Identifier
- St000002: Permutations ⟶ ℤ
Values
=>
[]=>0
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>1
[1,3,2]=>0
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>0
[1,2,3,4]=>4
[1,2,4,3]=>2
[1,3,2,4]=>2
[1,3,4,2]=>1
[1,4,2,3]=>1
[1,4,3,2]=>0
[2,1,3,4]=>2
[2,1,4,3]=>0
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>0
[2,4,3,1]=>0
[3,1,2,4]=>1
[3,1,4,2]=>0
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>0
[3,4,2,1]=>0
[4,1,2,3]=>1
[4,1,3,2]=>0
[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]=>10
[1,2,3,5,4]=>7
[1,2,4,3,5]=>7
[1,2,4,5,3]=>5
[1,2,5,3,4]=>5
[1,2,5,4,3]=>3
[1,3,2,4,5]=>7
[1,3,2,5,4]=>4
[1,3,4,2,5]=>5
[1,3,4,5,2]=>4
[1,3,5,2,4]=>3
[1,3,5,4,2]=>2
[1,4,2,3,5]=>5
[1,4,2,5,3]=>3
[1,4,3,2,5]=>3
[1,4,3,5,2]=>2
[1,4,5,2,3]=>2
[1,4,5,3,2]=>1
[1,5,2,3,4]=>4
[1,5,2,4,3]=>2
[1,5,3,2,4]=>2
[1,5,3,4,2]=>1
[1,5,4,2,3]=>1
[1,5,4,3,2]=>0
[2,1,3,4,5]=>7
[2,1,3,5,4]=>4
[2,1,4,3,5]=>4
[2,1,4,5,3]=>2
[2,1,5,3,4]=>2
[2,1,5,4,3]=>0
[2,3,1,4,5]=>5
[2,3,1,5,4]=>2
[2,3,4,1,5]=>4
[2,3,4,5,1]=>4
[2,3,5,1,4]=>2
[2,3,5,4,1]=>2
[2,4,1,3,5]=>3
[2,4,1,5,3]=>1
[2,4,3,1,5]=>2
[2,4,3,5,1]=>2
[2,4,5,1,3]=>1
[2,4,5,3,1]=>1
[2,5,1,3,4]=>2
[2,5,1,4,3]=>0
[2,5,3,1,4]=>1
[2,5,3,4,1]=>1
[2,5,4,1,3]=>0
[2,5,4,3,1]=>0
[3,1,2,4,5]=>5
[3,1,2,5,4]=>2
[3,1,4,2,5]=>3
[3,1,4,5,2]=>2
[3,1,5,2,4]=>1
[3,1,5,4,2]=>0
[3,2,1,4,5]=>3
[3,2,1,5,4]=>0
[3,2,4,1,5]=>2
[3,2,4,5,1]=>2
[3,2,5,1,4]=>0
[3,2,5,4,1]=>0
[3,4,1,2,5]=>2
[3,4,1,5,2]=>1
[3,4,2,1,5]=>1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>1
[3,4,5,2,1]=>1
[3,5,1,2,4]=>1
[3,5,1,4,2]=>0
[3,5,2,1,4]=>0
[3,5,2,4,1]=>0
[3,5,4,1,2]=>0
[3,5,4,2,1]=>0
[4,1,2,3,5]=>4
[4,1,2,5,3]=>2
[4,1,3,2,5]=>2
[4,1,3,5,2]=>1
[4,1,5,2,3]=>1
[4,1,5,3,2]=>0
[4,2,1,3,5]=>2
[4,2,1,5,3]=>0
[4,2,3,1,5]=>1
[4,2,3,5,1]=>1
[4,2,5,1,3]=>0
[4,2,5,3,1]=>0
[4,3,1,2,5]=>1
[4,3,1,5,2]=>0
[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]=>1
[4,5,1,3,2]=>0
[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]=>4
[5,1,2,4,3]=>2
[5,1,3,2,4]=>2
[5,1,3,4,2]=>1
[5,1,4,2,3]=>1
[5,1,4,3,2]=>0
[5,2,1,3,4]=>2
[5,2,1,4,3]=>0
[5,2,3,1,4]=>1
[5,2,3,4,1]=>1
[5,2,4,1,3]=>0
[5,2,4,3,1]=>0
[5,3,1,2,4]=>1
[5,3,1,4,2]=>0
[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]=>1
[5,4,1,3,2]=>0
[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]=>20
[1,2,3,4,6,5]=>16
[1,2,3,5,4,6]=>16
[1,2,3,5,6,4]=>13
[1,2,3,6,4,5]=>13
[1,2,3,6,5,4]=>10
[1,2,4,3,5,6]=>16
[1,2,4,3,6,5]=>12
[1,2,4,5,3,6]=>13
[1,2,4,5,6,3]=>11
[1,2,4,6,3,5]=>10
[1,2,4,6,5,3]=>8
[1,2,5,3,4,6]=>13
[1,2,5,3,6,4]=>10
[1,2,5,4,3,6]=>10
[1,2,5,4,6,3]=>8
[1,2,5,6,3,4]=>8
[1,2,5,6,4,3]=>6
[1,2,6,3,4,5]=>11
[1,2,6,3,5,4]=>8
[1,2,6,4,3,5]=>8
[1,2,6,4,5,3]=>6
[1,2,6,5,3,4]=>6
[1,2,6,5,4,3]=>4
[1,3,2,4,5,6]=>16
[1,3,2,4,6,5]=>12
[1,3,2,5,4,6]=>12
[1,3,2,5,6,4]=>9
[1,3,2,6,4,5]=>9
[1,3,2,6,5,4]=>6
[1,3,4,2,5,6]=>13
[1,3,4,2,6,5]=>9
[1,3,4,5,2,6]=>11
[1,3,4,5,6,2]=>10
[1,3,4,6,2,5]=>8
[1,3,4,6,5,2]=>7
[1,3,5,2,4,6]=>10
[1,3,5,2,6,4]=>7
[1,3,5,4,2,6]=>8
[1,3,5,4,6,2]=>7
[1,3,5,6,2,4]=>6
[1,3,5,6,4,2]=>5
[1,3,6,2,4,5]=>8
[1,3,6,2,5,4]=>5
[1,3,6,4,2,5]=>6
[1,3,6,4,5,2]=>5
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>3
[1,4,2,3,5,6]=>13
[1,4,2,3,6,5]=>9
[1,4,2,5,3,6]=>10
[1,4,2,5,6,3]=>8
[1,4,2,6,3,5]=>7
[1,4,2,6,5,3]=>5
[1,4,3,2,5,6]=>10
[1,4,3,2,6,5]=>6
[1,4,3,5,2,6]=>8
[1,4,3,5,6,2]=>7
[1,4,3,6,2,5]=>5
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>8
[1,4,5,2,6,3]=>6
[1,4,5,3,2,6]=>6
[1,4,5,3,6,2]=>5
[1,4,5,6,2,3]=>5
[1,4,5,6,3,2]=>4
[1,4,6,2,3,5]=>6
[1,4,6,2,5,3]=>4
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>3
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>2
[1,5,2,3,4,6]=>11
[1,5,2,3,6,4]=>8
[1,5,2,4,3,6]=>8
[1,5,2,4,6,3]=>6
[1,5,2,6,3,4]=>6
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>8
[1,5,3,2,6,4]=>5
[1,5,3,4,2,6]=>6
[1,5,3,4,6,2]=>5
[1,5,3,6,2,4]=>4
[1,5,3,6,4,2]=>3
[1,5,4,2,3,6]=>6
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>4
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>3
[1,5,4,6,3,2]=>2
[1,5,6,2,3,4]=>5
[1,5,6,2,4,3]=>3
[1,5,6,3,2,4]=>3
[1,5,6,3,4,2]=>2
[1,5,6,4,2,3]=>2
[1,5,6,4,3,2]=>1
[1,6,2,3,4,5]=>10
[1,6,2,3,5,4]=>7
[1,6,2,4,3,5]=>7
[1,6,2,4,5,3]=>5
[1,6,2,5,3,4]=>5
[1,6,2,5,4,3]=>3
[1,6,3,2,4,5]=>7
[1,6,3,2,5,4]=>4
[1,6,3,4,2,5]=>5
[1,6,3,4,5,2]=>4
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>2
[1,6,4,2,3,5]=>5
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>2
[1,6,4,5,3,2]=>1
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>2
[1,6,5,3,2,4]=>2
[1,6,5,3,4,2]=>1
[1,6,5,4,2,3]=>1
[1,6,5,4,3,2]=>0
[2,1,3,4,5,6]=>16
[2,1,3,4,6,5]=>12
[2,1,3,5,4,6]=>12
[2,1,3,5,6,4]=>9
[2,1,3,6,4,5]=>9
[2,1,3,6,5,4]=>6
[2,1,4,3,5,6]=>12
[2,1,4,3,6,5]=>8
[2,1,4,5,3,6]=>9
[2,1,4,5,6,3]=>7
[2,1,4,6,3,5]=>6
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>9
[2,1,5,3,6,4]=>6
[2,1,5,4,3,6]=>6
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>4
[2,1,5,6,4,3]=>2
[2,1,6,3,4,5]=>7
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>4
[2,1,6,4,5,3]=>2
[2,1,6,5,3,4]=>2
[2,1,6,5,4,3]=>0
[2,3,1,4,5,6]=>13
[2,3,1,4,6,5]=>9
[2,3,1,5,4,6]=>9
[2,3,1,5,6,4]=>6
[2,3,1,6,4,5]=>6
[2,3,1,6,5,4]=>3
[2,3,4,1,5,6]=>11
[2,3,4,1,6,5]=>7
[2,3,4,5,1,6]=>10
[2,3,4,5,6,1]=>10
[2,3,4,6,1,5]=>7
[2,3,4,6,5,1]=>7
[2,3,5,1,4,6]=>8
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>7
[2,3,5,4,6,1]=>7
[2,3,5,6,1,4]=>5
[2,3,5,6,4,1]=>5
[2,3,6,1,4,5]=>6
[2,3,6,1,5,4]=>3
[2,3,6,4,1,5]=>5
[2,3,6,4,5,1]=>5
[2,3,6,5,1,4]=>3
[2,3,6,5,4,1]=>3
[2,4,1,3,5,6]=>10
[2,4,1,3,6,5]=>6
[2,4,1,5,3,6]=>7
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>4
[2,4,1,6,5,3]=>2
[2,4,3,1,5,6]=>8
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>7
[2,4,3,5,6,1]=>7
[2,4,3,6,1,5]=>4
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>6
[2,4,5,1,6,3]=>4
[2,4,5,3,1,6]=>5
[2,4,5,3,6,1]=>5
[2,4,5,6,1,3]=>4
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>4
[2,4,6,1,5,3]=>2
[2,4,6,3,1,5]=>3
[2,4,6,3,5,1]=>3
[2,4,6,5,1,3]=>2
[2,4,6,5,3,1]=>2
[2,5,1,3,4,6]=>8
[2,5,1,3,6,4]=>5
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>3
[2,5,1,6,3,4]=>3
[2,5,1,6,4,3]=>1
[2,5,3,1,4,6]=>6
[2,5,3,1,6,4]=>3
[2,5,3,4,1,6]=>5
[2,5,3,4,6,1]=>5
[2,5,3,6,1,4]=>3
[2,5,3,6,4,1]=>3
[2,5,4,1,3,6]=>4
[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]=>2
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>1
[2,5,6,3,1,4]=>2
[2,5,6,3,4,1]=>2
[2,5,6,4,1,3]=>1
[2,5,6,4,3,1]=>1
[2,6,1,3,4,5]=>7
[2,6,1,3,5,4]=>4
[2,6,1,4,3,5]=>4
[2,6,1,4,5,3]=>2
[2,6,1,5,3,4]=>2
[2,6,1,5,4,3]=>0
[2,6,3,1,4,5]=>5
[2,6,3,1,5,4]=>2
[2,6,3,4,1,5]=>4
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>2
[2,6,3,5,4,1]=>2
[2,6,4,1,3,5]=>3
[2,6,4,1,5,3]=>1
[2,6,4,3,1,5]=>2
[2,6,4,3,5,1]=>2
[2,6,4,5,1,3]=>1
[2,6,4,5,3,1]=>1
[2,6,5,1,3,4]=>2
[2,6,5,1,4,3]=>0
[2,6,5,3,1,4]=>1
[2,6,5,3,4,1]=>1
[2,6,5,4,1,3]=>0
[2,6,5,4,3,1]=>0
[3,1,2,4,5,6]=>13
[3,1,2,4,6,5]=>9
[3,1,2,5,4,6]=>9
[3,1,2,5,6,4]=>6
[3,1,2,6,4,5]=>6
[3,1,2,6,5,4]=>3
[3,1,4,2,5,6]=>10
[3,1,4,2,6,5]=>6
[3,1,4,5,2,6]=>8
[3,1,4,5,6,2]=>7
[3,1,4,6,2,5]=>5
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>7
[3,1,5,2,6,4]=>4
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>4
[3,1,5,6,2,4]=>3
[3,1,5,6,4,2]=>2
[3,1,6,2,4,5]=>5
[3,1,6,2,5,4]=>2
[3,1,6,4,2,5]=>3
[3,1,6,4,5,2]=>2
[3,1,6,5,2,4]=>1
[3,1,6,5,4,2]=>0
[3,2,1,4,5,6]=>10
[3,2,1,4,6,5]=>6
[3,2,1,5,4,6]=>6
[3,2,1,5,6,4]=>3
[3,2,1,6,4,5]=>3
[3,2,1,6,5,4]=>0
