Identifier
- St000463: Permutations ⟶ ℤ
Values
=>
[]=>0
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>0
[2,3,1]=>2
[3,1,2]=>0
[3,2,1]=>0
[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]=>2
[2,1,3,4]=>0
[2,1,4,3]=>1
[2,3,1,4]=>2
[2,3,4,1]=>3
[2,4,1,3]=>3
[2,4,3,1]=>3
[3,1,2,4]=>0
[3,1,4,2]=>2
[3,2,1,4]=>0
[3,2,4,1]=>3
[3,4,1,2]=>4
[3,4,2,1]=>4
[4,1,2,3]=>0
[4,1,3,2]=>1
[4,2,1,3]=>0
[4,2,3,1]=>2
[4,3,1,2]=>0
[4,3,2,1]=>0
[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]=>2
[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]=>3
[1,4,2,3,5]=>2
[1,4,2,5,3]=>3
[1,4,3,2,5]=>2
[1,4,3,5,2]=>4
[1,4,5,2,3]=>4
[1,4,5,3,2]=>4
[1,5,2,3,4]=>3
[1,5,2,4,3]=>4
[1,5,3,2,4]=>3
[1,5,3,4,2]=>5
[1,5,4,2,3]=>3
[1,5,4,3,2]=>3
[2,1,3,4,5]=>0
[2,1,3,5,4]=>1
[2,1,4,3,5]=>1
[2,1,4,5,3]=>2
[2,1,5,3,4]=>2
[2,1,5,4,3]=>2
[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]=>4
[2,4,1,3,5]=>3
[2,4,1,5,3]=>4
[2,4,3,1,5]=>3
[2,4,3,5,1]=>5
[2,4,5,1,3]=>5
[2,4,5,3,1]=>5
[2,5,1,3,4]=>4
[2,5,1,4,3]=>5
[2,5,3,1,4]=>4
[2,5,3,4,1]=>6
[2,5,4,1,3]=>4
[2,5,4,3,1]=>4
[3,1,2,4,5]=>0
[3,1,2,5,4]=>1
[3,1,4,2,5]=>2
[3,1,4,5,2]=>3
[3,1,5,2,4]=>3
[3,1,5,4,2]=>3
[3,2,1,4,5]=>0
[3,2,1,5,4]=>1
[3,2,4,1,5]=>3
[3,2,4,5,1]=>4
[3,2,5,1,4]=>4
[3,2,5,4,1]=>4
[3,4,1,2,5]=>4
[3,4,1,5,2]=>5
[3,4,2,1,5]=>4
[3,4,2,5,1]=>6
[3,4,5,1,2]=>6
[3,4,5,2,1]=>6
[3,5,1,2,4]=>5
[3,5,1,4,2]=>6
[3,5,2,1,4]=>5
[3,5,2,4,1]=>7
[3,5,4,1,2]=>5
[3,5,4,2,1]=>5
[4,1,2,3,5]=>0
[4,1,2,5,3]=>2
[4,1,3,2,5]=>1
[4,1,3,5,2]=>3
[4,1,5,2,3]=>4
[4,1,5,3,2]=>4
[4,2,1,3,5]=>0
[4,2,1,5,3]=>2
[4,2,3,1,5]=>2
[4,2,3,5,1]=>4
[4,2,5,1,3]=>5
[4,2,5,3,1]=>5
[4,3,1,2,5]=>0
[4,3,1,5,2]=>3
[4,3,2,1,5]=>0
[4,3,2,5,1]=>4
[4,3,5,1,2]=>6
[4,3,5,2,1]=>6
[4,5,1,2,3]=>6
[4,5,1,3,2]=>7
[4,5,2,1,3]=>6
[4,5,2,3,1]=>8
[4,5,3,1,2]=>6
[4,5,3,2,1]=>6
[5,1,2,3,4]=>0
[5,1,2,4,3]=>1
[5,1,3,2,4]=>1
[5,1,3,4,2]=>2
[5,1,4,2,3]=>2
[5,1,4,3,2]=>2
[5,2,1,3,4]=>0
[5,2,1,4,3]=>1
[5,2,3,1,4]=>2
[5,2,3,4,1]=>3
[5,2,4,1,3]=>3
[5,2,4,3,1]=>3
[5,3,1,2,4]=>0
[5,3,1,4,2]=>2
[5,3,2,1,4]=>0
[5,3,2,4,1]=>3
[5,3,4,1,2]=>4
[5,3,4,2,1]=>4
[5,4,1,2,3]=>0
[5,4,1,3,2]=>1
[5,4,2,1,3]=>0
[5,4,2,3,1]=>2
[5,4,3,1,2]=>0
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>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]=>2
[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]=>3
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>3
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>4
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>5
[1,2,6,5,3,4]=>3
[1,2,6,5,4,3]=>3
[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]=>3
[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]=>4
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>5
[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>5
[1,3,6,2,4,5]=>4
[1,3,6,2,5,4]=>5
[1,3,6,4,2,5]=>4
[1,3,6,4,5,2]=>6
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>4
[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]=>4
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>3
[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]=>5
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>4
[1,4,5,3,6,2]=>6
[1,4,5,6,2,3]=>6
[1,4,5,6,3,2]=>6
[1,4,6,2,3,5]=>5
[1,4,6,2,5,3]=>6
[1,4,6,3,2,5]=>5
[1,4,6,3,5,2]=>7
[1,4,6,5,2,3]=>5
[1,4,6,5,3,2]=>5
[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]=>5
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>4
[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]=>6
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>5
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>6
[1,5,4,6,2,3]=>7
[1,5,4,6,3,2]=>7
[1,5,6,2,3,4]=>6
[1,5,6,2,4,3]=>7
[1,5,6,3,2,4]=>6
[1,5,6,3,4,2]=>8
[1,5,6,4,2,3]=>6
[1,5,6,4,3,2]=>6
[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]=>6
[1,6,3,2,4,5]=>4
[1,6,3,2,5,4]=>5
[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]=>7
[1,6,4,2,3,5]=>4
[1,6,4,2,5,3]=>6
[1,6,4,3,2,5]=>4
[1,6,4,3,5,2]=>7
[1,6,4,5,2,3]=>8
[1,6,4,5,3,2]=>8
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>5
[1,6,5,3,2,4]=>4
[1,6,5,3,4,2]=>6
[1,6,5,4,2,3]=>4
[1,6,5,4,3,2]=>4
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>1
[2,1,3,5,4,6]=>1
[2,1,3,5,6,4]=>2
[2,1,3,6,4,5]=>2
[2,1,3,6,5,4]=>2
[2,1,4,3,5,6]=>1
[2,1,4,3,6,5]=>2
[2,1,4,5,3,6]=>2
[2,1,4,5,6,3]=>3
[2,1,4,6,3,5]=>3
[2,1,4,6,5,3]=>3
[2,1,5,3,4,6]=>2
[2,1,5,3,6,4]=>3
[2,1,5,4,3,6]=>2
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>4
[2,1,5,6,4,3]=>4
[2,1,6,3,4,5]=>3
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>3
[2,1,6,4,5,3]=>5
[2,1,6,5,3,4]=>3
[2,1,6,5,4,3]=>3
[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]=>4
[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]=>5
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>4
[2,3,5,4,6,1]=>6
[2,3,5,6,1,4]=>6
[2,3,5,6,4,1]=>6
[2,3,6,1,4,5]=>5
[2,3,6,1,5,4]=>6
[2,3,6,4,1,5]=>5
[2,3,6,4,5,1]=>7
[2,3,6,5,1,4]=>5
[2,3,6,5,4,1]=>5
[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]=>5
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>4
[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]=>6
[2,4,5,1,3,6]=>5
[2,4,5,1,6,3]=>6
[2,4,5,3,1,6]=>5
[2,4,5,3,6,1]=>7
[2,4,5,6,1,3]=>7
[2,4,5,6,3,1]=>7
[2,4,6,1,3,5]=>6
[2,4,6,1,5,3]=>7
[2,4,6,3,1,5]=>6
[2,4,6,3,5,1]=>8
[2,4,6,5,1,3]=>6
[2,4,6,5,3,1]=>6
[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]=>6
[2,5,3,1,4,6]=>4
[2,5,3,1,6,4]=>5
[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]=>7
[2,5,4,1,3,6]=>4
[2,5,4,1,6,3]=>6
[2,5,4,3,1,6]=>4
[2,5,4,3,6,1]=>7
[2,5,4,6,1,3]=>8
[2,5,4,6,3,1]=>8
[2,5,6,1,3,4]=>7
[2,5,6,1,4,3]=>8
[2,5,6,3,1,4]=>7
[2,5,6,3,4,1]=>9
[2,5,6,4,1,3]=>7
