Identifier
- St000220: Permutations ⟶ ℤ
Values
=>
[]=>0
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>0
[1,2,3,4]=>0
[1,2,4,3]=>2
[1,3,2,4]=>1
[1,3,4,2]=>2
[1,4,2,3]=>2
[1,4,3,2]=>3
[2,1,3,4]=>0
[2,1,4,3]=>2
[2,3,1,4]=>0
[2,3,4,1]=>0
[2,4,1,3]=>1
[2,4,3,1]=>1
[3,1,2,4]=>0
[3,1,4,2]=>1
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>0
[3,4,2,1]=>0
[4,1,2,3]=>0
[4,1,3,2]=>1
[4,2,1,3]=>0
[4,2,3,1]=>0
[4,3,1,2]=>0
[4,3,2,1]=>0
[1,2,3,4,5]=>0
[1,2,3,5,4]=>3
[1,2,4,3,5]=>2
[1,2,4,5,3]=>4
[1,2,5,3,4]=>4
[1,2,5,4,3]=>6
[1,3,2,4,5]=>1
[1,3,2,5,4]=>4
[1,3,4,2,5]=>2
[1,3,4,5,2]=>3
[1,3,5,2,4]=>4
[1,3,5,4,2]=>5
[1,4,2,3,5]=>2
[1,4,2,5,3]=>4
[1,4,3,2,5]=>3
[1,4,3,5,2]=>4
[1,4,5,2,3]=>4
[1,4,5,3,2]=>5
[1,5,2,3,4]=>3
[1,5,2,4,3]=>5
[1,5,3,2,4]=>4
[1,5,3,4,2]=>5
[1,5,4,2,3]=>5
[1,5,4,3,2]=>6
[2,1,3,4,5]=>0
[2,1,3,5,4]=>3
[2,1,4,3,5]=>2
[2,1,4,5,3]=>4
[2,1,5,3,4]=>4
[2,1,5,4,3]=>6
[2,3,1,4,5]=>0
[2,3,1,5,4]=>3
[2,3,4,1,5]=>0
[2,3,4,5,1]=>0
[2,3,5,1,4]=>2
[2,3,5,4,1]=>2
[2,4,1,3,5]=>1
[2,4,1,5,3]=>3
[2,4,3,1,5]=>1
[2,4,3,5,1]=>1
[2,4,5,1,3]=>2
[2,4,5,3,1]=>2
[2,5,1,3,4]=>2
[2,5,1,4,3]=>4
[2,5,3,1,4]=>2
[2,5,3,4,1]=>2
[2,5,4,1,3]=>3
[2,5,4,3,1]=>3
[3,1,2,4,5]=>0
[3,1,2,5,4]=>3
[3,1,4,2,5]=>1
[3,1,4,5,2]=>2
[3,1,5,2,4]=>3
[3,1,5,4,2]=>4
[3,2,1,4,5]=>0
[3,2,1,5,4]=>3
[3,2,4,1,5]=>0
[3,2,4,5,1]=>0
[3,2,5,1,4]=>2
[3,2,5,4,1]=>2
[3,4,1,2,5]=>0
[3,4,1,5,2]=>1
[3,4,2,1,5]=>0
[3,4,2,5,1]=>0
[3,4,5,1,2]=>0
[3,4,5,2,1]=>0
[3,5,1,2,4]=>1
[3,5,1,4,2]=>2
[3,5,2,1,4]=>1
[3,5,2,4,1]=>1
[3,5,4,1,2]=>1
[3,5,4,2,1]=>1
[4,1,2,3,5]=>0
[4,1,2,5,3]=>2
[4,1,3,2,5]=>1
[4,1,3,5,2]=>2
[4,1,5,2,3]=>2
[4,1,5,3,2]=>3
[4,2,1,3,5]=>0
[4,2,1,5,3]=>2
[4,2,3,1,5]=>0
[4,2,3,5,1]=>0
[4,2,5,1,3]=>1
[4,2,5,3,1]=>1
[4,3,1,2,5]=>0
[4,3,1,5,2]=>1
[4,3,2,1,5]=>0
[4,3,2,5,1]=>0
[4,3,5,1,2]=>0
[4,3,5,2,1]=>0
[4,5,1,2,3]=>0
[4,5,1,3,2]=>1
[4,5,2,1,3]=>0
[4,5,2,3,1]=>0
[4,5,3,1,2]=>0
[4,5,3,2,1]=>0
[5,1,2,3,4]=>0
[5,1,2,4,3]=>2
[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]=>0
[5,2,1,4,3]=>2
[5,2,3,1,4]=>0
[5,2,3,4,1]=>0
[5,2,4,1,3]=>1
[5,2,4,3,1]=>1
[5,3,1,2,4]=>0
[5,3,1,4,2]=>1
[5,3,2,1,4]=>0
[5,3,2,4,1]=>0
[5,3,4,1,2]=>0
[5,3,4,2,1]=>0
[5,4,1,2,3]=>0
[5,4,1,3,2]=>1
[5,4,2,1,3]=>0
[5,4,2,3,1]=>0
[5,4,3,1,2]=>0
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>4
[1,2,3,5,4,6]=>3
[1,2,3,5,6,4]=>6
[1,2,3,6,4,5]=>6
[1,2,3,6,5,4]=>9
[1,2,4,3,5,6]=>2
[1,2,4,3,6,5]=>6
[1,2,4,5,3,6]=>4
[1,2,4,5,6,3]=>6
[1,2,4,6,3,5]=>7
[1,2,4,6,5,3]=>9
[1,2,5,3,4,6]=>4
[1,2,5,3,6,4]=>7
[1,2,5,4,3,6]=>6
[1,2,5,4,6,3]=>8
[1,2,5,6,3,4]=>8
[1,2,5,6,4,3]=>10
[1,2,6,3,4,5]=>6
[1,2,6,3,5,4]=>9
[1,2,6,4,3,5]=>8
[1,2,6,4,5,3]=>10
[1,2,6,5,3,4]=>10
[1,2,6,5,4,3]=>12
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>5
[1,3,2,5,4,6]=>4
[1,3,2,5,6,4]=>7
[1,3,2,6,4,5]=>7
[1,3,2,6,5,4]=>10
[1,3,4,2,5,6]=>2
[1,3,4,2,6,5]=>6
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>4
[1,3,4,6,2,5]=>6
[1,3,4,6,5,2]=>7
[1,3,5,2,4,6]=>4
[1,3,5,2,6,4]=>7
[1,3,5,4,2,6]=>5
[1,3,5,4,6,2]=>6
[1,3,5,6,2,4]=>7
[1,3,5,6,4,2]=>8
[1,3,6,2,4,5]=>6
[1,3,6,2,5,4]=>9
[1,3,6,4,2,5]=>7
[1,3,6,4,5,2]=>8
[1,3,6,5,2,4]=>9
[1,3,6,5,4,2]=>10
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>6
[1,4,2,5,3,6]=>4
[1,4,2,5,6,3]=>6
[1,4,2,6,3,5]=>7
[1,4,2,6,5,3]=>9
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>7
[1,4,3,5,2,6]=>4
[1,4,3,5,6,2]=>5
[1,4,3,6,2,5]=>7
[1,4,3,6,5,2]=>8
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>6
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>6
[1,4,5,6,2,3]=>6
[1,4,5,6,3,2]=>7
[1,4,6,2,3,5]=>6
[1,4,6,2,5,3]=>8
[1,4,6,3,2,5]=>7
[1,4,6,3,5,2]=>8
[1,4,6,5,2,3]=>8
[1,4,6,5,3,2]=>9
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>6
[1,5,2,4,3,6]=>5
[1,5,2,4,6,3]=>7
[1,5,2,6,3,4]=>7
[1,5,2,6,4,3]=>9
[1,5,3,2,4,6]=>4
[1,5,3,2,6,4]=>7
[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>6
[1,5,3,6,2,4]=>7
[1,5,3,6,4,2]=>8
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>7
[1,5,4,3,2,6]=>6
[1,5,4,3,6,2]=>7
[1,5,4,6,2,3]=>7
[1,5,4,6,3,2]=>8
[1,5,6,2,3,4]=>6
[1,5,6,2,4,3]=>8
[1,5,6,3,2,4]=>7
[1,5,6,3,4,2]=>8
[1,5,6,4,2,3]=>8
[1,5,6,4,3,2]=>9
[1,6,2,3,4,5]=>4
[1,6,2,3,5,4]=>7
[1,6,2,4,3,5]=>6
[1,6,2,4,5,3]=>8
[1,6,2,5,3,4]=>8
[1,6,2,5,4,3]=>10
[1,6,3,2,4,5]=>5
[1,6,3,2,5,4]=>8
[1,6,3,4,2,5]=>6
[1,6,3,4,5,2]=>7
[1,6,3,5,2,4]=>8
[1,6,3,5,4,2]=>9
[1,6,4,2,3,5]=>6
[1,6,4,2,5,3]=>8
[1,6,4,3,2,5]=>7
[1,6,4,3,5,2]=>8
[1,6,4,5,2,3]=>8
[1,6,4,5,3,2]=>9
[1,6,5,2,3,4]=>7
[1,6,5,2,4,3]=>9
[1,6,5,3,2,4]=>8
[1,6,5,3,4,2]=>9
[1,6,5,4,2,3]=>9
[1,6,5,4,3,2]=>10
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>3
[2,1,3,5,6,4]=>6
[2,1,3,6,4,5]=>6
[2,1,3,6,5,4]=>9
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>6
[2,1,4,5,3,6]=>4
[2,1,4,5,6,3]=>6
[2,1,4,6,3,5]=>7
[2,1,4,6,5,3]=>9
[2,1,5,3,4,6]=>4
[2,1,5,3,6,4]=>7
[2,1,5,4,3,6]=>6
[2,1,5,4,6,3]=>8
[2,1,5,6,3,4]=>8
[2,1,5,6,4,3]=>10
[2,1,6,3,4,5]=>6
[2,1,6,3,5,4]=>9
[2,1,6,4,3,5]=>8
[2,1,6,4,5,3]=>10
[2,1,6,5,3,4]=>10
[2,1,6,5,4,3]=>12
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>4
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>6
[2,3,1,6,4,5]=>6
[2,3,1,6,5,4]=>9
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>3
[2,3,4,6,5,1]=>3
[2,3,5,1,4,6]=>2
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>4
[2,3,6,1,4,5]=>4
[2,3,6,1,5,4]=>7
[2,3,6,4,1,5]=>4
[2,3,6,4,5,1]=>4
[2,3,6,5,1,4]=>6
[2,3,6,5,4,1]=>6
[2,4,1,3,5,6]=>1
[2,4,1,3,6,5]=>5
[2,4,1,5,3,6]=>3
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>6
[2,4,1,6,5,3]=>8
[2,4,3,1,5,6]=>1
[2,4,3,1,6,5]=>5
[2,4,3,5,1,6]=>1
[2,4,3,5,6,1]=>1
[2,4,3,6,1,5]=>4
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>2
[2,4,5,1,6,3]=>4
[2,4,5,3,1,6]=>2
[2,4,5,3,6,1]=>2
[2,4,5,6,1,3]=>3
[2,4,5,6,3,1]=>3
[2,4,6,1,3,5]=>4
[2,4,6,1,5,3]=>6
[2,4,6,3,1,5]=>4
[2,4,6,3,5,1]=>4
[2,4,6,5,1,3]=>5
[2,4,6,5,3,1]=>5
[2,5,1,3,4,6]=>2
[2,5,1,3,6,4]=>5
[2,5,1,4,3,6]=>4
[2,5,1,4,6,3]=>6
[2,5,1,6,3,4]=>6
[2,5,1,6,4,3]=>8
[2,5,3,1,4,6]=>2
[2,5,3,1,6,4]=>5
[2,5,3,4,1,6]=>2
[2,5,3,4,6,1]=>2
[2,5,3,6,1,4]=>4
[2,5,3,6,4,1]=>4
[2,5,4,1,3,6]=>3
[2,5,4,1,6,3]=>5
[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>3
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>4
[2,5,6,1,3,4]=>4
[2,5,6,1,4,3]=>6
[2,5,6,3,1,4]=>4
[2,5,6,3,4,1]=>4
[2,5,6,4,1,3]=>5
[2,5,6,4,3,1]=>5
[2,6,1,3,4,5]=>3
[2,6,1,3,5,4]=>6
[2,6,1,4,3,5]=>5
[2,6,1,4,5,3]=>7
[2,6,1,5,3,4]=>7
[2,6,1,5,4,3]=>9
[2,6,3,1,4,5]=>3
[2,6,3,1,5,4]=>6
[2,6,3,4,1,5]=>3
[2,6,3,4,5,1]=>3
[2,6,3,5,1,4]=>5
[2,6,3,5,4,1]=>5
[2,6,4,1,3,5]=>4
[2,6,4,1,5,3]=>6
[2,6,4,3,1,5]=>4
[2,6,4,3,5,1]=>4
[2,6,4,5,1,3]=>5
[2,6,4,5,3,1]=>5
[2,6,5,1,3,4]=>5
[2,6,5,1,4,3]=>7
[2,6,5,3,1,4]=>5
[2,6,5,3,4,1]=>5
[2,6,5,4,1,3]=>6
[2,6,5,4,3,1]=>6
[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>4
[3,1,2,5,4,6]=>3
[3,1,2,5,6,4]=>6
[3,1,2,6,4,5]=>6
[3,1,2,6,5,4]=>9
[3,1,4,2,5,6]=>1
[3,1,4,2,6,5]=>5
[3,1,4,5,2,6]=>2
[3,1,4,5,6,2]=>3
[3,1,4,6,2,5]=>5
[3,1,4,6,5,2]=>6
[3,1,5,2,4,6]=>3
[3,1,5,2,6,4]=>6
[3,1,5,4,2,6]=>4
[3,1,5,4,6,2]=>5
[3,1,5,6,2,4]=>6
[3,1,5,6,4,2]=>7
[3,1,6,2,4,5]=>5
[3,1,6,2,5,4]=>8
[3,1,6,4,2,5]=>6
[3,1,6,4,5,2]=>7
[3,1,6,5,2,4]=>8
[3,1,6,5,4,2]=>9
[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>4
[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>6
[3,2,1,6,4,5]=>6
[3,2,1,6,5,4]=>9
[3,2,4,1,5,6]=>0
[3,2,4,1,6,5]=>4
[3,2,4,5,1,6]=>0
[3,2,4,5,6,1]=>0
[3,2,4,6,1,5]=>3
[3,2,4,6,5,1]=>3
[3,2,5,1,4,6]=>2
[3,2,5,1,6,4]=>5
[3,2,5,4,1,6]=>2
