Identifier
- St000018: Permutations ⟶ ℤ
Values
=>
[]=>0
[1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>3
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>2
[1,4,2,3]=>2
[1,4,3,2]=>3
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>2
[2,3,4,1]=>3
[2,4,1,3]=>3
[2,4,3,1]=>4
[3,1,2,4]=>2
[3,1,4,2]=>3
[3,2,1,4]=>3
[3,2,4,1]=>4
[3,4,1,2]=>4
[3,4,2,1]=>5
[4,1,2,3]=>3
[4,1,3,2]=>4
[4,2,1,3]=>4
[4,2,3,1]=>5
[4,3,1,2]=>5
[4,3,2,1]=>6
[1,2,3,4,5]=>0
[1,2,3,5,4]=>1
[1,2,4,3,5]=>1
[1,2,4,5,3]=>2
[1,2,5,3,4]=>2
[1,2,5,4,3]=>3
[1,3,2,4,5]=>1
[1,3,2,5,4]=>2
[1,3,4,2,5]=>2
[1,3,4,5,2]=>3
[1,3,5,2,4]=>3
[1,3,5,4,2]=>4
[1,4,2,3,5]=>2
[1,4,2,5,3]=>3
[1,4,3,2,5]=>3
[1,4,3,5,2]=>4
[1,4,5,2,3]=>4
[1,4,5,3,2]=>5
[1,5,2,3,4]=>3
[1,5,2,4,3]=>4
[1,5,3,2,4]=>4
[1,5,3,4,2]=>5
[1,5,4,2,3]=>5
[1,5,4,3,2]=>6
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>3
[2,1,5,3,4]=>3
[2,1,5,4,3]=>4
[2,3,1,4,5]=>2
[2,3,1,5,4]=>3
[2,3,4,1,5]=>3
[2,3,4,5,1]=>4
[2,3,5,1,4]=>4
[2,3,5,4,1]=>5
[2,4,1,3,5]=>3
[2,4,1,5,3]=>4
[2,4,3,1,5]=>4
[2,4,3,5,1]=>5
[2,4,5,1,3]=>5
[2,4,5,3,1]=>6
[2,5,1,3,4]=>4
[2,5,1,4,3]=>5
[2,5,3,1,4]=>5
[2,5,3,4,1]=>6
[2,5,4,1,3]=>6
[2,5,4,3,1]=>7
[3,1,2,4,5]=>2
[3,1,2,5,4]=>3
[3,1,4,2,5]=>3
[3,1,4,5,2]=>4
[3,1,5,2,4]=>4
[3,1,5,4,2]=>5
[3,2,1,4,5]=>3
[3,2,1,5,4]=>4
[3,2,4,1,5]=>4
[3,2,4,5,1]=>5
[3,2,5,1,4]=>5
[3,2,5,4,1]=>6
[3,4,1,2,5]=>4
[3,4,1,5,2]=>5
[3,4,2,1,5]=>5
[3,4,2,5,1]=>6
[3,4,5,1,2]=>6
[3,4,5,2,1]=>7
[3,5,1,2,4]=>5
[3,5,1,4,2]=>6
[3,5,2,1,4]=>6
[3,5,2,4,1]=>7
[3,5,4,1,2]=>7
[3,5,4,2,1]=>8
[4,1,2,3,5]=>3
[4,1,2,5,3]=>4
[4,1,3,2,5]=>4
[4,1,3,5,2]=>5
[4,1,5,2,3]=>5
[4,1,5,3,2]=>6
[4,2,1,3,5]=>4
[4,2,1,5,3]=>5
[4,2,3,1,5]=>5
[4,2,3,5,1]=>6
[4,2,5,1,3]=>6
[4,2,5,3,1]=>7
[4,3,1,2,5]=>5
[4,3,1,5,2]=>6
[4,3,2,1,5]=>6
[4,3,2,5,1]=>7
[4,3,5,1,2]=>7
[4,3,5,2,1]=>8
[4,5,1,2,3]=>6
[4,5,1,3,2]=>7
[4,5,2,1,3]=>7
[4,5,2,3,1]=>8
[4,5,3,1,2]=>8
[4,5,3,2,1]=>9
[5,1,2,3,4]=>4
[5,1,2,4,3]=>5
[5,1,3,2,4]=>5
[5,1,3,4,2]=>6
[5,1,4,2,3]=>6
[5,1,4,3,2]=>7
[5,2,1,3,4]=>5
[5,2,1,4,3]=>6
[5,2,3,1,4]=>6
[5,2,3,4,1]=>7
[5,2,4,1,3]=>7
[5,2,4,3,1]=>8
[5,3,1,2,4]=>6
[5,3,1,4,2]=>7
[5,3,2,1,4]=>7
[5,3,2,4,1]=>8
[5,3,4,1,2]=>8
[5,3,4,2,1]=>9
[5,4,1,2,3]=>7
[5,4,1,3,2]=>8
[5,4,2,1,3]=>8
[5,4,2,3,1]=>9
[5,4,3,1,2]=>9
[5,4,3,2,1]=>10
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>3
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>2
[1,2,4,5,6,3]=>3
[1,2,4,6,3,5]=>3
[1,2,4,6,5,3]=>4
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>3
[1,2,5,4,3,6]=>3
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>4
[1,2,6,4,5,3]=>5
[1,2,6,5,3,4]=>5
[1,2,6,5,4,3]=>6
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>3
[1,3,2,6,4,5]=>3
[1,3,2,6,5,4]=>4
[1,3,4,2,5,6]=>2
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>4
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>5
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>4
[1,3,5,4,6,2]=>5
[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>6
[1,3,6,2,4,5]=>4
[1,3,6,2,5,4]=>5
[1,3,6,4,2,5]=>5
[1,3,6,4,5,2]=>6
[1,3,6,5,2,4]=>6
[1,3,6,5,4,2]=>7
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>3
[1,4,2,5,3,6]=>3
[1,4,2,5,6,3]=>4
[1,4,2,6,3,5]=>4
[1,4,2,6,5,3]=>5
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>4
[1,4,3,5,2,6]=>4
[1,4,3,5,6,2]=>5
[1,4,3,6,2,5]=>5
[1,4,3,6,5,2]=>6
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>6
[1,4,5,6,2,3]=>6
[1,4,5,6,3,2]=>7
[1,4,6,2,3,5]=>5
[1,4,6,2,5,3]=>6
[1,4,6,3,2,5]=>6
[1,4,6,3,5,2]=>7
[1,4,6,5,2,3]=>7
[1,4,6,5,3,2]=>8
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>4
[1,5,2,4,6,3]=>5
[1,5,2,6,3,4]=>5
[1,5,2,6,4,3]=>6
[1,5,3,2,4,6]=>4
[1,5,3,2,6,4]=>5
[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>6
[1,5,3,6,2,4]=>6
[1,5,3,6,4,2]=>7
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>6
[1,5,4,3,2,6]=>6
[1,5,4,3,6,2]=>7
[1,5,4,6,2,3]=>7
[1,5,4,6,3,2]=>8
[1,5,6,2,3,4]=>6
[1,5,6,2,4,3]=>7
[1,5,6,3,2,4]=>7
[1,5,6,3,4,2]=>8
[1,5,6,4,2,3]=>8
[1,5,6,4,3,2]=>9
[1,6,2,3,4,5]=>4
[1,6,2,3,5,4]=>5
[1,6,2,4,3,5]=>5
[1,6,2,4,5,3]=>6
[1,6,2,5,3,4]=>6
[1,6,2,5,4,3]=>7
[1,6,3,2,4,5]=>5
[1,6,3,2,5,4]=>6
[1,6,3,4,2,5]=>6
[1,6,3,4,5,2]=>7
[1,6,3,5,2,4]=>7
[1,6,3,5,4,2]=>8
[1,6,4,2,3,5]=>6
[1,6,4,2,5,3]=>7
[1,6,4,3,2,5]=>7
[1,6,4,3,5,2]=>8
[1,6,4,5,2,3]=>8
[1,6,4,5,3,2]=>9
[1,6,5,2,3,4]=>7
[1,6,5,2,4,3]=>8
[1,6,5,3,2,4]=>8
[1,6,5,3,4,2]=>9
[1,6,5,4,2,3]=>9
[1,6,5,4,3,2]=>10
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>3
[2,1,3,6,5,4]=>4
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>4
[2,1,4,6,3,5]=>4
[2,1,4,6,5,3]=>5
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>4
[2,1,5,4,3,6]=>4
[2,1,5,4,6,3]=>5
[2,1,5,6,3,4]=>5
[2,1,5,6,4,3]=>6
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>5
[2,1,6,4,3,5]=>5
[2,1,6,4,5,3]=>6
[2,1,6,5,3,4]=>6
[2,1,6,5,4,3]=>7
[2,3,1,4,5,6]=>2
[2,3,1,4,6,5]=>3
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>4
[2,3,1,6,4,5]=>4
[2,3,1,6,5,4]=>5
[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>4
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>5
[2,3,4,6,5,1]=>6
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>5
[2,3,5,4,6,1]=>6
[2,3,5,6,1,4]=>6
[2,3,5,6,4,1]=>7
[2,3,6,1,4,5]=>5
[2,3,6,1,5,4]=>6
[2,3,6,4,1,5]=>6
[2,3,6,4,5,1]=>7
[2,3,6,5,1,4]=>7
[2,3,6,5,4,1]=>8
[2,4,1,3,5,6]=>3
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>4
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>5
[2,4,1,6,5,3]=>6
[2,4,3,1,5,6]=>4
[2,4,3,1,6,5]=>5
[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>6
[2,4,3,6,1,5]=>6
[2,4,3,6,5,1]=>7
[2,4,5,1,3,6]=>5
[2,4,5,1,6,3]=>6
[2,4,5,3,1,6]=>6
[2,4,5,3,6,1]=>7
[2,4,5,6,1,3]=>7
[2,4,5,6,3,1]=>8
[2,4,6,1,3,5]=>6
[2,4,6,1,5,3]=>7
[2,4,6,3,1,5]=>7
[2,4,6,3,5,1]=>8
[2,4,6,5,1,3]=>8
[2,4,6,5,3,1]=>9
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>5
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>6
[2,5,1,6,3,4]=>6
[2,5,1,6,4,3]=>7
[2,5,3,1,4,6]=>5
[2,5,3,1,6,4]=>6
[2,5,3,4,1,6]=>6
[2,5,3,4,6,1]=>7
[2,5,3,6,1,4]=>7
[2,5,3,6,4,1]=>8
[2,5,4,1,3,6]=>6
[2,5,4,1,6,3]=>7
[2,5,4,3,1,6]=>7
[2,5,4,3,6,1]=>8
[2,5,4,6,1,3]=>8
[2,5,4,6,3,1]=>9
[2,5,6,1,3,4]=>7
[2,5,6,1,4,3]=>8
[2,5,6,3,1,4]=>8
[2,5,6,3,4,1]=>9
[2,5,6,4,1,3]=>9
[2,5,6,4,3,1]=>10
[2,6,1,3,4,5]=>5
[2,6,1,3,5,4]=>6
[2,6,1,4,3,5]=>6
[2,6,1,4,5,3]=>7
[2,6,1,5,3,4]=>7
[2,6,1,5,4,3]=>8
[2,6,3,1,4,5]=>6
[2,6,3,1,5,4]=>7
[2,6,3,4,1,5]=>7
[2,6,3,4,5,1]=>8
[2,6,3,5,1,4]=>8
[2,6,3,5,4,1]=>9
[2,6,4,1,3,5]=>7
[2,6,4,1,5,3]=>8
[2,6,4,3,1,5]=>8
[2,6,4,3,5,1]=>9
[2,6,4,5,1,3]=>9
[2,6,4,5,3,1]=>10
[2,6,5,1,3,4]=>8
[2,6,5,1,4,3]=>9
[2,6,5,3,1,4]=>9
[2,6,5,3,4,1]=>10
[2,6,5,4,1,3]=>10
[2,6,5,4,3,1]=>11
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>3
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>4
[3,1,2,6,5,4]=>5
[3,1,4,2,5,6]=>3
[3,1,4,2,6,5]=>4
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>5
[3,1,4,6,2,5]=>5
[3,1,4,6,5,2]=>6
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>5
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>6
[3,1,5,6,2,4]=>6
[3,1,5,6,4,2]=>7
[3,1,6,2,4,5]=>5
[3,1,6,2,5,4]=>6
[3,1,6,4,2,5]=>6
[3,1,6,4,5,2]=>7
[3,1,6,5,2,4]=>7
[3,1,6,5,4,2]=>8
[3,2,1,4,5,6]=>3
[3,2,1,4,6,5]=>4
[3,2,1,5,4,6]=>4
[3,2,1,5,6,4]=>5
[3,2,1,6,4,5]=>5
[3,2,1,6,5,4]=>6
[3,2,4,1,5,6]=>4
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>5
[3,2,4,5,6,1]=>6
[3,2,4,6,1,5]=>6
[3,2,4,6,5,1]=>7
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>6
[3,2,5,4,1,6]=>6
[3,2,5,4,6,1]=>7
[3,2,5,6,1,4]=>7
[3,2,5,6,4,1]=>8
[3,2,6,1,4,5]=>6
[3,2,6,1,5,4]=>7
[3,2,6,4,1,5]=>7