[2,5,6,4,3,1]=>7
[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]=>7
[2,6,3,1,4,5]=>5
[2,6,3,1,5,4]=>6
[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]=>8
[2,6,4,1,3,5]=>5
[2,6,4,1,5,3]=>7
[2,6,4,3,1,5]=>5
[2,6,4,3,5,1]=>8
[2,6,4,5,1,3]=>9
[2,6,4,5,3,1]=>9
[2,6,5,1,3,4]=>5
[2,6,5,1,4,3]=>6
[2,6,5,3,1,4]=>5
[2,6,5,3,4,1]=>7
[2,6,5,4,1,3]=>5
[2,6,5,4,3,1]=>5
[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>1
[3,1,2,5,4,6]=>1
[3,1,2,5,6,4]=>2
[3,1,2,6,4,5]=>2
[3,1,2,6,5,4]=>2
[3,1,4,2,5,6]=>2
[3,1,4,2,6,5]=>3
[3,1,4,5,2,6]=>3
[3,1,4,5,6,2]=>4
[3,1,4,6,2,5]=>4
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>3
[3,1,5,2,6,4]=>4
[3,1,5,4,2,6]=>3
[3,1,5,4,6,2]=>5
[3,1,5,6,2,4]=>5
[3,1,5,6,4,2]=>5
[3,1,6,2,4,5]=>4
[3,1,6,2,5,4]=>5
[3,1,6,4,2,5]=>4
[3,1,6,4,5,2]=>6
[3,1,6,5,2,4]=>4
[3,1,6,5,4,2]=>4
[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>1
[3,2,1,5,4,6]=>1
[3,2,1,5,6,4]=>2
[3,2,1,6,4,5]=>2
[3,2,1,6,5,4]=>2
[3,2,4,1,5,6]=>3
[3,2,4,1,6,5]=>4
[3,2,4,5,1,6]=>4
[3,2,4,5,6,1]=>5
[3,2,4,6,1,5]=>5
[3,2,4,6,5,1]=>5
[3,2,5,1,4,6]=>4
[3,2,5,1,6,4]=>5
[3,2,5,4,1,6]=>4
[3,2,5,4,6,1]=>6
[3,2,5,6,1,4]=>6
[3,2,5,6,4,1]=>6
[3,2,6,1,4,5]=>5
[3,2,6,1,5,4]=>6
[3,2,6,4,1,5]=>5
[3,2,6,4,5,1]=>7
[3,2,6,5,1,4]=>5
[3,2,6,5,4,1]=>5
[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]=>6
[3,4,2,1,5,6]=>4
[3,4,2,1,6,5]=>5
[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]=>7
[3,4,5,1,2,6]=>6
[3,4,5,1,6,2]=>7
[3,4,5,2,1,6]=>6
[3,4,5,2,6,1]=>8
[3,4,5,6,1,2]=>8
[3,4,5,6,2,1]=>8
[3,4,6,1,2,5]=>7
[3,4,6,1,5,2]=>8
[3,4,6,2,1,5]=>7
[3,4,6,2,5,1]=>9
[3,4,6,5,1,2]=>7
[3,4,6,5,2,1]=>7
[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]=>7
[3,5,2,1,4,6]=>5
[3,5,2,1,6,4]=>6
[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]=>8
[3,5,4,1,2,6]=>5
[3,5,4,1,6,2]=>7
[3,5,4,2,1,6]=>5
[3,5,4,2,6,1]=>8
[3,5,4,6,1,2]=>9
[3,5,4,6,2,1]=>9
[3,5,6,1,2,4]=>8
[3,5,6,1,4,2]=>9
[3,5,6,2,1,4]=>8
[3,5,6,2,4,1]=>10
[3,5,6,4,1,2]=>8
[3,5,6,4,2,1]=>8
[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]=>8
[3,6,2,1,4,5]=>6
[3,6,2,1,5,4]=>7
[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]=>9
[3,6,4,1,2,5]=>6
[3,6,4,1,5,2]=>8
[3,6,4,2,1,5]=>6
[3,6,4,2,5,1]=>9
[3,6,4,5,1,2]=>10
[3,6,4,5,2,1]=>10
[3,6,5,1,2,4]=>6
[3,6,5,1,4,2]=>7
[3,6,5,2,1,4]=>6
[3,6,5,2,4,1]=>8
[3,6,5,4,1,2]=>6
[3,6,5,4,2,1]=>6
[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>1
[4,1,2,5,3,6]=>2
[4,1,2,5,6,3]=>3
[4,1,2,6,3,5]=>3
[4,1,2,6,5,3]=>3
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>2
[4,1,3,5,2,6]=>3
[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>4
[4,1,3,6,5,2]=>4
[4,1,5,2,3,6]=>4
[4,1,5,2,6,3]=>5
[4,1,5,3,2,6]=>4
[4,1,5,3,6,2]=>6
[4,1,5,6,2,3]=>6
[4,1,5,6,3,2]=>6
[4,1,6,2,3,5]=>5
[4,1,6,2,5,3]=>6
[4,1,6,3,2,5]=>5
[4,1,6,3,5,2]=>7
[4,1,6,5,2,3]=>5
[4,1,6,5,3,2]=>5
[4,2,1,3,5,6]=>0
[4,2,1,3,6,5]=>1
[4,2,1,5,3,6]=>2
[4,2,1,5,6,3]=>3
[4,2,1,6,3,5]=>3
[4,2,1,6,5,3]=>3
[4,2,3,1,5,6]=>2
[4,2,3,1,6,5]=>3
[4,2,3,5,1,6]=>4
[4,2,3,5,6,1]=>5
[4,2,3,6,1,5]=>5
[4,2,3,6,5,1]=>5
[4,2,5,1,3,6]=>5
[4,2,5,1,6,3]=>6
[4,2,5,3,1,6]=>5
[4,2,5,3,6,1]=>7
[4,2,5,6,1,3]=>7
[4,2,5,6,3,1]=>7
[4,2,6,1,3,5]=>6
[4,2,6,1,5,3]=>7
[4,2,6,3,1,5]=>6
[4,2,6,3,5,1]=>8
[4,2,6,5,1,3]=>6
[4,2,6,5,3,1]=>6
[4,3,1,2,5,6]=>0
[4,3,1,2,6,5]=>1
[4,3,1,5,2,6]=>3
[4,3,1,5,6,2]=>4
[4,3,1,6,2,5]=>4
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>1
[4,3,2,5,1,6]=>4
[4,3,2,5,6,1]=>5
[4,3,2,6,1,5]=>5
[4,3,2,6,5,1]=>5
[4,3,5,1,2,6]=>6
[4,3,5,1,6,2]=>7
[4,3,5,2,1,6]=>6
[4,3,5,2,6,1]=>8
[4,3,5,6,1,2]=>8
[4,3,5,6,2,1]=>8
[4,3,6,1,2,5]=>7
[4,3,6,1,5,2]=>8
[4,3,6,2,1,5]=>7
[4,3,6,2,5,1]=>9
[4,3,6,5,1,2]=>7
[4,3,6,5,2,1]=>7
[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]=>8
[4,5,2,1,3,6]=>6
[4,5,2,1,6,3]=>7
[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]=>9
[4,5,3,1,2,6]=>6
[4,5,3,1,6,2]=>8
[4,5,3,2,1,6]=>6
[4,5,3,2,6,1]=>9
[4,5,3,6,1,2]=>10
[4,5,3,6,2,1]=>10
[4,5,6,1,2,3]=>9
[4,5,6,1,3,2]=>10
[4,5,6,2,1,3]=>9
[4,5,6,2,3,1]=>11
[4,5,6,3,1,2]=>9
[4,5,6,3,2,1]=>9
[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]=>9
[4,6,2,1,3,5]=>7
[4,6,2,1,5,3]=>8
[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]=>10
[4,6,3,1,2,5]=>7
[4,6,3,1,5,2]=>9
[4,6,3,2,1,5]=>7
[4,6,3,2,5,1]=>10
[4,6,3,5,1,2]=>11
[4,6,3,5,2,1]=>11
[4,6,5,1,2,3]=>7
[4,6,5,1,3,2]=>8
[4,6,5,2,1,3]=>7
[4,6,5,2,3,1]=>9
[4,6,5,3,1,2]=>7
[4,6,5,3,2,1]=>7
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>2
[5,1,2,4,3,6]=>1
[5,1,2,4,6,3]=>3
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>4
[5,1,3,2,4,6]=>1
[5,1,3,2,6,4]=>3
[5,1,3,4,2,6]=>2
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>5
[5,1,3,6,4,2]=>5
[5,1,4,2,3,6]=>2
[5,1,4,2,6,3]=>4
[5,1,4,3,2,6]=>2
[5,1,4,3,6,2]=>5
[5,1,4,6,2,3]=>6
[5,1,4,6,3,2]=>6
[5,1,6,2,3,4]=>6
[5,1,6,2,4,3]=>7
[5,1,6,3,2,4]=>6
[5,1,6,3,4,2]=>8
[5,1,6,4,2,3]=>6
[5,1,6,4,3,2]=>6
[5,2,1,3,4,6]=>0
[5,2,1,3,6,4]=>2
[5,2,1,4,3,6]=>1
[5,2,1,4,6,3]=>3
[5,2,1,6,3,4]=>4
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>2
[5,2,3,1,6,4]=>4
[5,2,3,4,1,6]=>3
[5,2,3,4,6,1]=>5
[5,2,3,6,1,4]=>6
[5,2,3,6,4,1]=>6
[5,2,4,1,3,6]=>3
[5,2,4,1,6,3]=>5
[5,2,4,3,1,6]=>3
[5,2,4,3,6,1]=>6
[5,2,4,6,1,3]=>7
[5,2,4,6,3,1]=>7
[5,2,6,1,3,4]=>7
[5,2,6,1,4,3]=>8
[5,2,6,3,1,4]=>7
[5,2,6,3,4,1]=>9
[5,2,6,4,1,3]=>7
[5,2,6,4,3,1]=>7
[5,3,1,2,4,6]=>0
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>2
[5,3,1,4,6,2]=>4
[5,3,1,6,2,4]=>5
[5,3,1,6,4,2]=>5
[5,3,2,1,4,6]=>0
[5,3,2,1,6,4]=>2
[5,3,2,4,1,6]=>3
[5,3,2,4,6,1]=>5
[5,3,2,6,1,4]=>6
[5,3,2,6,4,1]=>6
[5,3,4,1,2,6]=>4
[5,3,4,1,6,2]=>6
[5,3,4,2,1,6]=>4
[5,3,4,2,6,1]=>7