[3,2,4,1,5,6]=>8
[3,2,4,1,6,5]=>4
[3,2,4,5,1,6]=>7
[3,2,4,5,6,1]=>7
[3,2,4,6,1,5]=>4
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>2
[3,2,5,4,1,6]=>4
[3,2,5,4,6,1]=>4
[3,2,5,6,1,4]=>2
[3,2,5,6,4,1]=>2
[3,2,6,1,4,5]=>3
[3,2,6,1,5,4]=>0
[3,2,6,4,1,5]=>2
[3,2,6,4,5,1]=>2
[3,2,6,5,1,4]=>0
[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>8
[3,4,1,2,6,5]=>4
[3,4,1,5,2,6]=>6
[3,4,1,5,6,2]=>5
[3,4,1,6,2,5]=>3
[3,4,1,6,5,2]=>2
[3,4,2,1,5,6]=>6
[3,4,2,1,6,5]=>2
[3,4,2,5,1,6]=>5
[3,4,2,5,6,1]=>5
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>2
[3,4,5,1,2,6]=>5
[3,4,5,1,6,2]=>4
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>4
[3,4,5,6,2,1]=>4
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>2
[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]=>6
[3,5,1,2,6,4]=>3
[3,5,1,4,2,6]=>4
[3,5,1,4,6,2]=>3
[3,5,1,6,2,4]=>2
[3,5,1,6,4,2]=>1
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>1
[3,5,2,4,1,6]=>3
[3,5,2,4,6,1]=>3
[3,5,2,6,1,4]=>1
[3,5,2,6,4,1]=>1
[3,5,4,1,2,6]=>3
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>2
[3,5,4,2,6,1]=>2
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>2
[3,5,6,1,2,4]=>2
[3,5,6,1,4,2]=>1
[3,5,6,2,1,4]=>1
[3,5,6,2,4,1]=>1
[3,5,6,4,1,2]=>1
[3,5,6,4,2,1]=>1
[3,6,1,2,4,5]=>5
[3,6,1,2,5,4]=>2
[3,6,1,4,2,5]=>3
[3,6,1,4,5,2]=>2
[3,6,1,5,2,4]=>1
[3,6,1,5,4,2]=>0
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>0
[3,6,2,4,1,5]=>2
[3,6,2,4,5,1]=>2
[3,6,2,5,1,4]=>0
[3,6,2,5,4,1]=>0
[3,6,4,1,2,5]=>2
[3,6,4,1,5,2]=>1
[3,6,4,2,1,5]=>1
[3,6,4,2,5,1]=>1
[3,6,4,5,1,2]=>1
[3,6,4,5,2,1]=>1
[3,6,5,1,2,4]=>1
[3,6,5,1,4,2]=>0
[3,6,5,2,1,4]=>0
[3,6,5,2,4,1]=>0
[3,6,5,4,1,2]=>0
[3,6,5,4,2,1]=>0
[4,1,2,3,5,6]=>11
[4,1,2,3,6,5]=>7
[4,1,2,5,3,6]=>8
[4,1,2,5,6,3]=>6
[4,1,2,6,3,5]=>5
[4,1,2,6,5,3]=>3
[4,1,3,2,5,6]=>8
[4,1,3,2,6,5]=>4
[4,1,3,5,2,6]=>6
[4,1,3,5,6,2]=>5
[4,1,3,6,2,5]=>3
[4,1,3,6,5,2]=>2
[4,1,5,2,3,6]=>6
[4,1,5,2,6,3]=>4
[4,1,5,3,2,6]=>4
[4,1,5,3,6,2]=>3
[4,1,5,6,2,3]=>3
[4,1,5,6,3,2]=>2
[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>2
[4,1,6,3,2,5]=>2
[4,1,6,3,5,2]=>1
[4,1,6,5,2,3]=>1
[4,1,6,5,3,2]=>0
[4,2,1,3,5,6]=>8
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>5
[4,2,1,5,6,3]=>3
[4,2,1,6,3,5]=>2
[4,2,1,6,5,3]=>0
[4,2,3,1,5,6]=>6
[4,2,3,1,6,5]=>2
[4,2,3,5,1,6]=>5
[4,2,3,5,6,1]=>5
[4,2,3,6,1,5]=>2
[4,2,3,6,5,1]=>2
[4,2,5,1,3,6]=>4
[4,2,5,1,6,3]=>2
[4,2,5,3,1,6]=>3
[4,2,5,3,6,1]=>3
[4,2,5,6,1,3]=>2
[4,2,5,6,3,1]=>2
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>0
[4,2,6,3,1,5]=>1
[4,2,6,3,5,1]=>1
[4,2,6,5,1,3]=>0
[4,2,6,5,3,1]=>0
[4,3,1,2,5,6]=>6
[4,3,1,2,6,5]=>2
[4,3,1,5,2,6]=>4
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>1
[4,3,1,6,5,2]=>0
[4,3,2,1,5,6]=>4
[4,3,2,1,6,5]=>0
[4,3,2,5,1,6]=>3
[4,3,2,5,6,1]=>3
[4,3,2,6,1,5]=>0
[4,3,2,6,5,1]=>0
[4,3,5,1,2,6]=>3
[4,3,5,1,6,2]=>2
[4,3,5,2,1,6]=>2
[4,3,5,2,6,1]=>2
[4,3,5,6,1,2]=>2
[4,3,5,6,2,1]=>2
[4,3,6,1,2,5]=>1
[4,3,6,1,5,2]=>0
[4,3,6,2,1,5]=>0
[4,3,6,2,5,1]=>0
[4,3,6,5,1,2]=>0
[4,3,6,5,2,1]=>0
[4,5,1,2,3,6]=>5
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>3
[4,5,1,3,6,2]=>2
[4,5,1,6,2,3]=>2
[4,5,1,6,3,2]=>1
[4,5,2,1,3,6]=>3
[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]=>1
[4,5,3,1,2,6]=>2
[4,5,3,1,6,2]=>1
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>1
[4,5,3,6,2,1]=>1
[4,5,6,1,2,3]=>2
[4,5,6,1,3,2]=>1
[4,5,6,2,1,3]=>1
[4,5,6,2,3,1]=>1
[4,5,6,3,1,2]=>1
[4,5,6,3,2,1]=>1
[4,6,1,2,3,5]=>4
[4,6,1,2,5,3]=>2
[4,6,1,3,2,5]=>2
[4,6,1,3,5,2]=>1
[4,6,1,5,2,3]=>1
[4,6,1,5,3,2]=>0
[4,6,2,1,3,5]=>2
[4,6,2,1,5,3]=>0
[4,6,2,3,1,5]=>1
[4,6,2,3,5,1]=>1
[4,6,2,5,1,3]=>0
[4,6,2,5,3,1]=>0
[4,6,3,1,2,5]=>1
[4,6,3,1,5,2]=>0
[4,6,3,2,1,5]=>0
[4,6,3,2,5,1]=>0
[4,6,3,5,1,2]=>0
[4,6,3,5,2,1]=>0
[4,6,5,1,2,3]=>1
[4,6,5,1,3,2]=>0
[4,6,5,2,1,3]=>0
[4,6,5,2,3,1]=>0
[4,6,5,3,1,2]=>0
[4,6,5,3,2,1]=>0
[5,1,2,3,4,6]=>10
[5,1,2,3,6,4]=>7
[5,1,2,4,3,6]=>7
[5,1,2,4,6,3]=>5
[5,1,2,6,3,4]=>5
[5,1,2,6,4,3]=>3
[5,1,3,2,4,6]=>7
[5,1,3,2,6,4]=>4
[5,1,3,4,2,6]=>5
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>3
[5,1,3,6,4,2]=>2
[5,1,4,2,3,6]=>5
[5,1,4,2,6,3]=>3
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>2
[5,1,4,6,2,3]=>2
[5,1,4,6,3,2]=>1
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>2
[5,1,6,3,2,4]=>2
[5,1,6,3,4,2]=>1
[5,1,6,4,2,3]=>1
[5,1,6,4,3,2]=>0
[5,2,1,3,4,6]=>7
[5,2,1,3,6,4]=>4
[5,2,1,4,3,6]=>4
[5,2,1,4,6,3]=>2
[5,2,1,6,3,4]=>2
[5,2,1,6,4,3]=>0
[5,2,3,1,4,6]=>5
[5,2,3,1,6,4]=>2
[5,2,3,4,1,6]=>4
[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>2
[5,2,4,1,3,6]=>3
[5,2,4,1,6,3]=>1
[5,2,4,3,1,6]=>2
[5,2,4,3,6,1]=>2
[5,2,4,6,1,3]=>1
[5,2,4,6,3,1]=>1
[5,2,6,1,3,4]=>2
[5,2,6,1,4,3]=>0
[5,2,6,3,1,4]=>1
[5,2,6,3,4,1]=>1
[5,2,6,4,1,3]=>0
[5,2,6,4,3,1]=>0
[5,3,1,2,4,6]=>5
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>3
[5,3,1,4,6,2]=>2
[5,3,1,6,2,4]=>1
[5,3,1,6,4,2]=>0
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>0
[5,3,2,4,1,6]=>2
[5,3,2,4,6,1]=>2
[5,3,2,6,1,4]=>0
[5,3,2,6,4,1]=>0
[5,3,4,1,2,6]=>2
[5,3,4,1,6,2]=>1
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>1
[5,3,4,6,1,2]=>1
[5,3,4,6,2,1]=>1
[5,3,6,1,2,4]=>1
[5,3,6,1,4,2]=>0
[5,3,6,2,1,4]=>0
[5,3,6,2,4,1]=>0
[5,3,6,4,1,2]=>0
[5,3,6,4,2,1]=>0
[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>2
[5,4,1,3,2,6]=>2
[5,4,1,3,6,2]=>1
[5,4,1,6,2,3]=>1
[5,4,1,6,3,2]=>0
[5,4,2,1,3,6]=>2
[5,4,2,1,6,3]=>0
[5,4,2,3,1,6]=>1
[5,4,2,3,6,1]=>1
[5,4,2,6,1,3]=>0
[5,4,2,6,3,1]=>0
[5,4,3,1,2,6]=>1
[5,4,3,1,6,2]=>0
[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]=>1
[5,4,6,1,3,2]=>0
[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]=>4
[5,6,1,2,4,3]=>2
[5,6,1,3,2,4]=>2
[5,6,1,3,4,2]=>1
[5,6,1,4,2,3]=>1
[5,6,1,4,3,2]=>0
[5,6,2,1,3,4]=>2
[5,6,2,1,4,3]=>0
[5,6,2,3,1,4]=>1
[5,6,2,3,4,1]=>1
[5,6,2,4,1,3]=>0
[5,6,2,4,3,1]=>0
[5,6,3,1,2,4]=>1
[5,6,3,1,4,2]=>0
[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]=>1
[5,6,4,1,3,2]=>0
[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]=>10
[6,1,2,3,5,4]=>7
[6,1,2,4,3,5]=>7
[6,1,2,4,5,3]=>5
[6,1,2,5,3,4]=>5
[6,1,2,5,4,3]=>3
[6,1,3,2,4,5]=>7
[6,1,3,2,5,4]=>4
[6,1,3,4,2,5]=>5
[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>3
[6,1,3,5,4,2]=>2
[6,1,4,2,3,5]=>5
[6,1,4,2,5,3]=>3
[6,1,4,3,2,5]=>3
[6,1,4,3,5,2]=>2
[6,1,4,5,2,3]=>2
[6,1,4,5,3,2]=>1
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>2
[6,1,5,3,2,4]=>2
[6,1,5,3,4,2]=>1
[6,1,5,4,2,3]=>1
[6,1,5,4,3,2]=>0
[6,2,1,3,4,5]=>7
[6,2,1,3,5,4]=>4
[6,2,1,4,3,5]=>4
[6,2,1,4,5,3]=>2
[6,2,1,5,3,4]=>2
[6,2,1,5,4,3]=>0
[6,2,3,1,4,5]=>5
[6,2,3,1,5,4]=>2
[6,2,3,4,1,5]=>4
[6,2,3,4,5,1]=>4
[6,2,3,5,1,4]=>2
[6,2,3,5,4,1]=>2
[6,2,4,1,3,5]=>3
[6,2,4,1,5,3]=>1
[6,2,4,3,1,5]=>2
[6,2,4,3,5,1]=>2
[6,2,4,5,1,3]=>1
[6,2,4,5,3,1]=>1
[6,2,5,1,3,4]=>2
[6,2,5,1,4,3]=>0
[6,2,5,3,1,4]=>1
[6,2,5,3,4,1]=>1
[6,2,5,4,1,3]=>0
[6,2,5,4,3,1]=>0
[6,3,1,2,4,5]=>5
[6,3,1,2,5,4]=>2
[6,3,1,4,2,5]=>3
[6,3,1,4,5,2]=>2
[6,3,1,5,2,4]=>1
[6,3,1,5,4,2]=>0
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>0
[6,3,2,4,1,5]=>2
[6,3,2,4,5,1]=>2
[6,3,2,5,1,4]=>0
[6,3,2,5,4,1]=>0
[6,3,4,1,2,5]=>2
[6,3,4,1,5,2]=>1
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>1
[6,3,4,5,1,2]=>1
[6,3,4,5,2,1]=>1
[6,3,5,1,2,4]=>1
[6,3,5,1,4,2]=>0
[6,3,5,2,1,4]=>0
[6,3,5,2,4,1]=>0
[6,3,5,4,1,2]=>0
[6,3,5,4,2,1]=>0
[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>2
[6,4,1,3,2,5]=>2
[6,4,1,3,5,2]=>1
[6,4,1,5,2,3]=>1
[6,4,1,5,3,2]=>0