[3,2,6,4,5,1]=>8
[3,2,6,5,1,4]=>8
[3,2,6,5,4,1]=>9
[3,4,1,2,5,6]=>4
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>6
[3,4,1,6,2,5]=>6
[3,4,1,6,5,2]=>7
[3,4,2,1,5,6]=>5
[3,4,2,1,6,5]=>6
[3,4,2,5,1,6]=>6
[3,4,2,5,6,1]=>7
[3,4,2,6,1,5]=>7
[3,4,2,6,5,1]=>8
[3,4,5,1,2,6]=>6
[3,4,5,1,6,2]=>7
[3,4,5,2,1,6]=>7
[3,4,5,2,6,1]=>8
[3,4,5,6,1,2]=>8
[3,4,5,6,2,1]=>9
[3,4,6,1,2,5]=>7
[3,4,6,1,5,2]=>8
[3,4,6,2,1,5]=>8
[3,4,6,2,5,1]=>9
[3,4,6,5,1,2]=>9
[3,4,6,5,2,1]=>10
[3,5,1,2,4,6]=>5
[3,5,1,2,6,4]=>6
[3,5,1,4,2,6]=>6
[3,5,1,4,6,2]=>7
[3,5,1,6,2,4]=>7
[3,5,1,6,4,2]=>8
[3,5,2,1,4,6]=>6
[3,5,2,1,6,4]=>7
[3,5,2,4,1,6]=>7
[3,5,2,4,6,1]=>8
[3,5,2,6,1,4]=>8
[3,5,2,6,4,1]=>9
[3,5,4,1,2,6]=>7
[3,5,4,1,6,2]=>8
[3,5,4,2,1,6]=>8
[3,5,4,2,6,1]=>9
[3,5,4,6,1,2]=>9
[3,5,4,6,2,1]=>10
[3,5,6,1,2,4]=>8
[3,5,6,1,4,2]=>9
[3,5,6,2,1,4]=>9
[3,5,6,2,4,1]=>10
[3,5,6,4,1,2]=>10
[3,5,6,4,2,1]=>11
[3,6,1,2,4,5]=>6
[3,6,1,2,5,4]=>7
[3,6,1,4,2,5]=>7
[3,6,1,4,5,2]=>8
[3,6,1,5,2,4]=>8
[3,6,1,5,4,2]=>9
[3,6,2,1,4,5]=>7
[3,6,2,1,5,4]=>8
[3,6,2,4,1,5]=>8
[3,6,2,4,5,1]=>9
[3,6,2,5,1,4]=>9
[3,6,2,5,4,1]=>10
[3,6,4,1,2,5]=>8
[3,6,4,1,5,2]=>9
[3,6,4,2,1,5]=>9
[3,6,4,2,5,1]=>10
[3,6,4,5,1,2]=>10
[3,6,4,5,2,1]=>11
[3,6,5,1,2,4]=>9
[3,6,5,1,4,2]=>10
[3,6,5,2,1,4]=>10
[3,6,5,2,4,1]=>11
[3,6,5,4,1,2]=>11
[3,6,5,4,2,1]=>12
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>4
[4,1,2,5,6,3]=>5
[4,1,2,6,3,5]=>5
[4,1,2,6,5,3]=>6
[4,1,3,2,5,6]=>4
[4,1,3,2,6,5]=>5
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>6
[4,1,3,6,2,5]=>6
[4,1,3,6,5,2]=>7
[4,1,5,2,3,6]=>5
[4,1,5,2,6,3]=>6
[4,1,5,3,2,6]=>6
[4,1,5,3,6,2]=>7
[4,1,5,6,2,3]=>7
[4,1,5,6,3,2]=>8
[4,1,6,2,3,5]=>6
[4,1,6,2,5,3]=>7
[4,1,6,3,2,5]=>7
[4,1,6,3,5,2]=>8
[4,1,6,5,2,3]=>8
[4,1,6,5,3,2]=>9
[4,2,1,3,5,6]=>4
[4,2,1,3,6,5]=>5
[4,2,1,5,3,6]=>5
[4,2,1,5,6,3]=>6
[4,2,1,6,3,5]=>6
[4,2,1,6,5,3]=>7
[4,2,3,1,5,6]=>5
[4,2,3,1,6,5]=>6
[4,2,3,5,1,6]=>6
[4,2,3,5,6,1]=>7
[4,2,3,6,1,5]=>7
[4,2,3,6,5,1]=>8
[4,2,5,1,3,6]=>6
[4,2,5,1,6,3]=>7
[4,2,5,3,1,6]=>7
[4,2,5,3,6,1]=>8
[4,2,5,6,1,3]=>8
[4,2,5,6,3,1]=>9
[4,2,6,1,3,5]=>7
[4,2,6,1,5,3]=>8
[4,2,6,3,1,5]=>8
[4,2,6,3,5,1]=>9
[4,2,6,5,1,3]=>9
[4,2,6,5,3,1]=>10
[4,3,1,2,5,6]=>5
[4,3,1,2,6,5]=>6
[4,3,1,5,2,6]=>6
[4,3,1,5,6,2]=>7
[4,3,1,6,2,5]=>7
[4,3,1,6,5,2]=>8
[4,3,2,1,5,6]=>6
[4,3,2,1,6,5]=>7
[4,3,2,5,1,6]=>7
[4,3,2,5,6,1]=>8
[4,3,2,6,1,5]=>8
[4,3,2,6,5,1]=>9
[4,3,5,1,2,6]=>7
[4,3,5,1,6,2]=>8
[4,3,5,2,1,6]=>8
[4,3,5,2,6,1]=>9
[4,3,5,6,1,2]=>9
[4,3,5,6,2,1]=>10
[4,3,6,1,2,5]=>8
[4,3,6,1,5,2]=>9
[4,3,6,2,1,5]=>9
[4,3,6,2,5,1]=>10
[4,3,6,5,1,2]=>10
[4,3,6,5,2,1]=>11
[4,5,1,2,3,6]=>6
[4,5,1,2,6,3]=>7
[4,5,1,3,2,6]=>7
[4,5,1,3,6,2]=>8
[4,5,1,6,2,3]=>8
[4,5,1,6,3,2]=>9
[4,5,2,1,3,6]=>7
[4,5,2,1,6,3]=>8
[4,5,2,3,1,6]=>8
[4,5,2,3,6,1]=>9
[4,5,2,6,1,3]=>9
[4,5,2,6,3,1]=>10
[4,5,3,1,2,6]=>8
[4,5,3,1,6,2]=>9
[4,5,3,2,1,6]=>9
[4,5,3,2,6,1]=>10
[4,5,3,6,1,2]=>10
[4,5,3,6,2,1]=>11
[4,5,6,1,2,3]=>9
[4,5,6,1,3,2]=>10
[4,5,6,2,1,3]=>10
[4,5,6,2,3,1]=>11
[4,5,6,3,1,2]=>11
[4,5,6,3,2,1]=>12
[4,6,1,2,3,5]=>7
[4,6,1,2,5,3]=>8
[4,6,1,3,2,5]=>8
[4,6,1,3,5,2]=>9
[4,6,1,5,2,3]=>9
[4,6,1,5,3,2]=>10
[4,6,2,1,3,5]=>8
[4,6,2,1,5,3]=>9
[4,6,2,3,1,5]=>9
[4,6,2,3,5,1]=>10
[4,6,2,5,1,3]=>10
[4,6,2,5,3,1]=>11
[4,6,3,1,2,5]=>9
[4,6,3,1,5,2]=>10
[4,6,3,2,1,5]=>10
[4,6,3,2,5,1]=>11
[4,6,3,5,1,2]=>11
[4,6,3,5,2,1]=>12
[4,6,5,1,2,3]=>10
[4,6,5,1,3,2]=>11
[4,6,5,2,1,3]=>11
[4,6,5,2,3,1]=>12
[4,6,5,3,1,2]=>12
[4,6,5,3,2,1]=>13
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>5
[5,1,2,4,3,6]=>5
[5,1,2,4,6,3]=>6
[5,1,2,6,3,4]=>6
[5,1,2,6,4,3]=>7
[5,1,3,2,4,6]=>5
[5,1,3,2,6,4]=>6
[5,1,3,4,2,6]=>6
[5,1,3,4,6,2]=>7
[5,1,3,6,2,4]=>7
[5,1,3,6,4,2]=>8
[5,1,4,2,3,6]=>6
[5,1,4,2,6,3]=>7
[5,1,4,3,2,6]=>7
[5,1,4,3,6,2]=>8
[5,1,4,6,2,3]=>8
[5,1,4,6,3,2]=>9
[5,1,6,2,3,4]=>7
[5,1,6,2,4,3]=>8
[5,1,6,3,2,4]=>8
[5,1,6,3,4,2]=>9
[5,1,6,4,2,3]=>9
[5,1,6,4,3,2]=>10
[5,2,1,3,4,6]=>5
[5,2,1,3,6,4]=>6
[5,2,1,4,3,6]=>6
[5,2,1,4,6,3]=>7
[5,2,1,6,3,4]=>7
[5,2,1,6,4,3]=>8
[5,2,3,1,4,6]=>6
[5,2,3,1,6,4]=>7
[5,2,3,4,1,6]=>7
[5,2,3,4,6,1]=>8
[5,2,3,6,1,4]=>8
[5,2,3,6,4,1]=>9
[5,2,4,1,3,6]=>7
[5,2,4,1,6,3]=>8
[5,2,4,3,1,6]=>8
[5,2,4,3,6,1]=>9
[5,2,4,6,1,3]=>9
[5,2,4,6,3,1]=>10
[5,2,6,1,3,4]=>8
[5,2,6,1,4,3]=>9
[5,2,6,3,1,4]=>9
[5,2,6,3,4,1]=>10
[5,2,6,4,1,3]=>10
[5,2,6,4,3,1]=>11
[5,3,1,2,4,6]=>6
[5,3,1,2,6,4]=>7
[5,3,1,4,2,6]=>7
[5,3,1,4,6,2]=>8
[5,3,1,6,2,4]=>8
[5,3,1,6,4,2]=>9
[5,3,2,1,4,6]=>7
[5,3,2,1,6,4]=>8
[5,3,2,4,1,6]=>8
[5,3,2,4,6,1]=>9
[5,3,2,6,1,4]=>9
[5,3,2,6,4,1]=>10
[5,3,4,1,2,6]=>8
[5,3,4,1,6,2]=>9
[5,3,4,2,1,6]=>9
[5,3,4,2,6,1]=>10
[5,3,4,6,1,2]=>10
[5,3,4,6,2,1]=>11
[5,3,6,1,2,4]=>9
[5,3,6,1,4,2]=>10
[5,3,6,2,1,4]=>10
[5,3,6,2,4,1]=>11
[5,3,6,4,1,2]=>11
[5,3,6,4,2,1]=>12
[5,4,1,2,3,6]=>7
[5,4,1,2,6,3]=>8
[5,4,1,3,2,6]=>8
[5,4,1,3,6,2]=>9
[5,4,1,6,2,3]=>9
[5,4,1,6,3,2]=>10
[5,4,2,1,3,6]=>8
[5,4,2,1,6,3]=>9
[5,4,2,3,1,6]=>9
[5,4,2,3,6,1]=>10
[5,4,2,6,1,3]=>10
[5,4,2,6,3,1]=>11
[5,4,3,1,2,6]=>9
[5,4,3,1,6,2]=>10
[5,4,3,2,1,6]=>10
[5,4,3,2,6,1]=>11
[5,4,3,6,1,2]=>11
[5,4,3,6,2,1]=>12
[5,4,6,1,2,3]=>10
[5,4,6,1,3,2]=>11
[5,4,6,2,1,3]=>11
[5,4,6,2,3,1]=>12
[5,4,6,3,1,2]=>12
[5,4,6,3,2,1]=>13
[5,6,1,2,3,4]=>8
[5,6,1,2,4,3]=>9
[5,6,1,3,2,4]=>9
[5,6,1,3,4,2]=>10
[5,6,1,4,2,3]=>10
[5,6,1,4,3,2]=>11
[5,6,2,1,3,4]=>9
[5,6,2,1,4,3]=>10
[5,6,2,3,1,4]=>10
[5,6,2,3,4,1]=>11
[5,6,2,4,1,3]=>11
[5,6,2,4,3,1]=>12
[5,6,3,1,2,4]=>10
[5,6,3,1,4,2]=>11
[5,6,3,2,1,4]=>11
[5,6,3,2,4,1]=>12
[5,6,3,4,1,2]=>12
[5,6,3,4,2,1]=>13
[5,6,4,1,2,3]=>11
[5,6,4,1,3,2]=>12
[5,6,4,2,1,3]=>12
[5,6,4,2,3,1]=>13
[5,6,4,3,1,2]=>13
[5,6,4,3,2,1]=>14
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>6
[6,1,2,4,3,5]=>6
[6,1,2,4,5,3]=>7
[6,1,2,5,3,4]=>7
[6,1,2,5,4,3]=>8
[6,1,3,2,4,5]=>6
[6,1,3,2,5,4]=>7
[6,1,3,4,2,5]=>7
[6,1,3,4,5,2]=>8
[6,1,3,5,2,4]=>8
[6,1,3,5,4,2]=>9
[6,1,4,2,3,5]=>7
[6,1,4,2,5,3]=>8
[6,1,4,3,2,5]=>8
[6,1,4,3,5,2]=>9
[6,1,4,5,2,3]=>9
[6,1,4,5,3,2]=>10
[6,1,5,2,3,4]=>8
[6,1,5,2,4,3]=>9
[6,1,5,3,2,4]=>9
[6,1,5,3,4,2]=>10
[6,1,5,4,2,3]=>10
[6,1,5,4,3,2]=>11
[6,2,1,3,4,5]=>6
[6,2,1,3,5,4]=>7
[6,2,1,4,3,5]=>7
[6,2,1,4,5,3]=>8
[6,2,1,5,3,4]=>8
[6,2,1,5,4,3]=>9
[6,2,3,1,4,5]=>7
[6,2,3,1,5,4]=>8
[6,2,3,4,1,5]=>8
[6,2,3,4,5,1]=>9
[6,2,3,5,1,4]=>9
[6,2,3,5,4,1]=>10
[6,2,4,1,3,5]=>8
[6,2,4,1,5,3]=>9
[6,2,4,3,1,5]=>9
[6,2,4,3,5,1]=>10
[6,2,4,5,1,3]=>10
[6,2,4,5,3,1]=>11
[6,2,5,1,3,4]=>9
[6,2,5,1,4,3]=>10
[6,2,5,3,1,4]=>10
[6,2,5,3,4,1]=>11
[6,2,5,4,1,3]=>11
[6,2,5,4,3,1]=>12
[6,3,1,2,4,5]=>7
[6,3,1,2,5,4]=>8
[6,3,1,4,2,5]=>8
[6,3,1,4,5,2]=>9
[6,3,1,5,2,4]=>9
[6,3,1,5,4,2]=>10
[6,3,2,1,4,5]=>8
[6,3,2,1,5,4]=>9
[6,3,2,4,1,5]=>9
[6,3,2,4,5,1]=>10
[6,3,2,5,1,4]=>10
[6,3,2,5,4,1]=>11
[6,3,4,1,2,5]=>9
[6,3,4,1,5,2]=>10
[6,3,4,2,1,5]=>10
[6,3,4,2,5,1]=>11
[6,3,4,5,1,2]=>11
[6,3,4,5,2,1]=>12
[6,3,5,1,2,4]=>10
[6,3,5,1,4,2]=>11
[6,3,5,2,1,4]=>11
[6,3,5,2,4,1]=>12
[6,3,5,4,1,2]=>12
[6,3,5,4,2,1]=>13
[6,4,1,2,3,5]=>8
[6,4,1,2,5,3]=>9
[6,4,1,3,2,5]=>9
[6,4,1,3,5,2]=>10
[6,4,1,5,2,3]=>10
[6,4,1,5,3,2]=>11
[6,4,2,1,3,5]=>9
[6,4,2,1,5,3]=>10
[6,4,2,3,1,5]=>10
[6,4,2,3,5,1]=>11
[6,4,2,5,1,3]=>11
[6,4,2,5,3,1]=>12
[6,4,3,1,2,5]=>10
[6,4,3,1,5,2]=>11
[6,4,3,2,1,5]=>11
[6,4,3,2,5,1]=>12
[6,4,3,5,1,2]=>12
[6,4,3,5,2,1]=>13
[6,4,5,1,2,3]=>11
[6,4,5,1,3,2]=>12
[6,4,5,2,1,3]=>12
[6,4,5,2,3,1]=>13
[6,4,5,3,1,2]=>13
[6,4,5,3,2,1]=>14
[6,5,1,2,3,4]=>9
[6,5,1,2,4,3]=>10
[6,5,1,3,2,4]=>10
[6,5,1,3,4,2]=>11
[6,5,1,4,2,3]=>11
[6,5,1,4,3,2]=>12
[6,5,2,1,3,4]=>10
[6,5,2,1,4,3]=>11
[6,5,2,3,1,4]=>11
[6,5,2,3,4,1]=>12
[6,5,2,4,1,3]=>12
[6,5,2,4,3,1]=>13
[6,5,3,1,2,4]=>11
[6,5,3,1,4,2]=>12
