Identifier
- St000246: Permutations ⟶ ℤ (values match St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.)
Values
=>
[]=>0
[1]=>0
[1,2]=>1
[2,1]=>0
[1,2,3]=>3
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>0
[1,2,3,4]=>6
[1,2,4,3]=>5
[1,3,2,4]=>5
[1,3,4,2]=>4
[1,4,2,3]=>4
[1,4,3,2]=>3
[2,1,3,4]=>5
[2,1,4,3]=>4
[2,3,1,4]=>4
[2,3,4,1]=>3
[2,4,1,3]=>3
[2,4,3,1]=>2
[3,1,2,4]=>4
[3,1,4,2]=>3
[3,2,1,4]=>3
[3,2,4,1]=>2
[3,4,1,2]=>2
[3,4,2,1]=>1
[4,1,2,3]=>3
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>1
[4,3,1,2]=>1
[4,3,2,1]=>0
[1,2,3,4,5]=>10
[1,2,3,5,4]=>9
[1,2,4,3,5]=>9
[1,2,4,5,3]=>8
[1,2,5,3,4]=>8
[1,2,5,4,3]=>7
[1,3,2,4,5]=>9
[1,3,2,5,4]=>8
[1,3,4,2,5]=>8
[1,3,4,5,2]=>7
[1,3,5,2,4]=>7
[1,3,5,4,2]=>6
[1,4,2,3,5]=>8
[1,4,2,5,3]=>7
[1,4,3,2,5]=>7
[1,4,3,5,2]=>6
[1,4,5,2,3]=>6
[1,4,5,3,2]=>5
[1,5,2,3,4]=>7
[1,5,2,4,3]=>6
[1,5,3,2,4]=>6
[1,5,3,4,2]=>5
[1,5,4,2,3]=>5
[1,5,4,3,2]=>4
[2,1,3,4,5]=>9
[2,1,3,5,4]=>8
[2,1,4,3,5]=>8
[2,1,4,5,3]=>7
[2,1,5,3,4]=>7
[2,1,5,4,3]=>6
[2,3,1,4,5]=>8
[2,3,1,5,4]=>7
[2,3,4,1,5]=>7
[2,3,4,5,1]=>6
[2,3,5,1,4]=>6
[2,3,5,4,1]=>5
[2,4,1,3,5]=>7
[2,4,1,5,3]=>6
[2,4,3,1,5]=>6
[2,4,3,5,1]=>5
[2,4,5,1,3]=>5
[2,4,5,3,1]=>4
[2,5,1,3,4]=>6
[2,5,1,4,3]=>5
[2,5,3,1,4]=>5
[2,5,3,4,1]=>4
[2,5,4,1,3]=>4
[2,5,4,3,1]=>3
[3,1,2,4,5]=>8
[3,1,2,5,4]=>7
[3,1,4,2,5]=>7
[3,1,4,5,2]=>6
[3,1,5,2,4]=>6
[3,1,5,4,2]=>5
[3,2,1,4,5]=>7
[3,2,1,5,4]=>6
[3,2,4,1,5]=>6
[3,2,4,5,1]=>5
[3,2,5,1,4]=>5
[3,2,5,4,1]=>4
[3,4,1,2,5]=>6
[3,4,1,5,2]=>5
[3,4,2,1,5]=>5
[3,4,2,5,1]=>4
[3,4,5,1,2]=>4
[3,4,5,2,1]=>3
[3,5,1,2,4]=>5
[3,5,1,4,2]=>4
[3,5,2,1,4]=>4
[3,5,2,4,1]=>3
[3,5,4,1,2]=>3
[3,5,4,2,1]=>2
[4,1,2,3,5]=>7
[4,1,2,5,3]=>6
[4,1,3,2,5]=>6
[4,1,3,5,2]=>5
[4,1,5,2,3]=>5
[4,1,5,3,2]=>4
[4,2,1,3,5]=>6
[4,2,1,5,3]=>5
[4,2,3,1,5]=>5
[4,2,3,5,1]=>4
[4,2,5,1,3]=>4
[4,2,5,3,1]=>3
[4,3,1,2,5]=>5
[4,3,1,5,2]=>4
[4,3,2,1,5]=>4
[4,3,2,5,1]=>3
[4,3,5,1,2]=>3
[4,3,5,2,1]=>2
[4,5,1,2,3]=>4
[4,5,1,3,2]=>3
[4,5,2,1,3]=>3
[4,5,2,3,1]=>2
[4,5,3,1,2]=>2
[4,5,3,2,1]=>1
[5,1,2,3,4]=>6
[5,1,2,4,3]=>5
[5,1,3,2,4]=>5
[5,1,3,4,2]=>4
[5,1,4,2,3]=>4
[5,1,4,3,2]=>3
[5,2,1,3,4]=>5
[5,2,1,4,3]=>4
[5,2,3,1,4]=>4
[5,2,3,4,1]=>3
[5,2,4,1,3]=>3
[5,2,4,3,1]=>2
[5,3,1,2,4]=>4
[5,3,1,4,2]=>3
[5,3,2,1,4]=>3
[5,3,2,4,1]=>2
[5,3,4,1,2]=>2
[5,3,4,2,1]=>1
[5,4,1,2,3]=>3
[5,4,1,3,2]=>2
[5,4,2,1,3]=>2
[5,4,2,3,1]=>1
[5,4,3,1,2]=>1
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>15
[1,2,3,4,6,5]=>14
[1,2,3,5,4,6]=>14
[1,2,3,5,6,4]=>13
[1,2,3,6,4,5]=>13
[1,2,3,6,5,4]=>12
[1,2,4,3,5,6]=>14
[1,2,4,3,6,5]=>13
[1,2,4,5,3,6]=>13
[1,2,4,5,6,3]=>12
[1,2,4,6,3,5]=>12
[1,2,4,6,5,3]=>11
[1,2,5,3,4,6]=>13
[1,2,5,3,6,4]=>12
[1,2,5,4,3,6]=>12
[1,2,5,4,6,3]=>11
[1,2,5,6,3,4]=>11
[1,2,5,6,4,3]=>10
[1,2,6,3,4,5]=>12
[1,2,6,3,5,4]=>11
[1,2,6,4,3,5]=>11
[1,2,6,4,5,3]=>10
[1,2,6,5,3,4]=>10
[1,2,6,5,4,3]=>9
[1,3,2,4,5,6]=>14
[1,3,2,4,6,5]=>13
[1,3,2,5,4,6]=>13
[1,3,2,5,6,4]=>12
[1,3,2,6,4,5]=>12
[1,3,2,6,5,4]=>11
[1,3,4,2,5,6]=>13
[1,3,4,2,6,5]=>12
[1,3,4,5,2,6]=>12
[1,3,4,5,6,2]=>11
[1,3,4,6,2,5]=>11
[1,3,4,6,5,2]=>10
[1,3,5,2,4,6]=>12
[1,3,5,2,6,4]=>11
[1,3,5,4,2,6]=>11
[1,3,5,4,6,2]=>10
[1,3,5,6,2,4]=>10
[1,3,5,6,4,2]=>9
[1,3,6,2,4,5]=>11
[1,3,6,2,5,4]=>10
[1,3,6,4,2,5]=>10
[1,3,6,4,5,2]=>9
[1,3,6,5,2,4]=>9
[1,3,6,5,4,2]=>8
[1,4,2,3,5,6]=>13
[1,4,2,3,6,5]=>12
[1,4,2,5,3,6]=>12
[1,4,2,5,6,3]=>11
[1,4,2,6,3,5]=>11
[1,4,2,6,5,3]=>10
[1,4,3,2,5,6]=>12
[1,4,3,2,6,5]=>11
[1,4,3,5,2,6]=>11
[1,4,3,5,6,2]=>10
[1,4,3,6,2,5]=>10
[1,4,3,6,5,2]=>9
[1,4,5,2,3,6]=>11
[1,4,5,2,6,3]=>10
[1,4,5,3,2,6]=>10
[1,4,5,3,6,2]=>9
[1,4,5,6,2,3]=>9
[1,4,5,6,3,2]=>8
[1,4,6,2,3,5]=>10
[1,4,6,2,5,3]=>9
[1,4,6,3,2,5]=>9
[1,4,6,3,5,2]=>8
[1,4,6,5,2,3]=>8
[1,4,6,5,3,2]=>7
[1,5,2,3,4,6]=>12
[1,5,2,3,6,4]=>11
[1,5,2,4,3,6]=>11
[1,5,2,4,6,3]=>10
[1,5,2,6,3,4]=>10
[1,5,2,6,4,3]=>9
[1,5,3,2,4,6]=>11
[1,5,3,2,6,4]=>10
[1,5,3,4,2,6]=>10
[1,5,3,4,6,2]=>9
[1,5,3,6,2,4]=>9
[1,5,3,6,4,2]=>8
[1,5,4,2,3,6]=>10
[1,5,4,2,6,3]=>9
[1,5,4,3,2,6]=>9
[1,5,4,3,6,2]=>8
[1,5,4,6,2,3]=>8
[1,5,4,6,3,2]=>7
[1,5,6,2,3,4]=>9
[1,5,6,2,4,3]=>8
[1,5,6,3,2,4]=>8
[1,5,6,3,4,2]=>7
[1,5,6,4,2,3]=>7
[1,5,6,4,3,2]=>6
[1,6,2,3,4,5]=>11
[1,6,2,3,5,4]=>10
[1,6,2,4,3,5]=>10
[1,6,2,4,5,3]=>9
[1,6,2,5,3,4]=>9
[1,6,2,5,4,3]=>8
[1,6,3,2,4,5]=>10
[1,6,3,2,5,4]=>9
[1,6,3,4,2,5]=>9
[1,6,3,4,5,2]=>8
[1,6,3,5,2,4]=>8
[1,6,3,5,4,2]=>7
[1,6,4,2,3,5]=>9
[1,6,4,2,5,3]=>8
[1,6,4,3,2,5]=>8
[1,6,4,3,5,2]=>7
[1,6,4,5,2,3]=>7
[1,6,4,5,3,2]=>6
[1,6,5,2,3,4]=>8
[1,6,5,2,4,3]=>7
[1,6,5,3,2,4]=>7
[1,6,5,3,4,2]=>6
[1,6,5,4,2,3]=>6
[1,6,5,4,3,2]=>5
[2,1,3,4,5,6]=>14
[2,1,3,4,6,5]=>13
[2,1,3,5,4,6]=>13
[2,1,3,5,6,4]=>12
[2,1,3,6,4,5]=>12
[2,1,3,6,5,4]=>11
[2,1,4,3,5,6]=>13
[2,1,4,3,6,5]=>12
[2,1,4,5,3,6]=>12
[2,1,4,5,6,3]=>11
[2,1,4,6,3,5]=>11
[2,1,4,6,5,3]=>10
[2,1,5,3,4,6]=>12
[2,1,5,3,6,4]=>11
[2,1,5,4,3,6]=>11
[2,1,5,4,6,3]=>10
[2,1,5,6,3,4]=>10
[2,1,5,6,4,3]=>9
[2,1,6,3,4,5]=>11
[2,1,6,3,5,4]=>10
[2,1,6,4,3,5]=>10
[2,1,6,4,5,3]=>9
[2,1,6,5,3,4]=>9
[2,1,6,5,4,3]=>8
[2,3,1,4,5,6]=>13
[2,3,1,4,6,5]=>12
[2,3,1,5,4,6]=>12
[2,3,1,5,6,4]=>11
[2,3,1,6,4,5]=>11
[2,3,1,6,5,4]=>10
[2,3,4,1,5,6]=>12
[2,3,4,1,6,5]=>11
[2,3,4,5,1,6]=>11
[2,3,4,5,6,1]=>10
[2,3,4,6,1,5]=>10
[2,3,4,6,5,1]=>9
[2,3,5,1,4,6]=>11
[2,3,5,1,6,4]=>10
[2,3,5,4,1,6]=>10
[2,3,5,4,6,1]=>9
[2,3,5,6,1,4]=>9
[2,3,5,6,4,1]=>8
[2,3,6,1,4,5]=>10
[2,3,6,1,5,4]=>9
[2,3,6,4,1,5]=>9
[2,3,6,4,5,1]=>8
[2,3,6,5,1,4]=>8
[2,3,6,5,4,1]=>7
[2,4,1,3,5,6]=>12
[2,4,1,3,6,5]=>11
[2,4,1,5,3,6]=>11
[2,4,1,5,6,3]=>10
[2,4,1,6,3,5]=>10
[2,4,1,6,5,3]=>9
[2,4,3,1,5,6]=>11
[2,4,3,1,6,5]=>10
[2,4,3,5,1,6]=>10
[2,4,3,5,6,1]=>9
[2,4,3,6,1,5]=>9
[2,4,3,6,5,1]=>8
[2,4,5,1,3,6]=>10
[2,4,5,1,6,3]=>9
[2,4,5,3,1,6]=>9
[2,4,5,3,6,1]=>8
[2,4,5,6,1,3]=>8
[2,4,5,6,3,1]=>7
[2,4,6,1,3,5]=>9
[2,4,6,1,5,3]=>8
[2,4,6,3,1,5]=>8
[2,4,6,3,5,1]=>7
[2,4,6,5,1,3]=>7
[2,4,6,5,3,1]=>6
[2,5,1,3,4,6]=>11
[2,5,1,3,6,4]=>10
[2,5,1,4,3,6]=>10
[2,5,1,4,6,3]=>9
[2,5,1,6,3,4]=>9
[2,5,1,6,4,3]=>8
[2,5,3,1,4,6]=>10
[2,5,3,1,6,4]=>9
[2,5,3,4,1,6]=>9
[2,5,3,4,6,1]=>8
[2,5,3,6,1,4]=>8
[2,5,3,6,4,1]=>7
[2,5,4,1,3,6]=>9
[2,5,4,1,6,3]=>8
[2,5,4,3,1,6]=>8
[2,5,4,3,6,1]=>7
[2,5,4,6,1,3]=>7
[2,5,4,6,3,1]=>6
[2,5,6,1,3,4]=>8
[2,5,6,1,4,3]=>7
[2,5,6,3,1,4]=>7
[2,5,6,3,4,1]=>6
[2,5,6,4,1,3]=>6
[2,5,6,4,3,1]=>5
[2,6,1,3,4,5]=>10
[2,6,1,3,5,4]=>9
[2,6,1,4,3,5]=>9
[2,6,1,4,5,3]=>8
[2,6,1,5,3,4]=>8
[2,6,1,5,4,3]=>7
[2,6,3,1,4,5]=>9
[2,6,3,1,5,4]=>8
[2,6,3,4,1,5]=>8
[2,6,3,4,5,1]=>7
[2,6,3,5,1,4]=>7
[2,6,3,5,4,1]=>6
[2,6,4,1,3,5]=>8
[2,6,4,1,5,3]=>7
[2,6,4,3,1,5]=>7
[2,6,4,3,5,1]=>6
[2,6,4,5,1,3]=>6
[2,6,4,5,3,1]=>5
[2,6,5,1,3,4]=>7
[2,6,5,1,4,3]=>6
[2,6,5,3,1,4]=>6
[2,6,5,3,4,1]=>5
[2,6,5,4,1,3]=>5
[2,6,5,4,3,1]=>4
[3,1,2,4,5,6]=>13
[3,1,2,4,6,5]=>12
[3,1,2,5,4,6]=>12
[3,1,2,5,6,4]=>11
[3,1,2,6,4,5]=>11
[3,1,2,6,5,4]=>10
[3,1,4,2,5,6]=>12
[3,1,4,2,6,5]=>11
[3,1,4,5,2,6]=>11
[3,1,4,5,6,2]=>10
[3,1,4,6,2,5]=>10
[3,1,4,6,5,2]=>9
[3,1,5,2,4,6]=>11
[3,1,5,2,6,4]=>10
[3,1,5,4,2,6]=>10
[3,1,5,4,6,2]=>9
[3,1,5,6,2,4]=>9
[3,1,5,6,4,2]=>8
[3,1,6,2,4,5]=>10
[3,1,6,2,5,4]=>9
[3,1,6,4,2,5]=>9
[3,1,6,4,5,2]=>8
[3,1,6,5,2,4]=>8
[3,1,6,5,4,2]=>7
[3,2,1,4,5,6]=>12
[3,2,1,4,6,5]=>11
[3,2,1,5,4,6]=>11
[3,2,1,5,6,4]=>10
[3,2,1,6,4,5]=>10
[3,2,1,6,5,4]=>9
[3,2,4,1,5,6]=>11
[3,2,4,1,6,5]=>10
[3,2,4,5,1,6]=>10
[3,2,4,5,6,1]=>9
[3,2,4,6,1,5]=>9
[3,2,4,6,5,1]=>8
[3,2,5,1,4,6]=>10
[3,2,5,1,6,4]=>9
[3,2,5,4,1,6]=>9
[3,2,5,4,6,1]=>8
[3,2,5,6,1,4]=>8
