,1]=>6
[9,8,1,2,3,4,5,6,7]=>8
[7,8,9,1,2,3,4,5,6]=>8
[9,8,7,1,2,3,4,5,6]=>6
[6,7,8,9,1,2,3,4,5]=>8
[9,6,7,8,1,2,3,4,5]=>8
[8,9,6,7,1,2,3,4,5]=>8
[9,8,6,7,1,2,3,4,5]=>6
[9,8,7,6,1,2,3,4,5]=>6
[9,5,6,7,8,1,2,3,4]=>8
[8,9,5,6,7,1,2,3,4]=>8
[9,8,5,6,7,1,2,3,4]=>6
[9,7,8,5,6,1,2,3,4]=>6
[9,8,7,5,6,1,2,3,4]=>6
[9,8,7,6,5,1,2,3,4]=>4
[7,8,9,4,5,6,1,2,3]=>8
[9,7,8,4,5,6,1,2,3]=>6
[9,8,7,4,5,6,1,2,3]=>6
[8,9,6,7,4,5,1,2,3]=>6
[9,8,6,7,4,5,1,2,3]=>6
[9,8,7,6,4,5,1,2,3]=>4
[9,8,7,6,5,4,1,2,3]=>4
[9,7,8,5,6,3,4,1,2]=>6
[9,8,7,5,6,3,4,1,2]=>4
[9,8,7,6,5,3,4,1,2]=>4
[9,8,7,6,5,4,3,1,2]=>2
[7,8,6,5,4,3,2,1,9]=>4
[1,8,9,7,6,5,4,3,2]=>4
[7,6,8,5,4,3,2,1,9]=>2
[6,8,7,5,4,3,2,1,9]=>2
[1,8,7,9,6,5,4,3,2]=>2
[1,7,9,8,6,5,4,3,2]=>2
[8,1,2,3,4,5,6,7,9]=>8
[1,9,2,3,4,5,6,7,8]=>8
[7,8,1,2,3,4,5,6,9]=>8
[1,8,9,2,3,4,5,6,7]=>8
[7,1,8,2,3,4,5,6,9]=>6
[6,8,1,2,3,4,5,7,9]=>6
[1,8,2,9,3,4,5,6,7]=>6
[1,7,9,2,3,4,5,6,8]=>6
[7,1,2,3,4,5,6,8,9]=>8
[3,4,1,2,5,6,7,8,9]=>8
[3,2,1,4,5,6,7,8,9]=>8
[4,5,6,1,2,3,7,8,9]=>8
[4,2,5,1,3,6,7,8,9]=>6
[4,3,2,1,5,6,7,8,9]=>6
[5,6,7,8,1,2,3,4,9]=>8
[5,2,6,7,1,3,4,8,9]=>6
[5,6,3,4,1,2,7,8,9]=>8
[5,3,2,6,1,4,7,8,9]=>6
[5,4,3,2,1,6,7,8,9]=>6
[6,2,7,8,9,1,3,4,5]=>6
[6,7,3,4,8,1,2,5,9]=>6
[6,3,2,7,8,1,4,5,9]=>6
[6,4,7,2,5,1,3,8,9]=>4
[6,4,3,2,7,1,5,8,9]=>4
[6,5,4,3,2,1,7,8,9]=>4
[7,4,8,2,5,9,1,3,6]=>2
[7,4,3,2,8,9,1,5,6]=>4
[7,8,5,6,3,4,1,2,9]=>6
[7,5,3,8,2,6,1,4,9]=>4
[7,5,4,3,2,8,1,6,9]=>4
[7,6,5,4,3,2,1,8,9]=>4
[8,6,9,4,7,2,5,1,3]=>2
[8,6,4,3,9,2,7,1,5]=>2
[8,6,5,4,3,2,9,1,7]=>2
[2,1,4,3,6,5,8,7,10,9]=>1
[4,3,2,1,6,5,8,7,10,9]=>1
[6,3,2,5,4,1,8,7,10,9]=>1
[8,3,2,5,4,7,6,1,10,9]=>1
[10,3,2,5,4,7,6,9,8,1]=>1
[2,1,6,5,4,3,8,7,10,9]=>1
[6,5,4,3,2,1,8,7,10,9]=>1
[8,5,4,3,2,7,6,1,10,9]=>1
[10,5,4,3,2,7,6,9,8,1]=>1
[2,1,8,5,4,7,6,3,10,9]=>1
[8,7,4,3,6,5,2,1,10,9]=>1
[10,7,4,3,6,5,2,9,8,1]=>1
[2,1,10,5,4,7,6,9,8,3]=>1
[10,9,4,3,6,5,8,7,2,1]=>1
[8,9,5,6,3,4,10,1,2,7]=>7
[2,1,4,3,8,7,6,5,10,9]=>1
[4,3,2,1,8,7,6,5,10,9]=>1
[8,3,2,7,6,5,4,1,10,9]=>1
[10,3,2,7,6,5,4,9,8,1]=>1
[2,1,8,7,6,5,4,3,10,9]=>1
[8,7,6,5,4,3,2,1,10,9]=>1
[9,7,6,5,4,3,2,10,1,8]=>3
[10,7,6,5,4,3,2,9,8,1]=>1
[2,1,10,7,6,5,4,9,8,3]=>1
[10,9,6,5,4,3,8,7,2,1]=>1
[2,1,4,3,10,7,6,9,8,5]=>1
[4,3,2,1,10,7,6,9,8,5]=>1
[10,3,2,9,6,5,8,7,4,1]=>1
[2,1,10,9,6,5,8,7,4,3]=>1
[10,9,8,5,4,7,6,3,2,1]=>1
