Identifier
- St000692: Permutations ⟶ ℤ
Values
=>
[]=>0
[1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>3
[1,2,3,4]=>0
[1,2,4,3]=>2
[1,3,2,4]=>3
[1,3,4,2]=>2
[1,4,2,3]=>3
[1,4,3,2]=>5
[2,1,3,4]=>3
[2,1,4,3]=>5
[2,3,1,4]=>2
[2,3,4,1]=>1
[2,4,1,3]=>2
[2,4,3,1]=>4
[3,1,2,4]=>2
[3,1,4,2]=>4
[3,2,1,4]=>5
[3,2,4,1]=>4
[3,4,1,2]=>1
[3,4,2,1]=>3
[4,1,2,3]=>1
[4,1,3,2]=>3
[4,2,1,3]=>4
[4,2,3,1]=>3
[4,3,1,2]=>4
[4,3,2,1]=>6
[1,2,3,4,5]=>0
[1,2,3,5,4]=>2
[1,2,4,3,5]=>3
[1,2,4,5,3]=>2
[1,2,5,3,4]=>3
[1,2,5,4,3]=>5
[1,3,2,4,5]=>4
[1,3,2,5,4]=>6
[1,3,4,2,5]=>3
[1,3,4,5,2]=>2
[1,3,5,2,4]=>3
[1,3,5,4,2]=>5
[1,4,2,3,5]=>4
[1,4,2,5,3]=>6
[1,4,3,2,5]=>7
[1,4,3,5,2]=>6
[1,4,5,2,3]=>3
[1,4,5,3,2]=>5
[1,5,2,3,4]=>4
[1,5,2,4,3]=>6
[1,5,3,2,4]=>7
[1,5,3,4,2]=>6
[1,5,4,2,3]=>7
[1,5,4,3,2]=>9
[2,1,3,4,5]=>4
[2,1,3,5,4]=>6
[2,1,4,3,5]=>7
[2,1,4,5,3]=>6
[2,1,5,3,4]=>7
[2,1,5,4,3]=>9
[2,3,1,4,5]=>3
[2,3,1,5,4]=>5
[2,3,4,1,5]=>2
[2,3,4,5,1]=>1
[2,3,5,1,4]=>2
[2,3,5,4,1]=>4
[2,4,1,3,5]=>3
[2,4,1,5,3]=>5
[2,4,3,1,5]=>6
[2,4,3,5,1]=>5
[2,4,5,1,3]=>2
[2,4,5,3,1]=>4
[2,5,1,3,4]=>3
[2,5,1,4,3]=>5
[2,5,3,1,4]=>6
[2,5,3,4,1]=>5
[2,5,4,1,3]=>6
[2,5,4,3,1]=>8
[3,1,2,4,5]=>3
[3,1,2,5,4]=>5
[3,1,4,2,5]=>6
[3,1,4,5,2]=>5
[3,1,5,2,4]=>6
[3,1,5,4,2]=>8
[3,2,1,4,5]=>7
[3,2,1,5,4]=>9
[3,2,4,1,5]=>6
[3,2,4,5,1]=>5
[3,2,5,1,4]=>6
[3,2,5,4,1]=>8
[3,4,1,2,5]=>2
[3,4,1,5,2]=>4
[3,4,2,1,5]=>5
[3,4,2,5,1]=>4
[3,4,5,1,2]=>1
[3,4,5,2,1]=>3
[3,5,1,2,4]=>2
[3,5,1,4,2]=>4
[3,5,2,1,4]=>5
[3,5,2,4,1]=>4
[3,5,4,1,2]=>5
[3,5,4,2,1]=>7
[4,1,2,3,5]=>2
[4,1,2,5,3]=>4
[4,1,3,2,5]=>5
[4,1,3,5,2]=>4
[4,1,5,2,3]=>5
[4,1,5,3,2]=>7
[4,2,1,3,5]=>6
[4,2,1,5,3]=>8
[4,2,3,1,5]=>5
[4,2,3,5,1]=>4
[4,2,5,1,3]=>5
[4,2,5,3,1]=>7
[4,3,1,2,5]=>6
[4,3,1,5,2]=>8
[4,3,2,1,5]=>9
[4,3,2,5,1]=>8
[4,3,5,1,2]=>5
[4,3,5,2,1]=>7
[4,5,1,2,3]=>1
[4,5,1,3,2]=>3
[4,5,2,1,3]=>4
[4,5,2,3,1]=>3
[4,5,3,1,2]=>4
[4,5,3,2,1]=>6
[5,1,2,3,4]=>1
[5,1,2,4,3]=>3
[5,1,3,2,4]=>4
[5,1,3,4,2]=>3
[5,1,4,2,3]=>4
[5,1,4,3,2]=>6
[5,2,1,3,4]=>5
[5,2,1,4,3]=>7
[5,2,3,1,4]=>4
[5,2,3,4,1]=>3
[5,2,4,1,3]=>4
[5,2,4,3,1]=>6
[5,3,1,2,4]=>5
[5,3,1,4,2]=>7
[5,3,2,1,4]=>8
[5,3,2,4,1]=>7
[5,3,4,1,2]=>4
[5,3,4,2,1]=>6
[5,4,1,2,3]=>5
[5,4,1,3,2]=>7
[5,4,2,1,3]=>8
[5,4,2,3,1]=>7
[5,4,3,1,2]=>8
[5,4,3,2,1]=>10
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>2
[1,2,3,5,4,6]=>3
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>3
[1,2,3,6,5,4]=>5
[1,2,4,3,5,6]=>4
[1,2,4,3,6,5]=>6
[1,2,4,5,3,6]=>3
[1,2,4,5,6,3]=>2
[1,2,4,6,3,5]=>3
[1,2,4,6,5,3]=>5
[1,2,5,3,4,6]=>4
[1,2,5,3,6,4]=>6
[1,2,5,4,3,6]=>7
[1,2,5,4,6,3]=>6
[1,2,5,6,3,4]=>3
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>4
[1,2,6,3,5,4]=>6
[1,2,6,4,3,5]=>7
[1,2,6,4,5,3]=>6
[1,2,6,5,3,4]=>7
[1,2,6,5,4,3]=>9
[1,3,2,4,5,6]=>5
[1,3,2,4,6,5]=>7
[1,3,2,5,4,6]=>8
[1,3,2,5,6,4]=>7
[1,3,2,6,4,5]=>8
[1,3,2,6,5,4]=>10
[1,3,4,2,5,6]=>4
[1,3,4,2,6,5]=>6
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>2
[1,3,4,6,2,5]=>3
[1,3,4,6,5,2]=>5
[1,3,5,2,4,6]=>4
[1,3,5,2,6,4]=>6
[1,3,5,4,2,6]=>7
[1,3,5,4,6,2]=>6
[1,3,5,6,2,4]=>3
[1,3,5,6,4,2]=>5
[1,3,6,2,4,5]=>4
[1,3,6,2,5,4]=>6
[1,3,6,4,2,5]=>7
[1,3,6,4,5,2]=>6
[1,3,6,5,2,4]=>7
[1,3,6,5,4,2]=>9
[1,4,2,3,5,6]=>5
[1,4,2,3,6,5]=>7
[1,4,2,5,3,6]=>8
[1,4,2,5,6,3]=>7
[1,4,2,6,3,5]=>8
[1,4,2,6,5,3]=>10
[1,4,3,2,5,6]=>9
[1,4,3,2,6,5]=>11
[1,4,3,5,2,6]=>8
[1,4,3,5,6,2]=>7
[1,4,3,6,2,5]=>8
[1,4,3,6,5,2]=>10
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>6
[1,4,5,3,2,6]=>7
[1,4,5,3,6,2]=>6
[1,4,5,6,2,3]=>3
[1,4,5,6,3,2]=>5
[1,4,6,2,3,5]=>4
[1,4,6,2,5,3]=>6
[1,4,6,3,2,5]=>7
[1,4,6,3,5,2]=>6
[1,4,6,5,2,3]=>7
[1,4,6,5,3,2]=>9
[1,5,2,3,4,6]=>5
[1,5,2,3,6,4]=>7
[1,5,2,4,3,6]=>8
[1,5,2,4,6,3]=>7
[1,5,2,6,3,4]=>8
[1,5,2,6,4,3]=>10
[1,5,3,2,4,6]=>9
[1,5,3,2,6,4]=>11
[1,5,3,4,2,6]=>8
[1,5,3,4,6,2]=>7
[1,5,3,6,2,4]=>8
[1,5,3,6,4,2]=>10
[1,5,4,2,3,6]=>9
[1,5,4,2,6,3]=>11
[1,5,4,3,2,6]=>12
[1,5,4,3,6,2]=>11
[1,5,4,6,2,3]=>8
[1,5,4,6,3,2]=>10
[1,5,6,2,3,4]=>4
[1,5,6,2,4,3]=>6
[1,5,6,3,2,4]=>7
[1,5,6,3,4,2]=>6
[1,5,6,4,2,3]=>7
[1,5,6,4,3,2]=>9
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>7
[1,6,2,4,3,5]=>8
[1,6,2,4,5,3]=>7
[1,6,2,5,3,4]=>8
[1,6,2,5,4,3]=>10
[1,6,3,2,4,5]=>9
[1,6,3,2,5,4]=>11
[1,6,3,4,2,5]=>8
[1,6,3,4,5,2]=>7
[1,6,3,5,2,4]=>8
[1,6,3,5,4,2]=>10
[1,6,4,2,3,5]=>9
[1,6,4,2,5,3]=>11
[1,6,4,3,2,5]=>12
[1,6,4,3,5,2]=>11
[1,6,4,5,2,3]=>8
[1,6,4,5,3,2]=>10
[1,6,5,2,3,4]=>9
[1,6,5,2,4,3]=>11
[1,6,5,3,2,4]=>12
[1,6,5,3,4,2]=>11
[1,6,5,4,2,3]=>12
[1,6,5,4,3,2]=>14
[2,1,3,4,5,6]=>5
[2,1,3,4,6,5]=>7
[2,1,3,5,4,6]=>8
[2,1,3,5,6,4]=>7
[2,1,3,6,4,5]=>8
[2,1,3,6,5,4]=>10
[2,1,4,3,5,6]=>9
[2,1,4,3,6,5]=>11
[2,1,4,5,3,6]=>8
[2,1,4,5,6,3]=>7
[2,1,4,6,3,5]=>8
[2,1,4,6,5,3]=>10
[2,1,5,3,4,6]=>9
[2,1,5,3,6,4]=>11
[2,1,5,4,3,6]=>12
[2,1,5,4,6,3]=>11
[2,1,5,6,3,4]=>8
[2,1,5,6,4,3]=>10
[2,1,6,3,4,5]=>9
[2,1,6,3,5,4]=>11
[2,1,6,4,3,5]=>12
[2,1,6,4,5,3]=>11
[2,1,6,5,3,4]=>12
[2,1,6,5,4,3]=>14
[2,3,1,4,5,6]=>4
[2,3,1,4,6,5]=>6
[2,3,1,5,4,6]=>7
[2,3,1,5,6,4]=>6
[2,3,1,6,4,5]=>7
[2,3,1,6,5,4]=>9
[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>5
[2,3,4,5,1,6]=>2
[2,3,4,5,6,1]=>1
[2,3,4,6,1,5]=>2
[2,3,4,6,5,1]=>4
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>6
[2,3,5,4,6,1]=>5
[2,3,5,6,1,4]=>2
[2,3,5,6,4,1]=>4
[2,3,6,1,4,5]=>3
[2,3,6,1,5,4]=>5
[2,3,6,4,1,5]=>6
[2,3,6,4,5,1]=>5
[2,3,6,5,1,4]=>6
[2,3,6,5,4,1]=>8
[2,4,1,3,5,6]=>4
[2,4,1,3,6,5]=>6
[2,4,1,5,3,6]=>7
[2,4,1,5,6,3]=>6
[2,4,1,6,3,5]=>7
[2,4,1,6,5,3]=>9
[2,4,3,1,5,6]=>8
[2,4,3,1,6,5]=>10
[2,4,3,5,1,6]=>7
[2,4,3,5,6,1]=>6
[2,4,3,6,1,5]=>7
[2,4,3,6,5,1]=>9
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>5
[2,4,5,3,1,6]=>6
[2,4,5,3,6,1]=>5
[2,4,5,6,1,3]=>2
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>5
[2,4,6,3,1,5]=>6
[2,4,6,3,5,1]=>5
[2,4,6,5,1,3]=>6
[2,4,6,5,3,1]=>8
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>6
[2,5,1,4,3,6]=>7
[2,5,1,4,6,3]=>6
[2,5,1,6,3,4]=>7
[2,5,1,6,4,3]=>9
[2,5,3,1,4,6]=>8
[2,5,3,1,6,4]=>10
[2,5,3,4,1,6]=>7
[2,5,3,4,6,1]=>6
[2,5,3,6,1,4]=>7
[2,5,3,6,4,1]=>9
[2,5,4,1,3,6]=>8
[2,5,4,1,6,3]=>10
[2,5,4,3,1,6]=>11
[2,5,4,3,6,1]=>10
[2,5,4,6,1,3]=>7
[2,5,4,6,3,1]=>9
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>5
[2,5,6,3,1,4]=>6
[2,5,6,3,4,1]=>5
[2,5,6,4,1,3]=>6
[2,5,6,4,3,1]=>8
[2,6,1,3,4,5]=>4
[2,6,1,3,5,4]=>6
[2,6,1,4,3,5]=>7
[2,6,1,4,5,3]=>6
[2,6,1,5,3,4]=>7
[2,6,1,5,4,3]=>9
[2,6,3,1,4,5]=>8
[2,6,3,1,5,4]=>10
[2,6,3,4,1,5]=>7
[2,6,3,4,5,1]=>6
[2,6,3,5,1,4]=>7
[2,6,3,5,4,1]=>9
[2,6,4,1,3,5]=>8
[2,6,4,1,5,3]=>10
[2,6,4,3,1,5]=>11
[2,6,4,3,5,1]=>10
[2,6,4,5,1,3]=>7
[2,6,4,5,3,1]=>9
[2,6,5,1,3,4]=>8
[2,6,5,1,4,3]=>10
[2,6,5,3,1,4]=>11
[2,6,5,3,4,1]=>10
[2,6,5,4,1,3]=>11
[2,6,5,4,3,1]=>13
[3,1,2,4,5,6]=>4
[3,1,2,4,6,5]=>6
[3,1,2,5,4,6]=>7
[3,1,2,5,6,4]=>6
[3,1,2,6,4,5]=>7
[3,1,2,6,5,4]=>9
[3,1,4,2,5,6]=>8
[3,1,4,2,6,5]=>10
[3,1,4,5,2,6]=>7
[3,1,4,5,6,2]=>6
[3,1,4,6,2,5]=>7
[3,1,4,6,5,2]=>9
[3,1,5,2,4,6]=>8
[3,1,5,2,6,4]=>10
[3,1,5,4,2,6]=>11
[3,1,5,4,6,2]=>10
[3,1,5,6,2,4]=>7
[3,1,5,6,4,2]=>9
[3,1,6,2,4,5]=>8
[3,1,6,2,5,4]=>10
[3,1,6,4,2,5]=>11
[3,1,6,4,5,2]=>10
[3,1,6,5,2,4]=>11
[3,1,6,5,4,2]=>13
[3,2,1,4,5,6]=>9
[3,2,1,4,6,5]=>11
[3,2,1,5,4,6]=>12
[3,2,1,5,6,4]=>11
[3,2,1,6,4,5]=>12
[3,2,1,6,5,4]=>14
[3,2,4,1,5,6]=>8
[3,2,4,1,6,5]=>10
[3,2,4,5,1,6]=>7
[3,2,4,5,6,1]=>6
[3,2,4,6,1,5]=>7
[3,2,4,6,5,1]=>9
[3,2,5,1,4,6]=>8
[3,2,5,1,6,4]=>10
[3,2,5,4,1,6]=>11
[3,2,5,4,6,1]=>10
[3,2,5,6,1,4]=>7
[3,2,5,6,4,1]=>9
[3,2,6,1,4,5]=>8
[3,2,6,1,5,4]=>10
[3,2,6,4,1,5]=>11
[3,2,6,4,5,1]=>10
[3,2,6,5,1,4]=>11
[3,2,6,5,4,1]=>13
[3,4,1,2,5,6]=>3
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>6
[3,4,1,5,6,2]=>5
[3,4,1,6,2,5]=>6
[3,4,1,6,5,2]=>8
[3,4,2,1,5,6]=>7
[3,4,2,1,6,5]=>9
[3,4,2,5,1,6]=>6
[3,4,2,5,6,1]=>5
[3,4,2,6,1,5]=>6
[3,4,2,6,5,1]=>8
[3,4,5,1,2,6]=>2
[3,4,5,1,6,2]=>4
[3,4,5,2,1,6]=>5
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>3
[3,4,6,1,2,5]=>2
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>5
[3,4,6,2,5,1]=>4
[3,4,6,5,1,2]=>5
[3,4,6,5,2,1]=>7
[3,5,1,2,4,6]=>3
[3,5,1,2,6,4]=>5
[3,5,1,4,2,6]=>6
[3,5,1,4,6,2]=>5
[3,5,1,6,2,4]=>6
[3,5,1,6,4,2]=>8
[3,5,2,1,4,6]=>7
[3,5,2,1,6,4]=>9
[3,5,2,4,1,6]=>6
[3,5,2,4,6,1]=>5
[3,5,2,6,1,4]=>6
[3,5,2,6,4,1]=>8
[3,5,4,1,2,6]=>7
[3,5,4,1,6,2]=>9
[3,5,4,2,1,6]=>10
[3,5,4,2,6,1]=>9
[3,5,4,6,1,2]=>6
[3,5,4,6,2,1]=>8
[3,5,6,1,2,4]=>2
[3,5,6,1,4,2]=>4
[3,5,6,2,1,4]=>5
[3,5,6,2,4,1]=>4
[3,5,6,4,1,2]=>5
[3,5,6,4,2,1]=>7
