Identifier
- St000123: Permutations ⟶ ℤ
Values
=>
[]=>0
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>0
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>1
[1,2,3,4]=>0
[1,2,4,3]=>0
[1,3,2,4]=>0
[1,3,4,2]=>0
[1,4,2,3]=>0
[1,4,3,2]=>1
[2,1,3,4]=>0
[2,1,4,3]=>0
[2,3,1,4]=>0
[2,3,4,1]=>0
[2,4,1,3]=>0
[2,4,3,1]=>1
[3,1,2,4]=>0
[3,1,4,2]=>0
[3,2,1,4]=>1
[3,2,4,1]=>1
[3,4,1,2]=>0
[3,4,2,1]=>1
[4,1,2,3]=>0
[4,1,3,2]=>1
[4,2,1,3]=>1
[4,2,3,1]=>2
[4,3,1,2]=>2
[4,3,2,1]=>3
[1,2,3,4,5]=>0
[1,2,3,5,4]=>0
[1,2,4,3,5]=>0
[1,2,4,5,3]=>0
[1,2,5,3,4]=>0
[1,2,5,4,3]=>1
[1,3,2,4,5]=>0
[1,3,2,5,4]=>0
[1,3,4,2,5]=>0
[1,3,4,5,2]=>0
[1,3,5,2,4]=>0
[1,3,5,4,2]=>1
[1,4,2,3,5]=>0
[1,4,2,5,3]=>0
[1,4,3,2,5]=>1
[1,4,3,5,2]=>1
[1,4,5,2,3]=>0
[1,4,5,3,2]=>1
[1,5,2,3,4]=>0
[1,5,2,4,3]=>1
[1,5,3,2,4]=>1
[1,5,3,4,2]=>2
[1,5,4,2,3]=>2
[1,5,4,3,2]=>3
[2,1,3,4,5]=>0
[2,1,3,5,4]=>0
[2,1,4,3,5]=>0
[2,1,4,5,3]=>0
[2,1,5,3,4]=>0
[2,1,5,4,3]=>1
[2,3,1,4,5]=>0
[2,3,1,5,4]=>0
[2,3,4,1,5]=>0
[2,3,4,5,1]=>0
[2,3,5,1,4]=>0
[2,3,5,4,1]=>1
[2,4,1,3,5]=>0
[2,4,1,5,3]=>0
[2,4,3,1,5]=>1
[2,4,3,5,1]=>1
[2,4,5,1,3]=>0
[2,4,5,3,1]=>1
[2,5,1,3,4]=>0
[2,5,1,4,3]=>1
[2,5,3,1,4]=>1
[2,5,3,4,1]=>2
[2,5,4,1,3]=>2
[2,5,4,3,1]=>3
[3,1,2,4,5]=>0
[3,1,2,5,4]=>0
[3,1,4,2,5]=>0
[3,1,4,5,2]=>0
[3,1,5,2,4]=>0
[3,1,5,4,2]=>1
[3,2,1,4,5]=>1
[3,2,1,5,4]=>1
[3,2,4,1,5]=>1
[3,2,4,5,1]=>1
[3,2,5,1,4]=>1
[3,2,5,4,1]=>2
[3,4,1,2,5]=>0
[3,4,1,5,2]=>0
[3,4,2,1,5]=>1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>0
[3,4,5,2,1]=>1
[3,5,1,2,4]=>0
[3,5,1,4,2]=>1
[3,5,2,1,4]=>1
[3,5,2,4,1]=>2
[3,5,4,1,2]=>2
[3,5,4,2,1]=>3
[4,1,2,3,5]=>0
[4,1,2,5,3]=>0
[4,1,3,2,5]=>1
[4,1,3,5,2]=>1
[4,1,5,2,3]=>0
[4,1,5,3,2]=>1
[4,2,1,3,5]=>1
[4,2,1,5,3]=>1
[4,2,3,1,5]=>2
[4,2,3,5,1]=>2
[4,2,5,1,3]=>1
[4,2,5,3,1]=>2
[4,3,1,2,5]=>2
[4,3,1,5,2]=>2
[4,3,2,1,5]=>3
[4,3,2,5,1]=>3
[4,3,5,1,2]=>2
[4,3,5,2,1]=>3
[4,5,1,2,3]=>0
[4,5,1,3,2]=>1
[4,5,2,1,3]=>1
[4,5,2,3,1]=>2
[4,5,3,1,2]=>2
[4,5,3,2,1]=>3
[5,1,2,3,4]=>0
[5,1,2,4,3]=>1
[5,1,3,2,4]=>1
[5,1,3,4,2]=>2
[5,1,4,2,3]=>2
[5,1,4,3,2]=>3
[5,2,1,3,4]=>1
[5,2,1,4,3]=>2
[5,2,3,1,4]=>2
[5,2,3,4,1]=>3
[5,2,4,1,3]=>3
[5,2,4,3,1]=>4
[5,3,1,2,4]=>2
[5,3,1,4,2]=>3
[5,3,2,1,4]=>3
[5,3,2,4,1]=>4
[5,3,4,1,2]=>4
[5,3,4,2,1]=>5
[5,4,1,2,3]=>3
[5,4,1,3,2]=>4
[5,4,2,1,3]=>4
[5,4,2,3,1]=>5
[5,4,3,1,2]=>5
[5,4,3,2,1]=>6
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>0
[1,2,3,5,4,6]=>0
[1,2,3,5,6,4]=>0
[1,2,3,6,4,5]=>0
[1,2,3,6,5,4]=>1
[1,2,4,3,5,6]=>0
[1,2,4,3,6,5]=>0
[1,2,4,5,3,6]=>0
[1,2,4,5,6,3]=>0
[1,2,4,6,3,5]=>0
[1,2,4,6,5,3]=>1
[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>0
[1,2,5,4,3,6]=>1
[1,2,5,4,6,3]=>1
[1,2,5,6,3,4]=>0
[1,2,5,6,4,3]=>1
[1,2,6,3,4,5]=>0
[1,2,6,3,5,4]=>1
[1,2,6,4,3,5]=>1
[1,2,6,4,5,3]=>2
[1,2,6,5,3,4]=>2
[1,2,6,5,4,3]=>3
[1,3,2,4,5,6]=>0
[1,3,2,4,6,5]=>0
[1,3,2,5,4,6]=>0
[1,3,2,5,6,4]=>0
[1,3,2,6,4,5]=>0
[1,3,2,6,5,4]=>1
[1,3,4,2,5,6]=>0
[1,3,4,2,6,5]=>0
[1,3,4,5,2,6]=>0
[1,3,4,5,6,2]=>0
[1,3,4,6,2,5]=>0
[1,3,4,6,5,2]=>1
[1,3,5,2,4,6]=>0
[1,3,5,2,6,4]=>0
[1,3,5,4,2,6]=>1
[1,3,5,4,6,2]=>1
[1,3,5,6,2,4]=>0
[1,3,5,6,4,2]=>1
[1,3,6,2,4,5]=>0
[1,3,6,2,5,4]=>1
[1,3,6,4,2,5]=>1
[1,3,6,4,5,2]=>2
[1,3,6,5,2,4]=>2
[1,3,6,5,4,2]=>3
[1,4,2,3,5,6]=>0
[1,4,2,3,6,5]=>0
[1,4,2,5,3,6]=>0
[1,4,2,5,6,3]=>0
[1,4,2,6,3,5]=>0
[1,4,2,6,5,3]=>1
[1,4,3,2,5,6]=>1
[1,4,3,2,6,5]=>1
[1,4,3,5,2,6]=>1
[1,4,3,5,6,2]=>1
[1,4,3,6,2,5]=>1
[1,4,3,6,5,2]=>2
[1,4,5,2,3,6]=>0
[1,4,5,2,6,3]=>0
[1,4,5,3,2,6]=>1
[1,4,5,3,6,2]=>1
[1,4,5,6,2,3]=>0
[1,4,5,6,3,2]=>1
[1,4,6,2,3,5]=>0
[1,4,6,2,5,3]=>1
[1,4,6,3,2,5]=>1
[1,4,6,3,5,2]=>2
[1,4,6,5,2,3]=>2
[1,4,6,5,3,2]=>3
[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>0
[1,5,2,4,3,6]=>1
[1,5,2,4,6,3]=>1
[1,5,2,6,3,4]=>0
[1,5,2,6,4,3]=>1
[1,5,3,2,4,6]=>1
[1,5,3,2,6,4]=>1
[1,5,3,4,2,6]=>2
[1,5,3,4,6,2]=>2
[1,5,3,6,2,4]=>1
[1,5,3,6,4,2]=>2
[1,5,4,2,3,6]=>2
[1,5,4,2,6,3]=>2
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>2
[1,5,4,6,3,2]=>3
[1,5,6,2,3,4]=>0
[1,5,6,2,4,3]=>1
[1,5,6,3,2,4]=>1
[1,5,6,3,4,2]=>2
[1,5,6,4,2,3]=>2
[1,5,6,4,3,2]=>3
[1,6,2,3,4,5]=>0
[1,6,2,3,5,4]=>1
[1,6,2,4,3,5]=>1
[1,6,2,4,5,3]=>2
[1,6,2,5,3,4]=>2
[1,6,2,5,4,3]=>3
[1,6,3,2,4,5]=>1
[1,6,3,2,5,4]=>2
[1,6,3,4,2,5]=>2
[1,6,3,4,5,2]=>3
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>4
[1,6,4,2,3,5]=>2
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>4
[1,6,4,5,2,3]=>4
[1,6,4,5,3,2]=>5
[1,6,5,2,3,4]=>3
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>4
[1,6,5,3,4,2]=>5
[1,6,5,4,2,3]=>5
[1,6,5,4,3,2]=>6
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>0
[2,1,3,5,4,6]=>0
[2,1,3,5,6,4]=>0
[2,1,3,6,4,5]=>0
[2,1,3,6,5,4]=>1
[2,1,4,3,5,6]=>0
[2,1,4,3,6,5]=>0
[2,1,4,5,3,6]=>0
[2,1,4,5,6,3]=>0
[2,1,4,6,3,5]=>0
[2,1,4,6,5,3]=>1
[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>0
[2,1,5,4,3,6]=>1
[2,1,5,4,6,3]=>1
[2,1,5,6,3,4]=>0
[2,1,5,6,4,3]=>1
[2,1,6,3,4,5]=>0
[2,1,6,3,5,4]=>1
[2,1,6,4,3,5]=>1
[2,1,6,4,5,3]=>2
[2,1,6,5,3,4]=>2
[2,1,6,5,4,3]=>3
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>0
[2,3,1,5,4,6]=>0
[2,3,1,5,6,4]=>0
[2,3,1,6,4,5]=>0
[2,3,1,6,5,4]=>1
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>0
[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>0
[2,3,4,6,5,1]=>1
[2,3,5,1,4,6]=>0
[2,3,5,1,6,4]=>0
[2,3,5,4,1,6]=>1
[2,3,5,4,6,1]=>1
[2,3,5,6,1,4]=>0
[2,3,5,6,4,1]=>1
[2,3,6,1,4,5]=>0
[2,3,6,1,5,4]=>1
[2,3,6,4,1,5]=>1
[2,3,6,4,5,1]=>2
[2,3,6,5,1,4]=>2
[2,3,6,5,4,1]=>3
[2,4,1,3,5,6]=>0
[2,4,1,3,6,5]=>0
[2,4,1,5,3,6]=>0
[2,4,1,5,6,3]=>0
[2,4,1,6,3,5]=>0
[2,4,1,6,5,3]=>1
[2,4,3,1,5,6]=>1
[2,4,3,1,6,5]=>1
[2,4,3,5,1,6]=>1
[2,4,3,5,6,1]=>1
[2,4,3,6,1,5]=>1
[2,4,3,6,5,1]=>2
[2,4,5,1,3,6]=>0
[2,4,5,1,6,3]=>0
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>1
[2,4,5,6,1,3]=>0
[2,4,5,6,3,1]=>1
[2,4,6,1,3,5]=>0
[2,4,6,1,5,3]=>1
[2,4,6,3,1,5]=>1
[2,4,6,3,5,1]=>2
[2,4,6,5,1,3]=>2
[2,4,6,5,3,1]=>3
[2,5,1,3,4,6]=>0
[2,5,1,3,6,4]=>0
[2,5,1,4,3,6]=>1
[2,5,1,4,6,3]=>1
[2,5,1,6,3,4]=>0
[2,5,1,6,4,3]=>1
[2,5,3,1,4,6]=>1
[2,5,3,1,6,4]=>1
[2,5,3,4,1,6]=>2
[2,5,3,4,6,1]=>2
[2,5,3,6,1,4]=>1
[2,5,3,6,4,1]=>2
[2,5,4,1,3,6]=>2
[2,5,4,1,6,3]=>2
[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>3
[2,5,4,6,1,3]=>2
[2,5,4,6,3,1]=>3
[2,5,6,1,3,4]=>0
[2,5,6,1,4,3]=>1
[2,5,6,3,1,4]=>1
[2,5,6,3,4,1]=>2
[2,5,6,4,1,3]=>2
[2,5,6,4,3,1]=>3
[2,6,1,3,4,5]=>0
[2,6,1,3,5,4]=>1
[2,6,1,4,3,5]=>1
[2,6,1,4,5,3]=>2
[2,6,1,5,3,4]=>2
[2,6,1,5,4,3]=>3
[2,6,3,1,4,5]=>1
[2,6,3,1,5,4]=>2
[2,6,3,4,1,5]=>2
[2,6,3,4,5,1]=>3
[2,6,3,5,1,4]=>3
[2,6,3,5,4,1]=>4
[2,6,4,1,3,5]=>2
[2,6,4,1,5,3]=>3
[2,6,4,3,1,5]=>3
[2,6,4,3,5,1]=>4
[2,6,4,5,1,3]=>4
[2,6,4,5,3,1]=>5
[2,6,5,1,3,4]=>3
[2,6,5,1,4,3]=>4
[2,6,5,3,1,4]=>4
[2,6,5,3,4,1]=>5
[2,6,5,4,1,3]=>5
[2,6,5,4,3,1]=>6
[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>0
[3,1,2,5,4,6]=>0
[3,1,2,5,6,4]=>0
[3,1,2,6,4,5]=>0
[3,1,2,6,5,4]=>1
[3,1,4,2,5,6]=>0
[3,1,4,2,6,5]=>0
[3,1,4,5,2,6]=>0
[3,1,4,5,6,2]=>0
[3,1,4,6,2,5]=>0
[3,1,4,6,5,2]=>1
[3,1,5,2,4,6]=>0
[3,1,5,2,6,4]=>0
[3,1,5,4,2,6]=>1
[3,1,5,4,6,2]=>1
[3,1,5,6,2,4]=>0
[3,1,5,6,4,2]=>1
[3,1,6,2,4,5]=>0
[3,1,6,2,5,4]=>1
[3,1,6,4,2,5]=>1
[3,1,6,4,5,2]=>2
[3,1,6,5,2,4]=>2
[3,1,6,5,4,2]=>3
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>1
[3,2,1,5,4,6]=>1
[3,2,1,5,6,4]=>1
[3,2,1,6,4,5]=>1
[3,2,1,6,5,4]=>2
[3,2,4,1,5,6]=>1
[3,2,4,1,6,5]=>1
[3,2,4,5,1,6]=>1
[3,2,4,5,6,1]=>1
[3,2,4,6,1,5]=>1
[3,2,4,6,5,1]=>2
[3,2,5,1,4,6]=>1
[3,2,5,1,6,4]=>1
[3,2,5,4,1,6]=>2
[3,2,5,4,6,1]=>2
[3,2,5,6,1,4]=>1
[3,2,5,6,4,1]=>2
[3,2,6,1,4,5]=>1
[3,2,6,1,5,4]=>2
[3,2,6,4,1,5]=>2