[5,3,4,6,1,2]=>8
[5,3,4,6,2,1]=>8
[5,3,6,1,2,4]=>8
[5,3,6,1,4,2]=>9
[5,3,6,2,1,4]=>8
[5,3,6,2,4,1]=>10
[5,3,6,4,1,2]=>8
[5,3,6,4,2,1]=>8
[5,4,1,2,3,6]=>0
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>1
[5,4,1,3,6,2]=>4
[5,4,1,6,2,3]=>6
[5,4,1,6,3,2]=>6
[5,4,2,1,3,6]=>0
[5,4,2,1,6,3]=>3
[5,4,2,3,1,6]=>2
[5,4,2,3,6,1]=>5
[5,4,2,6,1,3]=>7
[5,4,2,6,3,1]=>7
[5,4,3,1,2,6]=>0
[5,4,3,1,6,2]=>4
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>5
[5,4,3,6,1,2]=>8
[5,4,3,6,2,1]=>8
[5,4,6,1,2,3]=>9
[5,4,6,1,3,2]=>10
[5,4,6,2,1,3]=>9
[5,4,6,2,3,1]=>11
[5,4,6,3,1,2]=>9
[5,4,6,3,2,1]=>9
[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]=>10
[5,6,2,1,3,4]=>8
[5,6,2,1,4,3]=>9
[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]=>11
[5,6,3,1,2,4]=>8
[5,6,3,1,4,2]=>10
[5,6,3,2,1,4]=>8
[5,6,3,2,4,1]=>11
[5,6,3,4,1,2]=>12
[5,6,3,4,2,1]=>12
[5,6,4,1,2,3]=>8
[5,6,4,1,3,2]=>9
[5,6,4,2,1,3]=>8
[5,6,4,2,3,1]=>10
[5,6,4,3,1,2]=>8
[5,6,4,3,2,1]=>8
[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>1
[6,1,2,4,3,5]=>1
[6,1,2,4,5,3]=>2
[6,1,2,5,3,4]=>2
[6,1,2,5,4,3]=>2
[6,1,3,2,4,5]=>1
[6,1,3,2,5,4]=>2
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>3
[6,1,3,5,4,2]=>3
[6,1,4,2,3,5]=>2
[6,1,4,2,5,3]=>3
[6,1,4,3,2,5]=>2
[6,1,4,3,5,2]=>4
[6,1,4,5,2,3]=>4
[6,1,4,5,3,2]=>4
[6,1,5,2,3,4]=>3
[6,1,5,2,4,3]=>4
[6,1,5,3,2,4]=>3
[6,1,5,3,4,2]=>5
[6,1,5,4,2,3]=>3
[6,1,5,4,3,2]=>3
[6,2,1,3,4,5]=>0
[6,2,1,3,5,4]=>1
[6,2,1,4,3,5]=>1
[6,2,1,4,5,3]=>2
[6,2,1,5,3,4]=>2
[6,2,1,5,4,3]=>2
[6,2,3,1,4,5]=>2
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>3
[6,2,3,4,5,1]=>4
[6,2,3,5,1,4]=>4
[6,2,3,5,4,1]=>4
[6,2,4,1,3,5]=>3
[6,2,4,1,5,3]=>4
[6,2,4,3,1,5]=>3
[6,2,4,3,5,1]=>5
[6,2,4,5,1,3]=>5
[6,2,4,5,3,1]=>5
[6,2,5,1,3,4]=>4
[6,2,5,1,4,3]=>5
[6,2,5,3,1,4]=>4
[6,2,5,3,4,1]=>6
[6,2,5,4,1,3]=>4
[6,2,5,4,3,1]=>4
[6,3,1,2,4,5]=>0
[6,3,1,2,5,4]=>1
[6,3,1,4,2,5]=>2
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>3
[6,3,1,5,4,2]=>3
[6,3,2,1,4,5]=>0
[6,3,2,1,5,4]=>1
[6,3,2,4,1,5]=>3
[6,3,2,4,5,1]=>4
[6,3,2,5,1,4]=>4
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>4
[6,3,4,1,5,2]=>5
[6,3,4,2,1,5]=>4
[6,3,4,2,5,1]=>6
[6,3,4,5,1,2]=>6
[6,3,4,5,2,1]=>6
[6,3,5,1,2,4]=>5
[6,3,5,1,4,2]=>6
[6,3,5,2,1,4]=>5
[6,3,5,2,4,1]=>7
[6,3,5,4,1,2]=>5
[6,3,5,4,2,1]=>5
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>2
[6,4,1,3,2,5]=>1
[6,4,1,3,5,2]=>3
[6,4,1,5,2,3]=>4
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>0
[6,4,2,1,5,3]=>2
[6,4,2,3,1,5]=>2
[6,4,2,3,5,1]=>4
[6,4,2,5,1,3]=>5
[6,4,2,5,3,1]=>5
[6,4,3,1,2,5]=>0
[6,4,3,1,5,2]=>3
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>4
[6,4,3,5,1,2]=>6
[6,4,3,5,2,1]=>6
[6,4,5,1,2,3]=>6
[6,4,5,1,3,2]=>7
[6,4,5,2,1,3]=>6
[6,4,5,2,3,1]=>8
[6,4,5,3,1,2]=>6
[6,4,5,3,2,1]=>6
[6,5,1,2,3,4]=>0
[6,5,1,2,4,3]=>1
[6,5,1,3,2,4]=>1
[6,5,1,3,4,2]=>2
[6,5,1,4,2,3]=>2
[6,5,1,4,3,2]=>2
[6,5,2,1,3,4]=>0
[6,5,2,1,4,3]=>1
[6,5,2,3,1,4]=>2
[6,5,2,3,4,1]=>3
[6,5,2,4,1,3]=>3
[6,5,2,4,3,1]=>3
[6,5,3,1,2,4]=>0
[6,5,3,1,4,2]=>2
[6,5,3,2,1,4]=>0
[6,5,3,2,4,1]=>3
[6,5,3,4,1,2]=>4
[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>0
[6,5,4,1,3,2]=>1
[6,5,4,2,1,3]=>0
[6,5,4,2,3,1]=>2
[6,5,4,3,1,2]=>0
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>1
[1,2,3,4,6,7,5]=>2
[1,2,3,4,7,5,6]=>2
[1,2,3,4,7,6,5]=>2
[1,2,3,5,4,6,7]=>1
[1,2,3,5,4,7,6]=>2
[1,2,3,5,6,4,7]=>2
[1,2,3,5,6,7,4]=>3
[1,2,3,5,7,4,6]=>3
[1,2,3,5,7,6,4]=>3
[1,2,3,6,4,5,7]=>2
[1,2,3,6,4,7,5]=>3
[1,2,3,6,5,4,7]=>2
[1,2,3,6,5,7,4]=>4
[1,2,3,6,7,4,5]=>4
[1,2,3,6,7,5,4]=>4
[1,2,3,7,4,5,6]=>3
[1,2,3,7,4,6,5]=>4
[1,2,3,7,5,4,6]=>3
[1,2,3,7,5,6,4]=>5
[1,2,3,7,6,4,5]=>3
[1,2,3,7,6,5,4]=>3
[1,2,4,3,5,6,7]=>1
[1,2,4,3,5,7,6]=>2
[1,2,4,3,6,5,7]=>2
[1,2,4,3,6,7,5]=>3
[1,2,4,3,7,5,6]=>3
[1,2,4,3,7,6,5]=>3
[1,2,4,5,3,6,7]=>2
[1,2,4,5,3,7,6]=>3
[1,2,4,5,6,3,7]=>3
[1,2,4,5,6,7,3]=>4
[1,2,4,5,7,3,6]=>4
[1,2,4,5,7,6,3]=>4
[1,2,4,6,3,5,7]=>3
[1,2,4,6,3,7,5]=>4
[1,2,4,6,5,3,7]=>3
[1,2,4,6,5,7,3]=>5
[1,2,4,6,7,3,5]=>5
[1,2,4,6,7,5,3]=>5
[1,2,4,7,3,5,6]=>4
[1,2,4,7,3,6,5]=>5
[1,2,4,7,5,3,6]=>4
[1,2,4,7,5,6,3]=>6
[1,2,4,7,6,3,5]=>4
[1,2,4,7,6,5,3]=>4
[1,2,5,3,4,6,7]=>2
[1,2,5,3,4,7,6]=>3
[1,2,5,3,6,4,7]=>3
[1,2,5,3,6,7,4]=>4
[1,2,5,3,7,4,6]=>4
[1,2,5,3,7,6,4]=>4
[1,2,5,4,3,6,7]=>2
[1,2,5,4,3,7,6]=>3
[1,2,5,4,6,3,7]=>4
[1,2,5,4,6,7,3]=>5
[1,2,5,4,7,3,6]=>5
[1,2,5,4,7,6,3]=>5
[1,2,5,6,3,4,7]=>4
[1,2,5,6,3,7,4]=>5
[1,2,5,6,4,3,7]=>4
[1,2,5,6,4,7,3]=>6
[1,2,5,6,7,3,4]=>6
[1,2,5,6,7,4,3]=>6
[1,2,5,7,3,4,6]=>5
[1,2,5,7,3,6,4]=>6
[1,2,5,7,4,3,6]=>5
[1,2,5,7,4,6,3]=>7
[1,2,5,7,6,3,4]=>5
[1,2,5,7,6,4,3]=>5
[1,2,6,3,4,5,7]=>3
[1,2,6,3,4,7,5]=>4
[1,2,6,3,5,4,7]=>4
[1,2,6,3,5,7,4]=>5
[1,2,6,3,7,4,5]=>5
[1,2,6,3,7,5,4]=>5
[1,2,6,4,3,5,7]=>3
[1,2,6,4,3,7,5]=>4
[1,2,6,4,5,3,7]=>5
[1,2,6,4,5,7,3]=>6
[1,2,6,4,7,3,5]=>6
[1,2,6,4,7,5,3]=>6
[1,2,6,5,3,4,7]=>3
[1,2,6,5,3,7,4]=>5
[1,2,6,5,4,3,7]=>3
[1,2,6,5,4,7,3]=>6
[1,2,6,5,7,3,4]=>7
[1,2,6,5,7,4,3]=>7
[1,2,6,7,3,4,5]=>6
[1,2,6,7,3,5,4]=>7
[1,2,6,7,4,3,5]=>6
[1,2,6,7,4,5,3]=>8
[1,2,6,7,5,3,4]=>6
[1,2,6,7,5,4,3]=>6
[1,2,7,3,4,5,6]=>4
[1,2,7,3,4,6,5]=>5
[1,2,7,3,5,4,6]=>5
[1,2,7,3,5,6,4]=>6
[1,2,7,3,6,4,5]=>6
[1,2,7,3,6,5,4]=>6
[1,2,7,4,3,5,6]=>4
[1,2,7,4,3,6,5]=>5
[1,2,7,4,5,3,6]=>6
[1,2,7,4,5,6,3]=>7
[1,2,7,4,6,3,5]=>7
[1,2,7,4,6,5,3]=>7
[1,2,7,5,3,4,6]=>4
[1,2,7,5,3,6,4]=>6
[1,2,7,5,4,3,6]=>4
[1,2,7,5,4,6,3]=>7
[1,2,7,5,6,3,4]=>8
[1,2,7,5,6,4,3]=>8
[1,2,7,6,3,4,5]=>4
[1,2,7,6,3,5,4]=>5
[1,2,7,6,4,3,5]=>4
[1,2,7,6,4,5,3]=>6
[1,2,7,6,5,3,4]=>4
[1,2,7,6,5,4,3]=>4
[1,3,2,4,5,6,7]=>1
[1,3,2,4,5,7,6]=>2
[1,3,2,4,6,5,7]=>2
[1,3,2,4,6,7,5]=>3
[1,3,2,4,7,5,6]=>3
[1,3,2,4,7,6,5]=>3