[6,5,3,2,1,4]=>12
[6,5,3,2,4,1]=>13
[6,5,3,4,1,2]=>13
[6,5,3,4,2,1]=>14
[6,5,4,1,2,3]=>12
[6,5,4,1,3,2]=>13
[6,5,4,2,1,3]=>13
[6,5,4,2,3,1]=>14
[6,5,4,3,1,2]=>14
[6,5,4,3,2,1]=>15
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>1
[1,2,3,6,4,7,5]=>3
[1,2,6,3,4,7,5]=>4
[1,3,2,4,5,6,7]=>1
[1,3,7,2,4,5,6]=>5
[1,3,7,6,5,4,2]=>11
[1,4,6,7,2,3,5]=>8
[1,4,6,7,5,3,2]=>11
[1,4,7,2,3,5,6]=>6
[1,4,7,6,5,3,2]=>12
[1,5,2,3,4,7,6]=>4
[1,5,2,7,3,4,6]=>6
[1,5,4,7,6,3,2]=>11
[1,5,6,2,7,3,4]=>8
[1,5,6,4,7,3,2]=>11
[1,5,6,7,2,3,4]=>9
[1,5,6,7,4,3,2]=>12
[1,5,7,2,3,4,6]=>7
[1,5,7,6,4,3,2]=>13
[1,6,2,3,4,7,5]=>5
[1,6,2,3,7,4,5]=>6
[1,6,2,7,3,4,5]=>7
[1,6,5,4,3,7,2]=>11
[1,6,5,4,7,3,2]=>12
[1,6,5,7,4,3,2]=>13
[1,6,7,2,3,4,5]=>8
[1,6,7,5,4,3,2]=>14
[1,7,2,3,4,5,6]=>5
[1,7,3,5,6,4,2]=>11
[1,7,3,6,5,4,2]=>12
[1,7,4,3,6,5,2]=>11
[1,7,4,5,3,6,2]=>11
[1,7,4,5,6,3,2]=>12
[1,7,4,6,5,3,2]=>13
[1,7,5,4,3,6,2]=>12
[1,7,5,4,6,3,2]=>13
[1,7,6,4,5,3,2]=>14
[1,7,6,5,4,3,2]=>15
[2,1,3,4,5,6,7]=>1
[2,1,3,4,7,5,6]=>3
[2,1,3,7,4,5,6]=>4
[2,1,6,3,4,5,7]=>4
[2,1,7,3,4,5,6]=>5
[2,1,7,6,5,4,3]=>11
[2,3,1,4,5,6,7]=>2
[2,3,4,1,5,6,7]=>3
[2,3,4,1,5,7,6]=>4
[2,3,4,5,1,6,7]=>4
[2,3,4,5,1,7,6]=>5
[2,3,4,5,6,1,7]=>5
[2,3,4,5,6,7,1]=>6
[2,3,4,5,7,1,6]=>6
[2,3,4,6,1,7,5]=>6
[2,3,4,6,7,1,5]=>7
[2,3,4,7,1,5,6]=>6
[2,3,5,6,7,1,4]=>8
[2,4,1,3,5,6,7]=>3
[2,5,1,3,4,6,7]=>4
[2,5,7,1,3,4,6]=>8
[2,6,1,3,4,5,7]=>5
[2,6,1,7,3,4,5]=>8
[2,6,5,4,3,1,7]=>11
[2,6,7,1,3,4,5]=>9
[2,7,1,3,4,5,6]=>6
[3,1,2,4,5,6,7]=>2
[3,1,2,4,5,7,6]=>3
[3,2,1,4,5,6,7]=>3
[3,2,4,5,6,7,1]=>7
[3,4,1,2,5,6,7]=>4
[3,4,2,5,6,7,1]=>8
[3,4,5,2,6,7,1]=>9
[3,4,5,6,2,7,1]=>10
[3,4,5,6,7,1,2]=>10
[3,5,6,1,2,4,7]=>8
[3,5,6,4,2,1,7]=>11
[3,6,1,2,4,5,7]=>6
[3,6,5,4,2,1,7]=>12
[4,1,2,3,5,6,7]=>3
[4,1,2,3,5,7,6]=>4
[4,1,6,2,3,5,7]=>6
[4,2,3,5,6,7,1]=>8
[4,2,5,1,3,6,7]=>6
[4,3,2,1,5,6,7]=>6
[4,3,2,5,6,7,1]=>9
[4,3,5,2,6,7,1]=>10
[4,3,6,5,2,1,7]=>11
[4,5,1,6,2,3,7]=>8
[4,5,2,3,6,7,1]=>10
[4,5,3,6,2,1,7]=>11
[4,5,6,1,2,3,7]=>9
[4,5,6,3,2,1,7]=>12
[4,6,1,2,3,5,7]=>7
[4,6,1,2,3,7,5]=>8
[4,6,5,3,2,1,7]=>13
[5,1,2,3,4,6,7]=>4
[5,1,2,3,4,7,6]=>5
[5,1,2,3,6,4,7]=>5
[5,1,2,3,6,7,4]=>6
[5,1,2,3,7,4,6]=>6
[5,1,2,6,3,4,7]=>6
[5,1,6,2,3,4,7]=>7
[5,1,6,2,3,7,4]=>8
[5,2,3,4,6,7,1]=>9
[5,2,6,7,1,3,4]=>11
[5,3,2,4,6,7,1]=>10
[5,3,2,6,1,4,7]=>9
[5,4,3,2,1,6,7]=>10
[5,4,3,2,1,7,6]=>11
[5,4,3,2,6,1,7]=>11
[5,4,3,6,2,1,7]=>12
[5,4,6,3,2,1,7]=>13
[5,6,1,2,3,4,7]=>8
[5,6,1,2,3,7,4]=>9
[5,6,3,4,1,2,7]=>12
[5,6,4,3,2,1,7]=>14
[5,6,7,1,2,3,4]=>12
[6,1,2,3,4,5,7]=>5
[6,1,2,3,4,7,5]=>6
[6,1,2,3,7,4,5]=>7
[6,1,2,7,3,4,5]=>8
[6,2,3,4,5,7,1]=>10
[6,2,4,5,3,1,7]=>11
[6,2,5,4,3,1,7]=>12
[6,3,2,5,4,1,7]=>11
[6,3,4,2,5,1,7]=>11
[6,3,4,5,2,1,7]=>12
[6,3,5,4,2,1,7]=>13
[6,4,3,2,5,1,7]=>12
[6,4,3,2,7,1,5]=>13
[6,4,3,5,2,1,7]=>13
[6,4,7,2,5,1,3]=>15
[6,5,3,4,2,1,7]=>14
[6,5,4,3,2,1,7]=>15
[6,7,1,2,3,4,5]=>10
[6,7,4,5,1,2,3]=>16
[7,1,2,3,4,5,6]=>6
[7,2,1,3,4,5,6]=>7
[7,2,3,1,4,5,6]=>8
[7,2,3,4,1,5,6]=>9
[7,2,3,4,5,1,6]=>10
[7,3,1,2,4,5,6]=>8
[7,3,2,1,4,5,6]=>9
[7,3,2,4,1,5,6]=>10
[7,3,4,1,2,5,6]=>10
[7,4,1,2,3,5,6]=>9
[7,4,2,1,3,5,6]=>10
[7,4,5,6,1,2,3]=>15
[7,5,1,2,3,4,6]=>10
[7,5,6,1,2,3,4]=>14
[7,5,6,3,4,1,2]=>18
[7,6,1,2,3,4,5]=>11
[7,6,4,5,1,2,3]=>17
[7,6,5,1,2,3,4]=>15
[7,6,5,3,4,1,2]=>19
[7,6,5,4,1,2,3]=>18
[7,6,5,4,3,1,2]=>20
[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]=>26
[7,8,5,6,4,3,2,1]=>26
[7,8,6,4,5,3,2,1]=>26
[8,6,7,4,5,3,2,1]=>26
[7,6,5,4,8,3,2,1]=>24
[6,5,7,4,8,3,2,1]=>22
[7,8,6,5,3,4,2,1]=>26
[8,6,7,5,3,4,2,1]=>26
[8,7,5,6,3,4,2,1]=>26
[6,7,8,3,4,5,2,1]=>22
[7,8,6,5,4,2,3,1]=>26
[8,6,7,5,4,2,3,1]=>26
[8,7,5,6,4,2,3,1]=>26
[8,7,6,4,5,2,3,1]=>26
[8,6,5,7,3,2,4,1]=>24
[6,7,8,5,2,3,4,1]=>22
[8,5,6,7,2,3,4,1]=>22
[7,8,3,2,4,5,6,1]=>18
[7,6,5,4,3,2,8,1]=>22
[6,5,7,4,3,2,8,1]=>20
[6,5,4,3,7,2,8,1]=>18
[5,4,6,3,7,2,8,1]=>16
[3,4,5,2,6,7,8,1]=>10
[5,2,3,4,6,7,8,1]=>10
[4,3,2,5,6,7,8,1]=>10
[3,4,2,5,6,7,8,1]=>9
[4,2,3,5,6,7,8,1]=>9
[3,2,4,5,6,7,8,1]=>8
[2,3,4,5,6,7,8,1]=>7
[8,7,6,5,4,3,1,2]=>27
[7,8,6,5,4,3,1,2]=>26
[8,6,7,5,4,3,1,2]=>26
[8,7,5,6,4,3,1,2]=>26
[8,7,6,4,5,3,1,2]=>26
[8,7,6,5,3,4,1,2]=>26
[8,7,5,6,3,4,1,2]=>25
[7,8,5,6,3,4,1,2]=>24
[5,6,7,8,3,4,1,2]=>20
[7,8,3,4,5,6,1,2]=>20
[3,4,5,6,7,8,1,2]=>12
[8,7,6,5,4,2,1,3]=>26
[7,6,8,5,4,2,1,3]=>24
[8,7,6,5,4,1,2,3]=>25
[6,7,8,5,4,1,2,3]=>22
[8,5,6,7,4,1,2,3]=>22
[8,7,6,4,5,1,2,3]=>24
[8,6,7,4,5,1,2,3]=>23
[8,7,4,5,6,1,2,3]=>22
[7,8,4,5,6,1,2,3]=>21
[7,6,5,8,3,2,1,4]=>22
[7,5,6,8,2,3,1,4]=>20
[6,7,5,8,3,1,2,4]=>20
[6,5,7,8,2,1,3,4]=>18
[8,7,6,5,1,2,3,4]=>22
[8,7,5,6,1,2,3,4]=>21
[7,8,5,6,1,2,3,4]=>20
[8,5,6,7,1,2,3,4]=>19
[5,6,7,8,1,2,3,4]=>16
[8,7,6,4,3,2,1,5]=>24
[8,7,6,4,2,1,3,5]=>22
[8,7,6,1,2,3,4,5]=>18
[8,6,7,1,2,3,4,5]=>17
[6,7,8,1,2,3,4,5]=>15
[7,8,5,4,2,1,3,6]=>20
[7,8,5,4,1,2,3,6]=>19
[8,7,1,2,3,4,5,6]=>13
[7,8,1,2,3,4,5,6]=>12
[8,6,5,4,3,2,1,7]=>22
[8,6,5,4,3,1,2,7]=>21
[8,5,6,3,4,1,2,7]=>19
[8,6,5,4,2,1,3,7]=>20
[8,6,4,3,2,1,5,7]=>18
[8,6,4,2,1,3,5,7]=>16
[8,2,3,4,1,5,6,7]=>10
[8,4,1,2,3,5,6,7]=>10
[8,3,2,1,4,5,6,7]=>10
[8,2,3,1,4,5,6,7]=>9
[8,3,1,2,4,5,6,7]=>9
[8,2,1,3,4,5,6,7]=>8
[8,1,2,3,4,5,6,7]=>7
[7,6,5,4,3,2,1,8]=>21
[6,7,5,4,3,2,1,8]=>20
[6,5,7,4,3,2,1,8]=>19
[5,6,7,4,3,2,1,8]=>18
[7,6,4,5,3,2,1,8]=>20
[6,5,4,7,3,2,1,8]=>18
[7,5,6,3,4,2,1,8]=>19
[7,6,4,3,5,2,1,8]=>19
[7,6,3,4,5,2,1,8]=>18
[7,5,4,3,6,2,1,8]=>18
[6,7,5,4,2,3,1,8]=>19
[6,5,7,3,2,4,1,8]=>17
[5,6,7,2,3,4,1,8]=>15
[2,3,4,5,6,7,1,8]=>6
[5,6,7,1,2,3,4,8]=>12
[6,7,1,2,3,4,5,8]=>10
[7,1,2,3,4,5,6,8]=>6
[6,5,4,3,2,1,7,8]=>15
[2,3,4,5,6,1,7,8]=>5
[5,6,3,4,1,2,7,8]=>12
[4,5,6,1,2,3,7,8]=>9
[6,1,2,3,4,5,7,8]=>5
[5,4,3,2,1,6,7,8]=>10
[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]=>6
[3,4,1,2,5,6,7,8]=>4
[3,2,1,4,5,6,7,8]=>3
[2,1,3,4,5,6,7,8]=>1
[1,2,3,4,5,6,7,8]=>0
[6,5,8,7,4,3,2,1]=>24
[3,5,8,7,6,4,2,1]=>20
[4,3,6,5,8,7,2,1]=>16
[2,6,8,7,5,4,3,1]=>20
[2,3,5,6,8,7,4,1]=>12
[3,2,6,5,4,8,7,1]=>12
[4,3,6,5,7,2,8,1]=>14
[3,2,6,5,7,4,8,1]=>12
[4,3,5,2,7,6,8,1]=>12
[3,2,5,4,7,6,8,1]=>10
[1,8,7,6,5,4,3,2]=>21
[1,7,8,6,5,4,3,2]=>20
[1,6,8,7,5,4,3,2]=>19
[1,7,6,8,5,4,3,2]=>19
[1,6,7,8,5,4,3,2]=>18
[1,5,8,7,6,4,3,2]=>18
[1,7,6,5,8,4,3,2]=>18
[1,3,5,7,8,6,4,2]=>12
[1,4,3,8,7,6,5,2]=>13
[1,6,5,4,3,8,7,2]=>13
[1,4,3,6,5,8,7,2]=>9
[2,1,8,7,6,5,4,3]=>16
[2,1,6,5,7,4,8,3]=>10
[2,1,5,4,7,6,8,3]=>8
[1,2,6,7,8,5,4,3]=>12
[3,2,1,8,7,6,5,4]=>13
[3,2,1,6,5,8,7,4]=>9
[1,2,3,5,6,7,8,4]=>4
[4,3,2,1,8,7,6,5]=>12
[3,4,2,1,7,8,6,5]=>10
[2,4,3,1,6,8,7,5]=>8
[2,4,3,1,7,6,8,5]=>8
[3,2,4,1,6,8,7,5]=>8
[3,2,4,1,7,6,8,5]=>8
[2,3,4,1,6,7,8,5]=>6
[2,1,4,3,8,7,6,5]=>8
[2,1,4,3,6,8,7,5]=>6
[2,1,4,3,7,6,8,5]=>6
[5,4,3,2,1,8,7,6]=>13
[3,2,5,4,1,8,7,6]=>9
[3,2,1,4,5,8,7,6]=>6
[2,3,1,4,5,7,8,6]=>4
[6,5,4,3,2,1,8,7]=>16
[4,3,5,2,6,1,8,7]=>10
[3,2,5,4,6,1,8,7]=>8
[2,3,4,5,6,1,8,7]=>6
[2,1,6,5,4,3,8,7]=>8
[2,1,4,6,5,3,8,7]=>6
[2,1,5,4,6,3,8,7]=>6
[4,3,2,1,6,5,8,7]=>8
[2,4,3,1,6,5,8,7]=>6
[3,2,4,1,6,5,8,7]=>6
[2,1,4,3,6,5,8,7]=>4
[2,1,3,4,5,6,8,7]=>2
[1,2,3,4,5,6,8,7]=>1
[5,7,6,4,3,2,1,8]=>19
[4,7,6,5,3,2,1,8]=>18
[3,2,7,6,5,4,1,8]=>13
[5,4,3,2,7,6,1,8]=>13
[3,2,5,4,7,6,1,8]=>9
[1,4,3,2,7,6,5,8]=>6
[1,3,4,2,6,7,5,8]=>4
[1,3,2,5,4,7,6,8]=>3
[1,2,3,5,4,7,6,8]=>2
[1,3,2,4,5,7,6,8]=>2
[1,2,3,4,5,7,6,8]=>1
[1,2,4,3,6,5,7,8]=>2
[1,3,2,5,4,6,7,8]=>2
[1,2,3,5,4,6,7,8]=>1
[1,3,2,4,5,6,7,8]=>1
[1,8,4,7,6,5,3,2]=>18
[1,8,5,4,7,6,3,2]=>17
[1,8,7,4,5,6,3,2]=>18
[1,8,7,4,6,5,3,2]=>19
[1,8,6,5,4,7,3,2]=>18
[1,8,7,5,4,6,3,2]=>19
[1,8,7,5,6,4,3,2]=>20
[2,1,4,5,8,6,7,3]=>8
[2,1,8,5,4,7,6,3]=>12
[2,3,4,8,5,6,7,1]=>10
[2,3,6,4,5,1,8,7]=>8
[2,3,7,4,5,6,8,1]=>10