[3,2,6,4,5,1]=>3
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>0
[3,4,1,2,6,5]=>0
[3,4,1,5,2,6]=>0
[3,4,1,5,6,2]=>0
[3,4,1,6,2,5]=>0
[3,4,1,6,5,2]=>1
[3,4,2,1,5,6]=>1
[3,4,2,1,6,5]=>1
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>1
[3,4,2,6,1,5]=>1
[3,4,2,6,5,1]=>2
[3,4,5,1,2,6]=>0
[3,4,5,1,6,2]=>0
[3,4,5,2,1,6]=>1
[3,4,5,2,6,1]=>1
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>1
[3,4,6,1,2,5]=>0
[3,4,6,1,5,2]=>1
[3,4,6,2,1,5]=>1
[3,4,6,2,5,1]=>2
[3,4,6,5,1,2]=>2
[3,4,6,5,2,1]=>3
[3,5,1,2,4,6]=>0
[3,5,1,2,6,4]=>0
[3,5,1,4,2,6]=>1
[3,5,1,4,6,2]=>1
[3,5,1,6,2,4]=>0
[3,5,1,6,4,2]=>1
[3,5,2,1,4,6]=>1
[3,5,2,1,6,4]=>1
[3,5,2,4,1,6]=>2
[3,5,2,4,6,1]=>2
[3,5,2,6,1,4]=>1
[3,5,2,6,4,1]=>2
[3,5,4,1,2,6]=>2
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>3
[3,5,4,2,6,1]=>3
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>3
[3,5,6,1,2,4]=>0
[3,5,6,1,4,2]=>1
[3,5,6,2,1,4]=>1
[3,5,6,2,4,1]=>2
[3,5,6,4,1,2]=>2
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>0
[3,6,1,2,5,4]=>1
[3,6,1,4,2,5]=>1
[3,6,1,4,5,2]=>2
[3,6,1,5,2,4]=>2
[3,6,1,5,4,2]=>3
[3,6,2,1,4,5]=>1
[3,6,2,1,5,4]=>2
[3,6,2,4,1,5]=>2
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>3
[3,6,2,5,4,1]=>4
[3,6,4,1,2,5]=>2
[3,6,4,1,5,2]=>3
[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>4
[3,6,4,5,1,2]=>4
[3,6,4,5,2,1]=>5
[3,6,5,1,2,4]=>3
[3,6,5,1,4,2]=>4
[3,6,5,2,1,4]=>4
[3,6,5,2,4,1]=>5
[3,6,5,4,1,2]=>5
[3,6,5,4,2,1]=>6
[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>0
[4,1,2,5,3,6]=>0
[4,1,2,5,6,3]=>0
[4,1,2,6,3,5]=>0
[4,1,2,6,5,3]=>1
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>1
[4,1,3,5,2,6]=>1
[4,1,3,5,6,2]=>1
[4,1,3,6,2,5]=>1
[4,1,3,6,5,2]=>2
[4,1,5,2,3,6]=>0
[4,1,5,2,6,3]=>0
[4,1,5,3,2,6]=>1
[4,1,5,3,6,2]=>1
[4,1,5,6,2,3]=>0
[4,1,5,6,3,2]=>1
[4,1,6,2,3,5]=>0
[4,1,6,2,5,3]=>1
[4,1,6,3,2,5]=>1
[4,1,6,3,5,2]=>2
[4,1,6,5,2,3]=>2
[4,1,6,5,3,2]=>3
[4,2,1,3,5,6]=>1
[4,2,1,3,6,5]=>1
[4,2,1,5,3,6]=>1
[4,2,1,5,6,3]=>1
[4,2,1,6,3,5]=>1
[4,2,1,6,5,3]=>2
[4,2,3,1,5,6]=>2
[4,2,3,1,6,5]=>2
[4,2,3,5,1,6]=>2
[4,2,3,5,6,1]=>2
[4,2,3,6,1,5]=>2
[4,2,3,6,5,1]=>3
[4,2,5,1,3,6]=>1
[4,2,5,1,6,3]=>1
[4,2,5,3,1,6]=>2
[4,2,5,3,6,1]=>2
[4,2,5,6,1,3]=>1
[4,2,5,6,3,1]=>2
[4,2,6,1,3,5]=>1
[4,2,6,1,5,3]=>2
[4,2,6,3,1,5]=>2
[4,2,6,3,5,1]=>3
[4,2,6,5,1,3]=>3
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>2
[4,3,1,2,6,5]=>2
[4,3,1,5,2,6]=>2
[4,3,1,5,6,2]=>2
[4,3,1,6,2,5]=>2
[4,3,1,6,5,2]=>3
[4,3,2,1,5,6]=>3
[4,3,2,1,6,5]=>3
[4,3,2,5,1,6]=>3
[4,3,2,5,6,1]=>3
[4,3,2,6,1,5]=>3
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>2
[4,3,5,1,6,2]=>2
[4,3,5,2,1,6]=>3
[4,3,5,2,6,1]=>3
[4,3,5,6,1,2]=>2
[4,3,5,6,2,1]=>3
[4,3,6,1,2,5]=>2
[4,3,6,1,5,2]=>3
[4,3,6,2,1,5]=>3
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>4
[4,3,6,5,2,1]=>5
[4,5,1,2,3,6]=>0
[4,5,1,2,6,3]=>0
[4,5,1,3,2,6]=>1
[4,5,1,3,6,2]=>1
[4,5,1,6,2,3]=>0
[4,5,1,6,3,2]=>1
[4,5,2,1,3,6]=>1
[4,5,2,1,6,3]=>1
[4,5,2,3,1,6]=>2
[4,5,2,3,6,1]=>2
[4,5,2,6,1,3]=>1
[4,5,2,6,3,1]=>2
[4,5,3,1,2,6]=>2
[4,5,3,1,6,2]=>2
[4,5,3,2,1,6]=>3
[4,5,3,2,6,1]=>3
[4,5,3,6,1,2]=>2
[4,5,3,6,2,1]=>3
[4,5,6,1,2,3]=>0
[4,5,6,1,3,2]=>1
[4,5,6,2,1,3]=>1
[4,5,6,2,3,1]=>2
[4,5,6,3,1,2]=>2
[4,5,6,3,2,1]=>3
[4,6,1,2,3,5]=>0
[4,6,1,2,5,3]=>1
[4,6,1,3,2,5]=>1
[4,6,1,3,5,2]=>2
[4,6,1,5,2,3]=>2
[4,6,1,5,3,2]=>3
[4,6,2,1,3,5]=>1
[4,6,2,1,5,3]=>2
[4,6,2,3,1,5]=>2
[4,6,2,3,5,1]=>3
[4,6,2,5,1,3]=>3
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>2
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>3
[4,6,3,2,5,1]=>4
[4,6,3,5,1,2]=>4
[4,6,3,5,2,1]=>5
[4,6,5,1,2,3]=>3
[4,6,5,1,3,2]=>4
[4,6,5,2,1,3]=>4
[4,6,5,2,3,1]=>5
[4,6,5,3,1,2]=>5
[4,6,5,3,2,1]=>6
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>0
[5,1,2,4,3,6]=>1
[5,1,2,4,6,3]=>1
[5,1,2,6,3,4]=>0
[5,1,2,6,4,3]=>1
[5,1,3,2,4,6]=>1
[5,1,3,2,6,4]=>1
[5,1,3,4,2,6]=>2
[5,1,3,4,6,2]=>2
[5,1,3,6,2,4]=>1
[5,1,3,6,4,2]=>2
[5,1,4,2,3,6]=>2
[5,1,4,2,6,3]=>2
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>3
[5,1,4,6,2,3]=>2
[5,1,4,6,3,2]=>3
[5,1,6,2,3,4]=>0
[5,1,6,2,4,3]=>1
[5,1,6,3,2,4]=>1
[5,1,6,3,4,2]=>2
[5,1,6,4,2,3]=>2
[5,1,6,4,3,2]=>3
[5,2,1,3,4,6]=>1
[5,2,1,3,6,4]=>1
[5,2,1,4,3,6]=>2
[5,2,1,4,6,3]=>2
[5,2,1,6,3,4]=>1
[5,2,1,6,4,3]=>2
[5,2,3,1,4,6]=>2
[5,2,3,1,6,4]=>2
[5,2,3,4,1,6]=>3
[5,2,3,4,6,1]=>3
[5,2,3,6,1,4]=>2
[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]=>4
[5,2,4,3,6,1]=>4
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>4
[5,2,6,1,3,4]=>1
[5,2,6,1,4,3]=>2
[5,2,6,3,1,4]=>2
[5,2,6,3,4,1]=>3
[5,2,6,4,1,3]=>3
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>2
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>3
[5,3,1,4,6,2]=>3
[5,3,1,6,2,4]=>2
[5,3,1,6,4,2]=>3
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>3
[5,3,2,4,1,6]=>4
[5,3,2,4,6,1]=>4
[5,3,2,6,1,4]=>3
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>4
[5,3,4,1,6,2]=>4
[5,3,4,2,1,6]=>5
[5,3,4,2,6,1]=>5
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>5
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>3
[5,3,6,2,1,4]=>3
[5,3,6,2,4,1]=>4
[5,3,6,4,1,2]=>4
[5,3,6,4,2,1]=>5
[5,4,1,2,3,6]=>3
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>4
[5,4,1,3,6,2]=>4
[5,4,1,6,2,3]=>3
[5,4,1,6,3,2]=>4
[5,4,2,1,3,6]=>4
[5,4,2,1,6,3]=>4
[5,4,2,3,1,6]=>5
[5,4,2,3,6,1]=>5
[5,4,2,6,1,3]=>4
[5,4,2,6,3,1]=>5
[5,4,3,1,2,6]=>5
[5,4,3,1,6,2]=>5
[5,4,3,2,1,6]=>6
[5,4,3,2,6,1]=>6
[5,4,3,6,1,2]=>5
[5,4,3,6,2,1]=>6
[5,4,6,1,2,3]=>3
[5,4,6,1,3,2]=>4
[5,4,6,2,1,3]=>4
[5,4,6,2,3,1]=>5
[5,4,6,3,1,2]=>5
[5,4,6,3,2,1]=>6
[5,6,1,2,3,4]=>0
[5,6,1,2,4,3]=>1
[5,6,1,3,2,4]=>1
[5,6,1,3,4,2]=>2
[5,6,1,4,2,3]=>2
[5,6,1,4,3,2]=>3
[5,6,2,1,3,4]=>1
[5,6,2,1,4,3]=>2
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>3
[5,6,2,4,1,3]=>3
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>2
[5,6,3,1,4,2]=>3
[5,6,3,2,1,4]=>3
[5,6,3,2,4,1]=>4
[5,6,3,4,1,2]=>4
[5,6,3,4,2,1]=>5
[5,6,4,1,2,3]=>3
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>4
[5,6,4,2,3,1]=>5
[5,6,4,3,1,2]=>5
[5,6,4,3,2,1]=>6
[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>1
[6,1,2,4,3,5]=>1
[6,1,2,4,5,3]=>2
[6,1,2,5,3,4]=>2
[6,1,2,5,4,3]=>3
[6,1,3,2,4,5]=>1
[6,1,3,2,5,4]=>2
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>3
[6,1,3,5,4,2]=>4
[6,1,4,2,3,5]=>2
[6,1,4,2,5,3]=>3
[6,1,4,3,2,5]=>3
[6,1,4,3,5,2]=>4
[6,1,4,5,2,3]=>4
[6,1,4,5,3,2]=>5
[6,1,5,2,3,4]=>3
[6,1,5,2,4,3]=>4
[6,1,5,3,2,4]=>4
[6,1,5,3,4,2]=>5
[6,1,5,4,2,3]=>5
[6,1,5,4,3,2]=>6
[6,2,1,3,4,5]=>1
[6,2,1,3,5,4]=>2
[6,2,1,4,3,5]=>2
[6,2,1,4,5,3]=>3
[6,2,1,5,3,4]=>3
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>2
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>3
[6,2,3,4,5,1]=>4
[6,2,3,5,1,4]=>4
[6,2,3,5,4,1]=>5
[6,2,4,1,3,5]=>3
[6,2,4,1,5,3]=>4
[6,2,4,3,1,5]=>4
[6,2,4,3,5,1]=>5
[6,2,4,5,1,3]=>5
[6,2,4,5,3,1]=>6
[6,2,5,1,3,4]=>4
[6,2,5,1,4,3]=>5
[6,2,5,3,1,4]=>5
[6,2,5,3,4,1]=>6
[6,2,5,4,1,3]=>6
[6,2,5,4,3,1]=>7
[6,3,1,2,4,5]=>2
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>3
[6,3,1,4,5,2]=>4
[6,3,1,5,2,4]=>4
[6,3,1,5,4,2]=>5
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>4
[6,3,2,4,1,5]=>4
[6,3,2,4,5,1]=>5
[6,3,2,5,1,4]=>5
[6,3,2,5,4,1]=>6
[6,3,4,1,2,5]=>4
[6,3,4,1,5,2]=>5
[6,3,4,2,1,5]=>5
[6,3,4,2,5,1]=>6
[6,3,4,5,1,2]=>6
[6,3,4,5,2,1]=>7
[6,3,5,1,2,4]=>5
[6,3,5,1,4,2]=>6
[6,3,5,2,1,4]=>6
[6,3,5,2,4,1]=>7
[6,3,5,4,1,2]=>7
[6,3,5,4,2,1]=>8
[6,4,1,2,3,5]=>3
[6,4,1,2,5,3]=>4
[6,4,1,3,2,5]=>4
[6,4,1,3,5,2]=>5
[6,4,1,5,2,3]=>5
[6,4,1,5,3,2]=>6
[6,4,2,1,3,5]=>4
[6,4,2,1,5,3]=>5
[6,4,2,3,1,5]=>5
[6,4,2,3,5,1]=>6