[3,2,5,6,4,1]=>7
[3,2,6,1,4,5]=>9
[3,2,6,1,5,4]=>8
[3,2,6,4,1,5]=>8
[3,2,6,4,5,1]=>7
[3,2,6,5,1,4]=>7
[3,2,6,5,4,1]=>6
[3,4,1,2,5,6]=>11
[3,4,1,2,6,5]=>10
[3,4,1,5,2,6]=>10
[3,4,1,5,6,2]=>9
[3,4,1,6,2,5]=>9
[3,4,1,6,5,2]=>8
[3,4,2,1,5,6]=>10
[3,4,2,1,6,5]=>9
[3,4,2,5,1,6]=>9
[3,4,2,5,6,1]=>8
[3,4,2,6,1,5]=>8
[3,4,2,6,5,1]=>7
[3,4,5,1,2,6]=>9
[3,4,5,1,6,2]=>8
[3,4,5,2,1,6]=>8
[3,4,5,2,6,1]=>7
[3,4,5,6,1,2]=>7
[3,4,5,6,2,1]=>6
[3,4,6,1,2,5]=>8
[3,4,6,1,5,2]=>7
[3,4,6,2,1,5]=>7
[3,4,6,2,5,1]=>6
[3,4,6,5,1,2]=>6
[3,4,6,5,2,1]=>5
[3,5,1,2,4,6]=>10
[3,5,1,2,6,4]=>9
[3,5,1,4,2,6]=>9
[3,5,1,4,6,2]=>8
[3,5,1,6,2,4]=>8
[3,5,1,6,4,2]=>7
[3,5,2,1,4,6]=>9
[3,5,2,1,6,4]=>8
[3,5,2,4,1,6]=>8
[3,5,2,4,6,1]=>7
[3,5,2,6,1,4]=>7
[3,5,2,6,4,1]=>6
[3,5,4,1,2,6]=>8
[3,5,4,1,6,2]=>7
[3,5,4,2,1,6]=>7
[3,5,4,2,6,1]=>6
[3,5,4,6,1,2]=>6
[3,5,4,6,2,1]=>5
[3,5,6,1,2,4]=>7
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>6
[3,5,6,2,4,1]=>5
[3,5,6,4,1,2]=>5
[3,5,6,4,2,1]=>4
[3,6,1,2,4,5]=>9
[3,6,1,2,5,4]=>8
[3,6,1,4,2,5]=>8
[3,6,1,4,5,2]=>7
[3,6,1,5,2,4]=>7
[3,6,1,5,4,2]=>6
[3,6,2,1,4,5]=>8
[3,6,2,1,5,4]=>7
[3,6,2,4,1,5]=>7
[3,6,2,4,5,1]=>6
[3,6,2,5,1,4]=>6
[3,6,2,5,4,1]=>5
[3,6,4,1,2,5]=>7
[3,6,4,1,5,2]=>6
[3,6,4,2,1,5]=>6
[3,6,4,2,5,1]=>5
[3,6,4,5,1,2]=>5
[3,6,4,5,2,1]=>4
[3,6,5,1,2,4]=>6
[3,6,5,1,4,2]=>5
[3,6,5,2,1,4]=>5
[3,6,5,2,4,1]=>4
[3,6,5,4,1,2]=>4
[3,6,5,4,2,1]=>3
[4,1,2,3,5,6]=>12
[4,1,2,3,6,5]=>11
[4,1,2,5,3,6]=>11
[4,1,2,5,6,3]=>10
[4,1,2,6,3,5]=>10
[4,1,2,6,5,3]=>9
[4,1,3,2,5,6]=>11
[4,1,3,2,6,5]=>10
[4,1,3,5,2,6]=>10
[4,1,3,5,6,2]=>9
[4,1,3,6,2,5]=>9
[4,1,3,6,5,2]=>8
[4,1,5,2,3,6]=>10
[4,1,5,2,6,3]=>9
[4,1,5,3,2,6]=>9
[4,1,5,3,6,2]=>8
[4,1,5,6,2,3]=>8
[4,1,5,6,3,2]=>7
[4,1,6,2,3,5]=>9
[4,1,6,2,5,3]=>8
[4,1,6,3,2,5]=>8
[4,1,6,3,5,2]=>7
[4,1,6,5,2,3]=>7
[4,1,6,5,3,2]=>6
[4,2,1,3,5,6]=>11
[4,2,1,3,6,5]=>10
[4,2,1,5,3,6]=>10
[4,2,1,5,6,3]=>9
[4,2,1,6,3,5]=>9
[4,2,1,6,5,3]=>8
[4,2,3,1,5,6]=>10
[4,2,3,1,6,5]=>9
[4,2,3,5,1,6]=>9
[4,2,3,5,6,1]=>8
[4,2,3,6,1,5]=>8
[4,2,3,6,5,1]=>7
[4,2,5,1,3,6]=>9
[4,2,5,1,6,3]=>8
[4,2,5,3,1,6]=>8
[4,2,5,3,6,1]=>7
[4,2,5,6,1,3]=>7
[4,2,5,6,3,1]=>6
[4,2,6,1,3,5]=>8
[4,2,6,1,5,3]=>7
[4,2,6,3,1,5]=>7
[4,2,6,3,5,1]=>6
[4,2,6,5,1,3]=>6
[4,2,6,5,3,1]=>5
[4,3,1,2,5,6]=>10
[4,3,1,2,6,5]=>9
[4,3,1,5,2,6]=>9
[4,3,1,5,6,2]=>8
[4,3,1,6,2,5]=>8
[4,3,1,6,5,2]=>7
[4,3,2,1,5,6]=>9
[4,3,2,1,6,5]=>8
[4,3,2,5,1,6]=>8
[4,3,2,5,6,1]=>7
[4,3,2,6,1,5]=>7
[4,3,2,6,5,1]=>6
[4,3,5,1,2,6]=>8
[4,3,5,1,6,2]=>7
[4,3,5,2,1,6]=>7
[4,3,5,2,6,1]=>6
[4,3,5,6,1,2]=>6
[4,3,5,6,2,1]=>5
[4,3,6,1,2,5]=>7
[4,3,6,1,5,2]=>6
[4,3,6,2,1,5]=>6
[4,3,6,2,5,1]=>5
[4,3,6,5,1,2]=>5
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>9
[4,5,1,2,6,3]=>8
[4,5,1,3,2,6]=>8
[4,5,1,3,6,2]=>7
[4,5,1,6,2,3]=>7
[4,5,1,6,3,2]=>6
[4,5,2,1,3,6]=>8
[4,5,2,1,6,3]=>7
[4,5,2,3,1,6]=>7
[4,5,2,3,6,1]=>6
[4,5,2,6,1,3]=>6
[4,5,2,6,3,1]=>5
[4,5,3,1,2,6]=>7
[4,5,3,1,6,2]=>6
[4,5,3,2,1,6]=>6
[4,5,3,2,6,1]=>5
[4,5,3,6,1,2]=>5
[4,5,3,6,2,1]=>4
[4,5,6,1,2,3]=>6
[4,5,6,1,3,2]=>5
[4,5,6,2,1,3]=>5
[4,5,6,2,3,1]=>4
[4,5,6,3,1,2]=>4
[4,5,6,3,2,1]=>3
[4,6,1,2,3,5]=>8
[4,6,1,2,5,3]=>7
[4,6,1,3,2,5]=>7
[4,6,1,3,5,2]=>6
[4,6,1,5,2,3]=>6
[4,6,1,5,3,2]=>5
[4,6,2,1,3,5]=>7
[4,6,2,1,5,3]=>6
[4,6,2,3,1,5]=>6
[4,6,2,3,5,1]=>5
[4,6,2,5,1,3]=>5
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>6
[4,6,3,1,5,2]=>5
[4,6,3,2,1,5]=>5
[4,6,3,2,5,1]=>4
[4,6,3,5,1,2]=>4
[4,6,3,5,2,1]=>3
[4,6,5,1,2,3]=>5
[4,6,5,1,3,2]=>4
[4,6,5,2,1,3]=>4
[4,6,5,2,3,1]=>3
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>11
[5,1,2,3,6,4]=>10
[5,1,2,4,3,6]=>10
[5,1,2,4,6,3]=>9
[5,1,2,6,3,4]=>9
[5,1,2,6,4,3]=>8
[5,1,3,2,4,6]=>10
[5,1,3,2,6,4]=>9
[5,1,3,4,2,6]=>9
[5,1,3,4,6,2]=>8
[5,1,3,6,2,4]=>8
[5,1,3,6,4,2]=>7
[5,1,4,2,3,6]=>9
[5,1,4,2,6,3]=>8
[5,1,4,3,2,6]=>8
[5,1,4,3,6,2]=>7
[5,1,4,6,2,3]=>7
[5,1,4,6,3,2]=>6
[5,1,6,2,3,4]=>8
[5,1,6,2,4,3]=>7
[5,1,6,3,2,4]=>7
[5,1,6,3,4,2]=>6
[5,1,6,4,2,3]=>6
[5,1,6,4,3,2]=>5
[5,2,1,3,4,6]=>10
[5,2,1,3,6,4]=>9
[5,2,1,4,3,6]=>9
[5,2,1,4,6,3]=>8
[5,2,1,6,3,4]=>8
[5,2,1,6,4,3]=>7
[5,2,3,1,4,6]=>9
[5,2,3,1,6,4]=>8
[5,2,3,4,1,6]=>8
[5,2,3,4,6,1]=>7
[5,2,3,6,1,4]=>7
[5,2,3,6,4,1]=>6
[5,2,4,1,3,6]=>8
[5,2,4,1,6,3]=>7
[5,2,4,3,1,6]=>7
[5,2,4,3,6,1]=>6
[5,2,4,6,1,3]=>6
[5,2,4,6,3,1]=>5
[5,2,6,1,3,4]=>7
[5,2,6,1,4,3]=>6
[5,2,6,3,1,4]=>6
[5,2,6,3,4,1]=>5
[5,2,6,4,1,3]=>5
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>9
[5,3,1,2,6,4]=>8
[5,3,1,4,2,6]=>8
[5,3,1,4,6,2]=>7
[5,3,1,6,2,4]=>7
[5,3,1,6,4,2]=>6
[5,3,2,1,4,6]=>8
[5,3,2,1,6,4]=>7
[5,3,2,4,1,6]=>7
[5,3,2,4,6,1]=>6
[5,3,2,6,1,4]=>6
[5,3,2,6,4,1]=>5
[5,3,4,1,2,6]=>7
[5,3,4,1,6,2]=>6
[5,3,4,2,1,6]=>6
[5,3,4,2,6,1]=>5
[5,3,4,6,1,2]=>5
[5,3,4,6,2,1]=>4
[5,3,6,1,2,4]=>6
[5,3,6,1,4,2]=>5
[5,3,6,2,1,4]=>5
[5,3,6,2,4,1]=>4
[5,3,6,4,1,2]=>4
[5,3,6,4,2,1]=>3
[5,4,1,2,3,6]=>8
[5,4,1,2,6,3]=>7
[5,4,1,3,2,6]=>7
[5,4,1,3,6,2]=>6
[5,4,1,6,2,3]=>6
[5,4,1,6,3,2]=>5
[5,4,2,1,3,6]=>7
[5,4,2,1,6,3]=>6
[5,4,2,3,1,6]=>6
[5,4,2,3,6,1]=>5
[5,4,2,6,1,3]=>5
[5,4,2,6,3,1]=>4
[5,4,3,1,2,6]=>6
[5,4,3,1,6,2]=>5
[5,4,3,2,1,6]=>5
[5,4,3,2,6,1]=>4
[5,4,3,6,1,2]=>4
[5,4,3,6,2,1]=>3
[5,4,6,1,2,3]=>5
[5,4,6,1,3,2]=>4
[5,4,6,2,1,3]=>4
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>3
[5,4,6,3,2,1]=>2
[5,6,1,2,3,4]=>7
[5,6,1,2,4,3]=>6
[5,6,1,3,2,4]=>6
[5,6,1,3,4,2]=>5
[5,6,1,4,2,3]=>5
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>6
[5,6,2,1,4,3]=>5
[5,6,2,3,1,4]=>5
[5,6,2,3,4,1]=>4
[5,6,2,4,1,3]=>4
[5,6,2,4,3,1]=>3
[5,6,3,1,2,4]=>5
[5,6,3,1,4,2]=>4
[5,6,3,2,1,4]=>4
[5,6,3,2,4,1]=>3
[5,6,3,4,1,2]=>3
[5,6,3,4,2,1]=>2
[5,6,4,1,2,3]=>4
[5,6,4,1,3,2]=>3
[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>2
[5,6,4,3,1,2]=>2
[5,6,4,3,2,1]=>1
[6,1,2,3,4,5]=>10
[6,1,2,3,5,4]=>9
[6,1,2,4,3,5]=>9
[6,1,2,4,5,3]=>8
[6,1,2,5,3,4]=>8
[6,1,2,5,4,3]=>7
[6,1,3,2,4,5]=>9
[6,1,3,2,5,4]=>8
[6,1,3,4,2,5]=>8
[6,1,3,4,5,2]=>7
[6,1,3,5,2,4]=>7
[6,1,3,5,4,2]=>6
[6,1,4,2,3,5]=>8
[6,1,4,2,5,3]=>7
[6,1,4,3,2,5]=>7
[6,1,4,3,5,2]=>6
[6,1,4,5,2,3]=>6
[6,1,4,5,3,2]=>5
[6,1,5,2,3,4]=>7
[6,1,5,2,4,3]=>6
[6,1,5,3,2,4]=>6
[6,1,5,3,4,2]=>5
[6,1,5,4,2,3]=>5
[6,1,5,4,3,2]=>4
[6,2,1,3,4,5]=>9
[6,2,1,3,5,4]=>8
[6,2,1,4,3,5]=>8
[6,2,1,4,5,3]=>7
[6,2,1,5,3,4]=>7
[6,2,1,5,4,3]=>6
[6,2,3,1,4,5]=>8
[6,2,3,1,5,4]=>7
[6,2,3,4,1,5]=>7
[6,2,3,4,5,1]=>6
[6,2,3,5,1,4]=>6
[6,2,3,5,4,1]=>5
[6,2,4,1,3,5]=>7
[6,2,4,1,5,3]=>6
[6,2,4,3,1,5]=>6
[6,2,4,3,5,1]=>5
[6,2,4,5,1,3]=>5
[6,2,4,5,3,1]=>4
[6,2,5,1,3,4]=>6
[6,2,5,1,4,3]=>5
[6,2,5,3,1,4]=>5
[6,2,5,3,4,1]=>4
[6,2,5,4,1,3]=>4
[6,2,5,4,3,1]=>3
[6,3,1,2,4,5]=>8
[6,3,1,2,5,4]=>7
[6,3,1,4,2,5]=>7
[6,3,1,4,5,2]=>6
[6,3,1,5,2,4]=>6
[6,3,1,5,4,2]=>5
[6,3,2,1,4,5]=>7
[6,3,2,1,5,4]=>6
[6,3,2,4,1,5]=>6
[6,3,2,4,5,1]=>5
[6,3,2,5,1,4]=>5
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>6
[6,3,4,1,5,2]=>5
[6,3,4,2,1,5]=>5
[6,3,4,2,5,1]=>4
[6,3,4,5,1,2]=>4
[6,3,4,5,2,1]=>3
[6,3,5,1,2,4]=>5
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>4
[6,3,5,2,4,1]=>3
[6,3,5,4,1,2]=>3
[6,3,5,4,2,1]=>2
[6,4,1,2,3,5]=>7
[6,4,1,2,5,3]=>6
[6,4,1,3,2,5]=>6
[6,4,1,3,5,2]=>5
[6,4,1,5,2,3]=>5
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>6
[6,4,2,1,5,3]=>5
[6,4,2,3,1,5]=>5
[6,4,2,3,5,1]=>4
[6,4,2,5,1,3]=>4
[6,4,2,5,3,1]=>3
[6,4,3,1,2,5]=>5
[6,4,3,1,5,2]=>4
[6,4,3,2,1,5]=>4
[6,4,3,2,5,1]=>3
[6,4,3,5,1,2]=>3
[6,4,3,5,2,1]=>2
[6,4,5,1,2,3]=>4
[6,4,5,1,3,2]=>3
[6,4,5,2,1,3]=>3
[6,4,5,2,3,1]=>2
[6,4,5,3,1,2]=>2
[6,4,5,3,2,1]=>1