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>5
[3,6,1,4,2,5]=>6
[3,6,1,4,5,2]=>5
[3,6,1,5,2,4]=>6
[3,6,1,5,4,2]=>8
[3,6,2,1,4,5]=>7
[3,6,2,1,5,4]=>9
[3,6,2,4,1,5]=>6
[3,6,2,4,5,1]=>5
[3,6,2,5,1,4]=>6
[3,6,2,5,4,1]=>8
[3,6,4,1,2,5]=>7
[3,6,4,1,5,2]=>9
[3,6,4,2,1,5]=>10
[3,6,4,2,5,1]=>9
[3,6,4,5,1,2]=>6
[3,6,4,5,2,1]=>8
[3,6,5,1,2,4]=>7
[3,6,5,1,4,2]=>9
[3,6,5,2,1,4]=>10
[3,6,5,2,4,1]=>9
[3,6,5,4,1,2]=>10
[3,6,5,4,2,1]=>12
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>5
[4,1,2,5,3,6]=>6
[4,1,2,5,6,3]=>5
[4,1,2,6,3,5]=>6
[4,1,2,6,5,3]=>8
[4,1,3,2,5,6]=>7
[4,1,3,2,6,5]=>9
[4,1,3,5,2,6]=>6
[4,1,3,5,6,2]=>5
[4,1,3,6,2,5]=>6
[4,1,3,6,5,2]=>8
[4,1,5,2,3,6]=>7
[4,1,5,2,6,3]=>9
[4,1,5,3,2,6]=>10
[4,1,5,3,6,2]=>9
[4,1,5,6,2,3]=>6
[4,1,5,6,3,2]=>8
[4,1,6,2,3,5]=>7
[4,1,6,2,5,3]=>9
[4,1,6,3,2,5]=>10
[4,1,6,3,5,2]=>9
[4,1,6,5,2,3]=>10
[4,1,6,5,3,2]=>12
[4,2,1,3,5,6]=>8
[4,2,1,3,6,5]=>10
[4,2,1,5,3,6]=>11
[4,2,1,5,6,3]=>10
[4,2,1,6,3,5]=>11
[4,2,1,6,5,3]=>13
[4,2,3,1,5,6]=>7
[4,2,3,1,6,5]=>9
[4,2,3,5,1,6]=>6
[4,2,3,5,6,1]=>5
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>8
[4,2,5,1,3,6]=>7
[4,2,5,1,6,3]=>9
[4,2,5,3,1,6]=>10
[4,2,5,3,6,1]=>9
[4,2,5,6,1,3]=>6
[4,2,5,6,3,1]=>8
[4,2,6,1,3,5]=>7
[4,2,6,1,5,3]=>9
[4,2,6,3,1,5]=>10
[4,2,6,3,5,1]=>9
[4,2,6,5,1,3]=>10
[4,2,6,5,3,1]=>12
[4,3,1,2,5,6]=>8
[4,3,1,2,6,5]=>10
[4,3,1,5,2,6]=>11
[4,3,1,5,6,2]=>10
[4,3,1,6,2,5]=>11
[4,3,1,6,5,2]=>13
[4,3,2,1,5,6]=>12
[4,3,2,1,6,5]=>14
[4,3,2,5,1,6]=>11
[4,3,2,5,6,1]=>10
[4,3,2,6,1,5]=>11
[4,3,2,6,5,1]=>13
[4,3,5,1,2,6]=>7
[4,3,5,1,6,2]=>9
[4,3,5,2,1,6]=>10
[4,3,5,2,6,1]=>9
[4,3,5,6,1,2]=>6
[4,3,5,6,2,1]=>8
[4,3,6,1,2,5]=>7
[4,3,6,1,5,2]=>9
[4,3,6,2,1,5]=>10
[4,3,6,2,5,1]=>9
[4,3,6,5,1,2]=>10
[4,3,6,5,2,1]=>12
[4,5,1,2,3,6]=>2
[4,5,1,2,6,3]=>4
[4,5,1,3,2,6]=>5
[4,5,1,3,6,2]=>4
[4,5,1,6,2,3]=>5
[4,5,1,6,3,2]=>7
[4,5,2,1,3,6]=>6
[4,5,2,1,6,3]=>8
[4,5,2,3,1,6]=>5
[4,5,2,3,6,1]=>4
[4,5,2,6,1,3]=>5
[4,5,2,6,3,1]=>7
[4,5,3,1,2,6]=>6
[4,5,3,1,6,2]=>8
[4,5,3,2,1,6]=>9
[4,5,3,2,6,1]=>8
[4,5,3,6,1,2]=>5
[4,5,3,6,2,1]=>7
[4,5,6,1,2,3]=>1
[4,5,6,1,3,2]=>3
[4,5,6,2,1,3]=>4
[4,5,6,2,3,1]=>3
[4,5,6,3,1,2]=>4
[4,5,6,3,2,1]=>6
[4,6,1,2,3,5]=>2
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>5
[4,6,1,3,5,2]=>4
[4,6,1,5,2,3]=>5
[4,6,1,5,3,2]=>7
[4,6,2,1,3,5]=>6
[4,6,2,1,5,3]=>8
[4,6,2,3,1,5]=>5
[4,6,2,3,5,1]=>4
[4,6,2,5,1,3]=>5
[4,6,2,5,3,1]=>7
[4,6,3,1,2,5]=>6
[4,6,3,1,5,2]=>8
[4,6,3,2,1,5]=>9
[4,6,3,2,5,1]=>8
[4,6,3,5,1,2]=>5
[4,6,3,5,2,1]=>7
[4,6,5,1,2,3]=>6
[4,6,5,1,3,2]=>8
[4,6,5,2,1,3]=>9
[4,6,5,2,3,1]=>8
[4,6,5,3,1,2]=>9
[4,6,5,3,2,1]=>11
[5,1,2,3,4,6]=>2
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>5
[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>5
[5,1,2,6,4,3]=>7
[5,1,3,2,4,6]=>6
[5,1,3,2,6,4]=>8
[5,1,3,4,2,6]=>5
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>5
[5,1,3,6,4,2]=>7
[5,1,4,2,3,6]=>6
[5,1,4,2,6,3]=>8
[5,1,4,3,2,6]=>9
[5,1,4,3,6,2]=>8
[5,1,4,6,2,3]=>5
[5,1,4,6,3,2]=>7
[5,1,6,2,3,4]=>6
[5,1,6,2,4,3]=>8
[5,1,6,3,2,4]=>9
[5,1,6,3,4,2]=>8
[5,1,6,4,2,3]=>9
[5,1,6,4,3,2]=>11
[5,2,1,3,4,6]=>7
[5,2,1,3,6,4]=>9
[5,2,1,4,3,6]=>10
[5,2,1,4,6,3]=>9
[5,2,1,6,3,4]=>10
[5,2,1,6,4,3]=>12
[5,2,3,1,4,6]=>6
[5,2,3,1,6,4]=>8
[5,2,3,4,1,6]=>5
[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>5
[5,2,3,6,4,1]=>7
[5,2,4,1,3,6]=>6
[5,2,4,1,6,3]=>8
[5,2,4,3,1,6]=>9
[5,2,4,3,6,1]=>8
[5,2,4,6,1,3]=>5
[5,2,4,6,3,1]=>7
[5,2,6,1,3,4]=>6
[5,2,6,1,4,3]=>8
[5,2,6,3,1,4]=>9
[5,2,6,3,4,1]=>8
[5,2,6,4,1,3]=>9
[5,2,6,4,3,1]=>11
[5,3,1,2,4,6]=>7
[5,3,1,2,6,4]=>9
[5,3,1,4,2,6]=>10
[5,3,1,4,6,2]=>9
[5,3,1,6,2,4]=>10
[5,3,1,6,4,2]=>12
[5,3,2,1,4,6]=>11
[5,3,2,1,6,4]=>13
[5,3,2,4,1,6]=>10
[5,3,2,4,6,1]=>9
[5,3,2,6,1,4]=>10
[5,3,2,6,4,1]=>12
[5,3,4,1,2,6]=>6
[5,3,4,1,6,2]=>8
[5,3,4,2,1,6]=>9
[5,3,4,2,6,1]=>8
[5,3,4,6,1,2]=>5
[5,3,4,6,2,1]=>7
[5,3,6,1,2,4]=>6
[5,3,6,1,4,2]=>8
[5,3,6,2,1,4]=>9
[5,3,6,2,4,1]=>8
[5,3,6,4,1,2]=>9
[5,3,6,4,2,1]=>11
[5,4,1,2,3,6]=>7
[5,4,1,2,6,3]=>9
[5,4,1,3,2,6]=>10
[5,4,1,3,6,2]=>9
[5,4,1,6,2,3]=>10
[5,4,1,6,3,2]=>12
[5,4,2,1,3,6]=>11
[5,4,2,1,6,3]=>13
[5,4,2,3,1,6]=>10
[5,4,2,3,6,1]=>9
[5,4,2,6,1,3]=>10
[5,4,2,6,3,1]=>12
[5,4,3,1,2,6]=>11
[5,4,3,1,6,2]=>13
[5,4,3,2,1,6]=>14
[5,4,3,2,6,1]=>13
[5,4,3,6,1,2]=>10
[5,4,3,6,2,1]=>12
[5,4,6,1,2,3]=>6
[5,4,6,1,3,2]=>8
[5,4,6,2,1,3]=>9
[5,4,6,2,3,1]=>8
[5,4,6,3,1,2]=>9
[5,4,6,3,2,1]=>11
[5,6,1,2,3,4]=>1
[5,6,1,2,4,3]=>3
[5,6,1,3,2,4]=>4
[5,6,1,3,4,2]=>3
[5,6,1,4,2,3]=>4
[5,6,1,4,3,2]=>6
[5,6,2,1,3,4]=>5
[5,6,2,1,4,3]=>7
[5,6,2,3,1,4]=>4
[5,6,2,3,4,1]=>3
[5,6,2,4,1,3]=>4
[5,6,2,4,3,1]=>6
[5,6,3,1,2,4]=>5
[5,6,3,1,4,2]=>7
[5,6,3,2,1,4]=>8
[5,6,3,2,4,1]=>7
[5,6,3,4,1,2]=>4
[5,6,3,4,2,1]=>6
[5,6,4,1,2,3]=>5
[5,6,4,1,3,2]=>7
[5,6,4,2,1,3]=>8
[5,6,4,2,3,1]=>7
[5,6,4,3,1,2]=>8
[5,6,4,3,2,1]=>10
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>3
[6,1,2,4,3,5]=>4
[6,1,2,4,5,3]=>3
[6,1,2,5,3,4]=>4
[6,1,2,5,4,3]=>6
[6,1,3,2,4,5]=>5
[6,1,3,2,5,4]=>7
[6,1,3,4,2,5]=>4
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>4
[6,1,3,5,4,2]=>6
[6,1,4,2,3,5]=>5
[6,1,4,2,5,3]=>7
[6,1,4,3,2,5]=>8
[6,1,4,3,5,2]=>7
[6,1,4,5,2,3]=>4
[6,1,4,5,3,2]=>6
[6,1,5,2,3,4]=>5
[6,1,5,2,4,3]=>7
[6,1,5,3,2,4]=>8
[6,1,5,3,4,2]=>7
[6,1,5,4,2,3]=>8
[6,1,5,4,3,2]=>10
[6,2,1,3,4,5]=>6
[6,2,1,3,5,4]=>8
[6,2,1,4,3,5]=>9
[6,2,1,4,5,3]=>8
[6,2,1,5,3,4]=>9
[6,2,1,5,4,3]=>11
[6,2,3,1,4,5]=>5
[6,2,3,1,5,4]=>7
[6,2,3,4,1,5]=>4
[6,2,3,4,5,1]=>3
[6,2,3,5,1,4]=>4
[6,2,3,5,4,1]=>6
[6,2,4,1,3,5]=>5
[6,2,4,1,5,3]=>7
[6,2,4,3,1,5]=>8
[6,2,4,3,5,1]=>7
[6,2,4,5,1,3]=>4
[6,2,4,5,3,1]=>6
[6,2,5,1,3,4]=>5
[6,2,5,1,4,3]=>7
[6,2,5,3,1,4]=>8
[6,2,5,3,4,1]=>7
[6,2,5,4,1,3]=>8
[6,2,5,4,3,1]=>10
[6,3,1,2,4,5]=>6
[6,3,1,2,5,4]=>8
[6,3,1,4,2,5]=>9
[6,3,1,4,5,2]=>8
[6,3,1,5,2,4]=>9
[6,3,1,5,4,2]=>11
[6,3,2,1,4,5]=>10
[6,3,2,1,5,4]=>12
[6,3,2,4,1,5]=>9
[6,3,2,4,5,1]=>8
[6,3,2,5,1,4]=>9
[6,3,2,5,4,1]=>11
[6,3,4,1,2,5]=>5
[6,3,4,1,5,2]=>7
[6,3,4,2,1,5]=>8
[6,3,4,2,5,1]=>7
[6,3,4,5,1,2]=>4
[6,3,4,5,2,1]=>6
[6,3,5,1,2,4]=>5
[6,3,5,1,4,2]=>7
[6,3,5,2,1,4]=>8
[6,3,5,2,4,1]=>7
[6,3,5,4,1,2]=>8
[6,3,5,4,2,1]=>10
[6,4,1,2,3,5]=>6
[6,4,1,2,5,3]=>8
[6,4,1,3,2,5]=>9
[6,4,1,3,5,2]=>8
[6,4,1,5,2,3]=>9
[6,4,1,5,3,2]=>11
[6,4,2,1,3,5]=>10
[6,4,2,1,5,3]=>12
[6,4,2,3,1,5]=>9
[6,4,2,3,5,1]=>8
[6,4,2,5,1,3]=>9
[6,4,2,5,3,1]=>11
[6,4,3,1,2,5]=>10
[6,4,3,1,5,2]=>12
[6,4,3,2,1,5]=>13
[6,4,3,2,5,1]=>12
[6,4,3,5,1,2]=>9
[6,4,3,5,2,1]=>11
[6,4,5,1,2,3]=>5
[6,4,5,1,3,2]=>7
[6,4,5,2,1,3]=>8
[6,4,5,2,3,1]=>7
[6,4,5,3,1,2]=>8
[6,4,5,3,2,1]=>10
[6,5,1,2,3,4]=>6
[6,5,1,2,4,3]=>8
[6,5,1,3,2,4]=>9
[6,5,1,3,4,2]=>8
[6,5,1,4,2,3]=>9
[6,5,1,4,3,2]=>11
[6,5,2,1,3,4]=>10
[6,5,2,1,4,3]=>12
[6,5,2,3,1,4]=>9
[6,5,2,3,4,1]=>8
[6,5,2,4,1,3]=>9
[6,5,2,4,3,1]=>11
[6,5,3,1,2,4]=>10
[6,5,3,1,4,2]=>12
[6,5,3,2,1,4]=>13
[6,5,3,2,4,1]=>12
[6,5,3,4,1,2]=>9
[6,5,3,4,2,1]=>11
[6,5,4,1,2,3]=>10
[6,5,4,1,3,2]=>12
[6,5,4,2,1,3]=>13
[6,5,4,2,3,1]=>12
[6,5,4,3,1,2]=>13
[6,5,4,3,2,1]=>15
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>2
[1,2,3,4,6,5,7]=>3
[1,2,3,4,6,7,5]=>2
[1,2,3,4,7,5,6]=>3
[1,2,3,4,7,6,5]=>5
[1,2,3,5,4,6,7]=>4
[1,2,3,5,4,7,6]=>6
[1,2,3,5,6,4,7]=>3
[1,2,3,5,6,7,4]=>2
[1,2,3,5,7,4,6]=>3
[1,2,3,5,7,6,4]=>5
[1,2,3,6,4,5,7]=>4
[1,2,3,6,4,7,5]=>6
[1,2,3,6,5,4,7]=>7
[1,2,3,6,5,7,4]=>6
[1,2,3,6,7,4,5]=>3
[1,2,3,6,7,5,4]=>5
[1,2,3,7,4,5,6]=>4
[1,2,3,7,4,6,5]=>6
[1,2,3,7,5,4,6]=>7
[1,2,3,7,5,6,4]=>6
[1,2,3,7,6,4,5]=>7
[1,2,3,7,6,5,4]=>9
[1,2,4,3,5,6,7]=>5
[1,2,4,3,5,7,6]=>7
[1,2,4,3,6,5,7]=>8
[1,2,4,3,6,7,5]=>7
[1,2,4,3,7,5,6]=>8
[1,2,4,3,7,6,5]=>10
[1,2,4,5,3,6,7]=>4
[1,2,4,5,3,7,6]=>6
[1,2,4,5,6,3,7]=>3
[1,2,4,5,6,7,3]=>2
[1,2,4,5,7,3,6]=>3
[1,2,4,5,7,6,3]=>5
[1,2,4,6,3,5,7]=>4
[1,2,4,6,3,7,5]=>6
[1,2,4,6,5,3,7]=>7
[1,2,4,6,5,7,3]=>6
[1,2,4,6,7,3,5]=>3
[1,2,4,6,7,5,3]=>5
[1,2,4,7,3,5,6]=>4
[1,2,4,7,3,6,5]=>6
[1,2,4,7,5,3,6]=>7
[1,2,4,7,5,6,3]=>6
[1,2,4,7,6,3,5]=>7
[1,2,4,7,6,5,3]=>9
[1,2,5,3,4,6,7]=>5
[1,2,5,3,4,7,6]=>7
[1,2,5,3,6,4,7]=>8
[1,2,5,3,6,7,4]=>7
[1,2,5,3,7,4,6]=>8
[1,2,5,3,7,6,4]=>10
[1,2,5,4,3,6,7]=>9
[1,2,5,4,3,7,6]=>11
[1,2,5,4,6,3,7]=>8
[1,2,5,4,6,7,3]=>7
[1,2,5,4,7,3,6]=>8
[1,2,5,4,7,6,3]=>10
[1,2,5,6,3,4,7]=>4
[1,2,5,6,3,7,4]=>6
[1,2,5,6,4,3,7]=>7
[1,2,5,6,4,7,3]=>6
[1,2,5,6,7,3,4]=>3
[1,2,5,6,7,4,3]=>5
[1,2,5,7,3,4,6]=>4
[1,2,5,7,3,6,4]=>6
[1,2,5,7,4,3,6]=>7
[1,2,5,7,4,6,3]=>6
[1,2,5,7,6,3,4]=>7
[1,2,5,7,6,4,3]=>9
[1,2,6,3,4,5,7]=>5
[1,2,6,3,4,7,5]=>7
[1,2,6,3,5,4,7]=>8
[1,2,6,3,5,7,4]=>7
[1,2,6,3,7,4,5]=>8