[1,3,2,5,4,6,7]=>2
[1,3,2,5,4,7,6]=>3
[1,3,2,5,6,4,7]=>3
[1,3,2,5,6,7,4]=>4
[1,3,2,5,7,4,6]=>4
[1,3,2,5,7,6,4]=>4
[1,3,2,6,4,5,7]=>3
[1,3,2,6,4,7,5]=>4
[1,3,2,6,5,4,7]=>3
[1,3,2,6,5,7,4]=>5
[1,3,2,6,7,4,5]=>5
[1,3,2,6,7,5,4]=>5
[1,3,2,7,4,5,6]=>4
[1,3,2,7,4,6,5]=>5
[1,3,2,7,5,4,6]=>4
[1,3,2,7,5,6,4]=>6
[1,3,2,7,6,4,5]=>4
[1,3,2,7,6,5,4]=>4
[1,3,4,2,5,6,7]=>2
[1,3,4,2,5,7,6]=>3
[1,3,4,2,6,5,7]=>3
[1,3,4,2,6,7,5]=>4
[1,3,4,2,7,5,6]=>4
[1,3,4,2,7,6,5]=>4
[1,3,4,5,2,6,7]=>3
[1,3,4,5,2,7,6]=>4
[1,3,4,5,6,2,7]=>4
[1,3,4,5,6,7,2]=>5
[1,3,4,5,7,2,6]=>5
[1,3,4,5,7,6,2]=>5
[1,3,4,6,2,5,7]=>4
[1,3,4,6,2,7,5]=>5
[1,3,4,6,5,2,7]=>4
[1,3,4,6,5,7,2]=>6
[1,3,4,6,7,2,5]=>6
[1,3,4,6,7,5,2]=>6
[1,3,4,7,2,5,6]=>5
[1,3,4,7,2,6,5]=>6
[1,3,4,7,5,2,6]=>5
[1,3,4,7,5,6,2]=>7
[1,3,4,7,6,2,5]=>5
[1,3,4,7,6,5,2]=>5
[1,3,5,2,4,6,7]=>3
[1,3,5,2,4,7,6]=>4
[1,3,5,2,6,4,7]=>4
[1,3,5,2,6,7,4]=>5
[1,3,5,2,7,4,6]=>5
[1,3,5,2,7,6,4]=>5
[1,3,5,4,2,6,7]=>3
[1,3,5,4,2,7,6]=>4
[1,3,5,4,6,2,7]=>5
[1,3,5,4,6,7,2]=>6
[1,3,5,4,7,2,6]=>6
[1,3,5,4,7,6,2]=>6
[1,3,5,6,2,4,7]=>5
[1,3,5,6,2,7,4]=>6
[1,3,5,6,4,2,7]=>5
[1,3,5,6,4,7,2]=>7
[1,3,5,6,7,2,4]=>7
[1,3,5,6,7,4,2]=>7
[1,3,5,7,2,4,6]=>6
[1,3,5,7,2,6,4]=>7
[1,3,5,7,4,2,6]=>6
[1,3,5,7,4,6,2]=>8
[1,3,5,7,6,2,4]=>6
[1,3,5,7,6,4,2]=>6
[1,3,6,2,4,5,7]=>4
[1,3,6,2,4,7,5]=>5
[1,3,6,2,5,4,7]=>5
[1,3,6,2,5,7,4]=>6
[1,3,6,2,7,4,5]=>6
[1,3,6,2,7,5,4]=>6
[1,3,6,4,2,5,7]=>4
[1,3,6,4,2,7,5]=>5
[1,3,6,4,5,2,7]=>6
[1,3,6,4,5,7,2]=>7
[1,3,6,4,7,2,5]=>7
[1,3,6,4,7,5,2]=>7
[1,3,6,5,2,4,7]=>4
[1,3,6,5,2,7,4]=>6
[1,3,6,5,4,2,7]=>4
[1,3,6,5,4,7,2]=>7
[1,3,6,5,7,2,4]=>8
[1,3,6,5,7,4,2]=>8
[1,3,6,7,2,4,5]=>7
[1,3,6,7,2,5,4]=>8
[1,3,6,7,4,2,5]=>7
[1,3,6,7,4,5,2]=>9
[1,3,6,7,5,2,4]=>7
[1,3,6,7,5,4,2]=>7
[1,3,7,2,4,5,6]=>5
[1,3,7,2,4,6,5]=>6
[1,3,7,2,5,4,6]=>6
[1,3,7,2,5,6,4]=>7
[1,3,7,2,6,4,5]=>7
[1,3,7,2,6,5,4]=>7
[1,3,7,4,2,5,6]=>5
[1,3,7,4,2,6,5]=>6
[1,3,7,4,5,2,6]=>7
[1,3,7,4,5,6,2]=>8
[1,3,7,4,6,2,5]=>8
[1,3,7,4,6,5,2]=>8
[1,3,7,5,2,4,6]=>5
[1,3,7,5,2,6,4]=>7
[1,3,7,5,4,2,6]=>5
[1,3,7,5,4,6,2]=>8
[1,3,7,5,6,2,4]=>9
[1,3,7,5,6,4,2]=>9
[1,3,7,6,2,4,5]=>5
[1,3,7,6,2,5,4]=>6
[1,3,7,6,4,2,5]=>5
[1,3,7,6,4,5,2]=>7
[1,3,7,6,5,2,4]=>5
[1,3,7,6,5,4,2]=>5
[1,4,2,3,5,6,7]=>2
[1,4,2,3,5,7,6]=>3
[1,4,2,3,6,5,7]=>3
[1,4,2,3,6,7,5]=>4
[1,4,2,3,7,5,6]=>4
[1,4,2,3,7,6,5]=>4
[1,4,2,5,3,6,7]=>3
[1,4,2,5,3,7,6]=>4
[1,4,2,5,6,3,7]=>4
[1,4,2,5,6,7,3]=>5
[1,4,2,5,7,3,6]=>5
[1,4,2,5,7,6,3]=>5
[1,4,2,6,3,5,7]=>4
[1,4,2,6,3,7,5]=>5
[1,4,2,6,5,3,7]=>4
[1,4,2,6,5,7,3]=>6
[1,4,2,6,7,3,5]=>6
[1,4,2,6,7,5,3]=>6
[1,4,2,7,3,5,6]=>5
[1,4,2,7,3,6,5]=>6
[1,4,2,7,5,3,6]=>5
[1,4,2,7,5,6,3]=>7
[1,4,2,7,6,3,5]=>5
[1,4,2,7,6,5,3]=>5
[1,4,3,2,5,6,7]=>2
[1,4,3,2,5,7,6]=>3
[1,4,3,2,6,5,7]=>3
[1,4,3,2,6,7,5]=>4
[1,4,3,2,7,5,6]=>4
[1,4,3,2,7,6,5]=>4
[1,4,3,5,2,6,7]=>4
[1,4,3,5,2,7,6]=>5
[1,4,3,5,6,2,7]=>5
[1,4,3,5,6,7,2]=>6
[1,4,3,5,7,2,6]=>6
[1,4,3,5,7,6,2]=>6
[1,4,3,6,2,5,7]=>5
[1,4,3,6,2,7,5]=>6
[1,4,3,6,5,2,7]=>5
[1,4,3,6,5,7,2]=>7
[1,4,3,6,7,2,5]=>7
[1,4,3,6,7,5,2]=>7
[1,4,3,7,2,5,6]=>6
[1,4,3,7,2,6,5]=>7
[1,4,3,7,5,2,6]=>6
[1,4,3,7,5,6,2]=>8
[1,4,3,7,6,2,5]=>6
[1,4,3,7,6,5,2]=>6
[1,4,5,2,3,6,7]=>4
[1,4,5,2,3,7,6]=>5
[1,4,5,2,6,3,7]=>5
[1,4,5,2,6,7,3]=>6
[1,4,5,2,7,3,6]=>6
[1,4,5,2,7,6,3]=>6
[1,4,5,3,2,6,7]=>4
[1,4,5,3,2,7,6]=>5
[1,4,5,3,6,2,7]=>6
[1,4,5,3,6,7,2]=>7
[1,4,5,3,7,2,6]=>7
[1,4,5,3,7,6,2]=>7
[1,4,5,6,2,3,7]=>6
[1,4,5,6,2,7,3]=>7
[1,4,5,6,3,2,7]=>6
[1,4,5,6,3,7,2]=>8
[1,4,5,6,7,2,3]=>8
[1,4,5,6,7,3,2]=>8
[1,4,5,7,2,3,6]=>7
[1,4,5,7,2,6,3]=>8
[1,4,5,7,3,2,6]=>7
[1,4,5,7,3,6,2]=>9
[1,4,5,7,6,2,3]=>7
[1,4,5,7,6,3,2]=>7
[1,4,6,2,3,5,7]=>5
[1,4,6,2,3,7,5]=>6
[1,4,6,2,5,3,7]=>6
[1,4,6,2,5,7,3]=>7
[1,4,6,2,7,3,5]=>7
[1,4,6,2,7,5,3]=>7
[1,4,6,3,2,5,7]=>5
[1,4,6,3,2,7,5]=>6
[1,4,6,3,5,2,7]=>7
[1,4,6,3,5,7,2]=>8
[1,4,6,3,7,2,5]=>8
[1,4,6,3,7,5,2]=>8
[1,4,6,5,2,3,7]=>5
[1,4,6,5,2,7,3]=>7
[1,4,6,5,3,2,7]=>5
[1,4,6,5,3,7,2]=>8
[1,4,6,7,2,3,5]=>8
[1,4,6,7,5,3,2]=>8
[1,4,7,2,3,5,6]=>6
[1,4,7,6,5,3,2]=>6
[1,5,2,3,4,7,6]=>4
[1,5,2,7,3,4,6]=>6
[1,5,4,7,6,3,2]=>8
[1,5,6,2,7,3,4]=>8
[1,5,6,4,7,3,2]=>10
[1,5,6,7,2,3,4]=>9
[1,5,6,7,4,3,2]=>9
[1,5,7,2,3,4,6]=>7
[1,5,7,6,4,3,2]=>7
[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]=>8
[1,6,5,4,7,3,2]=>10
[1,6,5,7,4,3,2]=>10
[1,6,7,2,3,4,5]=>8
[1,6,7,5,4,3,2]=>8
[1,7,2,3,4,5,6]=>5
[1,7,3,5,6,4,2]=>10
[1,7,3,6,5,4,2]=>9
[1,7,4,3,6,5,2]=>9
[1,7,4,5,3,6,2]=>11
[1,7,4,5,6,3,2]=>11
[1,7,4,6,5,3,2]=>10
[1,7,5,4,3,6,2]=>9
[1,7,5,4,6,3,2]=>11
[1,7,6,4,5,3,2]=>9
[1,7,6,5,4,3,2]=>5
[2,1,3,4,5,6,7]=>0
[2,1,3,4,7,5,6]=>2
[2,1,3,7,4,5,6]=>3
[2,1,6,3,4,5,7]=>3
[2,1,7,3,4,5,6]=>4
[2,1,7,6,5,4,3]=>4
[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]=>5
[2,6,7,1,3,4,5]=>9
[2,7,1,3,4,5,6]=>6
[3,1,2,4,5,6,7]=>0
[3,1,2,4,5,7,6]=>1
[3,2,1,4,5,6,7]=>0
[3,2,4,5,6,7,1]=>6
[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]=>8
[3,6,1,2,4,5,7]=>6
[3,6,5,4,2,1,7]=>6
[4,1,2,3,5,6,7]=>0
[4,1,2,3,5,7,6]=>1
[4,1,6,2,3,5,7]=>5
[4,2,3,5,6,7,1]=>6
[4,2,5,1,3,6,7]=>5
[4,3,2,1,5,6,7]=>0
[4,3,2,5,6,7,1]=>6
[4,3,5,2,6,7,1]=>9
[4,3,6,5,2,1,7]=>7
[4,5,1,6,2,3,7]=>8
[4,5,2,3,6,7,1]=>10
[4,5,3,6,2,1,7]=>10
[4,5,6,1,2,3,7]=>9
[4,5,6,3,2,1,7]=>9
[4,6,1,2,3,5,7]=>7
[4,6,1,2,3,7,5]=>8
[4,6,5,3,2,1,7]=>7
[5,1,2,3,4,6,7]=>0
[5,1,2,3,4,7,6]=>1
[5,1,2,3,6,4,7]=>2
[5,1,2,3,6,7,4]=>3
[5,1,2,3,7,4,6]=>3
[5,1,2,6,3,4,7]=>4
[5,1,6,2,3,4,7]=>6
[5,1,6,2,3,7,4]=>7
[5,2,3,4,6,7,1]=>6
[5,2,6,7,1,3,4]=>10
[5,3,2,4,6,7,1]=>6
[5,3,2,6,1,4,7]=>6
[5,3,6,7,1,2,4]=>11
[5,4,3,2,1,6,7]=>0
[5,4,3,2,1,7,6]=>1
[5,4,3,2,6,1,7]=>5
[5,4,3,6,2,1,7]=>8
[5,4,6,3,2,1,7]=>9
[5,4,6,7,1,2,3]=>12
[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]=>8