[6,7,8,9,10,1,2,3,4,5]=>9
[7,3,2,8,9,10,1,4,5,6]=>7
[8,5,4,3,2,9,10,1,6,7]=>5
[2,1,4,3,6,5,10,9,8,7]=>1
[4,3,2,1,6,5,10,9,8,7]=>1
[6,3,2,5,4,1,10,9,8,7]=>1
[10,3,2,5,4,9,8,7,6,1]=>1
[2,1,6,5,4,3,10,9,8,7]=>1
[6,5,4,3,2,1,10,9,8,7]=>1
[10,5,4,3,2,9,8,7,6,1]=>1
[2,1,10,5,4,9,8,7,6,3]=>1
[10,9,4,3,8,7,6,5,2,1]=>1
[9,7,5,10,3,8,2,6,1,4]=>1
[2,1,4,3,10,9,8,7,6,5]=>1
[4,3,2,1,10,9,8,7,6,5]=>1
[10,3,2,9,8,7,6,5,4,1]=>1
[2,1,10,9,8,7,6,5,4,3]=>1
[10,9,8,7,6,5,4,3,2,1]=>1
[2,3,4,5,6,7,8,9,10,1]=>9
[2,3,4,5,6,7,8,9,1,10]=>9
[10,8,9,5,6,7,1,2,3,4]=>7
[10,8,9,4,5,6,1,2,3,7]=>7
[10,7,8,5,6,9,1,2,3,4]=>7
[10,7,8,4,5,9,1,2,3,6]=>7
[10,6,7,4,5,8,1,2,3,9]=>5
[10,7,8,3,4,9,1,2,5,6]=>7
[10,6,7,3,4,8,1,2,5,9]=>5
[9,8,10,5,6,7,1,2,3,4]=>7
[9,8,10,4,5,6,1,2,3,7]=>5
[9,7,10,5,6,8,1,2,3,4]=>7
[9,7,10,4,5,8,1,2,3,6]=>5
[9,6,10,4,5,7,1,2,3,8]=>5
[9,7,10,3,4,8,1,2,5,6]=>5
[9,6,10,3,4,7,1,2,5,8]=>3
[8,7,9,5,6,10,1,2,3,4]=>5
[8,7,9,4,5,10,1,2,3,6]=>5
[8,6,9,4,5,10,1,2,3,7]=>5
[7,6,8,4,5,9,1,2,3,10]=>5
[8,7,9,3,4,10,1,2,5,6]=>5
[8,6,9,3,4,10,1,2,5,7]=>5
[7,6,8,3,4,9,1,2,5,10]=>5
[9,6,10,5,7,8,1,2,3,4]=>7
[9,6,10,4,7,8,1,2,3,5]=>5
[9,5,10,4,6,7,1,2,3,8]=>5
[9,6,10,3,7,8,1,2,4,5]=>5
[9,5,10,3,6,7,1,2,4,8]=>3
[8,6,9,5,7,10,1,2,3,4]=>5
[8,6,9,4,7,10,1,2,3,5]=>3
[8,5,9,4,6,10,1,2,3,7]=>5
[7,5,8,4,6,9,1,2,3,10]=>5
[8,6,9,3,7,10,1,2,4,5]=>3
[8,5,9,3,6,10,1,2,4,7]=>3
[7,5,8,3,6,9,1,2,4,10]=>3
[8,4,9,3,5,10,1,2,6,7]=>5
[7,4,8,3,5,9,1,2,6,10]=>5
[9,6,10,2,7,8,1,3,4,5]=>5
[9,5,10,2,6,7,1,3,4,8]=>3
[8,6,9,2,7,10,1,3,4,5]=>3
[8,5,9,2,6,10,1,3,4,7]=>3
[7,5,8,2,6,9,1,3,4,10]=>3
[8,4,9,2,5,10,1,3,6,7]=>3
[7,4,8,2,5,9,1,3,6,10]=>3
[1,2,3,4,5,6,7,8,10,9]=>9
[2,1,3,4,5,6,7,8,9,10]=>9
[9,1,2,3,4,5,6,7,10,8]=>7
[2,10,1,3,4,5,6,7,8,9]=>7
[1,2,3,4,5,6,7,8,9,10]=>11
[9,8,7,6,5,4,3,2,1,10]=>3
[10,1,2,3,4,5,6,7,8,9]=>9
[10,9,1,2,3,4,5,6,7,8]=>9
[1,10,9,8,7,6,5,4,3,2]=>3
[9,8,7,5,6,4,3,2,1,10]=>3
[1,10,9,8,6,7,5,4,3,2]=>3
[10,2,1,3,4,5,6,7,8,9]=>7
[3,2,4,5,6,7,8,9,10,1]=>7
[2,4,6,8,10,1,3,5,7,9]=>1
[2,4,6,9,10,1,3,5,7,8]=>3
[2,4,7,8,10,1,3,5,6,9]=>3
[2,4,7,9,10,1,3,5,6,8]=>3
[2,4,8,9,10,1,3,5,6,7]=>5
[2,5,6,8,10,1,3,4,7,9]=>3
[2,5,6,9,10,1,3,4,7,8]=>5
[2,5,7,8,10,1,3,4,6,9]=>3
[2,5,7,9,10,1,3,4,6,8]=>3
[2,5,8,9,10,1,3,4,6,7]=>5
[2,6,7,8,10,1,3,4,5,9]=>5
[2,6,7,9,10,1,3,4,5,8]=>5
[2,6,8,9,10,1,3,4,5,7]=>5