[6,4,2,1,3,5]=>2
[6,4,2,1,5,3]=>0
[6,4,2,3,1,5]=>1
[6,4,2,3,5,1]=>1
[6,4,2,5,1,3]=>0
[6,4,2,5,3,1]=>0
[6,4,3,1,2,5]=>1
[6,4,3,1,5,2]=>0
[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]=>1
[6,4,5,1,3,2]=>0
[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]=>4
[6,5,1,2,4,3]=>2
[6,5,1,3,2,4]=>2
[6,5,1,3,4,2]=>1
[6,5,1,4,2,3]=>1
[6,5,1,4,3,2]=>0
[6,5,2,1,3,4]=>2
[6,5,2,1,4,3]=>0
[6,5,2,3,1,4]=>1
[6,5,2,3,4,1]=>1
[6,5,2,4,1,3]=>0
[6,5,2,4,3,1]=>0
[6,5,3,1,2,4]=>1
[6,5,3,1,4,2]=>0
[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]=>1
[6,5,4,1,3,2]=>0
[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]=>35
[1,2,3,4,5,7,6]=>30
[1,2,3,4,6,5,7]=>30
[1,2,3,6,4,7,5]=>22
[1,2,6,3,4,7,5]=>19
[1,3,2,4,5,6,7]=>30
[1,3,7,2,4,5,6]=>17
[1,3,7,6,5,4,2]=>4
[1,4,6,7,2,3,5]=>9
[1,4,6,7,5,3,2]=>5
[1,4,7,2,3,5,6]=>14
[1,4,7,6,5,3,2]=>3
[1,5,2,3,4,7,6]=>18
[1,5,2,7,3,4,6]=>13
[1,5,4,7,6,3,2]=>4
[1,5,6,2,7,3,4]=>9
[1,5,6,4,7,3,2]=>5
[1,5,6,7,2,3,4]=>8
[1,5,6,7,4,3,2]=>4
[1,5,7,2,3,4,6]=>12
[1,5,7,6,4,3,2]=>2
[1,6,2,3,4,7,5]=>17
[1,6,2,3,7,4,5]=>14
[1,6,2,7,3,4,5]=>12
[1,6,5,4,3,7,2]=>4
[1,6,5,4,7,3,2]=>3
[1,6,5,7,4,3,2]=>2
[1,6,7,2,3,4,5]=>11
[1,6,7,5,4,3,2]=>1
[1,7,2,3,4,5,6]=>20
[1,7,3,5,6,4,2]=>5
[1,7,3,6,5,4,2]=>3
[1,7,4,3,6,5,2]=>4
[1,7,4,5,3,6,2]=>5
[1,7,4,5,6,3,2]=>4
[1,7,4,6,5,3,2]=>2
[1,7,5,4,3,6,2]=>3
[1,7,5,4,6,3,2]=>2
[1,7,6,4,5,3,2]=>1
[1,7,6,5,4,3,2]=>0
[2,1,3,4,5,6,7]=>30
[2,1,3,4,7,5,6]=>21
[2,1,3,7,4,5,6]=>18
[2,1,6,3,4,5,7]=>18
[2,1,7,3,4,5,6]=>16
[2,1,7,6,5,4,3]=>0
[2,3,1,4,5,6,7]=>26
[2,3,4,1,5,6,7]=>23
[2,3,4,1,5,7,6]=>18
[2,3,4,5,1,6,7]=>21
[2,3,4,5,1,7,6]=>16
[2,3,4,5,6,1,7]=>20
[2,3,4,5,6,7,1]=>20
[2,3,4,5,7,1,6]=>16
[2,3,4,6,1,7,5]=>13
[2,3,4,6,7,1,5]=>13
[2,3,4,7,1,5,6]=>14
[2,3,5,6,7,1,4]=>11
[2,4,1,3,5,6,7]=>22
[2,5,1,3,4,6,7]=>19
[2,5,7,1,3,4,6]=>9
[2,6,1,3,4,5,7]=>17
[2,6,1,7,3,4,5]=>8
[2,6,5,4,3,1,7]=>4
[2,6,7,1,3,4,5]=>8
[2,7,1,3,4,5,6]=>16
[3,1,2,4,5,6,7]=>26
[3,1,2,4,5,7,6]=>21
[3,2,1,4,5,6,7]=>22
[3,2,4,5,6,7,1]=>16
[3,4,1,2,5,6,7]=>19
[3,4,2,5,6,7,1]=>13
[3,4,5,2,6,7,1]=>11
[3,4,5,6,2,7,1]=>10
[3,4,5,6,7,1,2]=>10
[3,5,6,1,2,4,7]=>9
[3,5,6,4,2,1,7]=>5
[3,6,1,2,4,5,7]=>14
[3,6,5,4,2,1,7]=>3
[4,1,2,3,5,6,7]=>23
[4,1,2,3,5,7,6]=>18
[4,1,6,2,3,5,7]=>13
[4,2,3,5,6,7,1]=>13
[4,2,5,1,3,6,7]=>13
[4,3,2,1,5,6,7]=>13
[4,3,2,5,6,7,1]=>10
[4,3,5,2,6,7,1]=>8
[4,3,6,5,2,1,7]=>4
[4,5,1,6,2,3,7]=>9
[4,5,2,3,6,7,1]=>8
[4,5,3,6,2,1,7]=>5
[4,5,6,1,2,3,7]=>8
[4,5,6,3,2,1,7]=>4
[4,6,1,2,3,5,7]=>12
[4,6,1,2,3,7,5]=>8
[4,6,5,3,2,1,7]=>2
[5,1,2,3,4,6,7]=>21
[5,1,2,3,4,7,6]=>16
[5,1,2,3,6,4,7]=>17
[5,1,2,3,6,7,4]=>14
[5,1,2,3,7,4,6]=>13
[5,1,2,6,3,4,7]=>14
[5,1,6,2,3,4,7]=>12
[5,1,6,2,3,7,4]=>9
[5,2,3,4,6,7,1]=>11
[5,2,6,7,1,3,4]=>4
[5,3,2,4,6,7,1]=>8
[5,3,2,6,1,4,7]=>6
[5,4,3,2,1,6,7]=>5
[5,4,3,2,1,7,6]=>0
[5,4,3,2,6,1,7]=>4
[5,4,3,6,2,1,7]=>3
[5,4,6,3,2,1,7]=>2
[5,6,1,2,3,4,7]=>11
[5,6,1,2,3,7,4]=>8
[5,6,3,4,1,2,7]=>3
[5,6,4,3,2,1,7]=>1
[5,6,7,1,2,3,4]=>5
[6,1,2,3,4,5,7]=>20
[6,1,2,3,4,7,5]=>16
[6,1,2,3,7,4,5]=>13
[6,1,2,7,3,4,5]=>11
[6,2,3,4,5,7,1]=>10
[6,2,4,5,3,1,7]=>5
[6,2,5,4,3,1,7]=>3
[6,3,2,5,4,1,7]=>4
[6,3,4,2,5,1,7]=>5
[6,3,4,5,2,1,7]=>4
[6,3,5,4,2,1,7]=>2
[6,4,3,2,5,1,7]=>3
[6,4,3,2,7,1,5]=>0
[6,4,3,5,2,1,7]=>2
[6,4,7,2,5,1,3]=>0
[6,5,3,4,2,1,7]=>1
[6,5,4,3,2,1,7]=>0
[6,7,1,2,3,4,5]=>10
[6,7,4,5,1,2,3]=>1
[7,1,2,3,4,5,6]=>20
[7,2,1,3,4,5,6]=>16
[7,2,3,1,4,5,6]=>13
[7,2,3,4,1,5,6]=>11
[7,2,3,4,5,1,6]=>10
[7,3,1,2,4,5,6]=>13
[7,3,2,1,4,5,6]=>10
[7,3,2,4,1,5,6]=>8
[7,3,4,1,2,5,6]=>8
[7,4,1,2,3,5,6]=>11
[7,4,2,1,3,5,6]=>8
[7,4,5,6,1,2,3]=>2
[7,5,1,2,3,4,6]=>10
[7,5,6,1,2,3,4]=>4
[7,5,6,3,4,1,2]=>0
[7,6,1,2,3,4,5]=>10
[7,6,4,5,1,2,3]=>1
[7,6,5,1,2,3,4]=>4
[7,6,5,3,4,1,2]=>0
[7,6,5,4,1,2,3]=>1
[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]=>2
[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]=>2
[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]=>2
[8,5,6,7,2,3,4,1]=>2
[7,8,3,2,4,5,6,1]=>7
[7,6,5,4,3,2,8,1]=>0
[6,5,7,4,3,2,8,1]=>2
[6,5,4,3,7,2,8,1]=>4
[5,4,6,3,7,2,8,1]=>8
[3,4,5,2,6,7,8,1]=>23
[5,2,3,4,6,7,8,1]=>23
[4,3,2,5,6,7,8,1]=>22
[3,4,2,5,6,7,8,1]=>26
[4,2,3,5,6,7,8,1]=>26
[3,2,4,5,6,7,8,1]=>30
[2,3,4,5,6,7,8,1]=>35
[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]=>4
[7,8,3,4,5,6,1,2]=>4
[3,4,5,6,7,8,1,2]=>20
[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]=>1
[6,7,8,5,4,1,2,3]=>2
[8,5,6,7,4,1,2,3]=>2
[8,7,6,4,5,1,2,3]=>1
[8,6,7,4,5,1,2,3]=>1
[8,7,4,5,6,1,2,3]=>2
[7,8,4,5,6,1,2,3]=>2
[7,6,5,8,3,2,1,4]=>0
[7,5,6,8,2,3,1,4]=>2
[6,7,5,8,3,1,2,4]=>2
[6,5,7,8,2,1,3,4]=>4
[8,7,6,5,1,2,3,4]=>4
[8,7,5,6,1,2,3,4]=>4
[7,8,5,6,1,2,3,4]=>4
[8,5,6,7,1,2,3,4]=>5
[5,6,7,8,1,2,3,4]=>8
[8,7,6,4,3,2,1,5]=>0
[8,7,6,4,2,1,3,5]=>2
[8,7,6,1,2,3,4,5]=>10
[8,6,7,1,2,3,4,5]=>10
[6,7,8,1,2,3,4,5]=>11
[7,8,5,4,2,1,3,6]=>2
[7,8,5,4,1,2,3,6]=>4
[8,7,1,2,3,4,5,6]=>20
[7,8,1,2,3,4,5,6]=>20
[8,6,5,4,3,2,1,7]=>0
[8,6,5,4,3,1,2,7]=>1
[8,5,6,3,4,1,2,7]=>3
[8,6,5,4,2,1,3,7]=>2
[8,6,4,3,2,1,5,7]=>4
[8,6,4,2,1,3,5,7]=>8
[8,2,3,4,1,5,6,7]=>23
[8,4,1,2,3,5,6,7]=>23
[8,3,2,1,4,5,6,7]=>22
[8,2,3,1,4,5,6,7]=>26
[8,3,1,2,4,5,6,7]=>26
[8,2,1,3,4,5,6,7]=>30
[8,1,2,3,4,5,6,7]=>35
[7,6,5,4,3,2,1,8]=>0
[6,7,5,4,3,2,1,8]=>1
[6,5,7,4,3,2,1,8]=>2
[5,6,7,4,3,2,1,8]=>4
[7,6,4,5,3,2,1,8]=>1
[6,5,4,7,3,2,1,8]=>3
[7,5,6,3,4,2,1,8]=>2
[7,6,4,3,5,2,1,8]=>2
[7,6,3,4,5,2,1,8]=>4
[7,5,4,3,6,2,1,8]=>3
[6,7,5,4,2,3,1,8]=>2
[6,5,7,3,2,4,1,8]=>4
[5,6,7,2,3,4,1,8]=>8
[2,3,4,5,6,7,1,8]=>35
[5,6,7,1,2,3,4,8]=>14
[6,7,1,2,3,4,5,8]=>21
[7,1,2,3,4,5,6,8]=>35
[6,5,4,3,2,1,7,8]=>6
[2,3,4,5,6,1,7,8]=>36
[5,6,3,4,1,2,7,8]=>12
[4,5,6,1,2,3,7,8]=>20
[6,1,2,3,4,5,7,8]=>36
[5,4,3,2,1,6,7,8]=>16
[2,3,4,5,1,6,7,8]=>38
[5,1,2,3,4,6,7,8]=>38
[4,3,2,1,5,6,7,8]=>28
[3,4,1,2,5,6,7,8]=>36
[3,2,1,4,5,6,7,8]=>40
[2,1,3,4,5,6,7,8]=>50
[1,2,3,4,5,6,7,8]=>56
[6,5,8,7,4,3,2,1]=>0
[3,5,8,7,6,4,2,1]=>3
[4,3,6,5,8,7,2,1]=>8
[2,6,8,7,5,4,3,1]=>2
[2,3,5,6,8,7,4,1]=>17
[3,2,6,5,4,8,7,1]=>12
[4,3,6,5,7,2,8,1]=>12
[3,2,6,5,7,4,8,1]=>14
[4,3,5,2,7,6,8,1]=>14
[3,2,5,4,7,6,8,1]=>20
[1,8,7,6,5,4,3,2]=>0
[1,7,8,6,5,4,3,2]=>1
[1,6,8,7,5,4,3,2]=>2
[1,7,6,8,5,4,3,2]=>2
[1,6,7,8,5,4,3,2]=>4
[1,5,8,7,6,4,3,2]=>3
[1,7,6,5,8,4,3,2]=>3
[1,3,5,7,8,6,4,2]=>14
[1,4,3,8,7,6,5,2]=>8
[1,6,5,4,3,8,7,2]=>8
[1,4,3,6,5,8,7,2]=>20
[2,1,8,7,6,5,4,3]=>0
[2,1,6,5,7,4,8,3]=>14
[2,1,5,4,7,6,8,3]=>20
[1,2,6,7,8,5,4,3]=>13
[3,2,1,8,7,6,5,4]=>0
[3,2,1,6,5,8,7,4]=>12
[1,2,3,5,6,7,8,4]=>38
[4,3,2,1,8,7,6,5]=>0
[3,4,2,1,7,8,6,5]=>8
[2,4,3,1,6,8,7,5]=>16
[2,4,3,1,7,6,8,5]=>16
[3,2,4,1,6,8,7,5]=>16
[3,2,4,1,7,6,8,5]=>16
[2,3,4,1,6,7,8,5]=>26
[2,1,4,3,8,7,6,5]=>16
[2,1,4,3,6,8,7,5]=>24
[2,1,4,3,7,6,8,5]=>24
[5,4,3,2,1,8,7,6]=>0
[3,2,5,4,1,8,7,6]=>12
[3,2,1,4,5,8,7,6]=>24
[2,3,1,4,5,7,8,6]=>34
[6,5,4,3,2,1,8,7]=>0
[4,3,5,2,6,1,8,7]=>14
[3,2,5,4,6,1,8,7]=>20
[2,3,4,5,6,1,8,7]=>30
[2,1,6,5,4,3,8,7]=>16
[2,1,4,6,5,3,8,7]=>24
[2,1,5,4,6,3,8,7]=>24
[4,3,2,1,6,5,8,7]=>16
[2,4,3,1,6,5,8,7]=>24
[3,2,4,1,6,5,8,7]=>24
[2,1,4,3,6,5,8,7]=>32
[2,1,3,4,5,6,8,7]=>44
[1,2,3,4,5,6,8,7]=>50
[5,7,6,4,3,2,1,8]=>2
[4,7,6,5,3,2,1,8]=>3
[3,2,7,6,5,4,1,8]=>8
[5,4,3,2,7,6,1,8]=>8
[3,2,5,4,7,6,1,8]=>20
[1,4,3,2,7,6,5,8]=>24
[1,3,4,2,6,7,5,8]=>34
[1,3,2,5,4,7,6,8]=>38
[1,2,3,5,4,7,6,8]=>44
[1,3,2,4,5,7,6,8]=>44
[1,2,3,4,5,7,6,8]=>50
[1,2,4,3,6,5,7,8]=>44
[1,3,2,5,4,6,7,8]=>44
[1,2,3,5,4,6,7,8]=>50
[1,3,2,4,5,6,7,8]=>50
[1,8,4,7,6,5,3,2]=>3
[1,8,5,4,7,6,3,2]=>4
[1,8,7,4,5,6,3,2]=>4
[1,8,7,4,6,5,3,2]=>2
[1,8,6,5,4,7,3,2]=>3