[2,8,4,3,5,7,6,1]=>14
[4,2,3,1,8,6,7,5]=>10
[8,2,7,4,6,5,3,1]=>21
[4,3,2,7,5,6,8,1]=>12
[4,3,2,8,5,7,6,1]=>14
[6,3,2,5,4,1,8,7]=>12
[8,3,2,5,4,7,6,1]=>16
[8,3,2,7,6,5,4,1]=>20
[8,3,7,4,6,5,2,1]=>22
[7,3,6,5,4,2,1,8]=>18
[7,4,3,6,5,2,1,8]=>17
[7,6,3,5,4,2,1,8]=>19
[8,5,4,3,2,7,6,1]=>20
[8,7,4,3,6,5,2,1]=>24
[2,4,6,8,1,3,5,7]=>10
[2,4,6,1,7,3,8,5]=>9
[2,1,4,3,7,5,8,6]=>5
[2,4,1,3,7,5,8,6]=>6
[2,1,4,3,7,8,5,6]=>6
[2,4,7,8,1,3,5,6]=>11
[2,1,4,3,8,5,6,7]=>5
[2,4,5,6,7,1,8,3]=>10
[2,1,5,3,6,4,8,7]=>5
[2,1,5,6,3,4,8,7]=>6
[2,5,6,8,1,3,4,7]=>11
[2,1,5,3,7,4,8,6]=>6
[2,5,1,7,3,4,8,6]=>8
[2,1,5,7,3,8,4,6]=>8
[2,5,7,8,1,3,4,6]=>12
[2,3,5,6,1,7,8,4]=>8
[2,1,6,3,7,4,8,5]=>7
[2,6,7,1,3,4,8,5]=>10
[2,1,6,7,8,3,4,5]=>10
[2,6,7,8,1,3,4,5]=>13
[2,1,6,3,4,7,8,5]=>6
[2,1,6,3,4,5,8,7]=>5
[2,6,1,3,4,5,7,8]=>5
[2,7,8,1,3,4,5,6]=>11
[2,7,1,3,4,5,6,8]=>6
[2,3,4,5,7,8,1,6]=>8
[2,1,8,3,4,5,6,7]=>6
[2,8,1,3,4,5,6,7]=>7
[2,1,3,8,4,5,6,7]=>5
[2,3,4,5,6,8,1,7]=>7
[3,1,4,2,6,5,8,7]=>5
[3,4,1,2,6,5,8,7]=>6
[3,1,4,2,6,8,5,7]=>6
[3,4,6,8,1,2,5,7]=>11
[3,1,4,2,7,5,8,6]=>6
[3,4,1,2,7,8,5,6]=>8
[3,4,7,8,1,2,5,6]=>12
[3,1,5,2,6,4,8,7]=>6
[3,5,1,6,2,4,8,7]=>8
[3,1,5,6,2,8,4,7]=>8
[3,5,6,8,1,2,4,7]=>12
[3,1,5,2,7,4,8,6]=>7
[3,5,1,7,2,8,4,6]=>10
[3,5,7,8,1,2,4,6]=>13
[1,3,2,5,4,8,6,7]=>4
[1,3,5,8,2,4,6,7]=>7
[1,3,5,6,2,7,4,8]=>6
[3,1,6,2,7,4,8,5]=>8
[3,6,7,1,2,8,4,5]=>12
[3,6,1,7,8,2,4,5]=>12
[3,6,7,8,1,2,4,5]=>14
[1,3,2,6,4,7,5,8]=>4
[3,1,2,6,7,4,8,5]=>7
[1,3,2,6,4,8,5,7]=>5
[1,3,2,6,4,5,7,8]=>3
[1,3,2,7,4,8,5,6]=>6
[1,3,2,7,4,5,6,8]=>4
[1,3,2,8,4,5,6,7]=>5
[3,1,2,4,5,8,6,7]=>4
[1,3,2,4,5,8,6,7]=>3
[4,1,5,2,6,3,8,7]=>7
[4,5,6,1,2,3,8,7]=>10
[4,1,5,6,8,2,3,7]=>10
[4,5,6,8,1,2,3,7]=>13
[4,1,5,2,7,3,8,6]=>8
[4,1,5,2,7,8,3,6]=>9
[4,5,7,1,2,8,3,6]=>12
[4,5,1,7,8,2,3,6]=>12
[4,5,7,8,1,2,3,6]=>14
[1,4,2,5,3,7,6,8]=>4
[1,4,2,5,3,8,6,7]=>5
[1,4,2,5,3,6,7,8]=>3
[1,4,5,6,7,2,3,8]=>8
[4,1,6,2,7,3,8,5]=>9
[4,6,7,1,8,2,3,5]=>14
[4,6,7,8,1,2,3,5]=>15
[1,4,2,6,3,7,5,8]=>5
[1,4,2,6,7,8,3,5]=>8
[1,4,2,6,3,8,5,7]=>6
[4,1,2,3,6,5,8,7]=>5
[1,4,2,6,3,5,7,8]=>4
[1,4,2,7,3,8,5,6]=>7
[4,7,1,2,3,5,6,8]=>8
[1,4,2,7,3,5,6,8]=>5
[1,4,2,3,7,5,6,8]=>4
[1,4,2,3,5,7,6,8]=>3
[1,4,2,8,3,5,6,7]=>6
[4,1,2,3,8,5,6,7]=>6
[1,4,2,3,5,8,6,7]=>4
[1,4,2,3,5,6,7,8]=>2
[5,1,6,2,7,3,8,4]=>10
[1,5,2,6,3,7,4,8]=>6
[1,5,2,6,3,8,4,7]=>7
[1,5,2,6,3,4,7,8]=>5
[1,2,5,6,3,4,7,8]=>4
[1,5,2,7,3,8,4,6]=>8
[5,7,1,2,3,4,6,8]=>9
[1,5,2,7,3,4,6,8]=>6
[1,5,2,3,4,7,6,8]=>4
[5,1,2,8,3,4,6,7]=>8
[1,5,2,8,3,4,6,7]=>7
[1,5,8,2,3,4,6,7]=>8
[1,5,2,3,4,8,6,7]=>5
[1,2,3,5,4,8,6,7]=>3
[5,1,2,3,4,6,8,7]=>5
[1,5,2,3,4,6,7,8]=>3
[1,6,2,7,3,8,4,5]=>9
[1,6,7,8,2,3,4,5]=>12
[6,7,1,2,3,4,8,5]=>11
[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]=>7
[1,6,7,2,3,4,5,8]=>8
[1,6,2,3,4,7,5,8]=>5
[1,2,3,6,4,7,5,8]=>3
[6,1,8,2,3,4,5,7]=>10
[1,6,2,8,3,4,5,7]=>8
[1,6,8,2,3,4,5,7]=>9
[1,6,2,3,4,8,5,7]=>6
[1,2,3,6,4,8,5,7]=>4
[6,1,2,3,4,5,8,7]=>6
[1,6,2,3,4,5,7,8]=>4
[1,2,3,6,4,5,7,8]=>2
[1,7,2,8,3,4,5,6]=>9
[1,7,8,2,3,4,5,6]=>10
[1,7,2,3,8,4,5,6]=>8
[7,1,2,3,4,8,5,6]=>8
[1,7,2,3,4,8,5,6]=>7
[1,2,3,7,4,8,5,6]=>5
[7,1,2,3,4,5,8,6]=>7
[1,7,2,3,4,5,8,6]=>6
[1,2,7,3,4,5,8,6]=>5
[1,7,2,3,4,5,6,8]=>5
[1,2,3,7,4,5,6,8]=>3
[1,8,2,3,4,5,6,7]=>6
[1,2,3,8,4,5,6,7]=>4
[1,2,3,4,5,8,6,7]=>2
[5,3,2,6,1,4,8,7]=>10
[7,3,2,5,4,8,1,6]=>14
[8,4,5,2,3,7,6,1]=>18
[7,4,5,2,3,8,1,6]=>16
[6,4,5,2,3,1,8,7]=>14
[5,4,6,2,1,3,8,7]=>12
[3,6,1,5,4,2,8,7]=>10
[4,6,5,1,3,2,8,7]=>12
[5,6,4,3,1,2,8,7]=>14
[7,5,4,3,2,8,1,6]=>18
[8,6,4,3,7,2,5,1]=>22
[7,6,4,3,8,2,1,5]=>20
[6,7,4,3,8,1,2,5]=>18
[5,7,4,3,1,8,2,6]=>16
[4,7,5,1,3,8,2,6]=>14
[3,7,1,5,4,8,2,6]=>12
[2,1,7,5,4,8,3,6]=>10
[3,8,1,5,4,7,6,2]=>14
[4,8,5,1,3,7,6,2]=>16
[5,8,4,3,1,7,6,2]=>18
[6,8,4,3,7,1,5,2]=>20
[7,8,4,3,6,5,1,2]=>22
[6,8,5,7,3,1,4,2]=>22
[5,8,6,7,1,3,4,2]=>20
[4,8,6,1,7,3,5,2]=>18
[3,8,1,6,7,4,5,2]=>16
[2,1,8,6,7,4,5,3]=>14
[2,1,7,6,8,4,3,5]=>12
[3,7,1,6,8,4,2,5]=>14
[4,7,6,1,8,3,2,5]=>16
[5,7,6,8,1,3,2,4]=>18
[5,4,7,2,1,8,3,6]=>14
[6,4,7,2,8,1,3,5]=>16
[7,4,6,2,8,3,1,5]=>18
[8,4,6,2,7,3,5,1]=>20
[8,3,2,6,7,4,5,1]=>18
[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]=>12
[4,3,2,1,7,8,5,6]=>10
[3,4,1,2,8,7,6,5]=>10
[5,3,2,8,1,7,6,4]=>14
[6,3,2,8,7,1,5,4]=>16
[7,3,2,8,6,5,1,4]=>18
[8,4,7,2,6,5,3,1]=>22
[7,4,8,2,6,5,1,3]=>20
[6,4,8,2,7,1,5,3]=>18
[5,4,8,2,1,7,6,3]=>16
[4,5,8,1,2,7,6,3]=>14
[3,5,1,8,2,7,6,4]=>12
[2,1,5,8,3,7,6,4]=>10
[2,1,6,8,7,3,5,4]=>12
[3,6,1,8,7,2,5,4]=>14
[4,6,8,1,7,2,5,3]=>16
[5,6,8,7,1,2,4,3]=>18
[6,5,8,7,2,1,4,3]=>20
[7,5,8,6,2,4,1,3]=>22
[8,5,7,6,2,4,3,1]=>24
[5,7,8,6,1,4,2,3]=>20
[4,7,8,1,6,5,2,3]=>18
[3,7,1,8,6,5,2,4]=>16
[2,1,7,8,6,5,3,4]=>14
[3,8,1,7,6,5,4,2]=>18
[4,8,7,1,6,5,3,2]=>20
[5,8,7,6,1,4,3,2]=>22
[6,8,7,5,4,1,3,2]=>24
[4,2,5,1,3,6,7,8]=>6
[5,2,6,7,1,3,4,8]=>11
[3,2,7,8,1,4,5,6]=>11
[5,3,2,6,1,4,7,8]=>9
[7,4,3,8,1,2,5,6]=>15
[4,7,3,6,8,1,2,5]=>16
[6,7,3,4,8,1,2,5]=>17
[5,4,2,7,8,1,3,6]=>14
[6,4,7,2,5,1,3,8]=>15
[6,4,3,2,7,1,5,8]=>13
[5,4,3,2,8,1,6,7]=>13
[7,5,3,8,2,6,1,4]=>19
[8,5,4,7,2,6,1,3]=>21
[8,5,4,7,3,6,1,2]=>22
[7,5,3,1,8,6,4,2]=>18
[8,7,1,3,6,2,4,5]=>17
[5,4,1,3,8,2,6,7]=>11
[4,8,5,7,1,6,2,3]=>18
[8,7,6,5,1,4,2,3]=>24
[3,2,1,5,8,4,6,7]=>7
[1,8,2,7,3,6,4,5]=>12
[2,5,3,4,1,8,6,7]=>8
[2,4,8,3,5,7,6,1]=>13
[8,7,2,6,3,5,4,1]=>22
[5,4,3,2,1,8,6,7]=>12
[3,8,4,7,6,5,2,1]=>20
[3,6,7,4,5,8,1,2]=>16
[7,8,1,4,5,2,3,6]=>16
[1,6,7,4,5,2,3,8]=>12
[8,5,7,4,2,1,6,3]=>21
[8,6,3,5,2,4,1,7]=>19
[8,3,7,5,2,4,6,1]=>20
[8,7,6,3,5,2,4,1]=>25
[8,5,7,4,3,2,6,1]=>23
[8,4,7,6,3,5,2,1]=>24
[6,5,8,4,2,7,3,1]=>21
[7,5,3,6,4,2,8,1]=>19
[8,5,3,6,2,7,4,1]=>20
[8,6,4,7,5,3,2,1]=>25
[8,6,5,4,2,7,3,1]=>23
[8,7,5,2,6,4,3,1]=>24
[2,1,8,7,4,3,6,5]=>12
[6,5,2,1,4,3,8,7]=>12
[8,5,2,7,4,1,6,3]=>19
[8,7,2,1,4,5,6,3]=>17
[8,7,2,3,4,1,6,5]=>17
[8,1,6,3,2,5,4,7]=>13
[1,2,3,8,4,7,5,6]=>6
[1,8,2,3,4,7,5,6]=>8
[1,6,2,5,3,4,7,8]=>6
[1,8,2,5,3,4,6,7]=>8
[1,8,2,7,3,4,5,6]=>10
[8,7,2,1,4,3,6,5]=>16
[8,2,1,5,4,3,7,6]=>12
[8,7,6,5,2,1,4,3]=>24
[8,7,6,3,2,5,4,1]=>24
[8,5,4,7,6,3,2,1]=>24
[1,5,4,7,6,2,3,8]=>10
[5,4,3,8,7,6,1,2]=>18
[8,1,2,4,5,6,3,7]=>10
[1,8,2,6,3,5,4,7]=>10
[1,7,2,6,3,5,4,8]=>9
[1,7,2,6,3,4,5,8]=>8
[8,7,6,1,4,3,2,5]=>21
[7,1,8,6,5,4,3,2]=>21
[1,8,7,6,5,4,2,3]=>20
[3,2,1,4,8,5,6,7]=>6
[1,8,2,3,4,6,5,7]=>7
[1,6,2,7,3,5,4,8]=>8
[1,6,2,5,3,7,4,8]=>7
[1,5,3,7,2,6,4,8]=>8
[2,8,4,1,6,3,7,5]=>12
[5,3,6,4,7,1,8,2]=>14
[8,1,6,7,5,4,3,2]=>21
[8,1,6,7,4,5,2,3]=>19
[1,8,2,7,3,5,4,6]=>11
[1,7,2,8,3,5,4,6]=>10
[5,4,3,2,7,1,8,6]=>13
[3,5,2,7,1,8,6,4]=>12
[2,6,7,3,1,4,8,5]=>11
[5,4,1,8,7,2,3,6]=>14
[8,4,3,1,7,6,2,5]=>17
[5,7,4,3,2,1,8,6]=>16
[3,2,6,1,4,7,8,5]=>8
[3,6,7,2,1,8,5,4]=>14
[1,7,6,5,4,8,2,3]=>16
[1,5,4,2,8,3,6,7]=>8
[6,7,2,3,4,8,5,1]=>16
[4,6,2,5,8,3,7,1]=>15
[4,3,5,2,7,1,8,6]=>11
[3,2,6,1,7,4,8,5]=>9
[1,7,2,5,3,4,6,8]=>7
[1,6,2,4,3,5,7,8]=>5
[1,5,2,4,3,6,7,8]=>4
[1,6,2,4,3,7,5,8]=>6
[8,1,2,5,6,7,4,3]=>14
[7,8,3,2,1,6,5,4]=>18
[1,2,3,8,4,6,5,7]=>5
[8,7,1,6,4,5,3,2]=>22
[8,7,6,1,5,3,4,2]=>23
[4,8,7,5,6,3,2,1]=>23
[4,3,7,6,2,1,8,5]=>14
[4,7,6,3,2,8,1,5]=>17
[7,1,6,5,8,3,2,4]=>17
[7,1,6,5,4,8,2,3]=>17
[5,1,7,3,8,4,6,2]=>14
[4,3,6,2,7,1,8,5]=>12
[8,7,5,4,1,3,2,6]=>21
[6,4,3,8,2,1,5,7]=>15
[5,3,8,7,6,4,2,1]=>21
[8,4,7,6,5,1,3,2]=>23
[2,3,8,7,4,5,6,1]=>14
[7,6,5,3,2,1,8,4]=>19
[1,7,2,8,3,6,4,5]=>11
[1,5,2,8,3,7,4,6]=>9
[3,2,4,1,7,5,8,6]=>7
[4,3,6,1,7,2,8,5]=>11
[3,7,5,6,8,4,2,1]=>19
[5,4,6,3,7,1,8,2]=>15
[1,2,8,7,4,5,6,3]=>12
[2,8,6,3,7,4,5,1]=>17
[5,4,6,1,7,3,8,2]=>14
[1,8,2,6,3,4,5,7]=>9
[1,2,8,7,6,3,4,5]=>12
[6,3,8,4,2,5,7,1]=>17
[8,7,1,6,2,5,4,3]=>20
[8,2,7,6,3,5,4,1]=>21
[1,2,3,7,4,6,5,8]=>4