[6,5,1,2,3,4]=>6
[6,5,1,2,4,3]=>5
[6,5,1,3,2,4]=>5
[6,5,1,3,4,2]=>4
[6,5,1,4,2,3]=>4
[6,5,1,4,3,2]=>3
[6,5,2,1,3,4]=>5
[6,5,2,1,4,3]=>4
[6,5,2,3,1,4]=>4
[6,5,2,3,4,1]=>3
[6,5,2,4,1,3]=>3
[6,5,2,4,3,1]=>2
[6,5,3,1,2,4]=>4
[6,5,3,1,4,2]=>3
[6,5,3,2,1,4]=>3
[6,5,3,2,4,1]=>2
[6,5,3,4,1,2]=>2
[6,5,3,4,2,1]=>1
[6,5,4,1,2,3]=>3
[6,5,4,1,3,2]=>2
[6,5,4,2,1,3]=>2
[6,5,4,2,3,1]=>1
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>21
[1,2,3,4,5,7,6]=>20
[1,2,3,4,6,5,7]=>20
[1,2,3,6,4,7,5]=>18
[1,2,6,3,4,7,5]=>17
[1,3,2,4,5,6,7]=>20
[1,3,7,2,4,5,6]=>16
[1,3,7,6,5,4,2]=>10
[1,4,6,7,2,3,5]=>13
[1,4,6,7,5,3,2]=>10
[1,4,7,2,3,5,6]=>15
[1,4,7,6,5,3,2]=>9
[1,5,2,3,4,7,6]=>17
[1,5,2,7,3,4,6]=>15
[1,5,4,7,6,3,2]=>10
[1,5,6,2,7,3,4]=>13
[1,5,6,4,7,3,2]=>10
[1,5,6,7,2,3,4]=>12
[1,5,6,7,4,3,2]=>9
[1,5,7,2,3,4,6]=>14
[1,5,7,6,4,3,2]=>8
[1,6,2,3,4,7,5]=>16
[1,6,2,3,7,4,5]=>15
[1,6,2,7,3,4,5]=>14
[1,6,5,4,3,7,2]=>10
[1,6,5,4,7,3,2]=>9
[1,6,5,7,4,3,2]=>8
[1,6,7,2,3,4,5]=>13
[1,6,7,5,4,3,2]=>7
[1,7,2,3,4,5,6]=>16
[1,7,3,5,6,4,2]=>10
[1,7,3,6,5,4,2]=>9
[1,7,4,3,6,5,2]=>10
[1,7,4,5,3,6,2]=>10
[1,7,4,5,6,3,2]=>9
[1,7,4,6,5,3,2]=>8
[1,7,5,4,3,6,2]=>9
[1,7,5,4,6,3,2]=>8
[1,7,6,4,5,3,2]=>7
[1,7,6,5,4,3,2]=>6
[2,1,3,4,5,6,7]=>20
[2,1,3,4,7,5,6]=>18
[2,1,3,7,4,5,6]=>17
[2,1,6,3,4,5,7]=>17
[2,1,7,3,4,5,6]=>16
[2,1,7,6,5,4,3]=>10
[2,3,1,4,5,6,7]=>19
[2,3,4,1,5,6,7]=>18
[2,3,4,1,5,7,6]=>17
[2,3,4,5,1,6,7]=>17
[2,3,4,5,1,7,6]=>16
[2,3,4,5,6,1,7]=>16
[2,3,4,5,6,7,1]=>15
[2,3,4,5,7,1,6]=>15
[2,3,4,6,1,7,5]=>15
[2,3,4,6,7,1,5]=>14
[2,3,4,7,1,5,6]=>15
[2,3,5,6,7,1,4]=>13
[2,4,1,3,5,6,7]=>18
[2,5,1,3,4,6,7]=>17
[2,5,7,1,3,4,6]=>13
[2,6,1,3,4,5,7]=>16
[2,6,1,7,3,4,5]=>13
[2,6,5,4,3,1,7]=>10
[2,6,7,1,3,4,5]=>12
[2,7,1,3,4,5,6]=>15
[3,1,2,4,5,6,7]=>19
[3,1,2,4,5,7,6]=>18
[3,2,1,4,5,6,7]=>18
[3,2,4,5,6,7,1]=>14
[3,4,1,2,5,6,7]=>17
[3,4,2,5,6,7,1]=>13
[3,4,5,2,6,7,1]=>12
[3,4,5,6,2,7,1]=>11
[3,4,5,6,7,1,2]=>11
[3,5,6,1,2,4,7]=>13
[3,5,6,4,2,1,7]=>10
[3,6,1,2,4,5,7]=>15
[3,6,5,4,2,1,7]=>9
[4,1,2,3,5,6,7]=>18
[4,1,2,3,5,7,6]=>17
[4,1,6,2,3,5,7]=>15
[4,2,3,5,6,7,1]=>13
[4,2,5,1,3,6,7]=>15
[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]=>10
[4,5,1,6,2,3,7]=>13
[4,5,2,3,6,7,1]=>11
[4,5,3,6,2,1,7]=>10
[4,5,6,1,2,3,7]=>12
[4,5,6,3,2,1,7]=>9
[4,6,1,2,3,5,7]=>14
[4,6,1,2,3,7,5]=>13
[4,6,5,3,2,1,7]=>8
[5,1,2,3,4,6,7]=>17
[5,1,2,3,4,7,6]=>16
[5,1,2,3,6,4,7]=>16
[5,1,2,3,6,7,4]=>15
[5,1,2,3,7,4,6]=>15
[5,1,2,6,3,4,7]=>15
[5,1,6,2,3,4,7]=>14
[5,1,6,2,3,7,4]=>13
[5,2,3,4,6,7,1]=>12
[5,2,6,7,1,3,4]=>10
[5,3,2,4,6,7,1]=>11
[5,3,2,6,1,4,7]=>12
[5,3,6,7,1,2,4]=>9
[5,4,3,2,1,6,7]=>11
[5,4,3,2,1,7,6]=>10
[5,4,3,2,6,1,7]=>10
[5,4,3,6,2,1,7]=>9
[5,4,6,3,2,1,7]=>8
[5,4,6,7,1,2,3]=>8
[5,6,1,2,3,4,7]=>13
[5,6,1,2,3,7,4]=>12
[5,6,3,4,1,2,7]=>9
[5,6,4,3,2,1,7]=>7
[5,6,7,1,2,3,4]=>9
[6,1,2,3,4,5,7]=>16
[6,1,2,3,4,7,5]=>15
[6,1,2,3,7,4,5]=>14
[6,1,2,7,3,4,5]=>13
[6,2,3,4,5,7,1]=>11
[6,2,4,5,3,1,7]=>10
[6,2,5,4,3,1,7]=>9
[6,3,2,5,4,1,7]=>10
[6,3,4,2,5,1,7]=>10
[6,3,4,5,2,1,7]=>9
[6,3,4,7,1,2,5]=>9
[6,3,5,4,2,1,7]=>8
[6,4,3,2,5,1,7]=>9
[6,4,3,2,7,1,5]=>8
[6,4,3,5,2,1,7]=>8
[6,4,5,7,1,2,3]=>7
[6,4,7,2,5,1,3]=>6
[6,4,7,3,5,1,2]=>5
[6,5,3,4,2,1,7]=>7
[6,5,4,3,2,1,7]=>6
[6,5,7,3,4,1,2]=>4
[6,7,1,2,3,4,5]=>11
[6,7,3,4,1,2,5]=>7
[6,7,4,5,1,2,3]=>5
[7,1,2,3,4,5,6]=>15
[7,2,1,3,4,5,6]=>14
[7,2,3,1,4,5,6]=>13
[7,2,3,4,1,5,6]=>12
[7,2,3,4,5,1,6]=>11
[7,3,1,2,4,5,6]=>13
[7,3,2,1,4,5,6]=>12
[7,3,2,4,1,5,6]=>11
[7,3,4,1,2,5,6]=>11
[7,4,1,2,3,5,6]=>12
[7,4,2,1,3,5,6]=>11
[7,4,5,6,1,2,3]=>6
[7,5,1,2,3,4,6]=>11
[7,5,6,1,2,3,4]=>7
[7,5,6,3,4,1,2]=>3
[7,6,1,2,3,4,5]=>10
[7,6,4,5,1,2,3]=>4
[7,6,5,1,2,3,4]=>6
[7,6,5,3,4,1,2]=>2
[7,6,5,4,1,2,3]=>3
[7,6,5,4,3,1,2]=>1
[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]=>2
[7,8,5,6,4,3,2,1]=>2
[7,8,6,4,5,3,2,1]=>2
[8,6,7,4,5,3,2,1]=>2
[7,6,5,4,8,3,2,1]=>4
[6,5,7,4,8,3,2,1]=>6
[7,8,6,5,3,4,2,1]=>2
[8,6,7,5,3,4,2,1]=>2
[8,7,5,6,3,4,2,1]=>2
[6,7,8,3,4,5,2,1]=>6
[7,8,6,5,4,2,3,1]=>2
[8,6,7,5,4,2,3,1]=>2
[8,7,5,6,4,2,3,1]=>2
[8,7,6,4,5,2,3,1]=>2
[8,6,5,7,3,2,4,1]=>4
[6,7,8,5,2,3,4,1]=>6
[8,5,6,7,2,3,4,1]=>6
[7,8,3,2,4,5,6,1]=>10
[7,6,5,4,3,2,8,1]=>6
[6,5,7,4,3,2,8,1]=>8
[6,5,4,3,7,2,8,1]=>10
[5,4,6,3,7,2,8,1]=>12
[3,4,5,2,6,7,8,1]=>18
[5,2,3,4,6,7,8,1]=>18
[4,3,2,5,6,7,8,1]=>18
[3,4,2,5,6,7,8,1]=>19
[4,2,3,5,6,7,8,1]=>19
[3,2,4,5,6,7,8,1]=>20
[2,3,4,5,6,7,8,1]=>21
[8,7,6,5,4,3,1,2]=>1
[7,8,6,5,4,3,1,2]=>2
[8,6,7,5,4,3,1,2]=>2
[8,7,5,6,4,3,1,2]=>2
[8,7,6,4,5,3,1,2]=>2
[8,7,6,5,3,4,1,2]=>2
[8,7,5,6,3,4,1,2]=>3
[7,8,5,6,3,4,1,2]=>4
[5,6,7,8,3,4,1,2]=>8
[7,8,3,4,5,6,1,2]=>8
[3,4,5,6,7,8,1,2]=>16
[8,7,6,5,4,2,1,3]=>2
[7,6,8,5,4,2,1,3]=>4
[8,7,6,5,4,1,2,3]=>3
[6,7,8,5,4,1,2,3]=>6
[8,5,6,7,4,1,2,3]=>6
[8,7,6,4,5,1,2,3]=>4
[8,6,7,4,5,1,2,3]=>5
[8,7,4,5,6,1,2,3]=>6
[7,8,4,5,6,1,2,3]=>7
[6,7,4,5,8,1,2,3]=>9
[7,6,5,8,3,2,1,4]=>6
[7,5,6,8,2,3,1,4]=>8
[6,7,5,8,3,1,2,4]=>8
[6,5,7,8,2,1,3,4]=>10
[8,7,6,5,1,2,3,4]=>6
[8,7,5,6,1,2,3,4]=>7
[7,8,5,6,1,2,3,4]=>8
[8,5,6,7,1,2,3,4]=>9
[5,6,7,8,1,2,3,4]=>12
[8,7,6,4,3,2,1,5]=>4
[8,7,6,4,2,1,3,5]=>6
[8,7,6,1,2,3,4,5]=>10
[8,6,7,1,2,3,4,5]=>11
[6,7,8,1,2,3,4,5]=>13
[7,8,5,4,2,1,3,6]=>8
[7,8,5,4,1,2,3,6]=>9
[8,7,1,2,3,4,5,6]=>15
[7,8,1,2,3,4,5,6]=>16
[8,6,5,4,3,2,1,7]=>6
[8,6,5,4,3,1,2,7]=>7
[8,5,6,3,4,1,2,7]=>9
[8,6,5,4,2,1,3,7]=>8
[8,6,4,3,2,1,5,7]=>10
[8,6,4,2,1,3,5,7]=>12
[8,2,3,4,1,5,6,7]=>18
[8,4,1,2,3,5,6,7]=>18
[8,3,2,1,4,5,6,7]=>18
[8,2,3,1,4,5,6,7]=>19
[8,3,1,2,4,5,6,7]=>19
[8,2,1,3,4,5,6,7]=>20
[8,1,2,3,4,5,6,7]=>21
[7,6,5,4,3,2,1,8]=>7
[6,7,5,4,3,2,1,8]=>8
[6,5,7,4,3,2,1,8]=>9
[5,6,7,4,3,2,1,8]=>10
[7,6,4,5,3,2,1,8]=>8
[6,5,4,7,3,2,1,8]=>10
[7,5,6,3,4,2,1,8]=>9
[7,6,4,3,5,2,1,8]=>9
[7,6,3,4,5,2,1,8]=>10
[7,5,4,3,6,2,1,8]=>10
[6,7,5,4,2,3,1,8]=>9
[6,5,7,3,2,4,1,8]=>11
[5,6,7,2,3,4,1,8]=>13
[2,3,4,5,6,7,1,8]=>22
[5,6,7,1,2,3,4,8]=>16
[6,7,1,2,3,4,5,8]=>18
[7,1,2,3,4,5,6,8]=>22
[6,5,4,3,2,1,7,8]=>13
[2,3,4,5,6,1,7,8]=>23
[5,6,3,4,1,2,7,8]=>16
[4,5,6,1,2,3,7,8]=>19
[6,1,2,3,4,5,7,8]=>23
[5,4,3,2,1,6,7,8]=>18
[2,3,4,5,1,6,7,8]=>24
[5,1,2,3,4,6,7,8]=>24
[4,3,2,1,5,6,7,8]=>22
[3,4,1,2,5,6,7,8]=>24
[3,2,1,4,5,6,7,8]=>25
[2,1,3,4,5,6,7,8]=>27
[1,2,3,4,5,6,7,8]=>28
[6,5,8,7,4,3,2,1]=>4
[3,5,8,7,6,4,2,1]=>8
[4,3,6,5,8,7,2,1]=>12
[2,6,8,7,5,4,3,1]=>8
[2,3,5,6,8,7,4,1]=>16
[3,2,6,5,4,8,7,1]=>16
[4,3,6,5,7,2,8,1]=>14
[3,2,6,5,7,4,8,1]=>16
[4,3,5,2,7,6,8,1]=>16
[3,2,5,4,7,6,8,1]=>18
[1,8,7,6,5,4,3,2]=>7
[1,7,8,6,5,4,3,2]=>8
[1,6,8,7,5,4,3,2]=>9
[1,7,6,8,5,4,3,2]=>9
[1,6,7,8,5,4,3,2]=>10
[1,5,8,7,6,4,3,2]=>10
[1,7,6,5,8,4,3,2]=>10
[1,3,5,7,8,6,4,2]=>16
[1,4,3,8,7,6,5,2]=>15
[1,6,5,4,3,8,7,2]=>15
[1,4,3,6,5,8,7,2]=>19
[2,1,8,7,6,5,4,3]=>12
[2,1,6,5,7,4,8,3]=>18
[2,1,5,4,7,6,8,3]=>20
[1,2,6,7,8,5,4,3]=>16
[3,2,1,8,7,6,5,4]=>15
[3,2,1,6,5,8,7,4]=>19
[1,2,3,5,6,7,8,4]=>24
[4,3,2,1,8,7,6,5]=>16
[3,4,2,1,7,8,6,5]=>18
[2,4,3,1,6,8,7,5]=>20
[2,4,3,1,7,6,8,5]=>20
[3,2,4,1,6,8,7,5]=>20
[3,2,4,1,7,6,8,5]=>20
[2,3,4,1,6,7,8,5]=>22
[2,1,4,3,8,7,6,5]=>20
[2,1,4,3,6,8,7,5]=>22
[2,1,4,3,7,6,8,5]=>22
[5,4,3,2,1,8,7,6]=>15
[3,2,5,4,1,8,7,6]=>19
[3,2,1,4,5,8,7,6]=>22
[2,3,1,4,5,7,8,6]=>24
[6,5,4,3,2,1,8,7]=>12
[4,3,5,2,6,1,8,7]=>18
[3,2,5,4,6,1,8,7]=>20
[2,3,4,5,6,1,8,7]=>22
[2,1,6,5,4,3,8,7]=>20
[2,1,4,6,5,3,8,7]=>22
[2,1,5,4,6,3,8,7]=>22
[4,3,2,1,6,5,8,7]=>20
[2,4,3,1,6,5,8,7]=>22
[3,2,4,1,6,5,8,7]=>22
[2,1,4,3,6,5,8,7]=>24
[2,1,3,4,5,6,8,7]=>26
[1,2,3,4,5,6,8,7]=>27
[5,7,6,4,3,2,1,8]=>9