[1,2,6,3,7,5,4]=>10
[1,2,6,4,3,5,7]=>9
[1,2,6,4,3,7,5]=>11
[1,2,6,4,5,3,7]=>8
[1,2,6,4,5,7,3]=>7
[1,2,6,4,7,3,5]=>8
[1,2,6,4,7,5,3]=>10
[1,2,6,5,3,4,7]=>9
[1,2,6,5,3,7,4]=>11
[1,2,6,5,4,3,7]=>12
[1,2,6,5,4,7,3]=>11
[1,2,6,5,7,3,4]=>8
[1,2,6,5,7,4,3]=>10
[1,2,6,7,3,4,5]=>4
[1,2,6,7,3,5,4]=>6
[1,2,6,7,4,3,5]=>7
[1,2,6,7,4,5,3]=>6
[1,2,6,7,5,3,4]=>7
[1,2,6,7,5,4,3]=>9
[1,2,7,3,4,5,6]=>5
[1,2,7,3,4,6,5]=>7
[1,2,7,3,5,4,6]=>8
[1,2,7,3,5,6,4]=>7
[1,2,7,3,6,4,5]=>8
[1,2,7,3,6,5,4]=>10
[1,2,7,4,3,5,6]=>9
[1,2,7,4,3,6,5]=>11
[1,2,7,4,5,3,6]=>8
[1,2,7,4,5,6,3]=>7
[1,2,7,4,6,3,5]=>8
[1,2,7,4,6,5,3]=>10
[1,2,7,5,3,4,6]=>9
[1,2,7,5,3,6,4]=>11
[1,2,7,5,4,3,6]=>12
[1,2,7,5,4,6,3]=>11
[1,2,7,5,6,3,4]=>8
[1,2,7,5,6,4,3]=>10
[1,2,7,6,3,4,5]=>9
[1,2,7,6,3,5,4]=>11
[1,2,7,6,4,3,5]=>12
[1,2,7,6,4,5,3]=>11
[1,2,7,6,5,3,4]=>12
[1,2,7,6,5,4,3]=>14
[1,3,2,4,5,6,7]=>6
[1,3,2,4,5,7,6]=>8
[1,3,2,4,6,5,7]=>9
[1,3,2,4,6,7,5]=>8
[1,3,2,4,7,5,6]=>9
[1,3,2,4,7,6,5]=>11
[1,3,2,5,4,6,7]=>10
[1,3,2,5,4,7,6]=>12
[1,3,2,5,6,4,7]=>9
[1,3,2,5,6,7,4]=>8
[1,3,2,5,7,4,6]=>9
[1,3,2,5,7,6,4]=>11
[1,3,2,6,4,5,7]=>10
[1,3,2,6,4,7,5]=>12
[1,3,2,6,5,4,7]=>13
[1,3,2,6,5,7,4]=>12
[1,3,2,6,7,4,5]=>9
[1,3,2,6,7,5,4]=>11
[1,3,2,7,4,5,6]=>10
[1,3,2,7,4,6,5]=>12
[1,3,2,7,5,4,6]=>13
[1,3,2,7,5,6,4]=>12
[1,3,2,7,6,4,5]=>13
[1,3,2,7,6,5,4]=>15
[1,3,4,2,5,6,7]=>5
[1,3,4,2,5,7,6]=>7
[1,3,4,2,6,5,7]=>8
[1,3,4,2,6,7,5]=>7
[1,3,4,2,7,5,6]=>8
[1,3,4,2,7,6,5]=>10
[1,3,4,5,2,6,7]=>4
[1,3,4,5,2,7,6]=>6
[1,3,4,5,6,2,7]=>3
[1,3,4,5,6,7,2]=>2
[1,3,4,5,7,2,6]=>3
[1,3,4,5,7,6,2]=>5
[1,3,4,6,2,5,7]=>4
[1,3,4,6,2,7,5]=>6
[1,3,4,6,5,2,7]=>7
[1,3,4,6,5,7,2]=>6
[1,3,4,6,7,2,5]=>3
[1,3,4,6,7,5,2]=>5
[1,3,4,7,2,5,6]=>4
[1,3,4,7,2,6,5]=>6
[1,3,4,7,5,2,6]=>7
[1,3,4,7,5,6,2]=>6
[1,3,4,7,6,2,5]=>7
[1,3,4,7,6,5,2]=>9
[1,3,5,2,4,6,7]=>5
[1,3,5,2,4,7,6]=>7
[1,3,5,2,6,4,7]=>8
[1,3,5,2,6,7,4]=>7
[1,3,5,2,7,4,6]=>8
[1,3,5,2,7,6,4]=>10
[1,3,5,4,2,6,7]=>9
[1,3,5,4,2,7,6]=>11
[1,3,5,4,6,2,7]=>8
[1,3,5,4,6,7,2]=>7
[1,3,5,4,7,2,6]=>8
[1,3,5,4,7,6,2]=>10
[1,3,5,6,2,4,7]=>4
[1,3,5,6,2,7,4]=>6
[1,3,5,6,4,2,7]=>7
[1,3,5,6,4,7,2]=>6
[1,3,5,6,7,2,4]=>3
[1,3,5,6,7,4,2]=>5
[1,3,5,7,2,4,6]=>4
[1,3,5,7,2,6,4]=>6
[1,3,5,7,4,2,6]=>7
[1,3,5,7,4,6,2]=>6
[1,3,5,7,6,2,4]=>7
[1,3,5,7,6,4,2]=>9
[1,3,6,2,4,5,7]=>5
[1,3,6,2,4,7,5]=>7
[1,3,6,2,5,4,7]=>8
[1,3,6,2,5,7,4]=>7
[1,3,6,2,7,4,5]=>8
[1,3,6,2,7,5,4]=>10
[1,3,6,4,2,5,7]=>9
[1,3,6,4,2,7,5]=>11
[1,3,6,4,5,2,7]=>8
[1,3,6,4,5,7,2]=>7
[1,3,6,4,7,2,5]=>8
[1,3,6,4,7,5,2]=>10
[1,3,6,5,2,4,7]=>9
[1,3,6,5,2,7,4]=>11
[1,3,6,5,4,2,7]=>12
[1,3,6,5,4,7,2]=>11
[1,3,6,5,7,2,4]=>8
[1,3,6,5,7,4,2]=>10
[1,3,6,7,2,4,5]=>4
[1,3,6,7,2,5,4]=>6
[1,3,6,7,4,2,5]=>7
[1,3,6,7,4,5,2]=>6
[1,3,6,7,5,2,4]=>7
[1,3,6,7,5,4,2]=>9
[1,3,7,2,4,5,6]=>5
[1,3,7,2,4,6,5]=>7
[1,3,7,2,5,4,6]=>8
[1,3,7,2,5,6,4]=>7
[1,3,7,2,6,4,5]=>8
[1,3,7,2,6,5,4]=>10
[1,3,7,4,2,5,6]=>9
[1,3,7,4,2,6,5]=>11
[1,3,7,4,5,2,6]=>8
[1,3,7,4,5,6,2]=>7
[1,3,7,4,6,2,5]=>8
[1,3,7,4,6,5,2]=>10
[1,3,7,5,2,4,6]=>9
[1,3,7,5,2,6,4]=>11
[1,3,7,5,4,2,6]=>12
[1,3,7,5,4,6,2]=>11
[1,3,7,5,6,2,4]=>8
[1,3,7,5,6,4,2]=>10
[1,3,7,6,2,4,5]=>9
[1,3,7,6,2,5,4]=>11
[1,3,7,6,4,2,5]=>12
[1,3,7,6,4,5,2]=>11
[1,3,7,6,5,2,4]=>12
[1,3,7,6,5,4,2]=>14
[1,4,2,3,5,6,7]=>6
[1,4,2,3,5,7,6]=>8
[1,4,2,3,6,5,7]=>9
[1,4,2,3,6,7,5]=>8
[1,4,2,3,7,5,6]=>9
[1,4,2,3,7,6,5]=>11
[1,4,2,5,3,6,7]=>10
[1,4,2,5,3,7,6]=>12
[1,4,2,5,6,3,7]=>9
[1,4,2,5,6,7,3]=>8
[1,4,2,5,7,3,6]=>9
[1,4,2,5,7,6,3]=>11
[1,4,2,6,3,5,7]=>10
[1,4,2,6,3,7,5]=>12
[1,4,2,6,5,3,7]=>13
[1,4,2,6,5,7,3]=>12
[1,4,2,6,7,3,5]=>9
[1,4,2,6,7,5,3]=>11
[1,4,2,7,3,5,6]=>10
[1,4,2,7,3,6,5]=>12
[1,4,2,7,5,3,6]=>13
[1,4,2,7,5,6,3]=>12
[1,4,2,7,6,3,5]=>13
[1,4,2,7,6,5,3]=>15
[1,4,3,2,5,6,7]=>11
[1,4,3,2,5,7,6]=>13
[1,4,3,2,6,5,7]=>14
[1,4,3,2,6,7,5]=>13
[1,4,3,2,7,5,6]=>14
[1,4,3,2,7,6,5]=>16
[1,4,3,5,2,6,7]=>10
[1,4,3,5,2,7,6]=>12
[1,4,3,5,6,2,7]=>9
[1,4,3,5,6,7,2]=>8
[1,4,3,5,7,2,6]=>9
[1,4,3,5,7,6,2]=>11
[1,4,3,6,2,5,7]=>10
[1,4,3,6,2,7,5]=>12
[1,4,3,6,5,2,7]=>13
[1,4,3,6,5,7,2]=>12
[1,4,3,6,7,2,5]=>9
[1,4,3,6,7,5,2]=>11
[1,4,3,7,2,5,6]=>10
[1,4,3,7,2,6,5]=>12
[1,4,3,7,5,2,6]=>13
[1,4,3,7,5,6,2]=>12
[1,4,3,7,6,2,5]=>13
[1,4,3,7,6,5,2]=>15
[1,4,5,2,3,6,7]=>5
[1,4,5,2,3,7,6]=>7
[1,4,5,2,6,3,7]=>8
[1,4,5,2,6,7,3]=>7
[1,4,5,2,7,3,6]=>8
[1,4,5,2,7,6,3]=>10
[1,4,5,3,2,6,7]=>9
[1,4,5,3,2,7,6]=>11
[1,4,5,3,6,2,7]=>8
[1,4,5,3,6,7,2]=>7
[1,4,5,3,7,2,6]=>8
[1,4,5,3,7,6,2]=>10
[1,4,5,6,2,3,7]=>4
[1,4,5,6,2,7,3]=>6
[1,4,5,6,3,2,7]=>7
[1,4,5,6,3,7,2]=>6
[1,4,5,6,7,2,3]=>3
[1,4,5,6,7,3,2]=>5
[1,4,5,7,2,3,6]=>4
[1,4,5,7,2,6,3]=>6
[1,4,5,7,3,2,6]=>7
[1,4,5,7,3,6,2]=>6
[1,4,5,7,6,2,3]=>7
[1,4,5,7,6,3,2]=>9
[1,4,6,2,3,5,7]=>5
[1,4,6,2,3,7,5]=>7
[1,4,6,2,5,3,7]=>8
[1,4,6,2,5,7,3]=>7
[1,4,6,2,7,3,5]=>8
[1,4,6,2,7,5,3]=>10
[1,4,6,3,2,5,7]=>9
[1,4,6,3,2,7,5]=>11
[1,4,6,3,5,2,7]=>8
[1,4,6,3,5,7,2]=>7
[1,4,6,3,7,2,5]=>8
[1,4,6,3,7,5,2]=>10
[1,4,6,5,2,3,7]=>9
[1,4,6,5,2,7,3]=>11
[1,4,6,5,3,2,7]=>12
[1,4,6,5,3,7,2]=>11
[1,4,6,7,2,3,5]=>4
[1,4,6,7,5,3,2]=>9
[1,4,7,2,3,5,6]=>5
[1,4,7,6,5,3,2]=>14
[1,5,2,3,4,7,6]=>8
[1,5,2,7,3,4,6]=>10
[1,5,4,7,6,3,2]=>15
[1,5,6,2,7,3,4]=>8
[1,5,6,4,7,3,2]=>10
[1,5,6,7,2,3,4]=>4
[1,5,6,7,4,3,2]=>9
[1,5,7,2,3,4,6]=>5
[1,5,7,6,4,3,2]=>14
[1,6,2,3,4,7,5]=>8
[1,6,2,3,7,4,5]=>9
[1,6,2,7,3,4,5]=>10
[1,6,5,4,3,7,2]=>17
[1,6,5,4,7,3,2]=>16
[1,6,5,7,4,3,2]=>15
[1,6,7,2,3,4,5]=>5
[1,6,7,5,4,3,2]=>14
[1,7,2,3,4,5,6]=>6
[1,7,3,5,6,4,2]=>11
[1,7,3,6,5,4,2]=>15
[1,7,4,3,6,5,2]=>16
[1,7,4,5,3,6,2]=>12
[1,7,4,5,6,3,2]=>11
[1,7,4,6,5,3,2]=>15
[1,7,5,4,3,6,2]=>17
[1,7,5,4,6,3,2]=>16
[1,7,6,4,5,3,2]=>16
[1,7,6,5,4,3,2]=>20
[2,1,3,4,5,6,7]=>6
[2,1,3,4,7,5,6]=>9
[2,1,3,7,4,5,6]=>10
[2,1,6,3,4,5,7]=>11
[2,1,7,3,4,5,6]=>11
[2,1,7,6,5,4,3]=>20
[2,3,1,4,5,6,7]=>5
[2,3,4,1,5,6,7]=>4
[2,3,4,1,5,7,6]=>6
[2,3,4,5,1,6,7]=>3
[2,3,4,5,1,7,6]=>5
[2,3,4,5,6,1,7]=>2
[2,3,4,5,6,7,1]=>1
[2,3,4,5,7,1,6]=>2
[2,3,4,6,1,7,5]=>5
[2,3,4,6,7,1,5]=>2
[2,3,4,7,1,5,6]=>3
[2,3,5,6,7,1,4]=>2
[2,4,1,3,5,6,7]=>5
[2,5,1,3,4,6,7]=>5
[2,5,7,1,3,4,6]=>4
[2,6,1,3,4,5,7]=>5
[2,6,1,7,3,4,5]=>9
[2,6,5,4,3,1,7]=>17
[2,6,7,1,3,4,5]=>4
[2,7,1,3,4,5,6]=>5
[3,1,2,4,5,6,7]=>5
[3,1,2,4,5,7,6]=>7
[3,2,1,4,5,6,7]=>11
[3,2,4,5,6,7,1]=>7
[3,4,1,2,5,6,7]=>4
[3,4,2,5,6,7,1]=>6
[3,4,5,2,6,7,1]=>5
[3,4,5,6,2,7,1]=>4
[3,4,5,6,7,1,2]=>1
[3,5,6,1,2,4,7]=>3
[3,5,6,4,2,1,7]=>10
[3,6,1,2,4,5,7]=>4
[3,6,5,4,2,1,7]=>16
[4,1,2,3,5,6,7]=>4
[4,1,2,3,5,7,6]=>6
[4,1,6,2,3,5,7]=>9
[4,2,3,5,6,7,1]=>6
[4,2,5,1,3,6,7]=>9
[4,3,2,1,5,6,7]=>15
[4,3,2,5,6,7,1]=>12
[4,3,5,2,6,7,1]=>11
[4,3,6,5,2,1,7]=>16
[4,5,1,6,2,3,7]=>7
[4,5,2,3,6,7,1]=>5
[4,5,3,6,2,1,7]=>10
[4,5,6,1,2,3,7]=>2
[4,5,6,3,2,1,7]=>9
[4,6,1,2,3,5,7]=>3
[4,6,1,2,3,7,5]=>5
[4,6,5,3,2,1,7]=>15
[5,1,2,3,4,6,7]=>3
[5,1,2,3,4,7,6]=>5
[5,1,2,3,6,4,7]=>6
[5,1,2,3,6,7,4]=>5
[5,1,2,3,7,4,6]=>6
[5,1,2,6,3,4,7]=>7
[5,1,6,2,3,4,7]=>8
[5,1,6,2,3,7,4]=>10
[5,2,3,4,6,7,1]=>5
[5,2,6,7,1,3,4]=>7
[5,3,2,4,6,7,1]=>11
[5,3,2,6,1,4,7]=>13
[5,3,6,7,1,2,4]=>7
[5,4,3,2,1,6,7]=>18
[5,4,3,2,1,7,6]=>20
[5,4,3,2,6,1,7]=>17
[5,4,3,6,2,1,7]=>16
[5,4,6,3,2,1,7]=>15
[5,4,6,7,1,2,3]=>7
[5,6,1,2,3,4,7]=>2
[5,6,1,2,3,7,4]=>4
[5,6,3,4,1,2,7]=>6
[5,6,4,3,2,1,7]=>14
[5,6,7,1,2,3,4]=>1
[6,1,2,3,4,5,7]=>2
[6,1,2,3,4,7,5]=>4
[6,1,2,3,7,4,5]=>5
[6,1,2,7,3,4,5]=>6
[6,2,3,4,5,7,1]=>4
[6,2,4,5,3,1,7]=>9
[6,2,5,4,3,1,7]=>14
[6,3,2,5,4,1,7]=>15
[6,3,4,2,5,1,7]=>10
[6,3,4,5,2,1,7]=>9
[6,3,4,7,1,2,5]=>6
[6,3,5,4,2,1,7]=>14
[6,4,3,2,5,1,7]=>16
[6,4,3,2,7,1,5]=>16
[6,4,3,5,2,1,7]=>15
[6,4,5,7,1,2,3]=>6
[6,4,7,2,5,1,3]=>10
[6,4,7,3,5,1,2]=>10
[6,5,3,4,2,1,7]=>15
[6,5,4,3,2,1,7]=>20
[6,5,7,3,4,1,2]=>10
[6,7,1,2,3,4,5]=>1
[6,7,3,4,1,2,5]=>5
[6,7,4,5,1,2,3]=>5
[7,1,2,3,4,5,6]=>1
[7,2,1,3,4,5,6]=>7
[7,2,3,1,4,5,6]=>6
[7,2,3,4,1,5,6]=>5
[7,2,3,4,5,1,6]=>4
[7,3,1,2,4,5,6]=>7
[7,3,2,1,4,5,6]=>12
[7,3,2,4,1,5,6]=>11
[7,3,4,1,2,5,6]=>6
[7,4,1,2,3,5,6]=>7
[7,4,2,1,3,5,6]=>12
[7,4,5,6,1,2,3]=>5
[7,5,1,2,3,4,6]=>7
[7,5,6,1,2,3,4]=>6
[7,5,6,3,4,1,2]=>9
[7,6,1,2,3,4,5]=>7
[7,6,4,5,1,2,3]=>11
[7,6,5,1,2,3,4]=>12
[7,6,5,3,4,1,2]=>15
[7,6,5,4,1,2,3]=>16
[7,6,5,4,3,1,2]=>19
[7,6,5,4,3,2,1]=>21
[8,7,6,5,4,3,2,1]=>28
[7,6,8,5,4,3,2,1]=>22
[7,8,5,6,4,3,2,1]=>15
[7,8,6,4,5,3,2,1]=>16
[8,6,7,4,5,3,2,1]=>16
[7,6,5,4,8,3,2,1]=>24
[6,5,7,4,8,3,2,1]=>18
[7,8,6,5,3,4,2,1]=>17
[8,6,7,5,3,4,2,1]=>17
[8,7,5,6,3,4,2,1]=>18
[6,7,8,3,4,5,2,1]=>6
[7,8,6,5,4,2,3,1]=>18
[8,6,7,5,4,2,3,1]=>18
[8,7,5,6,4,2,3,1]=>19
[8,7,6,4,5,2,3,1]=>20
[8,6,5,7,3,2,4,1]=>19
[6,7,8,5,2,3,4,1]=>8