[1,8,7,5,4,6,3,2]=>2
[1,8,7,5,6,4,3,2]=>1
[2,1,4,5,8,6,7,3]=>21
[2,1,8,5,4,7,6,3]=>8
[2,3,4,8,5,6,7,1]=>23
[2,3,6,4,5,1,8,7]=>21
[2,3,7,4,5,6,8,1]=>23
[2,8,4,3,5,7,6,1]=>12
[4,2,3,1,8,6,7,5]=>8
[8,2,7,4,6,5,3,1]=>2
[4,3,2,7,5,6,8,1]=>13
[4,3,2,8,5,7,6,1]=>6
[6,3,2,5,4,1,8,7]=>8
[8,3,2,5,4,7,6,1]=>8
[8,3,2,7,6,5,4,1]=>0
[8,3,7,4,6,5,2,1]=>2
[7,3,6,5,4,2,1,8]=>3
[7,4,3,6,5,2,1,8]=>4
[7,6,3,5,4,2,1,8]=>2
[8,5,4,3,2,7,6,1]=>0
[8,7,4,3,6,5,2,1]=>0
[2,4,6,8,1,3,5,7]=>16
[2,4,6,1,7,3,8,5]=>16
[2,1,4,3,7,5,8,6]=>28
[2,4,1,3,7,5,8,6]=>24
[2,1,4,3,7,8,5,6]=>24
[2,4,7,8,1,3,5,6]=>14
[2,1,4,3,8,5,6,7]=>29
[2,4,5,6,7,1,8,3]=>20
[2,1,5,3,6,4,8,7]=>28
[2,1,5,6,3,4,8,7]=>24
[2,5,6,8,1,3,4,7]=>14
[2,1,5,3,7,4,8,6]=>24
[2,5,1,7,3,4,8,6]=>18
[2,1,5,7,3,8,4,6]=>18
[2,5,7,8,1,3,4,6]=>12
[2,3,5,6,1,7,8,4]=>22
[2,1,6,3,7,4,8,5]=>22
[2,6,7,1,3,4,8,5]=>16
[2,1,6,7,8,3,4,5]=>14
[2,6,7,8,1,3,4,5]=>11
[2,1,6,3,4,7,8,5]=>26
[2,1,6,3,4,5,8,7]=>29
[2,6,1,3,4,5,7,8]=>33
[2,7,8,1,3,4,5,6]=>17
[2,7,1,3,4,5,6,8]=>31
[2,3,4,5,7,8,1,6]=>26
[2,1,8,3,4,5,6,7]=>30
[2,8,1,3,4,5,6,7]=>30
[2,1,3,8,4,5,6,7]=>32
[2,3,4,5,6,8,1,7]=>30
[3,1,4,2,6,5,8,7]=>28
[3,4,1,2,6,5,8,7]=>24
[3,1,4,2,6,8,5,7]=>24
[3,4,6,8,1,2,5,7]=>14
[3,1,4,2,7,5,8,6]=>24
[3,4,1,2,7,8,5,6]=>16
[3,4,7,8,1,2,5,6]=>12
[3,1,5,2,6,4,8,7]=>24
[3,5,1,6,2,4,8,7]=>18
[3,1,5,6,2,8,4,7]=>18
[3,5,6,8,1,2,4,7]=>12
[3,1,5,2,7,4,8,6]=>20
[3,5,1,7,2,8,4,6]=>12
[3,5,7,8,1,2,4,6]=>10
[1,3,2,5,4,8,6,7]=>33
[1,3,5,8,2,4,6,7]=>25
[1,3,5,6,2,7,4,8]=>28
[3,1,6,2,7,4,8,5]=>18
[3,6,7,1,2,8,4,5]=>10
[3,6,1,7,8,2,4,5]=>10
[3,6,7,8,1,2,4,5]=>9
[1,3,2,6,4,7,5,8]=>34
[3,1,2,6,7,4,8,5]=>21
[1,3,2,6,4,8,5,7]=>29
[1,3,2,6,4,5,7,8]=>39
[1,3,2,7,4,8,5,6]=>26
[1,3,2,7,4,5,6,8]=>35
[1,3,2,8,4,5,6,7]=>32
[3,1,2,4,5,8,6,7]=>34
[1,3,2,4,5,8,6,7]=>39
[4,1,5,2,6,3,8,7]=>22
[4,5,6,1,2,3,8,7]=>14
[4,1,5,6,8,2,3,7]=>16
[4,5,6,8,1,2,3,7]=>11
[4,1,5,2,7,3,8,6]=>18
[4,1,5,2,7,8,3,6]=>16
[4,5,7,1,2,8,3,6]=>10
[4,5,1,7,8,2,3,6]=>10
[4,5,7,8,1,2,3,6]=>9
[1,4,2,5,3,7,6,8]=>34
[1,4,2,5,3,8,6,7]=>29
[1,4,2,5,3,6,7,8]=>40
[1,4,5,6,7,2,3,8]=>24
[4,1,6,2,7,3,8,5]=>16
[4,6,7,1,8,2,3,5]=>8
[4,6,7,8,1,2,3,5]=>8
[1,4,2,6,3,7,5,8]=>30
[1,4,2,6,7,8,3,5]=>21
[1,4,2,6,3,8,5,7]=>25
[4,1,2,3,6,5,8,7]=>29
[1,4,2,6,3,5,7,8]=>35
[1,4,2,7,3,8,5,6]=>22
[4,7,1,2,3,5,6,8]=>24
[1,4,2,7,3,5,6,8]=>31
[1,4,2,3,7,5,6,8]=>34
[1,4,2,3,5,7,6,8]=>39
[1,4,2,8,3,5,6,7]=>28
[4,1,2,3,8,5,6,7]=>26
[1,4,2,3,5,8,6,7]=>34
[1,4,2,3,5,6,7,8]=>45
[5,1,6,2,7,3,8,4]=>16
[1,5,2,6,3,7,4,8]=>28
[1,5,2,6,3,8,4,7]=>23
[1,5,2,6,3,4,7,8]=>32
[1,2,5,6,3,4,7,8]=>36
[1,5,2,7,3,8,4,6]=>20
[5,7,1,2,3,4,6,8]=>22
[1,5,2,7,3,4,6,8]=>28
[1,5,2,3,4,7,6,8]=>35
[5,1,2,8,3,4,6,7]=>22
[1,5,2,8,3,4,6,7]=>25
[1,5,8,2,3,4,6,7]=>24
[1,5,2,3,4,8,6,7]=>30
[1,2,3,5,4,8,6,7]=>39
[5,1,2,3,4,6,8,7]=>32
[1,5,2,3,4,6,7,8]=>41
[1,6,2,7,3,8,4,5]=>19
[1,6,7,8,2,3,4,5]=>14
[6,7,1,2,3,4,8,5]=>17
[6,1,7,2,3,4,5,8]=>22
[6,1,2,7,3,4,5,8]=>24
[1,6,2,7,3,4,5,8]=>26
[1,6,7,2,3,4,5,8]=>24
[1,6,2,3,4,7,5,8]=>33
[1,2,3,6,4,7,5,8]=>40
[6,1,8,2,3,4,5,7]=>20
[1,6,2,8,3,4,5,7]=>23
[1,6,8,2,3,4,5,7]=>22
[1,6,2,3,4,8,5,7]=>28
[1,2,3,6,4,8,5,7]=>35
[6,1,2,3,4,5,8,7]=>30
[1,6,2,3,4,5,7,8]=>38
[1,2,3,6,4,5,7,8]=>45
[1,7,2,8,3,4,5,6]=>22
[1,7,8,2,3,4,5,6]=>21
[1,7,2,3,8,4,5,6]=>24
[7,1,2,3,4,8,5,6]=>26
[1,7,2,3,4,8,5,6]=>27
[1,2,3,7,4,8,5,6]=>32
[7,1,2,3,4,5,8,6]=>30
[1,7,2,3,4,5,8,6]=>31
[1,2,7,3,4,5,8,6]=>33
[1,7,2,3,4,5,6,8]=>36
[1,2,3,7,4,5,6,8]=>41
[1,8,2,3,4,5,6,7]=>35
[1,2,3,8,4,5,6,7]=>38
[1,2,3,4,5,8,6,7]=>45
[5,3,2,6,1,4,8,7]=>12
[7,3,2,5,4,8,1,6]=>8
[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]=>4
[5,4,6,2,1,3,8,7]=>8
[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]=>4
[7,5,4,3,2,8,1,6]=>0
[8,6,4,3,7,2,5,1]=>0
[7,6,4,3,8,2,1,5]=>0
[6,7,4,3,8,1,2,5]=>2
[5,7,4,3,1,8,2,6]=>2
[4,7,5,1,3,8,2,6]=>6
[3,7,1,5,4,8,2,6]=>10
[2,1,7,5,4,8,3,6]=>12
[3,8,1,5,4,7,6,2]=>8
[4,8,5,1,3,7,6,2]=>4
[5,8,4,3,1,7,6,2]=>0
[6,8,4,3,7,1,5,2]=>0
[7,8,4,3,6,5,1,2]=>0
[6,8,5,7,3,1,4,2]=>0
[5,8,6,7,1,3,4,2]=>2
[4,8,6,1,7,3,5,2]=>2
[3,8,1,6,7,4,5,2]=>4
[2,1,8,6,7,4,5,3]=>4
[2,1,7,6,8,4,3,5]=>8
[3,7,1,6,8,4,2,5]=>6
[4,7,6,1,8,3,2,5]=>4
[5,7,6,8,1,3,2,4]=>4
[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]=>2
[8,4,6,2,7,3,5,1]=>2
[8,3,2,6,7,4,5,1]=>4
[7,3,2,6,8,4,1,5]=>4
[6,3,2,7,8,1,4,5]=>6
[5,3,2,7,1,8,4,6]=>6
[4,3,2,1,7,8,5,6]=>8
[3,4,1,2,8,7,6,5]=>8
[5,3,2,8,1,7,6,4]=>0
[6,3,2,8,7,1,5,4]=>0
[7,3,2,8,6,5,1,4]=>0
[8,4,7,2,6,5,3,1]=>0
[7,4,8,2,6,5,1,3]=>0
[6,4,8,2,7,1,5,3]=>0
[5,4,8,2,1,7,6,3]=>0
[4,5,8,1,2,7,6,3]=>6
[3,5,1,8,2,7,6,4]=>6
[2,1,5,8,3,7,6,4]=>12
[2,1,6,8,7,3,5,4]=>8
[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]=>4
[6,5,8,7,2,1,4,3]=>0
[7,5,8,6,2,4,1,3]=>0
[8,5,7,6,2,4,3,1]=>0
[5,7,8,6,1,4,2,3]=>2
[4,7,8,1,6,5,2,3]=>2
[3,7,1,8,6,5,2,4]=>2
[2,1,7,8,6,5,3,4]=>4
[3,8,1,7,6,5,4,2]=>0
[4,8,7,1,6,5,3,2]=>0
[5,8,7,6,1,4,3,2]=>0
[6,8,7,5,4,1,3,2]=>0
[4,2,5,1,3,6,7,8]=>28
[5,2,6,7,1,3,4,8]=>14
[3,2,7,8,1,4,5,6]=>12
[5,3,2,6,1,4,7,8]=>18
[7,4,3,8,1,2,5,6]=>6
[4,7,3,6,8,1,2,5]=>4
[6,7,3,4,8,1,2,5]=>4
[5,4,2,7,8,1,3,6]=>5
[6,4,7,2,5,1,3,8]=>6
[6,4,3,2,7,1,5,8]=>8
[5,4,3,2,8,1,6,7]=>5
[7,5,3,8,2,6,1,4]=>0
[8,5,4,7,2,6,1,3]=>0
[8,5,4,7,3,6,1,2]=>0
[8,1,2,7,6,3,4,5]=>12
[8,1,4,2,6,3,5,7]=>18
[8,3,1,2,4,7,5,6]=>17
[8,3,1,5,6,2,4,7]=>12
[6,3,8,1,2,7,4,5]=>6
[7,8,4,1,6,2,3,5]=>4
[8,3,4,1,6,7,2,5]=>7
[2,7,6,5,1,3,8,4]=>7
[8,3,6,5,1,7,2,4]=>3
[4,6,7,3,8,5,1,2]=>4
[3,5,2,7,1,8,6,4]=>6
[4,6,7,2,8,1,5,3]=>4
[5,6,7,8,2,1,4,3]=>4
[6,5,8,7,3,4,1,2]=>0
[3,6,7,4,5,8,1,2]=>8
[2,6,7,4,5,1,8,3]=>8
[1,6,7,4,5,2,3,8]=>12
[1,5,4,7,6,2,3,8]=>16
[2,5,4,7,6,1,8,3]=>12
[3,5,4,7,6,8,1,2]=>12
[4,5,3,7,8,6,1,2]=>6
[5,4,3,8,7,6,1,2]=>0
[6,4,8,3,7,5,1,2]=>0
[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]=>12
[3,2,5,6,1,8,7,4]=>12
[4,2,5,6,8,1,7,3]=>12
[5,2,4,8,6,1,7,3]=>6
[6,2,8,4,5,1,7,3]=>4
[7,8,2,4,5,1,6,3]=>4
[7,8,1,4,5,2,3,6]=>8
[6,1,8,4,5,2,3,7]=>8
[5,1,4,8,6,2,3,7]=>10
[4,1,3,2,8,6,5,7]=>16
[5,1,3,8,2,6,4,7]=>14
[6,1,8,3,2,5,4,7]=>12
[7,8,1,3,2,5,4,6]=>12
[7,8,2,3,1,5,6,4]=>6
[6,2,8,3,1,5,7,4]=>6
[5,2,3,8,1,6,7,4]=>8
[6,3,8,2,1,7,5,4]=>0
[7,8,3,2,1,6,5,4]=>0
[7,8,4,2,6,1,5,3]=>0
[5,4,2,8,7,1,6,3]=>0
[4,5,2,7,8,1,6,3]=>6
[2,5,3,7,1,6,8,4]=>14
[1,5,3,7,2,6,4,8]=>20
[1,6,7,3,2,5,4,8]=>16
[2,6,7,3,1,5,8,4]=>10
[3,6,7,2,1,8,5,4]=>4
[7,8,5,6,2,1,4,3]=>0
[6,5,8,7,1,2,3,4]=>4
[5,4,1,8,7,2,3,6]=>4
[6,4,8,1,7,2,3,5]=>4
[7,8,3,1,2,6,4,5]=>6
[5,3,1,8,2,7,4,6]=>6
[4,3,1,2,8,7,5,6]=>8
[4,2,1,3,8,5,7,6]=>16
[5,2,1,8,3,4,7,6]=>12
[6,2,8,1,3,4,7,5]=>12
[7,8,2,1,3,4,6,5]=>12
[6,3,1,5,2,4,8,7]=>13
[2,1,8,5,3,7,4,6]=>13
[8,2,6,1,4,3,7,5]=>9
[4,7,1,5,8,3,2,6]=>7
[8,6,1,3,4,2,5,7]=>13
[8,1,2,4,5,6,3,7]=>23
[8,2,5,1,3,6,4,7]=>15
[4,1,5,3,7,2,8,6]=>15
[5,2,7,1,3,8,4,6]=>11
[5,3,1,7,8,2,4,6]=>8
[1,7,3,4,2,5,8,6]=>22
[4,7,2,1,3,5,8,6]=>15
[4,5,2,3,7,6,1,8]=>14
[6,4,3,7,2,5,1,8]=>6
[8,4,3,6,5,1,2,7]=>5
[1,5,6,3,4,8,7,2]=>14
[4,6,2,7,3,5,1,8]=>10
[3,2,6,7,4,5,1,8]=>14
[4,7,2,6,5,3,1,8]=>6
[5,7,6,2,4,3,1,8]=>4
[1,7,5,4,8,3,6,2]=>6
[8,7,5,4,1,3,2,6]=>2
[6,8,5,4,2,1,3,7]=>2
[5,8,6,2,4,1,3,7]=>4
[4,8,2,6,5,1,3,7]=>6
[3,2,8,6,5,1,4,7]=>7
[4,1,2,6,5,8,7,3]=>17
[5,1,6,2,4,8,7,3]=>12
[6,1,5,4,2,8,7,3]=>7
[7,1,5,4,8,2,6,3]=>6
[8,1,5,4,7,6,2,3]=>5
[1,8,6,7,4,5,3,2]=>2
[8,1,6,7,4,5,2,3]=>3
[7,1,6,8,4,2,5,3]=>4
[6,1,7,8,2,4,5,3]=>7
[5,1,7,2,8,4,6,3]=>8
[4,1,2,7,8,5,6,3]=>11
[3,2,1,7,8,5,6,4]=>6
[3,2,8,7,1,5,4,6]=>6
[4,8,2,7,1,5,3,6]=>5
[5,8,7,2,1,4,3,6]=>4
[6,8,7,1,2,4,3,5]=>7