[5,6,7,1,2,3,4]=>12
[6,1,2,3,4,5,7]=>0
[6,1,2,3,4,7,5]=>2
[6,1,2,3,7,4,5]=>4
[6,1,2,7,3,4,5]=>6
[6,2,3,4,5,7,1]=>6
[6,2,4,5,3,1,7]=>5
[6,2,5,4,3,1,7]=>4
[6,3,2,5,4,1,7]=>4
[6,3,4,2,5,1,7]=>6
[6,3,4,5,2,1,7]=>6
[6,3,4,7,1,2,5]=>10
[6,3,5,4,2,1,7]=>5
[6,4,3,2,5,1,7]=>4
[6,4,3,2,7,1,5]=>7
[6,4,3,5,2,1,7]=>6
[6,4,5,7,1,2,3]=>12
[6,4,7,2,5,1,3]=>14
[6,4,7,3,5,1,2]=>15
[6,5,3,4,2,1,7]=>4
[6,5,4,3,2,1,7]=>0
[6,5,7,3,4,1,2]=>16
[6,7,1,2,3,4,5]=>10
[6,7,3,4,1,2,5]=>14
[6,7,4,5,1,2,3]=>16
[7,1,2,3,4,5,6]=>0
[7,2,1,3,4,5,6]=>0
[7,2,3,1,4,5,6]=>2
[7,2,3,4,1,5,6]=>3
[7,2,3,4,5,1,6]=>4
[7,3,1,2,4,5,6]=>0
[7,3,2,1,4,5,6]=>0
[7,3,2,4,1,5,6]=>3
[7,3,4,1,2,5,6]=>4
[7,4,1,2,3,5,6]=>0
[7,4,2,1,3,5,6]=>0
[7,4,5,6,1,2,3]=>9
[7,5,1,2,3,4,6]=>0
[7,5,6,1,2,3,4]=>8
[7,5,6,3,4,1,2]=>12
[7,6,1,2,3,4,5]=>0
[7,6,4,5,1,2,3]=>6
[7,6,5,1,2,3,4]=>0
[7,6,5,3,4,1,2]=>4
[7,6,5,4,1,2,3]=>0
[7,6,5,4,3,1,2]=>0
[7,6,5,4,3,2,1]=>0
[8,7,6,5,4,3,2,1]=>0
[7,6,8,5,4,3,2,1]=>15
[7,8,5,6,4,3,2,1]=>20
[7,8,6,4,5,3,2,1]=>18
[8,6,7,4,5,3,2,1]=>16
[7,6,5,4,8,3,2,1]=>15
[6,5,7,4,8,3,2,1]=>18
[7,8,6,5,3,4,2,1]=>16
[8,6,7,5,3,4,2,1]=>14
[8,7,5,6,3,4,2,1]=>12
[6,7,8,3,4,5,2,1]=>21
[7,8,6,5,4,2,3,1]=>14
[8,6,7,5,4,2,3,1]=>12
[8,7,5,6,4,2,3,1]=>10
[8,7,6,4,5,2,3,1]=>8
[8,6,5,7,3,2,4,1]=>15
[6,7,8,5,2,3,4,1]=>18
[8,5,6,7,2,3,4,1]=>15
[7,8,3,2,4,5,6,1]=>17
[7,6,5,4,3,2,8,1]=>7
[6,5,7,4,3,2,8,1]=>16
[6,5,4,3,7,2,8,1]=>12
[5,4,6,3,7,2,8,1]=>15
[3,4,5,2,6,7,8,1]=>10
[5,2,3,4,6,7,8,1]=>7
[4,3,2,5,6,7,8,1]=>7
[3,4,2,5,6,7,8,1]=>9
[4,2,3,5,6,7,8,1]=>7
[3,2,4,5,6,7,8,1]=>7
[2,3,4,5,6,7,8,1]=>7
[8,7,6,5,4,3,1,2]=>0
[7,8,6,5,4,3,1,2]=>12
[8,6,7,5,4,3,1,2]=>10
[8,7,5,6,4,3,1,2]=>8
[8,7,6,4,5,3,1,2]=>6
[8,7,6,5,3,4,1,2]=>4
[8,7,5,6,3,4,1,2]=>12
[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]=>0
[7,6,8,5,4,2,1,3]=>15
[8,7,6,5,4,1,2,3]=>0
[6,7,8,5,4,1,2,3]=>15
[8,5,6,7,4,1,2,3]=>12
[8,7,6,4,5,1,2,3]=>6
[8,6,7,4,5,1,2,3]=>16
[8,7,4,5,6,1,2,3]=>9
[7,8,4,5,6,1,2,3]=>21
[6,7,4,5,8,1,2,3]=>19
[7,6,5,8,3,2,1,4]=>16
[7,5,6,8,2,3,1,4]=>18
[6,7,5,8,3,1,2,4]=>18
[6,5,7,8,2,1,3,4]=>16
[8,7,6,5,1,2,3,4]=>0
[8,7,5,6,1,2,3,4]=>8
[7,8,5,6,1,2,3,4]=>20
[8,5,6,7,1,2,3,4]=>12
[5,6,7,8,1,2,3,4]=>16
[8,7,6,4,3,2,1,5]=>0
[8,7,6,4,2,1,3,5]=>0
[8,7,6,1,2,3,4,5]=>0
[8,6,7,1,2,3,4,5]=>10
[6,7,8,1,2,3,4,5]=>15
[7,8,5,4,2,1,3,6]=>12
[7,8,5,4,1,2,3,6]=>12
[8,7,1,2,3,4,5,6]=>0
[7,8,1,2,3,4,5,6]=>12
[8,6,5,4,3,2,1,7]=>0
[8,6,5,4,3,1,2,7]=>0
[8,5,6,3,4,1,2,7]=>12
[8,6,5,4,2,1,3,7]=>0
[8,6,4,3,2,1,5,7]=>0
[8,6,4,2,1,3,5,7]=>0
[8,2,3,4,1,5,6,7]=>3
[8,4,1,2,3,5,6,7]=>0
[8,3,2,1,4,5,6,7]=>0
[8,2,3,1,4,5,6,7]=>2
[8,3,1,2,4,5,6,7]=>0
[8,2,1,3,4,5,6,7]=>0
[8,1,2,3,4,5,6,7]=>0
[7,6,5,4,3,2,1,8]=>0
[6,7,5,4,3,2,1,8]=>10
[6,5,7,4,3,2,1,8]=>12
[5,6,7,4,3,2,1,8]=>12
[7,6,4,5,3,2,1,8]=>6
[6,5,4,7,3,2,1,8]=>12
[7,5,6,3,4,2,1,8]=>12
[7,6,4,3,5,2,1,8]=>6
[7,6,3,4,5,2,1,8]=>6
[7,5,4,3,6,2,1,8]=>8
[6,7,5,4,2,3,1,8]=>12
[6,5,7,3,2,4,1,8]=>15
[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]=>0
[6,5,4,3,2,1,7,8]=>0
[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]=>0
[5,4,3,2,1,6,7,8]=>0
[2,3,4,5,1,6,7,8]=>4
[5,1,2,3,4,6,7,8]=>0
[4,3,2,1,5,6,7,8]=>0
[3,4,1,2,5,6,7,8]=>4
[3,2,1,4,5,6,7,8]=>0
[2,1,3,4,5,6,7,8]=>0
[1,2,3,4,5,6,7,8]=>0
[6,5,8,7,4,3,2,1]=>13
[3,5,8,7,6,4,2,1]=>10
[4,3,6,5,8,7,2,1]=>12
[2,6,8,7,5,4,3,1]=>10
[2,3,5,6,8,7,4,1]=>9
[3,2,6,5,4,8,7,1]=>9
[4,3,6,5,7,2,8,1]=>13
[3,2,6,5,7,4,8,1]=>11
[4,3,5,2,7,6,8,1]=>11
[3,2,5,4,7,6,8,1]=>9
[1,8,7,6,5,4,3,2]=>6
[1,7,8,6,5,4,3,2]=>10
[1,6,8,7,5,4,3,2]=>9
[1,7,6,8,5,4,3,2]=>13
[1,6,7,8,5,4,3,2]=>12
[1,5,8,7,6,4,3,2]=>8
[1,7,6,5,8,4,3,2]=>14
[1,3,5,7,8,6,4,2]=>9
[1,4,3,8,7,6,5,2]=>7
[1,6,5,4,3,8,7,2]=>9
[1,4,3,6,5,8,7,2]=>8
[2,1,8,7,6,5,4,3]=>5
[2,1,6,5,7,4,8,3]=>9
[2,1,5,4,7,6,8,3]=>7
[1,2,6,7,8,5,4,3]=>9
[3,2,1,8,7,6,5,4]=>4
[3,2,1,6,5,8,7,4]=>5
[1,2,3,5,6,7,8,4]=>4
[4,3,2,1,8,7,6,5]=>3
[3,4,2,1,7,8,6,5]=>8
[2,4,3,1,6,8,7,5]=>6
[2,4,3,1,7,6,8,5]=>7
[3,2,4,1,6,8,7,5]=>6
[3,2,4,1,7,6,8,5]=>7
[2,3,4,1,6,7,8,5]=>6
[2,1,4,3,8,7,6,5]=>4
[2,1,4,3,6,8,7,5]=>4
[2,1,4,3,7,6,8,5]=>5
[5,4,3,2,1,8,7,6]=>2
[3,2,5,4,1,8,7,6]=>6
[3,2,1,4,5,8,7,6]=>2
[2,3,1,4,5,7,8,6]=>4
[6,5,4,3,2,1,8,7]=>1
[4,3,5,2,6,1,8,7]=>9
[3,2,5,4,6,1,8,7]=>7
[2,3,4,5,6,1,8,7]=>6
[2,1,6,5,4,3,8,7]=>4
[2,1,4,6,5,3,8,7]=>4
[2,1,5,4,6,3,8,7]=>5
[4,3,2,1,6,5,8,7]=>2
[2,4,3,1,6,5,8,7]=>5
[3,2,4,1,6,5,8,7]=>5
[2,1,4,3,6,5,8,7]=>3
[2,1,3,4,5,6,8,7]=>1
[1,2,3,4,5,6,8,7]=>1
[5,7,6,4,3,2,1,8]=>9
[4,7,6,5,3,2,1,8]=>8
[3,2,7,6,5,4,1,8]=>6
[5,4,3,2,7,6,1,8]=>6
[3,2,5,4,7,6,1,8]=>7
[1,4,3,2,7,6,5,8]=>4
[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]=>12
[1,8,5,4,7,6,3,2]=>13
[1,8,7,4,5,6,3,2]=>12
[1,8,7,4,6,5,3,2]=>11
[1,8,6,5,4,7,3,2]=>14
[1,8,7,5,4,6,3,2]=>12
[1,8,7,5,6,4,3,2]=>12
[2,1,4,5,8,6,7,3]=>7
[2,1,8,5,4,7,6,3]=>9
[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]=>12
[4,2,3,1,8,6,7,5]=>7
[8,2,7,4,6,5,3,1]=>11
[4,3,2,7,5,6,8,1]=>9
[4,3,2,8,5,7,6,1]=>10
[6,3,2,5,4,1,8,7]=>5
[8,3,2,5,4,7,6,1]=>7
[8,3,2,7,6,5,4,1]=>6
[8,3,7,4,6,5,2,1]=>12
[7,3,6,5,4,2,1,8]=>6
[7,4,3,6,5,2,1,8]=>7
[7,6,3,5,4,2,1,8]=>5
[8,5,4,3,2,7,6,1]=>6
[8,7,4,3,6,5,2,1]=>7
[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]=>4
[2,4,1,3,7,5,8,6]=>6
[2,1,4,3,7,8,5,6]=>5
[2,4,7,8,1,3,5,6]=>11
[2,1,4,3,8,5,6,7]=>4
[2,4,5,6,7,1,8,3]=>10
[2,1,5,3,6,4,8,7]=>4
[2,1,5,6,3,4,8,7]=>5
[2,5,6,8,1,3,4,7]=>11
[2,1,5,3,7,4,8,6]=>5
[2,5,1,7,3,4,8,6]=>8
[2,1,5,7,3,8,4,6]=>7
[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]=>6
[2,6,7,1,3,4,8,5]=>10
[2,1,6,7,8,3,4,5]=>9
[2,6,7,8,1,3,4,5]=>13
[2,1,6,3,4,7,8,5]=>5
[2,1,6,3,4,5,8,7]=>4