[4,7,6,5,3,2,1,8]=>10
[3,2,7,6,5,4,1,8]=>15
[5,4,3,2,7,6,1,8]=>15
[3,2,5,4,7,6,1,8]=>19
[1,4,3,2,7,6,5,8]=>22
[1,3,4,2,6,7,5,8]=>24
[1,3,2,5,4,7,6,8]=>25
[1,2,3,5,4,7,6,8]=>26
[1,3,2,4,5,7,6,8]=>26
[1,2,3,4,5,7,6,8]=>27
[1,2,4,3,6,5,7,8]=>26
[1,3,2,5,4,6,7,8]=>26
[1,2,3,5,4,6,7,8]=>27
[1,3,2,4,5,6,7,8]=>27
[1,8,4,7,6,5,3,2]=>10
[1,8,5,4,7,6,3,2]=>11
[1,8,7,4,5,6,3,2]=>10
[1,8,7,4,6,5,3,2]=>9
[1,8,6,5,4,7,3,2]=>10
[1,8,7,5,4,6,3,2]=>9
[1,8,7,5,6,4,3,2]=>8
[2,1,4,5,8,6,7,3]=>20
[2,1,8,5,4,7,6,3]=>16
[2,3,4,8,5,6,7,1]=>18
[2,3,6,4,5,1,8,7]=>20
[2,3,7,4,5,6,8,1]=>18
[2,8,4,3,5,7,6,1]=>14
[4,2,3,1,8,6,7,5]=>18
[8,2,7,4,6,5,3,1]=>7
[4,3,2,7,5,6,8,1]=>16
[4,3,2,8,5,7,6,1]=>14
[6,3,2,5,4,1,8,7]=>16
[8,3,2,5,4,7,6,1]=>12
[8,3,2,7,6,5,4,1]=>8
[8,3,7,4,6,5,2,1]=>6
[7,3,6,5,4,2,1,8]=>10
[7,4,3,6,5,2,1,8]=>11
[7,6,3,5,4,2,1,8]=>9
[8,5,4,3,2,7,6,1]=>8
[8,7,4,3,6,5,2,1]=>4
[2,4,6,8,1,3,5,7]=>18
[2,4,6,1,7,3,8,5]=>19
[2,1,4,3,7,5,8,6]=>23
[2,4,1,3,7,5,8,6]=>22
[2,1,4,3,7,8,5,6]=>22
[2,4,7,8,1,3,5,6]=>17
[2,1,4,3,8,5,6,7]=>23
[2,4,5,6,7,1,8,3]=>18
[2,1,5,3,6,4,8,7]=>23
[2,1,5,6,3,4,8,7]=>22
[2,5,6,8,1,3,4,7]=>17
[2,1,5,3,7,4,8,6]=>22
[2,5,1,7,3,4,8,6]=>20
[2,1,5,7,3,8,4,6]=>20
[2,5,7,8,1,3,4,6]=>16
[2,3,5,6,1,7,8,4]=>20
[2,1,6,3,7,4,8,5]=>21
[2,6,7,1,3,4,8,5]=>18
[2,1,6,7,8,3,4,5]=>18
[2,6,7,8,1,3,4,5]=>15
[2,1,6,3,4,7,8,5]=>22
[2,1,6,3,4,5,8,7]=>23
[2,6,1,3,4,5,7,8]=>23
[2,7,8,1,3,4,5,6]=>17
[2,7,1,3,4,5,6,8]=>22
[2,3,4,5,7,8,1,6]=>20
[2,1,8,3,4,5,6,7]=>22
[2,8,1,3,4,5,6,7]=>21
[2,1,3,8,4,5,6,7]=>23
[2,3,4,5,6,8,1,7]=>21
[3,1,4,2,6,5,8,7]=>23
[3,4,1,2,6,5,8,7]=>22
[3,1,4,2,6,8,5,7]=>22
[3,4,6,8,1,2,5,7]=>17
[3,1,4,2,7,5,8,6]=>22
[3,4,1,2,7,8,5,6]=>20
[3,4,7,8,1,2,5,6]=>16
[3,1,5,2,6,4,8,7]=>22
[3,5,1,6,2,4,8,7]=>20
[3,1,5,6,2,8,4,7]=>20
[3,5,6,8,1,2,4,7]=>16
[3,1,5,2,7,4,8,6]=>21
[3,5,1,7,2,8,4,6]=>18
[3,5,7,8,1,2,4,6]=>15
[1,3,2,5,4,8,6,7]=>24
[1,3,5,8,2,4,6,7]=>21
[1,3,5,6,2,7,4,8]=>22
[3,1,6,2,7,4,8,5]=>20
[3,6,7,1,2,8,4,5]=>16
[3,6,1,7,8,2,4,5]=>16
[3,6,7,8,1,2,4,5]=>14
[1,3,2,6,4,7,5,8]=>24
[3,1,2,6,7,4,8,5]=>21
[1,3,2,6,4,8,5,7]=>23
[1,3,2,6,4,5,7,8]=>25
[1,3,2,7,4,8,5,6]=>22
[1,3,2,7,4,5,6,8]=>24
[1,3,2,8,4,5,6,7]=>23
[3,1,2,4,5,8,6,7]=>24
[1,3,2,4,5,8,6,7]=>25
[4,1,5,2,6,3,8,7]=>21
[4,5,6,1,2,3,8,7]=>18
[4,1,5,6,8,2,3,7]=>18
[4,5,6,8,1,2,3,7]=>15
[4,1,5,2,7,3,8,6]=>20
[4,1,5,2,7,8,3,6]=>19
[4,5,7,1,2,8,3,6]=>16
[4,5,1,7,8,2,3,6]=>16
[4,5,7,8,1,2,3,6]=>14
[1,4,2,5,3,7,6,8]=>24
[1,4,2,5,3,8,6,7]=>23
[1,4,2,5,3,6,7,8]=>25
[1,4,5,6,7,2,3,8]=>20
[4,1,6,2,7,3,8,5]=>19
[4,6,7,1,8,2,3,5]=>14
[4,6,7,8,1,2,3,5]=>13
[1,4,2,6,3,7,5,8]=>23
[1,4,2,6,7,8,3,5]=>20
[1,4,2,6,3,8,5,7]=>22
[4,1,2,3,6,5,8,7]=>23
[1,4,2,6,3,5,7,8]=>24
[1,4,2,7,3,8,5,6]=>21
[4,7,1,2,3,5,6,8]=>20
[1,4,2,7,3,5,6,8]=>23
[1,4,2,3,7,5,6,8]=>24
[1,4,2,3,5,7,6,8]=>25
[1,4,2,8,3,5,6,7]=>22
[4,1,2,3,8,5,6,7]=>22
[1,4,2,3,5,8,6,7]=>24
[1,4,2,3,5,6,7,8]=>26
[5,1,6,2,7,3,8,4]=>18
[1,5,2,6,3,7,4,8]=>22
[1,5,2,6,3,8,4,7]=>21
[1,5,2,6,3,4,7,8]=>23
[1,2,5,6,3,4,7,8]=>24
[1,5,2,7,3,8,4,6]=>20
[5,7,1,2,3,4,6,8]=>19
[1,5,2,7,3,4,6,8]=>22
[1,5,2,3,4,7,6,8]=>24
[5,1,2,8,3,4,6,7]=>20
[1,5,2,8,3,4,6,7]=>21
[1,5,8,2,3,4,6,7]=>20
[1,5,2,3,4,8,6,7]=>23
[1,2,3,5,4,8,6,7]=>25
[5,1,2,3,4,6,8,7]=>23
[1,5,2,3,4,6,7,8]=>25
[1,6,2,7,3,8,4,5]=>19
[1,6,7,8,2,3,4,5]=>16
[6,7,1,2,3,4,8,5]=>17
[6,1,7,2,3,4,5,8]=>19
[6,1,2,7,3,4,5,8]=>20
[1,6,2,7,3,4,5,8]=>21
[1,6,7,2,3,4,5,8]=>20
[1,6,2,3,4,7,5,8]=>23
[1,2,3,6,4,7,5,8]=>25
[6,1,8,2,3,4,5,7]=>18
[1,6,2,8,3,4,5,7]=>20
[1,6,8,2,3,4,5,7]=>19
[1,6,2,3,4,8,5,7]=>22
[1,2,3,6,4,8,5,7]=>24
[6,1,2,3,4,5,8,7]=>22
[1,6,2,3,4,5,7,8]=>24
[1,2,3,6,4,5,7,8]=>26
[1,7,2,8,3,4,5,6]=>19
[1,7,8,2,3,4,5,6]=>18
[1,7,2,3,8,4,5,6]=>20
[7,1,2,3,4,8,5,6]=>20
[1,7,2,3,4,8,5,6]=>21
[1,2,3,7,4,8,5,6]=>23
[7,1,2,3,4,5,8,6]=>21
[1,7,2,3,4,5,8,6]=>22
[1,2,7,3,4,5,8,6]=>23
[1,7,2,3,4,5,6,8]=>23
[1,2,3,7,4,5,6,8]=>25
[1,8,2,3,4,5,6,7]=>22
[1,2,3,8,4,5,6,7]=>24
[1,2,3,4,5,8,6,7]=>26
[5,3,2,6,1,4,8,7]=>18
[7,3,2,5,4,8,1,6]=>14
[8,4,5,2,3,7,6,1]=>10
[7,4,5,2,3,8,1,6]=>12
[6,4,5,2,3,1,8,7]=>14
[5,4,6,2,1,3,8,7]=>16
[3,6,1,5,4,2,8,7]=>18
[4,6,5,1,3,2,8,7]=>16
[5,6,4,3,1,2,8,7]=>14
[7,5,4,3,2,8,1,6]=>10
[8,6,4,3,7,2,5,1]=>6
[7,6,4,3,8,2,1,5]=>8
[6,7,4,3,8,1,2,5]=>10
[5,7,4,3,1,8,2,6]=>12
[4,7,5,1,3,8,2,6]=>14
[3,7,1,5,4,8,2,6]=>16
[2,1,7,5,4,8,3,6]=>18
[3,8,1,5,4,7,6,2]=>14
[4,8,5,1,3,7,6,2]=>12
[5,8,4,3,1,7,6,2]=>10
[6,8,4,3,7,1,5,2]=>8
[7,8,4,3,6,5,1,2]=>6
[6,8,5,7,3,1,4,2]=>6
[5,8,6,7,1,3,4,2]=>8
[4,8,6,1,7,3,5,2]=>10
[3,8,1,6,7,4,5,2]=>12
[2,1,8,6,7,4,5,3]=>14
[2,1,7,6,8,4,3,5]=>16
[3,7,1,6,8,4,2,5]=>14
[4,7,6,1,8,3,2,5]=>12
[5,7,6,8,1,3,2,4]=>10
[5,4,7,2,1,8,3,6]=>14
[6,4,7,2,8,1,3,5]=>12
[7,4,6,2,8,3,1,5]=>10
[8,4,6,2,7,3,5,1]=>8
[8,3,2,6,7,4,5,1]=>10
[7,3,2,6,8,4,1,5]=>12
[6,3,2,7,8,1,4,5]=>14
[5,3,2,7,1,8,4,6]=>16
[4,3,2,1,7,8,5,6]=>18
[3,4,1,2,8,7,6,5]=>18
[5,3,2,8,1,7,6,4]=>14
[6,3,2,8,7,1,5,4]=>12
[7,3,2,8,6,5,1,4]=>10
[8,4,7,2,6,5,3,1]=>6
[7,4,8,2,6,5,1,3]=>8
[6,4,8,2,7,1,5,3]=>10
[5,4,8,2,1,7,6,3]=>12
[4,5,8,1,2,7,6,3]=>14
[3,5,1,8,2,7,6,4]=>16
[2,1,5,8,3,7,6,4]=>18
[2,1,6,8,7,3,5,4]=>16
[3,6,1,8,7,2,5,4]=>14
[4,6,8,1,7,2,5,3]=>12
[5,6,8,7,1,2,4,3]=>10
[6,5,8,7,2,1,4,3]=>8
[7,5,8,6,2,4,1,3]=>6
[8,5,7,6,2,4,3,1]=>4
[5,7,8,6,1,4,2,3]=>8
[4,7,8,1,6,5,2,3]=>10
[3,7,1,8,6,5,2,4]=>12
[2,1,7,8,6,5,3,4]=>14
[3,8,1,7,6,5,4,2]=>10
[4,8,7,1,6,5,3,2]=>8
[5,8,7,6,1,4,3,2]=>6
[6,8,7,5,4,1,3,2]=>4
[4,2,5,1,3,6,7,8]=>22
[5,2,6,7,1,3,4,8]=>17
[3,2,7,8,1,4,5,6]=>17
[5,3,2,6,1,4,7,8]=>19
[7,4,3,8,1,2,5,6]=>13
[4,7,3,6,8,1,2,5]=>12
[6,7,3,4,8,1,2,5]=>11
[5,4,2,7,8,1,3,6]=>14
[6,4,7,2,5,1,3,8]=>13
[6,4,3,2,7,1,5,8]=>15
[5,4,3,2,8,1,6,7]=>15
[7,5,3,8,2,6,1,4]=>9
[8,5,4,7,2,6,1,3]=>7
[8,5,4,7,3,6,1,2]=>6
[8,1,2,7,6,3,4,5]=>14
[8,1,4,2,6,3,5,7]=>17
[8,3,1,2,4,7,5,6]=>17
[8,3,1,5,6,2,4,7]=>15
[6,3,8,1,2,7,4,5]=>14
[7,8,4,1,6,2,3,5]=>10
[8,3,4,1,6,7,2,5]=>13
[2,7,6,5,1,3,8,4]=>14
[8,3,6,5,1,7,2,4]=>10
[4,6,7,3,8,5,1,2]=>10
[3,5,2,7,1,8,6,4]=>16
[4,6,7,2,8,1,5,3]=>12
[5,6,7,8,2,1,4,3]=>10
[6,5,8,7,3,4,1,2]=>6
[3,6,7,4,5,8,1,2]=>12
[2,6,7,4,5,1,8,3]=>14
[1,6,7,4,5,2,3,8]=>16
[1,5,4,7,6,2,3,8]=>18
[2,5,4,7,6,1,8,3]=>16
[3,5,4,7,6,8,1,2]=>14
[4,5,3,7,8,6,1,2]=>12
[5,4,3,8,7,6,1,2]=>10
[6,4,8,3,7,5,1,2]=>8
[6,3,8,4,5,7,1,2]=>10
[5,3,4,8,6,7,1,2]=>12
[4,3,5,6,8,7,1,2]=>14
[3,2,5,6,1,8,7,4]=>18
[4,2,5,6,8,1,7,3]=>16
[5,2,4,8,6,1,7,3]=>14
[6,2,8,4,5,1,7,3]=>12
[7,8,2,4,5,1,6,3]=>10
[7,8,1,4,5,2,3,6]=>12
[6,1,8,4,5,2,3,7]=>14
[5,1,4,8,6,2,3,7]=>16
[4,1,3,2,8,6,5,7]=>20
[5,1,3,8,2,6,4,7]=>18
[6,1,8,3,2,5,4,7]=>16
[7,8,1,3,2,5,4,6]=>14
[7,8,2,3,1,5,6,4]=>12
[6,2,8,3,1,5,7,4]=>14
[5,2,3,8,1,6,7,4]=>16
[6,3,8,2,1,7,5,4]=>12
[7,8,3,2,1,6,5,4]=>10
[7,8,4,2,6,1,5,3]=>8
[5,4,2,8,7,1,6,3]=>12
[4,5,2,7,8,1,6,3]=>14
[2,5,3,7,1,6,8,4]=>18
[1,5,3,7,2,6,4,8]=>20
[1,6,7,3,2,5,4,8]=>18
[2,6,7,3,1,5,8,4]=>16
[3,6,7,2,1,8,5,4]=>14
[7,8,5,6,2,1,4,3]=>6
[6,5,8,7,1,2,3,4]=>10
[5,4,1,8,7,2,3,6]=>14
[6,4,8,1,7,2,3,5]=>12
[7,8,3,1,2,6,4,5]=>12
[5,3,1,8,2,7,4,6]=>16
[4,3,1,2,8,7,5,6]=>18
[4,2,1,3,8,5,7,6]=>20
[5,2,1,8,3,4,7,6]=>18
[6,2,8,1,3,4,7,5]=>16
[7,8,2,1,3,4,6,5]=>14
[6,3,1,5,2,4,8,7]=>18
[2,1,8,5,3,7,4,6]=>18
[8,2,6,1,4,3,7,5]=>14
[4,7,1,5,8,3,2,6]=>14
[8,6,1,3,4,2,5,7]=>14
[8,1,2,4,5,6,3,7]=>18
[8,2,5,1,3,6,4,7]=>16
[4,1,5,3,7,2,8,6]=>19
[5,2,7,1,3,8,4,6]=>17
[5,3,1,7,8,2,4,6]=>16
[1,7,3,4,2,5,8,6]=>20
[4,7,2,1,3,5,8,6]=>18
[4,5,2,3,7,6,1,8]=>17
[6,4,3,7,2,5,1,8]=>13
[8,4,3,6,5,1,2,7]=>11