[7,8,6,1,4,2,3,5]=>5
[8,7,6,1,4,3,2,5]=>3
[1,7,6,8,4,3,5,2]=>4
[1,6,7,8,3,4,5,2]=>8
[8,6,7,1,3,4,2,5]=>5
[7,6,8,1,3,2,4,5]=>7
[5,7,8,2,1,3,4,6]=>8
[4,7,2,8,1,3,5,6]=>9
[3,2,6,8,4,1,5,7]=>12
[4,6,2,8,3,1,5,7]=>8
[5,6,8,2,3,1,4,7]=>7
[6,5,8,3,2,1,4,7]=>3
[7,5,8,3,1,2,4,6]=>5
[8,5,7,3,1,4,2,6]=>3
[1,5,7,3,8,4,6,2]=>10
[1,4,3,7,8,5,6,2]=>14
[8,4,3,7,1,5,2,6]=>4
[6,4,3,8,2,1,5,7]=>4
[4,5,2,3,8,1,6,7]=>11
[3,2,5,4,8,1,6,7]=>17
[4,5,2,3,1,8,7,6]=>6
[6,4,3,1,2,8,7,5]=>3
[7,4,3,1,8,2,6,5]=>2
[8,4,3,1,7,6,2,5]=>1
[1,5,8,3,7,6,4,2]=>6
[8,5,1,3,7,6,2,4]=>4
[7,5,1,3,8,2,6,4]=>5
[6,5,1,3,2,8,7,4]=>6
[5,6,1,2,3,8,7,4]=>12
[4,6,2,1,3,8,7,5]=>8
[3,2,6,1,4,8,7,5]=>13
[3,2,7,1,8,4,6,5]=>8
[4,7,2,1,8,3,6,5]=>5
[5,7,1,2,8,3,6,4]=>9
[6,7,1,8,2,3,5,4]=>8
[7,6,1,8,3,2,5,4]=>4
[8,6,1,7,3,5,2,4]=>3
[1,6,8,7,3,5,4,2]=>4
[1,7,8,6,5,3,4,2]=>2
[8,7,1,6,5,3,2,4]=>2
[7,8,1,6,5,2,3,4]=>4
[6,8,1,7,2,5,3,4]=>5
[5,8,1,2,7,6,3,4]=>6
[4,8,2,1,7,6,3,5]=>2
[3,2,8,1,7,6,4,5]=>3
[4,1,2,8,7,6,5,3]=>5
[5,1,8,2,7,6,4,3]=>4
[6,1,8,7,2,5,4,3]=>3
[7,1,8,6,5,2,4,3]=>2
[8,1,7,6,5,4,2,3]=>1
[1,4,3,8,7,5,6,2]=>11
[4,1,2,8,7,5,6,3]=>8
[3,2,5,1,6,4,8,7]=>20
[3,2,5,4,7,1,8,6]=>16
[4,2,5,3,7,6,8,1]=>17
[4,2,5,3,7,1,8,6]=>13
[4,2,5,3,6,1,8,7]=>17
[4,2,5,1,6,3,8,7]=>18
[3,1,5,4,6,2,8,7]=>22
[4,1,5,3,6,2,8,7]=>19
[4,3,5,1,6,2,8,7]=>16
[4,3,5,2,7,1,8,6]=>10
[4,3,6,2,7,5,8,1]=>11
[4,3,6,2,7,1,8,5]=>8
[4,3,6,1,7,2,8,5]=>10
[4,3,5,1,7,2,8,6]=>12
[3,1,5,4,7,2,8,6]=>18
[2,1,5,4,7,3,8,6]=>20
[3,1,5,4,7,6,8,2]=>20
[4,1,5,3,7,6,8,2]=>17
[4,3,5,1,7,6,8,2]=>14
[4,3,6,1,7,5,8,2]=>11
[4,3,6,5,7,1,8,2]=>12
[5,3,6,4,7,2,8,1]=>10
[5,3,6,4,7,1,8,2]=>10
[5,3,6,1,7,4,8,2]=>10
[5,1,6,3,7,4,8,2]=>13
[4,1,6,3,7,5,8,2]=>14
[3,1,6,4,7,5,8,2]=>17
[2,1,6,4,7,5,8,3]=>17
[2,1,6,4,7,3,8,5]=>18
[3,1,6,4,7,2,8,5]=>16
[4,1,6,3,7,2,8,5]=>13
[5,1,6,3,7,2,8,4]=>13
[5,3,6,1,7,2,8,4]=>10
[5,3,6,2,7,1,8,4]=>8
[5,3,6,2,7,4,8,1]=>10
[5,2,6,3,7,4,8,1]=>13
[5,2,6,3,7,1,8,4]=>11
[5,2,6,1,7,3,8,4]=>12
[4,2,5,1,7,3,8,6]=>14
[4,2,6,1,7,3,8,5]=>12
[4,2,6,3,7,1,8,5]=>11
[4,2,6,3,7,5,8,1]=>14
[3,2,6,4,7,5,8,1]=>17
[3,2,6,4,7,1,8,5]=>14
[3,2,6,1,7,4,8,5]=>14
[3,2,5,1,7,4,8,6]=>16
[3,2,4,1,7,5,8,6]=>20
[3,1,4,2,7,6,8,5]=>20
[3,2,5,1,7,6,8,4]=>14
[3,2,6,1,7,5,8,4]=>11
[3,2,6,5,7,1,8,4]=>12
[4,2,6,5,7,3,8,1]=>13
[4,2,6,5,7,1,8,3]=>12
[4,2,6,1,7,5,8,3]=>11
[4,2,5,1,7,6,8,3]=>14
[4,1,5,2,7,6,8,3]=>18
[3,1,5,2,7,6,8,4]=>18
[2,1,5,3,7,6,8,4]=>22
[2,1,6,3,7,5,8,4]=>19
[3,1,6,2,7,5,8,4]=>15
[4,1,6,2,7,5,8,3]=>15
[5,1,6,2,7,4,8,3]=>14
[5,2,6,1,7,4,8,3]=>10
[5,2,6,4,7,1,8,3]=>10
[5,2,6,4,7,3,8,1]=>11
[5,4,6,2,7,3,8,1]=>9
[5,4,6,2,7,1,8,3]=>8
[5,4,6,1,7,2,8,3]=>10
[5,1,6,4,7,2,8,3]=>12
[4,1,6,5,7,2,8,3]=>14
[3,1,6,5,7,2,8,4]=>14
[2,1,6,5,7,3,8,4]=>16
[3,1,6,5,7,4,8,2]=>14
[4,1,6,5,7,3,8,2]=>13
[5,1,6,4,7,3,8,2]=>11
[5,4,6,1,7,3,8,2]=>9
[5,4,6,3,7,1,8,2]=>8
[8,3,5,2,1,6,4,7]=>9
[8,6,3,5,2,4,1,7]=>3
[3,7,5,2,4,1,8,6]=>7
[8,3,7,5,2,4,6,1]=>3
[8,2,4,5,7,3,6,1]=>8
[2,4,5,7,3,1,8,6]=>15
[8,2,4,6,5,3,1,7]=>8
[8,2,5,4,6,1,3,7]=>9
[8,6,3,5,1,4,2,7]=>4
[8,6,1,4,5,3,2,7]=>6
[8,1,5,6,4,3,2,7]=>7
[5,7,4,3,2,1,8,6]=>1
[8,5,7,4,3,2,6,1]=>0
[4,6,8,3,2,7,5,1]=>2
[4,7,6,3,2,8,1,5]=>2
[1,4,6,7,3,2,8,5]=>15
[5,4,7,3,1,8,2,6]=>3
[1,7,4,5,3,2,8,6]=>12
[3,7,5,1,4,2,8,6]=>9
[5,7,4,2,1,3,8,6]=>5
[8,5,7,4,2,1,6,3]=>0
[8,3,7,5,1,4,6,2]=>3
[8,4,1,7,5,3,6,2]=>3
[4,6,3,8,7,1,5,2]=>2
[1,7,4,8,6,3,5,2]=>5
[8,4,7,6,3,5,2,1]=>0
[3,6,5,8,7,4,1,2]=>4
[3,1,5,8,6,7,4,2]=>9
[4,8,1,6,7,3,5,2]=>3
[3,6,4,1,8,7,5,2]=>5
[8,2,6,1,4,7,5,3]=>5
[2,7,6,8,1,4,3,5]=>6
[3,7,1,6,4,8,2,5]=>8
[1,7,3,5,6,8,2,4]=>13
[1,3,6,7,5,8,2,4]=>15
[3,7,6,5,8,2,1,4]=>3
[3,6,8,5,7,2,4,1]=>3
[2,3,5,7,6,8,1,4]=>17
[2,1,6,5,7,8,3,4]=>14
[4,2,7,6,8,3,1,5]=>5
[4,2,6,8,7,3,5,1]=>5
[3,8,2,4,6,7,5,1]=>9
[3,7,2,6,4,8,1,5]=>7
[3,2,6,1,4,7,8,5]=>18
[5,3,7,2,1,8,4,6]=>5
[4,7,3,2,1,5,8,6]=>9
[8,7,6,1,3,4,2,5]=>5
[8,5,7,3,2,1,6,4]=>0
[8,3,6,7,2,1,5,4]=>1
[3,7,8,6,2,1,5,4]=>1
[8,7,6,3,5,2,4,1]=>0
[2,7,4,8,1,6,5,3]=>4
[4,6,8,2,1,7,5,3]=>2
[8,4,1,5,7,2,6,3]=>6
[8,5,3,7,1,6,2,4]=>1
[8,5,7,2,1,3,6,4]=>4
[8,2,6,7,1,3,5,4]=>5
[8,3,6,1,7,5,2,4]=>2
[4,6,1,8,7,2,5,3]=>4
[8,1,2,5,6,7,4,3]=>12
[8,2,6,5,7,4,1,3]=>2
[2,1,7,8,5,6,4,3]=>4
[8,2,5,7,6,4,3,1]=>2
[2,7,6,8,5,4,1,3]=>2
[1,7,2,5,8,6,4,3]=>10
[1,7,4,8,2,6,5,3]=>7
[3,7,8,1,6,5,2,4]=>2
[2,7,8,6,1,3,5,4]=>5
[8,7,6,3,5,1,4,2]=>0
[8,4,7,6,5,1,3,2]=>0
[8,7,1,5,6,4,3,2]=>1
[8,1,6,7,5,4,3,2]=>1
[5,4,3,6,1,2,8,7]=>8
[2,7,6,4,5,8,1,3]=>6
[5,7,3,6,1,8,2,4]=>4
[2,1,7,6,5,8,3,4]=>8
[6,4,3,5,8,1,7,2]=>4
[7,3,5,4,8,6,1,2]=>4
[5,4,3,2,7,1,8,6]=>4
[4,3,6,2,8,7,5,1]=>4
[4,3,7,6,2,1,8,5]=>4
[6,4,3,1,7,2,8,5]=>6
[4,3,7,1,8,6,5,2]=>2
[5,3,8,7,6,4,2,1]=>0
[7,5,3,1,8,6,4,2]=>0
[1,8,6,5,3,7,4,2]=>4
[6,1,7,5,3,2,8,4]=>7
[7,6,5,3,2,1,8,4]=>0
[6,5,3,2,8,7,4,1]=>0
[5,2,6,3,8,7,4,1]=>7
[5,2,7,6,3,1,8,4]=>6
[6,5,2,1,7,3,8,4]=>8
[5,2,7,1,8,6,4,3]=>2
[6,2,8,7,5,4,3,1]=>0
[7,6,2,1,8,5,4,3]=>0
[6,1,7,2,8,5,4,3]=>6
[7,1,8,6,5,4,3,2]=>0
[4,5,2,6,3,1,8,7]=>11
[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]=>1
[8,3,7,5,2,1,6,4]=>1
[6,3,7,5,2,8,4,1]=>3
[3,1,6,5,4,2,8,7]=>14
[5,6,3,2,4,1,8,7]=>6
[3,6,2,4,1,5,8,7]=>16
[2,6,1,3,5,4,8,7]=>22
[6,7,2,3,4,8,5,1]=>8
[8,7,2,3,4,1,6,5]=>7
[5,1,7,3,8,4,6,2]=>7
[2,5,7,3,8,6,4,1]=>8
[7,6,1,3,5,8,4,2]=>5
[3,6,7,4,1,8,5,2]=>6
[5,6,3,7,4,8,1,2]=>6
[2,1,6,7,4,8,5,3]=>11
[2,1,8,7,4,3,6,5]=>8
[5,8,3,7,4,2,6,1]=>1
[3,8,7,4,1,2,6,5]=>4
[7,8,1,3,5,2,6,4]=>7
[5,8,7,3,2,6,1,4]=>0
[2,8,6,3,1,5,7,4]=>7
[8,1,6,3,2,5,4,7]=>13
[2,8,4,1,6,3,7,5]=>10
[4,8,1,2,7,6,3,5]=>6
[3,8,4,2,5,7,1,6]=>9
[6,8,3,5,2,7,4,1]=>1
[2,1,5,3,8,7,6,4]=>14
[6,5,3,2,8,7,1,4]=>0
[7,5,2,4,8,1,6,3]=>2
[3,4,2,8,5,7,6,1]=>10
[2,4,1,8,7,6,5,3]=>4
[8,4,2,1,7,5,3,6]=>5
[4,3,1,8,6,7,5,2]=>3
[3,1,4,8,6,5,7,2]=>14
[7,1,6,5,4,8,2,3]=>4
[3,7,5,6,8,4,2,1]=>5
[5,7,1,6,8,2,4,3]=>5
[8,6,2,5,1,7,4,3]=>1
[5,6,2,1,8,7,3,4]=>4
[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]=>21
[2,4,3,1,8,5,6,7]=>21
[7,5,2,8,3,4,6,1]=>4
[5,6,2,8,4,3,1,7]=>4
[4,7,2,8,1,5,3,6]=>6
[8,7,2,1,4,5,6,3]=>7
[3,6,8,7,1,5,4,2]=>2
[5,7,8,6,3,4,1,2]=>1
[7,1,8,5,4,3,6,2]=>3
[2,7,8,4,5,3,6,1]=>6
[5,7,3,8,1,4,6,2]=>3
[2,1,7,8,5,4,6,3]=>6
[2,1,5,8,4,6,3,7]=>16
[6,5,3,8,4,1,2,7]=>2
[7,5,8,4,3,6,2,1]=>0
[2,4,8,3,5,6,1,7]=>17
[4,1,8,3,6,5,2,7]=>10
[3,4,8,1,7,2,5,6]=>10
[8,4,1,3,7,2,6,5]=>5
[3,1,8,2,4,7,6,5]=>13
[2,3,8,1,4,6,7,5]=>18
[4,3,8,2,5,1,7,6]=>6
[6,3,8,4,2,5,7,1]=>5
[7,4,3,8,2,5,1,6]=>3
[2,1,4,8,3,5,7,6]=>22
[6,8,2,4,3,5,1,7]=>7
[4,8,2,3,5,1,6,7]=>14
[3,8,2,1,4,6,5,7]=>17
[2,8,1,3,4,5,7,6]=>25
[7,1,6,8,4,3,2,5]=>4
[7,1,6,5,8,3,2,4]=>4
[3,7,6,1,4,8,2,5]=>7
[2,7,8,4,1,6,5,3]=>3
[3,6,4,5,7,2,8,1]=>13
[1,8,2,7,3,4,5,6]=>21
[3,2,1,5,8,4,6,7]=>20
[5,4,3,2,1,8,6,7]=>5
[1,8,2,4,3,5,6,7]=>30
[1,7,2,4,3,5,6,8]=>31
[1,6,2,4,3,5,7,8]=>33
[1,5,2,4,3,6,7,8]=>36
[1,6,2,5,3,4,7,8]=>29
[1,7,2,5,3,4,6,8]=>27
[1,8,2,5,3,4,6,7]=>26
[1,8,2,6,3,4,5,7]=>23
[1,7,2,6,3,4,5,8]=>24
[1,8,2,7,3,5,4,6]=>17
[1,7,2,8,3,5,4,6]=>18
[1,6,2,8,3,5,4,7]=>19
[1,5,2,8,3,6,4,7]=>21
[1,4,2,8,3,6,5,7]=>23
[1,3,2,8,4,6,5,7]=>27
[1,2,3,8,4,6,5,7]=>33
[1,2,3,7,4,6,5,8]=>36
[1,3,2,7,4,6,5,8]=>30
[1,4,2,7,3,6,5,8]=>26
[1,5,2,7,3,6,4,8]=>24
[1,6,2,7,3,5,4,8]=>22
[1,7,2,6,3,5,4,8]=>20
[1,8,2,6,3,5,4,7]=>19
[1,8,2,5,3,6,4,7]=>22
[1,7,2,5,3,6,4,8]=>23
[1,6,2,5,3,7,4,8]=>25
[1,5,2,4,3,7,6,8]=>30
[1,6,2,4,3,7,5,8]=>28
[1,7,2,4,3,6,5,8]=>26
[1,8,2,4,3,6,5,7]=>25
[1,8,2,3,4,6,5,7]=>30
[1,7,2,3,4,6,5,8]=>31
[1,8,2,3,4,7,5,6]=>26
[1,8,2,4,3,7,5,6]=>21
[1,7,2,4,3,8,5,6]=>22
[1,6,2,4,3,8,5,7]=>23