[6,4,2,5,1,3]=>6
[6,4,2,5,3,1]=>7
[6,4,3,1,2,5]=>5
[6,4,3,1,5,2]=>6
[6,4,3,2,1,5]=>6
[6,4,3,2,5,1]=>7
[6,4,3,5,1,2]=>7
[6,4,3,5,2,1]=>8
[6,4,5,1,2,3]=>6
[6,4,5,1,3,2]=>7
[6,4,5,2,1,3]=>7
[6,4,5,2,3,1]=>8
[6,4,5,3,1,2]=>8
[6,4,5,3,2,1]=>9
[6,5,1,2,3,4]=>4
[6,5,1,2,4,3]=>5
[6,5,1,3,2,4]=>5
[6,5,1,3,4,2]=>6
[6,5,1,4,2,3]=>6
[6,5,1,4,3,2]=>7
[6,5,2,1,3,4]=>5
[6,5,2,1,4,3]=>6
[6,5,2,3,1,4]=>6
[6,5,2,3,4,1]=>7
[6,5,2,4,1,3]=>7
[6,5,2,4,3,1]=>8
[6,5,3,1,2,4]=>6
[6,5,3,1,4,2]=>7
[6,5,3,2,1,4]=>7
[6,5,3,2,4,1]=>8
[6,5,3,4,1,2]=>8
[6,5,3,4,2,1]=>9
[6,5,4,1,2,3]=>7
[6,5,4,1,3,2]=>8
[6,5,4,2,1,3]=>8
[6,5,4,2,3,1]=>9
[6,5,4,3,1,2]=>9
[6,5,4,3,2,1]=>10
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>0
[1,2,3,4,6,5,7]=>0
[1,2,3,6,4,7,5]=>0
[1,2,6,3,4,7,5]=>0
[1,3,2,4,5,6,7]=>0
[1,3,7,2,4,5,6]=>0
[1,3,7,6,5,4,2]=>6
[1,4,6,7,2,3,5]=>0
[1,4,6,7,5,3,2]=>3
[1,4,7,2,3,5,6]=>0
[1,4,7,6,5,3,2]=>6
[1,5,2,3,4,7,6]=>0
[1,5,2,7,3,4,6]=>0
[1,5,4,7,6,3,2]=>5
[1,5,6,2,7,3,4]=>0
[1,5,6,4,7,3,2]=>3
[1,5,6,7,2,3,4]=>0
[1,5,6,7,4,3,2]=>3
[1,5,7,2,3,4,6]=>0
[1,5,7,6,4,3,2]=>6
[1,6,2,3,4,7,5]=>0
[1,6,2,3,7,4,5]=>0
[1,6,2,7,3,4,5]=>0
[1,6,5,4,3,7,2]=>6
[1,6,5,4,7,3,2]=>6
[1,6,5,7,4,3,2]=>6
[1,6,7,2,3,4,5]=>0
[1,6,7,5,4,3,2]=>6
[1,7,2,3,4,5,6]=>0
[1,7,3,5,6,4,2]=>6
[1,7,3,6,5,4,2]=>7
[1,7,4,3,6,5,2]=>6
[1,7,4,5,3,6,2]=>6
[1,7,4,5,6,3,2]=>7
[1,7,4,6,5,3,2]=>8
[1,7,5,4,3,6,2]=>7
[1,7,5,4,6,3,2]=>8
[1,7,6,4,5,3,2]=>9
[1,7,6,5,4,3,2]=>10
[2,1,3,4,5,6,7]=>0
[2,1,3,4,7,5,6]=>0
[2,1,3,7,4,5,6]=>0
[2,1,6,3,4,5,7]=>0
[2,1,7,3,4,5,6]=>0
[2,1,7,6,5,4,3]=>6
[2,3,1,4,5,6,7]=>0
[2,3,4,1,5,6,7]=>0
[2,3,4,1,5,7,6]=>0
[2,3,4,5,1,6,7]=>0
[2,3,4,5,1,7,6]=>0
[2,3,4,5,6,1,7]=>0
[2,3,4,5,6,7,1]=>0
[2,3,4,5,7,1,6]=>0
[2,3,4,6,1,7,5]=>0
[2,3,4,6,7,1,5]=>0
[2,3,4,7,1,5,6]=>0
[2,3,5,6,7,1,4]=>0
[2,4,1,3,5,6,7]=>0
[2,5,1,3,4,6,7]=>0
[2,5,7,1,3,4,6]=>0
[2,6,1,3,4,5,7]=>0
[2,6,1,7,3,4,5]=>0
[2,6,5,4,3,1,7]=>6
[2,6,7,1,3,4,5]=>0
[2,7,1,3,4,5,6]=>0
[3,1,2,4,5,6,7]=>0
[3,1,2,4,5,7,6]=>0
[3,2,1,4,5,6,7]=>1
[3,2,4,5,6,7,1]=>1
[3,4,1,2,5,6,7]=>0
[3,4,2,5,6,7,1]=>1
[3,4,5,2,6,7,1]=>1
[3,4,5,6,2,7,1]=>1
[3,4,5,6,7,1,2]=>0
[3,5,6,1,2,4,7]=>0
[3,5,6,4,2,1,7]=>3
[3,6,1,2,4,5,7]=>0
[3,6,5,4,2,1,7]=>6
[4,1,2,3,5,6,7]=>0
[4,1,2,3,5,7,6]=>0
[4,1,6,2,3,5,7]=>0
[4,2,3,5,6,7,1]=>2
[4,2,5,1,3,6,7]=>1
[4,3,2,1,5,6,7]=>3
[4,3,2,5,6,7,1]=>3
[4,3,5,2,6,7,1]=>3
[4,3,6,5,2,1,7]=>5
[4,5,1,6,2,3,7]=>0
[4,5,2,3,6,7,1]=>2
[4,5,3,6,2,1,7]=>3
[4,5,6,1,2,3,7]=>0
[4,5,6,3,2,1,7]=>3
[4,6,1,2,3,5,7]=>0
[4,6,1,2,3,7,5]=>0
[4,6,5,3,2,1,7]=>6
[5,1,2,3,4,6,7]=>0
[5,1,2,3,4,7,6]=>0
[5,1,2,3,6,4,7]=>0
[5,1,2,3,6,7,4]=>0
[5,1,2,3,7,4,6]=>0
[5,1,2,6,3,4,7]=>0
[5,1,6,2,3,4,7]=>0
[5,1,6,2,3,7,4]=>0
[5,2,3,4,6,7,1]=>3
[5,2,6,7,1,3,4]=>1
[5,3,2,4,6,7,1]=>4
[5,3,2,6,1,4,7]=>3
[5,3,6,7,1,2,4]=>2
[5,4,3,2,1,6,7]=>6
[5,4,3,2,1,7,6]=>6
[5,4,3,2,6,1,7]=>6
[5,4,3,6,2,1,7]=>6
[5,4,6,3,2,1,7]=>6
[5,4,6,7,1,2,3]=>3
[5,6,1,2,3,4,7]=>0
[5,6,1,2,3,7,4]=>0
[5,6,3,4,1,2,7]=>4
[5,6,4,3,2,1,7]=>6
[5,6,7,1,2,3,4]=>0
[6,1,2,3,4,5,7]=>0
[6,1,2,3,4,7,5]=>0
[6,1,2,3,7,4,5]=>0
[6,1,2,7,3,4,5]=>0
[6,2,3,4,5,7,1]=>4
[6,2,4,5,3,1,7]=>6
[6,2,5,4,3,1,7]=>7
[6,3,2,5,4,1,7]=>6
[6,3,4,2,5,1,7]=>6
[6,3,4,5,2,1,7]=>7
[6,3,4,7,1,2,5]=>4
[6,3,5,4,2,1,7]=>8
[6,4,3,2,5,1,7]=>7
[6,4,3,2,7,1,5]=>6
[6,4,3,5,2,1,7]=>8
[6,4,5,7,1,2,3]=>6
[6,4,7,2,5,1,3]=>6
[6,4,7,3,5,1,2]=>7
[6,5,3,4,2,1,7]=>9
[6,5,4,3,2,1,7]=>10
[6,5,7,3,4,1,2]=>8
[6,7,1,2,3,4,5]=>0
[6,7,3,4,1,2,5]=>4
[6,7,4,5,1,2,3]=>6
[7,1,2,3,4,5,6]=>0
[7,2,1,3,4,5,6]=>1
[7,2,3,1,4,5,6]=>2
[7,2,3,4,1,5,6]=>3
[7,2,3,4,5,1,6]=>4
[7,3,1,2,4,5,6]=>2
[7,3,2,1,4,5,6]=>3
[7,3,2,4,1,5,6]=>4
[7,3,4,1,2,5,6]=>4
[7,4,1,2,3,5,6]=>3
[7,4,2,1,3,5,6]=>4
[7,4,5,6,1,2,3]=>9
[7,5,1,2,3,4,6]=>4
[7,5,6,1,2,3,4]=>8
[7,5,6,3,4,1,2]=>12
[7,6,1,2,3,4,5]=>5
[7,6,4,5,1,2,3]=>11
[7,6,5,1,2,3,4]=>9
[7,6,5,3,4,1,2]=>13
[7,6,5,4,1,2,3]=>12
[7,6,5,4,3,1,2]=>14
[7,6,5,4,3,2,1]=>15
[8,7,6,5,4,3,2,1]=>21
[7,6,8,5,4,3,2,1]=>15
[7,8,5,6,4,3,2,1]=>14
[7,8,6,4,5,3,2,1]=>14
[8,6,7,4,5,3,2,1]=>19
[7,6,5,4,8,3,2,1]=>15
[6,5,7,4,8,3,2,1]=>10
[7,8,6,5,3,4,2,1]=>14
[8,6,7,5,3,4,2,1]=>19
[8,7,5,6,3,4,2,1]=>19
[6,7,8,3,4,5,2,1]=>7
[7,8,6,5,4,2,3,1]=>14
[8,6,7,5,4,2,3,1]=>19
[8,7,5,6,4,2,3,1]=>19
[8,7,6,4,5,2,3,1]=>19
[8,6,5,7,3,2,4,1]=>17
[6,7,8,5,2,3,4,1]=>7
[8,5,6,7,2,3,4,1]=>15
[7,8,3,2,4,5,6,1]=>6
[7,6,5,4,3,2,8,1]=>15
[6,5,7,4,3,2,8,1]=>10
[6,5,4,3,7,2,8,1]=>10
[5,4,6,3,7,2,8,1]=>6
[3,4,5,2,6,7,8,1]=>1
[5,2,3,4,6,7,8,1]=>3
[4,3,2,5,6,7,8,1]=>3
[3,4,2,5,6,7,8,1]=>1
[4,2,3,5,6,7,8,1]=>2
[3,2,4,5,6,7,8,1]=>1
[2,3,4,5,6,7,8,1]=>0
[8,7,6,5,4,3,1,2]=>20
[7,8,6,5,4,3,1,2]=>14
[8,6,7,5,4,3,1,2]=>19
[8,7,5,6,4,3,1,2]=>19
[8,7,6,4,5,3,1,2]=>19
[8,7,6,5,3,4,1,2]=>19
[8,7,5,6,3,4,1,2]=>18
[7,8,5,6,3,4,1,2]=>12
[5,6,7,8,3,4,1,2]=>4
[7,8,3,4,5,6,1,2]=>8
[3,4,5,6,7,8,1,2]=>0
[8,7,6,5,4,2,1,3]=>19
[7,6,8,5,4,2,1,3]=>13
[8,7,6,5,4,1,2,3]=>18
[6,7,8,5,4,1,2,3]=>7
[8,5,6,7,4,1,2,3]=>15
[8,7,6,4,5,1,2,3]=>17
[8,6,7,4,5,1,2,3]=>16
[8,7,4,5,6,1,2,3]=>15
[7,8,4,5,6,1,2,3]=>9
[6,7,4,5,8,1,2,3]=>6
[7,6,5,8,3,2,1,4]=>12
[7,5,6,8,2,3,1,4]=>10
[6,7,5,8,3,1,2,4]=>6
[6,5,7,8,2,1,3,4]=>5
[8,7,6,5,1,2,3,4]=>15
[8,7,5,6,1,2,3,4]=>14
[7,8,5,6,1,2,3,4]=>8
[8,5,6,7,1,2,3,4]=>12
[5,6,7,8,1,2,3,4]=>0
[8,7,6,4,3,2,1,5]=>17
[8,7,6,4,2,1,3,5]=>15
[8,7,6,1,2,3,4,5]=>11
[8,6,7,1,2,3,4,5]=>10
[6,7,8,1,2,3,4,5]=>0
[7,8,5,4,2,1,3,6]=>8
[7,8,5,4,1,2,3,6]=>7
[8,7,1,2,3,4,5,6]=>6
[7,8,1,2,3,4,5,6]=>0
[8,6,5,4,3,2,1,7]=>15
[8,6,5,4,3,1,2,7]=>14
[8,5,6,3,4,1,2,7]=>12
[8,6,5,4,2,1,3,7]=>13
[8,6,4,3,2,1,5,7]=>11
[8,6,4,2,1,3,5,7]=>9
[8,2,3,4,1,5,6,7]=>3
[8,4,1,2,3,5,6,7]=>3
[8,3,2,1,4,5,6,7]=>3
[8,2,3,1,4,5,6,7]=>2
[8,3,1,2,4,5,6,7]=>2
[8,2,1,3,4,5,6,7]=>1
[8,1,2,3,4,5,6,7]=>0
[7,6,5,4,3,2,1,8]=>15
[6,7,5,4,3,2,1,8]=>10
[6,5,7,4,3,2,1,8]=>10
[5,6,7,4,3,2,1,8]=>6
[7,6,4,5,3,2,1,8]=>14
[6,5,4,7,3,2,1,8]=>10
[7,5,6,3,4,2,1,8]=>13
[7,6,4,3,5,2,1,8]=>13
[7,6,3,4,5,2,1,8]=>12
[7,5,4,3,6,2,1,8]=>12
[6,7,5,4,2,3,1,8]=>9
[6,5,7,3,2,4,1,8]=>8
[5,6,7,2,3,4,1,8]=>3
[2,3,4,5,6,7,1,8]=>0
[5,6,7,1,2,3,4,8]=>0
[6,7,1,2,3,4,5,8]=>0
[7,1,2,3,4,5,6,8]=>0
[6,5,4,3,2,1,7,8]=>10
[2,3,4,5,6,1,7,8]=>0
[5,6,3,4,1,2,7,8]=>4
[4,5,6,1,2,3,7,8]=>0
[6,1,2,3,4,5,7,8]=>0
[5,4,3,2,1,6,7,8]=>6
[2,3,4,5,1,6,7,8]=>0
[5,1,2,3,4,6,7,8]=>0
[4,3,2,1,5,6,7,8]=>3
[3,4,1,2,5,6,7,8]=>0
[3,2,1,4,5,6,7,8]=>1
[2,1,3,4,5,6,7,8]=>0
[1,2,3,4,5,6,7,8]=>0
[6,5,8,7,4,3,2,1]=>14
[3,5,8,7,6,4,2,1]=>10
[4,3,6,5,8,7,2,1]=>7
[2,6,8,7,5,4,3,1]=>10
[2,3,5,6,8,7,4,1]=>3
[3,2,6,5,4,8,7,1]=>5
[4,3,6,5,7,2,8,1]=>5
[3,2,6,5,7,4,8,1]=>4
[4,3,5,2,7,6,8,1]=>4
[3,2,5,4,7,6,8,1]=>3
[1,8,7,6,5,4,3,2]=>15
[1,7,8,6,5,4,3,2]=>10
[1,6,8,7,5,4,3,2]=>10
[1,7,6,8,5,4,3,2]=>10
[1,6,7,8,5,4,3,2]=>6
[1,5,8,7,6,4,3,2]=>10
[1,7,6,5,8,4,3,2]=>10
[1,3,5,7,8,6,4,2]=>3
[1,4,3,8,7,6,5,2]=>7
[1,6,5,4,3,8,7,2]=>7
[1,4,3,6,5,8,7,2]=>3
[2,1,8,7,6,5,4,3]=>10
[2,1,6,5,7,4,8,3]=>3
[2,1,5,4,7,6,8,3]=>2
[1,2,6,7,8,5,4,3]=>3
[3,2,1,8,7,6,5,4]=>7
[3,2,1,6,5,8,7,4]=>3
[1,2,3,5,6,7,8,4]=>0
[4,3,2,1,8,7,6,5]=>6
[3,4,2,1,7,8,6,5]=>2
[2,4,3,1,6,8,7,5]=>2
[2,4,3,1,7,6,8,5]=>2
[3,2,4,1,6,8,7,5]=>2
[3,2,4,1,7,6,8,5]=>2
[2,3,4,1,6,7,8,5]=>0
[2,1,4,3,8,7,6,5]=>3
[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]=>7
[3,2,5,4,1,8,7,6]=>3
[3,2,1,4,5,8,7,6]=>2
[2,3,1,4,5,7,8,6]=>0
[6,5,4,3,2,1,8,7]=>10
[4,3,5,2,6,1,8,7]=>3
[3,2,5,4,6,1,8,7]=>2
[2,3,4,5,6,1,8,7]=>0
[2,1,6,5,4,3,8,7]=>3
[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]=>3
[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]=>0
[2,1,3,4,5,6,8,7]=>0
[1,2,3,4,5,6,8,7]=>0
[5,7,6,4,3,2,1,8]=>10
[4,7,6,5,3,2,1,8]=>10
[3,2,7,6,5,4,1,8]=>7