[1,5,6,3,4,8,7,2]=>17
[4,6,2,7,3,5,1,8]=>15
[3,2,6,7,4,5,1,8]=>17
[4,7,2,6,5,3,1,8]=>13
[5,7,6,2,4,3,1,8]=>11
[1,7,5,4,8,3,6,2]=>13
[8,7,5,4,1,3,2,6]=>7
[6,8,5,4,2,1,3,7]=>9
[5,8,6,2,4,1,3,7]=>11
[4,8,2,6,5,1,3,7]=>13
[3,2,8,6,5,1,4,7]=>15
[4,1,2,6,5,8,7,3]=>19
[5,1,6,2,4,8,7,3]=>17
[6,1,5,4,2,8,7,3]=>15
[7,1,5,4,8,2,6,3]=>13
[8,1,5,4,7,6,2,3]=>11
[1,8,6,7,4,5,3,2]=>9
[8,1,6,7,4,5,2,3]=>9
[7,1,6,8,4,2,5,3]=>11
[6,1,7,8,2,4,5,3]=>13
[5,1,7,2,8,4,6,3]=>15
[4,1,2,7,8,5,6,3]=>17
[3,2,1,7,8,5,6,4]=>17
[3,2,8,7,1,5,4,6]=>15
[4,8,2,7,1,5,3,6]=>13
[5,8,7,2,1,4,3,6]=>11
[6,8,7,1,2,4,3,5]=>11
[7,8,6,1,4,2,3,5]=>9
[8,7,6,1,4,3,2,5]=>7
[1,7,6,8,4,3,5,2]=>11
[1,6,7,8,3,4,5,2]=>13
[8,6,7,1,3,4,2,5]=>9
[7,6,8,1,3,2,4,5]=>11
[5,7,8,2,1,3,4,6]=>13
[4,7,2,8,1,3,5,6]=>15
[3,2,6,8,4,1,5,7]=>17
[4,6,2,8,3,1,5,7]=>15
[5,6,8,2,3,1,4,7]=>13
[6,5,8,3,2,1,4,7]=>11
[7,5,8,3,1,2,4,6]=>11
[8,5,7,3,1,4,2,6]=>9
[1,5,7,3,8,4,6,2]=>15
[1,4,3,7,8,5,6,2]=>17
[8,4,3,7,1,5,2,6]=>11
[6,4,3,8,2,1,5,7]=>13
[4,5,2,3,8,1,6,7]=>17
[3,2,5,4,8,1,6,7]=>19
[4,5,2,3,1,8,7,6]=>17
[6,4,3,1,2,8,7,5]=>15
[7,4,3,1,8,2,6,5]=>13
[8,4,3,1,7,6,2,5]=>11
[1,5,8,3,7,6,4,2]=>13
[8,5,1,3,7,6,2,4]=>11
[7,5,1,3,8,2,6,4]=>13
[6,5,1,3,2,8,7,4]=>15
[5,6,1,2,3,8,7,4]=>17
[4,6,2,1,3,8,7,5]=>17
[3,2,6,1,4,8,7,5]=>19
[3,2,7,1,8,4,6,5]=>17
[4,7,2,1,8,3,6,5]=>15
[5,7,1,2,8,3,6,4]=>15
[6,7,1,8,2,3,5,4]=>13
[7,6,1,8,3,2,5,4]=>11
[8,6,1,7,3,5,2,4]=>9
[1,6,8,7,3,5,4,2]=>11
[1,7,8,6,5,3,4,2]=>9
[8,7,1,6,5,3,2,4]=>7
[7,8,1,6,5,2,3,4]=>9
[6,8,1,7,2,5,3,4]=>11
[5,8,1,2,7,6,3,4]=>13
[4,8,2,1,7,6,3,5]=>13
[3,2,8,1,7,6,4,5]=>15
[4,1,2,8,7,6,5,3]=>15
[5,1,8,2,7,6,4,3]=>13
[6,1,8,7,2,5,4,3]=>11
[7,1,8,6,5,2,4,3]=>9
[8,1,7,6,5,4,2,3]=>7
[1,4,3,8,7,5,6,2]=>16
[4,1,2,8,7,5,6,3]=>16
[3,2,5,1,6,4,8,7]=>21
[3,2,5,4,7,1,8,6]=>19
[4,2,5,3,7,6,8,1]=>17
[4,2,5,3,7,1,8,6]=>18
[4,2,5,3,6,1,8,7]=>19
[4,2,5,1,6,3,8,7]=>20
[3,1,5,4,6,2,8,7]=>21
[4,1,5,3,6,2,8,7]=>20
[4,3,5,1,6,2,8,7]=>19
[4,3,5,2,7,1,8,6]=>17
[4,3,6,2,7,5,8,1]=>15
[4,3,6,2,7,1,8,5]=>16
[4,3,6,1,7,2,8,5]=>17
[4,3,5,1,7,2,8,6]=>18
[3,1,5,4,7,2,8,6]=>20
[2,1,5,4,7,3,8,6]=>21
[3,1,5,4,7,6,8,2]=>19
[4,1,5,3,7,6,8,2]=>18
[4,3,5,1,7,6,8,2]=>17
[4,3,6,1,7,5,8,2]=>16
[4,3,6,5,7,1,8,2]=>15
[5,3,6,4,7,2,8,1]=>13
[5,3,6,4,7,1,8,2]=>14
[5,3,6,1,7,4,8,2]=>15
[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]=>20
[3,1,6,4,7,2,8,5]=>19
[4,1,6,3,7,2,8,5]=>18
[5,1,6,3,7,2,8,4]=>17
[5,3,6,1,7,2,8,4]=>16
[5,3,6,2,7,1,8,4]=>15
[5,3,6,2,7,4,8,1]=>14
[5,2,6,3,7,4,8,1]=>15
[5,2,6,3,7,1,8,4]=>16
[5,2,6,1,7,3,8,4]=>17
[4,2,5,1,7,3,8,6]=>19
[4,2,6,1,7,3,8,5]=>18
[4,2,6,3,7,1,8,5]=>17
[4,2,6,3,7,5,8,1]=>16
[3,2,6,4,7,5,8,1]=>17
[3,2,6,4,7,1,8,5]=>18
[3,2,6,1,7,4,8,5]=>19
[3,2,5,1,7,4,8,6]=>20
[3,2,4,1,7,5,8,6]=>21
[3,1,4,2,7,6,8,5]=>21
[3,2,5,1,7,6,8,4]=>19
[3,2,6,1,7,5,8,4]=>18
[3,2,6,5,7,1,8,4]=>17
[4,2,6,5,7,3,8,1]=>15
[4,2,6,5,7,1,8,3]=>16
[4,2,6,1,7,5,8,3]=>17
[4,2,5,1,7,6,8,3]=>18
[4,1,5,2,7,6,8,3]=>19
[3,1,5,2,7,6,8,4]=>20
[2,1,5,3,7,6,8,4]=>21
[2,1,6,3,7,5,8,4]=>20
[3,1,6,2,7,5,8,4]=>19
[4,1,6,2,7,5,8,3]=>18
[5,1,6,2,7,4,8,3]=>17
[5,2,6,1,7,4,8,3]=>16
[5,2,6,4,7,1,8,3]=>15
[5,2,6,4,7,3,8,1]=>14
[5,4,6,2,7,3,8,1]=>13
[5,4,6,2,7,1,8,3]=>14
[5,4,6,1,7,2,8,3]=>15
[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]=>17
[4,1,6,5,7,3,8,2]=>16
[5,1,6,4,7,3,8,2]=>15
[5,4,6,1,7,3,8,2]=>14
[5,4,6,3,7,1,8,2]=>13
[8,3,5,2,1,6,4,7]=>14
[8,6,3,5,2,4,1,7]=>9
[3,7,5,2,4,1,8,6]=>15
[8,3,7,5,2,4,6,1]=>8
[8,2,4,5,7,3,6,1]=>11
[2,4,5,7,3,1,8,6]=>18
[8,2,4,6,5,3,1,7]=>12
[8,2,5,4,6,1,3,7]=>13
[8,6,3,5,1,4,2,7]=>10
[8,6,1,4,5,3,2,7]=>11
[8,1,5,6,4,3,2,7]=>12
[5,7,4,3,2,1,8,6]=>12
[8,5,7,4,3,2,6,1]=>5
[4,6,8,3,2,7,5,1]=>10
[4,7,6,3,2,8,1,5]=>11
[1,4,6,7,3,2,8,5]=>18
[5,4,7,3,1,8,2,6]=>13
[1,7,4,5,3,2,8,6]=>17
[3,7,5,1,4,2,8,6]=>16
[5,7,4,2,1,3,8,6]=>14
[8,5,7,4,2,1,6,3]=>7
[8,3,7,5,1,4,6,2]=>9
[8,4,1,7,5,3,6,2]=>10
[4,6,3,8,7,1,5,2]=>11
[1,7,4,8,6,3,5,2]=>12
[8,4,7,6,3,5,2,1]=>4
[3,6,5,8,7,4,1,2]=>10
[3,1,5,8,6,7,4,2]=>15
[4,8,1,6,7,3,5,2]=>11
[3,6,4,1,8,7,5,2]=>14
[8,2,6,1,4,7,5,3]=>12
[2,7,6,8,1,4,3,5]=>13
[3,7,1,6,4,8,2,5]=>15
[1,7,3,5,6,8,2,4]=>16
[1,3,6,7,5,8,2,4]=>17
[3,7,6,5,8,2,1,4]=>10
[3,6,8,5,7,2,4,1]=>9
[2,3,5,7,6,8,1,4]=>17
[2,1,6,5,7,8,3,4]=>18
[4,2,7,6,8,3,1,5]=>13
[4,2,6,8,7,3,5,1]=>12
[3,8,2,4,6,7,5,1]=>13
[3,7,2,6,4,8,1,5]=>14
[3,2,6,1,4,7,8,5]=>20
[5,3,7,2,1,8,4,6]=>15
[4,7,3,2,1,5,8,6]=>16
[8,7,6,1,3,4,2,5]=>8
[8,5,7,3,2,1,6,4]=>8
[8,3,6,7,2,1,5,4]=>9
[3,7,8,6,2,1,5,4]=>10
[8,7,6,3,5,2,4,1]=>3
[2,7,4,8,1,6,5,3]=>13
[4,6,8,2,1,7,5,3]=>12
[8,4,1,5,7,2,6,3]=>12
[8,5,3,7,1,6,2,4]=>9
[8,5,7,2,1,3,6,4]=>10
[8,2,6,7,1,3,5,4]=>11
[8,3,6,1,7,5,2,4]=>10
[4,6,1,8,7,2,5,3]=>13
[8,1,2,5,6,7,4,3]=>14
[8,2,6,5,7,4,1,3]=>8
[2,1,7,8,5,6,4,3]=>14
[8,2,5,7,6,4,3,1]=>7
[2,7,6,8,5,4,1,3]=>9
[1,7,2,5,8,6,4,3]=>15
[1,7,4,8,2,6,5,3]=>14
[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]=>4
[8,4,7,6,5,1,3,2]=>5
[8,7,1,5,6,4,3,2]=>6
[8,1,6,7,5,4,3,2]=>7
[5,4,3,6,1,2,8,7]=>16
[2,7,6,4,5,8,1,3]=>12
[5,7,3,6,1,8,2,4]=>12
[2,1,7,6,5,8,3,4]=>16
[6,4,3,5,8,1,7,2]=>12
[7,3,5,4,8,6,1,2]=>10
[5,4,3,2,7,1,8,6]=>15
[4,3,6,2,8,7,5,1]=>13
[4,3,7,6,2,1,8,5]=>14
[6,4,3,1,7,2,8,5]=>15
[4,3,7,1,8,6,5,2]=>13
[5,3,8,7,6,4,2,1]=>7
[7,5,3,1,8,6,4,2]=>10
[1,8,6,5,3,7,4,2]=>11
[6,1,7,5,3,2,8,4]=>14
[7,6,5,3,2,1,8,4]=>9
[6,5,3,2,8,7,4,1]=>10
[5,2,6,3,8,7,4,1]=>13
[5,2,7,6,3,1,8,4]=>14
[6,5,2,1,7,3,8,4]=>15
[5,2,7,1,8,6,4,3]=>13
[6,2,8,7,5,4,3,1]=>7
[7,6,2,1,8,5,4,3]=>10
[6,1,7,2,8,5,4,3]=>13
[7,1,8,6,5,4,3,2]=>7
[4,5,2,6,3,1,8,7]=>17
[6,5,2,1,4,3,8,7]=>16
[6,5,2,7,4,8,3,1]=>10
[8,5,2,7,4,1,6,3]=>9
[8,3,7,5,2,1,6,4]=>9
[6,3,7,5,2,8,4,1]=>10
[3,1,6,5,4,2,8,7]=>19
[5,6,3,2,4,1,8,7]=>15
[3,6,2,4,1,5,8,7]=>19
[2,6,1,3,5,4,8,7]=>21
[6,7,2,3,4,8,5,1]=>12
[8,7,2,3,4,1,6,5]=>11
[5,1,7,3,8,4,6,2]=>14
[2,5,7,3,8,6,4,1]=>13
[7,6,1,3,5,8,4,2]=>11
[3,6,7,4,1,8,5,2]=>13
[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]=>16
[5,8,3,7,4,2,6,1]=>8
[3,8,7,4,1,2,6,5]=>12
[7,8,1,3,5,2,6,4]=>12
[5,8,7,3,2,6,1,4]=>8
[2,8,6,3,1,5,7,4]=>14
[8,1,6,3,2,5,4,7]=>15
[2,8,4,1,6,3,7,5]=>16
[4,8,1,2,7,6,3,5]=>14
[3,8,4,2,5,7,1,6]=>14
[6,8,3,5,2,7,4,1]=>8
[2,1,5,3,8,7,6,4]=>19
[6,5,3,2,8,7,1,4]=>11
[7,5,2,4,8,1,6,3]=>11
[3,4,2,8,5,7,6,1]=>15
[2,4,1,8,7,6,5,3]=>15
[8,4,2,1,7,5,3,6]=>13
[4,3,1,8,6,7,5,2]=>14
[3,1,4,8,6,5,7,2]=>17
[7,1,6,5,4,8,2,3]=>11
[3,7,5,6,8,4,2,1]=>9
[5,7,1,6,8,2,4,3]=>12
[8,6,2,5,1,7,4,3]=>9
[5,6,2,1,8,7,3,4]=>14
[4,6,2,5,8,3,7,1]=>13
[7,5,2,6,3,8,1,4]=>11
[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]=>10
[5,6,2,8,4,3,1,7]=>12
[4,7,2,8,1,5,3,6]=>14
[8,7,2,1,4,5,6,3]=>11
[3,6,8,7,1,5,4,2]=>10
[5,7,8,6,3,4,1,2]=>6
[7,1,8,5,4,3,6,2]=>10
[2,7,8,4,5,3,6,1]=>11
[5,7,3,8,1,4,6,2]=>11
[2,1,7,8,5,4,6,3]=>15
[2,1,5,8,4,6,3,7]=>19
[6,5,3,8,4,1,2,7]=>11
[7,5,8,4,3,6,2,1]=>5
[2,4,8,3,5,6,1,7]=>17
[4,1,8,3,6,5,2,7]=>16
[3,4,8,1,7,2,5,6]=>16
[8,4,1,3,7,2,6,5]=>13
[3,1,8,2,4,7,6,5]=>18
[2,3,8,1,4,6,7,5]=>19
[4,3,8,2,5,1,7,6]=>15
[6,3,8,4,2,5,7,1]=>11
[7,4,3,8,2,5,1,6]=>11
[2,1,4,8,3,5,7,6]=>21
[6,8,2,4,3,5,1,7]=>12
[4,8,2,3,5,1,6,7]=>16
[3,8,2,1,4,6,5,7]=>18
[2,8,1,3,4,5,7,6]=>20
[7,1,6,8,4,3,2,5]=>11
[7,1,6,5,8,3,2,4]=>11
[3,7,6,1,4,8,2,5]=>14
[2,7,8,4,1,6,5,3]=>12
[3,6,4,5,7,2,8,1]=>14
[1,8,2,7,3,4,5,6]=>18
[3,2,1,5,8,4,6,7]=>21
[5,4,3,2,1,8,6,7]=>16
[1,8,2,4,3,5,6,7]=>21
[1,7,2,4,3,5,6,8]=>22
[1,6,2,4,3,5,7,8]=>23
[1,5,2,4,3,6,7,8]=>24
[1,6,2,5,3,4,7,8]=>22