[1,5,2,4,3,8,6,7]=>25
[1,6,2,5,3,8,4,7]=>20
[1,7,2,5,3,8,4,6]=>19
[1,8,2,5,3,7,4,6]=>18
[1,8,2,6,3,7,4,5]=>16
[1,7,2,6,3,8,4,5]=>17
[1,2,3,8,4,7,5,6]=>29
[1,3,2,8,4,7,5,6]=>23
[1,4,2,8,3,7,5,6]=>19
[1,5,2,8,3,7,4,6]=>17
[1,6,2,8,3,7,4,5]=>16
[1,7,2,8,3,6,4,5]=>15
[1,8,2,7,3,6,4,5]=>14
[6,7,8,1,4,3,2,5]=>4
[2,8,4,1,6,7,5,3]=>6
[4,8,5,7,1,6,2,3]=>3
[8,7,6,5,2,1,4,3]=>0
[8,3,1,5,4,7,2,6]=>9
[8,7,6,5,1,4,2,3]=>1
[7,5,1,3,8,4,2,6]=>6
[7,6,1,4,8,3,2,5]=>4
[7,1,3,5,8,2,4,6]=>13
[7,5,3,6,4,2,8,1]=>3
[8,2,6,3,4,7,5,1]=>8
[7,2,6,3,5,4,8,1]=>8
[6,2,7,4,3,5,8,1]=>9
[3,7,6,4,5,2,8,1]=>6
[2,7,6,5,3,4,8,1]=>7
[8,6,5,4,2,7,3,1]=>0
[6,5,8,4,2,7,3,1]=>0
[1,8,6,3,7,5,2,4]=>5
[8,7,5,2,6,4,3,1]=>0
[8,7,1,6,2,5,4,3]=>3
[1,7,2,8,5,3,4,6]=>15
[7,6,1,8,4,3,2,5]=>3
[8,6,1,7,4,2,5,3]=>3
[8,1,2,7,3,4,6,5]=>17
[7,1,2,8,3,5,4,6]=>17
[8,2,6,1,7,3,5,4]=>5
[4,7,5,6,8,3,2,1]=>5
[8,6,4,7,5,3,2,1]=>0
[5,4,8,1,7,2,6,3]=>2
[2,3,8,7,4,5,6,1]=>12
[7,2,8,6,4,3,5,1]=>2
[8,2,7,6,3,5,4,1]=>2
[8,1,7,6,5,2,4,3]=>2
[7,1,8,6,5,3,2,4]=>2
[1,2,8,7,6,3,4,5]=>13
[3,8,7,6,4,5,2,1]=>1
[2,8,7,6,5,3,4,1]=>1
[1,8,7,6,5,4,2,3]=>1
[3,8,6,7,1,5,2,4]=>2
[5,4,7,1,3,8,2,6]=>5
[5,6,2,1,4,8,3,7]=>8
[2,1,8,4,7,5,6,3]=>9
[4,1,3,2,8,5,6,7]=>21
[3,2,1,4,8,5,6,7]=>25
[1,8,4,2,5,3,6,7]=>22
[8,1,5,3,2,4,6,7]=>19
[3,8,1,5,2,4,6,7]=>18
[1,6,7,2,8,4,3,5]=>12
[6,7,1,4,2,8,3,5]=>8
[6,3,7,1,4,8,2,5]=>7
[3,7,8,1,5,2,4,6]=>8
[7,1,2,8,5,3,4,6]=>14
[1,7,2,8,4,5,3,6]=>15
[1,2,7,5,8,3,4,6]=>19
[2,8,1,7,4,3,6,5]=>8
[4,2,6,5,8,3,7,1]=>9
[5,2,4,7,3,6,8,1]=>12
[5,1,2,4,8,3,6,7]=>20
[4,3,6,1,5,8,2,7]=>11
[2,6,1,4,5,8,3,7]=>16
[2,5,3,4,1,8,6,7]=>18
[4,3,5,2,1,8,6,7]=>11
[3,1,6,7,5,8,2,4]=>10
[2,8,1,7,5,6,3,4]=>4
[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]=>6
[5,2,6,8,4,3,7,1]=>6
[3,1,6,5,4,8,2,7]=>13
[4,1,6,5,8,3,2,7]=>10
[5,1,6,8,4,3,2,7]=>7
[8,5,4,7,6,3,2,1]=>0
[5,7,1,8,4,3,2,6]=>4
[2,7,1,5,4,3,8,6]=>13
[8,2,1,5,4,3,7,6]=>12
[8,4,1,5,7,3,2,6]=>6
[8,5,6,7,1,3,2,4]=>3
[8,4,6,1,7,3,2,5]=>3
[8,3,6,1,4,7,2,5]=>6
[2,7,6,1,4,3,8,5]=>10
[6,7,8,5,1,3,2,4]=>3
[5,7,6,8,2,3,4,1]=>3
[5,7,2,8,4,3,6,1]=>3
[6,7,8,2,4,3,5,1]=>3
[4,7,6,2,8,3,5,1]=>3
[8,3,6,2,4,7,5,1]=>5
[3,7,6,2,4,8,5,1]=>6
[5,7,3,8,4,6,2,1]=>2
[4,7,3,5,8,6,2,1]=>5
[8,7,2,1,4,3,6,5]=>8
[8,7,3,1,4,6,2,5]=>5
[8,7,6,3,2,5,4,1]=>0
[8,7,3,5,1,6,2,4]=>2
[8,7,2,5,1,3,6,4]=>5
[8,2,6,5,1,3,7,4]=>6
[8,4,6,5,7,1,2,3]=>3
[5,7,6,8,4,1,2,3]=>3
[4,7,6,5,8,1,2,3]=>4
[3,7,6,5,1,8,2,4]=>4
[2,6,5,7,3,4,8,1]=>11
[1,6,4,7,5,8,2,3]=>11
[8,5,3,6,2,7,4,1]=>2
[1,3,7,4,6,8,2,5]=>17
[4,7,5,6,3,2,8,1]=>5
[1,7,6,5,4,8,2,3]=>5
[8,1,6,5,7,2,4,3]=>4
[1,2,7,6,8,3,4,5]=>17
[6,1,7,5,3,8,2,4]=>6
[2,1,7,5,6,8,3,4]=>11
[5,4,1,7,6,8,2,3]=>7
[4,8,5,6,2,7,3,1]=>4
[3,8,6,4,2,7,5,1]=>3
[7,8,5,2,4,6,3,1]=>1
[2,8,6,3,7,4,5,1]=>6
[7,8,1,6,2,4,5,3]=>5
[6,8,1,4,7,2,5,3]=>4
[3,8,4,1,7,2,6,5]=>5
[5,4,7,1,8,3,2,6]=>4
[3,7,4,1,8,5,2,6]=>8
[6,7,1,4,8,3,2,5]=>5
[2,7,1,8,4,5,3,6]=>10
[6,1,2,8,4,3,5,7]=>17
[6,5,1,4,3,8,2,7]=>5
[1,6,2,5,8,3,4,7]=>18
[8,5,1,3,7,2,6,4]=>5
[8,4,2,1,7,3,6,5]=>4
[7,4,2,1,8,5,3,6]=>5
[1,5,4,2,8,3,6,7]=>19
[6,4,3,1,5,8,2,7]=>7
[3,7,6,8,4,5,2,1]=>3
[2,7,6,8,5,3,4,1]=>3
[1,7,6,8,5,4,2,3]=>3
[1,4,8,6,7,5,2,3]=>7
[2,4,8,6,7,3,5,1]=>7
[7,3,8,5,4,6,2,1]=>2
[3,4,8,5,6,7,2,1]=>11
[6,3,5,8,4,7,2,1]=>3
[5,4,3,8,6,7,2,1]=>3
[5,4,2,8,7,3,6,1]=>1
[6,2,5,8,7,3,4,1]=>3
[3,2,8,5,7,4,6,1]=>6
[1,3,8,7,5,6,2,4]=>8
[2,1,8,7,4,6,3,5]=>6
[3,1,8,5,7,6,2,4]=>5
[6,1,5,8,7,4,2,3]=>3
[5,4,1,8,7,6,2,3]=>1
[5,8,6,7,4,3,2,1]=>1
[4,8,7,5,6,3,2,1]=>1
[2,8,3,1,5,4,6,7]=>21
[2,5,3,4,7,1,8,6]=>17
[2,4,8,3,5,7,6,1]=>13
[4,2,5,3,1,8,6,7]=>14
[4,2,1,8,5,3,6,7]=>15
[5,4,1,3,8,2,6,7]=>10
[5,1,4,8,3,2,6,7]=>12
[1,5,8,4,3,2,6,7]=>14
[1,8,5,4,3,2,6,7]=>13
[1,7,4,3,8,5,2,6]=>11
[1,5,7,3,8,4,2,6]=>11
[5,1,4,7,8,3,2,6]=>8
[4,8,1,5,7,3,6,2]=>5
[8,1,5,3,7,4,6,2]=>7
[3,8,4,7,6,5,2,1]=>3
[1,6,8,5,3,7,4,2]=>5
[6,8,1,7,4,3,5,2]=>2
[6,4,8,1,7,3,5,2]=>1
[6,4,8,7,1,5,2,3]=>1
[7,6,4,1,3,8,2,5]=>3
[1,7,5,6,3,2,8,4]=>9
[4,2,1,7,8,5,3,6]=>8
[2,7,4,6,3,1,8,5]=>8
[2,6,8,4,3,7,5,1]=>6
[6,2,4,8,3,7,5,1]=>5
[7,2,6,3,4,1,8,5]=>8
[2,6,7,3,1,4,8,5]=>13
[2,7,1,8,3,5,4,6]=>13
[2,1,7,3,5,8,4,6]=>19
[8,7,1,3,6,2,4,5]=>8
[8,2,1,7,3,5,6,4]=>9
[7,8,2,6,3,1,5,4]=>2
[8,7,2,6,3,5,4,1]=>2
[1,2,8,7,4,5,6,3]=>13
[8,3,7,1,5,6,2,4]=>3
[8,6,1,2,7,5,3,4]=>6
[8,1,6,2,7,4,5,3]=>7
[1,8,5,2,6,7,4,3]=>9
[5,2,1,8,6,7,4,3]=>3
[2,8,5,7,6,4,3,1]=>2
[1,7,8,5,2,6,4,3]=>5
[7,8,1,6,4,2,5,3]=>3
[7,8,6,1,5,3,2,4]=>2
[7,3,8,6,1,5,2,4]=>1
[8,7,6,1,5,3,4,2]=>1
[8,7,1,6,4,5,3,2]=>1
[8,1,7,5,6,4,3,2]=>1
[1,8,6,7,5,4,3,2]=>1
[9,1,2,3,4,5,6,7,8]=>56
[8,1,2,3,4,5,6,9,7]=>50
[2,9,1,3,4,5,6,7,8]=>50
[9,3,1,2,4,5,6,7,8]=>45
[8,9,1,2,3,4,5,6,7]=>35
[9,7,8,1,2,3,4,5,6]=>20
[2,3,4,5,6,7,9,1,8]=>50
[2,3,4,5,6,7,8,9,1]=>56
[2,3,4,5,6,7,8,1,9]=>56
[2,3,4,5,6,7,1,8,9]=>57
[1,2,3,4,5,6,7,9,8]=>77
[2,1,3,4,5,6,7,8,9]=>77
[1,8,2,3,4,5,6,9,7]=>51
[7,1,2,3,4,5,6,9,8]=>50
[2,1,9,3,4,5,6,7,8]=>50
[2,8,1,3,4,5,6,7,9]=>51
[1,2,3,4,5,6,7,8,9]=>84
[3,2,4,5,6,7,8,9,1]=>50
[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]=>0
[8,7,6,4,5,3,2,1,9]=>1
[1,9,8,7,5,6,4,3,2]=>1
[8,7,5,4,6,3,2,1,9]=>2
[8,7,4,6,5,3,2,1,9]=>2
[1,9,8,6,5,7,4,3,2]=>2
[1,9,8,5,7,6,4,3,2]=>2
[9,2,1,3,4,5,6,7,8]=>50
[9,2,3,1,4,5,6,7,8]=>45
[4,2,3,5,6,7,8,9,1]=>45
[3,4,2,5,6,7,8,9,1]=>45
[9,8,1,2,3,4,5,6,7]=>35
[7,8,9,1,2,3,4,5,6]=>21
[9,8,7,1,2,3,4,5,6]=>20
[6,7,8,9,1,2,3,4,5]=>14
[9,6,7,8,1,2,3,4,5]=>11
[8,9,6,7,1,2,3,4,5]=>10
[9,8,6,7,1,2,3,4,5]=>10
[9,8,7,6,1,2,3,4,5]=>10
[9,5,6,7,8,1,2,3,4]=>8
[8,9,5,6,7,1,2,3,4]=>5
[9,8,5,6,7,1,2,3,4]=>5
[9,7,8,5,6,1,2,3,4]=>4
[9,8,7,5,6,1,2,3,4]=>4
[9,8,7,6,5,1,2,3,4]=>4
[7,8,9,4,5,6,1,2,3]=>3
[9,7,8,4,5,6,1,2,3]=>2
[9,8,7,4,5,6,1,2,3]=>2
[8,9,6,7,4,5,1,2,3]=>1
[9,8,6,7,4,5,1,2,3]=>1
[9,8,7,6,4,5,1,2,3]=>1
[9,8,7,6,5,4,1,2,3]=>1
[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]=>1
[1,8,9,7,6,5,4,3,2]=>1
[7,6,8,5,4,3,2,1,9]=>2
[6,8,7,5,4,3,2,1,9]=>2
[1,8,7,9,6,5,4,3,2]=>2
[1,7,9,8,6,5,4,3,2]=>2
[8,1,2,3,4,5,6,7,9]=>56
[1,9,2,3,4,5,6,7,8]=>56
[7,8,1,2,3,4,5,6,9]=>36
[1,8,9,2,3,4,5,6,7]=>36
[7,1,8,2,3,4,5,6,9]=>37
[6,8,1,2,3,4,5,7,9]=>37
[1,8,2,9,3,4,5,6,7]=>37
[1,7,9,2,3,4,5,6,8]=>37
[7,1,2,3,4,5,6,8,9]=>57
[3,4,1,2,5,6,7,8,9]=>60
[3,2,1,4,5,6,7,8,9]=>65
[4,5,6,1,2,3,7,8,9]=>39
[4,2,5,1,3,6,7,8,9]=>50
[4,3,2,1,5,6,7,8,9]=>50
[5,6,7,8,1,2,3,4,9]=>20
[5,2,6,7,1,3,4,8,9]=>31
[5,6,3,4,1,2,7,8,9]=>28
[5,3,2,6,1,4,7,8,9]=>37
[5,4,3,2,1,6,7,8,9]=>34
[6,2,7,8,9,1,3,4,5]=>14
[6,7,3,4,8,1,2,5,9]=>15
[6,3,2,7,8,1,4,5,9]=>20
[6,4,7,2,5,1,3,8,9]=>19
[6,4,3,2,7,1,5,8,9]=>23
[6,5,4,3,2,1,7,8,9]=>19
[7,4,8,2,5,9,1,3,6]=>8
[7,4,3,2,8,9,1,5,6]=>8
[7,8,5,6,3,4,1,2,9]=>4
[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]=>7
[8,6,9,4,7,2,5,1,3]=>0
[8,6,4,3,9,2,7,1,5]=>0
[8,6,5,4,3,2,9,1,7]=>0
[2,1,4,3,6,5,8,7,10,9]=>80
[4,3,2,1,6,5,8,7,10,9]=>56
[6,3,2,5,4,1,8,7,10,9]=>40
[8,3,2,5,4,7,6,1,10,9]=>32
[10,3,2,5,4,7,6,9,8,1]=>32
[2,1,6,5,4,3,8,7,10,9]=>56
[6,5,4,3,2,1,8,7,10,9]=>24
[8,5,4,3,2,7,6,1,10,9]=>16
[10,5,4,3,2,7,6,9,8,1]=>16
[2,1,8,5,4,7,6,3,10,9]=>40
[8,7,4,3,6,5,2,1,10,9]=>8
[10,7,4,3,6,5,2,9,8,1]=>8
[2,1,10,5,4,7,6,9,8,3]=>32
[10,9,4,3,6,5,8,7,2,1]=>8
[8,9,5,6,3,4,10,1,2,7]=>6
[2,1,4,3,8,7,6,5,10,9]=>56
[4,3,2,1,8,7,6,5,10,9]=>32
[8,3,2,7,6,5,4,1,10,9]=>16
[10,3,2,7,6,5,4,9,8,1]=>16
[2,1,8,7,6,5,4,3,10,9]=>24
[8,7,6,5,4,3,2,1,10,9]=>0
[9,7,6,5,4,3,2,10,1,8]=>0
[10,7,6,5,4,3,2,9,8,1]=>0
[2,1,10,7,6,5,4,9,8,3]=>16
[10,9,6,5,4,3,8,7,2,1]=>0
[2,1,4,3,10,7,6,9,8,5]=>40