[5,4,3,2,7,6,1,8]=>7
[3,2,5,4,7,6,1,8]=>3
[1,4,3,2,7,6,5,8]=>2
[1,3,4,2,6,7,5,8]=>0
[1,3,2,5,4,7,6,8]=>0
[1,2,3,5,4,7,6,8]=>0
[1,3,2,4,5,7,6,8]=>0
[1,2,3,4,5,7,6,8]=>0
[1,2,4,3,6,5,7,8]=>0
[1,3,2,5,4,6,7,8]=>0
[1,2,3,5,4,6,7,8]=>0
[1,3,2,4,5,6,7,8]=>0
[1,8,4,7,6,5,3,2]=>12
[1,8,5,4,7,6,3,2]=>11
[1,8,7,4,5,6,3,2]=>12
[1,8,7,4,6,5,3,2]=>13
[1,8,6,5,4,7,3,2]=>12
[1,8,7,5,4,6,3,2]=>13
[1,8,7,5,6,4,3,2]=>14
[2,1,4,5,8,6,7,3]=>2
[2,1,8,5,4,7,6,3]=>6
[2,3,4,8,5,6,7,1]=>3
[2,3,6,4,5,1,8,7]=>2
[2,3,7,4,5,6,8,1]=>3
[2,8,4,3,5,7,6,1]=>7
[4,2,3,1,8,6,7,5]=>4
[8,2,7,4,6,5,3,1]=>14
[4,3,2,7,5,6,8,1]=>5
[4,3,2,8,5,7,6,1]=>7
[6,3,2,5,4,1,8,7]=>6
[8,3,2,5,4,7,6,1]=>9
[8,3,2,7,6,5,4,1]=>13
[8,3,7,4,6,5,2,1]=>15
[7,3,6,5,4,2,1,8]=>12
[7,4,3,6,5,2,1,8]=>11
[7,6,3,5,4,2,1,8]=>13
[8,5,4,3,2,7,6,1]=>13
[8,7,4,3,6,5,2,1]=>17
[2,4,6,8,1,3,5,7]=>0
[2,4,6,1,7,3,8,5]=>0
[2,1,4,3,7,5,8,6]=>0
[2,4,1,3,7,5,8,6]=>0
[2,1,4,3,7,8,5,6]=>0
[2,4,7,8,1,3,5,6]=>0
[2,1,4,3,8,5,6,7]=>0
[2,4,5,6,7,1,8,3]=>0
[2,1,5,3,6,4,8,7]=>0
[2,1,5,6,3,4,8,7]=>0
[2,5,6,8,1,3,4,7]=>0
[2,1,5,3,7,4,8,6]=>0
[2,5,1,7,3,4,8,6]=>0
[2,1,5,7,3,8,4,6]=>0
[2,5,7,8,1,3,4,6]=>0
[2,3,5,6,1,7,8,4]=>0
[2,1,6,3,7,4,8,5]=>0
[2,6,7,1,3,4,8,5]=>0
[2,1,6,7,8,3,4,5]=>0
[2,6,7,8,1,3,4,5]=>0
[2,1,6,3,4,7,8,5]=>0
[2,1,6,3,4,5,8,7]=>0
[2,6,1,3,4,5,7,8]=>0
[2,7,8,1,3,4,5,6]=>0
[2,7,1,3,4,5,6,8]=>0
[2,3,4,5,7,8,1,6]=>0
[2,1,8,3,4,5,6,7]=>0
[2,8,1,3,4,5,6,7]=>0
[2,1,3,8,4,5,6,7]=>0
[2,3,4,5,6,8,1,7]=>0
[3,1,4,2,6,5,8,7]=>0
[3,4,1,2,6,5,8,7]=>0
[3,1,4,2,6,8,5,7]=>0
[3,4,6,8,1,2,5,7]=>0
[3,1,4,2,7,5,8,6]=>0
[3,4,1,2,7,8,5,6]=>0
[3,4,7,8,1,2,5,6]=>0
[3,1,5,2,6,4,8,7]=>0
[3,5,1,6,2,4,8,7]=>0
[3,1,5,6,2,8,4,7]=>0
[3,5,6,8,1,2,4,7]=>0
[3,1,5,2,7,4,8,6]=>0
[3,5,1,7,2,8,4,6]=>0
[3,5,7,8,1,2,4,6]=>0
[1,3,2,5,4,8,6,7]=>0
[1,3,5,8,2,4,6,7]=>0
[1,3,5,6,2,7,4,8]=>0
[3,1,6,2,7,4,8,5]=>0
[3,6,7,1,2,8,4,5]=>0
[3,6,1,7,8,2,4,5]=>0
[3,6,7,8,1,2,4,5]=>0
[1,3,2,6,4,7,5,8]=>0
[3,1,2,6,7,4,8,5]=>0
[1,3,2,6,4,8,5,7]=>0
[1,3,2,6,4,5,7,8]=>0
[1,3,2,7,4,8,5,6]=>0
[1,3,2,7,4,5,6,8]=>0
[1,3,2,8,4,5,6,7]=>0
[3,1,2,4,5,8,6,7]=>0
[1,3,2,4,5,8,6,7]=>0
[4,1,5,2,6,3,8,7]=>0
[4,5,6,1,2,3,8,7]=>0
[4,1,5,6,8,2,3,7]=>0
[4,5,6,8,1,2,3,7]=>0
[4,1,5,2,7,3,8,6]=>0
[4,1,5,2,7,8,3,6]=>0
[4,5,7,1,2,8,3,6]=>0
[4,5,1,7,8,2,3,6]=>0
[4,5,7,8,1,2,3,6]=>0
[1,4,2,5,3,7,6,8]=>0
[1,4,2,5,3,8,6,7]=>0
[1,4,2,5,3,6,7,8]=>0
[1,4,5,6,7,2,3,8]=>0
[4,1,6,2,7,3,8,5]=>0
[4,6,7,1,8,2,3,5]=>0
[4,6,7,8,1,2,3,5]=>0
[1,4,2,6,3,7,5,8]=>0
[1,4,2,6,7,8,3,5]=>0
[1,4,2,6,3,8,5,7]=>0
[4,1,2,3,6,5,8,7]=>0
[1,4,2,6,3,5,7,8]=>0
[1,4,2,7,3,8,5,6]=>0
[4,7,1,2,3,5,6,8]=>0
[1,4,2,7,3,5,6,8]=>0
[1,4,2,3,7,5,6,8]=>0
[1,4,2,3,5,7,6,8]=>0
[1,4,2,8,3,5,6,7]=>0
[4,1,2,3,8,5,6,7]=>0
[1,4,2,3,5,8,6,7]=>0
[1,4,2,3,5,6,7,8]=>0
[5,1,6,2,7,3,8,4]=>0
[1,5,2,6,3,7,4,8]=>0
[1,5,2,6,3,8,4,7]=>0
[1,5,2,6,3,4,7,8]=>0
[1,2,5,6,3,4,7,8]=>0
[1,5,2,7,3,8,4,6]=>0
[5,7,1,2,3,4,6,8]=>0
[1,5,2,7,3,4,6,8]=>0
[1,5,2,3,4,7,6,8]=>0
[5,1,2,8,3,4,6,7]=>0
[1,5,2,8,3,4,6,7]=>0
[1,5,8,2,3,4,6,7]=>0
[1,5,2,3,4,8,6,7]=>0
[1,2,3,5,4,8,6,7]=>0
[5,1,2,3,4,6,8,7]=>0
[1,5,2,3,4,6,7,8]=>0
[1,6,2,7,3,8,4,5]=>0
[1,6,7,8,2,3,4,5]=>0
[6,7,1,2,3,4,8,5]=>0
[6,1,7,2,3,4,5,8]=>0
[6,1,2,7,3,4,5,8]=>0
[1,6,2,7,3,4,5,8]=>0
[1,6,7,2,3,4,5,8]=>0
[1,6,2,3,4,7,5,8]=>0
[1,2,3,6,4,7,5,8]=>0
[6,1,8,2,3,4,5,7]=>0
[1,6,2,8,3,4,5,7]=>0
[1,6,8,2,3,4,5,7]=>0
[1,6,2,3,4,8,5,7]=>0
[1,2,3,6,4,8,5,7]=>0
[6,1,2,3,4,5,8,7]=>0
[1,6,2,3,4,5,7,8]=>0
[1,2,3,6,4,5,7,8]=>0
[1,7,2,8,3,4,5,6]=>0
[1,7,8,2,3,4,5,6]=>0
[1,7,2,3,8,4,5,6]=>0
[7,1,2,3,4,8,5,6]=>0
[1,7,2,3,4,8,5,6]=>0
[1,2,3,7,4,8,5,6]=>0
[7,1,2,3,4,5,8,6]=>0
[1,7,2,3,4,5,8,6]=>0
[1,2,7,3,4,5,8,6]=>0
[1,7,2,3,4,5,6,8]=>0
[1,2,3,7,4,5,6,8]=>0
[1,8,2,3,4,5,6,7]=>0
[1,2,3,8,4,5,6,7]=>0
[1,2,3,4,5,8,6,7]=>0
[5,3,2,6,1,4,8,7]=>3
[7,3,2,5,4,8,1,6]=>6
[8,4,5,2,3,7,6,1]=>11
[7,4,5,2,3,8,1,6]=>8
[6,4,5,2,3,1,8,7]=>8
[5,4,6,2,1,3,8,7]=>4
[3,6,1,5,4,2,8,7]=>3
[4,6,5,1,3,2,8,7]=>4
[5,6,4,3,1,2,8,7]=>5
[7,5,4,3,2,8,1,6]=>10
[8,6,4,3,7,2,5,1]=>15
[7,6,4,3,8,2,1,5]=>11
[6,7,4,3,8,1,2,5]=>5
[5,7,4,3,1,8,2,6]=>5
[4,7,5,1,3,8,2,6]=>4
[3,7,1,5,4,8,2,6]=>3
[2,1,7,5,4,8,3,6]=>3
[3,8,1,5,4,7,6,2]=>6
[4,8,5,1,3,7,6,2]=>7
[5,8,4,3,1,7,6,2]=>8
[6,8,4,3,7,1,5,2]=>9
[7,8,4,3,6,5,1,2]=>10
[6,8,5,7,3,1,4,2]=>11
[5,8,6,7,1,3,4,2]=>10
[4,8,6,1,7,3,5,2]=>9
[3,8,1,6,7,4,5,2]=>8
[2,1,8,6,7,4,5,3]=>8
[2,1,7,6,8,4,3,5]=>4
[3,7,1,6,8,4,2,5]=>4
[4,7,6,1,8,3,2,5]=>5
[5,7,6,8,1,3,2,4]=>5
[5,4,7,2,1,8,3,6]=>4
[6,4,7,2,8,1,3,5]=>4
[7,4,6,2,8,3,1,5]=>9
[8,4,6,2,7,3,5,1]=>13
[8,3,2,6,7,4,5,1]=>11
[7,3,2,6,8,4,1,5]=>7
[6,3,2,7,8,1,4,5]=>3
[5,3,2,7,1,8,4,6]=>3
[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]=>6
[6,3,2,8,7,1,5,4]=>7
[7,3,2,8,6,5,1,4]=>8
[8,4,7,2,6,5,3,1]=>15
[7,4,8,2,6,5,1,3]=>9
[6,4,8,2,7,1,5,3]=>8
[5,4,8,2,1,7,6,3]=>7
[4,5,8,1,2,7,6,3]=>3
[3,5,1,8,2,7,6,4]=>3
[2,1,5,8,3,7,6,4]=>3
[2,1,6,8,7,3,5,4]=>4
[3,6,1,8,7,2,5,4]=>4
[4,6,8,1,7,2,5,3]=>4
[5,6,8,7,1,2,4,3]=>5
[6,5,8,7,2,1,4,3]=>10
[7,5,8,6,2,4,1,3]=>11
[8,5,7,6,2,4,3,1]=>17
[5,7,8,6,1,4,2,3]=>6
[4,7,8,1,6,5,2,3]=>5
[3,7,1,8,6,5,2,4]=>5
[2,1,7,8,6,5,3,4]=>5
[3,8,1,7,6,5,4,2]=>10
[4,8,7,1,6,5,3,2]=>11
[5,8,7,6,1,4,3,2]=>12
[6,8,7,5,4,1,3,2]=>13
[4,2,5,1,3,6,7,8]=>1
[5,2,6,7,1,3,4,8]=>1
[3,2,7,8,1,4,5,6]=>1
[5,3,2,6,1,4,7,8]=>3
[7,4,3,8,1,2,5,6]=>5
[4,7,3,6,8,1,2,5]=>5
[6,7,3,4,8,1,2,5]=>4
[5,4,2,7,8,1,3,6]=>4
[6,4,7,2,5,1,3,8]=>6
[6,4,3,2,7,1,5,8]=>6
[5,4,3,2,8,1,6,7]=>6
[7,5,3,8,2,6,1,4]=>9
[8,5,4,7,2,6,1,3]=>14
[8,5,4,7,3,6,1,2]=>15
[8,1,2,7,6,3,4,5]=>7
[8,1,4,2,6,3,5,7]=>4
[8,3,1,2,4,7,5,6]=>4
[8,3,1,5,6,2,4,7]=>6
[6,3,8,1,2,7,4,5]=>4
[7,8,4,1,6,2,3,5]=>6
[8,3,4,1,6,7,2,5]=>8
[2,7,6,5,1,3,8,4]=>7
[8,3,6,5,1,7,2,4]=>11
[4,6,7,3,8,5,1,2]=>4
[3,5,2,7,1,8,6,4]=>2
[4,6,7,2,8,1,5,3]=>2
[5,6,7,8,2,1,4,3]=>2
[6,5,8,7,3,4,1,2]=>12
[3,6,7,4,5,8,1,2]=>4
[2,6,7,4,5,1,8,3]=>4
[1,6,7,4,5,2,3,8]=>4
[1,5,4,7,6,2,3,8]=>4
[2,5,4,7,6,1,8,3]=>4
[3,5,4,7,6,8,1,2]=>4
[4,5,3,7,8,6,1,2]=>4
[5,4,3,8,7,6,1,2]=>10
[6,4,8,3,7,5,1,2]=>10
[6,3,8,4,5,7,1,2]=>8
[5,3,4,8,6,7,1,2]=>8
[4,3,5,6,8,7,1,2]=>4
[3,2,5,6,1,8,7,4]=>2
[4,2,5,6,8,1,7,3]=>2
[5,2,4,8,6,1,7,3]=>6
[6,2,8,4,5,1,7,3]=>6
[7,8,2,4,5,1,6,3]=>6
[7,8,1,4,5,2,3,6]=>4
[6,1,8,4,5,2,3,7]=>4
[5,1,4,8,6,2,3,7]=>4
[4,1,3,2,8,6,5,7]=>2
[5,1,3,8,2,6,4,7]=>2
[6,1,8,3,2,5,4,7]=>2
[7,8,1,3,2,5,4,6]=>2
[7,8,2,3,1,5,6,4]=>4
[6,2,8,3,1,5,7,4]=>4
[5,2,3,8,1,6,7,4]=>4
[6,3,8,2,1,7,5,4]=>6
[7,8,3,2,1,6,5,4]=>6
[7,8,4,2,6,1,5,3]=>8
[5,4,2,8,7,1,6,3]=>8
[4,5,2,7,8,1,6,3]=>2
[2,5,3,7,1,6,8,4]=>2
[1,5,3,7,2,6,4,8]=>2
[1,6,7,3,2,5,4,8]=>2
[2,6,7,3,1,5,8,4]=>2
[3,6,7,2,1,8,5,4]=>2
[7,8,5,6,2,1,4,3]=>10
[6,5,8,7,1,2,3,4]=>8
[5,4,1,8,7,2,3,6]=>6
[6,4,8,1,7,2,3,5]=>6
[7,8,3,1,2,6,4,5]=>4
[5,3,1,8,2,7,4,6]=>4
[4,3,1,2,8,7,5,6]=>4
[4,2,1,3,8,5,7,6]=>2
[5,2,1,8,3,4,7,6]=>2
[6,2,8,1,3,4,7,5]=>2
[7,8,2,1,3,4,6,5]=>2
[6,3,1,5,2,4,8,7]=>4
[2,1,8,5,3,7,4,6]=>4
[8,2,6,1,4,3,7,5]=>7
[4,7,1,5,8,3,2,6]=>3
[8,6,1,3,4,2,5,7]=>7
[8,1,2,4,5,6,3,7]=>3
[8,2,5,1,3,6,4,7]=>5
[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]=>2
[1,7,3,4,2,5,8,6]=>2
[4,7,2,1,3,5,8,6]=>1
[4,5,2,3,7,6,1,8]=>3
[6,4,3,7,2,5,1,8]=>7
[8,4,3,6,5,1,2,7]=>10
[1,5,6,3,4,8,7,2]=>3
[4,6,2,7,3,5,1,8]=>3
[3,2,6,7,4,5,1,8]=>3
[4,7,2,6,5,3,1,8]=>7
[5,7,6,2,4,3,1,8]=>8
[1,7,5,4,8,3,6,2]=>7
[8,7,5,4,1,3,2,6]=>14
[6,8,5,4,2,1,3,7]=>8
[5,8,6,2,4,1,3,7]=>7
[4,8,2,6,5,1,3,7]=>6
[3,2,8,6,5,1,4,7]=>6
[4,1,2,6,5,8,7,3]=>2
[5,1,6,2,4,8,7,3]=>2
[6,1,5,4,2,8,7,3]=>6
[7,1,5,4,8,2,6,3]=>6
[8,1,5,4,7,6,2,3]=>10
[1,8,6,7,4,5,3,2]=>13
[8,1,6,7,4,5,2,3]=>12
[7,1,6,8,4,2,5,3]=>7
[6,1,7,8,2,4,5,3]=>2
[5,1,7,2,8,4,6,3]=>2