[4,5,2,3,8,1,6,7]=>11
[8,1,7,6,5,4,2,3]=>21
[1,8,6,7,5,4,3,2]=>20
[6,2,8,7,5,4,3,1]=>21
[7,1,3,5,8,2,4,6]=>12
[4,6,2,7,3,5,1,8]=>13
[1,5,7,3,8,4,6,2]=>13
[8,1,7,6,5,2,4,3]=>20
[1,3,2,8,4,7,5,6]=>7
[5,2,3,8,1,6,7,4]=>12
[1,8,2,4,3,5,6,7]=>7
[2,4,1,8,7,6,5,3]=>13
[2,8,7,6,5,3,4,1]=>21
[3,8,6,4,2,7,5,1]=>18
[1,8,5,4,3,2,6,7]=>12
[8,2,6,1,7,3,5,4]=>16
[7,1,8,6,5,3,2,4]=>19
[1,7,2,5,3,6,4,8]=>8
[1,8,2,6,3,7,4,5]=>11
[5,1,2,4,8,3,6,7]=>8
[1,6,2,8,3,7,4,5]=>10
[2,1,8,4,7,5,6,3]=>12
[6,5,1,4,3,8,2,7]=>14
[5,7,3,8,4,6,2,1]=>20
[8,7,3,5,1,6,2,4]=>20
[6,4,8,1,7,2,3,5]=>16
[5,4,8,1,7,2,6,3]=>16
[1,7,2,6,3,8,4,5]=>10
[2,8,1,3,4,5,7,6]=>8
[6,1,7,2,8,5,4,3]=>15
[7,1,2,8,3,5,4,6]=>11
[1,6,2,5,8,3,4,7]=>9
[8,7,1,5,6,4,3,2]=>22
[8,1,7,5,6,4,3,2]=>21
[1,7,2,8,4,5,3,6]=>11
[1,7,3,4,2,5,8,6]=>8
[8,2,5,1,3,6,4,7]=>12
[7,1,2,8,5,3,4,6]=>12
[7,1,6,8,4,3,2,5]=>17
[8,3,1,2,4,7,5,6]=>11
[5,2,1,8,6,7,4,3]=>14
[8,3,4,1,6,7,2,5]=>15
[1,8,2,4,3,6,5,7]=>8
[2,3,5,7,6,8,1,4]=>11
[5,2,6,3,7,4,8,1]=>13
[1,6,7,8,3,4,5,2]=>15
[1,6,2,8,3,5,4,7]=>9
[8,6,1,2,7,5,3,4]=>17
[2,8,1,7,5,6,3,4]=>15
[4,1,2,3,6,8,7,5]=>7
[6,7,1,8,2,3,5,4]=>15
[8,1,5,3,2,4,6,7]=>11
[7,8,5,6,2,1,4,3]=>22
[7,8,4,2,6,1,5,3]=>20
[8,6,1,3,4,2,5,7]=>14
[8,3,1,5,6,2,4,7]=>13
[6,5,8,7,3,4,1,2]=>22
[6,4,8,3,7,5,1,2]=>20
[3,6,4,5,7,2,8,1]=>14
[5,2,4,7,3,6,8,1]=>13
[4,2,5,1,6,3,8,7]=>8
[5,4,3,6,1,2,8,7]=>12
[4,5,2,3,7,6,1,8]=>11
[4,1,2,6,5,8,7,3]=>9
[5,1,6,2,4,8,7,3]=>11
[4,7,2,8,1,3,5,6]=>13
[7,6,2,1,8,5,4,3]=>18
[2,7,6,8,5,4,1,3]=>19
[8,7,1,6,5,3,2,4]=>21
[3,1,8,2,4,7,6,5]=>10
[5,4,6,2,7,1,8,3]=>14
[1,7,6,8,5,4,2,3]=>18
[6,8,5,4,2,1,3,7]=>19
[7,8,2,1,3,4,6,5]=>14
[8,5,7,3,2,1,6,4]=>20
[4,5,2,7,8,1,6,3]=>14
[4,2,5,3,7,6,8,1]=>11
[3,2,6,4,7,5,8,1]=>11
[4,2,6,3,7,5,8,1]=>12
[4,2,5,3,7,1,8,6]=>10
[2,7,6,5,3,4,8,1]=>16
[5,8,6,7,4,3,2,1]=>24
[4,2,5,1,7,6,8,3]=>10
[4,2,6,1,7,3,8,5]=>10
[4,3,1,2,8,7,5,6]=>10
[4,1,5,2,7,6,8,3]=>9
[4,1,6,2,7,5,8,3]=>10
[1,7,2,4,3,5,6,8]=>6
[6,2,8,4,5,1,7,3]=>16
[8,1,4,2,6,3,5,7]=>11
[4,3,5,1,6,2,8,7]=>9
[3,1,5,4,7,6,8,2]=>9
[4,1,5,3,7,6,8,2]=>10
[4,1,6,3,7,5,8,2]=>11
[4,6,7,2,8,1,5,3]=>16
[8,3,6,1,4,7,2,5]=>16
[5,6,7,8,2,1,4,3]=>18
[1,7,2,3,4,6,5,8]=>6
[1,7,2,5,3,8,4,6]=>9
[6,3,7,1,4,8,2,5]=>14
[2,1,7,5,6,8,3,4]=>11
[2,1,5,3,8,7,6,4]=>9
[1,8,4,2,5,3,6,7]=>9
[3,1,6,5,4,2,8,7]=>9
[5,6,1,2,3,8,7,4]=>11
[1,3,2,7,4,6,5,8]=>5
[1,2,7,6,8,3,4,5]=>10
[3,8,7,6,4,5,2,1]=>22
[4,8,2,3,5,1,6,7]=>12
[5,1,6,4,7,3,8,2]=>13
[6,1,8,7,2,5,4,3]=>17
[1,8,2,5,3,7,4,6]=>10
[2,6,8,4,3,7,5,1]=>16
[4,2,6,8,7,3,5,1]=>16
[8,5,1,3,7,2,6,4]=>16
[1,8,2,4,3,7,5,6]=>9
[3,7,6,2,4,8,5,1]=>16
[4,7,2,5,8,3,6,1]=>16
[5,4,6,2,7,3,8,1]=>15
[6,1,8,3,2,5,4,7]=>12
[8,4,1,5,7,2,6,3]=>16
[8,7,6,3,5,1,4,2]=>24
[3,4,8,5,6,7,2,1]=>16
[2,7,8,4,5,3,6,1]=>17
[3,1,6,5,7,4,8,2]=>11
[4,1,2,8,7,6,5,3]=>13
[5,8,1,2,7,6,3,4]=>15
[5,3,1,8,2,7,4,6]=>12
[4,3,6,2,7,5,8,1]=>13
[8,5,3,7,1,6,2,4]=>19
[7,5,1,3,8,2,6,4]=>15
[3,6,8,5,7,2,4,1]=>19
[8,2,1,7,3,5,6,4]=>14
[2,8,4,1,6,7,5,3]=>14
[3,6,8,7,1,5,4,2]=>18
[8,3,6,7,2,1,5,4]=>19
[4,6,8,2,1,7,5,3]=>16
[3,7,6,8,4,5,2,1]=>20
[2,7,6,8,5,3,4,1]=>19
[2,4,8,6,7,3,5,1]=>16
[6,8,2,4,3,5,1,7]=>16
[7,5,2,8,3,4,6,1]=>18
[5,6,2,8,4,3,1,7]=>16
[5,7,8,6,3,4,1,2]=>22
[4,1,6,5,7,3,8,2]=>12
[3,2,5,1,7,6,8,4]=>9
[3,2,6,1,7,5,8,4]=>10
[4,2,6,1,7,5,8,3]=>11
[5,1,8,2,7,6,4,3]=>15
[6,4,3,1,2,8,7,5]=>13
[7,4,3,1,8,2,6,5]=>15
[3,2,8,1,7,6,4,5]=>13
[3,2,8,7,1,5,4,6]=>13
[4,8,2,7,1,5,3,6]=>15
[1,4,2,8,3,7,5,6]=>8
[1,6,2,4,3,8,5,7]=>7
[6,3,8,2,1,7,5,4]=>16
[7,5,1,3,8,4,2,6]=>15
[2,6,5,7,3,4,8,1]=>14
[8,1,6,2,7,4,5,3]=>16
[5,7,3,6,1,8,2,4]=>16
[6,8,1,7,2,5,3,4]=>17
[4,2,1,3,8,5,7,6]=>8
[3,2,5,1,6,4,8,7]=>7
[5,8,7,2,1,4,3,6]=>17
[3,2,8,6,5,1,4,7]=>13
[6,1,5,8,7,4,2,3]=>17
[6,5,3,2,8,7,1,4]=>17
[3,7,6,5,1,8,2,4]=>16
[1,7,4,8,6,3,5,2]=>16
[3,8,6,7,1,5,2,4]=>18
[3,2,6,1,4,8,7,5]=>9
[5,7,2,8,4,3,6,1]=>18
[3,7,4,1,8,5,2,6]=>13
[1,7,5,4,8,3,6,2]=>15
[3,2,6,4,7,1,8,5]=>10
[4,3,5,1,7,2,8,6]=>10
[5,2,6,1,7,3,8,4]=>11
[8,5,6,7,1,3,2,4]=>20
[7,8,1,3,2,5,4,6]=>14
[6,1,2,8,4,3,5,7]=>10
[3,2,5,1,7,4,8,6]=>8
[5,4,6,1,7,2,8,3]=>13
[1,6,8,5,3,7,4,2]=>16
[7,8,2,3,1,5,6,4]=>16
[7,5,8,4,3,6,2,1]=>23
[8,6,1,7,4,2,5,3]=>19
[3,2,8,5,7,4,6,1]=>15
[2,8,5,7,6,4,3,1]=>20
[3,6,5,8,7,4,1,2]=>18
[4,3,6,1,5,8,2,7]=>11
[2,1,8,7,4,6,3,5]=>13
[1,3,6,7,5,8,2,4]=>11
[1,6,7,3,2,5,4,8]=>10
[3,1,6,4,7,5,8,2]=>10
[5,2,6,4,7,3,8,1]=>14
[3,8,1,5,2,4,6,7]=>10
[3,7,8,1,5,2,4,6]=>14
[1,2,7,5,8,3,4,6]=>9
[6,7,1,4,2,8,3,5]=>14
[1,6,7,2,8,4,3,5]=>12
[5,4,2,8,7,1,6,3]=>16
[4,7,2,1,3,5,8,6]=>10
[5,2,7,1,3,8,4,6]=>11
[5,3,1,7,8,2,4,6]=>12
[4,3,5,2,1,8,6,7]=>10
[5,6,2,1,4,8,3,7]=>12
[4,1,3,2,8,5,6,7]=>7
[2,6,1,4,5,8,3,7]=>9
[2,1,7,6,5,8,3,4]=>12
[6,4,3,5,8,1,7,2]=>16
[2,7,6,4,5,8,1,3]=>16
[7,3,5,4,8,6,1,2]=>18
[3,2,5,4,8,1,6,7]=>9
[3,2,6,7,4,5,1,8]=>11
[3,2,6,8,4,1,5,7]=>11
[4,6,2,8,3,1,5,7]=>13
[5,6,8,2,3,1,4,7]=>15
[5,7,8,2,1,3,4,6]=>15
[1,4,3,7,8,5,6,2]=>11
[1,5,6,3,4,8,7,2]=>11
[4,1,2,7,8,5,6,3]=>11
[5,1,7,2,8,4,6,3]=>13
[6,1,7,8,2,4,5,3]=>15
[5,7,1,2,8,3,6,4]=>13
[1,8,6,5,3,7,4,2]=>17
[5,8,7,3,2,6,1,4]=>20
[1,7,6,8,4,3,5,2]=>17
[2,5,3,7,1,6,8,4]=>10
[5,2,6,3,7,1,8,4]=>12
[2,6,1,3,5,4,8,7]=>7
[1,5,2,4,3,7,6,8]=>5
[1,3,2,8,4,6,5,7]=>6
[1,7,2,4,3,6,5,8]=>7
[2,8,3,1,5,4,6,7]=>9
[2,5,3,4,7,1,8,6]=>9
[4,2,5,3,1,8,6,7]=>9
[4,2,1,8,5,3,6,7]=>9
[5,1,4,8,3,2,6,7]=>11
[1,5,8,4,3,2,6,7]=>11
[4,3,6,2,8,7,5,1]=>15
[6,4,3,1,7,2,8,5]=>13
[1,7,4,3,8,5,2,6]=>12
[1,5,7,3,8,4,2,6]=>12
[5,1,4,7,8,3,2,6]=>13
[5,4,7,1,3,8,2,6]=>14
[4,8,1,5,7,3,6,2]=>16
[8,1,5,3,7,4,6,2]=>16
[1,4,3,8,7,5,6,2]=>12
[4,3,1,8,6,7,5,2]=>14
[4,3,7,1,8,6,5,2]=>15
[6,8,1,7,4,3,5,2]=>19
[6,4,8,1,7,3,5,2]=>18
[6,4,8,7,1,5,2,3]=>19
[7,6,4,1,3,8,2,5]=>17
[7,6,1,4,8,3,2,5]=>17
[1,7,5,6,3,2,8,4]=>13
[6,1,7,5,3,2,8,4]=>14
[6,5,3,2,8,7,4,1]=>18
[5,2,6,3,8,7,4,1]=>15
[5,2,7,6,3,1,8,4]=>14
[6,5,2,1,7,3,8,4]=>13
[4,2,1,7,8,5,3,6]=>11
[2,7,4,6,3,1,8,5]=>13
[6,2,4,8,3,7,5,1]=>16
[7,2,6,3,4,1,8,5]=>14
[2,7,1,8,3,5,4,6]=>11
[2,1,7,3,5,8,4,6]=>8
[8,1,2,7,6,3,4,5]=>14
[7,8,2,6,3,1,5,4]=>19
[2,7,8,4,1,6,5,3]=>16
[8,3,7,1,5,6,2,4]=>18
[1,8,5,2,6,7,4,3]=>14
[5,2,7,1,8,6,4,3]=>15
[1,7,8,5,2,6,4,3]=>16
[7,8,1,6,4,2,5,3]=>19
[7,8,6,1,5,3,2,4]=>21
[7,3,8,6,1,5,2,4]=>19
[2,7,6,8,1,4,3,5]=>15
[8,2,5,7,6,4,3,1]=>21
[6,5,8,7,1,2,3,4]=>18
[4,1,5,3,7,2,8,6]=>9
[4,7,3,2,1,5,8,6]=>12
[5,8,6,2,4,1,3,7]=>17
[5,1,6,2,7,4,8,3]=>11
[8,3,5,2,1,6,4,7]=>14
[5,7,3,8,1,4,6,2]=>17
[6,8,1,4,7,2,5,3]=>17
[3,2,1,7,8,5,6,4]=>11
[4,7,3,5,8,6,2,1]=>18
[4,3,6,5,7,1,8,2]=>13
[8,4,2,1,7,3,6,5]=>15
[3,7,5,1,4,2,8,6]=>12
[1,8,6,3,7,5,2,4]=>16
[6,2,8,1,3,4,7,5]=>12
[4,7,6,5,8,1,2,3]=>18
[5,3,6,2,7,1,8,4]=>13
[4,8,2,1,7,6,3,5]=>15
[2,7,4,8,1,6,5,3]=>15
[3,8,2,1,4,6,5,7]=>10
[1,4,2,8,3,6,5,7]=>7
[4,7,2,8,1,5,3,6]=>14
[5,2,1,8,3,4,7,6]=>10
[4,1,3,2,8,6,5,7]=>8
[3,1,6,7,5,8,2,4]=>12
[2,4,5,7,3,1,8,6]=>10
[4,6,8,3,2,7,5,1]=>18
[1,4,6,7,3,2,8,5]=>10
[3,7,6,5,8,2,1,4]=>18
[2,1,6,5,7,8,3,4]=>10
[2,1,7,8,5,6,4,3]=>14
[2,5,4,7,6,1,8,3]=>12
[3,2,5,6,1,8,7,4]=>10
[6,3,1,5,2,4,8,7]=>10
[1,3,7,4,6,8,2,5]=>10
[8,1,6,5,7,2,4,3]=>18
[7,8,1,6,2,4,5,3]=>18
[1,7,2,8,5,3,4,6]=>11
[7,6,1,8,4,3,2,5]=>18
[8,1,2,7,3,4,6,5]=>12
[1,3,8,7,5,6,2,4]=>14
[6,3,7,5,2,8,4,1]=>18
[8,5,7,3,1,4,2,6]=>19
[2,5,7,3,8,6,4,1]=>15
[2,8,6,3,1,5,7,4]=>14
[4,8,1,2,7,6,3,5]=>14
[4,1,2,8,7,5,6,3]=>12
[8,4,2,1,7,5,3,6]=>15
[3,1,4,8,6,5,7,2]=>11
[3,4,8,1,7,2,5,6]=>12
[2,3,8,1,4,6,7,5]=>9
[5,3,6,4,7,2,8,1]=>15
[5,3,6,1,7,4,8,2]=>13
[5,3,6,1,7,2,8,4]=>12
[5,3,6,2,7,4,8,1]=>14
[5,2,6,4,7,1,8,3]=>13
[8,1,5,4,7,6,2,3]=>17
[1,8,6,7,4,5,3,2]=>19
[7,1,6,8,4,2,5,3]=>17
[7,8,6,1,4,2,3,5]=>19
[8,6,7,1,3,4,2,5]=>19