[4,3,2,1,10,7,6,9,8,5]=>16
[10,3,2,9,6,5,8,7,4,1]=>8
[2,1,10,9,6,5,8,7,4,3]=>8
[10,9,8,5,4,7,6,3,2,1]=>0
[6,7,8,9,10,1,2,3,4,5]=>20
[7,3,2,8,9,10,1,4,5,6]=>20
[8,5,4,3,2,9,10,1,6,7]=>10
[2,1,4,3,6,5,10,9,8,7]=>56
[4,3,2,1,6,5,10,9,8,7]=>32
[6,3,2,5,4,1,10,9,8,7]=>16
[10,3,2,5,4,9,8,7,6,1]=>16
[2,1,6,5,4,3,10,9,8,7]=>32
[6,5,4,3,2,1,10,9,8,7]=>0
[10,5,4,3,2,9,8,7,6,1]=>0
[2,1,10,5,4,9,8,7,6,3]=>16
[10,9,4,3,8,7,6,5,2,1]=>0
[9,7,5,10,3,8,2,6,1,4]=>0
[2,1,4,3,10,9,8,7,6,5]=>24
[4,3,2,1,10,9,8,7,6,5]=>0
[10,3,2,9,8,7,6,5,4,1]=>0
[2,1,10,9,8,7,6,5,4,3]=>0
[10,9,8,7,6,5,4,3,2,1]=>0
[2,3,4,5,6,7,8,9,10,1]=>84
[2,3,4,5,6,7,8,9,1,10]=>84
[10,8,9,5,6,7,1,2,3,4]=>5
[10,8,9,4,5,6,1,2,3,7]=>8
[10,7,8,5,6,9,1,2,3,4]=>6
[10,7,8,4,5,9,1,2,3,6]=>7
[10,6,7,4,5,8,1,2,3,9]=>12
[10,7,8,3,4,9,1,2,5,6]=>10
[10,6,7,3,4,8,1,2,5,9]=>15
[9,8,10,5,6,7,1,2,3,4]=>5
[9,8,10,4,5,6,1,2,3,7]=>8
[9,7,10,5,6,8,1,2,3,4]=>5
[9,7,10,4,5,8,1,2,3,6]=>6
[9,6,10,4,5,7,1,2,3,8]=>9
[9,7,10,3,4,8,1,2,5,6]=>9
[9,6,10,3,4,7,1,2,5,8]=>12
[8,7,9,5,6,10,1,2,3,4]=>7
[8,7,9,4,5,10,1,2,3,6]=>8
[8,6,9,4,5,10,1,2,3,7]=>8
[7,6,8,4,5,9,1,2,3,10]=>15
[8,7,9,3,4,10,1,2,5,6]=>11
[8,6,9,3,4,10,1,2,5,7]=>11
[7,6,8,3,4,9,1,2,5,10]=>18
[9,6,10,5,7,8,1,2,3,4]=>6
[9,6,10,4,7,8,1,2,3,5]=>6
[9,5,10,4,6,7,1,2,3,8]=>11
[9,6,10,3,7,8,1,2,4,5]=>7
[9,5,10,3,6,7,1,2,4,8]=>12
[8,6,9,5,7,10,1,2,3,4]=>8
[8,6,9,4,7,10,1,2,3,5]=>8
[8,5,9,4,6,10,1,2,3,7]=>10
[7,5,8,4,6,9,1,2,3,10]=>17
[8,6,9,3,7,10,1,2,4,5]=>9
[8,5,9,3,6,10,1,2,4,7]=>11
[7,5,8,3,6,9,1,2,4,10]=>18
[8,4,9,3,5,10,1,2,6,7]=>15
[7,4,8,3,5,9,1,2,6,10]=>22
[9,6,10,2,7,8,1,3,4,5]=>9
[9,5,10,2,6,7,1,3,4,8]=>14
[8,6,9,2,7,10,1,3,4,5]=>11
[8,5,9,2,6,10,1,3,4,7]=>13
[7,5,8,2,6,9,1,3,4,10]=>20
[8,4,9,2,5,10,1,3,6,7]=>17
[7,4,8,2,5,9,1,3,6,10]=>24
[1,2,3,4,5,6,7,8,10,9]=>112
[2,1,3,4,5,6,7,8,9,10]=>112
[9,1,2,3,4,5,6,7,10,8]=>77
[2,10,1,3,4,5,6,7,8,9]=>77
[1,2,3,4,5,6,7,8,9,10]=>120
[9,8,7,6,5,4,3,2,1,10]=>0
[10,1,2,3,4,5,6,7,8,9]=>84
[10,9,1,2,3,4,5,6,7,8]=>56
[1,10,9,8,7,6,5,4,3,2]=>0
[9,8,7,5,6,4,3,2,1,10]=>1
[1,10,9,8,6,7,5,4,3,2]=>1
[10,2,1,3,4,5,6,7,8,9]=>77
[3,2,4,5,6,7,8,9,10,1]=>77
[2,4,6,8,10,1,3,5,7,9]=>40
[2,4,6,9,10,1,3,5,7,8]=>37
[2,4,7,8,10,1,3,5,6,9]=>37
[2,4,7,9,10,1,3,5,6,8]=>34
[2,4,8,9,10,1,3,5,6,7]=>32
[2,5,6,8,10,1,3,4,7,9]=>37
[2,5,6,9,10,1,3,4,7,8]=>34
[2,5,7,8,10,1,3,4,6,9]=>34
[2,5,7,9,10,1,3,4,6,8]=>31
[2,5,8,9,10,1,3,4,6,7]=>29
[2,6,7,8,10,1,3,4,5,9]=>32
[2,6,7,9,10,1,3,4,5,8]=>29
[2,6,8,9,10,1,3,4,5,7]=>27
[2,7,8,9,10,1,3,4,5,6]=>26
[3,4,6,8,10,1,2,5,7,9]=>37
[3,4,6,9,10,1,2,5,7,8]=>34
[3,4,7,8,10,1,2,5,6,9]=>34
[3,4,7,9,10,1,2,5,6,8]=>31
[3,4,8,9,10,1,2,5,6,7]=>29
[3,5,6,8,10,1,2,4,7,9]=>34
[3,5,6,9,10,1,2,4,7,8]=>31
[3,5,7,8,10,1,2,4,6,9]=>31
[3,5,7,9,10,1,2,4,6,8]=>28
[3,5,8,9,10,1,2,4,6,7]=>26
[3,6,7,8,10,1,2,4,5,9]=>29
[3,6,7,9,10,1,2,4,5,8]=>26
[3,6,8,9,10,1,2,4,5,7]=>24
[3,7,8,9,10,1,2,4,5,6]=>23
[4,5,6,8,10,1,2,3,7,9]=>32
[4,5,6,9,10,1,2,3,7,8]=>29
[4,5,7,8,10,1,2,3,6,9]=>29
[4,5,7,9,10,1,2,3,6,8]=>26
[4,5,8,9,10,1,2,3,6,7]=>24
[4,6,7,8,10,1,2,3,5,9]=>27
[4,6,7,9,10,1,2,3,5,8]=>24
[4,6,8,9,10,1,2,3,5,7]=>22
[4,7,8,9,10,1,2,3,5,6]=>21
[5,6,7,8,10,1,2,3,4,9]=>26
[5,6,7,9,10,1,2,3,4,8]=>23
[5,6,8,9,10,1,2,3,4,7]=>21
[5,7,8,9,10,1,2,3,4,6]=>20
[9,10,1,2,3,4,5,6,7,8]=>56
[8,9,10,1,2,3,4,5,6,7]=>36
[10,8,9,1,2,3,4,5,6,7]=>35
[10,9,8,1,2,3,4,5,6,7]=>35
[7,8,9,10,1,2,3,4,5,6]=>24
[10,7,8,9,1,2,3,4,5,6]=>21
[9,10,7,8,1,2,3,4,5,6]=>20
[10,9,7,8,1,2,3,4,5,6]=>20
[10,9,8,7,1,2,3,4,5,6]=>20
[10,6,7,8,9,1,2,3,4,5]=>14
[9,10,6,7,8,1,2,3,4,5]=>11
[10,9,6,7,8,1,2,3,4,5]=>11
[10,8,9,6,7,1,2,3,4,5]=>10
[10,9,8,6,7,1,2,3,4,5]=>10
[10,9,8,7,6,1,2,3,4,5]=>10
[9,10,5,6,7,8,1,2,3,4]=>8
[10,9,5,6,7,8,1,2,3,4]=>8
[8,9,10,5,6,7,1,2,3,4]=>6
[10,9,8,5,6,7,1,2,3,4]=>5
[9,10,7,8,5,6,1,2,3,4]=>4
[10,9,7,8,5,6,1,2,3,4]=>4
[10,9,8,7,5,6,1,2,3,4]=>4
[10,9,8,7,6,5,1,2,3,4]=>4
[10,7,8,9,4,5,6,1,2,3]=>3
[9,10,7,8,4,5,6,1,2,3]=>2
[10,9,7,8,4,5,6,1,2,3]=>2
[10,9,8,7,4,5,6,1,2,3]=>2
[10,8,9,6,7,4,5,1,2,3]=>1
[10,9,8,6,7,4,5,1,2,3]=>1
[10,9,8,7,6,4,5,1,2,3]=>1
[10,9,8,7,6,5,4,1,2,3]=>1
[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]=>1
[1,9,10,8,7,6,5,4,3,2]=>1
[9,1,2,3,4,5,6,7,8,10]=>84
[1,10,2,3,4,5,6,7,8,9]=>84
[8,9,1,2,3,4,5,6,7,10]=>57
[1,9,10,2,3,4,5,6,7,8]=>57
[3,4,1,2,5,6,7,8,9,10]=>92
[3,2,1,4,5,6,7,8,9,10]=>98
[4,5,6,1,2,3,7,8,9,10]=>66
[4,2,5,1,3,6,7,8,9,10]=>80
[4,3,2,1,5,6,7,8,9,10]=>80
[5,6,7,8,1,2,3,4,9,10]=>40
[5,2,6,7,1,3,4,8,9,10]=>56
[5,6,3,4,1,2,7,8,9,10]=>52
[5,3,2,6,1,4,7,8,9,10]=>64
[5,4,3,2,1,6,7,8,9,10]=>60
[6,2,7,8,9,1,3,4,5,10]=>32
[6,7,3,4,8,1,2,5,9,10]=>34
[6,3,2,7,8,1,4,5,9,10]=>42
[6,4,7,2,5,1,3,8,9,10]=>40
[6,4,3,2,7,1,5,8,9,10]=>46
[6,5,4,3,2,1,7,8,9,10]=>40
[7,8,3,4,9,10,1,2,5,6]=>16
[7,8,9,4,5,6,1,2,3,10]=>12
[7,4,3,2,8,9,1,5,6,10]=>26
[7,8,5,6,3,4,1,2,9,10]=>16
[7,5,3,8,2,6,1,4,9,10]=>26
[7,5,4,3,2,8,1,6,9,10]=>28
[7,6,5,4,3,2,1,8,9,10]=>22
[8,5,9,10,2,6,7,1,3,4]=>6
[8,5,3,9,2,6,10,1,4,7]=>12
[8,6,9,4,7,2,5,1,3,10]=>8
[8,6,4,3,9,2,7,1,5,10]=>12
[8,6,5,4,3,2,9,1,7,10]=>12
[8,7,6,5,4,3,2,1,9,10]=>8
[9,7,5,4,3,10,2,8,1,6]=>0
[1,2,3,4,5,6,7,8,9,11,10]=>156
[2,1,3,4,5,6,7,8,9,10,11]=>156
[11,1,2,3,4,5,6,7,8,9,10]=>120
[10,9,8,7,6,5,4,3,2,1,11]=>0
[1,11,10,9,8,7,6,5,4,3,2]=>0
[2,3,4,5,6,7,8,9,10,11,1]=>120
[10,1,2,3,4,5,6,7,8,9,11]=>120
[1,11,2,3,4,5,6,7,8,9,10]=>120
[2,1,4,3,6,5,8,7,10,9,12,11]=>160
[2,1,4,3,6,5,8,7,12,11,10,9]=>128
[2,1,4,3,6,5,10,9,8,7,12,11]=>128
[2,1,4,3,6,5,12,9,8,11,10,7]=>104
[2,1,4,3,6,5,12,11,10,9,8,7]=>80
[2,1,4,3,8,7,6,5,10,9,12,11]=>128
[2,1,4,3,8,7,6,5,12,11,10,9]=>96
[2,1,4,3,10,7,6,9,8,5,12,11]=>104
[2,1,4,3,12,7,6,9,8,11,10,5]=>88
[2,1,4,3,12,7,6,11,10,9,8,5]=>64
[2,1,4,3,10,9,8,7,6,5,12,11]=>80
[2,1,4,3,12,9,8,7,6,11,10,5]=>64
[2,1,4,3,12,11,8,7,10,9,6,5]=>48
[2,1,4,3,12,11,10,9,8,7,6,5]=>32
[2,1,6,5,4,3,8,7,10,9,12,11]=>128
[2,1,6,5,4,3,8,7,12,11,10,9]=>96
[2,1,6,5,4,3,10,9,8,7,12,11]=>96
[2,1,6,5,4,3,12,9,8,11,10,7]=>72
[2,1,6,5,4,3,12,11,10,9,8,7]=>48
[2,1,8,5,4,7,6,3,10,9,12,11]=>104
[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]=>88
[2,1,12,5,4,7,6,9,8,11,10,3]=>80
[2,1,12,5,4,7,6,11,10,9,8,3]=>56
[2,1,10,5,4,9,8,7,6,3,12,11]=>64
[2,1,12,5,4,9,8,7,6,11,10,3]=>56
[2,1,12,5,4,11,8,7,10,9,6,3]=>40
[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]=>80
[2,1,8,7,6,5,4,3,12,11,10,9]=>48
[2,1,10,7,6,5,4,9,8,3,12,11]=>64
[2,1,12,7,6,5,4,9,8,11,10,3]=>56
[2,1,12,7,6,5,4,11,10,9,8,3]=>32
[2,1,10,9,6,5,8,7,4,3,12,11]=>48
[2,1,12,9,6,5,8,7,4,11,10,3]=>40
[2,1,12,11,6,5,8,7,10,9,4,3]=>32
[2,1,12,11,6,5,10,9,8,7,4,3]=>16
[2,1,10,9,8,7,6,5,4,3,12,11]=>32
[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]=>16
[2,1,12,11,10,7,6,9,8,5,4,3]=>8
[2,1,12,11,10,9,8,7,6,5,4,3]=>0
[4,3,2,1,6,5,8,7,10,9,12,11]=>128
[4,3,2,1,6,5,8,7,12,11,10,9]=>96
[4,3,2,1,6,5,10,9,8,7,12,11]=>96
[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]=>48
[4,3,2,1,8,7,6,5,10,9,12,11]=>96
[4,3,2,1,8,7,6,5,12,11,10,9]=>64
[4,3,2,1,10,7,6,9,8,5,12,11]=>72
[4,3,2,1,12,7,6,9,8,11,10,5]=>56
[4,3,2,1,12,7,6,11,10,9,8,5]=>32
[4,3,2,1,10,9,8,7,6,5,12,11]=>48
[4,3,2,1,12,9,8,7,6,11,10,5]=>32
[4,3,2,1,12,11,8,7,10,9,6,5]=>16
[4,3,2,1,12,11,10,9,8,7,6,5]=>0
[6,3,2,5,4,1,8,7,10,9,12,11]=>104
[6,3,2,5,4,1,8,7,12,11,10,9]=>72
[6,3,2,5,4,1,10,9,8,7,12,11]=>72
[6,3,2,5,4,1,12,9,8,11,10,7]=>48
[6,3,2,5,4,1,12,11,10,9,8,7]=>24
[8,3,2,5,4,7,6,1,10,9,12,11]=>88
[8,3,2,5,4,7,6,1,12,11,10,9]=>56