[4,1,2,7,8,5,6,3]=>2
[3,2,1,7,8,5,6,4]=>3
[3,2,8,7,1,5,4,6]=>6
[4,8,2,7,1,5,3,6]=>6
[5,8,7,2,1,4,3,6]=>7
[6,8,7,1,2,4,3,5]=>6
[7,8,6,1,4,2,3,5]=>7
[8,7,6,1,4,3,2,5]=>14
[1,7,6,8,4,3,5,2]=>8
[1,6,7,8,3,4,5,2]=>3
[8,6,7,1,3,4,2,5]=>12
[7,6,8,1,3,2,4,5]=>6
[5,7,8,2,1,3,4,6]=>1
[4,7,2,8,1,3,5,6]=>1
[3,2,6,8,4,1,5,7]=>2
[4,6,2,8,3,1,5,7]=>2
[5,6,8,2,3,1,4,7]=>2
[6,5,8,3,2,1,4,7]=>7
[7,5,8,3,1,2,4,6]=>6
[8,5,7,3,1,4,2,6]=>12
[1,5,7,3,8,4,6,2]=>3
[1,4,3,7,8,5,6,2]=>3
[8,4,3,7,1,5,2,6]=>10
[6,4,3,8,2,1,5,7]=>6
[4,5,2,3,8,1,6,7]=>2
[3,2,5,4,8,1,6,7]=>2
[4,5,2,3,1,8,7,6]=>3
[6,4,3,1,2,8,7,5]=>6
[7,4,3,1,8,2,6,5]=>6
[8,4,3,1,7,6,2,5]=>10
[1,5,8,3,7,6,4,2]=>7
[8,5,1,3,7,6,2,4]=>10
[7,5,1,3,8,2,6,4]=>6
[6,5,1,3,2,8,7,4]=>6
[5,6,1,2,3,8,7,4]=>1
[4,6,2,1,3,8,7,5]=>2
[3,2,6,1,4,8,7,5]=>2
[3,2,7,1,8,4,6,5]=>2
[4,7,2,1,8,3,6,5]=>2
[5,7,1,2,8,3,6,4]=>1
[6,7,1,8,2,3,5,4]=>1
[7,6,1,8,3,2,5,4]=>7
[8,6,1,7,3,5,2,4]=>12
[1,6,8,7,3,5,4,2]=>8
[1,7,8,6,5,3,4,2]=>9
[8,7,1,6,5,3,2,4]=>14
[7,8,1,6,5,2,3,4]=>7
[6,8,1,7,2,5,3,4]=>6
[5,8,1,2,7,6,3,4]=>5
[4,8,2,1,7,6,3,5]=>6
[3,2,8,1,7,6,4,5]=>6
[4,1,2,8,7,6,5,3]=>6
[5,1,8,2,7,6,4,3]=>6
[6,1,8,7,2,5,4,3]=>7
[7,1,8,6,5,2,4,3]=>8
[8,1,7,6,5,4,2,3]=>14
[1,4,3,8,7,5,6,2]=>6
[4,1,2,8,7,5,6,3]=>5
[3,2,5,1,6,4,8,7]=>1
[3,2,5,4,7,1,8,6]=>2
[4,2,5,3,7,6,8,1]=>3
[4,2,5,3,7,1,8,6]=>2
[4,2,5,3,6,1,8,7]=>2
[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]=>2
[4,3,5,2,7,1,8,6]=>3
[4,3,6,2,7,5,8,1]=>4
[4,3,6,2,7,1,8,5]=>3
[4,3,6,1,7,2,8,5]=>2
[4,3,5,1,7,2,8,6]=>2
[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]=>2
[4,1,5,3,7,6,8,2]=>2
[4,3,5,1,7,6,8,2]=>3
[4,3,6,1,7,5,8,2]=>3
[4,3,6,5,7,1,8,2]=>4
[5,3,6,4,7,2,8,1]=>5
[5,3,6,4,7,1,8,2]=>4
[5,3,6,1,7,4,8,2]=>3
[5,1,6,3,7,4,8,2]=>2
[4,1,6,3,7,5,8,2]=>2
[3,1,6,4,7,5,8,2]=>2
[2,1,6,4,7,5,8,3]=>2
[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]=>2
[5,3,6,2,7,1,8,4]=>3
[5,3,6,2,7,4,8,1]=>4
[5,2,6,3,7,4,8,1]=>3
[5,2,6,3,7,1,8,4]=>2
[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]=>2
[4,2,6,3,7,5,8,1]=>3
[3,2,6,4,7,5,8,1]=>3
[3,2,6,4,7,1,8,5]=>2
[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]=>2
[3,2,6,1,7,5,8,4]=>2
[3,2,6,5,7,1,8,4]=>3
[4,2,6,5,7,3,8,1]=>4
[4,2,6,5,7,1,8,3]=>3
[4,2,6,1,7,5,8,3]=>2
[4,2,5,1,7,6,8,3]=>2
[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]=>2
[5,2,6,4,7,1,8,3]=>3
[5,2,6,4,7,3,8,1]=>4
[5,4,6,2,7,3,8,1]=>5
[5,4,6,2,7,1,8,3]=>4
[5,4,6,1,7,2,8,3]=>3
[5,1,6,4,7,2,8,3]=>2
[4,1,6,5,7,2,8,3]=>2
[3,1,6,5,7,2,8,4]=>2
[2,1,6,5,7,3,8,4]=>2
[3,1,6,5,7,4,8,2]=>3
[4,1,6,5,7,3,8,2]=>3
[5,1,6,4,7,3,8,2]=>3
[5,4,6,1,7,3,8,2]=>4
[5,4,6,3,7,1,8,2]=>5
[8,3,5,2,1,6,4,7]=>7
[8,6,3,5,2,4,1,7]=>12
[3,7,5,2,4,1,8,6]=>5
[8,3,7,5,2,4,6,1]=>13
[8,2,4,5,7,3,6,1]=>10
[2,4,5,7,3,1,8,6]=>1
[8,2,4,6,5,3,1,7]=>9
[8,2,5,4,6,1,3,7]=>8
[8,6,3,5,1,4,2,7]=>11
[8,6,1,4,5,3,2,7]=>10
[8,1,5,6,4,3,2,7]=>9
[5,7,4,3,2,1,8,6]=>6
[8,5,7,4,3,2,6,1]=>16
[4,6,8,3,2,7,5,1]=>6
[4,7,6,3,2,8,1,5]=>7
[1,4,6,7,3,2,8,5]=>1
[5,4,7,3,1,8,2,6]=>5
[1,7,4,5,3,2,8,6]=>5
[3,7,5,1,4,2,8,6]=>4
[5,7,4,2,1,3,8,6]=>4
[8,5,7,4,2,1,6,3]=>14
[8,3,7,5,1,4,6,2]=>12
[8,4,1,7,5,3,6,2]=>11
[4,6,3,8,7,1,5,2]=>6
[1,7,4,8,6,3,5,2]=>7
[8,4,7,6,3,5,2,1]=>17
[3,6,5,8,7,4,1,2]=>8
[3,1,5,8,6,7,4,2]=>5
[4,8,1,6,7,3,5,2]=>8
[3,6,4,1,8,7,5,2]=>5
[8,2,6,1,4,7,5,3]=>9
[2,7,6,8,1,4,3,5]=>5
[3,7,1,6,4,8,2,5]=>4
[1,7,3,5,6,8,2,4]=>5
[1,3,6,7,5,8,2,4]=>2
[3,7,6,5,8,2,1,4]=>8
[3,6,8,5,7,2,4,1]=>8
[2,3,5,7,6,8,1,4]=>2
[2,1,6,5,7,8,3,4]=>2
[4,2,7,6,8,3,1,5]=>5
[4,2,6,8,7,3,5,1]=>6
[3,8,2,4,6,7,5,1]=>7
[3,7,2,6,4,8,1,5]=>5
[3,2,6,1,4,7,8,5]=>1
[5,3,7,2,1,8,4,6]=>3
[4,7,3,2,1,5,8,6]=>3
[8,7,6,1,3,4,2,5]=>13
[8,5,7,3,2,1,6,4]=>13
[8,3,6,7,2,1,5,4]=>12
[3,7,8,6,2,1,5,4]=>6
[8,7,6,3,5,2,4,1]=>18
[2,7,4,8,1,6,5,3]=>5
[4,6,8,2,1,7,5,3]=>4
[8,4,1,5,7,2,6,3]=>9
[8,5,3,7,1,6,2,4]=>12
[8,5,7,2,1,3,6,4]=>11
[8,2,6,7,1,3,5,4]=>10
[8,3,6,1,7,5,2,4]=>11
[4,6,1,8,7,2,5,3]=>4
[8,1,2,5,6,7,4,3]=>7
[8,2,6,5,7,4,1,3]=>13
[2,1,7,8,5,6,4,3]=>5
[8,2,5,7,6,4,3,1]=>14
[2,7,6,8,5,4,1,3]=>9
[1,7,2,5,8,6,4,3]=>5
[1,7,4,8,2,6,5,3]=>5
[3,7,8,1,6,5,2,4]=>5
[2,7,8,6,1,3,5,4]=>5
[8,7,6,3,5,1,4,2]=>17
[8,4,7,6,5,1,3,2]=>16
[8,7,1,5,6,4,3,2]=>15
[8,1,6,7,5,4,3,2]=>14
[5,4,3,6,1,2,8,7]=>5
[2,7,6,4,5,8,1,3]=>8
[5,7,3,6,1,8,2,4]=>5
[2,1,7,6,5,8,3,4]=>5
[6,4,3,5,8,1,7,2]=>8
[7,3,5,4,8,6,1,2]=>9
[5,4,3,2,7,1,8,6]=>6
[4,3,6,2,8,7,5,1]=>6
[4,3,7,6,2,1,8,5]=>6
[6,4,3,1,7,2,8,5]=>5
[4,3,7,1,8,6,5,2]=>5
[5,3,8,7,6,4,2,1]=>12
[7,5,3,1,8,6,4,2]=>9
[1,8,6,5,3,7,4,2]=>11
[6,1,7,5,3,2,8,4]=>4
[7,6,5,3,2,1,8,4]=>12
[6,5,3,2,8,7,4,1]=>10
[5,2,6,3,8,7,4,1]=>5
[5,2,7,6,3,1,8,4]=>5
[6,5,2,1,7,3,8,4]=>5
[5,2,7,1,8,6,4,3]=>4
[6,2,8,7,5,4,3,1]=>11
[7,6,2,1,8,5,4,3]=>9
[6,1,7,2,8,5,4,3]=>3
[7,1,8,6,5,4,3,2]=>10
[4,5,2,6,3,1,8,7]=>2
[6,5,2,1,4,3,8,7]=>6
[6,5,2,7,4,8,3,1]=>8
[8,5,2,7,4,1,6,3]=>12
[8,3,7,5,2,1,6,4]=>12
[6,3,7,5,2,8,4,1]=>7
[3,1,6,5,4,2,8,7]=>3
[5,6,3,2,4,1,8,7]=>4
[3,6,2,4,1,5,8,7]=>2
[2,6,1,3,5,4,8,7]=>1
[6,7,2,3,4,8,5,1]=>4
[8,7,2,3,4,1,6,5]=>10
[5,1,7,3,8,4,6,2]=>3
[2,5,7,3,8,6,4,1]=>4
[7,6,1,3,5,8,4,2]=>9
[3,6,7,4,1,8,5,2]=>3
[5,6,3,7,4,8,1,2]=>4
[2,1,6,7,4,8,5,3]=>2
[2,1,8,7,4,3,6,5]=>6
[5,8,3,7,4,2,6,1]=>10
[3,8,7,4,1,2,6,5]=>8
[7,8,1,3,5,2,6,4]=>4
[5,8,7,3,2,6,1,4]=>10
[2,8,6,3,1,5,7,4]=>7
[8,1,6,3,2,5,4,7]=>6
[2,8,4,1,6,3,7,5]=>5
[4,8,1,2,7,6,3,5]=>5
[3,8,4,2,5,7,1,6]=>6
[6,8,3,5,2,7,4,1]=>9
[2,1,5,3,8,7,6,4]=>3
[6,5,3,2,8,7,1,4]=>9
[7,5,2,4,8,1,6,3]=>8
[3,4,2,8,5,7,6,1]=>5
[2,4,1,8,7,6,5,3]=>6
[8,4,2,1,7,5,3,6]=>8
[4,3,1,8,6,7,5,2]=>7
[3,1,4,8,6,5,7,2]=>4
[7,1,6,5,4,8,2,3]=>9
[3,7,5,6,8,4,2,1]=>9
[5,7,1,6,8,2,4,3]=>4
[8,6,2,5,1,7,4,3]=>12
[5,6,2,1,8,7,3,4]=>3
[4,6,2,5,8,3,7,1]=>5
[7,5,2,6,3,8,1,4]=>9
[4,1,2,3,6,8,7,5]=>1
[2,4,3,1,8,5,6,7]=>1
[7,5,2,8,3,4,6,1]=>8
[5,6,2,8,4,3,1,7]=>4
[4,7,2,8,1,5,3,6]=>2
[8,7,2,1,4,5,6,3]=>10
[3,6,8,7,1,5,4,2]=>7
[5,7,8,6,3,4,1,2]=>8
[7,1,8,5,4,3,6,2]=>7
[2,7,8,4,5,3,6,1]=>6
[5,7,3,8,1,4,6,2]=>4
[2,1,7,8,5,4,6,3]=>4
[2,1,5,8,4,6,3,7]=>2
[6,5,3,8,4,1,2,7]=>8
[7,5,8,4,3,6,2,1]=>12
[2,4,8,3,5,6,1,7]=>3
[4,1,8,3,6,5,2,7]=>4
[3,4,8,1,7,2,5,6]=>3
[8,4,1,3,7,2,6,5]=>8
[3,1,8,2,4,7,6,5]=>3
[2,3,8,1,4,6,7,5]=>2
[4,3,8,2,5,1,7,6]=>5
[6,3,8,4,2,5,7,1]=>7
[7,4,3,8,2,5,1,6]=>7
[2,1,4,8,3,5,7,6]=>1
[6,8,2,4,3,5,1,7]=>5
[4,8,2,3,5,1,6,7]=>3
[3,8,2,1,4,6,5,7]=>2
[2,8,1,3,4,5,7,6]=>1
[7,1,6,8,4,3,2,5]=>7
[7,1,6,5,8,3,2,4]=>8
[3,7,6,1,4,8,2,5]=>5
[2,7,8,4,1,6,5,3]=>5
[3,6,4,5,7,2,8,1]=>5
[1,8,2,7,3,4,5,6]=>4
[3,2,1,5,8,4,6,7]=>1
[5,4,3,2,1,8,6,7]=>6
[1,8,2,4,3,5,6,7]=>1
[1,7,2,4,3,5,6,8]=>1
[1,6,2,4,3,5,7,8]=>1
[1,5,2,4,3,6,7,8]=>1
[1,6,2,5,3,4,7,8]=>2
[1,7,2,5,3,4,6,8]=>2
[1,8,2,5,3,4,6,7]=>2
[1,8,2,6,3,4,5,7]=>3
[1,7,2,6,3,4,5,8]=>3
[1,8,2,7,3,5,4,6]=>5
[1,7,2,8,3,5,4,6]=>1
[1,6,2,8,3,5,4,7]=>1
[1,5,2,8,3,6,4,7]=>1
[1,4,2,8,3,6,5,7]=>1
[1,3,2,8,4,6,5,7]=>1
[1,2,3,8,4,6,5,7]=>1
[1,2,3,7,4,6,5,8]=>1
[1,3,2,7,4,6,5,8]=>1
[1,4,2,7,3,6,5,8]=>1
[1,5,2,7,3,6,4,8]=>1
[1,6,2,7,3,5,4,8]=>1
[1,7,2,6,3,5,4,8]=>4
[1,8,2,6,3,5,4,7]=>4
[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]=>2
[1,5,2,4,3,7,6,8]=>1
[1,6,2,4,3,7,5,8]=>1
[1,7,2,4,3,6,5,8]=>2
[1,8,2,4,3,6,5,7]=>2
[1,8,2,3,4,6,5,7]=>1
[1,7,2,3,4,6,5,8]=>1
[1,8,2,3,4,7,5,6]=>2
[1,8,2,4,3,7,5,6]=>3
[1,7,2,4,3,8,5,6]=>1
[1,6,2,4,3,8,5,7]=>1
[1,5,2,4,3,8,6,7]=>1
[1,6,2,5,3,8,4,7]=>2
[1,7,2,5,3,8,4,6]=>2
[1,8,2,5,3,7,4,6]=>4
[1,8,2,6,3,7,4,5]=>5
[1,7,2,6,3,8,4,5]=>3
[1,2,3,8,4,7,5,6]=>2
[1,3,2,8,4,7,5,6]=>2
[1,4,2,8,3,7,5,6]=>2
[1,5,2,8,3,7,4,6]=>2
[1,6,2,8,3,7,4,5]=>2
[1,7,2,8,3,6,4,5]=>2
[1,8,2,7,3,6,4,5]=>6
[6,7,8,1,4,3,2,5]=>3
[2,8,4,1,6,7,5,3]=>7
[4,8,5,7,1,6,2,3]=>9