[2,7,8,9,10,1,3,4,5,6]=>7
[3,4,6,8,10,1,2,5,7,9]=>3
[3,4,6,9,10,1,2,5,7,8]=>5
[3,4,7,8,10,1,2,5,6,9]=>5
[3,4,7,9,10,1,2,5,6,8]=>5
[3,4,8,9,10,1,2,5,6,7]=>7
[3,5,6,8,10,1,2,4,7,9]=>3
[3,5,6,9,10,1,2,4,7,8]=>5
[3,5,7,8,10,1,2,4,6,9]=>3
[3,5,7,9,10,1,2,4,6,8]=>3
[3,5,8,9,10,1,2,4,6,7]=>5
[3,6,7,8,10,1,2,4,5,9]=>5
[3,6,7,9,10,1,2,4,5,8]=>5
[3,6,8,9,10,1,2,4,5,7]=>5
[3,7,8,9,10,1,2,4,5,6]=>7
[4,5,6,8,10,1,2,3,7,9]=>5
[4,5,6,9,10,1,2,3,7,8]=>7
[4,5,7,8,10,1,2,3,6,9]=>5
[4,5,7,9,10,1,2,3,6,8]=>5
[4,5,8,9,10,1,2,3,6,7]=>7
[4,6,7,8,10,1,2,3,5,9]=>5
[4,6,7,9,10,1,2,3,5,8]=>5
[4,6,8,9,10,1,2,3,5,7]=>5
[4,7,8,9,10,1,2,3,5,6]=>7
[5,6,7,8,10,1,2,3,4,9]=>7
[5,6,7,9,10,1,2,3,4,8]=>7
[5,6,8,9,10,1,2,3,4,7]=>7
[5,7,8,9,10,1,2,3,4,6]=>7
[9,10,1,2,3,4,5,6,7,8]=>9
[8,9,10,1,2,3,4,5,6,7]=>9
[10,8,9,1,2,3,4,5,6,7]=>9
[10,9,8,1,2,3,4,5,6,7]=>7
[7,8,9,10,1,2,3,4,5,6]=>9
[10,7,8,9,1,2,3,4,5,6]=>9
[9,10,7,8,1,2,3,4,5,6]=>9
[10,9,7,8,1,2,3,4,5,6]=>7
[10,9,8,7,1,2,3,4,5,6]=>7
[10,6,7,8,9,1,2,3,4,5]=>9
[9,10,6,7,8,1,2,3,4,5]=>9
[10,9,6,7,8,1,2,3,4,5]=>7
[10,8,9,6,7,1,2,3,4,5]=>7
[10,9,8,6,7,1,2,3,4,5]=>7
[10,9,8,7,6,1,2,3,4,5]=>5
[9,10,5,6,7,8,1,2,3,4]=>9
[10,9,5,6,7,8,1,2,3,4]=>7
[8,9,10,5,6,7,1,2,3,4]=>9
[10,9,8,5,6,7,1,2,3,4]=>7
[9,10,7,8,5,6,1,2,3,4]=>7
[10,9,7,8,5,6,1,2,3,4]=>7
[10,9,8,7,5,6,1,2,3,4]=>5
[10,9,8,7,6,5,1,2,3,4]=>5
[10,7,8,9,4,5,6,1,2,3]=>7
[9,10,7,8,4,5,6,1,2,3]=>7
[10,9,7,8,4,5,6,1,2,3]=>7
[10,9,8,7,4,5,6,1,2,3]=>5
[10,8,9,6,7,4,5,1,2,3]=>7
[10,9,8,6,7,4,5,1,2,3]=>5
[10,9,8,7,6,4,5,1,2,3]=>5
[10,9,8,7,6,5,4,1,2,3]=>3
[9,10,7,8,5,6,3,4,1,2]=>7
[10,9,7,8,5,6,3,4,1,2]=>5
[10,9,8,7,5,6,3,4,1,2]=>5
[10,9,8,7,6,5,3,4,1,2]=>3
[10,9,8,7,6,5,4,3,1,2]=>3
[8,9,7,6,5,4,3,2,1,10]=>3
[1,9,10,8,7,6,5,4,3,2]=>3
[9,1,2,3,4,5,6,7,8,10]=>9
[1,10,2,3,4,5,6,7,8,9]=>9
[8,9,1,2,3,4,5,6,7,10]=>9
[1,9,10,2,3,4,5,6,7,8]=>9
[3,4,1,2,5,6,7,8,9,10]=>9
[3,2,1,4,5,6,7,8,9,10]=>9
[4,5,6,1,2,3,7,8,9,10]=>9
[4,2,5,1,3,6,7,8,9,10]=>7
[4,3,2,1,5,6,7,8,9,10]=>7
[5,6,7,8,1,2,3,4,9,10]=>9
[5,2,6,7,1,3,4,8,9,10]=>7
[5,6,3,4,1,2,7,8,9,10]=>9
[5,3,2,6,1,4,7,8,9,10]=>7
[5,4,3,2,1,6,7,8,9,10]=>7
[6,2,7,8,9,1,3,4,5,10]=>7
[6,7,3,4,8,1,2,5,9,10]=>7
[6,3,2,7,8,1,4,5,9,10]=>7
[6,4,7,2,5,1,3,8,9,10]=>5
[6,4,3,2,7,1,5,8,9,10]=>5
[6,5,4,3,2,1,7,8,9,10]=>5
[7,8,3,4,9,10,1,2,5,6]=>7
[7,8,9,4,5,6,1,2,3,10]=>9