[1,7,2,5,3,4,6,8]=>21
[1,8,2,5,3,4,6,7]=>20
[1,8,2,6,3,4,5,7]=>19
[1,7,2,6,3,4,5,8]=>20
[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]=>20
[1,4,2,8,3,6,5,7]=>21
[1,3,2,8,4,6,5,7]=>22
[1,2,3,8,4,6,5,7]=>23
[1,2,3,7,4,6,5,8]=>24
[1,3,2,7,4,6,5,8]=>23
[1,4,2,7,3,6,5,8]=>22
[1,5,2,7,3,6,4,8]=>21
[1,6,2,7,3,5,4,8]=>20
[1,7,2,6,3,5,4,8]=>19
[1,8,2,6,3,5,4,7]=>18
[1,8,2,5,3,6,4,7]=>19
[1,7,2,5,3,6,4,8]=>20
[1,6,2,5,3,7,4,8]=>21
[1,5,2,4,3,7,6,8]=>23
[1,6,2,4,3,7,5,8]=>22
[1,7,2,4,3,6,5,8]=>21
[1,8,2,4,3,6,5,7]=>20
[1,8,2,3,4,6,5,7]=>21
[1,7,2,3,4,6,5,8]=>22
[1,8,2,3,4,7,5,6]=>20
[1,8,2,4,3,7,5,6]=>19
[1,7,2,4,3,8,5,6]=>20
[1,6,2,4,3,8,5,7]=>21
[1,5,2,4,3,8,6,7]=>22
[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]=>17
[1,7,2,6,3,8,4,5]=>18
[1,2,3,8,4,7,5,6]=>22
[1,3,2,8,4,7,5,6]=>21
[1,4,2,8,3,7,5,6]=>20
[1,5,2,8,3,7,4,6]=>19
[1,6,2,8,3,7,4,5]=>18
[1,7,2,8,3,6,4,5]=>17
[1,8,2,7,3,6,4,5]=>16
[6,7,8,1,4,3,2,5]=>10
[2,8,4,1,6,7,5,3]=>14
[4,8,5,7,1,6,2,3]=>10
[8,7,6,5,2,1,4,3]=>4
[8,3,1,5,4,7,2,6]=>14
[8,7,6,5,1,4,2,3]=>4
[7,5,1,3,8,4,2,6]=>13
[7,6,1,4,8,3,2,5]=>11
[7,1,3,5,8,2,4,6]=>16
[7,5,3,6,4,2,8,1]=>9
[8,2,6,3,4,7,5,1]=>11
[7,2,6,3,5,4,8,1]=>12
[6,2,7,4,3,5,8,1]=>13
[3,7,6,4,5,2,8,1]=>11
[2,7,6,5,3,4,8,1]=>12
[8,6,5,4,2,7,3,1]=>5
[6,5,8,4,2,7,3,1]=>7
[1,8,6,3,7,5,2,4]=>12
[8,7,5,2,6,4,3,1]=>4
[8,7,1,6,2,5,4,3]=>8
[1,7,2,8,5,3,4,6]=>17
[7,6,1,8,4,3,2,5]=>10
[8,6,1,7,4,2,5,3]=>9
[8,1,2,7,3,4,6,5]=>16
[7,1,2,8,3,5,4,6]=>17
[8,2,6,1,7,3,5,4]=>12
[4,7,5,6,8,3,2,1]=>8
[8,6,4,7,5,3,2,1]=>3
[5,4,8,1,7,2,6,3]=>12
[2,3,8,7,4,5,6,1]=>14
[7,2,8,6,4,3,5,1]=>8
[8,2,7,6,3,5,4,1]=>7
[8,1,7,6,5,2,4,3]=>8
[7,1,8,6,5,3,2,4]=>9
[1,2,8,7,6,3,4,5]=>16
[3,8,7,6,4,5,2,1]=>6
[2,8,7,6,5,3,4,1]=>7
[1,8,7,6,5,4,2,3]=>8
[3,8,6,7,1,5,2,4]=>10
[5,4,7,1,3,8,2,6]=>14
[5,6,2,1,4,8,3,7]=>16
[2,1,8,4,7,5,6,3]=>16
[4,1,3,2,8,5,6,7]=>21
[3,2,1,4,8,5,6,7]=>22
[1,8,4,2,5,3,6,7]=>19
[8,1,5,3,2,4,6,7]=>17
[3,8,1,5,2,4,6,7]=>18
[1,6,7,2,8,4,3,5]=>16
[6,7,1,4,2,8,3,5]=>14
[6,3,7,1,4,8,2,5]=>14
[3,7,8,1,5,2,4,6]=>14
[7,1,2,8,5,3,4,6]=>16
[1,7,2,8,4,5,3,6]=>17
[1,2,7,5,8,3,4,6]=>19
[2,8,1,7,4,3,6,5]=>15
[4,2,6,5,8,3,7,1]=>14
[5,2,4,7,3,6,8,1]=>15
[5,1,2,4,8,3,6,7]=>20
[4,3,6,1,5,8,2,7]=>17
[2,6,1,4,5,8,3,7]=>19
[2,5,3,4,1,8,6,7]=>20
[4,3,5,2,1,8,6,7]=>18
[3,1,6,7,5,8,2,4]=>16
[2,8,1,7,5,6,3,4]=>13
[5,3,6,8,4,7,2,1]=>10
[3,7,2,5,4,8,6,1]=>14
[8,4,2,5,7,3,6,1]=>10
[4,7,2,5,8,3,6,1]=>12
[5,2,6,8,4,3,7,1]=>12
[3,1,6,5,4,8,2,7]=>18
[4,1,6,5,8,3,2,7]=>16
[5,1,6,8,4,3,2,7]=>14
[8,5,4,7,6,3,2,1]=>4
[5,7,1,8,4,3,2,6]=>12
[2,7,1,5,4,3,8,6]=>18
[8,2,1,5,4,3,7,6]=>16
[8,4,1,5,7,3,2,6]=>12
[8,5,6,7,1,3,2,4]=>8
[8,4,6,1,7,3,2,5]=>10
[8,3,6,1,4,7,2,5]=>12
[2,7,6,1,4,3,8,5]=>16
[6,7,8,5,1,3,2,4]=>8
[5,7,6,8,2,3,4,1]=>8
[5,7,2,8,4,3,6,1]=>10
[6,7,8,2,4,3,5,1]=>8
[4,7,6,2,8,3,5,1]=>10
[8,3,6,2,4,7,5,1]=>10
[3,7,6,2,4,8,5,1]=>12
[5,7,3,8,4,6,2,1]=>8
[4,7,3,5,8,6,2,1]=>10
[8,7,2,1,4,3,6,5]=>12
[8,7,3,1,4,6,2,5]=>10
[8,7,6,3,2,5,4,1]=>4
[8,7,3,5,1,6,2,4]=>8
[8,7,2,5,1,3,6,4]=>10
[8,2,6,5,1,3,7,4]=>12
[8,4,6,5,7,1,2,3]=>8
[5,7,6,8,4,1,2,3]=>8
[4,7,6,5,8,1,2,3]=>10
[3,7,6,5,1,8,2,4]=>12
[2,6,5,7,3,4,8,1]=>14
[1,6,4,7,5,8,2,3]=>15
[8,5,3,6,2,7,4,1]=>8
[1,3,7,4,6,8,2,5]=>18
[4,7,5,6,3,2,8,1]=>10
[1,7,6,5,4,8,2,3]=>12
[8,1,6,5,7,2,4,3]=>10
[1,2,7,6,8,3,4,5]=>18
[6,1,7,5,3,8,2,4]=>13
[2,1,7,5,6,8,3,4]=>17
[5,4,1,7,6,8,2,3]=>14
[4,8,5,6,2,7,3,1]=>9
[3,8,6,4,2,7,5,1]=>10
[7,8,5,2,4,6,3,1]=>6
[2,8,6,3,7,4,5,1]=>11
[7,8,1,6,2,4,5,3]=>10
[6,8,1,4,7,2,5,3]=>11
[3,8,4,1,7,2,6,5]=>14
[5,4,7,1,8,3,2,6]=>13
[3,7,4,1,8,5,2,6]=>15
[6,7,1,4,8,3,2,5]=>12
[2,7,1,8,4,5,3,6]=>16
[6,1,2,8,4,3,5,7]=>18
[6,5,1,4,3,8,2,7]=>14
[1,6,2,5,8,3,4,7]=>19
[8,5,1,3,7,2,6,4]=>12
[8,4,2,1,7,3,6,5]=>13
[7,4,2,1,8,5,3,6]=>14
[1,5,4,2,8,3,6,7]=>20
[6,4,3,1,5,8,2,7]=>15
[3,7,6,8,4,5,2,1]=>8
[2,7,6,8,5,3,4,1]=>9
[1,7,6,8,5,4,2,3]=>10
[1,4,8,6,7,5,2,3]=>13
[2,4,8,6,7,3,5,1]=>12
[7,3,8,5,4,6,2,1]=>7
[3,4,8,5,6,7,2,1]=>12
[6,3,5,8,4,7,2,1]=>9
[5,4,3,8,6,7,2,1]=>10
[5,4,2,8,7,3,6,1]=>11
[6,2,5,8,7,3,4,1]=>10
[3,2,8,5,7,4,6,1]=>13
[1,3,8,7,5,6,2,4]=>14
[2,1,8,7,4,6,3,5]=>15
[3,1,8,5,7,6,2,4]=>14
[6,1,5,8,7,4,2,3]=>11
[5,4,1,8,7,6,2,3]=>12
[5,8,6,7,4,3,2,1]=>4
[4,8,7,5,6,3,2,1]=>5
[2,8,3,1,5,4,6,7]=>19
[2,5,3,4,7,1,8,6]=>19
[2,4,8,3,5,7,6,1]=>15
[4,2,5,3,1,8,6,7]=>19
[4,2,1,8,5,3,6,7]=>19
[5,4,1,3,8,2,6,7]=>17
[5,1,4,8,3,2,6,7]=>17
[1,5,8,4,3,2,6,7]=>17
[1,8,5,4,3,2,6,7]=>16
[1,7,4,3,8,5,2,6]=>16
[1,5,7,3,8,4,2,6]=>16
[5,1,4,7,8,3,2,6]=>15
[4,8,1,5,7,3,6,2]=>12
[8,1,5,3,7,4,6,2]=>12
[3,8,4,7,6,5,2,1]=>8
[1,6,8,5,3,7,4,2]=>12
[6,8,1,7,4,3,5,2]=>9
[6,4,8,1,7,3,5,2]=>10
[6,4,8,7,1,5,2,3]=>9
[7,6,4,1,3,8,2,5]=>11
[1,7,5,6,3,2,8,4]=>15
[4,2,1,7,8,5,3,6]=>17
[2,7,4,6,3,1,8,5]=>15
[2,6,8,4,3,7,5,1]=>12
[6,2,4,8,3,7,5,1]=>12
[7,2,6,3,4,1,8,5]=>14
[2,6,7,3,1,4,8,5]=>17
[2,7,1,8,3,5,4,6]=>17
[2,1,7,3,5,8,4,6]=>20
[8,7,1,3,6,2,4,5]=>11
[8,2,1,7,3,5,6,4]=>14
[7,8,2,6,3,1,5,4]=>9
[8,7,2,6,3,5,4,1]=>6
[1,2,8,7,4,5,6,3]=>16
[8,3,7,1,5,6,2,4]=>10
[8,6,1,2,7,5,3,4]=>11
[8,1,6,2,7,4,5,3]=>12
[1,8,5,2,6,7,4,3]=>14
[5,2,1,8,6,7,4,3]=>14
[2,8,5,7,6,4,3,1]=>8
[1,7,8,5,2,6,4,3]=>12
[7,8,1,6,4,2,5,3]=>9
[7,8,6,1,5,3,2,4]=>7
[7,3,8,6,1,5,2,4]=>9
[8,7,6,1,5,3,4,2]=>5
[8,7,1,6,4,5,3,2]=>6
[8,1,7,5,6,4,3,2]=>7
[1,8,6,7,5,4,3,2]=>8
[9,1,2,3,4,5,6,7,8]=>28
[8,1,2,3,4,5,6,9,7]=>28
[2,9,1,3,4,5,6,7,8]=>28
[9,3,1,2,4,5,6,7,8]=>26
[8,9,1,2,3,4,5,6,7]=>22
[9,7,8,1,2,3,4,5,6]=>16
[2,3,4,5,6,7,9,1,8]=>28
[2,3,4,5,6,7,8,9,1]=>28
[2,3,4,5,6,7,8,1,9]=>29
[2,3,4,5,6,7,1,8,9]=>30
[1,2,3,4,5,6,7,9,8]=>35
[2,1,3,4,5,6,7,8,9]=>35
[1,8,2,3,4,5,6,9,7]=>29
[7,1,2,3,4,5,6,9,8]=>29
[2,1,9,3,4,5,6,7,8]=>29
[2,8,1,3,4,5,6,7,9]=>29
[1,2,3,4,5,6,7,8,9]=>36
[3,2,4,5,6,7,8,9,1]=>27
[9,8,7,6,5,4,3,2,1]=>0
[8,7,6,5,4,3,2,1,9]=>8
[1,9,8,7,6,5,4,3,2]=>8
[8,7,6,4,5,3,2,1,9]=>9
[1,9,8,7,5,6,4,3,2]=>9
[8,7,5,4,6,3,2,1,9]=>10
[8,7,4,6,5,3,2,1,9]=>10
[1,9,8,6,5,7,4,3,2]=>10
[1,9,8,5,7,6,4,3,2]=>10
[9,2,1,3,4,5,6,7,8]=>27
[9,2,3,1,4,5,6,7,8]=>26
[4,2,3,5,6,7,8,9,1]=>26
[3,4,2,5,6,7,8,9,1]=>26
[9,8,1,2,3,4,5,6,7]=>21
[7,8,9,1,2,3,4,5,6]=>18
[9,8,7,1,2,3,4,5,6]=>15
[6,7,8,9,1,2,3,4,5]=>16
[9,6,7,8,1,2,3,4,5]=>13
[8,9,6,7,1,2,3,4,5]=>12
[9,8,6,7,1,2,3,4,5]=>11
[9,8,7,6,1,2,3,4,5]=>10
[9,5,6,7,8,1,2,3,4]=>12
[8,9,5,6,7,1,2,3,4]=>10
[9,8,5,6,7,1,2,3,4]=>9
[9,7,8,5,6,1,2,3,4]=>8
[9,8,7,5,6,1,2,3,4]=>7
[9,8,7,6,5,1,2,3,4]=>6
[7,8,9,4,5,6,1,2,3]=>9
[9,7,8,4,5,6,1,2,3]=>7
[9,8,7,4,5,6,1,2,3]=>6
[8,9,6,7,4,5,1,2,3]=>6
[9,8,6,7,4,5,1,2,3]=>5
[9,8,7,6,4,5,1,2,3]=>4
[9,8,7,6,5,4,1,2,3]=>3
[9,7,8,5,6,3,4,1,2]=>4
[9,8,7,5,6,3,4,1,2]=>3
[9,8,7,6,5,3,4,1,2]=>2
[9,8,7,6,5,4,3,1,2]=>1
[7,8,6,5,4,3,2,1,9]=>9
[1,8,9,7,6,5,4,3,2]=>9
[7,6,8,5,4,3,2,1,9]=>10
[6,8,7,5,4,3,2,1,9]=>10
[1,8,7,9,6,5,4,3,2]=>10
[1,7,9,8,6,5,4,3,2]=>10
[8,1,2,3,4,5,6,7,9]=>29
[1,9,2,3,4,5,6,7,8]=>29
[7,8,1,2,3,4,5,6,9]=>24
[1,8,9,2,3,4,5,6,7]=>24
[7,1,8,2,3,4,5,6,9]=>25
[6,8,1,2,3,4,5,7,9]=>25
[1,8,2,9,3,4,5,6,7]=>25
[1,7,9,2,3,4,5,6,8]=>25
[7,1,2,3,4,5,6,8,9]=>30
[3,4,1,2,5,6,7,8,9]=>32
[3,2,1,4,5,6,7,8,9]=>33
[4,5,6,1,2,3,7,8,9]=>27
[4,2,5,1,3,6,7,8,9]=>30
[4,3,2,1,5,6,7,8,9]=>30
[5,6,7,8,1,2,3,4,9]=>20
[5,2,6,7,1,3,4,8,9]=>25
[5,6,3,4,1,2,7,8,9]=>24
[5,3,2,6,1,4,7,8,9]=>27
[5,4,3,2,1,6,7,8,9]=>26
[6,2,7,8,9,1,3,4,5]=>18
[6,7,3,4,8,1,2,5,9]=>19
[6,3,2,7,8,1,4,5,9]=>22
[6,4,7,2,5,1,3,8,9]=>21
[6,4,3,2,7,1,5,8,9]=>23
[6,5,4,3,2,1,7,8,9]=>21
[7,4,8,2,5,9,1,3,6]=>16