[8,7,6,5,2,1,4,3]=>17
[8,3,1,5,4,7,2,6]=>7
[8,7,6,5,1,4,2,3]=>17
[7,5,1,3,8,4,2,6]=>6
[7,6,1,4,8,3,2,5]=>8
[7,1,3,5,8,2,4,6]=>3
[7,5,3,6,4,2,8,1]=>12
[8,2,6,3,4,7,5,1]=>10
[7,2,6,3,5,4,8,1]=>9
[6,2,7,4,3,5,8,1]=>5
[3,7,6,4,5,2,8,1]=>9
[2,7,6,5,3,4,8,1]=>9
[8,6,5,4,2,7,3,1]=>16
[6,5,8,4,2,7,3,1]=>11
[1,8,6,3,7,5,2,4]=>10
[8,7,5,2,6,4,3,1]=>17
[8,7,1,6,2,5,4,3]=>13
[1,7,2,8,5,3,4,6]=>2
[7,6,1,8,4,3,2,5]=>8
[8,6,1,7,4,2,5,3]=>12
[8,1,2,7,3,4,6,5]=>5
[7,1,2,8,3,5,4,6]=>1
[8,2,6,1,7,3,5,4]=>9
[4,7,5,6,8,3,2,1]=>9
[8,6,4,7,5,3,2,1]=>18
[5,4,8,1,7,2,6,3]=>7
[2,3,8,7,4,5,6,1]=>7
[7,2,8,6,4,3,5,1]=>9
[8,2,7,6,3,5,4,1]=>14
[8,1,7,6,5,2,4,3]=>13
[7,1,8,6,5,3,2,4]=>8
[1,2,8,7,6,3,4,5]=>7
[3,8,7,6,4,5,2,1]=>14
[2,8,7,6,5,3,4,1]=>14
[1,8,7,6,5,4,2,3]=>14
[3,8,6,7,1,5,2,4]=>10
[5,4,7,1,3,8,2,6]=>4
[5,6,2,1,4,8,3,7]=>2
[2,1,8,4,7,5,6,3]=>6
[4,1,3,2,8,5,6,7]=>1
[3,2,1,4,8,5,6,7]=>1
[1,8,4,2,5,3,6,7]=>3
[8,1,5,3,2,4,6,7]=>4
[3,8,1,5,2,4,6,7]=>2
[1,6,7,2,8,4,3,5]=>1
[6,7,1,4,2,8,3,5]=>2
[6,3,7,1,4,8,2,5]=>3
[3,7,8,1,5,2,4,6]=>2
[7,1,2,8,5,3,4,6]=>2
[1,7,2,8,4,5,3,6]=>2
[1,2,7,5,8,3,4,6]=>2
[2,8,1,7,4,3,6,5]=>6
[4,2,6,5,8,3,7,1]=>5
[5,2,4,7,3,6,8,1]=>5
[5,1,2,4,8,3,6,7]=>1
[4,3,6,1,5,8,2,7]=>3
[2,6,1,4,5,8,3,7]=>2
[2,5,3,4,1,8,6,7]=>2
[4,3,5,2,1,8,6,7]=>3
[3,1,6,7,5,8,2,4]=>2
[2,8,1,7,5,6,3,4]=>8
[5,3,6,8,4,7,2,1]=>7
[3,7,2,5,4,8,6,1]=>5
[8,4,2,5,7,3,6,1]=>11
[4,7,2,5,8,3,6,1]=>5
[5,2,6,8,4,3,7,1]=>5
[3,1,6,5,4,8,2,7]=>3
[4,1,6,5,8,3,2,7]=>3
[5,1,6,8,4,3,2,7]=>3
[8,5,4,7,6,3,2,1]=>17
[5,7,1,8,4,3,2,6]=>3
[2,7,1,5,4,3,8,6]=>3
[8,2,1,5,4,3,7,6]=>5
[8,4,1,5,7,3,2,6]=>9
[8,5,6,7,1,3,2,4]=>13
[8,4,6,1,7,3,2,5]=>11
[8,3,6,1,4,7,2,5]=>9
[2,7,6,1,4,3,8,5]=>5
[6,7,8,5,1,3,2,4]=>5
[5,7,6,8,2,3,4,1]=>7
[5,7,2,8,4,3,6,1]=>5
[6,7,8,2,4,3,5,1]=>5
[4,7,6,2,8,3,5,1]=>7
[8,3,6,2,4,7,5,1]=>11
[3,7,6,2,4,8,5,1]=>7
[5,7,3,8,4,6,2,1]=>7
[4,7,3,5,8,6,2,1]=>7
[8,7,2,1,4,3,6,5]=>9
[8,7,3,1,4,6,2,5]=>11
[8,7,6,3,2,5,4,1]=>17
[8,7,3,5,1,6,2,4]=>13
[8,7,2,5,1,3,6,4]=>11
[8,2,6,5,1,3,7,4]=>9
[8,4,6,5,7,1,2,3]=>13
[5,7,6,8,4,1,2,3]=>7
[4,7,6,5,8,1,2,3]=>7
[3,7,6,5,1,8,2,4]=>7
[2,6,5,7,3,4,8,1]=>5
[1,6,4,7,5,8,2,3]=>4
[8,5,3,6,2,7,4,1]=>13
[1,3,7,4,6,8,2,5]=>3
[4,7,5,6,3,2,8,1]=>9
[1,7,6,5,4,8,2,3]=>9
[8,1,6,5,7,2,4,3]=>11
[1,2,7,6,8,3,4,5]=>3
[6,1,7,5,3,8,2,4]=>4
[2,1,7,5,6,8,3,4]=>4
[5,4,1,7,6,8,2,3]=>5
[4,8,5,6,2,7,3,1]=>10
[3,8,6,4,2,7,5,1]=>10
[7,8,5,2,4,6,3,1]=>10
[2,8,6,3,7,4,5,1]=>10
[7,8,1,6,2,4,5,3]=>6
[6,8,1,4,7,2,5,3]=>6
[3,8,4,1,7,2,6,5]=>6
[5,4,7,1,8,3,2,6]=>4
[3,7,4,1,8,5,2,6]=>3
[6,7,1,4,8,3,2,5]=>3
[2,7,1,8,4,5,3,6]=>2
[6,1,2,8,4,3,5,7]=>1
[6,5,1,4,3,8,2,7]=>7
[1,6,2,5,8,3,4,7]=>2
[8,5,1,3,7,2,6,4]=>9
[8,4,2,1,7,3,6,5]=>8
[7,4,2,1,8,5,3,6]=>5
[1,5,4,2,8,3,6,7]=>2
[6,4,3,1,5,8,2,7]=>6
[3,7,6,8,4,5,2,1]=>9
[2,7,6,8,5,3,4,1]=>9
[1,7,6,8,5,4,2,3]=>9
[1,4,8,6,7,5,2,3]=>8
[2,4,8,6,7,3,5,1]=>8
[7,3,8,5,4,6,2,1]=>10
[3,4,8,5,6,7,2,1]=>7
[6,3,5,8,4,7,2,1]=>10
[5,4,3,8,6,7,2,1]=>10
[5,4,2,8,7,3,6,1]=>9
[6,2,5,8,7,3,4,1]=>9
[3,2,8,5,7,4,6,1]=>8
[1,3,8,7,5,6,2,4]=>8
[2,1,8,7,4,6,3,5]=>7
[3,1,8,5,7,6,2,4]=>7
[6,1,5,8,7,4,2,3]=>8
[5,4,1,8,7,6,2,3]=>8
[5,8,6,7,4,3,2,1]=>14
[4,8,7,5,6,3,2,1]=>14
[2,8,3,1,5,4,6,7]=>2
[2,5,3,4,7,1,8,6]=>2
[2,4,8,3,5,7,6,1]=>5
[4,2,5,3,1,8,6,7]=>2
[4,2,1,8,5,3,6,7]=>2
[5,4,1,3,8,2,6,7]=>4
[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]=>6
[1,7,4,3,8,5,2,6]=>4
[1,5,7,3,8,4,2,6]=>2
[5,1,4,7,8,3,2,6]=>3
[4,8,1,5,7,3,6,2]=>7
[8,1,5,3,7,4,6,2]=>9
[3,8,4,7,6,5,2,1]=>12
[1,6,8,5,3,7,4,2]=>7
[6,8,1,7,4,3,5,2]=>8
[6,4,8,1,7,3,5,2]=>8
[6,4,8,7,1,5,2,3]=>9
[7,6,4,1,3,8,2,5]=>9
[1,7,5,6,3,2,8,4]=>7
[4,2,1,7,8,5,3,6]=>2
[2,7,4,6,3,1,8,5]=>6
[2,6,8,4,3,7,5,1]=>6
[6,2,4,8,3,7,5,1]=>7
[7,2,6,3,4,1,8,5]=>7
[2,6,7,3,1,4,8,5]=>1
[2,7,1,8,3,5,4,6]=>1
[2,1,7,3,5,8,4,6]=>1
[8,7,1,3,6,2,4,5]=>10
[8,2,1,7,3,5,6,4]=>7
[7,8,2,6,3,1,5,4]=>7
[8,7,2,6,3,5,4,1]=>15
[1,2,8,7,4,5,6,3]=>7
[8,3,7,1,5,6,2,4]=>11
[8,6,1,2,7,5,3,4]=>10
[8,1,6,2,7,4,5,3]=>9
[1,8,5,2,6,7,4,3]=>8
[5,2,1,8,6,7,4,3]=>6
[2,8,5,7,6,4,3,1]=>13
[1,7,8,5,2,6,4,3]=>6
[7,8,1,6,4,2,5,3]=>7
[7,8,6,1,5,3,2,4]=>9
[7,3,8,6,1,5,2,4]=>8
[8,7,6,1,5,3,4,2]=>16
[8,7,1,6,4,5,3,2]=>15
[8,1,7,5,6,4,3,2]=>14
[1,8,6,7,5,4,3,2]=>14
[9,1,2,3,4,5,6,7,8]=>0
[8,1,2,3,4,5,6,9,7]=>0
[2,9,1,3,4,5,6,7,8]=>0
[9,3,1,2,4,5,6,7,8]=>2
[8,9,1,2,3,4,5,6,7]=>0
[9,7,8,1,2,3,4,5,6]=>12
[2,3,4,5,6,7,9,1,8]=>0
[2,3,4,5,6,7,8,9,1]=>0
[2,3,4,5,6,7,8,1,9]=>0
[2,3,4,5,6,7,1,8,9]=>0
[1,2,3,4,5,6,7,9,8]=>0
[2,1,3,4,5,6,7,8,9]=>0
[1,8,2,3,4,5,6,9,7]=>0
[7,1,2,3,4,5,6,9,8]=>0
[2,1,9,3,4,5,6,7,8]=>0
[2,8,1,3,4,5,6,7,9]=>0
[1,2,3,4,5,6,7,8,9]=>0
[3,2,4,5,6,7,8,9,1]=>1
[9,8,7,6,5,4,3,2,1]=>28
[8,7,6,5,4,3,2,1,9]=>21
[1,9,8,7,6,5,4,3,2]=>21
[8,7,6,4,5,3,2,1,9]=>20
[1,9,8,7,5,6,4,3,2]=>20
[8,7,5,4,6,3,2,1,9]=>19
[8,7,4,6,5,3,2,1,9]=>19
[1,9,8,6,5,7,4,3,2]=>19
[1,9,8,5,7,6,4,3,2]=>19
[9,2,1,3,4,5,6,7,8]=>1
[9,2,3,1,4,5,6,7,8]=>2
[4,2,3,5,6,7,8,9,1]=>2
[3,4,2,5,6,7,8,9,1]=>1
[9,8,1,2,3,4,5,6,7]=>7
[7,8,9,1,2,3,4,5,6]=>0
[9,8,7,1,2,3,4,5,6]=>13
[6,7,8,9,1,2,3,4,5]=>0
[9,6,7,8,1,2,3,4,5]=>15
[8,9,6,7,1,2,3,4,5]=>10
[9,8,6,7,1,2,3,4,5]=>17
[9,8,7,6,1,2,3,4,5]=>18
[9,5,6,7,8,1,2,3,4]=>16
[8,9,5,6,7,1,2,3,4]=>12
[9,8,5,6,7,1,2,3,4]=>19
[9,7,8,5,6,1,2,3,4]=>20
[9,8,7,5,6,1,2,3,4]=>21
[9,8,7,6,5,1,2,3,4]=>22
[7,8,9,4,5,6,1,2,3]=>9
[9,7,8,4,5,6,1,2,3]=>21
[9,8,7,4,5,6,1,2,3]=>22
[8,9,6,7,4,5,1,2,3]=>16
[9,8,6,7,4,5,1,2,3]=>23
[9,8,7,6,4,5,1,2,3]=>24
[9,8,7,6,5,4,1,2,3]=>25
[9,7,8,5,6,3,4,1,2]=>24
[9,8,7,5,6,3,4,1,2]=>25
[9,8,7,6,5,3,4,1,2]=>26
[9,8,7,6,5,4,3,1,2]=>27
[7,8,6,5,4,3,2,1,9]=>15
[1,8,9,7,6,5,4,3,2]=>15
[7,6,8,5,4,3,2,1,9]=>15
[6,8,7,5,4,3,2,1,9]=>15
[1,8,7,9,6,5,4,3,2]=>15
[1,7,9,8,6,5,4,3,2]=>15
[8,1,2,3,4,5,6,7,9]=>0
[1,9,2,3,4,5,6,7,8]=>0
[7,8,1,2,3,4,5,6,9]=>0
[1,8,9,2,3,4,5,6,7]=>0
[7,1,8,2,3,4,5,6,9]=>0
[6,8,1,2,3,4,5,7,9]=>0
[1,8,2,9,3,4,5,6,7]=>0
[1,7,9,2,3,4,5,6,8]=>0
[7,1,2,3,4,5,6,8,9]=>0
[3,4,1,2,5,6,7,8,9]=>0
[3,2,1,4,5,6,7,8,9]=>1
[4,5,6,1,2,3,7,8,9]=>0
[4,2,5,1,3,6,7,8,9]=>1
[4,3,2,1,5,6,7,8,9]=>3
[5,6,7,8,1,2,3,4,9]=>0
[5,2,6,7,1,3,4,8,9]=>1
[5,6,3,4,1,2,7,8,9]=>4
[5,3,2,6,1,4,7,8,9]=>3
[5,4,3,2,1,6,7,8,9]=>6
[6,2,7,8,9,1,3,4,5]=>1
[6,7,3,4,8,1,2,5,9]=>4
[6,3,2,7,8,1,4,5,9]=>3
[6,4,7,2,5,1,3,8,9]=>6
[6,4,3,2,7,1,5,8,9]=>6
[6,5,4,3,2,1,7,8,9]=>10
[7,4,8,2,5,9,1,3,6]=>6
[7,4,3,2,8,9,1,5,6]=>6
[7,8,5,6,3,4,1,2,9]=>12
[7,5,3,8,2,6,1,4,9]=>9
[7,5,4,3,2,8,1,6,9]=>10
[7,6,5,4,3,2,1,8,9]=>15
[8,6,9,4,7,2,5,1,3]=>15
[8,6,4,3,9,2,7,1,5]=>13
[8,6,5,4,3,2,9,1,7]=>15
[2,1,4,3,6,5,8,7,10,9]=>0
[4,3,2,1,6,5,8,7,10,9]=>3
[6,3,2,5,4,1,8,7,10,9]=>6
[8,3,2,5,4,7,6,1,10,9]=>9
[10,3,2,5,4,7,6,9,8,1]=>12
[2,1,6,5,4,3,8,7,10,9]=>3
[6,5,4,3,2,1,8,7,10,9]=>10
[8,5,4,3,2,7,6,1,10,9]=>13
[10,5,4,3,2,7,6,9,8,1]=>16
[2,1,8,5,4,7,6,3,10,9]=>6
[8,7,4,3,6,5,2,1,10,9]=>17
[10,7,4,3,6,5,2,9,8,1]=>20
[2,1,10,5,4,7,6,9,8,3]=>9
[10,9,4,3,6,5,8,7,2,1]=>24
[8,9,5,6,3,4,10,1,2,7]=>12
[2,1,4,3,8,7,6,5,10,9]=>3
[4,3,2,1,8,7,6,5,10,9]=>6
[8,3,2,7,6,5,4,1,10,9]=>13
[10,3,2,7,6,5,4,9,8,1]=>16
[2,1,8,7,6,5,4,3,10,9]=>10
[8,7,6,5,4,3,2,1,10,9]=>21
[9,7,6,5,4,3,2,10,1,8]=>21
[10,7,6,5,4,3,2,9,8,1]=>24
[2,1,10,7,6,5,4,9,8,3]=>13
[10,9,6,5,4,3,8,7,2,1]=>28
[2,1,4,3,10,7,6,9,8,5]=>6
[4,3,2,1,10,7,6,9,8,5]=>9
[10,3,2,9,6,5,8,7,4,1]=>20
[2,1,10,9,6,5,8,7,4,3]=>17
[10,9,8,5,4,7,6,3,2,1]=>32
[6,7,8,9,10,1,2,3,4,5]=>0
[7,3,2,8,9,10,1,4,5,6]=>3
[8,5,4,3,2,9,10,1,6,7]=>10
[2,1,4,3,6,5,10,9,8,7]=>3
[4,3,2,1,6,5,10,9,8,7]=>6
[6,3,2,5,4,1,10,9,8,7]=>9
[10,3,2,5,4,9,8,7,6,1]=>16
[2,1,6,5,4,3,10,9,8,7]=>6
[6,5,4,3,2,1,10,9,8,7]=>13
[10,5,4,3,2,9,8,7,6,1]=>20
[2,1,10,5,4,9,8,7,6,3]=>13