[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]=>5
[2,8,1,3,4,5,6,7]=>7
[2,1,3,8,4,5,6,7]=>4
[2,3,4,5,6,8,1,7]=>7
[3,1,4,2,6,5,8,7]=>4
[3,4,1,2,6,5,8,7]=>6
[3,1,4,2,6,8,5,7]=>5
[3,4,6,8,1,2,5,7]=>11
[3,1,4,2,7,5,8,6]=>5
[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]=>5
[3,5,1,6,2,4,8,7]=>8
[3,1,5,6,2,8,4,7]=>7
[3,5,6,8,1,2,4,7]=>12
[3,1,5,2,7,4,8,6]=>6
[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]=>7
[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]=>5
[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]=>2
[1,3,2,4,5,8,6,7]=>3
[4,1,5,2,6,3,8,7]=>6
[4,5,6,1,2,3,8,7]=>10
[4,1,5,6,8,2,3,7]=>9
[4,5,6,8,1,2,3,7]=>13
[4,1,5,2,7,3,8,6]=>7
[4,1,5,2,7,8,3,6]=>8
[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]=>8
[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]=>2
[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]=>3
[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]=>9
[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]=>6
[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]=>1
[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]=>8
[6,1,2,7,3,4,5,8]=>6
[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]=>9
[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]=>1
[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]=>4
[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]=>2
[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]=>7
[7,3,2,5,4,8,1,6]=>9
[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]=>9
[5,4,6,2,1,3,8,7]=>10
[3,6,1,5,4,2,8,7]=>9
[4,6,5,1,3,2,8,7]=>9
[5,6,4,3,1,2,8,7]=>9
[7,5,4,3,2,8,1,6]=>8
[8,6,4,3,7,2,5,1]=>12
[7,6,4,3,8,2,1,5]=>13
[6,7,4,3,8,1,2,5]=>17
[5,7,4,3,1,8,2,6]=>13
[4,7,5,1,3,8,2,6]=>12
[3,7,1,5,4,8,2,6]=>12
[2,1,7,5,4,8,3,6]=>8
[3,8,1,5,4,7,6,2]=>13
[4,8,5,1,3,7,6,2]=>13
[5,8,4,3,1,7,6,2]=>14
[6,8,4,3,7,1,5,2]=>19
[7,8,4,3,6,5,1,2]=>19
[6,8,5,7,3,1,4,2]=>21
[5,8,6,7,1,3,4,2]=>20
[4,8,6,1,7,3,5,2]=>17
[3,8,1,6,7,4,5,2]=>16
[2,1,8,6,7,4,5,3]=>13
[2,1,7,6,8,4,3,5]=>10
[3,7,1,6,8,4,2,5]=>13
[4,7,6,1,8,3,2,5]=>14
[5,7,6,8,1,3,2,4]=>18
[5,4,7,2,1,8,3,6]=>12
[6,4,7,2,8,1,3,5]=>15
[7,4,6,2,8,3,1,5]=>14
[8,4,6,2,7,3,5,1]=>13
[8,3,2,6,7,4,5,1]=>10
[7,3,2,6,8,4,1,5]=>11
[6,3,2,7,8,1,4,5]=>11
[5,3,2,7,1,8,4,6]=>9
[4,3,2,1,7,8,5,6]=>4
[3,4,1,2,8,7,6,5]=>7
[5,3,2,8,1,7,6,4]=>10
[6,3,2,8,7,1,5,4]=>10
[7,3,2,8,6,5,1,4]=>10
[8,4,7,2,6,5,3,1]=>12
[7,4,8,2,6,5,1,3]=>17
[6,4,8,2,7,1,5,3]=>17
[5,4,8,2,1,7,6,3]=>13
[4,5,8,1,2,7,6,3]=>13
[3,5,1,8,2,7,6,4]=>11
[2,1,5,8,3,7,6,4]=>8
[2,1,6,8,7,3,5,4]=>8
[3,6,1,8,7,2,5,4]=>11
[4,6,8,1,7,2,5,3]=>16
[5,6,8,7,1,2,4,3]=>14
[6,5,8,7,2,1,4,3]=>14
[7,5,8,6,2,4,1,3]=>17
[8,5,7,6,2,4,3,1]=>12
[5,7,8,6,1,4,2,3]=>16
[4,7,8,1,6,5,2,3]=>16
[3,7,1,8,6,5,2,4]=>11
[2,1,7,8,6,5,3,4]=>8
[3,8,1,7,6,5,4,2]=>12
[4,8,7,1,6,5,3,2]=>12
[5,8,7,6,1,4,3,2]=>12
[6,8,7,5,4,1,3,2]=>12
[4,2,5,1,3,6,7,8]=>5
[5,2,6,7,1,3,4,8]=>10
[3,2,7,8,1,4,5,6]=>10
[5,3,2,6,1,4,7,8]=>6
[7,4,3,8,1,2,5,6]=>12
[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]=>11
[6,4,7,2,5,1,3,8]=>14
[6,4,3,2,7,1,5,8]=>7
[5,4,3,2,8,1,6,7]=>7
[7,5,3,8,2,6,1,4]=>16
[8,5,4,7,2,6,1,3]=>13
[8,5,4,7,3,6,1,2]=>14
[8,1,2,7,6,3,4,5]=>4
[8,1,4,2,6,3,5,7]=>4
[8,3,1,2,4,7,5,6]=>2
[8,3,1,5,6,2,4,7]=>5
[6,3,8,1,2,7,4,5]=>13
[7,8,4,1,6,2,3,5]=>17
[8,3,4,1,6,7,2,5]=>8
[2,7,6,5,1,3,8,4]=>9
[8,3,6,5,1,7,2,4]=>10
[4,6,7,3,8,5,1,2]=>16
[3,5,2,7,1,8,6,4]=>11
[4,6,7,2,8,1,5,3]=>16
[5,6,7,8,2,1,4,3]=>17
[6,5,8,7,3,4,1,2]=>17
[3,6,7,4,5,8,1,2]=>16
[2,6,7,4,5,1,8,3]=>14
[1,6,7,4,5,2,3,8]=>12
[1,5,4,7,6,2,3,8]=>8
[2,5,4,7,6,1,8,3]=>11
[3,5,4,7,6,8,1,2]=>14
[4,5,3,7,8,6,1,2]=>14
[5,4,3,8,7,6,1,2]=>10
[6,4,8,3,7,5,1,2]=>17
[6,3,8,4,5,7,1,2]=>17
[5,3,4,8,6,7,1,2]=>14
[4,3,5,6,8,7,1,2]=>11
[3,2,5,6,1,8,7,4]=>8
[4,2,5,6,8,1,7,3]=>11
[5,2,4,8,6,1,7,3]=>11
[6,2,8,4,5,1,7,3]=>15
[7,8,2,4,5,1,6,3]=>18
[7,8,1,4,5,2,3,6]=>16
[6,1,8,4,5,2,3,7]=>13
[5,1,4,8,6,2,3,7]=>8
[4,1,3,2,8,6,5,7]=>4
[5,1,3,8,2,6,4,7]=>8
[6,1,8,3,2,5,4,7]=>10
[7,8,1,3,2,5,4,6]=>14
[7,8,2,3,1,5,6,4]=>16
[6,2,8,3,1,5,7,4]=>12
[5,2,3,8,1,6,7,4]=>10
[6,3,8,2,1,7,5,4]=>13
[7,8,3,2,1,6,5,4]=>14
[7,8,4,2,6,1,5,3]=>19
[5,4,2,8,7,1,6,3]=>10
[4,5,2,7,8,1,6,3]=>14
[2,5,3,7,1,6,8,4]=>10
[1,5,3,7,2,6,4,8]=>8
[1,6,7,3,2,5,4,8]=>9
[2,6,7,3,1,5,8,4]=>11
[3,6,7,2,1,8,5,4]=>12
[7,8,5,6,2,1,4,3]=>21
[6,5,8,7,1,2,3,4]=>13
[5,4,1,8,7,2,3,6]=>8
[6,4,8,1,7,2,3,5]=>15
[7,8,3,1,2,6,4,5]=>14
[5,3,1,8,2,7,4,6]=>9
[4,3,1,2,8,7,5,6]=>3
[4,2,1,3,8,5,7,6]=>4
[5,2,1,8,3,4,7,6]=>7
[6,2,8,1,3,4,7,5]=>11
[7,8,2,1,3,4,6,5]=>13
[6,3,1,5,2,4,8,7]=>4
[2,1,8,5,3,7,4,6]=>8
[8,2,6,1,4,3,7,5]=>7
[4,7,1,5,8,3,2,6]=>13
[8,6,1,3,4,2,5,7]=>2
[8,1,2,4,5,6,3,7]=>3
[8,2,5,1,3,6,4,7]=>5
[4,1,5,3,7,2,8,6]=>8
[5,2,7,1,3,8,4,6]=>10
[5,3,1,7,8,2,4,6]=>9
[1,7,3,4,2,5,8,6]=>8
[4,7,2,1,3,5,8,6]=>9
[4,5,2,3,7,6,1,8]=>10
[6,4,3,7,2,5,1,8]=>12
[8,4,3,6,5,1,2,7]=>7
[1,5,6,3,4,8,7,2]=>10
[4,6,2,7,3,5,1,8]=>13
[3,2,6,7,4,5,1,8]=>10
[4,7,2,6,5,3,1,8]=>12
[5,7,6,2,4,3,1,8]=>12
[1,7,5,4,8,3,6,2]=>14
[8,7,5,4,1,3,2,6]=>1
[6,8,5,4,2,1,3,7]=>11
[5,8,6,2,4,1,3,7]=>13
[4,8,2,6,5,1,3,7]=>13
[3,2,8,6,5,1,4,7]=>7
[4,1,2,6,5,8,7,3]=>6
[5,1,6,2,4,8,7,3]=>9
[6,1,5,4,2,8,7,3]=>7
[7,1,5,4,8,2,6,3]=>12
[8,1,5,4,7,6,2,3]=>8
[1,8,6,7,4,5,3,2]=>18
[8,1,6,7,4,5,2,3]=>12
[7,1,6,8,4,2,5,3]=>14
[6,1,7,8,2,4,5,3]=>14
[5,1,7,2,8,4,6,3]=>12
[4,1,2,7,8,5,6,3]=>9
[3,2,1,7,8,5,6,4]=>8
[3,2,8,7,1,5,4,6]=>8
[4,8,2,7,1,5,3,6]=>15
[5,8,7,2,1,4,3,6]=>11
[6,8,7,1,2,4,3,5]=>12
[7,8,6,1,4,2,3,5]=>14
[8,7,6,1,4,3,2,5]=>2
[1,7,6,8,4,3,5,2]=>16
[1,6,7,8,3,4,5,2]=>15
[8,6,7,1,3,4,2,5]=>12
[7,6,8,1,3,2,4,5]=>16
[5,7,8,2,1,3,4,6]=>14
[4,7,2,8,1,3,5,6]=>13
[3,2,6,8,4,1,5,7]=>9