[8,5,6,7,2,3,4,1]=>8
[7,8,3,2,4,5,6,1]=>9
[7,6,5,4,3,2,8,1]=>26
[6,5,7,4,3,2,8,1]=>20
[6,5,4,3,7,2,8,1]=>22
[5,4,6,3,7,2,8,1]=>16
[3,4,5,2,6,7,8,1]=>6
[5,2,3,4,6,7,8,1]=>6
[4,3,2,5,6,7,8,1]=>14
[3,4,2,5,6,7,8,1]=>7
[4,2,3,5,6,7,8,1]=>7
[3,2,4,5,6,7,8,1]=>8
[2,3,4,5,6,7,8,1]=>1
[8,7,6,5,4,3,1,2]=>26
[7,8,6,5,4,3,1,2]=>19
[8,6,7,5,4,3,1,2]=>19
[8,7,5,6,4,3,1,2]=>20
[8,7,6,4,5,3,1,2]=>21
[8,7,6,5,3,4,1,2]=>22
[8,7,5,6,3,4,1,2]=>16
[7,8,5,6,3,4,1,2]=>9
[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]=>1
[8,7,6,5,4,2,1,3]=>26
[7,6,8,5,4,2,1,3]=>20
[8,7,6,5,4,1,2,3]=>23
[6,7,8,5,4,1,2,3]=>10
[8,5,6,7,4,1,2,3]=>10
[8,7,6,4,5,1,2,3]=>18
[8,6,7,4,5,1,2,3]=>11
[8,7,4,5,6,1,2,3]=>12
[7,8,4,5,6,1,2,3]=>5
[6,7,4,5,8,1,2,3]=>6
[7,6,5,8,3,2,1,4]=>21
[7,5,6,8,2,3,1,4]=>10
[6,7,5,8,3,1,2,4]=>11
[6,5,7,8,2,1,3,4]=>12
[8,7,6,5,1,2,3,4]=>19
[8,7,5,6,1,2,3,4]=>13
[7,8,5,6,1,2,3,4]=>6
[8,5,6,7,1,2,3,4]=>6
[5,6,7,8,1,2,3,4]=>1
[8,7,6,4,3,2,1,5]=>26
[8,7,6,4,2,1,3,5]=>23
[8,7,6,1,2,3,4,5]=>14
[8,6,7,1,2,3,4,5]=>7
[6,7,8,1,2,3,4,5]=>1
[7,8,5,4,2,1,3,6]=>16
[7,8,5,4,1,2,3,6]=>12
[8,7,1,2,3,4,5,6]=>8
[7,8,1,2,3,4,5,6]=>1
[8,6,5,4,3,2,1,7]=>26
[8,6,5,4,3,1,2,7]=>23
[8,5,6,3,4,1,2,7]=>11
[8,6,5,4,2,1,3,7]=>23
[8,6,4,3,2,1,5,7]=>23
[8,6,4,2,1,3,5,7]=>19
[8,2,3,4,1,5,6,7]=>6
[8,4,1,2,3,5,6,7]=>8
[8,3,2,1,4,5,6,7]=>14
[8,2,3,1,4,5,6,7]=>7
[8,3,1,2,4,5,6,7]=>8
[8,2,1,3,4,5,6,7]=>8
[8,1,2,3,4,5,6,7]=>1
[7,6,5,4,3,2,1,8]=>27
[6,7,5,4,3,2,1,8]=>20
[6,5,7,4,3,2,1,8]=>21
[5,6,7,4,3,2,1,8]=>14
[7,6,4,5,3,2,1,8]=>21
[6,5,4,7,3,2,1,8]=>22
[7,5,6,3,4,2,1,8]=>15
[7,6,4,3,5,2,1,8]=>22
[7,6,3,4,5,2,1,8]=>16
[7,5,4,3,6,2,1,8]=>22
[6,7,5,4,2,3,1,8]=>16
[6,5,7,3,2,4,1,8]=>17
[5,6,7,2,3,4,1,8]=>5
[2,3,4,5,6,7,1,8]=>2
[5,6,7,1,2,3,4,8]=>2
[6,7,1,2,3,4,5,8]=>2
[7,1,2,3,4,5,6,8]=>2
[6,5,4,3,2,1,7,8]=>25
[2,3,4,5,6,1,7,8]=>3
[5,6,3,4,1,2,7,8]=>8
[4,5,6,1,2,3,7,8]=>3
[6,1,2,3,4,5,7,8]=>3
[5,4,3,2,1,6,7,8]=>22
[2,3,4,5,1,6,7,8]=>4
[5,1,2,3,4,6,7,8]=>4
[4,3,2,1,5,6,7,8]=>18
[3,4,1,2,5,6,7,8]=>5
[3,2,1,4,5,6,7,8]=>13
[2,1,3,4,5,6,7,8]=>7
[1,2,3,4,5,6,7,8]=>0
[6,5,8,7,4,3,2,1]=>23
[3,5,8,7,6,4,2,1]=>18
[4,3,6,5,8,7,2,1]=>20
[2,6,8,7,5,4,3,1]=>19
[2,3,5,6,8,7,4,1]=>8
[3,2,6,5,4,8,7,1]=>22
[4,3,6,5,7,2,8,1]=>17
[3,2,6,5,7,4,8,1]=>18
[4,3,5,2,7,6,8,1]=>17
[3,2,5,4,7,6,8,1]=>18
[1,8,7,6,5,4,3,2]=>27
[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]=>21
[1,6,7,8,5,4,3,2]=>14
[1,5,8,7,6,4,3,2]=>20
[1,7,6,5,8,4,3,2]=>22
[1,3,5,7,8,6,4,2]=>9
[1,4,3,8,7,6,5,2]=>21
[1,6,5,4,3,8,7,2]=>23
[1,4,3,6,5,8,7,2]=>17
[2,1,8,7,6,5,4,3]=>27
[2,1,6,5,7,4,8,3]=>19
[2,1,5,4,7,6,8,3]=>19
[1,2,6,7,8,5,4,3]=>9
[3,2,1,8,7,6,5,4]=>27
[3,2,1,6,5,8,7,4]=>23
[1,2,3,5,6,7,8,4]=>2
[4,3,2,1,8,7,6,5]=>27
[3,4,2,1,7,8,6,5]=>16
[2,4,3,1,6,8,7,5]=>17
[2,4,3,1,7,6,8,5]=>18
[3,2,4,1,6,8,7,5]=>17
[3,2,4,1,7,6,8,5]=>18
[2,3,4,1,6,7,8,5]=>7
[2,1,4,3,8,7,6,5]=>22
[2,1,4,3,6,8,7,5]=>18
[2,1,4,3,7,6,8,5]=>19
[5,4,3,2,1,8,7,6]=>27
[3,2,5,4,1,8,7,6]=>22
[3,2,1,4,5,8,7,6]=>18
[2,3,1,4,5,7,8,6]=>8
[6,5,4,3,2,1,8,7]=>27
[4,3,5,2,6,1,8,7]=>17
[3,2,5,4,6,1,8,7]=>18
[2,3,4,5,6,1,8,7]=>5
[2,1,6,5,4,3,8,7]=>24
[2,1,4,6,5,3,8,7]=>18
[2,1,5,4,6,3,8,7]=>19
[4,3,2,1,6,5,8,7]=>24
[2,4,3,1,6,5,8,7]=>18
[3,2,4,1,6,5,8,7]=>18
[2,1,4,3,6,5,8,7]=>19
[2,1,3,4,5,6,8,7]=>9
[1,2,3,4,5,6,8,7]=>2
[5,7,6,4,3,2,1,8]=>21
[4,7,6,5,3,2,1,8]=>22
[3,2,7,6,5,4,1,8]=>24
[5,4,3,2,7,6,1,8]=>24
[3,2,5,4,7,6,1,8]=>19
[1,4,3,2,7,6,5,8]=>20
[1,3,4,2,6,7,5,8]=>9
[1,3,2,5,4,7,6,8]=>15
[1,2,3,5,4,7,6,8]=>8
[1,3,2,4,5,7,6,8]=>10
[1,2,3,4,5,7,6,8]=>3
[1,2,4,3,6,5,7,8]=>10
[1,3,2,5,4,6,7,8]=>12
[1,2,3,5,4,6,7,8]=>5
[1,3,2,4,5,6,7,8]=>7
[1,8,4,7,6,5,3,2]=>21
[1,8,5,4,7,6,3,2]=>22
[1,8,7,4,5,6,3,2]=>18
[1,8,7,4,6,5,3,2]=>22
[1,8,6,5,4,7,3,2]=>23
[1,8,7,5,4,6,3,2]=>23
[1,8,7,5,6,4,3,2]=>22
[2,1,4,5,8,6,7,3]=>13
[2,1,8,5,4,7,6,3]=>23
[2,3,4,8,5,6,7,1]=>6
[2,3,6,4,5,1,8,7]=>11
[2,3,7,4,5,6,8,1]=>7
[2,8,4,3,5,7,6,1]=>17
[4,2,3,1,8,6,7,5]=>17
[8,2,7,4,6,5,3,1]=>16
[4,3,2,7,5,6,8,1]=>19
[4,3,2,8,5,7,6,1]=>22
[6,3,2,5,4,1,8,7]=>21
[8,3,2,5,4,7,6,1]=>18
[8,3,2,7,6,5,4,1]=>22
[8,3,7,4,6,5,2,1]=>16
[7,3,6,5,4,2,1,8]=>20
[7,4,3,6,5,2,1,8]=>21
[7,6,3,5,4,2,1,8]=>21
[8,5,4,3,2,7,6,1]=>24
[8,7,4,3,6,5,2,1]=>23
[2,4,6,8,1,3,5,7]=>4
[2,4,6,1,7,3,8,5]=>11
[2,1,4,3,7,5,8,6]=>19
[2,4,1,3,7,5,8,6]=>12
[2,1,4,3,7,8,5,6]=>16
[2,4,7,8,1,3,5,6]=>4
[2,1,4,3,8,5,6,7]=>17
[2,4,5,6,7,1,8,3]=>5
[2,1,5,3,6,4,8,7]=>19
[2,1,5,6,3,4,8,7]=>14
[2,5,6,8,1,3,4,7]=>4
[2,1,5,3,7,4,8,6]=>19
[2,5,1,7,3,4,8,6]=>13
[2,1,5,7,3,8,4,6]=>15
[2,5,7,8,1,3,4,6]=>4
[2,3,5,6,1,7,8,4]=>6
[2,1,6,3,7,4,8,5]=>19
[2,6,7,1,3,4,8,5]=>7
[2,1,6,7,8,3,4,5]=>11
[2,6,7,8,1,3,4,5]=>4
[2,1,6,3,4,7,8,5]=>15
[2,1,6,3,4,5,8,7]=>15
[2,6,1,3,4,5,7,8]=>6
[2,7,8,1,3,4,5,6]=>5
[2,7,1,3,4,5,6,8]=>6
[2,3,4,5,7,8,1,6]=>2
[2,1,8,3,4,5,6,7]=>13
[2,8,1,3,4,5,6,7]=>6
[2,1,3,8,4,5,6,7]=>12
[2,3,4,5,6,8,1,7]=>2
[3,1,4,2,6,5,8,7]=>18
[3,4,1,2,6,5,8,7]=>11
[3,1,4,2,6,8,5,7]=>15
[3,4,6,8,1,2,5,7]=>3
[3,1,4,2,7,5,8,6]=>18
[3,4,1,2,7,8,5,6]=>8
[3,4,7,8,1,2,5,6]=>3
[3,1,5,2,6,4,8,7]=>18
[3,5,1,6,2,4,8,7]=>12
[3,1,5,6,2,8,4,7]=>14
[3,5,6,8,1,2,4,7]=>3
[3,1,5,2,7,4,8,6]=>18
[3,5,1,7,2,8,4,6]=>13
[3,5,7,8,1,2,4,6]=>3
[1,3,2,5,4,8,6,7]=>15
[1,3,5,8,2,4,6,7]=>5
[1,3,5,6,2,7,4,8]=>8
[3,1,6,2,7,4,8,5]=>18
[3,6,7,1,2,8,4,5]=>7
[3,6,1,7,8,2,4,5]=>9
[3,6,7,8,1,2,4,5]=>3
[1,3,2,6,4,7,5,8]=>15
[3,1,2,6,7,4,8,5]=>12
[1,3,2,6,4,8,5,7]=>15
[1,3,2,6,4,5,7,8]=>12
[1,3,2,7,4,8,5,6]=>15
[1,3,2,7,4,5,6,8]=>12
[1,3,2,8,4,5,6,7]=>12
[3,1,2,4,5,8,6,7]=>9
[1,3,2,4,5,8,6,7]=>10
[4,1,5,2,6,3,8,7]=>17
[4,5,6,1,2,3,8,7]=>5
[4,1,5,6,8,2,3,7]=>9
[4,5,6,8,1,2,3,7]=>2
[4,1,5,2,7,3,8,6]=>17
[4,1,5,2,7,8,3,6]=>14
[4,5,7,1,2,8,3,6]=>6
[4,5,1,7,8,2,3,6]=>8
[4,5,7,8,1,2,3,6]=>2
[1,4,2,5,3,7,6,8]=>15
[1,4,2,5,3,8,6,7]=>15
[1,4,2,5,3,6,7,8]=>12
[1,4,5,6,7,2,3,8]=>4
[4,1,6,2,7,3,8,5]=>17
[4,6,7,1,8,2,3,5]=>7
[4,6,7,8,1,2,3,5]=>2
[1,4,2,6,3,7,5,8]=>15
[1,4,2,6,7,8,3,5]=>10
[1,4,2,6,3,8,5,7]=>15
[4,1,2,3,6,5,8,7]=>11
[1,4,2,6,3,5,7,8]=>12
[1,4,2,7,3,8,5,6]=>15
[4,7,1,2,3,5,6,8]=>4
[1,4,2,7,3,5,6,8]=>12
[1,4,2,3,7,5,6,8]=>11
[1,4,2,3,5,7,6,8]=>10
[1,4,2,8,3,5,6,7]=>12
[4,1,2,3,8,5,6,7]=>9
[1,4,2,3,5,8,6,7]=>10
[1,4,2,3,5,6,7,8]=>7
[5,1,6,2,7,3,8,4]=>16
[1,5,2,6,3,7,4,8]=>15
[1,5,2,6,3,8,4,7]=>15
[1,5,2,6,3,4,7,8]=>12
[1,2,5,6,3,4,7,8]=>5
[1,5,2,7,3,8,4,6]=>15
[5,7,1,2,3,4,6,8]=>3
[1,5,2,7,3,4,6,8]=>12
[1,5,2,3,4,7,6,8]=>10
[5,1,2,8,3,4,6,7]=>9
[1,5,2,8,3,4,6,7]=>12
[1,5,8,2,3,4,6,7]=>6
[1,5,2,3,4,8,6,7]=>10
[1,2,3,5,4,8,6,7]=>8
[5,1,2,3,4,6,8,7]=>6
[1,5,2,3,4,6,7,8]=>7
[1,6,2,7,3,8,4,5]=>15
[1,6,7,8,2,3,4,5]=>5
[6,7,1,2,3,4,8,5]=>4
[6,1,7,2,3,4,5,8]=>9
[6,1,2,7,3,4,5,8]=>8
[1,6,2,7,3,4,5,8]=>12
[1,6,7,2,3,4,5,8]=>6
[1,6,2,3,4,7,5,8]=>10
[1,2,3,6,4,7,5,8]=>8
[6,1,8,2,3,4,5,7]=>9
[1,6,2,8,3,4,5,7]=>12
[1,6,8,2,3,4,5,7]=>6
[1,6,2,3,4,8,5,7]=>10
[1,2,3,6,4,8,5,7]=>8
[6,1,2,3,4,5,8,7]=>5
[1,6,2,3,4,5,7,8]=>7
[1,2,3,6,4,5,7,8]=>5
[1,7,2,8,3,4,5,6]=>12
[1,7,8,2,3,4,5,6]=>6
[1,7,2,3,8,4,5,6]=>11
[7,1,2,3,4,8,5,6]=>5
[1,7,2,3,4,8,5,6]=>10
[1,2,3,7,4,8,5,6]=>8
[7,1,2,3,4,5,8,6]=>4
[1,7,2,3,4,5,8,6]=>9
[1,2,7,3,4,5,8,6]=>8
[1,7,2,3,4,5,6,8]=>7
[1,2,3,7,4,5,6,8]=>5
[1,8,2,3,4,5,6,7]=>7
[1,2,3,8,4,5,6,7]=>5
[1,2,3,4,5,8,6,7]=>3
[5,3,2,6,1,4,8,7]=>18
[7,3,2,5,4,8,1,6]=>17
[8,4,5,2,3,7,6,1]=>12
[7,4,5,2,3,8,1,6]=>11
[6,4,5,2,3,1,8,7]=>15
[5,4,6,2,1,3,8,7]=>17
[3,6,1,5,4,2,8,7]=>16
[4,6,5,1,3,2,8,7]=>16
[5,6,4,3,1,2,8,7]=>16
[7,5,4,3,2,8,1,6]=>23
[8,6,4,3,7,2,5,1]=>20
[7,6,4,3,8,2,1,5]=>22
[6,7,4,3,8,1,2,5]=>12
[5,7,4,3,1,8,2,6]=>17
[4,7,5,1,3,8,2,6]=>13
[3,7,1,5,4,8,2,6]=>13
[2,1,7,5,4,8,3,6]=>21
[3,8,1,5,4,7,6,2]=>15
[4,8,5,1,3,7,6,2]=>15
[5,8,4,3,1,7,6,2]=>19
[6,8,4,3,7,1,5,2]=>14
[7,8,4,3,6,5,1,2]=>14
[6,8,5,7,3,1,4,2]=>13
[5,8,6,7,1,3,4,2]=>10
[4,8,6,1,7,3,5,2]=>16
[3,8,1,6,7,4,5,2]=>11
[2,1,8,6,7,4,5,3]=>19
[2,1,7,6,8,4,3,5]=>20
[3,7,1,6,8,4,2,5]=>12
[4,7,6,1,8,3,2,5]=>17
[5,7,6,8,1,3,2,4]=>11
[5,4,7,2,1,8,3,6]=>18
[6,4,7,2,8,1,3,5]=>13
[7,4,6,2,8,3,1,5]=>15
[8,4,6,2,7,3,5,1]=>13
[8,3,2,6,7,4,5,1]=>14
[7,3,2,6,8,4,1,5]=>16
[6,3,2,7,8,1,4,5]=>14
[5,3,2,7,1,8,4,6]=>19
[4,3,2,1,7,8,5,6]=>21
[3,4,1,2,8,7,6,5]=>14
[5,3,2,8,1,7,6,4]=>21
[6,3,2,8,7,1,5,4]=>21
[7,3,2,8,6,5,1,4]=>21
[8,4,7,2,6,5,3,1]=>16
[7,4,8,2,6,5,1,3]=>15
[6,4,8,2,7,1,5,3]=>15
[5,4,8,2,1,7,6,3]=>20
[4,5,8,1,2,7,6,3]=>8
[3,5,1,8,2,7,6,4]=>15
[2,1,5,8,3,7,6,4]=>17
[2,1,6,8,7,3,5,4]=>18
[3,6,1,8,7,2,5,4]=>16
[4,6,8,1,7,2,5,3]=>9
[5,6,8,7,1,2,4,3]=>9
[6,5,8,7,2,1,4,3]=>20