[10,9,4,3,8,7,6,5,2,1]=>28
[9,7,5,10,3,8,2,6,1,4]=>19
[2,1,4,3,10,9,8,7,6,5]=>10
[4,3,2,1,10,9,8,7,6,5]=>13
[10,3,2,9,8,7,6,5,4,1]=>24
[2,1,10,9,8,7,6,5,4,3]=>21
[10,9,8,7,6,5,4,3,2,1]=>36
[2,3,4,5,6,7,8,9,10,1]=>0
[2,3,4,5,6,7,8,9,1,10]=>0
[10,8,9,5,6,7,1,2,3,4]=>26
[10,8,9,4,5,6,1,2,3,7]=>23
[10,7,8,5,6,9,1,2,3,4]=>24
[10,7,8,4,5,9,1,2,3,6]=>22
[10,6,7,4,5,8,1,2,3,9]=>19
[10,7,8,3,4,9,1,2,5,6]=>20
[10,6,7,3,4,8,1,2,5,9]=>17
[9,8,10,5,6,7,1,2,3,4]=>19
[9,8,10,4,5,6,1,2,3,7]=>16
[9,7,10,5,6,8,1,2,3,4]=>18
[9,7,10,4,5,8,1,2,3,6]=>16
[9,6,10,4,5,7,1,2,3,8]=>14
[9,7,10,3,4,8,1,2,5,6]=>14
[9,6,10,3,4,7,1,2,5,8]=>12
[8,7,9,5,6,10,1,2,3,4]=>14
[8,7,9,4,5,10,1,2,3,6]=>12
[8,6,9,4,5,10,1,2,3,7]=>11
[7,6,8,4,5,9,1,2,3,10]=>11
[8,7,9,3,4,10,1,2,5,6]=>10
[8,6,9,3,4,10,1,2,5,7]=>9
[7,6,8,3,4,9,1,2,5,10]=>9
[9,6,10,5,7,8,1,2,3,4]=>17
[9,6,10,4,7,8,1,2,3,5]=>16
[9,5,10,4,6,7,1,2,3,8]=>13
[9,6,10,3,7,8,1,2,4,5]=>15
[9,5,10,3,6,7,1,2,4,8]=>12
[8,6,9,5,7,10,1,2,3,4]=>13
[8,6,9,4,7,10,1,2,3,5]=>12
[8,5,9,4,6,10,1,2,3,7]=>10
[7,5,8,4,6,9,1,2,3,10]=>10
[8,6,9,3,7,10,1,2,4,5]=>11
[8,5,9,3,6,10,1,2,4,7]=>9
[7,5,8,3,6,9,1,2,4,10]=>9
[8,4,9,3,5,10,1,2,6,7]=>7
[7,4,8,3,5,9,1,2,6,10]=>7
[9,6,10,2,7,8,1,3,4,5]=>14
[9,5,10,2,6,7,1,3,4,8]=>11
[8,6,9,2,7,10,1,3,4,5]=>10
[8,5,9,2,6,10,1,3,4,7]=>8
[7,5,8,2,6,9,1,3,4,10]=>8
[8,4,9,2,5,10,1,3,6,7]=>6
[7,4,8,2,5,9,1,3,6,10]=>6
[1,2,3,4,5,6,7,8,10,9]=>0
[2,1,3,4,5,6,7,8,9,10]=>0
[9,1,2,3,4,5,6,7,10,8]=>0
[2,10,1,3,4,5,6,7,8,9]=>0
[1,2,3,4,5,6,7,8,9,10]=>0
[9,8,7,6,5,4,3,2,1,10]=>28
[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,1,2,3,4,5,6,7,8]=>8
[1,10,9,8,7,6,5,4,3,2]=>28
[9,8,7,5,6,4,3,2,1,10]=>27
[1,10,9,8,6,7,5,4,3,2]=>27
[10,2,1,3,4,5,6,7,8,9]=>1
[3,2,4,5,6,7,8,9,10,1]=>1
[2,4,6,8,10,1,3,5,7,9]=>0
[2,4,6,9,10,1,3,5,7,8]=>0
[2,4,7,8,10,1,3,5,6,9]=>0
[2,4,7,9,10,1,3,5,6,8]=>0
[2,4,8,9,10,1,3,5,6,7]=>0
[2,5,6,8,10,1,3,4,7,9]=>0
[2,5,6,9,10,1,3,4,7,8]=>0
[2,5,7,8,10,1,3,4,6,9]=>0
[2,5,7,9,10,1,3,4,6,8]=>0
[2,5,8,9,10,1,3,4,6,7]=>0
[2,6,7,8,10,1,3,4,5,9]=>0
[2,6,7,9,10,1,3,4,5,8]=>0
[2,6,8,9,10,1,3,4,5,7]=>0
[2,7,8,9,10,1,3,4,5,6]=>0
[3,4,6,8,10,1,2,5,7,9]=>0
[3,4,6,9,10,1,2,5,7,8]=>0
[3,4,7,8,10,1,2,5,6,9]=>0
[3,4,7,9,10,1,2,5,6,8]=>0
[3,4,8,9,10,1,2,5,6,7]=>0
[3,5,6,8,10,1,2,4,7,9]=>0
[3,5,6,9,10,1,2,4,7,8]=>0
[3,5,7,8,10,1,2,4,6,9]=>0
[3,5,7,9,10,1,2,4,6,8]=>0
[3,5,8,9,10,1,2,4,6,7]=>0
[3,6,7,8,10,1,2,4,5,9]=>0
[3,6,7,9,10,1,2,4,5,8]=>0
[3,6,8,9,10,1,2,4,5,7]=>0
[3,7,8,9,10,1,2,4,5,6]=>0
[4,5,6,8,10,1,2,3,7,9]=>0
[4,5,6,9,10,1,2,3,7,8]=>0
[4,5,7,8,10,1,2,3,6,9]=>0
[4,5,7,9,10,1,2,3,6,8]=>0
[4,5,8,9,10,1,2,3,6,7]=>0
[4,6,7,8,10,1,2,3,5,9]=>0
[4,6,7,9,10,1,2,3,5,8]=>0
[4,6,8,9,10,1,2,3,5,7]=>0
[4,7,8,9,10,1,2,3,5,6]=>0
[5,6,7,8,10,1,2,3,4,9]=>0
[5,6,7,9,10,1,2,3,4,8]=>0
[5,6,8,9,10,1,2,3,4,7]=>0
[5,7,8,9,10,1,2,3,4,6]=>0
[9,10,1,2,3,4,5,6,7,8]=>0
[8,9,10,1,2,3,4,5,6,7]=>0
[10,8,9,1,2,3,4,5,6,7]=>14
[10,9,8,1,2,3,4,5,6,7]=>15
[7,8,9,10,1,2,3,4,5,6]=>0
[10,7,8,9,1,2,3,4,5,6]=>18
[9,10,7,8,1,2,3,4,5,6]=>12
[10,9,7,8,1,2,3,4,5,6]=>20
[10,9,8,7,1,2,3,4,5,6]=>21
[10,6,7,8,9,1,2,3,4,5]=>20
[9,10,6,7,8,1,2,3,4,5]=>15
[10,9,6,7,8,1,2,3,4,5]=>23
[10,8,9,6,7,1,2,3,4,5]=>24
[10,9,8,6,7,1,2,3,4,5]=>25
[10,9,8,7,6,1,2,3,4,5]=>26
[9,10,5,6,7,8,1,2,3,4]=>16
[10,9,5,6,7,8,1,2,3,4]=>24
[8,9,10,5,6,7,1,2,3,4]=>12
[10,9,8,5,6,7,1,2,3,4]=>27
[9,10,7,8,5,6,1,2,3,4]=>20
[10,9,7,8,5,6,1,2,3,4]=>28
[10,9,8,7,5,6,1,2,3,4]=>29
[10,9,8,7,6,5,1,2,3,4]=>30
[10,7,8,9,4,5,6,1,2,3]=>27
[9,10,7,8,4,5,6,1,2,3]=>21
[10,9,7,8,4,5,6,1,2,3]=>29
[10,9,8,7,4,5,6,1,2,3]=>30
[10,8,9,6,7,4,5,1,2,3]=>30
[10,9,8,6,7,4,5,1,2,3]=>31
[10,9,8,7,6,4,5,1,2,3]=>32
[10,9,8,7,6,5,4,1,2,3]=>33
[9,10,7,8,5,6,3,4,1,2]=>24
[10,9,7,8,5,6,3,4,1,2]=>32
[10,9,8,7,5,6,3,4,1,2]=>33
[10,9,8,7,6,5,3,4,1,2]=>34
[10,9,8,7,6,5,4,3,1,2]=>35
[8,9,7,6,5,4,3,2,1,10]=>21
[1,9,10,8,7,6,5,4,3,2]=>21
[9,1,2,3,4,5,6,7,8,10]=>0
[1,10,2,3,4,5,6,7,8,9]=>0
[8,9,1,2,3,4,5,6,7,10]=>0
[1,9,10,2,3,4,5,6,7,8]=>0
[3,4,1,2,5,6,7,8,9,10]=>0
[3,2,1,4,5,6,7,8,9,10]=>1
[4,5,6,1,2,3,7,8,9,10]=>0
[4,2,5,1,3,6,7,8,9,10]=>1
[4,3,2,1,5,6,7,8,9,10]=>3
[5,6,7,8,1,2,3,4,9,10]=>0
[5,2,6,7,1,3,4,8,9,10]=>1
[5,6,3,4,1,2,7,8,9,10]=>4
[5,3,2,6,1,4,7,8,9,10]=>3
[5,4,3,2,1,6,7,8,9,10]=>6
[6,2,7,8,9,1,3,4,5,10]=>1
[6,7,3,4,8,1,2,5,9,10]=>4
[6,3,2,7,8,1,4,5,9,10]=>3
[6,4,7,2,5,1,3,8,9,10]=>6
[6,4,3,2,7,1,5,8,9,10]=>6
[6,5,4,3,2,1,7,8,9,10]=>10
[7,8,3,4,9,10,1,2,5,6]=>4
[7,8,9,4,5,6,1,2,3,10]=>9
[7,4,3,2,8,9,1,5,6,10]=>6
[7,8,5,6,3,4,1,2,9,10]=>12
[7,5,3,8,2,6,1,4,9,10]=>9
[7,5,4,3,2,8,1,6,9,10]=>10
[7,6,5,4,3,2,1,8,9,10]=>15
[8,5,9,10,2,6,7,1,3,4]=>11
[8,5,3,9,2,6,10,1,4,7]=>9
[8,6,9,4,7,2,5,1,3,10]=>15
[8,6,4,3,9,2,7,1,5,10]=>13
[8,6,5,4,3,2,9,1,7,10]=>15
[8,7,6,5,4,3,2,1,9,10]=>21
[9,7,5,4,3,10,2,8,1,6]=>18
[1,2,3,4,5,6,7,8,9,11,10]=>0
[2,1,3,4,5,6,7,8,9,10,11]=>0
[11,1,2,3,4,5,6,7,8,9,10]=>0
[10,9,8,7,6,5,4,3,2,1,11]=>36
[1,11,10,9,8,7,6,5,4,3,2]=>36
[2,3,4,5,6,7,8,9,10,11,1]=>0
[10,1,2,3,4,5,6,7,8,9,11]=>0
[1,11,2,3,4,5,6,7,8,9,10]=>0
[2,1,4,3,6,5,8,7,10,9,12,11]=>0
[2,1,4,3,6,5,8,7,12,11,10,9]=>3
[2,1,4,3,6,5,10,9,8,7,12,11]=>3
[2,1,4,3,6,5,12,9,8,11,10,7]=>6
[2,1,4,3,6,5,12,11,10,9,8,7]=>10
[2,1,4,3,8,7,6,5,10,9,12,11]=>3
[2,1,4,3,8,7,6,5,12,11,10,9]=>6
[2,1,4,3,10,7,6,9,8,5,12,11]=>6
[2,1,4,3,12,7,6,9,8,11,10,5]=>9
[2,1,4,3,12,7,6,11,10,9,8,5]=>13
[2,1,4,3,10,9,8,7,6,5,12,11]=>10
[2,1,4,3,12,9,8,7,6,11,10,5]=>13
[2,1,4,3,12,11,8,7,10,9,6,5]=>17
[2,1,4,3,12,11,10,9,8,7,6,5]=>21
[2,1,6,5,4,3,8,7,10,9,12,11]=>3
[2,1,6,5,4,3,8,7,12,11,10,9]=>6
[2,1,6,5,4,3,10,9,8,7,12,11]=>6
[2,1,6,5,4,3,12,9,8,11,10,7]=>9
[2,1,6,5,4,3,12,11,10,9,8,7]=>13
[2,1,8,5,4,7,6,3,10,9,12,11]=>6
[2,1,8,5,4,7,6,3,12,11,10,9]=>9
[2,1,10,5,4,7,6,9,8,3,12,11]=>9
[2,1,12,5,4,7,6,9,8,11,10,3]=>12
[2,1,12,5,4,7,6,11,10,9,8,3]=>16
[2,1,10,5,4,9,8,7,6,3,12,11]=>13
[2,1,12,5,4,9,8,7,6,11,10,3]=>16
[2,1,12,5,4,11,8,7,10,9,6,3]=>20
[2,1,12,5,4,11,10,9,8,7,6,3]=>24
[2,1,8,7,6,5,4,3,10,9,12,11]=>10
[2,1,8,7,6,5,4,3,12,11,10,9]=>13
[2,1,10,7,6,5,4,9,8,3,12,11]=>13
[2,1,12,7,6,5,4,9,8,11,10,3]=>16
[2,1,12,7,6,5,4,11,10,9,8,3]=>20
[2,1,10,9,6,5,8,7,4,3,12,11]=>17
[2,1,12,9,6,5,8,7,4,11,10,3]=>20
[2,1,12,11,6,5,8,7,10,9,4,3]=>24
[2,1,12,11,6,5,10,9,8,7,4,3]=>28
[2,1,10,9,8,7,6,5,4,3,12,11]=>21
[2,1,12,9,8,7,6,5,4,11,10,3]=>24
[2,1,12,11,8,7,6,5,10,9,4,3]=>28
[2,1,12,11,10,7,6,9,8,5,4,3]=>32
[2,1,12,11,10,9,8,7,6,5,4,3]=>36
[4,3,2,1,6,5,8,7,10,9,12,11]=>3
[4,3,2,1,6,5,8,7,12,11,10,9]=>6
[4,3,2,1,6,5,10,9,8,7,12,11]=>6
[4,3,2,1,6,5,12,9,8,11,10,7]=>9
[4,3,2,1,6,5,12,11,10,9,8,7]=>13
[4,3,2,1,8,7,6,5,10,9,12,11]=>6
[4,3,2,1,8,7,6,5,12,11,10,9]=>9
[4,3,2,1,10,7,6,9,8,5,12,11]=>9
[4,3,2,1,12,7,6,9,8,11,10,5]=>12
[4,3,2,1,12,7,6,11,10,9,8,5]=>16
[4,3,2,1,10,9,8,7,6,5,12,11]=>13
[4,3,2,1,12,9,8,7,6,11,10,5]=>16
[4,3,2,1,12,11,8,7,10,9,6,5]=>20
[4,3,2,1,12,11,10,9,8,7,6,5]=>24
[6,3,2,5,4,1,8,7,10,9,12,11]=>6
[6,3,2,5,4,1,8,7,12,11,10,9]=>9
[6,3,2,5,4,1,10,9,8,7,12,11]=>9
[6,3,2,5,4,1,12,9,8,11,10,7]=>12
[6,3,2,5,4,1,12,11,10,9,8,7]=>16
[8,3,2,5,4,7,6,1,10,9,12,11]=>9
[8,3,2,5,4,7,6,1,12,11,10,9]=>12
[10,3,2,5,4,7,6,9,8,1,12,11]=>12
[12,3,2,5,4,7,6,9,8,11,10,1]=>15
[12,3,2,5,4,7,6,11,10,9,8,1]=>19
[10,3,2,5,4,9,8,7,6,1,12,11]=>16
[12,3,2,5,4,9,8,7,6,11,10,1]=>19
[12,3,2,5,4,11,8,7,10,9,6,1]=>23
[12,3,2,5,4,11,10,9,8,7,6,1]=>27
[8,3,2,7,6,5,4,1,10,9,12,11]=>13
[8,3,2,7,6,5,4,1,12,11,10,9]=>16
[10,3,2,7,6,5,4,9,8,1,12,11]=>16
[12,3,2,7,6,5,4,9,8,11,10,1]=>19
[12,3,2,7,6,5,4,11,10,9,8,1]=>23
[10,3,2,9,6,5,8,7,4,1,12,11]=>20