[7,4,3,2,8,9,1,5,6,10]=>5
[7,8,5,6,3,4,1,2,9,10]=>7
[7,5,3,8,2,6,1,4,9,10]=>5
[7,5,4,3,2,8,1,6,9,10]=>5
[7,6,5,4,3,2,1,8,9,10]=>5
[8,5,9,10,2,6,7,1,3,4]=>5
[8,5,3,9,2,6,10,1,4,7]=>3
[8,6,9,4,7,2,5,1,3,10]=>3
[8,6,4,3,9,2,7,1,5,10]=>3
[8,6,5,4,3,2,9,1,7,10]=>3
[8,7,6,5,4,3,2,1,9,10]=>3
[9,7,5,4,3,10,2,8,1,6]=>3
[1,2,3,4,5,6,7,8,9,11,10]=>10
[2,1,3,4,5,6,7,8,9,10,11]=>10
[11,1,2,3,4,5,6,7,8,9,10]=>10
[10,9,8,7,6,5,4,3,2,1,11]=>2
[1,11,10,9,8,7,6,5,4,3,2]=>2
[2,3,4,5,6,7,8,9,10,11,1]=>10
[10,1,2,3,4,5,6,7,8,9,11]=>10
[1,11,2,3,4,5,6,7,8,9,10]=>10
[2,1,4,3,6,5,8,7,10,9,12,11]=>1
[2,1,4,3,6,5,8,7,12,11,10,9]=>1
[2,1,4,3,6,5,10,9,8,7,12,11]=>1
[2,1,4,3,6,5,12,9,8,11,10,7]=>1
[2,1,4,3,6,5,12,11,10,9,8,7]=>1
[2,1,4,3,8,7,6,5,10,9,12,11]=>1
[2,1,4,3,8,7,6,5,12,11,10,9]=>1
[2,1,4,3,10,7,6,9,8,5,12,11]=>1
[2,1,4,3,12,7,6,9,8,11,10,5]=>1
[2,1,4,3,12,7,6,11,10,9,8,5]=>1
[2,1,4,3,10,9,8,7,6,5,12,11]=>1
[2,1,4,3,12,9,8,7,6,11,10,5]=>1
[2,1,4,3,12,11,8,7,10,9,6,5]=>1
[2,1,4,3,12,11,10,9,8,7,6,5]=>1
[2,1,6,5,4,3,8,7,10,9,12,11]=>1
[2,1,6,5,4,3,8,7,12,11,10,9]=>1
[2,1,6,5,4,3,10,9,8,7,12,11]=>1
[2,1,6,5,4,3,12,9,8,11,10,7]=>1
[2,1,6,5,4,3,12,11,10,9,8,7]=>1
[2,1,8,5,4,7,6,3,10,9,12,11]=>1
[2,1,8,5,4,7,6,3,12,11,10,9]=>1
[2,1,10,5,4,7,6,9,8,3,12,11]=>1
[2,1,12,5,4,7,6,9,8,11,10,3]=>1
[2,1,12,5,4,7,6,11,10,9,8,3]=>1
[2,1,10,5,4,9,8,7,6,3,12,11]=>1
[2,1,12,5,4,9,8,7,6,11,10,3]=>1
[2,1,12,5,4,11,8,7,10,9,6,3]=>1
[2,1,12,5,4,11,10,9,8,7,6,3]=>1
[2,1,8,7,6,5,4,3,10,9,12,11]=>1
[2,1,8,7,6,5,4,3,12,11,10,9]=>1
[2,1,10,7,6,5,4,9,8,3,12,11]=>1
[2,1,12,7,6,5,4,9,8,11,10,3]=>1
[2,1,12,7,6,5,4,11,10,9,8,3]=>1
[2,1,10,9,6,5,8,7,4,3,12,11]=>1
[2,1,12,9,6,5,8,7,4,11,10,3]=>1
[2,1,12,11,6,5,8,7,10,9,4,3]=>1
[2,1,12,11,6,5,10,9,8,7,4,3]=>1
[2,1,10,9,8,7,6,5,4,3,12,11]=>1
[2,1,12,9,8,7,6,5,4,11,10,3]=>1
[2,1,12,11,8,7,6,5,10,9,4,3]=>1
[2,1,12,11,10,7,6,9,8,5,4,3]=>1
[2,1,12,11,10,9,8,7,6,5,4,3]=>1
[4,3,2,1,6,5,8,7,10,9,12,11]=>1
[4,3,2,1,6,5,8,7,12,11,10,9]=>1
[4,3,2,1,6,5,10,9,8,7,12,11]=>1
[4,3,2,1,6,5,12,9,8,11,10,7]=>1
[4,3,2,1,6,5,12,11,10,9,8,7]=>1
[4,3,2,1,8,7,6,5,10,9,12,11]=>1
[4,3,2,1,8,7,6,5,12,11,10,9]=>1
[4,3,2,1,10,7,6,9,8,5,12,11]=>1
[4,3,2,1,12,7,6,9,8,11,10,5]=>1
[4,3,2,1,12,7,6,11,10,9,8,5]=>1
[4,3,2,1,10,9,8,7,6,5,12,11]=>1
[4,3,2,1,12,9,8,7,6,11,10,5]=>1