[7,5,8,6,2,4,1,3]=>16
[8,5,7,6,2,4,3,1]=>17
[5,7,8,6,1,4,2,3]=>10
[4,7,8,1,6,5,2,3]=>10
[3,7,1,8,6,5,2,4]=>17
[2,1,7,8,6,5,3,4]=>19
[3,8,1,7,6,5,4,2]=>19
[4,8,7,1,6,5,3,2]=>19
[5,8,7,6,1,4,3,2]=>19
[6,8,7,5,4,1,3,2]=>19
[4,2,5,1,3,6,7,8]=>11
[5,2,6,7,1,3,4,8]=>9
[3,2,7,8,1,4,5,6]=>11
[5,3,2,6,1,4,7,8]=>16
[7,4,3,8,1,2,5,6]=>14
[4,7,3,6,8,1,2,5]=>8
[6,7,3,4,8,1,2,5]=>6
[5,4,2,7,8,1,3,6]=>15
[6,4,7,2,5,1,3,8]=>13
[6,4,3,2,7,1,5,8]=>20
[5,4,3,2,8,1,6,7]=>21
[7,5,3,8,2,6,1,4]=>17
[8,5,4,7,2,6,1,3]=>16
[8,5,4,7,3,6,1,2]=>16
[8,1,2,7,6,3,4,5]=>10
[8,1,4,2,6,3,5,7]=>11
[8,3,1,2,4,7,5,6]=>11
[8,3,1,5,6,2,4,7]=>12
[6,3,8,1,2,7,4,5]=>12
[7,8,4,1,6,2,3,5]=>11
[8,3,4,1,6,7,2,5]=>10
[2,7,6,5,1,3,8,4]=>19
[8,3,6,5,1,7,2,4]=>15
[4,6,7,3,8,5,1,2]=>10
[3,5,2,7,1,8,6,4]=>15
[4,6,7,2,8,1,5,3]=>9
[5,6,7,8,2,1,4,3]=>7
[6,5,8,7,3,4,1,2]=>17
[3,6,7,4,5,8,1,2]=>7
[2,6,7,4,5,1,8,3]=>11
[1,6,7,4,5,2,3,8]=>10
[1,5,4,7,6,2,3,8]=>16
[2,5,4,7,6,1,8,3]=>17
[3,5,4,7,6,8,1,2]=>13
[4,5,3,7,8,6,1,2]=>11
[5,4,3,8,7,6,1,2]=>23
[6,4,8,3,7,5,1,2]=>16
[6,3,8,4,5,7,1,2]=>12
[5,3,4,8,6,7,1,2]=>12
[4,3,5,6,8,7,1,2]=>12
[3,2,5,6,1,8,7,4]=>16
[4,2,5,6,8,1,7,3]=>11
[5,2,4,8,6,1,7,3]=>15
[6,2,8,4,5,1,7,3]=>15
[7,8,2,4,5,1,6,3]=>7
[7,8,1,4,5,2,3,6]=>5
[6,1,8,4,5,2,3,7]=>13
[5,1,4,8,6,2,3,7]=>13
[4,1,3,2,8,6,5,7]=>18
[5,1,3,8,2,6,4,7]=>12
[6,1,8,3,2,5,4,7]=>17
[7,8,1,3,2,5,4,6]=>9
[7,8,2,3,1,5,6,4]=>8
[6,2,8,3,1,5,7,4]=>16
[5,2,3,8,1,6,7,4]=>11
[6,3,8,2,1,7,5,4]=>19
[7,8,3,2,1,6,5,4]=>17
[7,8,4,2,6,1,5,3]=>13
[5,4,2,8,7,1,6,3]=>22
[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]=>15
[1,6,7,3,2,5,4,8]=>14
[2,6,7,3,1,5,8,4]=>12
[3,6,7,2,1,8,5,4]=>14
[7,8,5,6,2,1,4,3]=>12
[6,5,8,7,1,2,3,4]=>14
[5,4,1,8,7,2,3,6]=>20
[6,4,8,1,7,2,3,5]=>13
[7,8,3,1,2,6,4,5]=>10
[5,3,1,8,2,7,4,6]=>19
[4,3,1,2,8,7,5,6]=>19
[4,2,1,3,8,5,7,6]=>18
[5,2,1,8,3,4,7,6]=>18
[6,2,8,1,3,4,7,5]=>11
[7,8,2,1,3,4,6,5]=>9
[6,3,1,5,2,4,8,7]=>17
[2,1,8,5,3,7,4,6]=>21
[8,2,6,1,4,3,7,5]=>13
[4,7,1,5,8,3,2,6]=>11
[8,6,1,3,4,2,5,7]=>12
[8,1,2,4,5,6,3,7]=>4
[8,2,5,1,3,6,4,7]=>10
[4,1,5,3,7,2,8,6]=>17
[5,2,7,1,3,8,4,6]=>13
[5,3,1,7,8,2,4,6]=>15
[1,7,3,4,2,5,8,6]=>14
[4,7,2,1,3,5,8,6]=>12
[4,5,2,3,7,6,1,8]=>11
[6,4,3,7,2,5,1,8]=>18
[8,4,3,6,5,1,2,7]=>17
[1,5,6,3,4,8,7,2]=>11
[4,6,2,7,3,5,1,8]=>12
[3,2,6,7,4,5,1,8]=>14
[4,7,2,6,5,3,1,8]=>16
[5,7,6,2,4,3,1,8]=>16
[1,7,5,4,8,3,6,2]=>19
[8,7,5,4,1,3,2,6]=>22
[6,8,5,4,2,1,3,7]=>17
[5,8,6,2,4,1,3,7]=>13
[4,8,2,6,5,1,3,7]=>13
[3,2,8,6,5,1,4,7]=>21
[4,1,2,6,5,8,7,3]=>15
[5,1,6,2,4,8,7,3]=>15
[6,1,5,4,2,8,7,3]=>19
[7,1,5,4,8,2,6,3]=>14
[8,1,5,4,7,6,2,3]=>14
[1,8,6,7,4,5,3,2]=>17
[8,1,6,7,4,5,2,3]=>9
[7,1,6,8,4,2,5,3]=>13
[6,1,7,8,2,4,5,3]=>10
[5,1,7,2,8,4,6,3]=>16
[4,1,2,7,8,5,6,3]=>11
[3,2,1,7,8,5,6,4]=>19
[3,2,8,7,1,5,4,6]=>20
[4,8,2,7,1,5,3,6]=>12
[5,8,7,2,1,4,3,6]=>17
[6,8,7,1,2,4,3,5]=>11
[7,8,6,1,4,2,3,5]=>11
[8,7,6,1,4,3,2,5]=>21
[1,7,6,8,4,3,5,2]=>18
[1,6,7,8,3,4,5,2]=>7
[8,6,7,1,3,4,2,5]=>10
[7,6,8,1,3,2,4,5]=>12
[5,7,8,2,1,3,4,6]=>7
[4,7,2,8,1,3,5,6]=>9
[3,2,6,8,4,1,5,7]=>15
[4,6,2,8,3,1,5,7]=>13
[5,6,8,2,3,1,4,7]=>6
[6,5,8,3,2,1,4,7]=>18
[7,5,8,3,1,2,4,6]=>13
[8,5,7,3,1,4,2,6]=>15
[1,5,7,3,8,4,6,2]=>12
[1,4,3,7,8,5,6,2]=>13
[8,4,3,7,1,5,2,6]=>16
[6,4,3,8,2,1,5,7]=>19
[4,5,2,3,8,1,6,7]=>8
[3,2,5,4,8,1,6,7]=>16
[4,5,2,3,1,8,7,6]=>14
[6,4,3,1,2,8,7,5]=>21
[7,4,3,1,8,2,6,5]=>21
[8,4,3,1,7,6,2,5]=>21
[1,5,8,3,7,6,4,2]=>15
[8,5,1,3,7,6,2,4]=>15
[7,5,1,3,8,2,6,4]=>15
[6,5,1,3,2,8,7,4]=>20
[5,6,1,2,3,8,7,4]=>8
[4,6,2,1,3,8,7,5]=>15
[3,2,6,1,4,8,7,5]=>17
[3,2,7,1,8,4,6,5]=>18
[4,7,2,1,8,3,6,5]=>16
[5,7,1,2,8,3,6,4]=>9
[6,7,1,8,2,3,5,4]=>9
[7,6,1,8,3,2,5,4]=>20
[8,6,1,7,3,5,2,4]=>16
[1,6,8,7,3,5,4,2]=>16
[1,7,8,6,5,3,4,2]=>17
[8,7,1,6,5,3,2,4]=>20
[7,8,1,6,5,2,3,4]=>10
[6,8,1,7,2,5,3,4]=>10
[5,8,1,2,7,6,3,4]=>10
[4,8,2,1,7,6,3,5]=>17
[3,2,8,1,7,6,4,5]=>19
[4,1,2,8,7,6,5,3]=>19
[5,1,8,2,7,6,4,3]=>19
[6,1,8,7,2,5,4,3]=>19
[7,1,8,6,5,2,4,3]=>19
[8,1,7,6,5,4,2,3]=>19
[1,4,3,8,7,5,6,2]=>18
[4,1,2,8,7,5,6,3]=>16
[3,2,5,1,6,4,8,7]=>18
[3,2,5,4,7,1,8,6]=>18
[4,2,5,3,7,6,8,1]=>17
[4,2,5,3,7,1,8,6]=>17
[4,2,5,3,6,1,8,7]=>17
[4,2,5,1,6,3,8,7]=>17
[3,1,5,4,6,2,8,7]=>18
[4,1,5,3,6,2,8,7]=>17
[4,3,5,1,6,2,8,7]=>17
[4,3,5,2,7,1,8,6]=>17
[4,3,6,2,7,5,8,1]=>17
[4,3,6,2,7,1,8,5]=>17
[4,3,6,1,7,2,8,5]=>17
[4,3,5,1,7,2,8,6]=>17
[3,1,5,4,7,2,8,6]=>18
[2,1,5,4,7,3,8,6]=>19
[3,1,5,4,7,6,8,2]=>18
[4,1,5,3,7,6,8,2]=>17
[4,3,5,1,7,6,8,2]=>17
[4,3,6,1,7,5,8,2]=>17
[4,3,6,5,7,1,8,2]=>17
[5,3,6,4,7,2,8,1]=>16
[5,3,6,4,7,1,8,2]=>16
[5,3,6,1,7,4,8,2]=>16
[5,1,6,3,7,4,8,2]=>16
[4,1,6,3,7,5,8,2]=>17
[3,1,6,4,7,5,8,2]=>18
[2,1,6,4,7,5,8,3]=>19
[2,1,6,4,7,3,8,5]=>19
[3,1,6,4,7,2,8,5]=>18
[4,1,6,3,7,2,8,5]=>17
[5,1,6,3,7,2,8,4]=>16
[5,3,6,1,7,2,8,4]=>16
[5,3,6,2,7,1,8,4]=>16
[5,3,6,2,7,4,8,1]=>16
[5,2,6,3,7,4,8,1]=>16
[5,2,6,3,7,1,8,4]=>16
[5,2,6,1,7,3,8,4]=>16
[4,2,5,1,7,3,8,6]=>17
[4,2,6,1,7,3,8,5]=>17
[4,2,6,3,7,1,8,5]=>17
[4,2,6,3,7,5,8,1]=>17
[3,2,6,4,7,5,8,1]=>18
[3,2,6,4,7,1,8,5]=>18
[3,2,6,1,7,4,8,5]=>18
[3,2,5,1,7,4,8,6]=>18
[3,2,4,1,7,5,8,6]=>18
[3,1,4,2,7,6,8,5]=>18
[3,2,5,1,7,6,8,4]=>18
[3,2,6,1,7,5,8,4]=>18
[3,2,6,5,7,1,8,4]=>18
[4,2,6,5,7,3,8,1]=>17
[4,2,6,5,7,1,8,3]=>17
[4,2,6,1,7,5,8,3]=>17
[4,2,5,1,7,6,8,3]=>17
[4,1,5,2,7,6,8,3]=>17
[3,1,5,2,7,6,8,4]=>18
[2,1,5,3,7,6,8,4]=>19
[2,1,6,3,7,5,8,4]=>19
[3,1,6,2,7,5,8,4]=>18
[4,1,6,2,7,5,8,3]=>17
[5,1,6,2,7,4,8,3]=>16
[5,2,6,1,7,4,8,3]=>16
[5,2,6,4,7,1,8,3]=>16
[5,2,6,4,7,3,8,1]=>16
[5,4,6,2,7,3,8,1]=>16
[5,4,6,2,7,1,8,3]=>16
[5,4,6,1,7,2,8,3]=>16
[5,1,6,4,7,2,8,3]=>16
[4,1,6,5,7,2,8,3]=>17
[3,1,6,5,7,2,8,4]=>18
[2,1,6,5,7,3,8,4]=>19
[3,1,6,5,7,4,8,2]=>18
[4,1,6,5,7,3,8,2]=>17
[5,1,6,4,7,3,8,2]=>16
[5,4,6,1,7,3,8,2]=>16
[5,4,6,3,7,1,8,2]=>16
[8,3,5,2,1,6,4,7]=>15
[8,6,3,5,2,4,1,7]=>16
[3,7,5,2,4,1,8,6]=>17
[8,3,7,5,2,4,6,1]=>14
[8,2,4,5,7,3,6,1]=>7
[2,4,5,7,3,1,8,6]=>10
[8,2,4,6,5,3,1,7]=>13
[8,2,5,4,6,1,3,7]=>11
[8,6,3,5,1,4,2,7]=>16
[8,6,1,4,5,3,2,7]=>15
[8,1,5,6,4,3,2,7]=>13
[5,7,4,3,2,1,8,6]=>20
[8,5,7,4,3,2,6,1]=>18
[4,6,8,3,2,7,5,1]=>13
[4,7,6,3,2,8,1,5]=>18
[1,4,6,7,3,2,8,5]=>11
[5,4,7,3,1,8,2,6]=>18
[1,7,4,5,3,2,8,6]=>18
[3,7,5,1,4,2,8,6]=>17
[5,7,4,2,1,3,8,6]=>16
[8,5,7,4,2,1,6,3]=>18
[8,3,7,5,1,4,6,2]=>14
[8,4,1,7,5,3,6,2]=>19
[4,6,3,8,7,1,5,2]=>15
[1,7,4,8,6,3,5,2]=>18
[8,4,7,6,3,5,2,1]=>17
[3,6,5,8,7,4,1,2]=>17
[3,1,5,8,6,7,4,2]=>16
[4,8,1,6,7,3,5,2]=>10
[3,6,4,1,8,7,5,2]=>20
[8,2,6,1,4,7,5,3]=>12
[2,7,6,8,1,4,3,5]=>14
[3,7,1,6,4,8,2,5]=>13
[1,7,3,5,6,8,2,4]=>10
[1,3,6,7,5,8,2,4]=>8
[3,7,6,5,8,2,1,4]=>18
[3,6,8,5,7,2,4,1]=>10
[2,3,5,7,6,8,1,4]=>7
[2,1,6,5,7,8,3,4]=>16
[4,2,7,6,8,3,1,5]=>18
[4,2,6,8,7,3,5,1]=>16
[3,8,2,4,6,7,5,1]=>10
[3,7,2,6,4,8,1,5]=>13
[3,2,6,1,4,7,8,5]=>14
[5,3,7,2,1,8,4,6]=>18
[4,7,3,2,1,5,8,6]=>17
[8,7,6,1,3,4,2,5]=>17
[8,5,7,3,2,1,6,4]=>18
[8,3,6,7,2,1,5,4]=>12
[3,7,8,6,2,1,5,4]=>15
[8,7,6,3,5,2,4,1]=>20
[2,7,4,8,1,6,5,3]=>16
[4,6,8,2,1,7,5,3]=>13
[8,4,1,5,7,2,6,3]=>14
[8,5,3,7,1,6,2,4]=>16
[8,5,7,2,1,3,6,4]=>14
[8,2,6,7,1,3,5,4]=>8
[8,3,6,1,7,5,2,4]=>14
[4,6,1,8,7,2,5,3]=>15
[8,1,2,5,6,7,4,3]=>6
[8,2,6,5,7,4,1,3]=>14
[2,1,7,8,5,6,4,3]=>17
[8,2,5,7,6,4,3,1]=>15
[2,7,6,8,5,4,1,3]=>18
[1,7,2,5,8,6,4,3]=>16
[1,7,4,8,2,6,5,3]=>17
[3,7,8,1,6,5,2,4]=>11
[2,7,8,6,1,3,5,4]=>12
[8,7,6,3,5,1,4,2]=>20
[8,4,7,6,5,1,3,2]=>18
[8,7,1,5,6,4,3,2]=>17
[8,1,6,7,5,4,3,2]=>15
[5,4,3,6,1,2,8,7]=>18
[2,7,6,4,5,8,1,3]=>15
[5,7,3,6,1,8,2,4]=>11
[2,1,7,6,5,8,3,4]=>21
[6,4,3,5,8,1,7,2]=>16
[7,3,5,4,8,6,1,2]=>15
[5,4,3,2,7,1,8,6]=>23
[4,3,6,2,8,7,5,1]=>20
[4,3,7,6,2,1,8,5]=>22
[6,4,3,1,7,2,8,5]=>22
[4,3,7,1,8,6,5,2]=>20
[5,3,8,7,6,4,2,1]=>24
[7,5,3,1,8,6,4,2]=>24
[1,8,6,5,3,7,4,2]=>23
[6,1,7,5,3,2,8,4]=>20
[7,6,5,3,2,1,8,4]=>26
[6,5,3,2,8,7,4,1]=>25
[5,2,6,3,8,7,4,1]=>19
[5,2,7,6,3,1,8,4]=>21
[6,5,2,1,7,3,8,4]=>22
[5,2,7,1,8,6,4,3]=>19
[6,2,8,7,5,4,3,1]=>23
[7,6,2,1,8,5,4,3]=>24
[6,1,7,2,8,5,4,3]=>18
[7,1,8,6,5,4,3,2]=>22
[4,5,2,6,3,1,8,7]=>15
[6,5,2,1,4,3,8,7]=>22
[6,5,2,7,4,8,3,1]=>20
[8,5,2,7,4,1,6,3]=>19
[8,3,7,5,2,1,6,4]=>18
[6,3,7,5,2,8,4,1]=>19
[3,1,6,5,4,2,8,7]=>23
[5,6,3,2,4,1,8,7]=>15
[3,6,2,4,1,5,8,7]=>12
[2,6,1,3,5,4,8,7]=>12
[6,7,2,3,4,8,5,1]=>7
[8,7,2,3,4,1,6,5]=>14
[5,1,7,3,8,4,6,2]=>16
[2,5,7,3,8,6,4,1]=>14
[7,6,1,3,5,8,4,2]=>14
[3,6,7,4,1,8,5,2]=>14
[5,6,3,7,4,8,1,2]=>11
[2,1,6,7,4,8,5,3]=>17
[2,1,8,7,4,3,6,5]=>24
[5,8,3,7,4,2,6,1]=>14
[3,8,7,4,1,2,6,5]=>18
[7,8,1,3,5,2,6,4]=>7
[5,8,7,3,2,6,1,4]=>17
[2,8,6,3,1,5,7,4]=>19
[8,1,6,3,2,5,4,7]=>15
[2,8,4,1,6,3,7,5]=>18