[7,4,3,2,8,9,1,5,6]=>18
[7,8,5,6,3,4,1,2,9]=>12
[7,5,3,8,2,6,1,4,9]=>17
[7,5,4,3,2,8,1,6,9]=>18
[7,6,5,4,3,2,1,8,9]=>15
[8,6,9,4,7,2,5,1,3]=>8
[8,6,4,3,9,2,7,1,5]=>12
[8,6,5,4,3,2,9,1,7]=>12
[2,1,4,3,6,5,8,7,10,9]=>40
[4,3,2,1,6,5,8,7,10,9]=>36
[6,3,2,5,4,1,8,7,10,9]=>32
[8,3,2,5,4,7,6,1,10,9]=>28
[10,3,2,5,4,7,6,9,8,1]=>24
[2,1,6,5,4,3,8,7,10,9]=>36
[6,5,4,3,2,1,8,7,10,9]=>28
[8,5,4,3,2,7,6,1,10,9]=>24
[10,5,4,3,2,7,6,9,8,1]=>20
[2,1,8,5,4,7,6,3,10,9]=>32
[8,7,4,3,6,5,2,1,10,9]=>20
[10,7,4,3,6,5,2,9,8,1]=>16
[2,1,10,5,4,7,6,9,8,3]=>28
[10,9,4,3,6,5,8,7,2,1]=>12
[8,9,5,6,3,4,10,1,2,7]=>16
[2,1,4,3,8,7,6,5,10,9]=>36
[4,3,2,1,8,7,6,5,10,9]=>32
[8,3,2,7,6,5,4,1,10,9]=>24
[10,3,2,7,6,5,4,9,8,1]=>20
[2,1,8,7,6,5,4,3,10,9]=>28
[8,7,6,5,4,3,2,1,10,9]=>16
[9,7,6,5,4,3,2,10,1,8]=>14
[10,7,6,5,4,3,2,9,8,1]=>12
[2,1,10,7,6,5,4,9,8,3]=>24
[10,9,6,5,4,3,8,7,2,1]=>8
[2,1,4,3,10,7,6,9,8,5]=>32
[4,3,2,1,10,7,6,9,8,5]=>28
[10,3,2,9,6,5,8,7,4,1]=>16
[2,1,10,9,6,5,8,7,4,3]=>20
[10,9,8,5,4,7,6,3,2,1]=>4
[6,7,8,9,10,1,2,3,4,5]=>20
[7,3,2,8,9,10,1,4,5,6]=>24
[8,5,4,3,2,9,10,1,6,7]=>22
[2,1,4,3,6,5,10,9,8,7]=>36
[4,3,2,1,6,5,10,9,8,7]=>32
[6,3,2,5,4,1,10,9,8,7]=>28
[10,3,2,5,4,9,8,7,6,1]=>20
[2,1,6,5,4,3,10,9,8,7]=>32
[6,5,4,3,2,1,10,9,8,7]=>24
[10,5,4,3,2,9,8,7,6,1]=>16
[2,1,10,5,4,9,8,7,6,3]=>24
[10,9,4,3,8,7,6,5,2,1]=>8
[9,7,5,10,3,8,2,6,1,4]=>12
[2,1,4,3,10,9,8,7,6,5]=>28
[4,3,2,1,10,9,8,7,6,5]=>24
[10,3,2,9,8,7,6,5,4,1]=>12
[2,1,10,9,8,7,6,5,4,3]=>16
[10,9,8,7,6,5,4,3,2,1]=>0
[2,3,4,5,6,7,8,9,10,1]=>36
[2,3,4,5,6,7,8,9,1,10]=>37
[10,8,9,5,6,7,1,2,3,4]=>10
[10,8,9,4,5,6,1,2,3,7]=>13
[10,7,8,5,6,9,1,2,3,4]=>12
[10,7,8,4,5,9,1,2,3,6]=>14
[10,6,7,4,5,8,1,2,3,9]=>17
[10,7,8,3,4,9,1,2,5,6]=>16
[10,6,7,3,4,8,1,2,5,9]=>19
[9,8,10,5,6,7,1,2,3,4]=>11
[9,8,10,4,5,6,1,2,3,7]=>14
[9,7,10,5,6,8,1,2,3,4]=>12
[9,7,10,4,5,8,1,2,3,6]=>14
[9,6,10,4,5,7,1,2,3,8]=>16
[9,7,10,3,4,8,1,2,5,6]=>16
[9,6,10,3,4,7,1,2,5,8]=>18
[8,7,9,5,6,10,1,2,3,4]=>14
[8,7,9,4,5,10,1,2,3,6]=>16
[8,6,9,4,5,10,1,2,3,7]=>17
[7,6,8,4,5,9,1,2,3,10]=>20
[8,7,9,3,4,10,1,2,5,6]=>18
[8,6,9,3,4,10,1,2,5,7]=>19
[7,6,8,3,4,9,1,2,5,10]=>22
[9,6,10,5,7,8,1,2,3,4]=>13
[9,6,10,4,7,8,1,2,3,5]=>14
[9,5,10,4,6,7,1,2,3,8]=>17
[9,6,10,3,7,8,1,2,4,5]=>15
[9,5,10,3,6,7,1,2,4,8]=>18
[8,6,9,5,7,10,1,2,3,4]=>15
[8,6,9,4,7,10,1,2,3,5]=>16
[8,5,9,4,6,10,1,2,3,7]=>18
[7,5,8,4,6,9,1,2,3,10]=>21
[8,6,9,3,7,10,1,2,4,5]=>17
[8,5,9,3,6,10,1,2,4,7]=>19
[7,5,8,3,6,9,1,2,4,10]=>22
[8,4,9,3,5,10,1,2,6,7]=>21
[7,4,8,3,5,9,1,2,6,10]=>24
[9,6,10,2,7,8,1,3,4,5]=>16
[9,5,10,2,6,7,1,3,4,8]=>19
[8,6,9,2,7,10,1,3,4,5]=>18
[8,5,9,2,6,10,1,3,4,7]=>20
[7,5,8,2,6,9,1,3,4,10]=>23
[8,4,9,2,5,10,1,3,6,7]=>22
[7,4,8,2,5,9,1,3,6,10]=>25
[1,2,3,4,5,6,7,8,10,9]=>44
[2,1,3,4,5,6,7,8,9,10]=>44
[9,1,2,3,4,5,6,7,10,8]=>36
[2,10,1,3,4,5,6,7,8,9]=>36
[1,2,3,4,5,6,7,8,9,10]=>45
[9,8,7,6,5,4,3,2,1,10]=>9
[10,1,2,3,4,5,6,7,8,9]=>36
[10,9,1,2,3,4,5,6,7,8]=>28
[1,10,9,8,7,6,5,4,3,2]=>9
[9,8,7,5,6,4,3,2,1,10]=>10
[1,10,9,8,6,7,5,4,3,2]=>10
[10,2,1,3,4,5,6,7,8,9]=>35
[3,2,4,5,6,7,8,9,10,1]=>35
[2,4,6,8,10,1,3,5,7,9]=>30
[2,4,6,9,10,1,3,5,7,8]=>29
[2,4,7,8,10,1,3,5,6,9]=>29
[2,4,7,9,10,1,3,5,6,8]=>28
[2,4,8,9,10,1,3,5,6,7]=>27
[2,5,6,8,10,1,3,4,7,9]=>29
[2,5,6,9,10,1,3,4,7,8]=>28
[2,5,7,8,10,1,3,4,6,9]=>28
[2,5,7,9,10,1,3,4,6,8]=>27
[2,5,8,9,10,1,3,4,6,7]=>26
[2,6,7,8,10,1,3,4,5,9]=>27
[2,6,7,9,10,1,3,4,5,8]=>26
[2,6,8,9,10,1,3,4,5,7]=>25
[2,7,8,9,10,1,3,4,5,6]=>24
[3,4,6,8,10,1,2,5,7,9]=>29
[3,4,6,9,10,1,2,5,7,8]=>28
[3,4,7,8,10,1,2,5,6,9]=>28
[3,4,7,9,10,1,2,5,6,8]=>27
[3,4,8,9,10,1,2,5,6,7]=>26
[3,5,6,8,10,1,2,4,7,9]=>28
[3,5,6,9,10,1,2,4,7,8]=>27
[3,5,7,8,10,1,2,4,6,9]=>27
[3,5,7,9,10,1,2,4,6,8]=>26
[3,5,8,9,10,1,2,4,6,7]=>25
[3,6,7,8,10,1,2,4,5,9]=>26
[3,6,7,9,10,1,2,4,5,8]=>25
[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]=>27
[4,5,6,9,10,1,2,3,7,8]=>26
[4,5,7,8,10,1,2,3,6,9]=>26
[4,5,7,9,10,1,2,3,6,8]=>25
[4,5,8,9,10,1,2,3,6,7]=>24
[4,6,7,8,10,1,2,3,5,9]=>25
[4,6,7,9,10,1,2,3,5,8]=>24
[4,6,8,9,10,1,2,3,5,7]=>23
[4,7,8,9,10,1,2,3,5,6]=>22
[5,6,7,8,10,1,2,3,4,9]=>24
[5,6,7,9,10,1,2,3,4,8]=>23
[5,6,8,9,10,1,2,3,4,7]=>22
[5,7,8,9,10,1,2,3,4,6]=>21
[9,10,1,2,3,4,5,6,7,8]=>29
[8,9,10,1,2,3,4,5,6,7]=>24
[10,8,9,1,2,3,4,5,6,7]=>22
[10,9,8,1,2,3,4,5,6,7]=>21
[7,8,9,10,1,2,3,4,5,6]=>21
[10,7,8,9,1,2,3,4,5,6]=>18
[9,10,7,8,1,2,3,4,5,6]=>17
[10,9,7,8,1,2,3,4,5,6]=>16
[10,9,8,7,1,2,3,4,5,6]=>15
[10,6,7,8,9,1,2,3,4,5]=>16
[9,10,6,7,8,1,2,3,4,5]=>14
[10,9,6,7,8,1,2,3,4,5]=>13
[10,8,9,6,7,1,2,3,4,5]=>12
[10,9,8,6,7,1,2,3,4,5]=>11
[10,9,8,7,6,1,2,3,4,5]=>10
[9,10,5,6,7,8,1,2,3,4]=>13
[10,9,5,6,7,8,1,2,3,4]=>12
[8,9,10,5,6,7,1,2,3,4]=>12
[10,9,8,5,6,7,1,2,3,4]=>9
[9,10,7,8,5,6,1,2,3,4]=>9
[10,9,7,8,5,6,1,2,3,4]=>8
[10,9,8,7,5,6,1,2,3,4]=>7
[10,9,8,7,6,5,1,2,3,4]=>6
[10,7,8,9,4,5,6,1,2,3]=>9
[9,10,7,8,4,5,6,1,2,3]=>8
[10,9,7,8,4,5,6,1,2,3]=>7
[10,9,8,7,4,5,6,1,2,3]=>6
[10,8,9,6,7,4,5,1,2,3]=>6
[10,9,8,6,7,4,5,1,2,3]=>5
[10,9,8,7,6,4,5,1,2,3]=>4
[10,9,8,7,6,5,4,1,2,3]=>3
[9,10,7,8,5,6,3,4,1,2]=>5
[10,9,7,8,5,6,3,4,1,2]=>4
[10,9,8,7,5,6,3,4,1,2]=>3
[10,9,8,7,6,5,3,4,1,2]=>2
[10,9,8,7,6,5,4,3,1,2]=>1
[8,9,7,6,5,4,3,2,1,10]=>10
[1,9,10,8,7,6,5,4,3,2]=>10
[9,1,2,3,4,5,6,7,8,10]=>37
[1,10,2,3,4,5,6,7,8,9]=>37
[8,9,1,2,3,4,5,6,7,10]=>31
[1,9,10,2,3,4,5,6,7,8]=>31
[3,4,1,2,5,6,7,8,9,10]=>41
[3,2,1,4,5,6,7,8,9,10]=>42
[4,5,6,1,2,3,7,8,9,10]=>36
[4,2,5,1,3,6,7,8,9,10]=>39
[4,3,2,1,5,6,7,8,9,10]=>39
[5,6,7,8,1,2,3,4,9,10]=>29
[5,2,6,7,1,3,4,8,9,10]=>34
[5,6,3,4,1,2,7,8,9,10]=>33
[5,3,2,6,1,4,7,8,9,10]=>36
[5,4,3,2,1,6,7,8,9,10]=>35
[6,2,7,8,9,1,3,4,5,10]=>27
[6,7,3,4,8,1,2,5,9,10]=>28
[6,3,2,7,8,1,4,5,9,10]=>31
[6,4,7,2,5,1,3,8,9,10]=>30
[6,4,3,2,7,1,5,8,9,10]=>32
[6,5,4,3,2,1,7,8,9,10]=>30
[7,8,3,4,9,10,1,2,5,6]=>21
[7,8,9,4,5,6,1,2,3,10]=>18
[7,4,3,2,8,9,1,5,6,10]=>27
[7,8,5,6,3,4,1,2,9,10]=>21
[7,5,3,8,2,6,1,4,9,10]=>26
[7,5,4,3,2,8,1,6,9,10]=>27
[7,6,5,4,3,2,1,8,9,10]=>24
[8,5,9,10,2,6,7,1,3,4]=>15
[8,5,3,9,2,6,10,1,4,7]=>21
[8,6,9,4,7,2,5,1,3,10]=>17
[8,6,4,3,9,2,7,1,5,10]=>21
[8,6,5,4,3,2,9,1,7,10]=>21
[8,7,6,5,4,3,2,1,9,10]=>17
[9,7,5,4,3,10,2,8,1,6]=>15
[1,2,3,4,5,6,7,8,9,11,10]=>54
[2,1,3,4,5,6,7,8,9,10,11]=>54
[11,1,2,3,4,5,6,7,8,9,10]=>45
[10,9,8,7,6,5,4,3,2,1,11]=>10
[1,11,10,9,8,7,6,5,4,3,2]=>10
[2,3,4,5,6,7,8,9,10,11,1]=>45
[10,1,2,3,4,5,6,7,8,9,11]=>46
[1,11,2,3,4,5,6,7,8,9,10]=>46
[2,1,4,3,6,5,8,7,12,11,10,9]=>56
[2,1,4,3,6,5,12,9,8,11,10,7]=>52
[2,1,4,3,6,5,12,11,10,9,8,7]=>48
[2,1,4,3,8,7,6,5,12,11,10,9]=>52
[2,1,4,3,12,7,6,9,8,11,10,5]=>48
[2,1,4,3,12,7,6,11,10,9,8,5]=>44
[2,1,4,3,10,9,8,7,6,5,12,11]=>48
[2,1,4,3,12,9,8,7,6,11,10,5]=>44
[2,1,4,3,12,11,8,7,10,9,6,5]=>40
[2,1,4,3,12,11,10,9,8,7,6,5]=>36
[2,1,6,5,4,3,8,7,12,11,10,9]=>52
[2,1,6,5,4,3,10,9,8,7,12,11]=>52
[2,1,6,5,4,3,12,9,8,11,10,7]=>48
[2,1,6,5,4,3,12,11,10,9,8,7]=>44
[2,1,8,5,4,7,6,3,12,11,10,9]=>48
[2,1,12,5,4,7,6,9,8,11,10,3]=>44
[2,1,12,5,4,7,6,11,10,9,8,3]=>40
[2,1,10,5,4,9,8,7,6,3,12,11]=>44
[2,1,12,5,4,9,8,7,6,11,10,3]=>40
[2,1,12,5,4,11,8,7,10,9,6,3]=>36
[2,1,12,5,4,11,10,9,8,7,6,3]=>32
[2,1,8,7,6,5,4,3,10,9,12,11]=>48
[2,1,8,7,6,5,4,3,12,11,10,9]=>44
[2,1,12,7,6,5,4,9,8,11,10,3]=>40
[2,1,12,7,6,5,4,11,10,9,8,3]=>36
[2,1,10,9,6,5,8,7,4,3,12,11]=>40
[2,1,12,9,6,5,8,7,4,11,10,3]=>36
[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]=>28
[2,1,10,9,8,7,6,5,4,3,12,11]=>36
[2,1,12,9,8,7,6,5,4,11,10,3]=>32
[2,1,12,11,8,7,6,5,10,9,4,3]=>28