[3,2,5,4,6,1]=>2
[3,2,5,6,1,4]=>4
[3,2,5,6,4,1]=>4
[3,2,6,1,4,5]=>4
[3,2,6,1,5,4]=>7
[3,2,6,4,1,5]=>4
[3,2,6,4,5,1]=>4
[3,2,6,5,1,4]=>6
[3,2,6,5,4,1]=>6
[3,4,1,2,5,6]=>0
[3,4,1,2,6,5]=>4
[3,4,1,5,2,6]=>1
[3,4,1,5,6,2]=>2
[3,4,1,6,2,5]=>4
[3,4,1,6,5,2]=>5
[3,4,2,1,5,6]=>0
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>0
[3,4,2,5,6,1]=>0
[3,4,2,6,1,5]=>3
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>0
[3,4,5,1,6,2]=>1
[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>0
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>0
[3,4,6,1,2,5]=>2
[3,4,6,1,5,2]=>3
[3,4,6,2,1,5]=>2
[3,4,6,2,5,1]=>2
[3,4,6,5,1,2]=>2
[3,4,6,5,2,1]=>2
[3,5,1,2,4,6]=>1
[3,5,1,2,6,4]=>4
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>3
[3,5,1,6,2,4]=>4
[3,5,1,6,4,2]=>5
[3,5,2,1,4,6]=>1
[3,5,2,1,6,4]=>4
[3,5,2,4,1,6]=>1
[3,5,2,4,6,1]=>1
[3,5,2,6,1,4]=>3
[3,5,2,6,4,1]=>3
[3,5,4,1,2,6]=>1
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>1
[3,5,4,6,1,2]=>1
[3,5,4,6,2,1]=>1
[3,5,6,1,2,4]=>2
[3,5,6,1,4,2]=>3
[3,5,6,2,1,4]=>2
[3,5,6,2,4,1]=>2
[3,5,6,4,1,2]=>2
[3,5,6,4,2,1]=>2
[3,6,1,2,4,5]=>2
[3,6,1,2,5,4]=>5
[3,6,1,4,2,5]=>3
[3,6,1,4,5,2]=>4
[3,6,1,5,2,4]=>5
[3,6,1,5,4,2]=>6
[3,6,2,1,4,5]=>2
[3,6,2,1,5,4]=>5
[3,6,2,4,1,5]=>2
[3,6,2,4,5,1]=>2
[3,6,2,5,1,4]=>4
[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]=>2
[3,6,4,2,5,1]=>2
[3,6,4,5,1,2]=>2
[3,6,4,5,2,1]=>2
[3,6,5,1,2,4]=>3
[3,6,5,1,4,2]=>4
[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>3
[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>3
[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>2
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>5
[4,1,2,6,5,3]=>7
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>5
[4,1,3,5,2,6]=>2
[4,1,3,5,6,2]=>3
[4,1,3,6,2,5]=>5
[4,1,3,6,5,2]=>6
[4,1,5,2,3,6]=>2
[4,1,5,2,6,3]=>4
[4,1,5,3,2,6]=>3
[4,1,5,3,6,2]=>4
[4,1,5,6,2,3]=>4
[4,1,5,6,3,2]=>5
[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>6
[4,1,6,3,2,5]=>5
[4,1,6,3,5,2]=>6
[4,1,6,5,2,3]=>6
[4,1,6,5,3,2]=>7
[4,2,1,3,5,6]=>0
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>2
[4,2,1,5,6,3]=>4
[4,2,1,6,3,5]=>5
[4,2,1,6,5,3]=>7
[4,2,3,1,5,6]=>0
[4,2,3,1,6,5]=>4
[4,2,3,5,1,6]=>0
[4,2,3,5,6,1]=>0
[4,2,3,6,1,5]=>3
[4,2,3,6,5,1]=>3
[4,2,5,1,3,6]=>1
[4,2,5,1,6,3]=>3
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>2
[4,2,5,6,3,1]=>2
[4,2,6,1,3,5]=>3
[4,2,6,1,5,3]=>5
[4,2,6,3,1,5]=>3
[4,2,6,3,5,1]=>3
[4,2,6,5,1,3]=>4
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>0
[4,3,1,2,6,5]=>4
[4,3,1,5,2,6]=>1
[4,3,1,5,6,2]=>2
[4,3,1,6,2,5]=>4
[4,3,1,6,5,2]=>5
[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>0
[4,3,2,5,6,1]=>0
[4,3,2,6,1,5]=>3
[4,3,2,6,5,1]=>3
[4,3,5,1,2,6]=>0
[4,3,5,1,6,2]=>1
[4,3,5,2,1,6]=>0
[4,3,5,2,6,1]=>0
[4,3,5,6,1,2]=>0
[4,3,5,6,2,1]=>0
[4,3,6,1,2,5]=>2
[4,3,6,1,5,2]=>3
[4,3,6,2,1,5]=>2
[4,3,6,2,5,1]=>2
[4,3,6,5,1,2]=>2
[4,3,6,5,2,1]=>2
[4,5,1,2,3,6]=>0
[4,5,1,2,6,3]=>2
[4,5,1,3,2,6]=>1
[4,5,1,3,6,2]=>2
[4,5,1,6,2,3]=>2
[4,5,1,6,3,2]=>3
[4,5,2,1,3,6]=>0
[4,5,2,1,6,3]=>2
[4,5,2,3,1,6]=>0
[4,5,2,3,6,1]=>0
[4,5,2,6,1,3]=>1
[4,5,2,6,3,1]=>1
[4,5,3,1,2,6]=>0
[4,5,3,1,6,2]=>1
[4,5,3,2,1,6]=>0
[4,5,3,2,6,1]=>0
[4,5,3,6,1,2]=>0
[4,5,3,6,2,1]=>0
[4,5,6,1,2,3]=>0
[4,5,6,1,3,2]=>1
[4,5,6,2,1,3]=>0
[4,5,6,2,3,1]=>0
[4,5,6,3,1,2]=>0
[4,5,6,3,2,1]=>0
[4,6,1,2,3,5]=>1
[4,6,1,2,5,3]=>3
[4,6,1,3,2,5]=>2
[4,6,1,3,5,2]=>3
[4,6,1,5,2,3]=>3
[4,6,1,5,3,2]=>4
[4,6,2,1,3,5]=>1
[4,6,2,1,5,3]=>3
[4,6,2,3,1,5]=>1
[4,6,2,3,5,1]=>1
[4,6,2,5,1,3]=>2
[4,6,2,5,3,1]=>2
[4,6,3,1,2,5]=>1
[4,6,3,1,5,2]=>2
[4,6,3,2,1,5]=>1
[4,6,3,2,5,1]=>1
[4,6,3,5,1,2]=>1
[4,6,3,5,2,1]=>1
[4,6,5,1,2,3]=>1
[4,6,5,1,3,2]=>2
[4,6,5,2,1,3]=>1
[4,6,5,2,3,1]=>1
[4,6,5,3,1,2]=>1
[4,6,5,3,2,1]=>1
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>3
[5,1,2,4,3,6]=>2
[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>6
[5,1,3,2,4,6]=>1
[5,1,3,2,6,4]=>4
[5,1,3,4,2,6]=>2
[5,1,3,4,6,2]=>3
[5,1,3,6,2,4]=>4
[5,1,3,6,4,2]=>5
[5,1,4,2,3,6]=>2
[5,1,4,2,6,3]=>4
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>4
[5,1,4,6,2,3]=>4
[5,1,4,6,3,2]=>5
[5,1,6,2,3,4]=>3
[5,1,6,2,4,3]=>5
[5,1,6,3,2,4]=>4
[5,1,6,3,4,2]=>5
[5,1,6,4,2,3]=>5
[5,1,6,4,3,2]=>6
[5,2,1,3,4,6]=>0
[5,2,1,3,6,4]=>3
[5,2,1,4,3,6]=>2
[5,2,1,4,6,3]=>4
[5,2,1,6,3,4]=>4
[5,2,1,6,4,3]=>6
[5,2,3,1,4,6]=>0
[5,2,3,1,6,4]=>3
[5,2,3,4,1,6]=>0
[5,2,3,4,6,1]=>0
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>2
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>3
[5,2,4,3,1,6]=>1
[5,2,4,3,6,1]=>1
[5,2,4,6,1,3]=>2
[5,2,4,6,3,1]=>2
[5,2,6,1,3,4]=>2
[5,2,6,1,4,3]=>4
[5,2,6,3,1,4]=>2
[5,2,6,3,4,1]=>2
[5,2,6,4,1,3]=>3
[5,2,6,4,3,1]=>3
[5,3,1,2,4,6]=>0
[5,3,1,2,6,4]=>3
[5,3,1,4,2,6]=>1
[5,3,1,4,6,2]=>2
[5,3,1,6,2,4]=>3
[5,3,1,6,4,2]=>4
[5,3,2,1,4,6]=>0
[5,3,2,1,6,4]=>3
[5,3,2,4,1,6]=>0
[5,3,2,4,6,1]=>0
[5,3,2,6,1,4]=>2
[5,3,2,6,4,1]=>2
[5,3,4,1,2,6]=>0
[5,3,4,1,6,2]=>1
[5,3,4,2,1,6]=>0
[5,3,4,2,6,1]=>0
[5,3,4,6,1,2]=>0
[5,3,4,6,2,1]=>0
[5,3,6,1,2,4]=>1
[5,3,6,1,4,2]=>2
[5,3,6,2,1,4]=>1
[5,3,6,2,4,1]=>1
[5,3,6,4,1,2]=>1
[5,3,6,4,2,1]=>1
[5,4,1,2,3,6]=>0
[5,4,1,2,6,3]=>2
[5,4,1,3,2,6]=>1
[5,4,1,3,6,2]=>2
[5,4,1,6,2,3]=>2
[5,4,1,6,3,2]=>3
[5,4,2,1,3,6]=>0
[5,4,2,1,6,3]=>2
[5,4,2,3,1,6]=>0
[5,4,2,3,6,1]=>0
[5,4,2,6,1,3]=>1
[5,4,2,6,3,1]=>1
[5,4,3,1,2,6]=>0
[5,4,3,1,6,2]=>1
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>0
[5,4,3,6,1,2]=>0
[5,4,3,6,2,1]=>0
[5,4,6,1,2,3]=>0
[5,4,6,1,3,2]=>1
[5,4,6,2,1,3]=>0
[5,4,6,2,3,1]=>0
[5,4,6,3,1,2]=>0
[5,4,6,3,2,1]=>0
[5,6,1,2,3,4]=>0
[5,6,1,2,4,3]=>2
[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]=>0
[5,6,2,1,4,3]=>2
[5,6,2,3,1,4]=>0
[5,6,2,3,4,1]=>0
[5,6,2,4,1,3]=>1
[5,6,2,4,3,1]=>1
[5,6,3,1,2,4]=>0
[5,6,3,1,4,2]=>1
[5,6,3,2,1,4]=>0
[5,6,3,2,4,1]=>0
[5,6,3,4,1,2]=>0
[5,6,3,4,2,1]=>0
[5,6,4,1,2,3]=>0
[5,6,4,1,3,2]=>1
[5,6,4,2,1,3]=>0
[5,6,4,2,3,1]=>0
[5,6,4,3,1,2]=>0
[5,6,4,3,2,1]=>0
[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>3
[6,1,2,4,3,5]=>2
[6,1,2,4,5,3]=>4
[6,1,2,5,3,4]=>4
[6,1,2,5,4,3]=>6
[6,1,3,2,4,5]=>1
[6,1,3,2,5,4]=>4
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>4
[6,1,3,5,4,2]=>5
[6,1,4,2,3,5]=>2
[6,1,4,2,5,3]=>4
[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]=>5
[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]=>0
[6,2,1,3,5,4]=>3
[6,2,1,4,3,5]=>2
[6,2,1,4,5,3]=>4
[6,2,1,5,3,4]=>4
[6,2,1,5,4,3]=>6
[6,2,3,1,4,5]=>0
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>0
[6,2,3,4,5,1]=>0
[6,2,3,5,1,4]=>2
[6,2,3,5,4,1]=>2
[6,2,4,1,3,5]=>1
[6,2,4,1,5,3]=>3
[6,2,4,3,1,5]=>1
[6,2,4,3,5,1]=>1
[6,2,4,5,1,3]=>2
[6,2,4,5,3,1]=>2
[6,2,5,1,3,4]=>2
[6,2,5,1,4,3]=>4
[6,2,5,3,1,4]=>2
[6,2,5,3,4,1]=>2
[6,2,5,4,1,3]=>3
[6,2,5,4,3,1]=>3
[6,3,1,2,4,5]=>0
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>1
[6,3,1,4,5,2]=>2
[6,3,1,5,2,4]=>3
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>0
[6,3,2,1,5,4]=>3
[6,3,2,4,1,5]=>0
[6,3,2,4,5,1]=>0
[6,3,2,5,1,4]=>2
[6,3,2,5,4,1]=>2
[6,3,4,1,2,5]=>0
[6,3,4,1,5,2]=>1
[6,3,4,2,1,5]=>0
[6,3,4,2,5,1]=>0
[6,3,4,5,1,2]=>0
[6,3,4,5,2,1]=>0
[6,3,5,1,2,4]=>1
[6,3,5,1,4,2]=>2
[6,3,5,2,1,4]=>1
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>1
[6,3,5,4,2,1]=>1
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>2
[6,4,1,3,2,5]=>1
[6,4,1,3,5,2]=>2
[6,4,1,5,2,3]=>2
[6,4,1,5,3,2]=>3
[6,4,2,1,3,5]=>0
[6,4,2,1,5,3]=>2
[6,4,2,3,1,5]=>0
[6,4,2,3,5,1]=>0
[6,4,2,5,1,3]=>1
[6,4,2,5,3,1]=>1
[6,4,3,1,2,5]=>0
[6,4,3,1,5,2]=>1