[7,6,8,1,3,2,4,5]=>17
[7,5,8,3,1,2,4,6]=>17
[8,6,1,7,3,5,2,4]=>19
[1,7,8,6,5,3,4,2]=>19
[7,8,1,6,5,2,3,4]=>19
[6,4,3,7,2,5,1,8]=>15
[8,4,3,6,5,1,2,7]=>17
[6,5,8,3,2,1,4,7]=>17
[1,8,2,5,3,6,4,7]=>9
[1,5,2,8,3,6,4,7]=>8
[6,7,8,1,4,3,2,5]=>18
[6,7,8,5,1,3,2,4]=>20
[5,7,6,8,2,3,4,1]=>20
[6,7,8,2,4,3,5,1]=>20
[1,5,2,4,3,8,6,7]=>6
[3,2,7,1,8,4,6,5]=>11
[7,8,4,1,6,2,3,5]=>18
[6,1,8,4,5,2,3,7]=>14
[7,8,3,1,2,6,4,5]=>16
[7,8,2,4,5,1,6,3]=>18
[6,2,8,3,1,5,7,4]=>14
[6,3,8,4,5,7,1,2]=>18
[2,6,7,4,5,1,8,3]=>14
[2,6,7,3,1,5,8,4]=>12
[3,5,4,7,6,8,1,2]=>14
[5,3,4,8,6,7,1,2]=>16
[5,2,4,8,6,1,7,3]=>14
[6,3,8,1,2,7,4,5]=>14
[5,1,3,8,2,6,4,7]=>10
[5,1,4,8,6,2,3,7]=>12
[4,6,7,3,8,5,1,2]=>18
[4,5,3,7,8,6,1,2]=>16
[4,2,5,6,8,1,7,3]=>12
[4,3,5,6,8,7,1,2]=>14
[3,7,5,2,4,1,8,6]=>13
[8,2,4,5,7,3,6,1]=>17
[8,2,4,6,5,3,1,7]=>16
[8,2,5,4,6,1,3,7]=>15
[8,6,3,5,1,4,2,7]=>18
[8,6,1,4,5,3,2,7]=>17
[8,1,5,6,4,3,2,7]=>16
[5,4,7,3,1,8,2,6]=>15
[1,7,4,5,3,2,8,6]=>11
[5,7,4,2,1,3,8,6]=>14
[8,3,7,5,1,4,6,2]=>19
[8,4,1,7,5,3,6,2]=>18
[4,6,3,8,7,1,5,2]=>17
[3,1,5,8,6,7,4,2]=>13
[4,8,1,6,7,3,5,2]=>17
[3,6,4,1,8,7,5,2]=>14
[8,2,6,1,4,7,5,3]=>16
[3,7,1,6,4,8,2,5]=>13
[1,7,3,5,6,8,2,4]=>12
[4,2,7,6,8,3,1,5]=>15
[3,8,2,4,6,7,5,1]=>15
[3,7,2,6,4,8,1,5]=>14
[5,3,7,2,1,8,4,6]=>13
[8,7,6,1,3,4,2,5]=>20
[3,7,8,6,2,1,5,4]=>18
[8,5,7,2,1,3,6,4]=>18
[8,2,6,7,1,3,5,4]=>17
[8,3,6,1,7,5,2,4]=>18
[4,6,1,8,7,2,5,3]=>15
[8,2,6,5,7,4,1,3]=>20
[1,7,2,5,8,6,4,3]=>13
[1,7,4,8,2,6,5,3]=>14
[3,7,8,1,6,5,2,4]=>17
[2,7,8,6,1,3,5,4]=>16
[1,6,4,7,5,8,2,3]=>13
[8,2,6,3,4,7,5,1]=>17
[7,2,6,3,5,4,8,1]=>16
[6,2,7,4,3,5,8,1]=>15
[4,7,5,6,3,2,8,1]=>18
[3,7,6,4,5,2,8,1]=>17
[6,1,7,5,3,8,2,4]=>15
[5,4,1,7,6,8,2,3]=>14
[4,8,5,6,2,7,3,1]=>19
[7,8,5,2,4,6,3,1]=>22
[2,8,1,7,4,3,6,5]=>13
[3,8,4,1,7,2,6,5]=>14
[5,4,7,1,8,3,2,6]=>15
[6,7,1,4,8,3,2,5]=>16
[2,7,1,8,4,5,3,6]=>12
[7,4,2,1,8,5,3,6]=>14
[6,4,3,1,5,8,2,7]=>13
[4,7,5,6,8,3,2,1]=>20
[1,4,8,6,7,5,2,3]=>15
[7,3,8,5,4,6,2,1]=>21
[6,3,5,8,4,7,2,1]=>19
[5,4,3,8,6,7,2,1]=>18
[5,4,2,8,7,3,6,1]=>17
[6,2,5,8,7,3,4,1]=>18
[7,2,8,6,4,3,5,1]=>20
[3,1,8,5,7,6,2,4]=>14
[5,4,1,8,7,6,2,3]=>16
[4,5,2,6,3,1,8,7]=>11
[6,5,2,7,4,8,3,1]=>18
[8,3,7,5,2,1,6,4]=>19
[5,6,3,2,4,1,8,7]=>13
[3,6,2,4,1,5,8,7]=>9
[7,6,1,3,5,8,4,2]=>17
[3,6,7,4,1,8,5,2]=>15
[5,6,3,7,4,8,1,2]=>17
[2,1,6,7,4,8,5,3]=>11
[5,8,3,7,4,2,6,1]=>20
[3,8,7,4,1,2,6,5]=>16
[7,8,1,3,5,2,6,4]=>16
[3,8,4,2,5,7,1,6]=>14
[6,8,3,5,2,7,4,1]=>20
[2,1,8,5,3,7,4,6]=>10
[7,5,2,4,8,1,6,3]=>17
[3,4,2,8,5,7,6,1]=>13
[5,7,1,6,8,2,4,3]=>16
[8,6,2,5,1,7,4,3]=>19
[5,6,2,1,8,7,3,4]=>14
[7,5,2,6,3,8,1,4]=>17
[2,4,3,1,8,5,6,7]=>7
[7,1,8,5,4,3,6,2]=>18
[2,1,7,8,5,4,6,3]=>13
[2,1,5,8,4,6,3,7]=>9
[6,5,3,8,4,1,2,7]=>17
[2,4,8,3,5,6,1,7]=>11
[4,1,8,3,6,5,2,7]=>12
[8,4,1,3,7,2,6,5]=>15
[4,3,8,2,5,1,7,6]=>13
[7,4,3,8,2,5,1,6]=>17
[2,1,4,8,3,5,7,6]=>7
[3,2,5,4,7,1,8,6]=>9
[4,2,5,3,6,1,8,7]=>9
[3,1,5,4,6,2,8,7]=>7
[4,1,5,3,6,2,8,7]=>8
[3,1,5,4,7,2,8,6]=>8
[2,1,5,4,7,3,8,6]=>7
[4,3,5,1,7,6,8,2]=>11
[4,3,6,1,7,5,8,2]=>12
[5,1,6,3,7,4,8,2]=>12
[2,1,6,4,7,5,8,3]=>9
[2,1,6,4,7,3,8,5]=>8
[3,1,6,4,7,2,8,5]=>9
[4,1,6,3,7,2,8,5]=>10
[5,1,6,3,7,2,8,4]=>11
[4,2,5,1,7,3,8,6]=>9
[4,2,6,3,7,1,8,5]=>11
[3,1,4,2,7,6,8,5]=>7
[3,2,6,5,7,1,8,4]=>11
[4,2,6,5,7,3,8,1]=>13
[4,2,6,5,7,1,8,3]=>12
[3,1,5,2,7,6,8,4]=>8
[2,1,5,3,7,6,8,4]=>7
[2,1,6,3,7,5,8,4]=>8
[3,1,6,2,7,5,8,4]=>9
[5,2,6,1,7,4,8,3]=>12
[5,1,6,4,7,2,8,3]=>12
[4,1,6,5,7,2,8,3]=>11
[3,1,6,5,7,2,8,4]=>10
[2,1,6,5,7,3,8,4]=>9
[4,7,2,6,5,3,1,8]=>15
[5,7,6,2,4,3,1,8]=>17
[4,8,2,6,5,1,3,7]=>15
[6,1,5,4,2,8,7,3]=>13
[7,1,5,4,8,2,6,3]=>15
[6,8,7,1,2,4,3,5]=>17
[8,4,3,7,1,5,2,6]=>17
[4,5,2,3,1,8,7,6]=>11
[1,5,8,3,7,6,4,2]=>15
[8,5,1,3,7,6,2,4]=>17
[6,5,1,3,2,8,7,4]=>13
[4,6,2,1,3,8,7,5]=>11
[4,7,2,1,8,3,6,5]=>13
[7,6,1,8,3,2,5,4]=>17
[1,6,8,7,3,5,4,2]=>17
[7,1,8,6,5,2,4,3]=>19
[1,4,2,7,3,6,5,8]=>6
[1,5,2,7,3,6,4,8]=>7
[1,7,2,4,3,8,5,6]=>8
[1,6,2,5,3,8,4,7]=>8
[5,3,6,8,4,7,2,1]=>18
[3,7,2,5,4,8,6,1]=>14
[8,4,2,5,7,3,6,1]=>18
[4,2,6,5,8,3,7,1]=>14
[5,2,6,8,4,3,7,1]=>16
[3,1,6,5,4,8,2,7]=>10
[4,1,6,5,8,3,2,7]=>12
[5,1,6,8,4,3,2,7]=>14
[5,7,1,8,4,3,2,6]=>16
[4,7,1,5,8,3,2,6]=>14
[2,7,1,5,4,3,8,6]=>10
[8,3,1,5,4,7,2,6]=>14
[8,4,1,5,7,3,2,6]=>16
[8,4,6,1,7,3,2,5]=>18
[8,2,6,1,4,3,7,5]=>14
[2,7,6,1,4,3,8,5]=>12
[3,7,6,1,4,8,2,5]=>14
[4,7,6,2,8,3,5,1]=>18
[8,3,6,2,4,7,5,1]=>18
[8,7,3,1,4,6,2,5]=>18
[8,7,2,5,1,3,6,4]=>18
[8,2,6,5,1,3,7,4]=>16
[8,3,6,5,1,7,2,4]=>18
[8,4,6,5,7,1,2,3]=>20
[5,7,6,8,4,1,2,3]=>20
[2,7,6,5,1,3,8,4]=>14
[9,7,8,4,5,6,1,2,3]=>29
[9,7,8,5,6,1,2,3,4]=>28
[9,8,5,6,7,1,2,3,4]=>27
[8,9,5,6,7,1,2,3,4]=>26
[7,4,8,2,5,9,1,3,6]=>20
[6,4,7,2,5,1,3,8,9]=>15
[6,3,2,7,8,1,4,5,9]=>14
[6,7,3,4,8,1,2,5,9]=>17
[8,7,6,5,4,3,2,1,9]=>28
[1,9,8,7,6,5,4,3,2]=>28
[8,7,6,4,5,3,2,1,9]=>27
[1,9,8,7,5,6,4,3,2]=>27
[8,7,5,4,6,3,2,1,9]=>26
[8,7,4,6,5,3,2,1,9]=>26
[1,9,8,6,5,7,4,3,2]=>26
[1,9,8,5,7,6,4,3,2]=>26
[9,1,2,3,4,5,6,7,8]=>8
[2,3,4,5,6,7,8,9,1]=>8
[8,1,2,3,4,5,6,7,9]=>7
[2,3,4,5,6,7,8,1,9]=>7
[8,1,2,3,4,5,6,9,7]=>8
[7,1,2,3,4,5,6,8,9]=>6
[2,3,4,5,6,7,1,8,9]=>6
[2,3,4,5,6,7,9,1,8]=>8
[9,2,1,3,4,5,6,7,8]=>9
[3,2,4,5,6,7,8,9,1]=>9
[9,3,1,2,4,5,6,7,8]=>10
[9,2,3,1,4,5,6,7,8]=>10
[4,2,3,5,6,7,8,9,1]=>10
[3,4,2,5,6,7,8,9,1]=>10
[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]=>26
[6,8,7,5,4,3,2,1,9]=>26
[1,8,7,9,6,5,4,3,2]=>26
[1,7,9,8,6,5,4,3,2]=>26
[1,9,2,3,4,5,6,7,8]=>7
[7,8,1,2,3,4,5,6,9]=>12
[1,8,9,2,3,4,5,6,7]=>12
[7,1,8,2,3,4,5,6,9]=>11
[6,8,1,2,3,4,5,7,9]=>11
[1,8,2,9,3,4,5,6,7]=>11
[1,7,9,2,3,4,5,6,8]=>11
[1,2,3,4,5,6,7,9,8]=>1
[2,1,3,4,5,6,7,8,9]=>1
[2,9,1,3,4,5,6,7,8]=>8
[1,8,2,3,4,5,6,9,7]=>7
[7,1,2,3,4,5,6,9,8]=>7
[2,1,9,3,4,5,6,7,8]=>7
[2,8,1,3,4,5,6,7,9]=>7
[1,2,3,4,5,6,7,8,9]=>0
[8,9,1,2,3,4,5,6,7]=>14
[9,8,1,2,3,4,5,6,7]=>15
[7,8,9,1,2,3,4,5,6]=>18
[9,7,8,1,2,3,4,5,6]=>20
[9,8,7,1,2,3,4,5,6]=>21
[6,7,8,9,1,2,3,4,5]=>20
[9,6,7,8,1,2,3,4,5]=>23
[8,9,6,7,1,2,3,4,5]=>24
[9,8,6,7,1,2,3,4,5]=>25
[9,8,7,6,1,2,3,4,5]=>26
[9,5,6,7,8,1,2,3,4]=>24
[9,8,7,5,6,1,2,3,4]=>29
[9,8,7,6,5,1,2,3,4]=>30
[7,8,9,4,5,6,1,2,3]=>27
[9,8,7,4,5,6,1,2,3]=>30
[8,9,6,7,4,5,1,2,3]=>30
[9,8,6,7,4,5,1,2,3]=>31
[9,8,7,6,4,5,1,2,3]=>32
[9,8,7,6,5,4,1,2,3]=>33
[9,7,8,5,6,3,4,1,2]=>32
[9,8,7,5,6,3,4,1,2]=>33
[9,8,7,6,5,3,4,1,2]=>34
[9,8,7,6,5,4,3,1,2]=>35
[9,8,7,6,5,4,3,2,1]=>36
[3,4,1,2,5,6,7,8,9]=>4
[3,2,1,4,5,6,7,8,9]=>3
[4,5,6,1,2,3,7,8,9]=>9
[4,2,5,1,3,6,7,8,9]=>6
[4,3,2,1,5,6,7,8,9]=>6
[5,6,7,8,1,2,3,4,9]=>16
[5,2,6,7,1,3,4,8,9]=>11
[5,6,3,4,1,2,7,8,9]=>12
[5,3,2,6,1,4,7,8,9]=>9
[5,4,3,2,1,6,7,8,9]=>10
[6,2,7,8,9,1,3,4,5]=>18
[6,4,3,2,7,1,5,8,9]=>13
[6,5,4,3,2,1,7,8,9]=>15
[7,4,3,2,8,9,1,5,6]=>18
[7,8,5,6,3,4,1,2,9]=>24
[7,5,3,8,2,6,1,4,9]=>19
[7,5,4,3,2,8,1,6,9]=>18
[7,6,5,4,3,2,1,8,9]=>21
[8,6,9,4,7,2,5,1,3]=>28
[8,6,4,3,9,2,7,1,5]=>24
[8,6,5,4,3,2,9,1,7]=>24
[2,1,4,3,6,5,8,7,10,9]=>5
[4,3,2,1,6,5,8,7,10,9]=>9
[6,3,2,5,4,1,8,7,10,9]=>13
[8,3,2,5,4,7,6,1,10,9]=>17
[10,3,2,5,4,7,6,9,8,1]=>21
[2,1,6,5,4,3,8,7,10,9]=>9
[6,5,4,3,2,1,8,7,10,9]=>17
[8,5,4,3,2,7,6,1,10,9]=>21
[10,5,4,3,2,7,6,9,8,1]=>25
[2,1,8,5,4,7,6,3,10,9]=>13
[8,7,4,3,6,5,2,1,10,9]=>25
[10,7,4,3,6,5,2,9,8,1]=>29
[2,1,10,5,4,7,6,9,8,3]=>17
[10,9,4,3,6,5,8,7,2,1]=>33
[8,9,5,6,3,4,10,1,2,7]=>29
[2,1,4,3,8,7,6,5,10,9]=>9
[4,3,2,1,8,7,6,5,10,9]=>13
[8,3,2,7,6,5,4,1,10,9]=>21
[10,3,2,7,6,5,4,9,8,1]=>25
[2,1,8,7,6,5,4,3,10,9]=>17
[8,7,6,5,4,3,2,1,10,9]=>29
[9,7,6,5,4,3,2,10,1,8]=>31
[10,7,6,5,4,3,2,9,8,1]=>33
[2,1,10,7,6,5,4,9,8,3]=>21
[10,9,6,5,4,3,8,7,2,1]=>37
[2,1,4,3,10,7,6,9,8,5]=>13
[4,3,2,1,10,7,6,9,8,5]=>17
[10,3,2,9,6,5,8,7,4,1]=>29
[2,1,10,9,6,5,8,7,4,3]=>25