[4,8,1,2,7,6,3,5]=>11
[3,8,4,2,5,7,1,6]=>14
[6,8,3,5,2,7,4,1]=>12
[2,1,5,3,8,7,6,4]=>22
[6,5,3,2,8,7,1,4]=>23
[7,5,2,4,8,1,6,3]=>15
[3,4,2,8,5,7,6,1]=>15
[2,4,1,8,7,6,5,3]=>20
[8,4,2,1,7,5,3,6]=>21
[4,3,1,8,6,7,5,2]=>22
[3,1,4,8,6,5,7,2]=>17
[7,1,6,5,4,8,2,3]=>16
[3,7,5,6,8,4,2,1]=>14
[5,7,1,6,8,2,4,3]=>9
[8,6,2,5,1,7,4,3]=>18
[5,6,2,1,8,7,3,4]=>16
[4,6,2,5,8,3,7,1]=>10
[7,5,2,6,3,8,1,4]=>17
[4,1,2,3,6,8,7,5]=>10
[2,4,3,1,8,5,6,7]=>16
[7,5,2,8,3,4,6,1]=>16
[5,6,2,8,4,3,1,7]=>15
[4,7,2,8,1,5,3,6]=>12
[8,7,2,1,4,5,6,3]=>16
[3,6,8,7,1,5,4,2]=>14
[5,7,8,6,3,4,1,2]=>10
[7,1,8,5,4,3,6,2]=>19
[2,7,8,4,5,3,6,1]=>11
[5,7,3,8,1,4,6,2]=>10
[2,1,7,8,5,4,6,3]=>18
[2,1,5,8,4,6,3,7]=>15
[6,5,3,8,4,1,2,7]=>19
[7,5,8,4,3,6,2,1]=>18
[2,4,8,3,5,6,1,7]=>8
[4,1,8,3,6,5,2,7]=>18
[3,4,8,1,7,2,5,6]=>8
[8,4,1,3,7,2,6,5]=>14
[3,1,8,2,4,7,6,5]=>17
[2,3,8,1,4,6,7,5]=>7
[4,3,8,2,5,1,7,6]=>17
[6,3,8,4,2,5,7,1]=>16
[7,4,3,8,2,5,1,6]=>17
[2,1,4,8,3,5,7,6]=>14
[6,8,2,4,3,5,1,7]=>10
[4,8,2,3,5,1,6,7]=>8
[3,8,2,1,4,6,5,7]=>14
[2,8,1,3,4,5,7,6]=>8
[7,1,6,8,4,3,2,5]=>14
[7,1,6,5,8,3,2,4]=>15
[3,7,6,1,4,8,2,5]=>14
[2,7,8,4,1,6,5,3]=>15
[3,6,4,5,7,2,8,1]=>11
[1,8,2,7,3,4,5,6]=>12
[3,2,1,5,8,4,6,7]=>17
[5,4,3,2,1,8,6,7]=>25
[1,8,2,4,3,5,6,7]=>12
[1,7,2,4,3,5,6,8]=>12
[1,6,2,4,3,5,7,8]=>12
[1,5,2,4,3,6,7,8]=>12
[1,6,2,5,3,4,7,8]=>12
[1,7,2,5,3,4,6,8]=>12
[1,8,2,5,3,4,6,7]=>12
[1,8,2,6,3,4,5,7]=>12
[1,7,2,6,3,4,5,8]=>12
[1,8,2,7,3,5,4,6]=>15
[1,7,2,8,3,5,4,6]=>15
[1,6,2,8,3,5,4,7]=>15
[1,5,2,8,3,6,4,7]=>15
[1,4,2,8,3,6,5,7]=>15
[1,3,2,8,4,6,5,7]=>15
[1,2,3,8,4,6,5,7]=>8
[1,2,3,7,4,6,5,8]=>8
[1,3,2,7,4,6,5,8]=>15
[1,4,2,7,3,6,5,8]=>15
[1,5,2,7,3,6,4,8]=>15
[1,6,2,7,3,5,4,8]=>15
[1,7,2,6,3,5,4,8]=>15
[1,8,2,6,3,5,4,7]=>15
[1,8,2,5,3,6,4,7]=>15
[1,7,2,5,3,6,4,8]=>15
[1,6,2,5,3,7,4,8]=>15
[1,5,2,4,3,7,6,8]=>15
[1,6,2,4,3,7,5,8]=>15
[1,7,2,4,3,6,5,8]=>15
[1,8,2,4,3,6,5,7]=>15
[1,8,2,3,4,6,5,7]=>10
[1,7,2,3,4,6,5,8]=>10
[1,8,2,3,4,7,5,6]=>10
[1,8,2,4,3,7,5,6]=>15
[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]=>15
[1,7,2,5,3,8,4,6]=>15
[1,8,2,5,3,7,4,6]=>15
[1,8,2,6,3,7,4,5]=>15
[1,7,2,6,3,8,4,5]=>15
[1,2,3,8,4,7,5,6]=>8
[1,3,2,8,4,7,5,6]=>15
[1,4,2,8,3,7,5,6]=>15
[1,5,2,8,3,7,4,6]=>15
[1,6,2,8,3,7,4,5]=>15
[1,7,2,8,3,6,4,5]=>15
[1,8,2,7,3,6,4,5]=>15
[6,7,8,1,4,3,2,5]=>8
[2,8,4,1,6,7,5,3]=>17
[4,8,5,7,1,6,2,3]=>12
[8,7,6,5,2,1,4,3]=>25
[8,3,1,5,4,7,2,6]=>16
[8,7,6,5,1,4,2,3]=>22
[7,5,1,3,8,4,2,6]=>16
[7,6,1,4,8,3,2,5]=>16
[7,1,3,5,8,2,4,6]=>6
[7,5,3,6,4,2,8,1]=>20
[8,2,6,3,4,7,5,1]=>12
[7,2,6,3,5,4,8,1]=>14
[6,2,7,4,3,5,8,1]=>16
[3,7,6,4,5,2,8,1]=>17
[2,7,6,5,3,4,8,1]=>19
[8,6,5,4,2,7,3,1]=>24
[6,5,8,4,2,7,3,1]=>19
[1,8,6,3,7,5,2,4]=>20
[8,7,5,2,6,4,3,1]=>23
[8,7,1,6,2,5,4,3]=>18
[1,7,2,8,5,3,4,6]=>16
[7,6,1,8,4,3,2,5]=>21
[8,6,1,7,4,2,5,3]=>19
[8,1,2,7,3,4,6,5]=>8
[7,1,2,8,3,5,4,6]=>10
[8,2,6,1,7,3,5,4]=>13
[4,7,5,6,8,3,2,1]=>13
[8,6,4,7,5,3,2,1]=>22
[5,4,8,1,7,2,6,3]=>16
[2,3,8,7,4,5,6,1]=>12
[7,2,8,6,4,3,5,1]=>19
[8,2,7,6,3,5,4,1]=>17
[8,1,7,6,5,2,4,3]=>18
[7,1,8,6,5,3,2,4]=>20
[1,2,8,7,6,3,4,5]=>15
[3,8,7,6,4,5,2,1]=>21
[2,8,7,6,5,3,4,1]=>23
[1,8,7,6,5,4,2,3]=>25
[3,8,6,7,1,5,2,4]=>13
[5,4,7,1,3,8,2,6]=>13
[5,6,2,1,4,8,3,7]=>12
[2,1,8,4,7,5,6,3]=>19
[4,1,3,2,8,5,6,7]=>15
[3,2,1,4,8,5,6,7]=>17
[1,8,4,2,5,3,6,7]=>17
[8,1,5,3,2,4,6,7]=>12
[3,8,1,5,2,4,6,7]=>10
[1,6,7,2,8,4,3,5]=>13
[6,7,1,4,2,8,3,5]=>10
[6,3,7,1,4,8,2,5]=>12
[3,7,8,1,5,2,4,6]=>8
[7,1,2,8,5,3,4,6]=>11
[1,7,2,8,4,5,3,6]=>15
[1,2,7,5,8,3,4,6]=>10
[2,8,1,7,4,3,6,5]=>17
[4,2,6,5,8,3,7,1]=>17
[5,2,4,7,3,6,8,1]=>11
[5,1,2,4,8,3,6,7]=>8
[4,3,6,1,5,8,2,7]=>14
[2,6,1,4,5,8,3,7]=>9
[2,5,3,4,1,8,6,7]=>14
[4,3,5,2,1,8,6,7]=>19
[3,1,6,7,5,8,2,4]=>14
[2,8,1,7,5,6,3,4]=>14
[5,3,6,8,4,7,2,1]=>14
[3,7,2,5,4,8,6,1]=>15
[8,4,2,5,7,3,6,1]=>14
[4,7,2,5,8,3,6,1]=>10
[5,2,6,8,4,3,7,1]=>15
[3,1,6,5,4,8,2,7]=>20
[4,1,6,5,8,3,2,7]=>18
[5,1,6,8,4,3,2,7]=>16
[8,5,4,7,6,3,2,1]=>22
[5,7,1,8,4,3,2,6]=>15
[2,7,1,5,4,3,8,6]=>17
[8,2,1,5,4,3,7,6]=>19
[8,4,1,5,7,3,2,6]=>15
[8,5,6,7,1,3,2,4]=>9
[8,4,6,1,7,3,2,5]=>14
[8,3,6,1,4,7,2,5]=>10
[2,7,6,1,4,3,8,5]=>18
[6,7,8,5,1,3,2,4]=>9
[5,7,6,8,2,3,4,1]=>10
[5,7,2,8,4,3,6,1]=>14
[6,7,8,2,4,3,5,1]=>7
[4,7,6,2,8,3,5,1]=>16
[8,3,6,2,4,7,5,1]=>12
[3,7,6,2,4,8,5,1]=>16
[5,7,3,8,4,6,2,1]=>13
[4,7,3,5,8,6,2,1]=>13
[8,7,2,1,4,3,6,5]=>20
[8,7,3,1,4,6,2,5]=>17
[8,7,6,3,2,5,4,1]=>24
[8,7,3,5,1,6,2,4]=>16
[8,7,2,5,1,3,6,4]=>15
[8,2,6,5,1,3,7,4]=>14
[8,4,6,5,7,1,2,3]=>11
[5,7,6,8,4,1,2,3]=>12
[4,7,6,5,8,1,2,3]=>14
[3,7,6,5,1,8,2,4]=>19
[2,6,5,7,3,4,8,1]=>13
[1,6,4,7,5,8,2,3]=>15
[8,5,3,6,2,7,4,1]=>18
[1,3,7,4,6,8,2,5]=>9
[4,7,5,6,3,2,8,1]=>15
[1,7,6,5,4,8,2,3]=>21
[8,1,6,5,7,2,4,3]=>13
[1,2,7,6,8,3,4,5]=>10
[6,1,7,5,3,8,2,4]=>17
[2,1,7,5,6,8,3,4]=>16
[5,4,1,7,6,8,2,3]=>19
[4,8,5,6,2,7,3,1]=>14
[3,8,6,4,2,7,5,1]=>21
[7,8,5,2,4,6,3,1]=>12
[2,8,6,3,7,4,5,1]=>18
[7,8,1,6,2,4,5,3]=>8
[6,8,1,4,7,2,5,3]=>8
[3,8,4,1,7,2,6,5]=>17
[5,4,7,1,8,3,2,6]=>17
[3,7,4,1,8,5,2,6]=>18
[6,7,1,4,8,3,2,5]=>9
[2,7,1,8,4,5,3,6]=>14
[6,1,2,8,4,3,5,7]=>12
[6,5,1,4,3,8,2,7]=>18
[1,6,2,5,8,3,4,7]=>11
[8,5,1,3,7,2,6,4]=>14
[8,4,2,1,7,3,6,5]=>20
[7,4,2,1,8,5,3,6]=>22
[1,5,4,2,8,3,6,7]=>17
[6,4,3,1,5,8,2,7]=>19
[3,7,6,8,4,5,2,1]=>15
[2,7,6,8,5,3,4,1]=>17
[1,7,6,8,5,4,2,3]=>19
[1,4,8,6,7,5,2,3]=>13
[2,4,8,6,7,3,5,1]=>11
[7,3,8,5,4,6,2,1]=>18
[3,4,8,5,6,7,2,1]=>9
[6,3,5,8,4,7,2,1]=>13
[5,4,3,8,6,7,2,1]=>21
[5,4,2,8,7,3,6,1]=>22
[6,2,5,8,7,3,4,1]=>14
[3,2,8,5,7,4,6,1]=>18
[1,3,8,7,5,6,2,4]=>14
[2,1,8,7,4,6,3,5]=>21
[3,1,8,5,7,6,2,4]=>19
[6,1,5,8,7,4,2,3]=>15
[5,4,1,8,7,6,2,3]=>23
[5,8,6,7,4,3,2,1]=>17
[4,8,7,5,6,3,2,1]=>19
[2,8,3,1,5,4,6,7]=>16
[2,5,3,4,7,1,8,6]=>12
[2,4,8,3,5,7,6,1]=>10
[4,2,5,3,1,8,6,7]=>19
[4,2,1,8,5,3,6,7]=>21
[5,4,1,3,8,2,6,7]=>15
[5,1,4,8,3,2,6,7]=>13
[1,5,8,4,3,2,6,7]=>15
[1,8,5,4,3,2,6,7]=>22
[1,7,4,3,8,5,2,6]=>20
[1,5,7,3,8,4,2,6]=>13
[5,1,4,7,8,3,2,6]=>11
[4,8,1,5,7,3,6,2]=>10
[8,1,5,3,7,4,6,2]=>13
[3,8,4,7,6,5,2,1]=>19
[1,6,8,5,3,7,4,2]=>16
[6,8,1,7,4,3,5,2]=>13
[6,4,8,1,7,3,5,2]=>15
[6,4,8,7,1,5,2,3]=>17
[7,6,4,1,3,8,2,5]=>18
[1,7,5,6,3,2,8,4]=>18
[4,2,1,7,8,5,3,6]=>19
[2,7,4,6,3,1,8,5]=>17
[2,6,8,4,3,7,5,1]=>15
[6,2,4,8,3,7,5,1]=>13
[7,2,6,3,4,1,8,5]=>14
[2,6,7,3,1,4,8,5]=>12
[2,7,1,8,3,5,4,6]=>14
[2,1,7,3,5,8,4,6]=>16
[8,7,1,3,6,2,4,5]=>12
[8,2,1,7,3,5,6,4]=>15
[7,8,2,6,3,1,5,4]=>12
[8,7,2,6,3,5,4,1]=>18
[1,2,8,7,4,5,6,3]=>13
[8,3,7,1,5,6,2,4]=>10
[8,6,1,2,7,5,3,4]=>15
[8,1,6,2,7,4,5,3]=>13
[1,8,5,2,6,7,4,3]=>18
[5,2,1,8,6,7,4,3]=>21
[2,8,5,7,6,4,3,1]=>20
[1,7,8,5,2,6,4,3]=>16
[7,8,1,6,4,2,5,3]=>12
[7,8,6,1,5,3,2,4]=>14
[7,3,8,6,1,5,2,4]=>16
[8,7,6,1,5,3,4,2]=>20
[8,7,1,6,4,5,3,2]=>18
[8,1,7,5,6,4,3,2]=>16
[1,8,6,7,5,4,3,2]=>21
[9,1,2,3,4,5,6,7,8]=>1
[8,1,2,3,4,5,6,9,7]=>4
[2,9,1,3,4,5,6,7,8]=>7
[9,3,1,2,4,5,6,7,8]=>9
[8,9,1,2,3,4,5,6,7]=>1
[9,7,8,1,2,3,4,5,6]=>8
[2,3,4,5,6,7,9,1,8]=>2
[2,3,4,5,6,7,8,9,1]=>1
[2,3,4,5,6,7,8,1,9]=>2
[2,3,4,5,6,7,1,8,9]=>3
[1,2,3,4,5,6,7,9,8]=>2
[2,1,3,4,5,6,7,8,9]=>8
[1,8,2,3,4,5,6,9,7]=>10
[7,1,2,3,4,5,6,9,8]=>5
[2,1,9,3,4,5,6,7,8]=>15
[2,8,1,3,4,5,6,7,9]=>7
[1,2,3,4,5,6,7,8,9]=>0
[3,2,4,5,6,7,8,9,1]=>9
[9,8,7,6,5,4,3,2,1]=>36
[8,7,6,5,4,3,2,1,9]=>35
[1,9,8,7,6,5,4,3,2]=>35
[8,7,6,4,5,3,2,1,9]=>29
[1,9,8,7,5,6,4,3,2]=>30
[8,7,5,4,6,3,2,1,9]=>29
[8,7,4,6,5,3,2,1,9]=>28
[1,9,8,6,5,7,4,3,2]=>30
[1,9,8,5,7,6,4,3,2]=>29
[9,2,1,3,4,5,6,7,8]=>9
[9,2,3,1,4,5,6,7,8]=>8
[4,2,3,5,6,7,8,9,1]=>8
[3,4,2,5,6,7,8,9,1]=>8
[9,8,1,2,3,4,5,6,7]=>9
[7,8,9,1,2,3,4,5,6]=>1
[9,8,7,1,2,3,4,5,6]=>16
[6,7,8,9,1,2,3,4,5]=>1
[9,6,7,8,1,2,3,4,5]=>7
[8,9,6,7,1,2,3,4,5]=>7
[9,8,6,7,1,2,3,4,5]=>15
[9,8,7,6,1,2,3,4,5]=>22
[9,5,6,7,8,1,2,3,4]=>6
[8,9,5,6,7,1,2,3,4]=>6
[9,8,5,6,7,1,2,3,4]=>14
[9,7,8,5,6,1,2,3,4]=>13
[9,8,7,5,6,1,2,3,4]=>21
[9,8,7,6,5,1,2,3,4]=>27
[7,8,9,4,5,6,1,2,3]=>5
[9,7,8,4,5,6,1,2,3]=>12
[9,8,7,4,5,6,1,2,3]=>20
[8,9,6,7,4,5,1,2,3]=>11
[9,8,6,7,4,5,1,2,3]=>19
[9,8,7,6,4,5,1,2,3]=>26
[9,8,7,6,5,4,1,2,3]=>31
[9,7,8,5,6,3,4,1,2]=>16
[9,8,7,5,6,3,4,1,2]=>24
[9,8,7,6,5,3,4,1,2]=>30
[9,8,7,6,5,4,3,1,2]=>34
[7,8,6,5,4,3,2,1,9]=>27
[1,8,9,7,6,5,4,3,2]=>27
[7,6,8,5,4,3,2,1,9]=>28
[6,8,7,5,4,3,2,1,9]=>28
[1,8,7,9,6,5,4,3,2]=>28
[1,7,9,8,6,5,4,3,2]=>27
[8,1,2,3,4,5,6,7,9]=>2
[1,9,2,3,4,5,6,7,8]=>8
[7,8,1,2,3,4,5,6,9]=>2
[1,8,9,2,3,4,5,6,7]=>7
[7,1,8,2,3,4,5,6,9]=>10
[6,8,1,2,3,4,5,7,9]=>3
[1,8,2,9,3,4,5,6,7]=>14
[1,7,9,2,3,4,5,6,8]=>7
[7,1,2,3,4,5,6,8,9]=>3
[3,4,1,2,5,6,7,8,9]=>6
[3,2,1,4,5,6,7,8,9]=>15
[4,5,6,1,2,3,7,8,9]=>4