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>0
[6,4,3,5,2,1]=>0
[6,4,5,1,2,3]=>0
[6,4,5,1,3,2]=>1
[6,4,5,2,1,3]=>0
[6,4,5,2,3,1]=>0
[6,4,5,3,1,2]=>0
[6,4,5,3,2,1]=>0
[6,5,1,2,3,4]=>0
[6,5,1,2,4,3]=>2
[6,5,1,3,2,4]=>1
[6,5,1,3,4,2]=>2
[6,5,1,4,2,3]=>2
[6,5,1,4,3,2]=>3
[6,5,2,1,3,4]=>0
[6,5,2,1,4,3]=>2
[6,5,2,3,1,4]=>0
[6,5,2,3,4,1]=>0
[6,5,2,4,1,3]=>1
[6,5,2,4,3,1]=>1
[6,5,3,1,2,4]=>0
[6,5,3,1,4,2]=>1
[6,5,3,2,1,4]=>0
[6,5,3,2,4,1]=>0
[6,5,3,4,1,2]=>0
[6,5,3,4,2,1]=>0
[6,5,4,1,2,3]=>0
[6,5,4,1,3,2]=>1
[6,5,4,2,1,3]=>0
[6,5,4,2,3,1]=>0
[6,5,4,3,1,2]=>0
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>5
[1,2,3,4,6,5,7]=>4
[1,2,3,6,4,7,5]=>10
[1,2,6,3,4,7,5]=>10
[1,3,2,4,5,6,7]=>1
[1,3,7,2,4,5,6]=>8
[1,3,7,6,5,4,2]=>17
[1,4,6,7,2,3,5]=>10
[1,4,6,7,5,3,2]=>13
[1,4,7,2,3,5,6]=>8
[1,4,7,6,5,3,2]=>15
[1,5,2,3,4,7,6]=>8
[1,5,2,7,3,4,6]=>10
[1,5,4,7,6,3,2]=>13
[1,5,6,2,7,3,4]=>10
[1,5,6,4,7,3,2]=>11
[1,5,6,7,2,3,4]=>9
[1,5,6,7,4,3,2]=>12
[1,5,7,2,3,4,6]=>8
[1,5,7,6,4,3,2]=>14
[1,6,2,3,4,7,5]=>8
[1,6,2,3,7,4,5]=>10
[1,6,2,7,3,4,5]=>10
[1,6,5,4,3,7,2]=>11
[1,6,5,4,7,3,2]=>12
[1,6,5,7,4,3,2]=>13
[1,6,7,2,3,4,5]=>8
[1,6,7,5,4,3,2]=>14
[1,7,2,3,4,5,6]=>5
[1,7,3,5,6,4,2]=>13
[1,7,3,6,5,4,2]=>15
[1,7,4,3,6,5,2]=>13
[1,7,4,5,3,6,2]=>11
[1,7,4,5,6,3,2]=>12
[1,7,4,6,5,3,2]=>14
[1,7,5,4,3,6,2]=>12
[1,7,5,4,6,3,2]=>13
[1,7,6,4,5,3,2]=>14
[1,7,6,5,4,3,2]=>15
[2,1,3,4,5,6,7]=>0
[2,1,3,4,7,5,6]=>8
[2,1,3,7,4,5,6]=>9
[2,1,6,3,4,5,7]=>6
[2,1,7,3,4,5,6]=>8
[2,1,7,6,5,4,3]=>20
[2,3,1,4,5,6,7]=>0
[2,3,4,1,5,6,7]=>0
[2,3,4,1,5,7,6]=>5
[2,3,4,5,1,6,7]=>0
[2,3,4,5,1,7,6]=>5
[2,3,4,5,6,1,7]=>0
[2,3,4,5,6,7,1]=>0
[2,3,4,5,7,1,6]=>4
[2,3,4,6,1,7,5]=>7
[2,3,4,6,7,1,5]=>6
[2,3,4,7,1,5,6]=>6
[2,3,5,6,7,1,4]=>6
[2,4,1,3,5,6,7]=>1
[2,5,1,3,4,6,7]=>2
[2,5,7,1,3,4,6]=>6
[2,6,1,3,4,5,7]=>3
[2,6,1,7,3,4,5]=>9
[2,6,5,4,3,1,7]=>6
[2,6,7,1,3,4,5]=>6
[2,7,1,3,4,5,6]=>4
[3,1,2,4,5,6,7]=>0
[3,1,2,4,5,7,6]=>5
[3,2,1,4,5,6,7]=>0
[3,2,4,5,6,7,1]=>0
[3,4,1,2,5,6,7]=>0
[3,4,2,5,6,7,1]=>0
[3,4,5,2,6,7,1]=>0
[3,4,5,6,2,7,1]=>0
[3,4,5,6,7,1,2]=>0
[3,5,6,1,2,4,7]=>2
[3,5,6,4,2,1,7]=>2
[3,6,1,2,4,5,7]=>2
[3,6,5,4,2,1,7]=>3
[4,1,2,3,5,6,7]=>0
[4,1,2,3,5,7,6]=>5
[4,1,6,2,3,5,7]=>4
[4,2,3,5,6,7,1]=>0
[4,2,5,1,3,6,7]=>1
[4,3,2,1,5,6,7]=>0
[4,3,2,5,6,7,1]=>0
[4,3,5,2,6,7,1]=>0
[4,3,6,5,2,1,7]=>2
[4,5,1,6,2,3,7]=>2
[4,5,2,3,6,7,1]=>0
[4,5,3,6,2,1,7]=>0
[4,5,6,1,2,3,7]=>0
[4,5,6,3,2,1,7]=>0
[4,6,1,2,3,5,7]=>1
[4,6,1,2,3,7,5]=>5
[4,6,5,3,2,1,7]=>1
[5,1,2,3,4,6,7]=>0
[5,1,2,3,4,7,6]=>5
[5,1,2,3,6,4,7]=>3
[5,1,2,3,6,7,4]=>6
[5,1,2,3,7,4,6]=>7
[5,1,2,6,3,4,7]=>4
[5,1,6,2,3,4,7]=>3
[5,1,6,2,3,7,4]=>6
[5,2,3,4,6,7,1]=>0
[5,2,6,7,1,3,4]=>4
[5,3,2,4,6,7,1]=>0
[5,3,2,6,1,4,7]=>2
[5,3,6,7,1,2,4]=>2
[5,4,3,2,1,6,7]=>0
[5,4,3,2,1,7,6]=>5
[5,4,3,2,6,1,7]=>0
[5,4,3,6,2,1,7]=>0
[5,4,6,3,2,1,7]=>0
[5,4,6,7,1,2,3]=>0
[5,6,1,2,3,4,7]=>0
[5,6,1,2,3,7,4]=>3
[5,6,3,4,1,2,7]=>0
[5,6,4,3,2,1,7]=>0
[5,6,7,1,2,3,4]=>0
[6,1,2,3,4,5,7]=>0
[6,1,2,3,4,7,5]=>4
[6,1,2,3,7,4,5]=>6
[6,1,2,7,3,4,5]=>6
[6,2,3,4,5,7,1]=>0
[6,2,4,5,3,1,7]=>2
[6,2,5,4,3,1,7]=>3
[6,3,2,5,4,1,7]=>2
[6,3,4,2,5,1,7]=>0
[6,3,4,5,2,1,7]=>0
[6,3,4,7,1,2,5]=>2
[6,3,5,4,2,1,7]=>1
[6,4,3,2,5,1,7]=>0
[6,4,3,2,7,1,5]=>3
[6,4,3,5,2,1,7]=>0
[6,4,5,7,1,2,3]=>0
[6,4,7,2,5,1,3]=>2
[6,4,7,3,5,1,2]=>1
[6,5,3,4,2,1,7]=>0
[6,5,4,3,2,1,7]=>0
[6,5,7,3,4,1,2]=>0
[6,7,1,2,3,4,5]=>0
[6,7,3,4,1,2,5]=>0
[6,7,4,5,1,2,3]=>0
[7,1,2,3,4,5,6]=>0
[7,2,1,3,4,5,6]=>0
[7,2,3,1,4,5,6]=>0
[7,2,3,4,1,5,6]=>0
[7,2,3,4,5,1,6]=>0
[7,3,1,2,4,5,6]=>0
[7,3,2,1,4,5,6]=>0
[7,3,2,4,1,5,6]=>0
[7,3,4,1,2,5,6]=>0
[7,4,1,2,3,5,6]=>0
[7,4,2,1,3,5,6]=>0
[7,4,5,6,1,2,3]=>0
[7,5,1,2,3,4,6]=>0
[7,5,6,1,2,3,4]=>0
[7,5,6,3,4,1,2]=>0
[7,6,1,2,3,4,5]=>0
[7,6,4,5,1,2,3]=>0
[7,6,5,1,2,3,4]=>0
[7,6,5,3,4,1,2]=>0
[7,6,5,4,1,2,3]=>0
[7,6,5,4,3,1,2]=>0
[7,6,5,4,3,2,1]=>0
[8,7,6,5,4,3,2,1]=>0
[7,6,8,5,4,3,2,1]=>0
[7,8,5,6,4,3,2,1]=>0
[7,8,6,4,5,3,2,1]=>0
[8,6,7,4,5,3,2,1]=>0
[7,6,5,4,8,3,2,1]=>0
[6,5,7,4,8,3,2,1]=>0
[7,8,6,5,3,4,2,1]=>0
[8,6,7,5,3,4,2,1]=>0
[8,7,5,6,3,4,2,1]=>0
[6,7,8,3,4,5,2,1]=>0
[7,8,6,5,4,2,3,1]=>0
[8,6,7,5,4,2,3,1]=>0
[8,7,5,6,4,2,3,1]=>0
[8,7,6,4,5,2,3,1]=>0
[8,6,5,7,3,2,4,1]=>0
[6,7,8,5,2,3,4,1]=>0
[8,5,6,7,2,3,4,1]=>0
[7,8,3,2,4,5,6,1]=>0
[7,6,5,4,3,2,8,1]=>0
[6,5,7,4,3,2,8,1]=>0
[6,5,4,3,7,2,8,1]=>0
[5,4,6,3,7,2,8,1]=>0
[3,4,5,2,6,7,8,1]=>0
[5,2,3,4,6,7,8,1]=>0
[4,3,2,5,6,7,8,1]=>0
[3,4,2,5,6,7,8,1]=>0
[4,2,3,5,6,7,8,1]=>0
[3,2,4,5,6,7,8,1]=>0
[2,3,4,5,6,7,8,1]=>0
[8,7,6,5,4,3,1,2]=>0
[7,8,6,5,4,3,1,2]=>0
[8,6,7,5,4,3,1,2]=>0
[8,7,5,6,4,3,1,2]=>0
[8,7,6,4,5,3,1,2]=>0
[8,7,6,5,3,4,1,2]=>0
[8,7,5,6,3,4,1,2]=>0
[7,8,5,6,3,4,1,2]=>0
[5,6,7,8,3,4,1,2]=>0
[7,8,3,4,5,6,1,2]=>0
[3,4,5,6,7,8,1,2]=>0
[8,7,6,5,4,2,1,3]=>0
[7,6,8,5,4,2,1,3]=>0
[8,7,6,5,4,1,2,3]=>0
[6,7,8,5,4,1,2,3]=>0
[8,5,6,7,4,1,2,3]=>0
[8,7,6,4,5,1,2,3]=>0
[8,6,7,4,5,1,2,3]=>0
[8,7,4,5,6,1,2,3]=>0
[7,8,4,5,6,1,2,3]=>0
[6,7,4,5,8,1,2,3]=>0
[7,6,5,8,3,2,1,4]=>0
[7,5,6,8,2,3,1,4]=>0
[6,7,5,8,3,1,2,4]=>0
[6,5,7,8,2,1,3,4]=>0
[8,7,6,5,1,2,3,4]=>0
[8,7,5,6,1,2,3,4]=>0
[7,8,5,6,1,2,3,4]=>0
[8,5,6,7,1,2,3,4]=>0
[5,6,7,8,1,2,3,4]=>0
[8,7,6,4,3,2,1,5]=>0
[8,7,6,4,2,1,3,5]=>0
[8,7,6,1,2,3,4,5]=>0
[8,6,7,1,2,3,4,5]=>0
[6,7,8,1,2,3,4,5]=>0
[7,8,5,4,2,1,3,6]=>0
[7,8,5,4,1,2,3,6]=>0
[8,7,1,2,3,4,5,6]=>0
[7,8,1,2,3,4,5,6]=>0
[8,6,5,4,3,2,1,7]=>0
[8,6,5,4,3,1,2,7]=>0
[8,5,6,3,4,1,2,7]=>0
[8,6,5,4,2,1,3,7]=>0
[8,6,4,3,2,1,5,7]=>0
[8,6,4,2,1,3,5,7]=>0
[8,2,3,4,1,5,6,7]=>0
[8,4,1,2,3,5,6,7]=>0
[8,3,2,1,4,5,6,7]=>0
[8,2,3,1,4,5,6,7]=>0
[8,3,1,2,4,5,6,7]=>0
[8,2,1,3,4,5,6,7]=>0
[8,1,2,3,4,5,6,7]=>0
[7,6,5,4,3,2,1,8]=>0
[6,7,5,4,3,2,1,8]=>0
[6,5,7,4,3,2,1,8]=>0
[5,6,7,4,3,2,1,8]=>0
[7,6,4,5,3,2,1,8]=>0
[6,5,4,7,3,2,1,8]=>0
[7,5,6,3,4,2,1,8]=>0
[7,6,4,3,5,2,1,8]=>0
[7,6,3,4,5,2,1,8]=>0
[7,5,4,3,6,2,1,8]=>0
[6,7,5,4,2,3,1,8]=>0
[6,5,7,3,2,4,1,8]=>0
[5,6,7,2,3,4,1,8]=>0
[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]=>0
[2,3,4,5,6,1,7,8]=>0
[5,6,3,4,1,2,7,8]=>0
[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]=>0
[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]=>0
[3,4,1,2,5,6,7,8]=>0
[3,2,1,4,5,6,7,8]=>0
[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]=>2
[3,5,8,7,6,4,2,1]=>10
[4,3,6,5,8,7,2,1]=>6
[2,6,8,7,5,4,3,1]=>14
[2,3,5,6,8,7,4,1]=>12
[3,2,6,5,4,8,7,1]=>11
[4,3,6,5,7,2,8,1]=>2
[3,2,6,5,7,4,8,1]=>8
[4,3,5,2,7,6,8,1]=>4
[3,2,5,4,7,6,8,1]=>6
[1,8,7,6,5,4,3,2]=>21
[1,7,8,6,5,4,3,2]=>20
[1,6,8,7,5,4,3,2]=>20
[1,7,6,8,5,4,3,2]=>19
[1,6,7,8,5,4,3,2]=>18
[1,5,8,7,6,4,3,2]=>21
[1,7,6,5,8,4,3,2]=>18
[1,3,5,7,8,6,4,2]=>20
[1,4,3,8,7,6,5,2]=>25
[1,6,5,4,3,8,7,2]=>17
[1,4,3,6,5,8,7,2]=>15
[2,1,8,7,6,5,4,3]=>30
[2,1,6,5,7,4,8,3]=>18
[2,1,5,4,7,6,8,3]=>16
[1,2,6,7,8,5,4,3]=>24
[3,2,1,8,7,6,5,4]=>30
[3,2,1,6,5,8,7,4]=>20
[1,2,3,5,6,7,8,4]=>12
[4,3,2,1,8,7,6,5]=>24
[3,4,2,1,7,8,6,5]=>20
[2,4,3,1,6,8,7,5]=>18
[2,4,3,1,7,6,8,5]=>17
[3,2,4,1,6,8,7,5]=>17
[3,2,4,1,7,6,8,5]=>16
[2,3,4,1,6,7,8,5]=>12
[2,1,4,3,8,7,6,5]=>26
[2,1,4,3,6,8,7,5]=>19
[2,1,4,3,7,6,8,5]=>18
[5,4,3,2,1,8,7,6]=>15
[3,2,5,4,1,8,7,6]=>17
[3,2,1,4,5,8,7,6]=>15
[2,3,1,4,5,7,8,6]=>10
[6,5,4,3,2,1,8,7]=>6
[4,3,5,2,6,1,8,7]=>6
[3,2,5,4,6,1,8,7]=>8
[2,3,4,5,6,1,8,7]=>6
[2,1,6,5,4,3,8,7]=>18
[2,1,4,6,5,3,8,7]=>15
[2,1,5,4,6,3,8,7]=>14
[4,3,2,1,6,5,8,7]=>10
[2,4,3,1,6,5,8,7]=>11
[3,2,4,1,6,5,8,7]=>10
[2,1,4,3,6,5,8,7]=>12
[2,1,3,4,5,6,8,7]=>6
[1,2,3,4,5,6,8,7]=>6
[5,7,6,4,3,2,1,8]=>1
[4,7,6,5,3,2,1,8]=>3
[3,2,7,6,5,4,1,8]=>12
[5,4,3,2,7,6,1,8]=>4