[2,1,12,11,10,7,6,9,8,5,4,3]=>24
[2,1,12,11,10,9,8,7,6,5,4,3]=>20
[4,3,2,1,6,5,8,7,10,9,12,11]=>56
[4,3,2,1,6,5,8,7,12,11,10,9]=>52
[4,3,2,1,6,5,10,9,8,7,12,11]=>52
[4,3,2,1,6,5,12,9,8,11,10,7]=>48
[4,3,2,1,6,5,12,11,10,9,8,7]=>44
[4,3,2,1,8,7,6,5,10,9,12,11]=>52
[4,3,2,1,8,7,6,5,12,11,10,9]=>48
[4,3,2,1,10,7,6,9,8,5,12,11]=>48
[4,3,2,1,12,7,6,9,8,11,10,5]=>44
[4,3,2,1,12,7,6,11,10,9,8,5]=>40
[4,3,2,1,10,9,8,7,6,5,12,11]=>44
[4,3,2,1,12,9,8,7,6,11,10,5]=>40
[4,3,2,1,12,11,8,7,10,9,6,5]=>36
[4,3,2,1,12,11,10,9,8,7,6,5]=>32
[6,3,2,5,4,1,8,7,10,9,12,11]=>52
[6,3,2,5,4,1,8,7,12,11,10,9]=>48
[6,3,2,5,4,1,10,9,8,7,12,11]=>48
[6,3,2,5,4,1,12,9,8,11,10,7]=>44
[6,3,2,5,4,1,12,11,10,9,8,7]=>40
[8,3,2,5,4,7,6,1,10,9,12,11]=>48
[8,3,2,5,4,7,6,1,12,11,10,9]=>44
[10,3,2,5,4,7,6,9,8,1,12,11]=>44
[12,3,2,5,4,7,6,9,8,11,10,1]=>40
[12,3,2,5,4,7,6,11,10,9,8,1]=>36
[10,3,2,5,4,9,8,7,6,1,12,11]=>40
[12,3,2,5,4,9,8,7,6,11,10,1]=>36
[12,3,2,5,4,11,8,7,10,9,6,1]=>32
[12,3,2,5,4,11,10,9,8,7,6,1]=>28
[8,3,2,7,6,5,4,1,10,9,12,11]=>44
[8,3,2,7,6,5,4,1,12,11,10,9]=>40
[10,3,2,7,6,5,4,9,8,1,12,11]=>40
[12,3,2,7,6,5,4,9,8,11,10,1]=>36
[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]=>36
[12,3,2,9,6,5,8,7,4,11,10,1]=>32
[12,3,2,11,6,5,8,7,10,9,4,1]=>28
[12,3,2,11,6,5,10,9,8,7,4,1]=>24
[10,3,2,9,8,7,6,5,4,1,12,11]=>32
[12,3,2,9,8,7,6,5,4,11,10,1]=>28
[12,3,2,11,8,7,6,5,10,9,4,1]=>24
[6,5,4,3,2,1,8,7,10,9,12,11]=>48
[6,5,4,3,2,1,8,7,12,11,10,9]=>44
[6,5,4,3,2,1,10,9,8,7,12,11]=>44
[6,5,4,3,2,1,12,9,8,11,10,7]=>40
[6,5,4,3,2,1,12,11,10,9,8,7]=>36
[8,5,4,3,2,7,6,1,12,11,10,9]=>40
[10,5,4,3,2,7,6,9,8,1,12,11]=>40
[12,5,4,3,2,7,6,9,8,11,10,1]=>36
[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]=>36
[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]=>28
[8,7,4,3,6,5,2,1,10,9,12,11]=>40
[8,7,4,3,6,5,2,1,12,11,10,9]=>36
[10,7,4,3,6,5,2,9,8,1,12,11]=>36
[12,7,4,3,6,5,2,9,8,11,10,1]=>32
[12,7,4,3,6,5,2,11,10,9,8,1]=>28
[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]=>28
[12,11,4,3,6,5,8,7,10,9,2,1]=>24
[10,9,4,3,8,7,6,5,2,1,12,11]=>28
[12,9,4,3,8,7,6,5,2,11,10,1]=>24
[8,7,6,5,4,3,2,1,10,9,12,11]=>36
[8,7,6,5,4,3,2,1,12,11,10,9]=>32
[10,7,6,5,4,3,2,9,8,1,12,11]=>32
[12,7,6,5,4,3,2,9,8,11,10,1]=>28
[10,9,6,5,4,3,8,7,2,1,12,11]=>28
[12,9,6,5,4,3,8,7,2,11,10,1]=>24
[12,11,6,5,4,3,8,7,10,9,2,1]=>20
[10,9,8,5,4,7,6,3,2,1,12,11]=>24
[10,9,8,7,6,5,4,3,2,1,12,11]=>20
[2,4,6,8,10,12,1,3,5,7,9,11]=>45
[2,4,6,8,11,12,1,3,5,7,9,10]=>44
[2,4,6,9,10,12,1,3,5,7,8,11]=>44
[2,4,6,9,11,12,1,3,5,7,8,10]=>43
[2,4,6,10,11,12,1,3,5,7,8,9]=>42
[2,4,7,8,10,12,1,3,5,6,9,11]=>44
[2,4,7,8,11,12,1,3,5,6,9,10]=>43
[2,4,7,9,10,12,1,3,5,6,8,11]=>43
[2,4,7,9,11,12,1,3,5,6,8,10]=>42
[2,4,7,10,11,12,1,3,5,6,8,9]=>41
[2,4,8,9,10,12,1,3,5,6,7,11]=>42
[2,4,8,9,11,12,1,3,5,6,7,10]=>41
[2,4,8,10,11,12,1,3,5,6,7,9]=>40
[2,4,9,10,11,12,1,3,5,6,7,8]=>39
[2,5,6,8,10,12,1,3,4,7,9,11]=>44
[2,5,6,8,11,12,1,3,4,7,9,10]=>43
[2,5,6,9,10,12,1,3,4,7,8,11]=>43
[2,5,6,9,11,12,1,3,4,7,8,10]=>42
[2,5,6,10,11,12,1,3,4,7,8,9]=>41
[2,5,7,8,10,12,1,3,4,6,9,11]=>43
[2,5,7,8,11,12,1,3,4,6,9,10]=>42
[2,5,7,9,11,12,1,3,4,6,8,10]=>41
[2,5,7,10,11,12,1,3,4,6,8,9]=>40
[2,5,8,9,10,12,1,3,4,6,7,11]=>41
[2,5,8,9,11,12,1,3,4,6,7,10]=>40
[2,5,8,10,11,12,1,3,4,6,7,9]=>39
[2,5,9,10,11,12,1,3,4,6,7,8]=>38
[2,6,7,8,10,12,1,3,4,5,9,11]=>42
[2,6,7,8,11,12,1,3,4,5,9,10]=>41
[2,6,7,9,10,12,1,3,4,5,8,11]=>41
[2,6,7,9,11,12,1,3,4,5,8,10]=>40
[2,6,7,10,11,12,1,3,4,5,8,9]=>39
[2,6,8,9,10,12,1,3,4,5,7,11]=>40
[2,6,8,9,11,12,1,3,4,5,7,10]=>39
[2,6,8,10,11,12,1,3,4,5,7,9]=>38
[2,6,9,10,11,12,1,3,4,5,7,8]=>37
[2,7,8,9,10,12,1,3,4,5,6,11]=>39
[2,7,8,9,11,12,1,3,4,5,6,10]=>38
[2,7,8,10,11,12,1,3,4,5,6,9]=>37
[2,7,9,10,11,12,1,3,4,5,6,8]=>36
[2,8,9,10,11,12,1,3,4,5,6,7]=>35
[3,4,6,8,10,12,1,2,5,7,9,11]=>44
[3,4,6,8,11,12,1,2,5,7,9,10]=>43
[3,4,6,9,10,12,1,2,5,7,8,11]=>43
[3,4,6,9,11,12,1,2,5,7,8,10]=>42
[3,4,6,10,11,12,1,2,5,7,8,9]=>41
[3,4,7,8,10,12,1,2,5,6,9,11]=>43
[3,4,7,8,11,12,1,2,5,6,9,10]=>42
[3,4,7,9,10,12,1,2,5,6,8,11]=>42
[3,4,7,9,11,12,1,2,5,6,8,10]=>41
[3,4,7,10,11,12,1,2,5,6,8,9]=>40
[3,4,8,9,10,12,1,2,5,6,7,11]=>41
[3,4,8,9,11,12,1,2,5,6,7,10]=>40
[3,4,8,10,11,12,1,2,5,6,7,9]=>39
[3,4,9,10,11,12,1,2,5,6,7,8]=>38
[3,5,6,8,10,12,1,2,4,7,9,11]=>43
[3,5,6,8,11,12,1,2,4,7,9,10]=>42
[3,5,6,9,10,12,1,2,4,7,8,11]=>42
[3,5,6,9,11,12,1,2,4,7,8,10]=>41
[3,5,6,10,11,12,1,2,4,7,8,9]=>40
[3,5,7,8,10,12,1,2,4,6,9,11]=>42
[3,5,7,8,11,12,1,2,4,6,9,10]=>41
[3,5,7,9,10,12,1,2,4,6,8,11]=>41
[3,5,7,9,11,12,1,2,4,6,8,10]=>40
[3,5,7,10,11,12,1,2,4,6,8,9]=>39
[3,5,8,9,10,12,1,2,4,6,7,11]=>40
[3,5,8,9,11,12,1,2,4,6,7,10]=>39
[3,5,8,10,11,12,1,2,4,6,7,9]=>38
[3,5,9,10,11,12,1,2,4,6,7,8]=>37
[3,6,7,8,10,12,1,2,4,5,9,11]=>41
[3,6,7,8,11,12,1,2,4,5,9,10]=>40
[3,6,7,9,10,12,1,2,4,5,8,11]=>40
[3,6,7,9,11,12,1,2,4,5,8,10]=>39
[3,6,7,10,11,12,1,2,4,5,8,9]=>38
[3,6,8,9,10,12,1,2,4,5,7,11]=>39
[3,6,8,9,11,12,1,2,4,5,7,10]=>38
[3,6,8,10,11,12,1,2,4,5,7,9]=>37
[3,6,9,10,11,12,1,2,4,5,7,8]=>36
[3,7,8,9,10,12,1,2,4,5,6,11]=>38
[3,7,8,9,11,12,1,2,4,5,6,10]=>37
[3,7,8,10,11,12,1,2,4,5,6,9]=>36
[3,7,9,10,11,12,1,2,4,5,6,8]=>35
[3,8,9,10,11,12,1,2,4,5,6,7]=>34
[4,5,6,8,10,12,1,2,3,7,9,11]=>42
[4,5,6,8,11,12,1,2,3,7,9,10]=>41
[4,5,6,9,10,12,1,2,3,7,8,11]=>41
[4,5,6,9,11,12,1,2,3,7,8,10]=>40
[4,5,6,10,11,12,1,2,3,7,8,9]=>39
[4,5,7,8,10,12,1,2,3,6,9,11]=>41
[4,5,7,8,11,12,1,2,3,6,9,10]=>40
[4,5,7,9,10,12,1,2,3,6,8,11]=>40
[4,5,7,9,11,12,1,2,3,6,8,10]=>39
[4,5,7,10,11,12,1,2,3,6,8,9]=>38
[4,5,8,9,10,12,1,2,3,6,7,11]=>39
[4,5,8,9,11,12,1,2,3,6,7,10]=>38
[4,5,8,10,11,12,1,2,3,6,7,9]=>37
[4,5,9,10,11,12,1,2,3,6,7,8]=>36
[4,6,7,8,10,12,1,2,3,5,9,11]=>40
[4,6,7,8,11,12,1,2,3,5,9,10]=>39
[4,6,7,9,10,12,1,2,3,5,8,11]=>39
[4,6,7,9,11,12,1,2,3,5,8,10]=>38
[4,6,7,10,11,12,1,2,3,5,8,9]=>37
[4,6,8,9,10,12,1,2,3,5,7,11]=>38
[4,6,8,9,11,12,1,2,3,5,7,10]=>37
[4,6,8,10,11,12,1,2,3,5,7,9]=>36
[4,6,9,10,11,12,1,2,3,5,7,8]=>35
[4,7,8,9,10,12,1,2,3,5,6,11]=>37
[4,7,8,9,11,12,1,2,3,5,6,10]=>36
[4,7,8,10,11,12,1,2,3,5,6,9]=>35
[4,7,9,10,11,12,1,2,3,5,6,8]=>34
[4,8,9,10,11,12,1,2,3,5,6,7]=>33
[5,6,7,8,10,12,1,2,3,4,9,11]=>39
[5,6,7,8,11,12,1,2,3,4,9,10]=>38
[5,6,7,9,10,12,1,2,3,4,8,11]=>38
[5,6,7,9,11,12,1,2,3,4,8,10]=>37
[5,6,7,10,11,12,1,2,3,4,8,9]=>36
[5,6,8,9,10,12,1,2,3,4,7,11]=>37
[5,6,8,9,11,12,1,2,3,4,7,10]=>36
[5,6,8,10,11,12,1,2,3,4,7,9]=>35
[5,6,9,10,11,12,1,2,3,4,7,8]=>34
[5,7,8,9,10,12,1,2,3,4,6,11]=>36
[5,7,8,9,11,12,1,2,3,4,6,10]=>35
[5,7,8,10,11,12,1,2,3,4,6,9]=>34
[5,7,9,10,11,12,1,2,3,4,6,8]=>33
[5,8,9,10,11,12,1,2,3,4,6,7]=>32
[6,7,8,9,10,12,1,2,3,4,5,11]=>35
[6,7,8,9,11,12,1,2,3,4,5,10]=>34
[6,7,8,10,11,12,1,2,3,4,5,9]=>33
[6,7,9,10,11,12,1,2,3,4,5,8]=>32
[6,8,9,10,11,12,1,2,3,4,5,7]=>31
[7,8,9,10,11,12,1,2,3,4,5,6]=>30
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of non-inversions of a permutation.
For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
References
[1] Reiner, V., Saliola, F., Welker, V. Spectra of Symmetrized Shuffling Operators arXiv:1102.2460
[2] The number of inversions of a permutation. St000018
[2] The number of inversions of a permutation. St000018
Code
def statistic(pi):
return binomial(len(pi),2)-pi.number_of_inversions()
Created
Feb 27, 2015 at 10:43 by Christian Stump
Updated
Jan 11, 2018 at 21:35 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!