[4,3,2,1,12,11,8,7,10,9,6,5]=>1
[4,3,2,1,12,11,10,9,8,7,6,5]=>1
[6,3,2,5,4,1,8,7,10,9,12,11]=>1
[6,3,2,5,4,1,8,7,12,11,10,9]=>1
[6,3,2,5,4,1,10,9,8,7,12,11]=>1
[6,3,2,5,4,1,12,9,8,11,10,7]=>1
[6,3,2,5,4,1,12,11,10,9,8,7]=>1
[8,3,2,5,4,7,6,1,10,9,12,11]=>1
[8,3,2,5,4,7,6,1,12,11,10,9]=>1
[10,3,2,5,4,7,6,9,8,1,12,11]=>1
[12,3,2,5,4,7,6,9,8,11,10,1]=>1
[12,3,2,5,4,7,6,11,10,9,8,1]=>1
[10,3,2,5,4,9,8,7,6,1,12,11]=>1
[12,3,2,5,4,9,8,7,6,11,10,1]=>1
[12,3,2,5,4,11,8,7,10,9,6,1]=>1
[12,3,2,5,4,11,10,9,8,7,6,1]=>1
[8,3,2,7,6,5,4,1,10,9,12,11]=>1
[8,3,2,7,6,5,4,1,12,11,10,9]=>1
[10,3,2,7,6,5,4,9,8,1,12,11]=>1
[12,3,2,7,6,5,4,9,8,11,10,1]=>1
[12,3,2,7,6,5,4,11,10,9,8,1]=>1
[10,3,2,9,6,5,8,7,4,1,12,11]=>1
[12,3,2,9,6,5,8,7,4,11,10,1]=>1
[12,3,2,11,6,5,8,7,10,9,4,1]=>1
[12,3,2,11,6,5,10,9,8,7,4,1]=>1
[10,3,2,9,8,7,6,5,4,1,12,11]=>1
[12,3,2,9,8,7,6,5,4,11,10,1]=>1
[12,3,2,11,8,7,6,5,10,9,4,1]=>1
[12,3,2,11,10,7,6,9,8,5,4,1]=>1
[12,3,2,11,10,9,8,7,6,5,4,1]=>1
[6,5,4,3,2,1,8,7,10,9,12,11]=>1
[6,5,4,3,2,1,8,7,12,11,10,9]=>1
[6,5,4,3,2,1,10,9,8,7,12,11]=>1
[6,5,4,3,2,1,12,9,8,11,10,7]=>1
[6,5,4,3,2,1,12,11,10,9,8,7]=>1
[8,5,4,3,2,7,6,1,10,9,12,11]=>1
[8,5,4,3,2,7,6,1,12,11,10,9]=>1
[10,5,4,3,2,7,6,9,8,1,12,11]=>1
[12,5,4,3,2,7,6,9,8,11,10,1]=>1
[12,5,4,3,2,7,6,11,10,9,8,1]=>1
[10,5,4,3,2,9,8,7,6,1,12,11]=>1
[12,5,4,3,2,9,8,7,6,11,10,1]=>1
[12,5,4,3,2,11,8,7,10,9,6,1]=>1
[12,5,4,3,2,11,10,9,8,7,6,1]=>1
[8,7,4,3,6,5,2,1,10,9,12,11]=>1
[8,7,4,3,6,5,2,1,12,11,10,9]=>1
[10,7,4,3,6,5,2,9,8,1,12,11]=>1
[12,7,4,3,6,5,2,9,8,11,10,1]=>1
[12,7,4,3,6,5,2,11,10,9,8,1]=>1
[10,9,4,3,6,5,8,7,2,1,12,11]=>1
[12,9,4,3,6,5,8,7,2,11,10,1]=>1
[12,11,4,3,6,5,8,7,10,9,2,1]=>1
[12,11,4,3,6,5,10,9,8,7,2,1]=>1
[10,9,4,3,8,7,6,5,2,1,12,11]=>1
[12,9,4,3,8,7,6,5,2,11,10,1]=>1
[12,11,4,3,8,7,6,5,10,9,2,1]=>1
[12,11,4,3,10,7,6,9,8,5,2,1]=>1
[12,11,4,3,10,9,8,7,6,5,2,1]=>1
[8,7,6,5,4,3,2,1,10,9,12,11]=>1
[8,7,6,5,4,3,2,1,12,11,10,9]=>1
[10,7,6,5,4,3,2,9,8,1,12,11]=>1
[12,7,6,5,4,3,2,9,8,11,10,1]=>1
[12,7,6,5,4,3,2,11,10,9,8,1]=>1
[10,9,6,5,4,3,8,7,2,1,12,11]=>1
[12,9,6,5,4,3,8,7,2,11,10,1]=>1
[12,11,6,5,4,3,8,7,10,9,2,1]=>1
[12,11,6,5,4,3,10,9,8,7,2,1]=>1
[10,9,8,5,4,7,6,3,2,1,12,11]=>1
[12,9,8,5,4,7,6,3,2,11,10,1]=>1
[12,11,8,5,4,7,6,3,10,9,2,1]=>1
[12,11,10,5,4,7,6,9,8,3,2,1]=>1