[12,3,2,9,6,5,8,7,4,11,10,1]=>23
[12,3,2,11,6,5,8,7,10,9,4,1]=>27
[12,3,2,11,6,5,10,9,8,7,4,1]=>31
[10,3,2,9,8,7,6,5,4,1,12,11]=>24
[12,3,2,9,8,7,6,5,4,11,10,1]=>27
[12,3,2,11,8,7,6,5,10,9,4,1]=>31
[12,3,2,11,10,7,6,9,8,5,4,1]=>35
[12,3,2,11,10,9,8,7,6,5,4,1]=>39
[6,5,4,3,2,1,8,7,10,9,12,11]=>10
[6,5,4,3,2,1,8,7,12,11,10,9]=>13
[6,5,4,3,2,1,10,9,8,7,12,11]=>13
[6,5,4,3,2,1,12,9,8,11,10,7]=>16
[6,5,4,3,2,1,12,11,10,9,8,7]=>20
[8,5,4,3,2,7,6,1,10,9,12,11]=>13
[8,5,4,3,2,7,6,1,12,11,10,9]=>16
[10,5,4,3,2,7,6,9,8,1,12,11]=>16
[12,5,4,3,2,7,6,9,8,11,10,1]=>19
[12,5,4,3,2,7,6,11,10,9,8,1]=>23
[10,5,4,3,2,9,8,7,6,1,12,11]=>20
[12,5,4,3,2,9,8,7,6,11,10,1]=>23
[12,5,4,3,2,11,8,7,10,9,6,1]=>27
[12,5,4,3,2,11,10,9,8,7,6,1]=>31
[8,7,4,3,6,5,2,1,10,9,12,11]=>17
[8,7,4,3,6,5,2,1,12,11,10,9]=>20
[10,7,4,3,6,5,2,9,8,1,12,11]=>20
[12,7,4,3,6,5,2,9,8,11,10,1]=>23
[12,7,4,3,6,5,2,11,10,9,8,1]=>27
[10,9,4,3,6,5,8,7,2,1,12,11]=>24
[12,9,4,3,6,5,8,7,2,11,10,1]=>27
[12,11,4,3,6,5,8,7,10,9,2,1]=>31
[12,11,4,3,6,5,10,9,8,7,2,1]=>35
[10,9,4,3,8,7,6,5,2,1,12,11]=>28
[12,9,4,3,8,7,6,5,2,11,10,1]=>31
[12,11,4,3,8,7,6,5,10,9,2,1]=>35
[12,11,4,3,10,7,6,9,8,5,2,1]=>39
[12,11,4,3,10,9,8,7,6,5,2,1]=>43
[8,7,6,5,4,3,2,1,10,9,12,11]=>21
[8,7,6,5,4,3,2,1,12,11,10,9]=>24
[10,7,6,5,4,3,2,9,8,1,12,11]=>24
[12,7,6,5,4,3,2,9,8,11,10,1]=>27
[12,7,6,5,4,3,2,11,10,9,8,1]=>31
[10,9,6,5,4,3,8,7,2,1,12,11]=>28
[12,9,6,5,4,3,8,7,2,11,10,1]=>31
[12,11,6,5,4,3,8,7,10,9,2,1]=>35
[12,11,6,5,4,3,10,9,8,7,2,1]=>39
[10,9,8,5,4,7,6,3,2,1,12,11]=>32
[12,9,8,5,4,7,6,3,2,11,10,1]=>35
[12,11,8,5,4,7,6,3,10,9,2,1]=>39
[12,11,10,5,4,7,6,9,8,3,2,1]=>43
[12,11,10,5,4,9,8,7,6,3,2,1]=>47
[10,9,8,7,6,5,4,3,2,1,12,11]=>36
[12,9,8,7,6,5,4,3,2,11,10,1]=>39
[12,11,8,7,6,5,4,3,10,9,2,1]=>43
[12,11,10,7,6,5,4,9,8,3,2,1]=>47
[12,11,10,9,6,5,8,7,4,3,2,1]=>51
[12,11,10,9,8,7,6,5,4,3,2,1]=>55
[2,4,6,8,10,12,1,3,5,7,9,11]=>0
[2,4,6,8,11,12,1,3,5,7,9,10]=>0
[2,4,6,9,10,12,1,3,5,7,8,11]=>0
[2,4,6,9,11,12,1,3,5,7,8,10]=>0
[2,4,6,10,11,12,1,3,5,7,8,9]=>0
[2,4,7,8,10,12,1,3,5,6,9,11]=>0
[2,4,7,8,11,12,1,3,5,6,9,10]=>0
[2,4,7,9,10,12,1,3,5,6,8,11]=>0
[2,4,7,9,11,12,1,3,5,6,8,10]=>0
[2,4,7,10,11,12,1,3,5,6,8,9]=>0
[2,4,8,9,10,12,1,3,5,6,7,11]=>0
[2,4,8,9,11,12,1,3,5,6,7,10]=>0
[2,4,8,10,11,12,1,3,5,6,7,9]=>0
[2,4,9,10,11,12,1,3,5,6,7,8]=>0
[2,5,6,8,10,12,1,3,4,7,9,11]=>0
[2,5,6,8,11,12,1,3,4,7,9,10]=>0
[2,5,6,9,10,12,1,3,4,7,8,11]=>0
[2,5,6,9,11,12,1,3,4,7,8,10]=>0
[2,5,6,10,11,12,1,3,4,7,8,9]=>0
[2,5,7,8,10,12,1,3,4,6,9,11]=>0
[2,5,7,8,11,12,1,3,4,6,9,10]=>0
[2,5,7,9,10,12,1,3,4,6,8,11]=>0
[2,5,7,9,11,12,1,3,4,6,8,10]=>0
[2,5,7,10,11,12,1,3,4,6,8,9]=>0
[2,5,8,9,10,12,1,3,4,6,7,11]=>0
[2,5,8,9,11,12,1,3,4,6,7,10]=>0
[2,5,8,10,11,12,1,3,4,6,7,9]=>0
[2,5,9,10,11,12,1,3,4,6,7,8]=>0
[2,6,7,8,10,12,1,3,4,5,9,11]=>0
[2,6,7,8,11,12,1,3,4,5,9,10]=>0
[2,6,7,9,10,12,1,3,4,5,8,11]=>0
[2,6,7,9,11,12,1,3,4,5,8,10]=>0
[2,6,7,10,11,12,1,3,4,5,8,9]=>0
[2,6,8,9,10,12,1,3,4,5,7,11]=>0
[2,6,8,9,11,12,1,3,4,5,7,10]=>0
[2,6,8,10,11,12,1,3,4,5,7,9]=>0
[2,6,9,10,11,12,1,3,4,5,7,8]=>0
[2,7,8,9,10,12,1,3,4,5,6,11]=>0
[2,7,8,9,11,12,1,3,4,5,6,10]=>0
[2,7,8,10,11,12,1,3,4,5,6,9]=>0
[2,7,9,10,11,12,1,3,4,5,6,8]=>0
[2,8,9,10,11,12,1,3,4,5,6,7]=>0
[3,4,6,8,10,12,1,2,5,7,9,11]=>0
[3,4,6,8,11,12,1,2,5,7,9,10]=>0
[3,4,6,9,10,12,1,2,5,7,8,11]=>0
[3,4,6,9,11,12,1,2,5,7,8,10]=>0
[3,4,6,10,11,12,1,2,5,7,8,9]=>0
[3,4,7,8,10,12,1,2,5,6,9,11]=>0
[3,4,7,8,11,12,1,2,5,6,9,10]=>0
[3,4,7,9,10,12,1,2,5,6,8,11]=>0
[3,4,7,9,11,12,1,2,5,6,8,10]=>0
[3,4,7,10,11,12,1,2,5,6,8,9]=>0
[3,4,8,9,10,12,1,2,5,6,7,11]=>0
[3,4,8,9,11,12,1,2,5,6,7,10]=>0
[3,4,8,10,11,12,1,2,5,6,7,9]=>0
[3,4,9,10,11,12,1,2,5,6,7,8]=>0
[3,5,6,8,10,12,1,2,4,7,9,11]=>0
[3,5,6,8,11,12,1,2,4,7,9,10]=>0
[3,5,6,9,10,12,1,2,4,7,8,11]=>0
[3,5,6,9,11,12,1,2,4,7,8,10]=>0
[3,5,6,10,11,12,1,2,4,7,8,9]=>0
[3,5,7,8,10,12,1,2,4,6,9,11]=>0
[3,5,7,8,11,12,1,2,4,6,9,10]=>0
[3,5,7,9,10,12,1,2,4,6,8,11]=>0
[3,5,7,9,11,12,1,2,4,6,8,10]=>0
[3,5,7,10,11,12,1,2,4,6,8,9]=>0
[3,5,8,9,10,12,1,2,4,6,7,11]=>0
[3,5,8,9,11,12,1,2,4,6,7,10]=>0
[3,5,8,10,11,12,1,2,4,6,7,9]=>0
[3,5,9,10,11,12,1,2,4,6,7,8]=>0
[3,6,7,8,10,12,1,2,4,5,9,11]=>0
[3,6,7,8,11,12,1,2,4,5,9,10]=>0
[3,6,7,9,10,12,1,2,4,5,8,11]=>0
[3,6,7,9,11,12,1,2,4,5,8,10]=>0
[3,6,7,10,11,12,1,2,4,5,8,9]=>0
[3,6,8,9,10,12,1,2,4,5,7,11]=>0
[3,6,8,9,11,12,1,2,4,5,7,10]=>0
[3,6,8,10,11,12,1,2,4,5,7,9]=>0
[3,6,9,10,11,12,1,2,4,5,7,8]=>0
[3,7,8,9,10,12,1,2,4,5,6,11]=>0
[3,7,8,9,11,12,1,2,4,5,6,10]=>0
[3,7,8,10,11,12,1,2,4,5,6,9]=>0
[3,7,9,10,11,12,1,2,4,5,6,8]=>0
[3,8,9,10,11,12,1,2,4,5,6,7]=>0
[4,5,6,8,10,12,1,2,3,7,9,11]=>0
[4,5,6,8,11,12,1,2,3,7,9,10]=>0
[4,5,6,9,10,12,1,2,3,7,8,11]=>0
[4,5,6,9,11,12,1,2,3,7,8,10]=>0
[4,5,6,10,11,12,1,2,3,7,8,9]=>0
[4,5,7,8,10,12,1,2,3,6,9,11]=>0
[4,5,7,8,11,12,1,2,3,6,9,10]=>0
[4,5,7,9,10,12,1,2,3,6,8,11]=>0
[4,5,7,9,11,12,1,2,3,6,8,10]=>0
[4,5,7,10,11,12,1,2,3,6,8,9]=>0
[4,5,8,9,10,12,1,2,3,6,7,11]=>0
[4,5,8,9,11,12,1,2,3,6,7,10]=>0
[4,5,8,10,11,12,1,2,3,6,7,9]=>0
[4,5,9,10,11,12,1,2,3,6,7,8]=>0
[4,6,7,8,10,12,1,2,3,5,9,11]=>0
[4,6,7,8,11,12,1,2,3,5,9,10]=>0
[4,6,7,9,10,12,1,2,3,5,8,11]=>0
[4,6,7,9,11,12,1,2,3,5,8,10]=>0
[4,6,7,10,11,12,1,2,3,5,8,9]=>0
[4,6,8,9,10,12,1,2,3,5,7,11]=>0
[4,6,8,9,11,12,1,2,3,5,7,10]=>0
[4,6,8,10,11,12,1,2,3,5,7,9]=>0
[4,6,9,10,11,12,1,2,3,5,7,8]=>0
[4,7,8,9,10,12,1,2,3,5,6,11]=>0
[4,7,8,9,11,12,1,2,3,5,6,10]=>0
[4,7,8,10,11,12,1,2,3,5,6,9]=>0
[4,7,9,10,11,12,1,2,3,5,6,8]=>0
[4,8,9,10,11,12,1,2,3,5,6,7]=>0
[5,6,7,8,10,12,1,2,3,4,9,11]=>0
[5,6,7,8,11,12,1,2,3,4,9,10]=>0
[5,6,7,9,10,12,1,2,3,4,8,11]=>0
[5,6,7,9,11,12,1,2,3,4,8,10]=>0
[5,6,7,10,11,12,1,2,3,4,8,9]=>0
[5,6,8,9,10,12,1,2,3,4,7,11]=>0
[5,6,8,9,11,12,1,2,3,4,7,10]=>0
[5,6,8,10,11,12,1,2,3,4,7,9]=>0
[5,6,9,10,11,12,1,2,3,4,7,8]=>0
[5,7,8,9,10,12,1,2,3,4,6,11]=>0
[5,7,8,9,11,12,1,2,3,4,6,10]=>0
[5,7,8,10,11,12,1,2,3,4,6,9]=>0
[5,7,9,10,11,12,1,2,3,4,6,8]=>0
[5,8,9,10,11,12,1,2,3,4,6,7]=>0
[6,7,8,9,10,12,1,2,3,4,5,11]=>0
[6,7,8,9,11,12,1,2,3,4,5,10]=>0
[6,7,8,10,11,12,1,2,3,4,5,9]=>0
[6,7,9,10,11,12,1,2,3,4,5,8]=>0
[6,8,9,10,11,12,1,2,3,4,5,7]=>0
[7,8,9,10,11,12,1,2,3,4,5,6]=>0
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Description
The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map.
The Simion-Schmidt map takes a permutation and turns each occcurrence of [3,2,1] into an occurrence of [3,1,2], thus reducing the number of inversions of the permutation. This statistic records the difference in length of the permutation and its image.
Apparently, this statistic can be described as the number of occurrences of the mesh pattern ([3,2,1], {(0,3),(0,2)}). Equivalent mesh patterns are ([3,2,1], {(0,2),(1,2)}), ([3,2,1], {(0,3),(1,3)}) and ([3,2,1], {(1,2),(1,3)}).
The Simion-Schmidt map takes a permutation and turns each occcurrence of [3,2,1] into an occurrence of [3,1,2], thus reducing the number of inversions of the permutation. This statistic records the difference in length of the permutation and its image.
Apparently, this statistic can be described as the number of occurrences of the mesh pattern ([3,2,1], {(0,3),(0,2)}). Equivalent mesh patterns are ([3,2,1], {(0,2),(1,2)}), ([3,2,1], {(0,3),(1,3)}) and ([3,2,1], {(1,2),(1,3)}).
References
[1] Bóna, Miklós Combinatorics of permutations MathSciNet:2919720
Code
def statistic(pi):
return pi.length()-pi.simion_schmidt(avoid=[3,2,1]).length()
Created
Jun 18, 2013 at 18:16 by Tom Denton
Updated
Dec 26, 2017 at 13:28 by Martin Rubey
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