[3,2,5,4,7,6,1,8]=>6
[1,4,3,2,7,6,5,8]=>15
[1,3,4,2,6,7,5,8]=>10
[1,3,2,5,4,7,6,8]=>9
[1,2,3,5,4,7,6,8]=>8
[1,3,2,4,5,7,6,8]=>6
[1,2,3,4,5,7,6,8]=>5
[1,2,4,3,6,5,7,8]=>6
[1,3,2,5,4,6,7,8]=>4
[1,2,3,5,4,6,7,8]=>3
[1,3,2,4,5,6,7,8]=>1
[1,8,4,7,6,5,3,2]=>21
[1,8,5,4,7,6,3,2]=>19
[1,8,7,4,5,6,3,2]=>18
[1,8,7,4,6,5,3,2]=>20
[1,8,6,5,4,7,3,2]=>18
[1,8,7,5,4,6,3,2]=>19
[1,8,7,5,6,4,3,2]=>20
[2,1,4,5,8,6,7,3]=>18
[2,1,8,5,4,7,6,3]=>24
[2,3,4,8,5,6,7,1]=>9
[2,3,6,4,5,1,8,7]=>10
[2,3,7,4,5,6,8,1]=>6
[2,8,4,3,5,7,6,1]=>10
[4,2,3,1,8,6,7,5]=>20
[8,2,7,4,6,5,3,1]=>9
[4,3,2,7,5,6,8,1]=>6
[4,3,2,8,5,7,6,1]=>13
[6,3,2,5,4,1,8,7]=>8
[8,3,2,5,4,7,6,1]=>6
[8,3,2,7,6,5,4,1]=>12
[8,3,7,4,6,5,2,1]=>5
[7,3,6,5,4,2,1,8]=>3
[7,4,3,6,5,2,1,8]=>2
[7,6,3,5,4,2,1,8]=>1
[8,5,4,3,2,7,6,1]=>4
[8,7,4,3,6,5,2,1]=>2
[2,4,6,8,1,3,5,7]=>10
[2,4,6,1,7,3,8,5]=>13
[2,1,4,3,7,5,8,6]=>15
[2,4,1,3,7,5,8,6]=>14
[2,1,4,3,7,8,5,6]=>18
[2,4,7,8,1,3,5,6]=>11
[2,1,4,3,8,5,6,7]=>14
[2,4,5,6,7,1,8,3]=>6
[2,1,5,3,6,4,8,7]=>13
[2,1,5,6,3,4,8,7]=>14
[2,5,6,8,1,3,4,7]=>9
[2,1,5,3,7,4,8,6]=>16
[2,5,1,7,3,4,8,6]=>14
[2,1,5,7,3,8,4,6]=>18
[2,5,7,8,1,3,4,6]=>10
[2,3,5,6,1,7,8,4]=>10
[2,1,6,3,7,4,8,5]=>16
[2,6,7,1,3,4,8,5]=>10
[2,1,6,7,8,3,4,5]=>18
[2,6,7,8,1,3,4,5]=>9
[2,1,6,3,4,7,8,5]=>14
[2,1,6,3,4,5,8,7]=>12
[2,6,1,3,4,5,7,8]=>3
[2,7,8,1,3,4,5,6]=>8
[2,7,1,3,4,5,6,8]=>4
[2,3,4,5,7,8,1,6]=>8
[2,1,8,3,4,5,6,7]=>10
[2,8,1,3,4,5,6,7]=>5
[2,1,3,8,4,5,6,7]=>12
[2,3,4,5,6,8,1,7]=>5
[3,1,4,2,6,5,8,7]=>11
[3,4,1,2,6,5,8,7]=>10
[3,1,4,2,6,8,5,7]=>14
[3,4,6,8,1,2,5,7]=>7
[3,1,4,2,7,5,8,6]=>14
[3,4,1,2,7,8,5,6]=>16
[3,4,7,8,1,2,5,6]=>8
[3,1,5,2,6,4,8,7]=>12
[3,5,1,6,2,4,8,7]=>10
[3,1,5,6,2,8,4,7]=>14
[3,5,6,8,1,2,4,7]=>6
[3,1,5,2,7,4,8,6]=>15
[3,5,1,7,2,8,4,6]=>14
[3,5,7,8,1,2,4,6]=>7
[1,3,2,5,4,8,6,7]=>14
[1,3,5,8,2,4,6,7]=>13
[1,3,5,6,2,7,4,8]=>10
[3,1,6,2,7,4,8,5]=>15
[3,6,7,1,2,8,4,5]=>10
[3,6,1,7,8,2,4,5]=>12
[3,6,7,8,1,2,4,5]=>6
[1,3,2,6,4,7,5,8]=>11
[3,1,2,6,7,4,8,5]=>16
[1,3,2,6,4,8,5,7]=>16
[1,3,2,6,4,5,7,8]=>7
[1,3,2,7,4,8,5,6]=>18
[1,3,2,7,4,5,6,8]=>10
[1,3,2,8,4,5,6,7]=>13
[3,1,2,4,5,8,6,7]=>10
[1,3,2,4,5,8,6,7]=>11
[4,1,5,2,6,3,8,7]=>10
[4,5,6,1,2,3,8,7]=>6
[4,1,5,6,8,2,3,7]=>10
[4,5,6,8,1,2,3,7]=>3
[4,1,5,2,7,3,8,6]=>13
[4,1,5,2,7,8,3,6]=>14
[4,5,7,1,2,8,3,6]=>8
[4,5,1,7,8,2,3,6]=>10
[4,5,7,8,1,2,3,6]=>4
[1,4,2,5,3,7,6,8]=>9
[1,4,2,5,3,8,6,7]=>14
[1,4,2,5,3,6,7,8]=>4
[1,4,5,6,7,2,3,8]=>8
[4,1,6,2,7,3,8,5]=>13
[4,6,7,1,8,2,3,5]=>6
[4,6,7,8,1,2,3,5]=>3
[1,4,2,6,3,7,5,8]=>11
[1,4,2,6,7,8,3,5]=>17
[1,4,2,6,3,8,5,7]=>16
[4,1,2,3,6,5,8,7]=>10
[1,4,2,6,3,5,7,8]=>7
[1,4,2,7,3,8,5,6]=>18
[4,7,1,2,3,5,6,8]=>2
[1,4,2,7,3,5,6,8]=>10
[1,4,2,3,7,5,6,8]=>10
[1,4,2,3,5,7,6,8]=>7
[1,4,2,8,3,5,6,7]=>13
[4,1,2,3,8,5,6,7]=>12
[1,4,2,3,5,8,6,7]=>12
[1,4,2,3,5,6,7,8]=>2
[5,1,6,2,7,3,8,4]=>10
[1,5,2,6,3,7,4,8]=>10
[1,5,2,6,3,8,4,7]=>15
[1,5,2,6,3,4,7,8]=>7
[1,2,5,6,3,4,7,8]=>8
[1,5,2,7,3,8,4,6]=>17
[5,7,1,2,3,4,6,8]=>1
[1,5,2,7,3,4,6,8]=>10
[1,5,2,3,4,7,6,8]=>8
[5,1,2,8,3,4,6,7]=>10
[1,5,2,8,3,4,6,7]=>13
[1,5,8,2,3,4,6,7]=>10
[1,5,2,3,4,8,6,7]=>13
[1,2,3,5,4,8,6,7]=>13
[5,1,2,3,4,6,8,7]=>6
[1,5,2,3,4,6,7,8]=>3
[1,6,2,7,3,8,4,5]=>16
[1,6,7,8,2,3,4,5]=>12
[6,7,1,2,3,4,8,5]=>4
[6,1,7,2,3,4,5,8]=>4
[6,1,2,7,3,4,5,8]=>6
[1,6,2,7,3,4,5,8]=>10
[1,6,7,2,3,4,5,8]=>8
[1,6,2,3,4,7,5,8]=>8
[1,2,3,6,4,7,5,8]=>10
[6,1,8,2,3,4,5,7]=>6
[1,6,2,8,3,4,5,7]=>13
[1,6,8,2,3,4,5,7]=>10
[1,6,2,3,4,8,5,7]=>13
[1,2,3,6,4,8,5,7]=>15
[6,1,2,3,4,5,8,7]=>6
[1,6,2,3,4,5,7,8]=>4
[1,2,3,6,4,5,7,8]=>6
[1,7,2,8,3,4,5,6]=>13
[1,7,8,2,3,4,5,6]=>10
[1,7,2,3,8,4,5,6]=>14
[7,1,2,3,4,8,5,6]=>8
[1,7,2,3,4,8,5,6]=>13
[1,2,3,7,4,8,5,6]=>17
[7,1,2,3,4,5,8,6]=>5
[1,7,2,3,4,5,8,6]=>10
[1,2,7,3,4,5,8,6]=>13
[1,7,2,3,4,5,6,8]=>5
[1,2,3,7,4,5,6,8]=>9
[1,8,2,3,4,5,6,7]=>6
[1,2,3,8,4,5,6,7]=>12
[1,2,3,4,5,8,6,7]=>10
[5,3,2,6,1,4,8,7]=>8
[7,3,2,5,4,8,1,6]=>6
[8,4,5,2,3,7,6,1]=>4
[7,4,5,2,3,8,1,6]=>4
[6,4,5,2,3,1,8,7]=>6
[5,4,6,2,1,3,8,7]=>6
[3,6,1,5,4,2,8,7]=>12
[4,6,5,1,3,2,8,7]=>8
[5,6,4,3,1,2,8,7]=>6
[7,5,4,3,2,8,1,6]=>4
[8,6,4,3,7,2,5,1]=>2
[7,6,4,3,8,2,1,5]=>2
[6,7,4,3,8,1,2,5]=>2
[5,7,4,3,1,8,2,6]=>6
[4,7,5,1,3,8,2,6]=>8
[3,7,1,5,4,8,2,6]=>12
[2,1,7,5,4,8,3,6]=>20
[3,8,1,5,4,7,6,2]=>14
[4,8,5,1,3,7,6,2]=>10
[5,8,4,3,1,7,6,2]=>8
[6,8,4,3,7,1,5,2]=>4
[7,8,4,3,6,5,1,2]=>2
[6,8,5,7,3,1,4,2]=>2
[5,8,6,7,1,3,4,2]=>4
[4,8,6,1,7,3,5,2]=>10
[3,8,1,6,7,4,5,2]=>16
[2,1,8,6,7,4,5,3]=>26
[2,1,7,6,8,4,3,5]=>22
[3,7,1,6,8,4,2,5]=>14
[4,7,6,1,8,3,2,5]=>8
[5,7,6,8,1,3,2,4]=>2
[5,4,7,2,1,8,3,6]=>8
[6,4,7,2,8,1,3,5]=>4
[7,4,6,2,8,3,1,5]=>4
[8,4,6,2,7,3,5,1]=>4
[8,3,2,6,7,4,5,1]=>8
[7,3,2,6,8,4,1,5]=>8
[6,3,2,7,8,1,4,5]=>8
[5,3,2,7,1,8,4,6]=>12
[4,3,2,1,7,8,5,6]=>16
[3,4,1,2,8,7,6,5]=>24
[5,3,2,8,1,7,6,4]=>18
[6,3,2,8,7,1,5,4]=>14
[7,3,2,8,6,5,1,4]=>12
[8,4,7,2,6,5,3,1]=>6
[7,4,8,2,6,5,1,3]=>6
[6,4,8,2,7,1,5,3]=>8
[5,4,8,2,1,7,6,3]=>12
[4,5,8,1,2,7,6,3]=>12
[3,5,1,8,2,7,6,4]=>20
[2,1,5,8,3,7,6,4]=>24
[2,1,6,8,7,3,5,4]=>24
[3,6,1,8,7,2,5,4]=>18
[4,6,8,1,7,2,5,3]=>10
[5,6,8,7,1,2,4,3]=>4
[6,5,8,7,2,1,4,3]=>4
[7,5,8,6,2,4,1,3]=>2
[8,5,7,6,2,4,3,1]=>2
[5,7,8,6,1,4,2,3]=>4
[4,7,8,1,6,5,2,3]=>10
[3,7,1,8,6,5,2,4]=>18
[2,1,7,8,6,5,3,4]=>26
[3,8,1,7,6,5,4,2]=>20
[4,8,7,1,6,5,3,2]=>12
[5,8,7,6,1,4,3,2]=>6
[6,8,7,5,4,1,3,2]=>2
[4,2,5,1,3,6,7,8]=>1
[5,2,6,7,1,3,4,8]=>4
[3,2,7,8,1,4,5,6]=>12
[5,3,2,6,1,4,7,8]=>2
[7,4,3,8,1,2,5,6]=>4
[4,7,3,6,8,1,2,5]=>6
[6,7,3,4,8,1,2,5]=>2
[5,4,2,7,8,1,3,6]=>8
[6,4,7,2,5,1,3,8]=>2
[6,4,3,2,7,1,5,8]=>3
[5,4,3,2,8,1,6,7]=>8
[7,5,3,8,2,6,1,4]=>5
[8,5,4,7,2,6,1,3]=>3
[8,5,4,7,3,6,1,2]=>2
[8,1,2,7,6,3,4,5]=>14
[8,1,4,2,6,3,5,7]=>7
[8,3,1,2,4,7,5,6]=>8
[8,3,1,5,6,2,4,7]=>6
[6,3,8,1,2,7,4,5]=>10
[7,8,4,1,6,2,3,5]=>4
[8,3,4,1,6,7,2,5]=>8
[2,7,6,5,1,3,8,4]=>12
[8,3,6,5,1,7,2,4]=>6
[4,6,7,3,8,5,1,2]=>4
[3,5,2,7,1,8,6,4]=>16
[4,6,7,2,8,1,5,3]=>7
[5,6,7,8,2,1,4,3]=>2
[6,5,8,7,3,4,1,2]=>2
[3,6,7,4,5,8,1,2]=>4
[2,6,7,4,5,1,8,3]=>10
[1,6,7,4,5,2,3,8]=>12
[1,5,4,7,6,2,3,8]=>12
[2,5,4,7,6,1,8,3]=>10
[3,5,4,7,6,8,1,2]=>4
[4,5,3,7,8,6,1,2]=>6
[5,4,3,8,7,6,1,2]=>9
[6,4,8,3,7,5,1,2]=>5
[6,3,8,4,5,7,1,2]=>4
[5,3,4,8,6,7,1,2]=>6
[4,3,5,6,8,7,1,2]=>4
[3,2,5,6,1,8,7,4]=>15
[4,2,5,6,8,1,7,3]=>9
[5,2,4,8,6,1,7,3]=>11
[6,2,8,4,5,1,7,3]=>9
[7,8,2,4,5,1,6,3]=>4
[7,8,1,4,5,2,3,6]=>4
[6,1,8,4,5,2,3,7]=>10
[5,1,4,8,6,2,3,7]=>12
[4,1,3,2,8,6,5,7]=>17
[5,1,3,8,2,6,4,7]=>13
[6,1,8,3,2,5,4,7]=>10
[7,8,1,3,2,5,4,6]=>4
[7,8,2,3,1,5,6,4]=>6
[6,2,8,3,1,5,7,4]=>11
[5,2,3,8,1,6,7,4]=>14
[6,3,8,2,1,7,5,4]=>13
[7,8,3,2,1,6,5,4]=>9
[7,8,4,2,6,1,5,3]=>5
[5,4,2,8,7,1,6,3]=>13
[4,5,2,7,8,1,6,3]=>10
[2,5,3,7,1,6,8,4]=>13
[1,5,3,7,2,6,4,8]=>13
[1,6,7,3,2,5,4,8]=>12
[2,6,7,3,1,5,8,4]=>12
[3,6,7,2,1,8,5,4]=>13
[7,8,5,6,2,1,4,3]=>2
[6,5,8,7,1,2,3,4]=>2
[5,4,1,8,7,2,3,6]=>13
[6,4,8,1,7,2,3,5]=>7
[7,8,3,1,2,6,4,5]=>6
[5,3,1,8,2,7,4,6]=>16
[4,3,1,2,8,7,5,6]=>20
[4,2,1,3,8,5,7,6]=>17
[5,2,1,8,3,4,7,6]=>15
[6,2,8,1,3,4,7,5]=>9
[7,8,2,1,3,4,6,5]=>4
[6,3,1,5,2,4,8,7]=>9
[2,1,8,5,3,7,4,6]=>21
[8,2,6,1,4,3,7,5]=>9
[4,7,1,5,8,3,2,6]=>10
[8,6,1,3,4,2,5,7]=>2
[8,1,2,4,5,6,3,7]=>6
[8,2,5,1,3,6,4,7]=>5
[4,1,5,3,7,2,8,6]=>13
[5,2,7,1,3,8,4,6]=>11
[5,3,1,7,8,2,4,6]=>12
[1,7,3,4,2,5,8,6]=>12
[4,7,2,1,3,5,8,6]=>7
[4,5,2,3,7,6,1,8]=>4
[6,4,3,7,2,5,1,8]=>2
[8,4,3,6,5,1,2,7]=>2
[1,5,6,3,4,8,7,2]=>15
[4,6,2,7,3,5,1,8]=>4
[3,2,6,7,4,5,1,8]=>8
[4,7,2,6,5,3,1,8]=>6
[5,7,6,2,4,3,1,8]=>2
[1,7,5,4,8,3,6,2]=>17
[8,7,5,4,1,3,2,6]=>1
[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]=>7
[3,2,8,6,5,1,4,7]=>14
[4,1,2,6,5,8,7,3]=>16