[12,11,10,5,4,9,8,7,6,3,2,1]=>1
[10,9,8,7,6,5,4,3,2,1,12,11]=>1
[12,9,8,7,6,5,4,3,2,11,10,1]=>1
[12,11,8,7,6,5,4,3,10,9,2,1]=>1
[12,11,10,7,6,5,4,9,8,3,2,1]=>1
[12,11,10,9,6,5,8,7,4,3,2,1]=>1
[12,11,10,9,8,7,6,5,4,3,2,1]=>1
[2,4,6,8,10,12,1,3,5,7,9,11]=>1
[2,4,6,8,11,12,1,3,5,7,9,10]=>3
[2,4,6,9,10,12,1,3,5,7,8,11]=>3
[2,4,6,9,11,12,1,3,5,7,8,10]=>3
[2,4,6,10,11,12,1,3,5,7,8,9]=>5
[2,4,7,8,10,12,1,3,5,6,9,11]=>3
[2,4,7,8,11,12,1,3,5,6,9,10]=>5
[2,4,7,9,10,12,1,3,5,6,8,11]=>3
[2,4,7,9,11,12,1,3,5,6,8,10]=>3
[2,4,7,10,11,12,1,3,5,6,8,9]=>5
[2,4,8,9,10,12,1,3,5,6,7,11]=>5
[2,4,8,9,11,12,1,3,5,6,7,10]=>5
[2,4,8,10,11,12,1,3,5,6,7,9]=>5
[2,4,9,10,11,12,1,3,5,6,7,8]=>7
[2,5,6,8,10,12,1,3,4,7,9,11]=>3
[2,5,6,8,11,12,1,3,4,7,9,10]=>5
[2,5,6,9,10,12,1,3,4,7,8,11]=>5
[2,5,6,9,11,12,1,3,4,7,8,10]=>5
[2,5,6,10,11,12,1,3,4,7,8,9]=>7
[2,5,7,8,10,12,1,3,4,6,9,11]=>3
[2,5,7,8,11,12,1,3,4,6,9,10]=>5
[2,5,7,9,10,12,1,3,4,6,8,11]=>3
[2,5,7,9,11,12,1,3,4,6,8,10]=>3
[2,5,7,10,11,12,1,3,4,6,8,9]=>5
[2,5,8,9,10,12,1,3,4,6,7,11]=>5
[2,5,8,9,11,12,1,3,4,6,7,10]=>5
[2,5,8,10,11,12,1,3,4,6,7,9]=>5
[2,5,9,10,11,12,1,3,4,6,7,8]=>7
[2,6,7,8,10,12,1,3,4,5,9,11]=>5
[2,6,7,8,11,12,1,3,4,5,9,10]=>7
[2,6,7,9,10,12,1,3,4,5,8,11]=>5
[2,6,7,9,11,12,1,3,4,5,8,10]=>5
[2,6,7,10,11,12,1,3,4,5,8,9]=>7
[2,6,8,9,10,12,1,3,4,5,7,11]=>5
[2,6,8,9,11,12,1,3,4,5,7,10]=>5
[2,6,8,10,11,12,1,3,4,5,7,9]=>5
[2,6,9,10,11,12,1,3,4,5,7,8]=>7
[2,7,8,9,10,12,1,3,4,5,6,11]=>7
[2,7,8,9,11,12,1,3,4,5,6,10]=>7
[2,7,8,10,11,12,1,3,4,5,6,9]=>7
[2,7,9,10,11,12,1,3,4,5,6,8]=>7
[2,8,9,10,11,12,1,3,4,5,6,7]=>9
[3,4,6,8,10,12,1,2,5,7,9,11]=>3
[3,4,6,8,11,12,1,2,5,7,9,10]=>5
[3,4,6,9,10,12,1,2,5,7,8,11]=>5
[3,4,6,9,11,12,1,2,5,7,8,10]=>5
[3,4,6,10,11,12,1,2,5,7,8,9]=>7
[3,4,7,8,10,12,1,2,5,6,9,11]=>5
[3,4,7,8,11,12,1,2,5,6,9,10]=>7
[3,4,7,9,10,12,1,2,5,6,8,11]=>5
[3,4,7,9,11,12,1,2,5,6,8,10]=>5
[3,4,7,10,11,12,1,2,5,6,8,9]=>7
[3,4,8,9,10,12,1,2,5,6,7,11]=>7
[3,4,8,9,11,12,1,2,5,6,7,10]=>7
[3,4,8,10,11,12,1,2,5,6,7,9]=>7
[3,4,9,10,11,12,1,2,5,6,7,8]=>9
[3,5,6,8,10,12,1,2,4,7,9,11]=>3
[3,5,6,8,11,12,1,2,4,7,9,10]=>5
[3,5,6,9,10,12,1,2,4,7,8,11]=>5
[3,5,6,9,11,12,1,2,4,7,8,10]=>5
[3,5,6,10,11,12,1,2,4,7,8,9]=>7
[3,5,7,8,10,12,1,2,4,6,9,11]=>3
[3,5,7,8,11,12,1,2,4,6,9,10]=>5
[3,5,7,9,10,12,1,2,4,6,8,11]=>3
[3,5,7,9,11,12,1,2,4,6,8,10]=>3