[4,2,5,1,3,6,7,8,9]=>13
[4,3,2,1,5,6,7,8,9]=>21
[5,6,7,8,1,2,3,4,9]=>2
[5,2,6,7,1,3,4,8,9]=>11
[5,6,3,4,1,2,7,8,9]=>10
[5,3,2,6,1,4,7,8,9]=>19
[5,4,3,2,1,6,7,8,9]=>26
[6,2,7,8,9,1,3,4,5]=>9
[6,7,3,4,8,1,2,5,9]=>8
[6,3,2,7,8,1,4,5,9]=>17
[6,4,7,2,5,1,3,8,9]=>16
[6,4,3,2,7,1,5,8,9]=>24
[6,5,4,3,2,1,7,8,9]=>30
[7,4,8,2,5,9,1,3,6]=>14
[7,4,3,2,8,9,1,5,6]=>22
[7,8,5,6,3,4,1,2,9]=>12
[7,5,3,8,2,6,1,4,9]=>21
[7,5,4,3,2,8,1,6,9]=>28
[7,6,5,4,3,2,1,8,9]=>33
[8,6,9,4,7,2,5,1,3]=>17
[8,6,4,3,9,2,7,1,5]=>25
[8,6,5,4,3,2,9,1,7]=>31
[2,1,4,3,6,5,8,7,10,9]=>29
[4,3,2,1,6,5,8,7,10,9]=>36
[6,3,2,5,4,1,8,7,10,9]=>33
[8,3,2,5,4,7,6,1,10,9]=>30
[10,3,2,5,4,7,6,9,8,1]=>27
[2,1,6,5,4,3,8,7,10,9]=>36
[6,5,4,3,2,1,8,7,10,9]=>41
[8,5,4,3,2,7,6,1,10,9]=>38
[10,5,4,3,2,7,6,9,8,1]=>35
[2,1,8,5,4,7,6,3,10,9]=>35
[8,7,4,3,6,5,2,1,10,9]=>37
[10,7,4,3,6,5,2,9,8,1]=>34
[2,1,10,5,4,7,6,9,8,3]=>34
[10,9,4,3,6,5,8,7,2,1]=>33
[8,9,5,6,3,4,10,1,2,7]=>13
[2,1,4,3,8,7,6,5,10,9]=>34
[4,3,2,1,8,7,6,5,10,9]=>41
[8,3,2,7,6,5,4,1,10,9]=>36
[10,3,2,7,6,5,4,9,8,1]=>33
[2,1,8,7,6,5,4,3,10,9]=>41
[8,7,6,5,4,3,2,1,10,9]=>44
[9,7,6,5,4,3,2,10,1,8]=>40
[10,7,6,5,4,3,2,9,8,1]=>41
[2,1,10,7,6,5,4,9,8,3]=>40
[10,9,6,5,4,3,8,7,2,1]=>40
[2,1,4,3,10,7,6,9,8,5]=>33
[4,3,2,1,10,7,6,9,8,5]=>40
[10,3,2,9,6,5,8,7,4,1]=>32
[2,1,10,9,6,5,8,7,4,3]=>39
[10,9,8,5,4,7,6,3,2,1]=>39
[6,7,8,9,10,1,2,3,4,5]=>1
[7,3,2,8,9,10,1,4,5,6]=>18
[8,5,4,3,2,9,10,1,6,7]=>31
[2,1,4,3,6,5,10,9,8,7]=>32
[4,3,2,1,6,5,10,9,8,7]=>39
[6,3,2,5,4,1,10,9,8,7]=>36
[10,3,2,5,4,9,8,7,6,1]=>31
[2,1,6,5,4,3,10,9,8,7]=>39
[6,5,4,3,2,1,10,9,8,7]=>44
[10,5,4,3,2,9,8,7,6,1]=>39
[2,1,10,5,4,9,8,7,6,3]=>38
[10,9,4,3,8,7,6,5,2,1]=>38
[9,7,5,10,3,8,2,6,1,4]=>26
[2,1,4,3,10,9,8,7,6,5]=>37
[4,3,2,1,10,9,8,7,6,5]=>44
[10,3,2,9,8,7,6,5,4,1]=>37
[2,1,10,9,8,7,6,5,4,3]=>44
[10,9,8,7,6,5,4,3,2,1]=>45
[2,3,4,5,6,7,8,9,10,1]=>1
[2,3,4,5,6,7,8,9,1,10]=>2
[10,8,9,5,6,7,1,2,3,4]=>14
[10,8,9,4,5,6,1,2,3,7]=>14
[10,7,8,5,6,9,1,2,3,4]=>14
[10,7,8,4,5,9,1,2,3,6]=>14
[10,6,7,4,5,8,1,2,3,9]=>14
[10,7,8,3,4,9,1,2,5,6]=>14
[10,6,7,3,4,8,1,2,5,9]=>14
[9,8,10,5,6,7,1,2,3,4]=>15
[9,8,10,4,5,6,1,2,3,7]=>15
[9,7,10,5,6,8,1,2,3,4]=>15
[9,7,10,4,5,8,1,2,3,6]=>15
[9,6,10,4,5,7,1,2,3,8]=>15
[9,7,10,3,4,8,1,2,5,6]=>15
[9,6,10,3,4,7,1,2,5,8]=>15
[8,7,9,5,6,10,1,2,3,4]=>16
[8,7,9,4,5,10,1,2,3,6]=>16
[8,6,9,4,5,10,1,2,3,7]=>16
[7,6,8,4,5,9,1,2,3,10]=>17
[8,7,9,3,4,10,1,2,5,6]=>16
[8,6,9,3,4,10,1,2,5,7]=>16
[7,6,8,3,4,9,1,2,5,10]=>17
[9,6,10,5,7,8,1,2,3,4]=>15
[9,6,10,4,7,8,1,2,3,5]=>15
[9,5,10,4,6,7,1,2,3,8]=>15
[9,6,10,3,7,8,1,2,4,5]=>15
[9,5,10,3,6,7,1,2,4,8]=>15
[8,6,9,5,7,10,1,2,3,4]=>16
[8,6,9,4,7,10,1,2,3,5]=>16
[8,5,9,4,6,10,1,2,3,7]=>16
[7,5,8,4,6,9,1,2,3,10]=>17
[8,6,9,3,7,10,1,2,4,5]=>16
[8,5,9,3,6,10,1,2,4,7]=>16
[7,5,8,3,6,9,1,2,4,10]=>17
[8,4,9,3,5,10,1,2,6,7]=>16
[7,4,8,3,5,9,1,2,6,10]=>17
[9,6,10,2,7,8,1,3,4,5]=>15
[9,5,10,2,6,7,1,3,4,8]=>15
[8,6,9,2,7,10,1,3,4,5]=>16
[8,5,9,2,6,10,1,3,4,7]=>16
[7,5,8,2,6,9,1,3,4,10]=>17
[8,4,9,2,5,10,1,3,6,7]=>16
[7,4,8,2,5,9,1,3,6,10]=>17
[1,2,3,4,5,6,7,8,10,9]=>2
[2,1,3,4,5,6,7,8,9,10]=>9
[9,1,2,3,4,5,6,7,10,8]=>4
[2,10,1,3,4,5,6,7,8,9]=>8
[1,2,3,4,5,6,7,8,9,10]=>0
[9,8,7,6,5,4,3,2,1,10]=>44
[10,1,2,3,4,5,6,7,8,9]=>1
[10,9,1,2,3,4,5,6,7,8]=>10
[1,10,9,8,7,6,5,4,3,2]=>44
[9,8,7,5,6,4,3,2,1,10]=>37
[1,10,9,8,6,7,5,4,3,2]=>38
[10,2,1,3,4,5,6,7,8,9]=>10
[3,2,4,5,6,7,8,9,10,1]=>10
[2,4,6,8,10,1,3,5,7,9]=>5
[2,4,6,9,10,1,3,5,7,8]=>5
[2,4,7,8,10,1,3,5,6,9]=>5
[2,4,7,9,10,1,3,5,6,8]=>5
[2,4,8,9,10,1,3,5,6,7]=>5
[2,5,6,8,10,1,3,4,7,9]=>5
[2,5,6,9,10,1,3,4,7,8]=>5
[2,5,7,8,10,1,3,4,6,9]=>5
[2,5,7,9,10,1,3,4,6,8]=>5
[2,5,8,9,10,1,3,4,6,7]=>5
[2,6,7,8,10,1,3,4,5,9]=>5
[2,6,7,9,10,1,3,4,5,8]=>5
[2,6,8,9,10,1,3,4,5,7]=>5
[2,7,8,9,10,1,3,4,5,6]=>5
[3,4,6,8,10,1,2,5,7,9]=>4
[3,4,6,9,10,1,2,5,7,8]=>4
[3,4,7,8,10,1,2,5,6,9]=>4
[3,4,7,9,10,1,2,5,6,8]=>4
[3,4,8,9,10,1,2,5,6,7]=>4
[3,5,6,8,10,1,2,4,7,9]=>4
[3,5,6,9,10,1,2,4,7,8]=>4
[3,5,7,8,10,1,2,4,6,9]=>4
[3,5,7,9,10,1,2,4,6,8]=>4
[3,5,8,9,10,1,2,4,6,7]=>4
[3,6,7,8,10,1,2,4,5,9]=>4
[3,6,7,9,10,1,2,4,5,8]=>4
[3,6,8,9,10,1,2,4,5,7]=>4
[3,7,8,9,10,1,2,4,5,6]=>4
[4,5,6,8,10,1,2,3,7,9]=>3
[4,5,6,9,10,1,2,3,7,8]=>3
[4,5,7,8,10,1,2,3,6,9]=>3
[4,5,7,9,10,1,2,3,6,8]=>3
[4,5,8,9,10,1,2,3,6,7]=>3
[4,6,7,8,10,1,2,3,5,9]=>3
[4,6,7,9,10,1,2,3,5,8]=>3
[4,6,8,9,10,1,2,3,5,7]=>3
[4,7,8,9,10,1,2,3,5,6]=>3
[5,6,7,8,10,1,2,3,4,9]=>2
[5,6,7,9,10,1,2,3,4,8]=>2
[5,6,8,9,10,1,2,3,4,7]=>2
[5,7,8,9,10,1,2,3,4,6]=>2
[9,10,1,2,3,4,5,6,7,8]=>1
[8,9,10,1,2,3,4,5,6,7]=>1
[10,8,9,1,2,3,4,5,6,7]=>9
[10,9,8,1,2,3,4,5,6,7]=>18
[7,8,9,10,1,2,3,4,5,6]=>1
[10,7,8,9,1,2,3,4,5,6]=>8
[9,10,7,8,1,2,3,4,5,6]=>8
[10,9,7,8,1,2,3,4,5,6]=>17
[10,9,8,7,1,2,3,4,5,6]=>25
[10,6,7,8,9,1,2,3,4,5]=>7
[9,10,6,7,8,1,2,3,4,5]=>7
[10,9,6,7,8,1,2,3,4,5]=>16
[10,8,9,6,7,1,2,3,4,5]=>15
[10,9,8,6,7,1,2,3,4,5]=>24
[10,9,8,7,6,1,2,3,4,5]=>31
[9,10,5,6,7,8,1,2,3,4]=>6
[10,9,5,6,7,8,1,2,3,4]=>15
[8,9,10,5,6,7,1,2,3,4]=>6
[10,9,8,5,6,7,1,2,3,4]=>23
[9,10,7,8,5,6,1,2,3,4]=>13
[10,9,7,8,5,6,1,2,3,4]=>22
[10,9,8,7,5,6,1,2,3,4]=>30
[10,9,8,7,6,5,1,2,3,4]=>36
[10,7,8,9,4,5,6,1,2,3]=>12
[9,10,7,8,4,5,6,1,2,3]=>12
[10,9,7,8,4,5,6,1,2,3]=>21
[10,9,8,7,4,5,6,1,2,3]=>29
[10,8,9,6,7,4,5,1,2,3]=>19
[10,9,8,6,7,4,5,1,2,3]=>28
[10,9,8,7,6,4,5,1,2,3]=>35
[10,9,8,7,6,5,4,1,2,3]=>40
[9,10,7,8,5,6,3,4,1,2]=>16
[10,9,7,8,5,6,3,4,1,2]=>25
[10,9,8,7,5,6,3,4,1,2]=>33
[10,9,8,7,6,5,3,4,1,2]=>39
[10,9,8,7,6,5,4,3,1,2]=>43
[8,9,7,6,5,4,3,2,1,10]=>35
[1,9,10,8,7,6,5,4,3,2]=>35
[9,1,2,3,4,5,6,7,8,10]=>2
[1,10,2,3,4,5,6,7,8,9]=>9
[8,9,1,2,3,4,5,6,7,10]=>2
[1,9,10,2,3,4,5,6,7,8]=>8
[3,4,1,2,5,6,7,8,9,10]=>7
[3,2,1,4,5,6,7,8,9,10]=>17
[4,5,6,1,2,3,7,8,9,10]=>5
[4,2,5,1,3,6,7,8,9,10]=>15
[4,3,2,1,5,6,7,8,9,10]=>24
[5,6,7,8,1,2,3,4,9,10]=>3
[5,2,6,7,1,3,4,8,9,10]=>13
[5,6,3,4,1,2,7,8,9,10]=>12
[5,3,2,6,1,4,7,8,9,10]=>22
[5,4,3,2,1,6,7,8,9,10]=>30
[6,2,7,8,9,1,3,4,5,10]=>11
[6,7,3,4,8,1,2,5,9,10]=>10
[6,3,2,7,8,1,4,5,9,10]=>20
[6,4,7,2,5,1,3,8,9,10]=>19
[6,4,3,2,7,1,5,8,9,10]=>28
[6,5,4,3,2,1,7,8,9,10]=>35
[7,8,3,4,9,10,1,2,5,6]=>8
[7,8,9,4,5,6,1,2,3,10]=>7
[7,4,3,2,8,9,1,5,6,10]=>26
[7,8,5,6,3,4,1,2,9,10]=>15
[7,5,3,8,2,6,1,4,9,10]=>25
[7,5,4,3,2,8,1,6,9,10]=>33
[7,6,5,4,3,2,1,8,9,10]=>39
[8,5,9,10,2,6,7,1,3,4]=>14
[8,5,3,9,2,6,10,1,4,7]=>23
[8,6,9,4,7,2,5,1,3,10]=>21
[8,6,4,3,9,2,7,1,5,10]=>30
[8,6,5,4,3,2,9,1,7,10]=>37
[8,7,6,5,4,3,2,1,9,10]=>42
[9,7,5,4,3,10,2,8,1,6]=>34
[1,2,3,4,5,6,7,8,9,11,10]=>2
[2,1,3,4,5,6,7,8,9,10,11]=>10
[11,1,2,3,4,5,6,7,8,9,10]=>1
[10,9,8,7,6,5,4,3,2,1,11]=>54
[1,11,10,9,8,7,6,5,4,3,2]=>54
[2,3,4,5,6,7,8,9,10,11,1]=>1
[10,1,2,3,4,5,6,7,8,9,11]=>2
[1,11,2,3,4,5,6,7,8,9,10]=>10
[2,1,4,3,6,5,8,7,12,11,10,9]=>44
[2,1,4,3,6,5,12,9,8,11,10,7]=>45
[2,1,4,3,6,5,12,11,10,9,8,7]=>49
[2,1,4,3,8,7,6,5,12,11,10,9]=>51
[2,1,4,3,12,7,6,9,8,11,10,5]=>46
[2,1,4,3,12,7,6,11,10,9,8,5]=>50
[2,1,4,3,10,9,8,7,6,5,12,11]=>53
[2,1,4,3,12,9,8,7,6,11,10,5]=>52
[2,1,4,3,12,11,8,7,10,9,6,5]=>51
[2,1,4,3,12,11,10,9,8,7,6,5]=>56
[2,1,6,5,4,3,8,7,12,11,10,9]=>53
[2,1,6,5,4,3,10,9,8,7,12,11]=>55
[2,1,6,5,4,3,12,9,8,11,10,7]=>54
[2,1,6,5,4,3,12,11,10,9,8,7]=>58
[2,1,8,5,4,7,6,3,12,11,10,9]=>52
[2,1,12,5,4,7,6,9,8,11,10,3]=>47
[2,1,12,5,4,7,6,11,10,9,8,3]=>51
[2,1,10,5,4,9,8,7,6,3,12,11]=>54
[2,1,12,5,4,9,8,7,6,11,10,3]=>53
[2,1,12,5,4,11,8,7,10,9,6,3]=>52
[2,1,12,5,4,11,10,9,8,7,6,3]=>57
[2,1,8,7,6,5,4,3,10,9,12,11]=>57
[2,1,8,7,6,5,4,3,12,11,10,9]=>60
[2,1,12,7,6,5,4,9,8,11,10,3]=>55
[2,1,12,7,6,5,4,11,10,9,8,3]=>59
[2,1,10,9,6,5,8,7,4,3,12,11]=>55
[2,1,12,9,6,5,8,7,4,11,10,3]=>54
[2,1,12,11,6,5,8,7,10,9,4,3]=>53
[2,1,12,11,6,5,10,9,8,7,4,3]=>58
[2,1,10,9,8,7,6,5,4,3,12,11]=>62
[2,1,12,9,8,7,6,5,4,11,10,3]=>61
[2,1,12,11,8,7,6,5,10,9,4,3]=>60
[2,1,12,11,10,7,6,9,8,5,4,3]=>59
[2,1,12,11,10,9,8,7,6,5,4,3]=>65
[4,3,2,1,6,5,8,7,10,9,12,11]=>50
[4,3,2,1,6,5,8,7,12,11,10,9]=>53
[4,3,2,1,6,5,10,9,8,7,12,11]=>55
[4,3,2,1,6,5,12,9,8,11,10,7]=>54
[4,3,2,1,6,5,12,11,10,9,8,7]=>58
[4,3,2,1,8,7,6,5,10,9,12,11]=>57
[4,3,2,1,8,7,6,5,12,11,10,9]=>60
[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]=>55
[4,3,2,1,12,7,6,11,10,9,8,5]=>59
[4,3,2,1,10,9,8,7,6,5,12,11]=>62
[4,3,2,1,12,9,8,7,6,11,10,5]=>61
[4,3,2,1,12,11,8,7,10,9,6,5]=>60
[4,3,2,1,12,11,10,9,8,7,6,5]=>65
[6,3,2,5,4,1,8,7,10,9,12,11]=>47
[6,3,2,5,4,1,8,7,12,11,10,9]=>50
[6,3,2,5,4,1,12,9,8,11,10,7]=>51
[6,3,2,5,4,1,12,11,10,9,8,7]=>55
[8,3,2,5,4,7,6,1,10,9,12,11]=>44