[5,1,6,2,4,8,7,3]=>14
[6,1,5,4,2,8,7,3]=>14
[7,1,5,4,8,2,6,3]=>12
[8,1,5,4,7,6,2,3]=>12
[1,8,6,7,4,5,3,2]=>19
[8,1,6,7,4,5,2,3]=>12
[7,1,6,8,4,2,5,3]=>12
[6,1,7,8,2,4,5,3]=>12
[5,1,7,2,8,4,6,3]=>16
[4,1,2,7,8,5,6,3]=>20
[3,2,1,7,8,5,6,4]=>24
[3,2,8,7,1,5,4,6]=>17
[4,8,2,7,1,5,3,6]=>10
[5,8,7,2,1,4,3,6]=>5
[6,8,7,1,2,4,3,5]=>3
[7,8,6,1,4,2,3,5]=>2
[8,7,6,1,4,3,2,5]=>3
[1,7,6,8,4,3,5,2]=>17
[1,6,7,8,3,4,5,2]=>15
[8,6,7,1,3,4,2,5]=>2
[7,6,8,1,3,2,4,5]=>1
[5,7,8,2,1,3,4,6]=>2
[4,7,2,8,1,3,5,6]=>7
[3,2,6,8,4,1,5,7]=>11
[4,6,2,8,3,1,5,7]=>7
[5,6,8,2,3,1,4,7]=>2
[6,5,8,3,2,1,4,7]=>2
[7,5,8,3,1,2,4,6]=>1
[8,5,7,3,1,4,2,6]=>2
[1,5,7,3,8,4,6,2]=>17
[1,4,3,7,8,5,6,2]=>19
[8,4,3,7,1,5,2,6]=>5
[6,4,3,8,2,1,5,7]=>5
[4,5,2,3,8,1,6,7]=>8
[3,2,5,4,8,1,6,7]=>10
[4,5,2,3,1,8,7,6]=>15
[6,4,3,1,2,8,7,5]=>13
[7,4,3,1,8,2,6,5]=>11
[8,4,3,1,7,6,2,5]=>11
[1,5,8,3,7,6,4,2]=>21
[8,5,1,3,7,6,2,4]=>10
[7,5,1,3,8,2,6,4]=>10
[6,5,1,3,2,8,7,4]=>12
[5,6,1,2,3,8,7,4]=>11
[4,6,2,1,3,8,7,5]=>14
[3,2,6,1,4,8,7,5]=>17
[3,2,7,1,8,4,6,5]=>19
[4,7,2,1,8,3,6,5]=>14
[5,7,1,2,8,3,6,4]=>11
[6,7,1,8,2,3,5,4]=>7
[7,6,1,8,3,2,5,4]=>8
[8,6,1,7,3,5,2,4]=>8
[1,6,8,7,3,5,4,2]=>19
[1,7,8,6,5,3,4,2]=>19
[8,7,1,6,5,3,2,4]=>8
[7,8,1,6,5,2,3,4]=>7
[6,8,1,7,2,5,3,4]=>9
[5,8,1,2,7,6,3,4]=>13
[4,8,2,1,7,6,3,5]=>16
[3,2,8,1,7,6,4,5]=>23
[4,1,2,8,7,6,5,3]=>26
[5,1,8,2,7,6,4,3]=>20
[6,1,8,7,2,5,4,3]=>16
[7,1,8,6,5,2,4,3]=>14
[8,1,7,6,5,4,2,3]=>14
[1,4,3,8,7,5,6,2]=>22
[4,1,2,8,7,5,6,3]=>23
[3,2,5,1,6,4,8,7]=>11
[3,2,5,4,7,1,8,6]=>11
[4,2,5,3,7,6,8,1]=>5
[4,2,5,3,7,1,8,6]=>10
[4,2,5,3,6,1,8,7]=>7
[4,2,5,1,6,3,8,7]=>9
[3,1,5,4,6,2,8,7]=>11
[4,1,5,3,6,2,8,7]=>10
[4,3,5,1,6,2,8,7]=>7
[4,3,5,2,7,1,8,6]=>9
[4,3,6,2,7,5,8,1]=>5
[4,3,6,2,7,1,8,5]=>9
[4,3,6,1,7,2,8,5]=>10
[4,3,5,1,7,2,8,6]=>10
[3,1,5,4,7,2,8,6]=>14
[2,1,5,4,7,3,8,6]=>17
[3,1,5,4,7,6,8,2]=>11
[4,1,5,3,7,6,8,2]=>10
[4,3,5,1,7,6,8,2]=>7
[4,3,6,1,7,5,8,2]=>8
[4,3,6,5,7,1,8,2]=>3
[5,3,6,4,7,2,8,1]=>1
[5,3,6,4,7,1,8,2]=>2
[5,3,6,1,7,4,8,2]=>6
[5,1,6,3,7,4,8,2]=>9
[4,1,6,3,7,5,8,2]=>11
[3,1,6,4,7,5,8,2]=>12
[2,1,6,4,7,5,8,3]=>17
[2,1,6,4,7,3,8,5]=>17
[3,1,6,4,7,2,8,5]=>14
[4,1,6,3,7,2,8,5]=>13
[5,1,6,3,7,2,8,4]=>10
[5,3,6,1,7,2,8,4]=>7
[5,3,6,2,7,1,8,4]=>6
[5,3,6,2,7,4,8,1]=>3
[5,2,6,3,7,4,8,1]=>4
[5,2,6,3,7,1,8,4]=>7
[5,2,6,1,7,3,8,4]=>9
[4,2,5,1,7,3,8,6]=>12
[4,2,6,1,7,3,8,5]=>12
[4,2,6,3,7,1,8,5]=>10
[4,2,6,3,7,5,8,1]=>6
[3,2,6,4,7,5,8,1]=>7
[3,2,6,4,7,1,8,5]=>11
[3,2,6,1,7,4,8,5]=>14
[3,2,5,1,7,4,8,6]=>14
[3,2,4,1,7,5,8,6]=>13
[3,1,4,2,7,6,8,5]=>17
[3,2,5,1,7,6,8,4]=>15
[3,2,6,1,7,5,8,4]=>16
[3,2,6,5,7,1,8,4]=>11
[4,2,6,5,7,3,8,1]=>5
[4,2,6,5,7,1,8,3]=>7
[4,2,6,1,7,5,8,3]=>12
[4,2,5,1,7,6,8,3]=>11
[4,1,5,2,7,6,8,3]=>12
[3,1,5,2,7,6,8,4]=>16
[2,1,5,3,7,6,8,4]=>17
[2,1,6,3,7,5,8,4]=>18
[3,1,6,2,7,5,8,4]=>17
[4,1,6,2,7,5,8,3]=>13
[5,1,6,2,7,4,8,3]=>11
[5,2,6,1,7,4,8,3]=>10
[5,2,6,4,7,1,8,3]=>6
[5,2,6,4,7,3,8,1]=>4
[5,4,6,2,7,3,8,1]=>1
[5,4,6,2,7,1,8,3]=>3
[5,4,6,1,7,2,8,3]=>4
[5,1,6,4,7,2,8,3]=>9
[4,1,6,5,7,2,8,3]=>10
[3,1,6,5,7,2,8,4]=>14
[2,1,6,5,7,3,8,4]=>17
[3,1,6,5,7,4,8,2]=>13
[4,1,6,5,7,3,8,2]=>10
[5,1,6,4,7,3,8,2]=>9
[5,4,6,1,7,3,8,2]=>4
[5,4,6,3,7,1,8,2]=>1
[8,3,5,2,1,6,4,7]=>4
[8,6,3,5,2,4,1,7]=>1
[3,7,5,2,4,1,8,6]=>9
[8,3,7,5,2,4,6,1]=>4
[8,2,4,5,7,3,6,1]=>6
[2,4,5,7,3,1,8,6]=>11
[8,2,4,6,5,3,1,7]=>5
[8,2,5,4,6,1,3,7]=>4
[8,6,3,5,1,4,2,7]=>2
[8,6,1,4,5,3,2,7]=>5
[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]=>1
[4,6,8,3,2,7,5,1]=>7
[4,7,6,3,2,8,1,5]=>6
[1,4,6,7,3,2,8,5]=>15
[5,4,7,3,1,8,2,6]=>7
[1,7,4,5,3,2,8,6]=>15
[3,7,5,1,4,2,8,6]=>10
[5,7,4,2,1,3,8,6]=>6
[8,5,7,4,2,1,6,3]=>3
[8,3,7,5,1,4,6,2]=>6
[8,4,1,7,5,3,6,2]=>10
[4,6,3,8,7,1,5,2]=>9
[1,7,4,8,6,3,5,2]=>19
[8,4,7,6,3,5,2,1]=>3
[3,6,5,8,7,4,1,2]=>8
[3,1,5,8,6,7,4,2]=>19
[4,8,1,6,7,3,5,2]=>13
[3,6,4,1,8,7,5,2]=>15
[8,2,6,1,4,7,5,3]=>12
[2,7,6,8,1,4,3,5]=>12
[3,7,1,6,4,8,2,5]=>13
[1,7,3,5,6,8,2,4]=>15
[1,3,6,7,5,8,2,4]=>17
[3,7,6,5,8,2,1,4]=>7
[3,6,8,5,7,2,4,1]=>8
[2,3,5,7,6,8,1,4]=>11
[2,1,6,5,7,8,3,4]=>18
[4,2,7,6,8,3,1,5]=>11
[4,2,6,8,7,3,5,1]=>12
[3,8,2,4,6,7,5,1]=>10
[3,7,2,6,4,8,1,5]=>10
[3,2,6,1,4,7,8,5]=>12
[5,3,7,2,1,8,4,6]=>10
[4,7,3,2,1,5,8,6]=>7
[8,7,6,1,3,4,2,5]=>2
[8,5,7,3,2,1,6,4]=>4
[8,3,6,7,2,1,5,4]=>7
[3,7,8,6,2,1,5,4]=>11
[8,7,6,3,5,2,4,1]=>1
[2,7,4,8,1,6,5,3]=>17
[4,6,8,2,1,7,5,3]=>11
[8,4,1,5,7,2,6,3]=>9
[8,5,3,7,1,6,2,4]=>6
[8,5,7,2,1,3,6,4]=>4
[8,2,6,7,1,3,5,4]=>9
[8,3,6,1,7,5,2,4]=>10
[4,6,1,8,7,2,5,3]=>14
[8,1,2,5,6,7,4,3]=>14
[8,2,6,5,7,4,1,3]=>8
[2,1,7,8,5,6,4,3]=>26
[8,2,5,7,6,4,3,1]=>9
[2,7,6,8,5,4,1,3]=>13
[1,7,2,5,8,6,4,3]=>22
[1,7,4,8,2,6,5,3]=>20
[3,7,8,1,6,5,2,4]=>14
[2,7,8,6,1,3,5,4]=>14
[8,7,6,3,5,1,4,2]=>2
[8,4,7,6,5,1,3,2]=>4
[8,7,1,5,6,4,3,2]=>9
[8,1,6,7,5,4,3,2]=>14
[5,4,3,6,1,2,8,7]=>6
[2,7,6,4,5,8,1,3]=>10
[5,7,3,6,1,8,2,4]=>5
[2,1,7,6,5,8,3,4]=>22
[6,4,3,5,8,1,7,2]=>5
[7,3,5,4,8,6,1,2]=>4
[5,4,3,2,7,1,8,6]=>9
[4,3,6,2,8,7,5,1]=>12
[4,3,7,6,2,1,8,5]=>10
[6,4,3,1,7,2,8,5]=>8
[4,3,7,1,8,6,5,2]=>16
[5,3,8,7,6,4,2,1]=>9
[7,5,3,1,8,6,4,2]=>10
[1,8,6,5,3,7,4,2]=>18
[6,1,7,5,3,2,8,4]=>11
[7,6,5,3,2,1,8,4]=>3
[6,5,3,2,8,7,4,1]=>8
[5,2,6,3,8,7,4,1]=>10
[5,2,7,6,3,1,8,4]=>9
[6,5,2,1,7,3,8,4]=>7
[5,2,7,1,8,6,4,3]=>17
[6,2,8,7,5,4,3,1]=>11
[7,6,2,1,8,5,4,3]=>12
[6,1,7,2,8,5,4,3]=>16
[7,1,8,6,5,4,3,2]=>15
[4,5,2,6,3,1,8,7]=>7
[6,5,2,1,4,3,8,7]=>8
[6,5,2,7,4,8,3,1]=>4
[8,5,2,7,4,1,6,3]=>7
[8,3,7,5,2,1,6,4]=>7
[6,3,7,5,2,8,4,1]=>5
[3,1,6,5,4,2,8,7]=>15
[5,6,3,2,4,1,8,7]=>6
[3,6,2,4,1,5,8,7]=>8
[2,6,1,3,5,4,8,7]=>12
[6,7,2,3,4,8,5,1]=>3
[8,7,2,3,4,1,6,5]=>4
[5,1,7,3,8,4,6,2]=>14
[2,5,7,3,8,6,4,1]=>13
[7,6,1,3,5,8,4,2]=>8
[3,6,7,4,1,8,5,2]=>9
[5,6,3,7,4,8,1,2]=>1
[2,1,6,7,4,8,5,3]=>21
[2,1,8,7,4,3,6,5]=>24
[5,8,3,7,4,2,6,1]=>5
[3,8,7,4,1,2,6,5]=>11
[7,8,1,3,5,2,6,4]=>7
[5,8,7,3,2,6,1,4]=>5
[2,8,6,3,1,5,7,4]=>14
[8,1,6,3,2,5,4,7]=>8
[2,8,4,1,6,3,7,5]=>15
[4,8,1,2,7,6,3,5]=>16
[3,8,4,2,5,7,1,6]=>8
[6,8,3,5,2,7,4,1]=>4
[2,1,5,3,8,7,6,4]=>25
[6,5,3,2,8,7,1,4]=>8
[7,5,2,4,8,1,6,3]=>7
[3,4,2,8,5,7,6,1]=>13
[2,4,1,8,7,6,5,3]=>27
[8,4,2,1,7,5,3,6]=>10
[4,3,1,8,6,7,5,2]=>19
[3,1,4,8,6,5,7,2]=>17
[7,1,6,5,4,8,2,3]=>11
[3,7,5,6,8,4,2,1]=>6
[5,7,1,6,8,2,4,3]=>9
[8,6,2,5,1,7,4,3]=>8
[5,6,2,1,8,7,3,4]=>12
[4,6,2,5,8,3,7,1]=>7
[7,5,2,6,3,8,1,4]=>4
[4,1,2,3,6,8,7,5]=>17
[2,4,3,1,8,5,6,7]=>13
[7,5,2,8,3,4,6,1]=>4
[5,6,2,8,4,3,1,7]=>6
[4,7,2,8,1,5,3,6]=>9
[8,7,2,1,4,5,6,3]=>6
[3,6,8,7,1,5,4,2]=>12
[5,7,8,6,3,4,1,2]=>2
[7,1,8,5,4,3,6,2]=>12
[2,7,8,4,5,3,6,1]=>10
[5,7,3,8,1,4,6,2]=>6
[2,1,7,8,5,4,6,3]=>24
[2,1,5,8,4,6,3,7]=>18
[6,5,3,8,4,1,2,7]=>4
[7,5,8,4,3,6,2,1]=>1
[2,4,8,3,5,6,1,7]=>8
[4,1,8,3,6,5,2,7]=>14
[3,4,8,1,7,2,5,6]=>13
[8,4,1,3,7,2,6,5]=>12
[3,1,8,2,4,7,6,5]=>21
[2,3,8,1,4,6,7,5]=>16
[4,3,8,2,5,1,7,6]=>11
[6,3,8,4,2,5,7,1]=>4
[7,4,3,8,2,5,1,6]=>4
[2,1,4,8,3,5,7,6]=>18
[6,8,2,4,3,5,1,7]=>2
[4,8,2,3,5,1,6,7]=>3
[3,8,2,1,4,6,5,7]=>8
[2,8,1,3,4,5,7,6]=>10
[7,1,6,8,4,3,2,5]=>11
[7,1,6,5,8,3,2,4]=>11
[3,7,6,1,4,8,2,5]=>10
[2,7,8,4,1,6,5,3]=>16
[3,6,4,5,7,2,8,1]=>2
[1,8,2,7,3,4,5,6]=>14
[3,2,1,5,8,4,6,7]=>14
[5,4,3,2,1,8,6,7]=>10
[1,8,2,4,3,5,6,7]=>8
[1,7,2,4,3,5,6,8]=>7
[1,6,2,4,3,5,7,8]=>6
[1,5,2,4,3,6,7,8]=>5
[1,6,2,5,3,4,7,8]=>8
[1,7,2,5,3,4,6,8]=>9
[1,8,2,5,3,4,6,7]=>10
[1,8,2,6,3,4,5,7]=>12
[1,7,2,6,3,4,5,8]=>11
[1,8,2,7,3,5,4,6]=>17
[1,7,2,8,3,5,4,6]=>16
[1,6,2,8,3,5,4,7]=>16
[1,5,2,8,3,6,4,7]=>16
[1,4,2,8,3,6,5,7]=>17
[1,3,2,8,4,6,5,7]=>17
[1,2,3,8,4,6,5,7]=>16
[1,2,3,7,4,6,5,8]=>13
[1,3,2,7,4,6,5,8]=>14
[1,4,2,7,3,6,5,8]=>14