[4,6,2,8,3,1,5,7]=>12
[5,6,8,2,3,1,4,7]=>15
[6,5,8,3,2,1,4,7]=>13
[7,5,8,3,1,2,4,6]=>14
[8,5,7,3,1,4,2,6]=>11
[1,5,7,3,8,4,6,2]=>13
[1,4,3,7,8,5,6,2]=>11
[8,4,3,7,1,5,2,6]=>9
[6,4,3,8,2,1,5,7]=>11
[4,5,2,3,8,1,6,7]=>11
[3,2,5,4,8,1,6,7]=>8
[4,5,2,3,1,8,7,6]=>10
[6,4,3,1,2,8,7,5]=>3
[7,4,3,1,8,2,6,5]=>9
[8,4,3,1,7,6,2,5]=>5
[1,5,8,3,7,6,4,2]=>12
[8,5,1,3,7,6,2,4]=>6
[7,5,1,3,8,2,6,4]=>10
[6,5,1,3,2,8,7,4]=>5
[5,6,1,2,3,8,7,4]=>10
[4,6,2,1,3,8,7,5]=>9
[3,2,6,1,4,8,7,5]=>7
[3,2,7,1,8,4,6,5]=>10
[4,7,2,1,8,3,6,5]=>12
[5,7,1,2,8,3,6,4]=>13
[6,7,1,8,2,3,5,4]=>15
[7,6,1,8,3,2,5,4]=>13
[8,6,1,7,3,5,2,4]=>11
[1,6,8,7,3,5,4,2]=>12
[1,7,8,6,5,3,4,2]=>12
[8,7,1,6,5,3,2,4]=>4
[7,8,1,6,5,2,3,4]=>16
[6,8,1,7,2,5,3,4]=>17
[5,8,1,2,7,6,3,4]=>13
[4,8,2,1,7,6,3,5]=>12
[3,2,8,1,7,6,4,5]=>10
[4,1,2,8,7,6,5,3]=>5
[5,1,8,2,7,6,4,3]=>11
[6,1,8,7,2,5,4,3]=>11
[7,1,8,6,5,2,4,3]=>11
[8,1,7,6,5,4,2,3]=>5
[1,4,3,8,7,5,6,2]=>9
[4,1,2,8,7,5,6,3]=>7
[3,2,5,1,6,4,8,7]=>6
[3,2,5,4,7,1,8,6]=>8
[4,2,5,3,7,6,8,1]=>10
[4,2,5,3,7,1,8,6]=>9
[4,2,5,3,6,1,8,7]=>8
[4,2,5,1,6,3,8,7]=>7
[3,1,5,4,6,2,8,7]=>6
[4,1,5,3,6,2,8,7]=>7
[4,3,5,1,6,2,8,7]=>8
[4,3,5,2,7,1,8,6]=>10
[4,3,6,2,7,5,8,1]=>12
[4,3,6,2,7,1,8,5]=>11
[4,3,6,1,7,2,8,5]=>10
[4,3,5,1,7,2,8,6]=>9
[3,1,5,4,7,2,8,6]=>7
[2,1,5,4,7,3,8,6]=>6
[3,1,5,4,7,6,8,2]=>8
[4,1,5,3,7,6,8,2]=>9
[4,3,5,1,7,6,8,2]=>10
[4,3,6,1,7,5,8,2]=>11
[4,3,6,5,7,1,8,2]=>12
[5,3,6,4,7,2,8,1]=>14
[5,3,6,4,7,1,8,2]=>13
[5,3,6,1,7,4,8,2]=>12
[5,1,6,3,7,4,8,2]=>11
[4,1,6,3,7,5,8,2]=>10
[3,1,6,4,7,5,8,2]=>9
[2,1,6,4,7,5,8,3]=>8
[2,1,6,4,7,3,8,5]=>7
[3,1,6,4,7,2,8,5]=>8
[4,1,6,3,7,2,8,5]=>9
[5,1,6,3,7,2,8,4]=>10
[5,3,6,1,7,2,8,4]=>11
[5,3,6,2,7,1,8,4]=>12
[5,3,6,2,7,4,8,1]=>13
[5,2,6,3,7,4,8,1]=>12
[5,2,6,3,7,1,8,4]=>11
[5,2,6,1,7,3,8,4]=>10
[4,2,5,1,7,3,8,6]=>8
[4,2,6,1,7,3,8,5]=>9
[4,2,6,3,7,1,8,5]=>10
[4,2,6,3,7,5,8,1]=>11
[3,2,6,4,7,5,8,1]=>10
[3,2,6,4,7,1,8,5]=>9
[3,2,6,1,7,4,8,5]=>8
[3,2,5,1,7,4,8,6]=>7
[3,2,4,1,7,5,8,6]=>6
[3,1,4,2,7,6,8,5]=>6
[3,2,5,1,7,6,8,4]=>8
[3,2,6,1,7,5,8,4]=>9
[3,2,6,5,7,1,8,4]=>10
[4,2,6,5,7,3,8,1]=>12
[4,2,6,5,7,1,8,3]=>11
[4,2,6,1,7,5,8,3]=>10
[4,2,5,1,7,6,8,3]=>9
[4,1,5,2,7,6,8,3]=>8
[3,1,5,2,7,6,8,4]=>7
[2,1,5,3,7,6,8,4]=>6
[2,1,6,3,7,5,8,4]=>7
[3,1,6,2,7,5,8,4]=>8
[4,1,6,2,7,5,8,3]=>9
[5,1,6,2,7,4,8,3]=>10
[5,2,6,1,7,4,8,3]=>11
[5,2,6,4,7,1,8,3]=>12
[5,2,6,4,7,3,8,1]=>13
[5,4,6,2,7,3,8,1]=>14
[5,4,6,2,7,1,8,3]=>13
[5,4,6,1,7,2,8,3]=>12
[5,1,6,4,7,2,8,3]=>11
[4,1,6,5,7,2,8,3]=>10
[3,1,6,5,7,2,8,4]=>9
[2,1,6,5,7,3,8,4]=>8
[3,1,6,5,7,4,8,2]=>10
[4,1,6,5,7,3,8,2]=>11
[5,1,6,4,7,3,8,2]=>12
[5,4,6,1,7,3,8,2]=>13
[5,4,6,3,7,1,8,2]=>14
[8,3,5,2,1,6,4,7]=>6
[8,6,3,5,2,4,1,7]=>7
[3,7,5,2,4,1,8,6]=>10
[8,3,7,5,2,4,6,1]=>11
[8,2,4,5,7,3,6,1]=>10
[2,4,5,7,3,1,8,6]=>9
[8,2,4,6,5,3,1,7]=>6
[8,2,5,4,6,1,3,7]=>8
[8,6,3,5,1,4,2,7]=>6
[8,6,1,4,5,3,2,7]=>4
[8,1,5,6,4,3,2,7]=>6
[5,7,4,3,2,1,8,6]=>10
[8,5,7,4,3,2,6,1]=>13
[4,6,8,3,2,7,5,1]=>16
[4,7,6,3,2,8,1,5]=>14
[1,4,6,7,3,2,8,5]=>9
[5,4,7,3,1,8,2,6]=>13
[1,7,4,5,3,2,8,6]=>10
[3,7,5,1,4,2,8,6]=>9
[5,7,4,2,1,3,8,6]=>10
[8,5,7,4,2,1,6,3]=>11
[8,3,7,5,1,4,6,2]=>10
[8,4,1,7,5,3,6,2]=>9
[4,6,3,8,7,1,5,2]=>14
[1,7,4,8,6,3,5,2]=>13
[8,4,7,6,3,5,2,1]=>12
[3,6,5,8,7,4,1,2]=>13
[3,1,5,8,6,7,4,2]=>11
[4,8,1,6,7,3,5,2]=>17
[3,6,4,1,8,7,5,2]=>10
[8,2,6,1,4,7,5,3]=>8
[2,7,6,8,1,4,3,5]=>15
[3,7,1,6,4,8,2,5]=>13
[1,7,3,5,6,8,2,4]=>12
[1,3,6,7,5,8,2,4]=>11
[3,7,6,5,8,2,1,4]=>16
[3,6,8,5,7,2,4,1]=>19
[2,3,5,7,6,8,1,4]=>11
[2,1,6,5,7,8,3,4]=>9
[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]=>14
[3,7,2,6,4,8,1,5]=>14
[3,2,6,1,4,7,8,5]=>7
[5,3,7,2,1,8,4,6]=>11
[4,7,3,2,1,5,8,6]=>9
[8,7,6,1,3,4,2,5]=>2
[8,5,7,3,2,1,6,4]=>10
[8,3,6,7,2,1,5,4]=>11
[3,7,8,6,2,1,5,4]=>13
[8,7,6,3,5,2,4,1]=>7
[2,7,4,8,1,6,5,3]=>14
[4,6,8,2,1,7,5,3]=>14
[8,4,1,5,7,2,6,3]=>8
[8,5,3,7,1,6,2,4]=>11
[8,5,7,2,1,3,6,4]=>10
[8,2,6,7,1,3,5,4]=>10
[8,3,6,1,7,5,2,4]=>9
[4,6,1,8,7,2,5,3]=>12
[8,1,2,5,6,7,4,3]=>6
[8,2,6,5,7,4,1,3]=>11
[2,1,7,8,5,6,4,3]=>12
[8,2,5,7,6,4,3,1]=>8
[2,7,6,8,5,4,1,3]=>14
[1,7,2,5,8,6,4,3]=>10
[1,7,4,8,2,6,5,3]=>13
[3,7,8,1,6,5,2,4]=>15
[2,7,8,6,1,3,5,4]=>12
[8,7,6,3,5,1,4,2]=>6
[8,4,7,6,5,1,3,2]=>9
[8,7,1,5,6,4,3,2]=>6
[8,1,6,7,5,4,3,2]=>8
[5,4,3,6,1,2,8,7]=>9
[2,7,6,4,5,8,1,3]=>14
[5,7,3,6,1,8,2,4]=>16
[2,1,7,6,5,8,3,4]=>10
[6,4,3,5,8,1,7,2]=>12
[7,3,5,4,8,6,1,2]=>13
[5,4,3,2,7,1,8,6]=>7
[4,3,6,2,8,7,5,1]=>11
[4,3,7,6,2,1,8,5]=>10
[6,4,3,1,7,2,8,5]=>7
[4,3,7,1,8,6,5,2]=>11
[5,3,8,7,6,4,2,1]=>10
[7,5,3,1,8,6,4,2]=>9
[1,8,6,5,3,7,4,2]=>13
[6,1,7,5,3,2,8,4]=>10
[7,6,5,3,2,1,8,4]=>4
[6,5,3,2,8,7,4,1]=>9
[5,2,6,3,8,7,4,1]=>11
[5,2,7,6,3,1,8,4]=>10
[6,5,2,1,7,3,8,4]=>7
[5,2,7,1,8,6,4,3]=>11
[6,2,8,7,5,4,3,1]=>10
[7,6,2,1,8,5,4,3]=>9
[6,1,7,2,8,5,4,3]=>11
[7,1,8,6,5,4,3,2]=>10
[4,5,2,6,3,1,8,7]=>10
[6,5,2,1,4,3,8,7]=>2
[6,5,2,7,4,8,3,1]=>14
[8,5,2,7,4,1,6,3]=>10
[8,3,7,5,2,1,6,4]=>9
[6,3,7,5,2,8,4,1]=>15
[3,1,6,5,4,2,8,7]=>5
[5,6,3,2,4,1,8,7]=>12
[3,6,2,4,1,5,8,7]=>9
[2,6,1,3,5,4,8,7]=>7
[6,7,2,3,4,8,5,1]=>15
[8,7,2,3,4,1,6,5]=>4
[5,1,7,3,8,4,6,2]=>13
[2,5,7,3,8,6,4,1]=>12
[7,6,1,3,5,8,4,2]=>9
[3,6,7,4,1,8,5,2]=>13
[5,6,3,7,4,8,1,2]=>17
[2,1,6,7,4,8,5,3]=>9
[2,1,8,7,4,3,6,5]=>6
[5,8,3,7,4,2,6,1]=>19
[3,8,7,4,1,2,6,5]=>9
[7,8,1,3,5,2,6,4]=>16
[5,8,7,3,2,6,1,4]=>14
[2,8,6,3,1,5,7,4]=>10
[8,1,6,3,2,5,4,7]=>5
[2,8,4,1,6,3,7,5]=>11
[4,8,1,2,7,6,3,5]=>12
[3,8,4,2,5,7,1,6]=>13
[6,8,3,5,2,7,4,1]=>19
[2,1,5,3,8,7,6,4]=>5
[6,5,3,2,8,7,1,4]=>9
[7,5,2,4,8,1,6,3]=>12
[3,4,2,8,5,7,6,1]=>12
[2,4,1,8,7,6,5,3]=>7
[8,4,2,1,7,5,3,6]=>4
[4,3,1,8,6,7,5,2]=>10
[3,1,4,8,6,5,7,2]=>9
[7,1,6,5,4,8,2,3]=>12
[3,7,5,6,8,4,2,1]=>16
[5,7,1,6,8,2,4,3]=>16