[8,3,2,5,4,7,6,1,12,11,10,9]=>47
[10,3,2,5,4,7,6,9,8,1,12,11]=>41
[12,3,2,5,4,7,6,9,8,11,10,1]=>38
[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]=>47
[12,3,2,5,4,9,8,7,6,11,10,1]=>44
[12,3,2,5,4,11,8,7,10,9,6,1]=>43
[12,3,2,5,4,11,10,9,8,7,6,1]=>48
[8,3,2,7,6,5,4,1,10,9,12,11]=>52
[8,3,2,7,6,5,4,1,12,11,10,9]=>55
[10,3,2,7,6,5,4,9,8,1,12,11]=>49
[12,3,2,7,6,5,4,9,8,11,10,1]=>46
[12,3,2,7,6,5,4,11,10,9,8,1]=>50
[10,3,2,9,6,5,8,7,4,1,12,11]=>48
[12,3,2,9,6,5,8,7,4,11,10,1]=>45
[12,3,2,11,6,5,8,7,10,9,4,1]=>44
[12,3,2,11,6,5,10,9,8,7,4,1]=>49
[10,3,2,9,8,7,6,5,4,1,12,11]=>55
[12,3,2,9,8,7,6,5,4,11,10,1]=>52
[6,5,4,3,2,1,8,7,10,9,12,11]=>57
[6,5,4,3,2,1,8,7,12,11,10,9]=>60
[6,5,4,3,2,1,10,9,8,7,12,11]=>62
[6,5,4,3,2,1,12,9,8,11,10,7]=>61
[6,5,4,3,2,1,12,11,10,9,8,7]=>65
[8,5,4,3,2,7,6,1,12,11,10,9]=>57
[10,5,4,3,2,7,6,9,8,1,12,11]=>51
[12,5,4,3,2,7,6,9,8,11,10,1]=>48
[12,5,4,3,2,7,6,11,10,9,8,1]=>52
[10,5,4,3,2,9,8,7,6,1,12,11]=>57
[12,5,4,3,2,9,8,7,6,11,10,1]=>54
[12,5,4,3,2,11,8,7,10,9,6,1]=>53
[8,7,4,3,6,5,2,1,10,9,12,11]=>53
[8,7,4,3,6,5,2,1,12,11,10,9]=>56
[10,7,4,3,6,5,2,9,8,1,12,11]=>50
[12,7,4,3,6,5,2,9,8,11,10,1]=>47
[12,7,4,3,6,5,2,11,10,9,8,1]=>51
[10,9,4,3,6,5,8,7,2,1,12,11]=>49
[12,9,4,3,6,5,8,7,2,11,10,1]=>46
[12,11,4,3,6,5,8,7,10,9,2,1]=>45
[10,9,4,3,8,7,6,5,2,1,12,11]=>56
[12,9,4,3,8,7,6,5,2,11,10,1]=>53
[8,7,6,5,4,3,2,1,10,9,12,11]=>62
[8,7,6,5,4,3,2,1,12,11,10,9]=>65
[10,7,6,5,4,3,2,9,8,1,12,11]=>59
[12,7,6,5,4,3,2,9,8,11,10,1]=>56
[10,9,6,5,4,3,8,7,2,1,12,11]=>58
[12,9,6,5,4,3,8,7,2,11,10,1]=>55
[12,11,6,5,4,3,8,7,10,9,2,1]=>54
[10,9,8,5,4,7,6,3,2,1,12,11]=>57
[10,9,8,7,6,5,4,3,2,1,12,11]=>65
[2,4,6,8,10,12,1,3,5,7,9,11]=>6
[2,4,6,8,11,12,1,3,5,7,9,10]=>6
[2,4,6,9,10,12,1,3,5,7,8,11]=>6
[2,4,6,9,11,12,1,3,5,7,8,10]=>6
[2,4,6,10,11,12,1,3,5,7,8,9]=>6
[2,4,7,8,10,12,1,3,5,6,9,11]=>6
[2,4,7,8,11,12,1,3,5,6,9,10]=>6
[2,4,7,9,10,12,1,3,5,6,8,11]=>6
[2,4,7,9,11,12,1,3,5,6,8,10]=>6
[2,4,7,10,11,12,1,3,5,6,8,9]=>6
[2,4,8,9,10,12,1,3,5,6,7,11]=>6
[2,4,8,9,11,12,1,3,5,6,7,10]=>6
[2,4,8,10,11,12,1,3,5,6,7,9]=>6
[2,4,9,10,11,12,1,3,5,6,7,8]=>6
[2,5,6,8,10,12,1,3,4,7,9,11]=>6
[2,5,6,8,11,12,1,3,4,7,9,10]=>6
[2,5,6,9,10,12,1,3,4,7,8,11]=>6
[2,5,6,9,11,12,1,3,4,7,8,10]=>6
[2,5,6,10,11,12,1,3,4,7,8,9]=>6
[2,5,7,8,10,12,1,3,4,6,9,11]=>6
[2,5,7,8,11,12,1,3,4,6,9,10]=>6
[2,5,7,9,11,12,1,3,4,6,8,10]=>6
[2,5,7,10,11,12,1,3,4,6,8,9]=>6
[2,5,8,9,10,12,1,3,4,6,7,11]=>6
[2,5,8,9,11,12,1,3,4,6,7,10]=>6
[2,5,8,10,11,12,1,3,4,6,7,9]=>6
[2,5,9,10,11,12,1,3,4,6,7,8]=>6
[2,6,7,8,10,12,1,3,4,5,9,11]=>6
[2,6,7,8,11,12,1,3,4,5,9,10]=>6
[2,6,7,9,10,12,1,3,4,5,8,11]=>6
[2,6,7,9,11,12,1,3,4,5,8,10]=>6
[2,6,7,10,11,12,1,3,4,5,8,9]=>6
[2,6,8,9,10,12,1,3,4,5,7,11]=>6
[2,6,8,9,11,12,1,3,4,5,7,10]=>6
[2,6,8,10,11,12,1,3,4,5,7,9]=>6
[2,6,9,10,11,12,1,3,4,5,7,8]=>6
[2,7,8,9,10,12,1,3,4,5,6,11]=>6
[2,7,8,9,11,12,1,3,4,5,6,10]=>6
[2,7,8,10,11,12,1,3,4,5,6,9]=>6
[2,7,9,10,11,12,1,3,4,5,6,8]=>6
[2,8,9,10,11,12,1,3,4,5,6,7]=>6
[3,4,6,8,10,12,1,2,5,7,9,11]=>5
[3,4,6,8,11,12,1,2,5,7,9,10]=>5
[3,4,6,9,10,12,1,2,5,7,8,11]=>5
[3,4,6,9,11,12,1,2,5,7,8,10]=>5
[3,4,6,10,11,12,1,2,5,7,8,9]=>5
[3,4,7,8,10,12,1,2,5,6,9,11]=>5
[3,4,7,8,11,12,1,2,5,6,9,10]=>5
[3,4,7,9,10,12,1,2,5,6,8,11]=>5
[3,4,7,9,11,12,1,2,5,6,8,10]=>5
[3,4,7,10,11,12,1,2,5,6,8,9]=>5
[3,4,8,9,10,12,1,2,5,6,7,11]=>5
[3,4,8,9,11,12,1,2,5,6,7,10]=>5
[3,4,8,10,11,12,1,2,5,6,7,9]=>5
[3,4,9,10,11,12,1,2,5,6,7,8]=>5
[3,5,6,8,10,12,1,2,4,7,9,11]=>5
[3,5,6,8,11,12,1,2,4,7,9,10]=>5
[3,5,6,9,10,12,1,2,4,7,8,11]=>5
[3,5,6,9,11,12,1,2,4,7,8,10]=>5
[3,5,6,10,11,12,1,2,4,7,8,9]=>5
[3,5,7,8,10,12,1,2,4,6,9,11]=>5
[3,5,7,8,11,12,1,2,4,6,9,10]=>5
[3,5,7,9,10,12,1,2,4,6,8,11]=>5
[3,5,7,9,11,12,1,2,4,6,8,10]=>5
[3,5,7,10,11,12,1,2,4,6,8,9]=>5
[3,5,8,9,10,12,1,2,4,6,7,11]=>5
[3,5,8,9,11,12,1,2,4,6,7,10]=>5
[3,5,8,10,11,12,1,2,4,6,7,9]=>5
[3,5,9,10,11,12,1,2,4,6,7,8]=>5
[3,6,7,8,10,12,1,2,4,5,9,11]=>5
[3,6,7,8,11,12,1,2,4,5,9,10]=>5
[3,6,7,9,10,12,1,2,4,5,8,11]=>5
[3,6,7,9,11,12,1,2,4,5,8,10]=>5
[3,6,7,10,11,12,1,2,4,5,8,9]=>5
[3,6,8,9,10,12,1,2,4,5,7,11]=>5
[3,6,8,9,11,12,1,2,4,5,7,10]=>5
[3,6,8,10,11,12,1,2,4,5,7,9]=>5
[3,6,9,10,11,12,1,2,4,5,7,8]=>5
[3,7,8,9,10,12,1,2,4,5,6,11]=>5
[3,7,8,9,11,12,1,2,4,5,6,10]=>5
[3,7,8,10,11,12,1,2,4,5,6,9]=>5
[3,7,9,10,11,12,1,2,4,5,6,8]=>5
[3,8,9,10,11,12,1,2,4,5,6,7]=>5
[4,5,6,8,10,12,1,2,3,7,9,11]=>4
[4,5,6,8,11,12,1,2,3,7,9,10]=>4
[4,5,6,9,10,12,1,2,3,7,8,11]=>4
[4,5,6,9,11,12,1,2,3,7,8,10]=>4
[4,5,6,10,11,12,1,2,3,7,8,9]=>4
[4,5,7,8,10,12,1,2,3,6,9,11]=>4
[4,5,7,8,11,12,1,2,3,6,9,10]=>4
[4,5,7,9,10,12,1,2,3,6,8,11]=>4
[4,5,7,9,11,12,1,2,3,6,8,10]=>4
[4,5,7,10,11,12,1,2,3,6,8,9]=>4
[4,5,8,9,10,12,1,2,3,6,7,11]=>4
[4,5,8,9,11,12,1,2,3,6,7,10]=>4
[4,5,8,10,11,12,1,2,3,6,7,9]=>4
[4,5,9,10,11,12,1,2,3,6,7,8]=>4
[4,6,7,8,10,12,1,2,3,5,9,11]=>4
[4,6,7,8,11,12,1,2,3,5,9,10]=>4
[4,6,7,9,10,12,1,2,3,5,8,11]=>4
[4,6,7,9,11,12,1,2,3,5,8,10]=>4
[4,6,7,10,11,12,1,2,3,5,8,9]=>4
[4,6,8,9,10,12,1,2,3,5,7,11]=>4
[4,6,8,9,11,12,1,2,3,5,7,10]=>4
[4,6,8,10,11,12,1,2,3,5,7,9]=>4
[4,6,9,10,11,12,1,2,3,5,7,8]=>4
[4,7,8,9,10,12,1,2,3,5,6,11]=>4
[4,7,8,9,11,12,1,2,3,5,6,10]=>4
[4,7,8,10,11,12,1,2,3,5,6,9]=>4
[4,7,9,10,11,12,1,2,3,5,6,8]=>4
[4,8,9,10,11,12,1,2,3,5,6,7]=>4
[5,6,7,8,10,12,1,2,3,4,9,11]=>3
[5,6,7,8,11,12,1,2,3,4,9,10]=>3
[5,6,7,9,10,12,1,2,3,4,8,11]=>3
[5,6,7,9,11,12,1,2,3,4,8,10]=>3
[5,6,7,10,11,12,1,2,3,4,8,9]=>3
[5,6,8,9,10,12,1,2,3,4,7,11]=>3
[5,6,8,9,11,12,1,2,3,4,7,10]=>3
[5,6,8,10,11,12,1,2,3,4,7,9]=>3
[5,6,9,10,11,12,1,2,3,4,7,8]=>3
[5,7,8,9,10,12,1,2,3,4,6,11]=>3
[5,7,8,9,11,12,1,2,3,4,6,10]=>3
[5,7,8,10,11,12,1,2,3,4,6,9]=>3
[5,7,9,10,11,12,1,2,3,4,6,8]=>3
[5,8,9,10,11,12,1,2,3,4,6,7]=>3
[6,7,8,9,10,12,1,2,3,4,5,11]=>2
[6,7,8,9,11,12,1,2,3,4,5,10]=>2
[6,7,8,10,11,12,1,2,3,4,5,9]=>2
[6,7,9,10,11,12,1,2,3,4,5,8]=>2
[6,8,9,10,11,12,1,2,3,4,5,7]=>2
[7,8,9,10,11,12,1,2,3,4,5,6]=>1
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Description
Babson and Steingrímsson's statistic of a permutation.
In terms of generalized patterns this is
$$ (13-2) + (21-3) + (32-1) + (21). $$
Here, $(\pi)$ denotes the number of times the pattern $\pi$ occurs in a permutation, and letters in the pattern which are not separated by a dash must appear consecutively.
In terms of generalized patterns this is
$$ (13-2) + (21-3) + (32-1) + (21). $$
Here, $(\pi)$ denotes the number of times the pattern $\pi$ occurs in a permutation, and letters in the pattern which are not separated by a dash must appear consecutively.
References
[1] Babson, E., Steingr'ımsson, E. Generalized permutation patterns and a classification of the Mahonian statistics MathSciNet:1758852
[2] Foata, D., Zeilberger, D. Babson-Steingrímsson statistics are indeed Mahonian (and sometimes even Euler-Mahonian) MathSciNet:1868972
[3] Burstein, A. On joint distribution of adjacencies, descents and some Mahonian statistics MathSciNet:2673870
[4] Chen, J. N., Li, S. A new bijective proof of Babson and Steingr'$\{$$\backslash $i$\}$msson's conjecture arXiv:1701.08044
[2] Foata, D., Zeilberger, D. Babson-Steingrímsson statistics are indeed Mahonian (and sometimes even Euler-Mahonian) MathSciNet:1868972
[3] Burstein, A. On joint distribution of adjacencies, descents and some Mahonian statistics MathSciNet:2673870
[4] Chen, J. N., Li, S. A new bijective proof of Babson and Steingr'$\{$$\backslash $i$\}$msson's conjecture arXiv:1701.08044
Code
def statistic(pi):
return (mesh_pattern_occurrences(pi, [1,3,2], [(1,0),(1,1),(1,2),(1,3)])
+ mesh_pattern_occurrences(pi, [2,1,3], [(1,0),(1,1),(1,2),(1,3)])
+ mesh_pattern_occurrences(pi, [3,2,1], [(1,0),(1,1),(1,2),(1,3)])
+ mesh_pattern_occurrences(pi, [2,1], [(1,0),(1,1),(1,2)]))
def G(w):
return [ (x+1,y) for (x,y) in enumerate(w) ]
def mesh_pattern_occurrences(perm, pat, R=[]):
occs = 0
k = len(pat)
n = len(perm)
pat = G(pat)
perm = G(perm)
for H in Subsets(perm, k):
H = sorted(H)
X = dict(G(sorted(i for (i,_) in H)))
Y = dict(G(sorted(j for (_,j) in H)))
if H == [ (X[i], Y[j]) for (i,j) in pat ]:
X[0], X[k+1] = 0, n+1
Y[0], Y[k+1] = 0, n+1
shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1]
for (i,j) in R
for (x,y) in perm
)
if not any(shady):
occs = occs + 1
return occs
Created
Jan 30, 2017 at 08:13 by Martin Rubey
Updated
Feb 07, 2023 at 20:43 by Will Dowling
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