[10,3,2,5,4,7,6,9,8,1,12,11]=>80
[12,3,2,5,4,7,6,9,8,11,10,1]=>80
[12,3,2,5,4,7,6,11,10,9,8,1]=>56
[10,3,2,5,4,9,8,7,6,1,12,11]=>56
[12,3,2,5,4,9,8,7,6,11,10,1]=>56
[12,3,2,5,4,11,8,7,10,9,6,1]=>40
[12,3,2,5,4,11,10,9,8,7,6,1]=>24
[8,3,2,7,6,5,4,1,10,9,12,11]=>64
[8,3,2,7,6,5,4,1,12,11,10,9]=>32
[10,3,2,7,6,5,4,9,8,1,12,11]=>56
[12,3,2,7,6,5,4,9,8,11,10,1]=>56
[12,3,2,7,6,5,4,11,10,9,8,1]=>32
[10,3,2,9,6,5,8,7,4,1,12,11]=>40
[12,3,2,9,6,5,8,7,4,11,10,1]=>40
[12,3,2,11,6,5,8,7,10,9,4,1]=>32
[12,3,2,11,6,5,10,9,8,7,4,1]=>16
[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]=>24
[12,3,2,11,8,7,6,5,10,9,4,1]=>16
[12,3,2,11,10,7,6,9,8,5,4,1]=>8
[12,3,2,11,10,9,8,7,6,5,4,1]=>0
[6,5,4,3,2,1,8,7,10,9,12,11]=>80
[6,5,4,3,2,1,8,7,12,11,10,9]=>48
[6,5,4,3,2,1,10,9,8,7,12,11]=>48
[6,5,4,3,2,1,12,9,8,11,10,7]=>24
[6,5,4,3,2,1,12,11,10,9,8,7]=>0
[8,5,4,3,2,7,6,1,10,9,12,11]=>64
[8,5,4,3,2,7,6,1,12,11,10,9]=>32
[10,5,4,3,2,7,6,9,8,1,12,11]=>56
[12,5,4,3,2,7,6,9,8,11,10,1]=>56
[12,5,4,3,2,7,6,11,10,9,8,1]=>32
[10,5,4,3,2,9,8,7,6,1,12,11]=>32
[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]=>16
[12,5,4,3,2,11,10,9,8,7,6,1]=>0
[8,7,4,3,6,5,2,1,10,9,12,11]=>48
[8,7,4,3,6,5,2,1,12,11,10,9]=>16
[10,7,4,3,6,5,2,9,8,1,12,11]=>40
[12,7,4,3,6,5,2,9,8,11,10,1]=>40
[12,7,4,3,6,5,2,11,10,9,8,1]=>16
[10,9,4,3,6,5,8,7,2,1,12,11]=>32
[12,9,4,3,6,5,8,7,2,11,10,1]=>32
[12,11,4,3,6,5,8,7,10,9,2,1]=>32
[12,11,4,3,6,5,10,9,8,7,2,1]=>16
[10,9,4,3,8,7,6,5,2,1,12,11]=>16
[12,9,4,3,8,7,6,5,2,11,10,1]=>16
[12,11,4,3,8,7,6,5,10,9,2,1]=>16
[12,11,4,3,10,7,6,9,8,5,2,1]=>8
[12,11,4,3,10,9,8,7,6,5,2,1]=>0
[8,7,6,5,4,3,2,1,10,9,12,11]=>32
[8,7,6,5,4,3,2,1,12,11,10,9]=>0
[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]=>24
[12,7,6,5,4,3,2,11,10,9,8,1]=>0
[10,9,6,5,4,3,8,7,2,1,12,11]=>16
[12,9,6,5,4,3,8,7,2,11,10,1]=>16
[12,11,6,5,4,3,8,7,10,9,2,1]=>16
[12,11,6,5,4,3,10,9,8,7,2,1]=>0
[10,9,8,5,4,7,6,3,2,1,12,11]=>8
[12,9,8,5,4,7,6,3,2,11,10,1]=>8
[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]=>8
[12,11,10,5,4,9,8,7,6,3,2,1]=>0
[10,9,8,7,6,5,4,3,2,1,12,11]=>0
[12,9,8,7,6,5,4,3,2,11,10,1]=>0
[12,11,8,7,6,5,4,3,10,9,2,1]=>0
[12,11,10,7,6,5,4,9,8,3,2,1]=>0
[12,11,10,9,6,5,8,7,4,3,2,1]=>0
[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]=>80
[2,4,6,8,11,12,1,3,5,7,9,10]=>76
[2,4,6,9,10,12,1,3,5,7,8,11]=>76
[2,4,6,9,11,12,1,3,5,7,8,10]=>72
[2,4,6,10,11,12,1,3,5,7,8,9]=>69
[2,4,7,8,10,12,1,3,5,6,9,11]=>76
[2,4,7,8,11,12,1,3,5,6,9,10]=>72
[2,4,7,9,10,12,1,3,5,6,8,11]=>72
[2,4,7,9,11,12,1,3,5,6,8,10]=>68
[2,4,7,10,11,12,1,3,5,6,8,9]=>65
[2,4,8,9,10,12,1,3,5,6,7,11]=>69
[2,4,8,9,11,12,1,3,5,6,7,10]=>65
[2,4,8,10,11,12,1,3,5,6,7,9]=>62
[2,4,9,10,11,12,1,3,5,6,7,8]=>60
[2,5,6,8,10,12,1,3,4,7,9,11]=>76
[2,5,6,8,11,12,1,3,4,7,9,10]=>72
[2,5,6,9,10,12,1,3,4,7,8,11]=>72
[2,5,6,9,11,12,1,3,4,7,8,10]=>68
[2,5,6,10,11,12,1,3,4,7,8,9]=>65
[2,5,7,8,10,12,1,3,4,6,9,11]=>72
[2,5,7,8,11,12,1,3,4,6,9,10]=>68
[2,5,7,9,10,12,1,3,4,6,8,11]=>68
[2,5,7,9,11,12,1,3,4,6,8,10]=>64
[2,5,7,10,11,12,1,3,4,6,8,9]=>61
[2,5,8,9,10,12,1,3,4,6,7,11]=>65
[2,5,8,9,11,12,1,3,4,6,7,10]=>61
[2,5,8,10,11,12,1,3,4,6,7,9]=>58
[2,5,9,10,11,12,1,3,4,6,7,8]=>56
[2,6,7,8,10,12,1,3,4,5,9,11]=>69
[2,6,7,8,11,12,1,3,4,5,9,10]=>65
[2,6,7,9,10,12,1,3,4,5,8,11]=>65
[2,6,7,9,11,12,1,3,4,5,8,10]=>61
[2,6,7,10,11,12,1,3,4,5,8,9]=>58
[2,6,8,9,10,12,1,3,4,5,7,11]=>62
[2,6,8,9,11,12,1,3,4,5,7,10]=>58
[2,6,8,10,11,12,1,3,4,5,7,9]=>55
[2,6,9,10,11,12,1,3,4,5,7,8]=>53
[2,7,8,9,10,12,1,3,4,5,6,11]=>60
[2,7,8,9,11,12,1,3,4,5,6,10]=>56
[2,7,8,10,11,12,1,3,4,5,6,9]=>53
[2,7,9,10,11,12,1,3,4,5,6,8]=>51
[2,8,9,10,11,12,1,3,4,5,6,7]=>50
[3,4,6,8,10,12,1,2,5,7,9,11]=>76
[3,4,6,8,11,12,1,2,5,7,9,10]=>72
[3,4,6,9,10,12,1,2,5,7,8,11]=>72
[3,4,6,9,11,12,1,2,5,7,8,10]=>68
[3,4,6,10,11,12,1,2,5,7,8,9]=>65
[3,4,7,8,10,12,1,2,5,6,9,11]=>72
[3,4,7,8,11,12,1,2,5,6,9,10]=>68
[3,4,7,9,10,12,1,2,5,6,8,11]=>68
[3,4,7,9,11,12,1,2,5,6,8,10]=>64
[3,4,7,10,11,12,1,2,5,6,8,9]=>61
[3,4,8,9,10,12,1,2,5,6,7,11]=>65
[3,4,8,9,11,12,1,2,5,6,7,10]=>61
[3,4,8,10,11,12,1,2,5,6,7,9]=>58
[3,4,9,10,11,12,1,2,5,6,7,8]=>56
[3,5,6,8,10,12,1,2,4,7,9,11]=>72
[3,5,6,8,11,12,1,2,4,7,9,10]=>68
[3,5,6,9,10,12,1,2,4,7,8,11]=>68
[3,5,6,9,11,12,1,2,4,7,8,10]=>64
[3,5,6,10,11,12,1,2,4,7,8,9]=>61
[3,5,7,8,10,12,1,2,4,6,9,11]=>68
[3,5,7,8,11,12,1,2,4,6,9,10]=>64
[3,5,7,9,10,12,1,2,4,6,8,11]=>64
[3,5,7,9,11,12,1,2,4,6,8,10]=>60
[3,5,7,10,11,12,1,2,4,6,8,9]=>57
[3,5,8,9,10,12,1,2,4,6,7,11]=>61
[3,5,8,9,11,12,1,2,4,6,7,10]=>57
[3,5,8,10,11,12,1,2,4,6,7,9]=>54
[3,5,9,10,11,12,1,2,4,6,7,8]=>52
[3,6,7,8,10,12,1,2,4,5,9,11]=>65
[3,6,7,8,11,12,1,2,4,5,9,10]=>61
[3,6,7,9,10,12,1,2,4,5,8,11]=>61
[3,6,7,9,11,12,1,2,4,5,8,10]=>57
[3,6,7,10,11,12,1,2,4,5,8,9]=>54
[3,6,8,9,10,12,1,2,4,5,7,11]=>58
[3,6,8,9,11,12,1,2,4,5,7,10]=>54
[3,6,8,10,11,12,1,2,4,5,7,9]=>51
[3,6,9,10,11,12,1,2,4,5,7,8]=>49
[3,7,8,9,10,12,1,2,4,5,6,11]=>56
[3,7,8,9,11,12,1,2,4,5,6,10]=>52
[3,7,8,10,11,12,1,2,4,5,6,9]=>49
[3,7,9,10,11,12,1,2,4,5,6,8]=>47
[3,8,9,10,11,12,1,2,4,5,6,7]=>46
[4,5,6,8,10,12,1,2,3,7,9,11]=>69
[4,5,6,8,11,12,1,2,3,7,9,10]=>65
[4,5,6,9,10,12,1,2,3,7,8,11]=>65
[4,5,6,9,11,12,1,2,3,7,8,10]=>61
[4,5,6,10,11,12,1,2,3,7,8,9]=>58
[4,5,7,8,10,12,1,2,3,6,9,11]=>65
[4,5,7,8,11,12,1,2,3,6,9,10]=>61
[4,5,7,9,10,12,1,2,3,6,8,11]=>61
[4,5,7,9,11,12,1,2,3,6,8,10]=>57
[4,5,7,10,11,12,1,2,3,6,8,9]=>54
[4,5,8,9,10,12,1,2,3,6,7,11]=>58
[4,5,8,9,11,12,1,2,3,6,7,10]=>54
[4,5,8,10,11,12,1,2,3,6,7,9]=>51
[4,5,9,10,11,12,1,2,3,6,7,8]=>49
[4,6,7,8,10,12,1,2,3,5,9,11]=>62
[4,6,7,8,11,12,1,2,3,5,9,10]=>58
[4,6,7,9,10,12,1,2,3,5,8,11]=>58
[4,6,7,9,11,12,1,2,3,5,8,10]=>54
[4,6,7,10,11,12,1,2,3,5,8,9]=>51
[4,6,8,9,10,12,1,2,3,5,7,11]=>55
[4,6,8,9,11,12,1,2,3,5,7,10]=>51
[4,6,8,10,11,12,1,2,3,5,7,9]=>48
[4,6,9,10,11,12,1,2,3,5,7,8]=>46
[4,7,8,9,10,12,1,2,3,5,6,11]=>53
[4,7,8,9,11,12,1,2,3,5,6,10]=>49
[4,7,8,10,11,12,1,2,3,5,6,9]=>46
[4,7,9,10,11,12,1,2,3,5,6,8]=>44
[4,8,9,10,11,12,1,2,3,5,6,7]=>43
[5,6,7,8,10,12,1,2,3,4,9,11]=>60
[5,6,7,8,11,12,1,2,3,4,9,10]=>56
[5,6,7,9,10,12,1,2,3,4,8,11]=>56
[5,6,7,9,11,12,1,2,3,4,8,10]=>52
[5,6,7,10,11,12,1,2,3,4,8,9]=>49
[5,6,8,9,10,12,1,2,3,4,7,11]=>53
[5,6,8,9,11,12,1,2,3,4,7,10]=>49
[5,6,8,10,11,12,1,2,3,4,7,9]=>46
[5,6,9,10,11,12,1,2,3,4,7,8]=>44
[5,7,8,9,10,12,1,2,3,4,6,11]=>51
[5,7,8,9,11,12,1,2,3,4,6,10]=>47
[5,7,8,10,11,12,1,2,3,4,6,9]=>44
[5,7,9,10,11,12,1,2,3,4,6,8]=>42
[5,8,9,10,11,12,1,2,3,4,6,7]=>41
[6,7,8,9,10,12,1,2,3,4,5,11]=>50
[6,7,8,9,11,12,1,2,3,4,5,10]=>46
[6,7,8,10,11,12,1,2,3,4,5,9]=>43
[6,7,9,10,11,12,1,2,3,4,5,8]=>41
[6,8,9,10,11,12,1,2,3,4,5,7]=>40
[7,8,9,10,11,12,1,2,3,4,5,6]=>40
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Description
The number of occurrences of the pattern 123 in a permutation.
References
[1] Number of permutations on 1,...,n containing any given pattern alpha in the symmetric group S_3. OEIS:A056986
[2] Triangle read by rows: T(n,k) is the number of permutations of [n] having k occurrences of the pattern 321 (n>=1, 0<=k<=n(n-1)(n-2)/6). OEIS:A138159
[2] Triangle read by rows: T(n,k) is the number of permutations of [n] having k occurrences of the pattern 321 (n>=1, 0<=k<=n(n-1)(n-2)/6). OEIS:A138159
Code
def statistic(x):
return len(x.pattern_positions([1,2,3]))
Created
Sep 14, 2011 at 03:28 by Christian Stump
Updated
Sep 02, 2020 at 09:45 by Martin Rubey
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