[10,9,8,5,4,7,6,3,2,1]=>41
[6,7,8,9,10,1,2,3,4,5]=>25
[7,3,2,8,9,10,1,4,5,6]=>21
[8,5,4,3,2,9,10,1,6,7]=>23
[2,1,4,3,6,5,10,9,8,7]=>9
[4,3,2,1,6,5,10,9,8,7]=>13
[6,3,2,5,4,1,10,9,8,7]=>17
[10,3,2,5,4,9,8,7,6,1]=>25
[2,1,6,5,4,3,10,9,8,7]=>13
[6,5,4,3,2,1,10,9,8,7]=>21
[10,5,4,3,2,9,8,7,6,1]=>29
[2,1,10,5,4,9,8,7,6,3]=>21
[10,9,4,3,8,7,6,5,2,1]=>37
[9,7,5,10,3,8,2,6,1,4]=>33
[2,1,4,3,10,9,8,7,6,5]=>17
[4,3,2,1,10,9,8,7,6,5]=>21
[10,3,2,9,8,7,6,5,4,1]=>33
[2,1,10,9,8,7,6,5,4,3]=>29
[10,9,8,7,6,5,4,3,2,1]=>45
[2,4,6,8,10,1,3,5,7,9]=>15
[5,6,7,8,10,1,2,3,4,9]=>21
[4,7,8,9,10,1,2,3,5,6]=>23
[5,7,8,9,10,1,2,3,4,6]=>24
[4,5,6,8,10,1,2,3,7,9]=>18
[3,7,8,9,10,1,2,4,5,6]=>22
[3,6,7,8,10,1,2,4,5,9]=>19
[3,5,8,9,10,1,2,4,6,7]=>20
[3,6,8,9,10,1,2,4,5,7]=>21
[4,6,7,8,10,1,2,3,5,9]=>20
[4,5,8,9,10,1,2,3,6,7]=>21
[5,6,8,9,10,1,2,3,4,7]=>23
[4,6,8,9,10,1,2,3,5,7]=>22
[3,4,6,8,10,1,2,5,7,9]=>16
[2,7,8,9,10,1,3,4,5,6]=>21
[2,6,7,8,10,1,3,4,5,9]=>18
[2,5,8,9,10,1,3,4,6,7]=>19
[2,6,8,9,10,1,3,4,5,7]=>20
[2,5,6,8,10,1,3,4,7,9]=>16
[2,4,8,9,10,1,3,5,6,7]=>18
[2,4,7,8,10,1,3,5,6,9]=>16
[2,4,6,9,10,1,3,5,7,8]=>16
[2,4,7,9,10,1,3,5,6,8]=>17
[2,5,7,8,10,1,3,4,6,9]=>17
[4,5,6,9,10,1,2,3,7,8]=>19
[5,6,7,9,10,1,2,3,4,8]=>22
[2,5,7,9,10,1,3,4,6,8]=>18
[3,5,6,8,10,1,2,4,7,9]=>17
[3,4,8,9,10,1,2,5,6,7]=>19
[3,4,7,8,10,1,2,5,6,9]=>17
[3,4,6,9,10,1,2,5,7,8]=>17
[3,4,7,9,10,1,2,5,6,8]=>18
[4,5,7,8,10,1,2,3,6,9]=>19
[2,5,6,9,10,1,3,4,7,8]=>17
[2,6,7,9,10,1,3,4,5,8]=>19
[4,5,7,9,10,1,2,3,6,8]=>20
[3,5,7,8,10,1,2,4,6,9]=>18
[3,5,6,9,10,1,2,4,7,8]=>18
[3,6,7,9,10,1,2,4,5,8]=>20
[4,6,7,9,10,1,2,3,5,8]=>21
[3,5,7,9,10,1,2,4,6,8]=>19
[10,8,9,5,6,7,1,2,3,4]=>35
[9,6,10,2,7,8,1,3,4,5]=>29
[10,7,8,3,4,9,1,2,5,6]=>29
[9,5,10,4,6,7,1,2,3,8]=>28
[8,4,9,3,5,10,1,2,6,7]=>24
[8,4,9,2,5,10,1,3,6,7]=>23
[10,8,9,4,5,6,1,2,3,7]=>32
[9,6,10,5,7,8,1,2,3,4]=>32
[10,7,8,5,6,9,1,2,3,4]=>33
[9,8,10,5,6,7,1,2,3,4]=>34
[8,7,9,5,6,10,1,2,3,4]=>31
[8,6,9,2,7,10,1,3,4,5]=>27
[10,6,7,4,5,8,1,2,3,9]=>28
[9,5,10,2,6,7,1,3,4,8]=>26
[10,6,7,3,4,8,1,2,5,9]=>26
[9,8,10,4,5,6,1,2,3,7]=>31
[8,7,9,3,4,10,1,2,5,6]=>27
[8,6,9,5,7,10,1,2,3,4]=>30
[7,6,8,4,5,9,1,2,3,10]=>25
[7,5,8,2,6,9,1,3,4,10]=>22
[7,6,8,3,4,9,1,2,5,10]=>23
[7,5,8,4,6,9,1,2,3,10]=>24
[7,4,8,3,5,9,1,2,6,10]=>21
[7,4,8,2,5,9,1,3,6,10]=>20
[7,8,9,10,1,2,3,4,5,6]=>24
[9,10,7,8,5,6,3,4,1,2]=>40
[9,1,2,3,4,5,6,7,8,10]=>8
[1,2,3,4,5,6,7,8,9,10]=>0
[9,10,7,8,5,6,1,2,3,4]=>36
[9,10,5,6,7,8,1,2,3,4]=>32
[9,10,7,8,1,2,3,4,5,6]=>28
[9,10,1,2,3,4,5,6,7,8]=>16
[10,1,2,3,4,5,6,7,8,9]=>9
[9,8,7,6,5,4,3,2,1,10]=>36
[1,10,9,8,7,6,5,4,3,2]=>36
[1,10,2,3,4,5,6,7,8,9]=>8
[3,2,1,4,5,6,7,8,9,10]=>3
[5,4,3,2,1,6,7,8,9,10]=>10
[7,6,5,4,3,2,1,8,9,10]=>21
[9,7,10,5,6,8,1,2,3,4]=>33
[10,7,8,4,5,9,1,2,3,6]=>31
[9,7,10,4,5,8,1,2,3,6]=>31
[8,7,9,4,5,10,1,2,3,6]=>29
[9,6,10,4,5,7,1,2,3,8]=>29
[8,6,9,4,5,10,1,2,3,7]=>28
[8,6,9,4,7,10,1,2,3,5]=>29
[9,6,10,3,4,7,1,2,5,8]=>27
[8,5,9,3,6,10,1,2,4,7]=>26
[9,5,10,3,6,7,1,2,4,8]=>27
[8,6,9,3,4,10,1,2,5,7]=>26
[8,6,9,3,7,10,1,2,4,5]=>28
[9,6,10,3,7,8,1,2,4,5]=>30
[9,7,10,3,4,8,1,2,5,6]=>29
[8,5,9,4,6,10,1,2,3,7]=>27
[9,6,10,4,7,8,1,2,3,5]=>31
[9,8,7,5,6,4,3,2,1,10]=>35
[10,8,9,1,2,3,4,5,6,7]=>23
[1,10,9,8,6,7,5,4,3,2]=>35
[2,3,4,5,6,7,8,9,10,1]=>9
[2,3,4,5,6,7,8,9,1,10]=>8
[10,2,1,3,4,5,6,7,8,9]=>10
[3,2,4,5,6,7,8,9,10,1]=>10
[8,9,7,6,5,4,3,2,1,10]=>35
[1,9,10,8,7,6,5,4,3,2]=>35
[8,9,1,2,3,4,5,6,7,10]=>14
[1,9,10,2,3,4,5,6,7,8]=>14
[1,2,3,4,5,6,7,8,10,9]=>1
[2,1,3,4,5,6,7,8,9,10]=>1
[9,1,2,3,4,5,6,7,10,8]=>9
[2,10,1,3,4,5,6,7,8,9]=>9
[10,9,1,2,3,4,5,6,7,8]=>17
[8,9,10,1,2,3,4,5,6,7]=>21
[10,9,8,1,2,3,4,5,6,7]=>24
[10,7,8,9,1,2,3,4,5,6]=>27
[10,9,7,8,1,2,3,4,5,6]=>29
[10,9,8,7,1,2,3,4,5,6]=>30
[10,6,7,8,9,1,2,3,4,5]=>29
[9,10,6,7,8,1,2,3,4,5]=>31
[10,9,6,7,8,1,2,3,4,5]=>32
[10,8,9,6,7,1,2,3,4,5]=>33
[10,9,8,6,7,1,2,3,4,5]=>34
[10,9,8,7,6,1,2,3,4,5]=>35
[10,9,5,6,7,8,1,2,3,4]=>33
[8,9,10,5,6,7,1,2,3,4]=>33
[10,9,8,5,6,7,1,2,3,4]=>36
[10,9,7,8,5,6,1,2,3,4]=>37
[10,9,8,7,5,6,1,2,3,4]=>38
[10,9,8,7,6,5,1,2,3,4]=>39
[10,7,8,9,4,5,6,1,2,3]=>36
[9,10,7,8,4,5,6,1,2,3]=>37
[10,9,7,8,4,5,6,1,2,3]=>38
[10,9,8,7,4,5,6,1,2,3]=>39
[10,8,9,6,7,4,5,1,2,3]=>39
[10,9,8,6,7,4,5,1,2,3]=>40
[10,9,8,7,6,4,5,1,2,3]=>41
[10,9,8,7,6,5,4,1,2,3]=>42
[10,9,7,8,5,6,3,4,1,2]=>41
[10,9,8,7,5,6,3,4,1,2]=>42
[10,9,8,7,6,5,3,4,1,2]=>43
[10,9,8,7,6,5,4,3,1,2]=>44
[3,4,1,2,5,6,7,8,9,10]=>4
[4,5,6,1,2,3,7,8,9,10]=>9
[4,2,5,1,3,6,7,8,9,10]=>6
[4,3,2,1,5,6,7,8,9,10]=>6
[5,6,7,8,1,2,3,4,9,10]=>16
[5,2,6,7,1,3,4,8,9,10]=>11
[5,6,3,4,1,2,7,8,9,10]=>12
[5,3,2,6,1,4,7,8,9,10]=>9
[6,2,7,8,9,1,3,4,5,10]=>18
[6,7,3,4,8,1,2,5,9,10]=>17
[6,3,2,7,8,1,4,5,9,10]=>14
[6,4,7,2,5,1,3,8,9,10]=>15
[6,4,3,2,7,1,5,8,9,10]=>13
[6,5,4,3,2,1,7,8,9,10]=>15
[7,8,3,4,9,10,1,2,5,6]=>24
[7,8,9,4,5,6,1,2,3,10]=>27
[7,4,3,2,8,9,1,5,6,10]=>18
[7,8,5,6,3,4,1,2,9,10]=>24
[7,5,3,8,2,6,1,4,9,10]=>19
[7,5,4,3,2,8,1,6,9,10]=>18
[8,5,9,10,2,6,7,1,3,4]=>30
[8,5,3,9,2,6,10,1,4,7]=>24
[8,6,9,4,7,2,5,1,3,10]=>28
[8,6,4,3,9,2,7,1,5,10]=>24
[8,6,5,4,3,2,9,1,7,10]=>24
[8,7,6,5,4,3,2,1,9,10]=>28
[9,7,5,4,3,10,2,8,1,6]=>30
[7,5,8,3,6,9,1,2,4,10]=>23
[8,5,9,2,6,10,1,3,4,7]=>25
[10,9,8,7,6,5,4,3,2,1,11]=>45
[1,11,10,9,8,7,6,5,4,3,2]=>45
[11,1,2,3,4,5,6,7,8,9,10]=>10
[2,3,4,5,6,7,8,9,10,11,1]=>10
[10,1,2,3,4,5,6,7,8,9,11]=>9
[1,11,2,3,4,5,6,7,8,9,10]=>9
[1,2,3,4,5,6,7,8,9,11,10]=>1
[2,1,3,4,5,6,7,8,9,10,11]=>1
[6,7,8,9,10,12,1,2,3,4,5,11]=>31
[2,8,9,10,11,12,1,3,4,5,6,7]=>31
[10,9,8,7,6,5,4,3,2,1,12,11]=>46
[2,1,12,11,10,9,8,7,6,5,4,3]=>46
[2,7,9,10,11,12,1,3,4,5,6,8]=>30
[5,7,8,9,10,12,1,2,3,4,6,11]=>30
[2,6,9,10,11,12,1,3,4,5,7,8]=>29
[2,7,8,10,11,12,1,3,4,5,6,9]=>29
[4,7,8,9,10,12,1,2,3,5,6,11]=>29
[5,6,8,9,10,12,1,2,3,4,7,11]=>29
[2,5,9,10,11,12,1,3,4,6,7,8]=>28
[2,6,8,10,11,12,1,3,4,5,7,9]=>28
[2,7,8,9,11,12,1,3,4,5,6,10]=>28
[3,4,9,10,11,12,1,2,5,6,7,8]=>28
[3,7,8,9,10,12,1,2,4,5,6,11]=>28
[4,6,8,9,10,12,1,2,3,5,7,11]=>28
[5,6,7,8,11,12,1,2,3,4,9,10]=>28
[5,6,7,9,10,12,1,2,3,4,8,11]=>28
[2,4,9,10,11,12,1,3,5,6,7,8]=>27
[2,5,8,10,11,12,1,3,4,6,7,9]=>27
[2,6,7,10,11,12,1,3,4,5,8,9]=>27
[2,6,8,9,11,12,1,3,4,5,7,10]=>27
[2,7,8,9,10,12,1,3,4,5,6,11]=>27
[3,4,8,10,11,12,1,2,5,6,7,9]=>27
[3,6,8,9,10,12,1,2,4,5,7,11]=>27
[4,5,6,10,11,12,1,2,3,7,8,9]=>27
[4,5,8,9,10,12,1,2,3,6,7,11]=>27
[4,6,7,8,11,12,1,2,3,5,9,10]=>27
[4,6,7,9,10,12,1,2,3,5,8,11]=>27
[5,6,7,8,10,12,1,2,3,4,9,11]=>27
[2,4,8,10,11,12,1,3,5,6,7,9]=>26
[2,5,7,10,11,12,1,3,4,6,8,9]=>26
[2,5,8,9,11,12,1,3,4,6,7,10]=>26
[2,6,7,9,11,12,1,3,4,5,8,10]=>26
[2,6,8,9,10,12,1,3,4,5,7,11]=>26
[3,4,7,10,11,12,1,2,5,6,8,9]=>26
[3,4,8,9,11,12,1,2,5,6,7,10]=>26
[3,5,6,10,11,12,1,2,4,7,8,9]=>26
[3,5,8,9,10,12,1,2,4,6,7,11]=>26
[3,6,7,8,11,12,1,2,4,5,9,10]=>26
[3,6,7,9,10,12,1,2,4,5,8,11]=>26
[4,5,6,9,11,12,1,2,3,7,8,10]=>26
[4,5,7,8,11,12,1,2,3,6,9,10]=>26
[4,5,7,9,10,12,1,2,3,6,8,11]=>26
[4,6,7,8,10,12,1,2,3,5,9,11]=>26
[2,1,12,11,10,7,6,9,8,5,4,3]=>42
[10,9,8,5,4,7,6,3,2,1,12,11]=>42
[2,1,12,11,6,5,10,9,8,7,4,3]=>38
[2,1,12,11,8,7,6,5,10,9,4,3]=>38
[10,9,4,3,8,7,6,5,2,1,12,11]=>38
[10,9,6,5,4,3,8,7,2,1,12,11]=>38
[2,1,12,5,4,11,10,9,8,7,6,3]=>34
[2,1,12,11,6,5,8,7,10,9,4,3]=>34
[2,1,12,9,8,7,6,5,4,11,10,3]=>34
[4,3,2,1,12,11,10,9,8,7,6,5]=>34
[10,3,2,9,8,7,6,5,4,1,12,11]=>34
[10,9,4,3,6,5,8,7,2,1,12,11]=>34
[8,7,6,5,4,3,2,1,12,11,10,9]=>34
[10,7,6,5,4,3,2,9,8,1,12,11]=>34
[2,1,4,3,12,11,10,9,8,7,6,5]=>30
[2,1,12,5,4,11,8,7,10,9,6,3]=>30
[2,1,12,7,6,5,4,11,10,9,8,3]=>30
[2,1,12,9,6,5,8,7,4,11,10,3]=>30
[2,1,10,9,8,7,6,5,4,3,12,11]=>30