[1,5,2,7,3,6,4,8]=>13
[1,6,2,7,3,5,4,8]=>13
[1,7,2,6,3,5,4,8]=>14
[1,8,2,6,3,5,4,7]=>15
[1,8,2,5,3,6,4,7]=>13
[1,7,2,5,3,6,4,8]=>12
[1,6,2,5,3,7,4,8]=>11
[1,5,2,4,3,7,6,8]=>10
[1,6,2,4,3,7,5,8]=>10
[1,7,2,4,3,6,5,8]=>11
[1,8,2,4,3,6,5,7]=>12
[1,8,2,3,4,6,5,7]=>10
[1,7,2,3,4,6,5,8]=>9
[1,8,2,3,4,7,5,6]=>14
[1,8,2,4,3,7,5,6]=>16
[1,7,2,4,3,8,5,6]=>15
[1,6,2,4,3,8,5,7]=>15
[1,5,2,4,3,8,6,7]=>15
[1,6,2,5,3,8,4,7]=>16
[1,7,2,5,3,8,4,6]=>16
[1,8,2,5,3,7,4,6]=>17
[1,8,2,6,3,7,4,5]=>18
[1,7,2,6,3,8,4,5]=>17
[1,2,3,8,4,7,5,6]=>20
[1,3,2,8,4,7,5,6]=>21
[1,4,2,8,3,7,5,6]=>21
[1,5,2,8,3,7,4,6]=>20
[1,6,2,8,3,7,4,5]=>19
[1,7,2,8,3,6,4,5]=>19
[1,8,2,7,3,6,4,5]=>20
[6,7,8,1,4,3,2,5]=>3
[2,8,4,1,6,7,5,3]=>18
[4,8,5,7,1,6,2,3]=>7
[8,7,6,5,2,1,4,3]=>2
[8,3,1,5,4,7,2,6]=>9
[8,7,6,5,1,4,2,3]=>2
[7,5,1,3,8,4,2,6]=>8
[7,6,1,4,8,3,2,5]=>7
[7,1,3,5,8,2,4,6]=>10
[7,5,3,6,4,2,8,1]=>1
[8,2,6,3,4,7,5,1]=>6
[7,2,6,3,5,4,8,1]=>5
[6,2,7,4,3,5,8,1]=>4
[3,7,6,4,5,2,8,1]=>5
[2,7,6,5,3,4,8,1]=>9
[8,6,5,4,2,7,3,1]=>1
[6,5,8,4,2,7,3,1]=>3
[1,8,6,3,7,5,2,4]=>19
[8,7,5,2,6,4,3,1]=>3
[8,7,1,6,2,5,4,3]=>10
[1,7,2,8,5,3,4,6]=>17
[7,6,1,8,4,3,2,5]=>7
[8,6,1,7,4,2,5,3]=>8
[8,1,2,7,3,4,6,5]=>12
[7,1,2,8,3,5,4,6]=>11
[8,2,6,1,7,3,5,4]=>12
[4,7,5,6,8,3,2,1]=>2
[8,6,4,7,5,3,2,1]=>1
[5,4,8,1,7,2,6,3]=>11
[2,3,8,7,4,5,6,1]=>14
[7,2,8,6,4,3,5,1]=>8
[8,2,7,6,3,5,4,1]=>9
[8,1,7,6,5,2,4,3]=>14
[7,1,8,6,5,3,2,4]=>13
[1,2,8,7,6,3,4,5]=>24
[3,8,7,6,4,5,2,1]=>9
[2,8,7,6,5,3,4,1]=>14
[1,8,7,6,5,4,2,3]=>20
[3,8,6,7,1,5,2,4]=>11
[5,4,7,1,3,8,2,6]=>8
[5,6,2,1,4,8,3,7]=>9
[2,1,8,4,7,5,6,3]=>24
[4,1,3,2,8,5,6,7]=>13
[3,2,1,4,8,5,6,7]=>12
[1,8,4,2,5,3,6,7]=>10
[8,1,5,3,2,4,6,7]=>4
[3,8,1,5,2,4,6,7]=>7
[1,6,7,2,8,4,3,5]=>16
[6,7,1,4,2,8,3,5]=>7
[6,3,7,1,4,8,2,5]=>7
[3,7,8,1,5,2,4,6]=>9
[7,1,2,8,5,3,4,6]=>12
[1,7,2,8,4,5,3,6]=>17
[1,2,7,5,8,3,4,6]=>19
[2,8,1,7,4,3,6,5]=>19
[4,2,6,5,8,3,7,1]=>9
[5,2,4,7,3,6,8,1]=>5
[5,1,2,4,8,3,6,7]=>12
[4,3,6,1,5,8,2,7]=>9
[2,6,1,4,5,8,3,7]=>14
[2,5,3,4,1,8,6,7]=>12
[4,3,5,2,1,8,6,7]=>10
[3,1,6,7,5,8,2,4]=>16
[2,8,1,7,5,6,3,4]=>21
[5,3,6,8,4,7,2,1]=>5
[3,7,2,5,4,8,6,1]=>9
[8,4,2,5,7,3,6,1]=>5
[4,7,2,5,8,3,6,1]=>7
[5,2,6,8,4,3,7,1]=>8
[3,1,6,5,4,8,2,7]=>15
[4,1,6,5,8,3,2,7]=>13
[5,1,6,8,4,3,2,7]=>12
[8,5,4,7,6,3,2,1]=>2
[5,7,1,8,4,3,2,6]=>9
[2,7,1,5,4,3,8,6]=>15
[8,2,1,5,4,3,7,6]=>11
[8,4,1,5,7,3,2,6]=>8
[8,5,6,7,1,3,2,4]=>1
[8,4,6,1,7,3,2,5]=>6
[8,3,6,1,4,7,2,5]=>7
[2,7,6,1,4,3,8,5]=>13
[6,7,8,5,1,3,2,4]=>1
[5,7,6,8,2,3,4,1]=>1
[5,7,2,8,4,3,6,1]=>6
[6,7,8,2,4,3,5,1]=>1
[4,7,6,2,8,3,5,1]=>6
[8,3,6,2,4,7,5,1]=>5
[3,7,6,2,4,8,5,1]=>8
[5,7,3,8,4,6,2,1]=>4
[4,7,3,5,8,6,2,1]=>5
[8,7,2,1,4,3,6,5]=>6
[8,7,3,1,4,6,2,5]=>5
[8,7,6,3,2,5,4,1]=>2
[8,7,3,5,1,6,2,4]=>4
[8,7,2,5,1,3,6,4]=>5
[8,2,6,5,1,3,7,4]=>8
[8,4,6,5,7,1,2,3]=>1
[5,7,6,8,4,1,2,3]=>1
[4,7,6,5,8,1,2,3]=>3
[3,7,6,5,1,8,2,4]=>9
[2,6,5,7,3,4,8,1]=>7
[1,6,4,7,5,8,2,3]=>14
[8,5,3,6,2,7,4,1]=>3
[1,3,7,4,6,8,2,5]=>17
[4,7,5,6,3,2,8,1]=>2
[1,7,6,5,4,8,2,3]=>16
[8,1,6,5,7,2,4,3]=>12
[1,2,7,6,8,3,4,5]=>20
[6,1,7,5,3,8,2,4]=>11
[2,1,7,5,6,8,3,4]=>20
[5,4,1,7,6,8,2,3]=>9
[4,8,5,6,2,7,3,1]=>4
[3,8,6,4,2,7,5,1]=>9
[7,8,5,2,4,6,3,1]=>2
[2,8,6,3,7,4,5,1]=>12
[7,8,1,6,2,4,5,3]=>8
[6,8,1,4,7,2,5,3]=>9
[3,8,4,1,7,2,6,5]=>15
[5,4,7,1,8,3,2,6]=>8
[3,7,4,1,8,5,2,6]=>11
[6,7,1,4,8,3,2,5]=>7
[2,7,1,8,4,5,3,6]=>16
[6,1,2,8,4,3,5,7]=>11
[6,5,1,4,3,8,2,7]=>9
[1,6,2,5,8,3,4,7]=>16
[8,5,1,3,7,2,6,4]=>10
[8,4,2,1,7,3,6,5]=>12
[7,4,2,1,8,5,3,6]=>10
[1,5,4,2,8,3,6,7]=>15
[6,4,3,1,5,8,2,7]=>7
[3,7,6,8,4,5,2,1]=>7
[2,7,6,8,5,3,4,1]=>12
[1,7,6,8,5,4,2,3]=>18
[1,4,8,6,7,5,2,3]=>20
[2,4,8,6,7,3,5,1]=>14
[7,3,8,5,4,6,2,1]=>4
[3,4,8,5,6,7,2,1]=>6
[6,3,5,8,4,7,2,1]=>5
[5,4,3,8,6,7,2,1]=>6
[5,4,2,8,7,3,6,1]=>11
[6,2,5,8,7,3,4,1]=>9
[3,2,8,5,7,4,6,1]=>15
[1,3,8,7,5,6,2,4]=>23
[2,1,8,7,4,6,3,5]=>25
[3,1,8,5,7,6,2,4]=>21
[6,1,5,8,7,4,2,3]=>14
[5,4,1,8,7,6,2,3]=>15
[5,8,6,7,4,3,2,1]=>2
[4,8,7,5,6,3,2,1]=>5
[2,8,3,1,5,4,6,7]=>8
[2,5,3,4,7,1,8,6]=>11
[2,4,8,3,5,7,6,1]=>12
[4,2,5,3,1,8,6,7]=>11
[4,2,1,8,5,3,6,7]=>13
[5,4,1,3,8,2,6,7]=>10
[5,1,4,8,3,2,6,7]=>11
[1,5,8,4,3,2,6,7]=>13
[1,8,5,4,3,2,6,7]=>12
[1,7,4,3,8,5,2,6]=>16
[1,5,7,3,8,4,2,6]=>16
[5,1,4,7,8,3,2,6]=>13
[4,8,1,5,7,3,6,2]=>12
[8,1,5,3,7,4,6,2]=>12
[3,8,4,7,6,5,2,1]=>10
[1,6,8,5,3,7,4,2]=>18
[6,8,1,7,4,3,5,2]=>9
[6,4,8,1,7,3,5,2]=>9
[6,4,8,7,1,5,2,3]=>6
[7,6,4,1,3,8,2,5]=>5
[1,7,5,6,3,2,8,4]=>15
[4,2,1,7,8,5,3,6]=>18
[2,7,4,6,3,1,8,5]=>12
[2,6,8,4,3,7,5,1]=>12
[6,2,4,8,3,7,5,1]=>10
[7,2,6,3,4,1,8,5]=>7
[2,6,7,3,1,4,8,5]=>10
[2,7,1,8,3,5,4,6]=>15
[2,1,7,3,5,8,4,6]=>18
[8,7,1,3,6,2,4,5]=>6
[8,2,1,7,3,5,6,4]=>14
[7,8,2,6,3,1,5,4]=>6
[8,7,2,6,3,5,4,1]=>5
[1,2,8,7,4,5,6,3]=>24
[8,3,7,1,5,6,2,4]=>9
[8,6,1,2,7,5,3,4]=>10
[8,1,6,2,7,4,5,3]=>14
[1,8,5,2,6,7,4,3]=>19
[5,2,1,8,6,7,4,3]=>20
[2,8,5,7,6,4,3,1]=>14
[1,7,8,5,2,6,4,3]=>19
[7,8,1,6,4,2,5,3]=>8
[7,8,6,1,5,3,2,4]=>4
[7,3,8,6,1,5,2,4]=>8
[8,7,6,1,5,3,4,2]=>5
[8,7,1,6,4,5,3,2]=>9
[8,1,7,5,6,4,3,2]=>14
[1,8,6,7,5,4,3,2]=>20
[9,1,2,3,4,5,6,7,8]=>0
[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]=>0
[8,9,1,2,3,4,5,6,7]=>0
[9,7,8,1,2,3,4,5,6]=>0
[2,3,4,5,6,7,9,1,8]=>6
[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]=>7
[2,1,3,4,5,6,7,8,9]=>0
[1,8,2,3,4,5,6,9,7]=>12
[7,1,2,3,4,5,6,9,8]=>7
[2,1,9,3,4,5,6,7,8]=>12
[2,8,1,3,4,5,6,7,9]=>5
[1,2,3,4,5,6,7,8,9]=>0
[3,2,4,5,6,7,8,9,1]=>0
[9,8,7,6,5,4,3,2,1]=>0
[8,7,6,5,4,3,2,1,9]=>0
[1,9,8,7,6,5,4,3,2]=>28
[8,7,6,4,5,3,2,1,9]=>0
[1,9,8,7,5,6,4,3,2]=>27
[8,7,5,4,6,3,2,1,9]=>0
[8,7,4,6,5,3,2,1,9]=>1
[1,9,8,6,5,7,4,3,2]=>26
[1,9,8,5,7,6,4,3,2]=>27
[9,2,1,3,4,5,6,7,8]=>0
[9,2,3,1,4,5,6,7,8]=>0
[4,2,3,5,6,7,8,9,1]=>0
[3,4,2,5,6,7,8,9,1]=>0
[9,8,1,2,3,4,5,6,7]=>0
[7,8,9,1,2,3,4,5,6]=>0
[9,8,7,1,2,3,4,5,6]=>0
[6,7,8,9,1,2,3,4,5]=>0
[9,6,7,8,1,2,3,4,5]=>0
[8,9,6,7,1,2,3,4,5]=>0
[9,8,6,7,1,2,3,4,5]=>0
[9,8,7,6,1,2,3,4,5]=>0
[9,5,6,7,8,1,2,3,4]=>0
[8,9,5,6,7,1,2,3,4]=>0
[9,8,5,6,7,1,2,3,4]=>0
[9,7,8,5,6,1,2,3,4]=>0
[9,8,7,5,6,1,2,3,4]=>0
[9,8,7,6,5,1,2,3,4]=>0
[7,8,9,4,5,6,1,2,3]=>0
[9,7,8,4,5,6,1,2,3]=>0
[9,8,7,4,5,6,1,2,3]=>0
[8,9,6,7,4,5,1,2,3]=>0
[9,8,6,7,4,5,1,2,3]=>0
[9,8,7,6,4,5,1,2,3]=>0
[9,8,7,6,5,4,1,2,3]=>0
[9,7,8,5,6,3,4,1,2]=>0
[9,8,7,5,6,3,4,1,2]=>0
[9,8,7,6,5,3,4,1,2]=>0
[9,8,7,6,5,4,3,1,2]=>0
[7,8,6,5,4,3,2,1,9]=>0
[1,8,9,7,6,5,4,3,2]=>27
[7,6,8,5,4,3,2,1,9]=>0
[6,8,7,5,4,3,2,1,9]=>1
[1,8,7,9,6,5,4,3,2]=>26
[1,7,9,8,6,5,4,3,2]=>27
[8,1,2,3,4,5,6,7,9]=>0
[1,9,2,3,4,5,6,7,8]=>7
[7,8,1,2,3,4,5,6,9]=>0
[1,8,9,2,3,4,5,6,7]=>12
[7,1,8,2,3,4,5,6,9]=>5
[6,8,1,2,3,4,5,7,9]=>1
[1,8,2,9,3,4,5,6,7]=>16
[1,7,9,2,3,4,5,6,8]=>12
[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]=>0
[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]=>0
[5,6,7,8,1,2,3,4,9]=>0
[5,2,6,7,1,3,4,8,9]=>4
[5,6,3,4,1,2,7,8,9]=>0
[5,3,2,6,1,4,7,8,9]=>2
[5,4,3,2,1,6,7,8,9]=>0
[6,2,7,8,9,1,3,4,5]=>9
[6,7,3,4,8,1,2,5,9]=>2
[6,3,2,7,8,1,4,5,9]=>8
[6,4,7,2,5,1,3,8,9]=>2
[6,4,3,2,7,1,5,8,9]=>3
[6,5,4,3,2,1,7,8,9]=>0
[7,4,8,2,5,9,1,3,6]=>7
[7,4,3,2,8,9,1,5,6]=>12
[7,8,5,6,3,4,1,2,9]=>0
[7,5,3,8,2,6,1,4,9]=>5
[7,5,4,3,2,8,1,6,9]=>4
[7,6,5,4,3,2,1,8,9]=>0
[8,6,9,4,7,2,5,1,3]=>3
[8,6,4,3,9,2,7,1,5]=>8
[8,6,5,4,3,2,9,1,7]=>5
[2,1,4,3,6,5,8,7,10,9]=>20
[4,3,2,1,6,5,8,7,10,9]=>18
[6,3,2,5,4,1,8,7,10,9]=>16
[8,3,2,5,4,7,6,1,10,9]=>14
[10,3,2,5,4,7,6,9,8,1]=>12
[2,1,6,5,4,3,8,7,10,9]=>26
[6,5,4,3,2,1,8,7,10,9]=>14
[8,5,4,3,2,7,6,1,10,9]=>12
[10,5,4,3,2,7,6,9,8,1]=>10
[2,1,8,5,4,7,6,3,10,9]=>32
[8,7,4,3,6,5,2,1,10,9]=>10