[3,5,7,10,11,12,1,2,4,6,8,9]=>5
[3,5,8,9,10,12,1,2,4,6,7,11]=>5
[3,5,8,9,11,12,1,2,4,6,7,10]=>5
[3,5,8,10,11,12,1,2,4,6,7,9]=>5
[3,5,9,10,11,12,1,2,4,6,7,8]=>7
[3,6,7,8,10,12,1,2,4,5,9,11]=>5
[3,6,7,8,11,12,1,2,4,5,9,10]=>7
[3,6,7,9,10,12,1,2,4,5,8,11]=>5
[3,6,7,9,11,12,1,2,4,5,8,10]=>5
[3,6,7,10,11,12,1,2,4,5,8,9]=>7
[3,6,8,9,10,12,1,2,4,5,7,11]=>5
[3,6,8,9,11,12,1,2,4,5,7,10]=>5
[3,6,8,10,11,12,1,2,4,5,7,9]=>5
[3,6,9,10,11,12,1,2,4,5,7,8]=>7
[3,7,8,9,10,12,1,2,4,5,6,11]=>7
[3,7,8,9,11,12,1,2,4,5,6,10]=>7
[3,7,8,10,11,12,1,2,4,5,6,9]=>7
[3,7,9,10,11,12,1,2,4,5,6,8]=>7
[3,8,9,10,11,12,1,2,4,5,6,7]=>9
[4,5,6,8,10,12,1,2,3,7,9,11]=>5
[4,5,6,8,11,12,1,2,3,7,9,10]=>7
[4,5,6,9,10,12,1,2,3,7,8,11]=>7
[4,5,6,9,11,12,1,2,3,7,8,10]=>7
[4,5,6,10,11,12,1,2,3,7,8,9]=>9
[4,5,7,8,10,12,1,2,3,6,9,11]=>5
[4,5,7,8,11,12,1,2,3,6,9,10]=>7
[4,5,7,9,10,12,1,2,3,6,8,11]=>5
[4,5,7,9,11,12,1,2,3,6,8,10]=>5
[4,5,7,10,11,12,1,2,3,6,8,9]=>7
[4,5,8,9,10,12,1,2,3,6,7,11]=>7
[4,5,8,9,11,12,1,2,3,6,7,10]=>7
[4,5,8,10,11,12,1,2,3,6,7,9]=>7
[4,5,9,10,11,12,1,2,3,6,7,8]=>9
[4,6,7,8,10,12,1,2,3,5,9,11]=>5
[4,6,7,8,11,12,1,2,3,5,9,10]=>7
[4,6,7,9,10,12,1,2,3,5,8,11]=>5
[4,6,7,9,11,12,1,2,3,5,8,10]=>5
[4,6,7,10,11,12,1,2,3,5,8,9]=>7
[4,6,8,9,10,12,1,2,3,5,7,11]=>5
[4,6,8,9,11,12,1,2,3,5,7,10]=>5
[4,6,8,10,11,12,1,2,3,5,7,9]=>5
[4,6,9,10,11,12,1,2,3,5,7,8]=>7
[4,7,8,9,10,12,1,2,3,5,6,11]=>7
[4,7,8,9,11,12,1,2,3,5,6,10]=>7
[4,7,8,10,11,12,1,2,3,5,6,9]=>7
[4,7,9,10,11,12,1,2,3,5,6,8]=>7
[4,8,9,10,11,12,1,2,3,5,6,7]=>9
[5,6,7,8,10,12,1,2,3,4,9,11]=>7
[5,6,7,8,11,12,1,2,3,4,9,10]=>9
[5,6,7,9,10,12,1,2,3,4,8,11]=>7
[5,6,7,9,11,12,1,2,3,4,8,10]=>7
[5,6,7,10,11,12,1,2,3,4,8,9]=>9
[5,6,8,9,10,12,1,2,3,4,7,11]=>7
[5,6,8,9,11,12,1,2,3,4,7,10]=>7
[5,6,8,10,11,12,1,2,3,4,7,9]=>7
[5,6,9,10,11,12,1,2,3,4,7,8]=>9
[5,7,8,9,10,12,1,2,3,4,6,11]=>7
[5,7,8,9,11,12,1,2,3,4,6,10]=>7
[5,7,8,10,11,12,1,2,3,4,6,9]=>7
[5,7,9,10,11,12,1,2,3,4,6,8]=>7
[5,8,9,10,11,12,1,2,3,4,6,7]=>9
[6,7,8,9,10,12,1,2,3,4,5,11]=>9
[6,7,8,9,11,12,1,2,3,4,5,10]=>9
[6,7,8,10,11,12,1,2,3,4,5,9]=>9
[6,7,9,10,11,12,1,2,3,4,5,8]=>9
[6,8,9,10,11,12,1,2,3,4,5,7]=>9
[7,8,9,10,11,12,1,2,3,4,5,6]=>11
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Description
The number of cycles in the breakpoint graph of a permutation.