[4,3,2,1,12,11,8,7,10,9,6,5]=>30
[10,3,2,9,6,5,8,7,4,1,12,11]=>30
[6,5,4,3,2,1,12,11,10,9,8,7]=>30
[10,5,4,3,2,9,8,7,6,1,12,11]=>30
[8,7,4,3,6,5,2,1,12,11,10,9]=>30
[10,7,4,3,6,5,2,9,8,1,12,11]=>30
[8,7,6,5,4,3,2,1,10,9,12,11]=>30
[2,1,4,3,12,11,8,7,10,9,6,5]=>26
[2,1,12,5,4,7,6,11,10,9,8,3]=>26
[2,1,12,5,4,9,8,7,6,11,10,3]=>26
[2,1,12,7,6,5,4,9,8,11,10,3]=>26
[2,1,10,9,6,5,8,7,4,3,12,11]=>26
[4,3,2,1,12,7,6,11,10,9,8,5]=>26
[4,3,2,1,12,9,8,7,6,11,10,5]=>26
[6,3,2,5,4,1,12,11,10,9,8,7]=>26
[10,3,2,5,4,9,8,7,6,1,12,11]=>26
[8,3,2,7,6,5,4,1,12,11,10,9]=>26
[10,3,2,7,6,5,4,9,8,1,12,11]=>26
[6,5,4,3,2,1,12,9,8,11,10,7]=>26
[8,5,4,3,2,7,6,1,12,11,10,9]=>26
[10,5,4,3,2,7,6,9,8,1,12,11]=>26
[8,7,4,3,6,5,2,1,10,9,12,11]=>26
[2,4,6,9,11,12,1,3,5,7,8,10]=>23
[2,4,6,8,11,12,1,3,5,7,9,10]=>22
[3,4,6,9,11,12,1,2,5,7,8,10]=>24
[3,4,6,8,11,12,1,2,5,7,9,10]=>23
[3,5,6,9,11,12,1,2,4,7,8,10]=>25
[2,5,6,9,11,12,1,3,4,7,8,10]=>24
[3,5,6,8,11,12,1,2,4,7,9,10]=>24
[2,5,6,8,11,12,1,3,4,7,9,10]=>23
[2,4,8,9,11,12,1,3,5,6,7,10]=>25
[2,5,7,9,11,12,1,3,4,6,8,10]=>25
[2,5,7,8,11,12,1,3,4,6,9,10]=>24
[4,5,6,8,11,12,1,2,3,7,9,10]=>25
[2,4,7,9,11,12,1,3,5,6,8,10]=>24
[2,4,7,8,11,12,1,3,5,6,9,10]=>23
[4,5,8,9,11,12,1,2,3,6,7,10]=>28
[3,5,8,9,11,12,1,2,4,6,7,10]=>27
[2,4,7,10,11,12,1,3,5,6,8,9]=>25
[4,5,7,9,11,12,1,2,3,6,8,10]=>27
[3,5,7,9,11,12,1,2,4,6,8,10]=>26
[3,5,7,8,11,12,1,2,4,6,9,10]=>25
[3,4,7,9,11,12,1,2,5,6,8,10]=>25
[3,4,7,8,11,12,1,2,5,6,9,10]=>24
[2,4,6,10,11,12,1,3,5,7,8,9]=>24
[4,7,8,9,11,12,1,2,3,5,6,10]=>30
[3,7,8,9,11,12,1,2,4,5,6,10]=>29
[4,6,8,9,11,12,1,2,3,5,7,10]=>29
[3,6,8,9,11,12,1,2,4,5,7,10]=>28
[4,6,7,9,11,12,1,2,3,5,8,10]=>28
[3,6,7,9,11,12,1,2,4,5,8,10]=>27
[2,6,7,8,11,12,1,3,4,5,9,10]=>25
[3,4,6,10,11,12,1,2,5,7,8,9]=>25
[4,5,6,8,10,12,1,2,3,7,9,11]=>24
[3,6,7,8,10,12,1,2,4,5,9,11]=>25
[2,6,7,8,10,12,1,3,4,5,9,11]=>24
[3,4,8,9,10,12,1,2,5,6,7,11]=>25
[2,4,8,9,10,12,1,3,5,6,7,11]=>24
[4,6,8,10,11,12,1,2,3,5,7,9]=>30
[4,6,7,10,11,12,1,2,3,5,8,9]=>29
[4,5,7,10,11,12,1,2,3,6,8,9]=>28
[3,5,7,10,11,12,1,2,4,6,8,9]=>27
[2,5,8,9,10,12,1,3,4,6,7,11]=>25
[5,6,8,10,11,12,1,2,3,4,7,9]=>31
[4,5,8,10,11,12,1,2,3,6,7,9]=>29
[5,6,8,9,11,12,1,2,3,4,7,10]=>30
[3,6,7,10,11,12,1,2,4,5,8,9]=>28
[5,6,7,9,11,12,1,2,3,4,8,10]=>29
[2,5,6,10,11,12,1,3,4,7,8,9]=>25
[4,5,6,9,10,12,1,2,3,7,8,11]=>25
[2,5,6,9,10,12,1,3,4,7,8,11]=>23
[3,4,6,8,10,12,1,2,5,7,9,11]=>22
[3,4,6,9,10,12,1,2,5,7,8,11]=>23
[3,5,8,10,11,12,1,2,4,6,7,9]=>28
[3,4,7,8,10,12,1,2,5,6,9,11]=>23
[3,5,6,8,10,12,1,2,4,7,9,11]=>23
[3,5,9,10,11,12,1,2,4,6,7,8]=>29
[3,5,7,9,10,12,1,2,4,6,8,11]=>25
[3,6,8,10,11,12,1,2,4,5,7,9]=>29
[3,4,7,9,10,12,1,2,5,6,8,11]=>24
[3,5,7,8,10,12,1,2,4,6,9,11]=>24
[3,6,9,10,11,12,1,2,4,5,7,8]=>30
[3,5,6,9,10,12,1,2,4,7,8,11]=>24
[3,7,8,10,11,12,1,2,4,5,6,9]=>30
[3,7,9,10,11,12,1,2,4,5,6,8]=>31
[4,6,9,10,11,12,1,2,3,5,7,8]=>31
[2,5,7,8,10,12,1,3,4,6,9,11]=>23
[2,4,7,9,10,12,1,3,5,6,8,11]=>23
[2,5,6,8,10,12,1,3,4,7,9,11]=>22
[2,4,7,8,10,12,1,3,5,6,9,11]=>22
[2,4,6,9,10,12,1,3,5,7,8,11]=>22
[2,4,6,8,10,12,1,3,5,7,9,11]=>21
[6,7,8,9,11,12,1,2,3,4,5,10]=>32
[5,7,8,9,11,12,1,2,3,4,6,10]=>31
[5,6,7,10,11,12,1,2,3,4,8,9]=>30
[6,7,8,10,11,12,1,2,3,4,5,9]=>33
[5,7,8,10,11,12,1,2,3,4,6,9]=>32
[4,5,7,8,10,12,1,2,3,6,9,11]=>25
[2,6,7,9,10,12,1,3,4,5,8,11]=>25
[6,7,9,10,11,12,1,2,3,4,5,8]=>34
[6,8,9,10,11,12,1,2,3,4,5,7]=>35
[4,7,8,10,11,12,1,2,3,5,6,9]=>31
[5,6,9,10,11,12,1,2,3,4,7,8]=>32
[4,7,9,10,11,12,1,2,3,5,6,8]=>32
[5,7,9,10,11,12,1,2,3,4,6,8]=>33
[4,8,9,10,11,12,1,2,3,5,6,7]=>33
[7,8,9,10,11,12,1,2,3,4,5,6]=>36
[5,8,9,10,11,12,1,2,3,4,6,7]=>34
[3,8,9,10,11,12,1,2,4,5,6,7]=>32
[4,5,9,10,11,12,1,2,3,6,7,8]=>30
[2,1,4,3,6,5,12,9,8,11,10,7]=>14
[2,1,4,3,6,5,8,7,12,11,10,9]=>10
[4,3,2,1,6,5,12,9,8,11,10,7]=>18
[4,3,2,1,6,5,8,7,12,11,10,9]=>14
[6,3,2,5,4,1,12,9,8,11,10,7]=>22
[2,1,6,5,4,3,12,9,8,11,10,7]=>18
[6,3,2,5,4,1,8,7,12,11,10,9]=>18
[2,1,6,5,4,3,8,7,12,11,10,9]=>14
[2,1,4,3,12,9,8,7,6,11,10,5]=>22
[2,1,12,5,4,7,6,9,8,11,10,3]=>22
[2,1,8,5,4,7,6,3,12,11,10,9]=>18
[6,5,4,3,2,1,8,7,12,11,10,9]=>22
[2,1,4,3,12,7,6,9,8,11,10,5]=>18
[2,1,4,3,8,7,6,5,12,11,10,9]=>14
[12,5,4,3,2,9,8,7,6,11,10,1]=>34
[12,3,2,5,4,9,8,7,6,11,10,1]=>30
[2,1,4,3,12,7,6,11,10,9,8,5]=>22
[12,5,4,3,2,7,6,9,8,11,10,1]=>30
[12,3,2,5,4,7,6,9,8,11,10,1]=>26
[8,3,2,5,4,7,6,1,12,11,10,9]=>22
[4,3,2,1,12,7,6,9,8,11,10,5]=>22
[4,3,2,1,8,7,6,5,12,11,10,9]=>18
[2,1,4,3,6,5,12,11,10,9,8,7]=>18
[12,9,4,3,8,7,6,5,2,11,10,1]=>42
[12,3,2,9,8,7,6,5,4,11,10,1]=>38
[12,9,4,3,6,5,8,7,2,11,10,1]=>38
[12,3,2,9,6,5,8,7,4,11,10,1]=>34
[12,7,4,3,6,5,2,9,8,11,10,1]=>34
[12,3,2,7,6,5,4,9,8,11,10,1]=>30
[2,1,8,7,6,5,4,3,12,11,10,9]=>22
[4,3,2,1,6,5,12,11,10,9,8,7]=>22
[6,5,4,3,2,1,8,7,10,9,12,11]=>18
[8,3,2,7,6,5,4,1,10,9,12,11]=>22
[2,1,8,7,6,5,4,3,10,9,12,11]=>18
[4,3,2,1,10,9,8,7,6,5,12,11]=>22
[2,1,4,3,10,9,8,7,6,5,12,11]=>18
[12,11,4,3,6,5,8,7,10,9,2,1]=>42
[12,7,4,3,6,5,2,11,10,9,8,1]=>38
[12,5,4,3,2,7,6,11,10,9,8,1]=>34
[12,3,2,5,4,7,6,11,10,9,8,1]=>30
[2,1,10,5,4,9,8,7,6,3,12,11]=>22
[12,11,6,5,4,3,8,7,10,9,2,1]=>46
[12,5,4,3,2,11,8,7,10,9,6,1]=>38
[12,9,6,5,4,3,8,7,2,11,10,1]=>42
[12,3,2,7,6,5,4,11,10,9,8,1]=>34
[12,7,6,5,4,3,2,9,8,11,10,1]=>38
[2,1,6,5,4,3,12,11,10,9,8,7]=>22
[6,5,4,3,2,1,10,9,8,7,12,11]=>22
[2,1,6,5,4,3,10,9,8,7,12,11]=>14
[4,3,2,1,6,5,8,7,10,9,12,11]=>10
[4,3,2,1,6,5,10,9,8,7,12,11]=>14
[12,3,2,5,4,11,8,7,10,9,6,1]=>34
[4,3,2,1,8,7,6,5,10,9,12,11]=>14
[6,3,2,5,4,1,8,7,10,9,12,11]=>14
[12,3,2,5,4,11,10,9,8,7,6,1]=>38
[10,3,2,5,4,7,6,9,8,1,12,11]=>22
[12,3,2,11,6,5,8,7,10,9,4,1]=>38
[4,3,2,1,10,7,6,9,8,5,12,11]=>18
[8,3,2,5,4,7,6,1,10,9,12,11]=>18
[12,3,2,11,6,5,10,9,8,7,4,1]=>42
[6,3,2,5,4,1,10,9,8,7,12,11]=>18
[12,3,2,11,8,7,6,5,10,9,4,1]=>42
[12,3,2,11,10,7,6,9,8,5,4,1]=>46
[12,11,4,3,6,5,10,9,8,7,2,1]=>46
[2,1,8,5,4,7,6,3,10,9,12,11]=>14
[2,1,4,3,10,7,6,9,8,5,12,11]=>14
[2,1,6,5,4,3,8,7,10,9,12,11]=>10
[2,1,4,3,8,7,6,5,10,9,12,11]=>10
[2,1,4,3,6,5,10,9,8,7,12,11]=>10
[2,1,4,3,6,5,8,7,10,9,12,11]=>6
[12,9,8,7,6,5,4,3,2,11,10,1]=>50
[12,9,8,5,4,7,6,3,2,11,10,1]=>46
[12,7,6,5,4,3,2,11,10,9,8,1]=>42
[12,11,8,7,6,5,4,3,10,9,2,1]=>54
[12,11,8,5,4,7,6,3,10,9,2,1]=>50
[8,5,4,3,2,7,6,1,10,9,12,11]=>22
[2,1,10,7,6,5,4,9,8,3,12,11]=>22
[12,11,10,7,6,5,4,9,8,3,2,1]=>58
[12,11,10,9,6,5,8,7,4,3,2,1]=>62
[12,11,4,3,8,7,6,5,10,9,2,1]=>46
[12,11,6,5,4,3,10,9,8,7,2,1]=>50
[12,11,4,3,10,7,6,9,8,5,2,1]=>50
[12,11,10,5,4,7,6,9,8,3,2,1]=>54
[12,11,4,3,10,9,8,7,6,5,2,1]=>54
[12,11,10,9,8,7,6,5,4,3,2,1]=>66
[12,11,10,5,4,9,8,7,6,3,2,1]=>58
[12,3,2,11,10,9,8,7,6,5,4,1]=>50
[12,5,4,3,2,11,10,9,8,7,6,1]=>42
[2,1,10,5,4,7,6,9,8,3,12,11]=>18
[2,5,7,9,10,12,1,3,4,6,8,11]=>24
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 inversions of a permutation.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
References
[1] Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product_i=0..n-1 (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). OEIS:A008302
[2] List of permutations of 1,2,3,...,n for n=1,2,3,..., in lexicographic order. OEIS:A030298
[3] Array of digit sums of factorial representation of numbers 0,1,...,n!-1 for n>=1. OEIS:A139365
[2] List of permutations of 1,2,3,...,n for n=1,2,3,..., in lexicographic order. OEIS:A030298
[3] Array of digit sums of factorial representation of numbers 0,1,...,n!-1 for n>=1. OEIS:A139365
Code
def statistic(x):
return x.number_of_inversions()
Created
Sep 27, 2011 at 23:29 by Christian Stump
Updated
May 12, 2020 at 15:17 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!