[10,7,4,3,6,5,2,9,8,1]=>8
[2,1,10,5,4,7,6,9,8,3]=>38
[10,9,4,3,6,5,8,7,2,1]=>6
[8,9,5,6,3,4,10,1,2,7]=>4
[2,1,4,3,8,7,6,5,10,9]=>34
[4,3,2,1,8,7,6,5,10,9]=>32
[8,3,2,7,6,5,4,1,10,9]=>20
[10,3,2,7,6,5,4,9,8,1]=>18
[2,1,8,7,6,5,4,3,10,9]=>38
[8,7,6,5,4,3,2,1,10,9]=>8
[9,7,6,5,4,3,2,10,1,8]=>6
[10,7,6,5,4,3,2,9,8,1]=>6
[2,1,10,7,6,5,4,9,8,3]=>44
[10,9,6,5,4,3,8,7,2,1]=>4
[2,1,4,3,10,7,6,9,8,5]=>48
[4,3,2,1,10,7,6,9,8,5]=>46
[10,3,2,9,6,5,8,7,4,1]=>24
[2,1,10,9,6,5,8,7,4,3]=>50
[10,9,8,5,4,7,6,3,2,1]=>2
[6,7,8,9,10,1,2,3,4,5]=>0
[7,3,2,8,9,10,1,4,5,6]=>18
[8,5,4,3,2,9,10,1,6,7]=>16
[2,1,4,3,6,5,10,9,8,7]=>42
[4,3,2,1,6,5,10,9,8,7]=>40
[6,3,2,5,4,1,10,9,8,7]=>38
[10,3,2,5,4,9,8,7,6,1]=>26
[2,1,6,5,4,3,10,9,8,7]=>48
[6,5,4,3,2,1,10,9,8,7]=>36
[10,5,4,3,2,9,8,7,6,1]=>24
[2,1,10,5,4,9,8,7,6,3]=>52
[10,9,4,3,8,7,6,5,2,1]=>12
[9,7,5,10,3,8,2,6,1,4]=>8
[2,1,4,3,10,9,8,7,6,5]=>62
[4,3,2,1,10,9,8,7,6,5]=>60
[10,3,2,9,8,7,6,5,4,1]=>30
[2,1,10,9,8,7,6,5,4,3]=>56
[10,9,8,7,6,5,4,3,2,1]=>0
[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]=>0
[10,8,9,4,5,6,1,2,3,7]=>0
[10,7,8,5,6,9,1,2,3,4]=>0
[10,7,8,4,5,9,1,2,3,6]=>2
[10,6,7,4,5,8,1,2,3,9]=>0
[10,7,8,3,4,9,1,2,5,6]=>4
[10,6,7,3,4,8,1,2,5,9]=>2
[9,8,10,5,6,7,1,2,3,4]=>0
[9,8,10,4,5,6,1,2,3,7]=>0
[9,7,10,5,6,8,1,2,3,4]=>1
[9,7,10,4,5,8,1,2,3,6]=>3
[9,6,10,4,5,7,1,2,3,8]=>2
[9,7,10,3,4,8,1,2,5,6]=>5
[9,6,10,3,4,7,1,2,5,8]=>4
[8,7,9,5,6,10,1,2,3,4]=>0
[8,7,9,4,5,10,1,2,3,6]=>2
[8,6,9,4,5,10,1,2,3,7]=>4
[7,6,8,4,5,9,1,2,3,10]=>0
[8,7,9,3,4,10,1,2,5,6]=>4
[8,6,9,3,4,10,1,2,5,7]=>6
[7,6,8,3,4,9,1,2,5,10]=>2
[9,6,10,5,7,8,1,2,3,4]=>2
[9,6,10,4,7,8,1,2,3,5]=>4
[9,5,10,4,6,7,1,2,3,8]=>3
[9,6,10,3,7,8,1,2,4,5]=>6
[9,5,10,3,6,7,1,2,4,8]=>5
[8,6,9,5,7,10,1,2,3,4]=>1
[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]=>1
[8,6,9,3,7,10,1,2,4,5]=>5
[8,5,9,3,6,10,1,2,4,7]=>7
[7,5,8,3,6,9,1,2,4,10]=>3
[8,4,9,3,5,10,1,2,6,7]=>9
[7,4,8,3,5,9,1,2,6,10]=>5
[9,6,10,2,7,8,1,3,4,5]=>8
[9,5,10,2,6,7,1,3,4,8]=>7
[8,6,9,2,7,10,1,3,4,5]=>7
[8,5,9,2,6,10,1,3,4,7]=>9
[7,5,8,2,6,9,1,3,4,10]=>5
[8,4,9,2,5,10,1,3,6,7]=>11
[7,4,8,2,5,9,1,3,6,10]=>7
[1,2,3,4,5,6,7,8,10,9]=>8
[2,1,3,4,5,6,7,8,9,10]=>0
[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]=>0
[9,8,7,6,5,4,3,2,1,10]=>0
[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,1,2,3,4,5,6,7,8]=>0
[1,10,9,8,7,6,5,4,3,2]=>36
[9,8,7,5,6,4,3,2,1,10]=>0
[1,10,9,8,6,7,5,4,3,2]=>35
[10,2,1,3,4,5,6,7,8,9]=>0
[3,2,4,5,6,7,8,9,10,1]=>0
[2,4,6,8,10,1,3,5,7,9]=>20
[2,4,6,9,10,1,3,5,7,8]=>22
[2,4,7,8,10,1,3,5,6,9]=>20
[2,4,7,9,10,1,3,5,6,8]=>22
[2,4,8,9,10,1,3,5,6,7]=>22
[2,5,6,8,10,1,3,4,7,9]=>18
[2,5,6,9,10,1,3,4,7,8]=>20
[2,5,7,8,10,1,3,4,6,9]=>18
[2,5,7,9,10,1,3,4,6,8]=>20
[2,5,8,9,10,1,3,4,6,7]=>20
[2,6,7,8,10,1,3,4,5,9]=>16
[2,6,7,9,10,1,3,4,5,8]=>18
[2,6,8,9,10,1,3,4,5,7]=>18
[2,7,8,9,10,1,3,4,5,6]=>16
[3,4,6,8,10,1,2,5,7,9]=>16
[3,4,6,9,10,1,2,5,7,8]=>18
[3,4,7,8,10,1,2,5,6,9]=>16
[3,4,7,9,10,1,2,5,6,8]=>18
[3,4,8,9,10,1,2,5,6,7]=>18
[3,5,6,8,10,1,2,4,7,9]=>14
[3,5,6,9,10,1,2,4,7,8]=>16
[3,5,7,8,10,1,2,4,6,9]=>14
[3,5,7,9,10,1,2,4,6,8]=>16
[3,5,8,9,10,1,2,4,6,7]=>16
[3,6,7,8,10,1,2,4,5,9]=>12
[3,6,7,9,10,1,2,4,5,8]=>14
[3,6,8,9,10,1,2,4,5,7]=>14
[3,7,8,9,10,1,2,4,5,6]=>12
[4,5,6,8,10,1,2,3,7,9]=>10
[4,5,6,9,10,1,2,3,7,8]=>12
[4,5,7,8,10,1,2,3,6,9]=>10
[4,5,7,9,10,1,2,3,6,8]=>12
[4,5,8,9,10,1,2,3,6,7]=>12
[4,6,7,8,10,1,2,3,5,9]=>8
[4,6,7,9,10,1,2,3,5,8]=>10
[4,6,8,9,10,1,2,3,5,7]=>10
[4,7,8,9,10,1,2,3,5,6]=>8
[5,6,7,8,10,1,2,3,4,9]=>4
[5,6,7,9,10,1,2,3,4,8]=>6
[5,6,8,9,10,1,2,3,4,7]=>6
[5,7,8,9,10,1,2,3,4,6]=>4
[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]=>0
[10,9,8,1,2,3,4,5,6,7]=>0
[7,8,9,10,1,2,3,4,5,6]=>0
[10,7,8,9,1,2,3,4,5,6]=>0
[9,10,7,8,1,2,3,4,5,6]=>0
[10,9,7,8,1,2,3,4,5,6]=>0
[10,9,8,7,1,2,3,4,5,6]=>0
[10,6,7,8,9,1,2,3,4,5]=>0
[9,10,6,7,8,1,2,3,4,5]=>0
[10,9,6,7,8,1,2,3,4,5]=>0
[10,8,9,6,7,1,2,3,4,5]=>0
[10,9,8,6,7,1,2,3,4,5]=>0
[10,9,8,7,6,1,2,3,4,5]=>0
[9,10,5,6,7,8,1,2,3,4]=>0
[10,9,5,6,7,8,1,2,3,4]=>0
[8,9,10,5,6,7,1,2,3,4]=>0
[10,9,8,5,6,7,1,2,3,4]=>0
[9,10,7,8,5,6,1,2,3,4]=>0
[10,9,7,8,5,6,1,2,3,4]=>0
[10,9,8,7,5,6,1,2,3,4]=>0
[10,9,8,7,6,5,1,2,3,4]=>0
[10,7,8,9,4,5,6,1,2,3]=>0
[9,10,7,8,4,5,6,1,2,3]=>0
[10,9,7,8,4,5,6,1,2,3]=>0
[10,9,8,7,4,5,6,1,2,3]=>0
[10,8,9,6,7,4,5,1,2,3]=>0
[10,9,8,6,7,4,5,1,2,3]=>0
[10,9,8,7,6,4,5,1,2,3]=>0
[10,9,8,7,6,5,4,1,2,3]=>0
[9,10,7,8,5,6,3,4,1,2]=>0
[10,9,7,8,5,6,3,4,1,2]=>0
[10,9,8,7,5,6,3,4,1,2]=>0
[10,9,8,7,6,5,3,4,1,2]=>0
[10,9,8,7,6,5,4,3,1,2]=>0
[8,9,7,6,5,4,3,2,1,10]=>0
[1,9,10,8,7,6,5,4,3,2]=>35
[9,1,2,3,4,5,6,7,8,10]=>0
[1,10,2,3,4,5,6,7,8,9]=>8
[8,9,1,2,3,4,5,6,7,10]=>0
[1,9,10,2,3,4,5,6,7,8]=>14
[3,4,1,2,5,6,7,8,9,10]=>0
[3,2,1,4,5,6,7,8,9,10]=>0
[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]=>0
[5,6,7,8,1,2,3,4,9,10]=>0
[5,2,6,7,1,3,4,8,9,10]=>4
[5,6,3,4,1,2,7,8,9,10]=>0
[5,3,2,6,1,4,7,8,9,10]=>2
[5,4,3,2,1,6,7,8,9,10]=>0
[6,2,7,8,9,1,3,4,5,10]=>9
[6,7,3,4,8,1,2,5,9,10]=>2
[6,3,2,7,8,1,4,5,9,10]=>8
[6,4,7,2,5,1,3,8,9,10]=>2
[6,4,3,2,7,1,5,8,9,10]=>3
[6,5,4,3,2,1,7,8,9,10]=>0
[7,8,3,4,9,10,1,2,5,6]=>8
[7,8,9,4,5,6,1,2,3,10]=>0
[7,4,3,2,8,9,1,5,6,10]=>12
[7,8,5,6,3,4,1,2,9,10]=>0
[7,5,3,8,2,6,1,4,9,10]=>5
[7,5,4,3,2,8,1,6,9,10]=>4
[7,6,5,4,3,2,1,8,9,10]=>0
[8,5,9,10,2,6,7,1,3,4]=>8
[8,5,3,9,2,6,10,1,4,7]=>13
[8,6,9,4,7,2,5,1,3,10]=>3
[8,6,4,3,9,2,7,1,5,10]=>8
[8,6,5,4,3,2,9,1,7,10]=>5
[8,7,6,5,4,3,2,1,9,10]=>0
[9,7,5,4,3,10,2,8,1,6]=>11
[1,2,3,4,5,6,7,8,9,11,10]=>9
[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]=>0
[1,11,10,9,8,7,6,5,4,3,2]=>45
[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]=>9
[2,1,4,3,6,5,8,7,10,9,12,11]=>30
[2,1,4,3,6,5,8,7,12,11,10,9]=>60
[2,1,4,3,6,5,10,9,8,7,12,11]=>52
[2,1,4,3,6,5,12,9,8,11,10,7]=>74
[2,1,4,3,6,5,12,11,10,9,8,7]=>96
[2,1,4,3,8,7,6,5,10,9,12,11]=>44
[2,1,4,3,8,7,6,5,12,11,10,9]=>74
[2,1,4,3,10,7,6,9,8,5,12,11]=>58
[2,1,4,3,12,7,6,9,8,11,10,5]=>72
[2,1,4,3,12,7,6,11,10,9,8,5]=>94
[2,1,4,3,10,9,8,7,6,5,12,11]=>72
[2,1,4,3,12,9,8,7,6,11,10,5]=>86
[2,1,4,3,12,11,8,7,10,9,6,5]=>100
[2,1,4,3,12,11,10,9,8,7,6,5]=>114
[2,1,6,5,4,3,8,7,10,9,12,11]=>36
[2,1,6,5,4,3,8,7,12,11,10,9]=>66
[2,1,6,5,4,3,10,9,8,7,12,11]=>58
[2,1,6,5,4,3,12,9,8,11,10,7]=>80
[2,1,6,5,4,3,12,11,10,9,8,7]=>102
[2,1,8,5,4,7,6,3,10,9,12,11]=>42
[2,1,8,5,4,7,6,3,12,11,10,9]=>72
[2,1,10,5,4,7,6,9,8,3,12,11]=>48
[2,1,12,5,4,7,6,9,8,11,10,3]=>54
[2,1,12,5,4,7,6,11,10,9,8,3]=>76
[2,1,10,5,4,9,8,7,6,3,12,11]=>62
[2,1,12,5,4,9,8,7,6,11,10,3]=>68
[2,1,12,5,4,11,8,7,10,9,6,3]=>82
[2,1,12,5,4,11,10,9,8,7,6,3]=>96
[2,1,8,7,6,5,4,3,10,9,12,11]=>48
[2,1,8,7,6,5,4,3,12,11,10,9]=>78
[2,1,10,7,6,5,4,9,8,3,12,11]=>54
[2,1,12,7,6,5,4,9,8,11,10,3]=>60
[2,1,12,7,6,5,4,11,10,9,8,3]=>82
[2,1,10,9,6,5,8,7,4,3,12,11]=>60
[2,1,12,9,6,5,8,7,4,11,10,3]=>66
[2,1,12,11,6,5,8,7,10,9,4,3]=>72
[2,1,12,11,6,5,10,9,8,7,4,3]=>86
[2,1,10,9,8,7,6,5,4,3,12,11]=>66
[2,1,12,9,8,7,6,5,4,11,10,3]=>72
[2,1,12,11,8,7,6,5,10,9,4,3]=>78
[2,1,12,11,10,7,6,9,8,5,4,3]=>84
[2,1,12,11,10,9,8,7,6,5,4,3]=>90
[4,3,2,1,6,5,8,7,10,9,12,11]=>28
[4,3,2,1,6,5,8,7,12,11,10,9]=>58
[4,3,2,1,6,5,10,9,8,7,12,11]=>50
[4,3,2,1,6,5,12,9,8,11,10,7]=>72
[4,3,2,1,6,5,12,11,10,9,8,7]=>94
[4,3,2,1,8,7,6,5,10,9,12,11]=>42
[4,3,2,1,8,7,6,5,12,11,10,9]=>72
[4,3,2,1,10,7,6,9,8,5,12,11]=>56
[4,3,2,1,12,7,6,9,8,11,10,5]=>70
[4,3,2,1,12,7,6,11,10,9,8,5]=>92
[4,3,2,1,10,9,8,7,6,5,12,11]=>70
[4,3,2,1,12,9,8,7,6,11,10,5]=>84
[4,3,2,1,12,11,8,7,10,9,6,5]=>98