The breakpoint graph of a permutation $\pi_1,\dots,\pi_n$ is the directed, bicoloured graph with vertices $0,\dots,n$, a grey edge from $i$ to $i+1$ and a black edge from $\pi_i$ to $\pi_{i-1}$ for $0\leq i\leq n$, all indices taken modulo $n+1$.
This graph decomposes into alternating cycles, which this statistic counts.
The distribution of this statistic on permutations of $n-1$ is, according to [cor.1, 5] and [eq.6, 6], given by
$$ \frac{1}{n(n+1)}((q+n)_{n+1}-(q)_{n+1}), $$
where $(x)_n=x(x-1)\dots(x-n+1)$.
The breakpoint graph of a permutation $\pi_1,\dots,\pi_n$ is the directed, bicoloured graph with vertices $0,\dots,n$, a grey edge from $i$ to $i+1$ and a black edge from $\pi_i$ to $\pi_{i-1}$ for $0\leq i\leq n$, all indices taken modulo $n+1$.
This graph decomposes into alternating cycles, which this statistic counts.
The distribution of this statistic on permutations of $n-1$ is, according to [cor.1, 5] and [eq.6, 6], given by
$$ \frac{1}{n(n+1)}((q+n)_{n+1}-(q)_{n+1}), $$
where $(x)_n=x(x-1)\dots(x-n+1)$.
References
[1] Grusea, S., Labarre, A. The distribution of cycles in breakpoint graphs of signed permutations arXiv:1104.3353
[2] Alexeev, N., Zograf, P. Hultman numbers, polygon gluings and matrix integrals arXiv:1111.3061
[3] Doignon, J.-P., Labarre, A. On Hultman numbers MathSciNet:2312248
[4] Alexeev, N., Pologova, A., Alekseyev, M. A. Generalized Hultman Numbers and Cycle Structures of Breakpoint Graphs arXiv:1503.05285
[5] Bona, M., Flynn, R. The Average Number of Block Interchanges Needed to Sort A Permutation and a recent result of Stanley arXiv:0811.0740
[6] Stanley, R. P. Two Enumerative Results on Cycles of Permutations arXiv:0901.2008
[2] Alexeev, N., Zograf, P. Hultman numbers, polygon gluings and matrix integrals arXiv:1111.3061
[3] Doignon, J.-P., Labarre, A. On Hultman numbers MathSciNet:2312248
[4] Alexeev, N., Pologova, A., Alekseyev, M. A. Generalized Hultman Numbers and Cycle Structures of Breakpoint Graphs arXiv:1503.05285
[5] Bona, M., Flynn, R. The Average Number of Block Interchanges Needed to Sort A Permutation and a recent result of Stanley arXiv:0811.0740
[6] Stanley, R. P. Two Enumerative Results on Cycles of Permutations arXiv:0901.2008
Code
def statistic(pi):
return len(Hultman_class(pi))
def Hultman_class(pi):
"""
sage: Hultman_class([1,2])
[1, 1, 1]
sage: Hultman_class([2,1])
[3]
sage: Hultman_class([2,3,1,4])
[3, 1, 1]
sage: Hultman_class([4,1,6,2,5,7,3])
[5, 3]
sage: [len(set([Hultman_class(pi) for pi in Permutations(r)])) for r in range(10)]
[1, 1, 2, 3, 4, 6, 8, 12, 16, 22]
"""
n = len(pi)
grey = {i: (i+1) % (n+1) for i in range(n+1)}
pi_list = [0] + list(pi)
black = {pi_list[i]: pi_list[(i-1) % (n+1)] for i in range(n+1)}
blocks = []
size = 0
start = 0
odd = 0
for i in range(n+1):
even = grey.pop(odd)
odd = black.pop(even)
size += 1
if start == odd:
blocks.append(size)
size = 0
try:
start = odd = next(iter(grey))
except StopIteration:
return Partition(sorted(blocks, reverse=True))
raise ValueError
Created
Feb 14, 2017 at 17:21 by Martin Rubey
Updated
Dec 03, 2020 at 20:32 by Martin Rubey
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