[4,3,2,1,12,11,10,9,8,7,6,5]=>112
[6,3,2,5,4,1,8,7,10,9,12,11]=>26
[6,3,2,5,4,1,8,7,12,11,10,9]=>56
[6,3,2,5,4,1,10,9,8,7,12,11]=>48
[6,3,2,5,4,1,12,9,8,11,10,7]=>70
[6,3,2,5,4,1,12,11,10,9,8,7]=>92
[8,3,2,5,4,7,6,1,10,9,12,11]=>24
[8,3,2,5,4,7,6,1,12,11,10,9]=>54
[10,3,2,5,4,7,6,9,8,1,12,11]=>22
[12,3,2,5,4,7,6,9,8,11,10,1]=>20
[12,3,2,5,4,7,6,11,10,9,8,1]=>42
[10,3,2,5,4,9,8,7,6,1,12,11]=>36
[12,3,2,5,4,9,8,7,6,11,10,1]=>34
[12,3,2,5,4,11,8,7,10,9,6,1]=>48
[12,3,2,5,4,11,10,9,8,7,6,1]=>62
[8,3,2,7,6,5,4,1,10,9,12,11]=>30
[8,3,2,7,6,5,4,1,12,11,10,9]=>60
[10,3,2,7,6,5,4,9,8,1,12,11]=>28
[12,3,2,7,6,5,4,9,8,11,10,1]=>26
[12,3,2,7,6,5,4,11,10,9,8,1]=>48
[10,3,2,9,6,5,8,7,4,1,12,11]=>34
[12,3,2,9,6,5,8,7,4,11,10,1]=>32
[12,3,2,11,6,5,8,7,10,9,4,1]=>38
[12,3,2,11,6,5,10,9,8,7,4,1]=>52
[10,3,2,9,8,7,6,5,4,1,12,11]=>40
[12,3,2,9,8,7,6,5,4,11,10,1]=>38
[12,3,2,11,8,7,6,5,10,9,4,1]=>44
[12,3,2,11,10,7,6,9,8,5,4,1]=>50
[12,3,2,11,10,9,8,7,6,5,4,1]=>56
[6,5,4,3,2,1,8,7,10,9,12,11]=>24
[6,5,4,3,2,1,8,7,12,11,10,9]=>54
[6,5,4,3,2,1,10,9,8,7,12,11]=>46
[6,5,4,3,2,1,12,9,8,11,10,7]=>68
[6,5,4,3,2,1,12,11,10,9,8,7]=>90
[8,5,4,3,2,7,6,1,10,9,12,11]=>22
[8,5,4,3,2,7,6,1,12,11,10,9]=>52
[10,5,4,3,2,7,6,9,8,1,12,11]=>20
[12,5,4,3,2,7,6,9,8,11,10,1]=>18
[12,5,4,3,2,7,6,11,10,9,8,1]=>40
[10,5,4,3,2,9,8,7,6,1,12,11]=>34
[12,5,4,3,2,9,8,7,6,11,10,1]=>32
[12,5,4,3,2,11,8,7,10,9,6,1]=>46
[12,5,4,3,2,11,10,9,8,7,6,1]=>60
[8,7,4,3,6,5,2,1,10,9,12,11]=>20
[8,7,4,3,6,5,2,1,12,11,10,9]=>50
[10,7,4,3,6,5,2,9,8,1,12,11]=>18
[12,7,4,3,6,5,2,9,8,11,10,1]=>16
[12,7,4,3,6,5,2,11,10,9,8,1]=>38
[10,9,4,3,6,5,8,7,2,1,12,11]=>16
[12,9,4,3,6,5,8,7,2,11,10,1]=>14
[12,11,4,3,6,5,8,7,10,9,2,1]=>12
[12,11,4,3,6,5,10,9,8,7,2,1]=>26
[10,9,4,3,8,7,6,5,2,1,12,11]=>22
[12,9,4,3,8,7,6,5,2,11,10,1]=>20
[12,11,4,3,8,7,6,5,10,9,2,1]=>18
[12,11,4,3,10,7,6,9,8,5,2,1]=>24
[12,11,4,3,10,9,8,7,6,5,2,1]=>30
[8,7,6,5,4,3,2,1,10,9,12,11]=>18
[8,7,6,5,4,3,2,1,12,11,10,9]=>48
[10,7,6,5,4,3,2,9,8,1,12,11]=>16
[12,7,6,5,4,3,2,9,8,11,10,1]=>14
[12,7,6,5,4,3,2,11,10,9,8,1]=>36
[10,9,6,5,4,3,8,7,2,1,12,11]=>14
[12,9,6,5,4,3,8,7,2,11,10,1]=>12
[12,11,6,5,4,3,8,7,10,9,2,1]=>10
[12,11,6,5,4,3,10,9,8,7,2,1]=>24
[10,9,8,5,4,7,6,3,2,1,12,11]=>12
[12,9,8,5,4,7,6,3,2,11,10,1]=>10
[12,11,8,5,4,7,6,3,10,9,2,1]=>8
[12,11,10,5,4,7,6,9,8,3,2,1]=>6
[12,11,10,5,4,9,8,7,6,3,2,1]=>12
[10,9,8,7,6,5,4,3,2,1,12,11]=>10
[12,9,8,7,6,5,4,3,2,11,10,1]=>8
[12,11,8,7,6,5,4,3,10,9,2,1]=>6
[12,11,10,7,6,5,4,9,8,3,2,1]=>4
[12,11,10,9,6,5,8,7,4,3,2,1]=>2
[12,11,10,9,8,7,6,5,4,3,2,1]=>0
[2,4,6,8,10,12,1,3,5,7,9,11]=>35
[2,4,6,8,11,12,1,3,5,7,9,10]=>38
[2,4,6,9,10,12,1,3,5,7,8,11]=>36
[2,4,6,9,11,12,1,3,5,7,8,10]=>39
[2,4,6,10,11,12,1,3,5,7,8,9]=>40
[2,4,7,8,10,12,1,3,5,6,9,11]=>34
[2,4,7,8,11,12,1,3,5,6,9,10]=>37
[2,4,7,9,10,12,1,3,5,6,8,11]=>35
[2,4,7,9,11,12,1,3,5,6,8,10]=>38
[2,4,7,10,11,12,1,3,5,6,8,9]=>39
[2,4,8,9,10,12,1,3,5,6,7,11]=>34
[2,4,8,9,11,12,1,3,5,6,7,10]=>37
[2,4,8,10,11,12,1,3,5,6,7,9]=>38
[2,4,9,10,11,12,1,3,5,6,7,8]=>37
[2,5,6,8,10,12,1,3,4,7,9,11]=>32
[2,5,6,8,11,12,1,3,4,7,9,10]=>35
[2,5,6,9,10,12,1,3,4,7,8,11]=>33
[2,5,6,9,11,12,1,3,4,7,8,10]=>36
[2,5,6,10,11,12,1,3,4,7,8,9]=>37
[2,5,7,8,10,12,1,3,4,6,9,11]=>31
[2,5,7,8,11,12,1,3,4,6,9,10]=>34
[2,5,7,9,10,12,1,3,4,6,8,11]=>32
[2,5,7,9,11,12,1,3,4,6,8,10]=>35
[2,5,7,10,11,12,1,3,4,6,8,9]=>36
[2,5,8,9,10,12,1,3,4,6,7,11]=>31
[2,5,8,9,11,12,1,3,4,6,7,10]=>34
[2,5,8,10,11,12,1,3,4,6,7,9]=>35
[2,5,9,10,11,12,1,3,4,6,7,8]=>34
[2,6,7,8,10,12,1,3,4,5,9,11]=>28
[2,6,7,8,11,12,1,3,4,5,9,10]=>31
[2,6,7,9,10,12,1,3,4,5,8,11]=>29
[2,6,7,9,11,12,1,3,4,5,8,10]=>32
[2,6,7,10,11,12,1,3,4,5,8,9]=>33
[2,6,8,9,10,12,1,3,4,5,7,11]=>28
[2,6,8,9,11,12,1,3,4,5,7,10]=>31
[2,6,8,10,11,12,1,3,4,5,7,9]=>32
[2,6,9,10,11,12,1,3,4,5,7,8]=>31
[2,7,8,9,10,12,1,3,4,5,6,11]=>25
[2,7,8,9,11,12,1,3,4,5,6,10]=>28
[2,7,8,10,11,12,1,3,4,5,6,9]=>29
[2,7,9,10,11,12,1,3,4,5,6,8]=>28
[2,8,9,10,11,12,1,3,4,5,6,7]=>25
[3,4,6,8,10,12,1,2,5,7,9,11]=>30
[3,4,6,8,11,12,1,2,5,7,9,10]=>33
[3,4,6,9,10,12,1,2,5,7,8,11]=>31
[3,4,6,9,11,12,1,2,5,7,8,10]=>34
[3,4,6,10,11,12,1,2,5,7,8,9]=>35
[3,4,7,8,10,12,1,2,5,6,9,11]=>29
[3,4,7,8,11,12,1,2,5,6,9,10]=>32
[3,4,7,9,10,12,1,2,5,6,8,11]=>30
[3,4,7,9,11,12,1,2,5,6,8,10]=>33
[3,4,7,10,11,12,1,2,5,6,8,9]=>34
[3,4,8,9,10,12,1,2,5,6,7,11]=>29
[3,4,8,9,11,12,1,2,5,6,7,10]=>32
[3,4,8,10,11,12,1,2,5,6,7,9]=>33
[3,4,9,10,11,12,1,2,5,6,7,8]=>32
[3,5,6,8,10,12,1,2,4,7,9,11]=>27
[3,5,6,8,11,12,1,2,4,7,9,10]=>30
[3,5,6,9,10,12,1,2,4,7,8,11]=>28
[3,5,6,9,11,12,1,2,4,7,8,10]=>31
[3,5,6,10,11,12,1,2,4,7,8,9]=>32
[3,5,7,8,10,12,1,2,4,6,9,11]=>26
[3,5,7,8,11,12,1,2,4,6,9,10]=>29
[3,5,7,9,10,12,1,2,4,6,8,11]=>27
[3,5,7,9,11,12,1,2,4,6,8,10]=>30
[3,5,7,10,11,12,1,2,4,6,8,9]=>31
[3,5,8,9,10,12,1,2,4,6,7,11]=>26
[3,5,8,9,11,12,1,2,4,6,7,10]=>29
[3,5,8,10,11,12,1,2,4,6,7,9]=>30
[3,5,9,10,11,12,1,2,4,6,7,8]=>29
[3,6,7,8,10,12,1,2,4,5,9,11]=>23
[3,6,7,8,11,12,1,2,4,5,9,10]=>26
[3,6,7,9,10,12,1,2,4,5,8,11]=>24
[3,6,7,9,11,12,1,2,4,5,8,10]=>27
[3,6,7,10,11,12,1,2,4,5,8,9]=>28
[3,6,8,9,10,12,1,2,4,5,7,11]=>23
[3,6,8,9,11,12,1,2,4,5,7,10]=>26
[3,6,8,10,11,12,1,2,4,5,7,9]=>27
[3,6,9,10,11,12,1,2,4,5,7,8]=>26
[3,7,8,9,10,12,1,2,4,5,6,11]=>20
[3,7,8,9,11,12,1,2,4,5,6,10]=>23
[3,7,8,10,11,12,1,2,4,5,6,9]=>24
[3,7,9,10,11,12,1,2,4,5,6,8]=>23
[3,8,9,10,11,12,1,2,4,5,6,7]=>20
[4,5,6,8,10,12,1,2,3,7,9,11]=>22
[4,5,6,8,11,12,1,2,3,7,9,10]=>25
[4,5,6,9,10,12,1,2,3,7,8,11]=>23
[4,5,6,9,11,12,1,2,3,7,8,10]=>26
[4,5,6,10,11,12,1,2,3,7,8,9]=>27
[4,5,7,8,10,12,1,2,3,6,9,11]=>21
[4,5,7,8,11,12,1,2,3,6,9,10]=>24
[4,5,7,9,10,12,1,2,3,6,8,11]=>22
[4,5,7,9,11,12,1,2,3,6,8,10]=>25
[4,5,7,10,11,12,1,2,3,6,8,9]=>26
[4,5,8,9,10,12,1,2,3,6,7,11]=>21
[4,5,8,9,11,12,1,2,3,6,7,10]=>24
[4,5,8,10,11,12,1,2,3,6,7,9]=>25
[4,5,9,10,11,12,1,2,3,6,7,8]=>24
[4,6,7,8,10,12,1,2,3,5,9,11]=>18
[4,6,7,8,11,12,1,2,3,5,9,10]=>21
[4,6,7,9,10,12,1,2,3,5,8,11]=>19
[4,6,7,9,11,12,1,2,3,5,8,10]=>22
[4,6,7,10,11,12,1,2,3,5,8,9]=>23
[4,6,8,9,10,12,1,2,3,5,7,11]=>18
[4,6,8,9,11,12,1,2,3,5,7,10]=>21
[4,6,8,10,11,12,1,2,3,5,7,9]=>22
[4,6,9,10,11,12,1,2,3,5,7,8]=>21
[4,7,8,9,10,12,1,2,3,5,6,11]=>15
[4,7,8,9,11,12,1,2,3,5,6,10]=>18
[4,7,8,10,11,12,1,2,3,5,6,9]=>19
[4,7,9,10,11,12,1,2,3,5,6,8]=>18
[4,8,9,10,11,12,1,2,3,5,6,7]=>15
[5,6,7,8,10,12,1,2,3,4,9,11]=>13
[5,6,7,8,11,12,1,2,3,4,9,10]=>16
[5,6,7,9,10,12,1,2,3,4,8,11]=>14
[5,6,7,9,11,12,1,2,3,4,8,10]=>17
[5,6,7,10,11,12,1,2,3,4,8,9]=>18
[5,6,8,9,10,12,1,2,3,4,7,11]=>13
[5,6,8,9,11,12,1,2,3,4,7,10]=>16
[5,6,8,10,11,12,1,2,3,4,7,9]=>17
[5,6,9,10,11,12,1,2,3,4,7,8]=>16
[5,7,8,9,10,12,1,2,3,4,6,11]=>10
[5,7,8,9,11,12,1,2,3,4,6,10]=>13
[5,7,8,10,11,12,1,2,3,4,6,9]=>14
[5,7,9,10,11,12,1,2,3,4,6,8]=>13
[5,8,9,10,11,12,1,2,3,4,6,7]=>10
[6,7,8,9,10,12,1,2,3,4,5,11]=>5
[6,7,8,9,11,12,1,2,3,4,5,10]=>8
[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]=>8
[6,8,9,10,11,12,1,2,3,4,5,7]=>5
[7,8,9,10,11,12,1,2,3,4,5,6]=>0
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Description
The number of occurrences of the pattern 132 in a permutation.
References
[1] Number of permutations on 1,...,n containing any given pattern alpha in the symmetric group S_3. OEIS:A056986
Code
def statistic(x):
return len(x.pattern_positions([1,3,2]))
Created
Sep 14, 2014 at 08:01 by Martin Rubey
Updated
Sep 14, 2018 at 19:22 by Martin Rubey
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