[8,6,2,5,1,7,4,3]=>8
[5,6,2,1,8,7,3,4]=>11
[4,6,2,5,8,3,7,1]=>15
[7,5,2,6,3,8,1,4]=>12
[4,1,2,3,6,8,7,5]=>3
[2,4,3,1,8,5,6,7]=>6
[7,5,2,8,3,4,6,1]=>15
[5,6,2,8,4,3,1,7]=>13
[4,7,2,8,1,5,3,6]=>14
[8,7,2,1,4,5,6,3]=>3
[3,6,8,7,1,5,4,2]=>13
[5,7,8,6,3,4,1,2]=>18
[7,1,8,5,4,3,6,2]=>14
[2,7,8,4,5,3,6,1]=>17
[5,7,3,8,1,4,6,2]=>17
[2,1,7,8,5,4,6,3]=>11
[2,1,5,8,4,6,3,7]=>8
[6,5,3,8,4,1,2,7]=>12
[7,5,8,4,3,6,2,1]=>20
[2,4,8,3,5,6,1,7]=>11
[4,1,8,3,6,5,2,7]=>10
[3,4,8,1,7,2,5,6]=>12
[8,4,1,3,7,2,6,5]=>6
[3,1,8,2,4,7,6,5]=>8
[2,3,8,1,4,6,7,5]=>9
[4,3,8,2,5,1,7,6]=>12
[6,3,8,4,2,5,7,1]=>15
[7,4,3,8,2,5,1,6]=>14
[2,1,4,8,3,5,7,6]=>6
[6,8,2,4,3,5,1,7]=>16
[4,8,2,3,5,1,6,7]=>12
[3,8,2,1,4,6,5,7]=>9
[2,8,1,3,4,5,7,6]=>8
[7,1,6,8,4,3,2,5]=>12
[7,1,6,5,8,3,2,4]=>13
[3,7,6,1,4,8,2,5]=>12
[2,7,8,4,1,6,5,3]=>14
[3,6,4,5,7,2,8,1]=>14
[1,8,2,7,3,4,5,6]=>10
[3,2,1,5,8,4,6,7]=>4
[5,4,3,2,1,8,6,7]=>2
[1,8,2,4,3,5,6,7]=>7
[1,7,2,4,3,5,6,8]=>6
[1,6,2,4,3,5,7,8]=>5
[1,5,2,4,3,6,7,8]=>4
[1,6,2,5,3,4,7,8]=>6
[1,7,2,5,3,4,6,8]=>7
[1,8,2,5,3,4,6,7]=>8
[1,8,2,6,3,4,5,7]=>9
[1,7,2,6,3,4,5,8]=>8
[1,8,2,7,3,5,4,6]=>11
[1,7,2,8,3,5,4,6]=>10
[1,6,2,8,3,5,4,7]=>9
[1,5,2,8,3,6,4,7]=>8
[1,4,2,8,3,6,5,7]=>7
[1,3,2,8,4,6,5,7]=>6
[1,2,3,8,4,6,5,7]=>5
[1,2,3,7,4,6,5,8]=>4
[1,3,2,7,4,6,5,8]=>5
[1,4,2,7,3,6,5,8]=>6
[1,5,2,7,3,6,4,8]=>7
[1,6,2,7,3,5,4,8]=>8
[1,7,2,6,3,5,4,8]=>9
[1,8,2,6,3,5,4,7]=>10
[1,8,2,5,3,6,4,7]=>9
[1,7,2,5,3,6,4,8]=>8
[1,6,2,5,3,7,4,8]=>7
[1,5,2,4,3,7,6,8]=>5
[1,6,2,4,3,7,5,8]=>6
[1,7,2,4,3,6,5,8]=>7
[1,8,2,4,3,6,5,7]=>8
[1,8,2,3,4,6,5,7]=>7
[1,7,2,3,4,6,5,8]=>6
[1,8,2,3,4,7,5,6]=>8
[1,8,2,4,3,7,5,6]=>9
[1,7,2,4,3,8,5,6]=>8
[1,6,2,4,3,8,5,7]=>7
[1,5,2,4,3,8,6,7]=>6
[1,6,2,5,3,8,4,7]=>8
[1,7,2,5,3,8,4,6]=>9
[1,8,2,5,3,7,4,6]=>10
[1,8,2,6,3,7,4,5]=>11
[1,7,2,6,3,8,4,5]=>10
[1,2,3,8,4,7,5,6]=>6
[1,3,2,8,4,7,5,6]=>7
[1,4,2,8,3,7,5,6]=>8
[1,5,2,8,3,7,4,6]=>9
[1,6,2,8,3,7,4,5]=>10
[1,7,2,8,3,6,4,5]=>11
[1,8,2,7,3,6,4,5]=>12
[6,7,8,1,4,3,2,5]=>17
[2,8,4,1,6,7,5,3]=>12
[4,8,5,7,1,6,2,3]=>18
[8,7,6,5,2,1,4,3]=>1
[8,3,1,5,4,7,2,6]=>6
[8,7,6,5,1,4,2,3]=>2
[7,5,1,3,8,4,2,6]=>9
[7,6,1,4,8,3,2,5]=>11
[7,1,3,5,8,2,4,6]=>9
[7,5,3,6,4,2,8,1]=>12
[8,2,6,3,4,7,5,1]=>9
[7,2,6,3,5,4,8,1]=>11
[6,2,7,4,3,5,8,1]=>13
[3,7,6,4,5,2,8,1]=>14
[2,7,6,5,3,4,8,1]=>11
[8,6,5,4,2,7,3,1]=>9
[6,5,8,4,2,7,3,1]=>18
[1,8,6,3,7,5,2,4]=>13
[8,7,5,2,6,4,3,1]=>7
[8,7,1,6,2,5,4,3]=>6
[1,7,2,8,5,3,4,6]=>9
[7,6,1,8,4,3,2,5]=>12
[8,6,1,7,4,2,5,3]=>10
[8,1,2,7,3,4,6,5]=>5
[7,1,2,8,3,5,4,6]=>9
[8,2,6,1,7,3,5,4]=>9
[4,7,5,6,8,3,2,1]=>17
[8,6,4,7,5,3,2,1]=>11
[5,4,8,1,7,2,6,3]=>15
[2,3,8,7,4,5,6,1]=>10
[7,2,8,6,4,3,5,1]=>14
[8,2,7,6,3,5,4,1]=>9
[8,1,7,6,5,2,4,3]=>6
[7,1,8,6,5,3,2,4]=>10
[1,2,8,7,6,3,4,5]=>5
[3,8,7,6,4,5,2,1]=>12
[2,8,7,6,5,3,4,1]=>9
[1,8,7,6,5,4,2,3]=>6
[3,8,6,7,1,5,2,4]=>18
[5,4,7,1,3,8,2,6]=>13
[5,6,2,1,4,8,3,7]=>11
[2,1,8,4,7,5,6,3]=>11
[4,1,3,2,8,5,6,7]=>4
[3,2,1,4,8,5,6,7]=>3
[1,8,4,2,5,3,6,7]=>8
[8,1,5,3,2,4,6,7]=>3
[3,8,1,5,2,4,6,7]=>10
[1,6,7,2,8,4,3,5]=>11
[6,7,1,4,2,8,3,5]=>14
[6,3,7,1,4,8,2,5]=>13
[3,7,8,1,5,2,4,6]=>14
[7,1,2,8,5,3,4,6]=>8
[1,7,2,8,4,5,3,6]=>11
[1,2,7,5,8,3,4,6]=>9
[2,8,1,7,4,3,6,5]=>12
[4,2,6,5,8,3,7,1]=>13
[5,2,4,7,3,6,8,1]=>11
[5,1,2,4,8,3,6,7]=>5
[4,3,6,1,5,8,2,7]=>10
[2,6,1,4,5,8,3,7]=>9
[2,5,3,4,1,8,6,7]=>8
[4,3,5,2,1,8,6,7]=>8
[3,1,6,7,5,8,2,4]=>11
[2,8,1,7,5,6,3,4]=>15
[5,3,6,8,4,7,2,1]=>16
[3,7,2,5,4,8,6,1]=>13
[8,4,2,5,7,3,6,1]=>10
[4,7,2,5,8,3,6,1]=>16
[5,2,6,8,4,3,7,1]=>14
[3,1,6,5,4,8,2,7]=>8
[4,1,6,5,8,3,2,7]=>10
[5,1,6,8,4,3,2,7]=>10
[8,5,4,7,6,3,2,1]=>10
[5,7,1,8,4,3,2,6]=>13
[2,7,1,5,4,3,8,6]=>9
[8,2,1,5,4,3,7,6]=>3
[8,4,1,5,7,3,2,6]=>7
[8,5,6,7,1,3,2,4]=>13
[8,4,6,1,7,3,2,5]=>10
[8,3,6,1,4,7,2,5]=>9
[2,7,6,1,4,3,8,5]=>9
[6,7,8,5,1,3,2,4]=>16
[5,7,6,8,2,3,4,1]=>20
[5,7,2,8,4,3,6,1]=>17
[6,7,8,2,4,3,5,1]=>20
[4,7,6,2,8,3,5,1]=>17
[8,3,6,2,4,7,5,1]=>10
[3,7,6,2,4,8,5,1]=>13
[5,7,3,8,4,6,2,1]=>19
[4,7,3,5,8,6,2,1]=>15
[8,7,2,1,4,3,6,5]=>2
[8,7,3,1,4,6,2,5]=>4
[8,7,6,3,2,5,4,1]=>4
[8,7,3,5,1,6,2,4]=>7
[8,7,2,5,1,3,6,4]=>5
[8,2,6,5,1,3,7,4]=>7
[8,4,6,5,7,1,2,3]=>13
[5,7,6,8,4,1,2,3]=>17
[4,7,6,5,8,1,2,3]=>17
[3,7,6,5,1,8,2,4]=>13
[2,6,5,7,3,4,8,1]=>14
[1,6,4,7,5,8,2,3]=>13
[8,5,3,6,2,7,4,1]=>11
[1,3,7,4,6,8,2,5]=>10
[4,7,5,6,3,2,8,1]=>17
[1,7,6,5,4,8,2,3]=>13
[8,1,6,5,7,2,4,3]=>11
[1,2,7,6,8,3,4,5]=>10
[6,1,7,5,3,8,2,4]=>13
[2,1,7,5,6,8,3,4]=>10
[5,4,1,7,6,8,2,3]=>11
[4,8,5,6,2,7,3,1]=>18
[3,8,6,4,2,7,5,1]=>14
[7,8,5,2,4,6,3,1]=>19
[2,8,6,3,7,4,5,1]=>16
[7,8,1,6,2,4,5,3]=>18
[6,8,1,4,7,2,5,3]=>17
[3,8,4,1,7,2,6,5]=>13
[5,4,7,1,8,3,2,6]=>13
[3,7,4,1,8,5,2,6]=>11
[6,7,1,4,8,3,2,5]=>15
[2,7,1,8,4,5,3,6]=>12
[6,1,2,8,4,3,5,7]=>7
[6,5,1,4,3,8,2,7]=>7
[1,6,2,5,8,3,4,7]=>9
[8,5,1,3,7,2,6,4]=>7
[8,4,2,1,7,3,6,5]=>5
[7,4,2,1,8,5,3,6]=>7
[1,5,4,2,8,3,6,7]=>7
[6,4,3,1,5,8,2,7]=>6
[3,7,6,8,4,5,2,1]=>19
[2,7,6,8,5,3,4,1]=>16
[1,7,6,8,5,4,2,3]=>13
[1,4,8,6,7,5,2,3]=>13
[2,4,8,6,7,3,5,1]=>16
[7,3,8,5,4,6,2,1]=>18
[3,4,8,5,6,7,2,1]=>15
[6,3,5,8,4,7,2,1]=>16
[5,4,3,8,6,7,2,1]=>14
[5,4,2,8,7,3,6,1]=>11
[6,2,5,8,7,3,4,1]=>13
[3,2,8,5,7,4,6,1]=>14
[1,3,8,7,5,6,2,4]=>10
[2,1,8,7,4,6,3,5]=>8
[3,1,8,5,7,6,2,4]=>11
[6,1,5,8,7,4,2,3]=>10
[5,4,1,8,7,6,2,3]=>8
[5,8,6,7,4,3,2,1]=>18
[4,8,7,5,6,3,2,1]=>15
[2,8,3,1,5,4,6,7]=>8
[2,5,3,4,7,1,8,6]=>9
[2,4,8,3,5,7,6,1]=>12
[4,2,5,3,1,8,6,7]=>7
[4,2,1,8,5,3,6,7]=>5
[5,4,1,3,8,2,6,7]=>6
[5,1,4,8,3,2,6,7]=>8
[1,5,8,4,3,2,6,7]=>8
[1,8,5,4,3,2,6,7]=>6
[1,7,4,3,8,5,2,6]=>10
[1,5,7,3,8,4,2,6]=>11
[5,1,4,7,8,3,2,6]=>10
[4,8,1,5,7,3,6,2]=>16
[8,1,5,3,7,4,6,2]=>9
[3,8,4,7,6,5,2,1]=>14
[1,6,8,5,3,7,4,2]=>14
[6,8,1,7,4,3,5,2]=>18
[6,4,8,1,7,3,5,2]=>17
[6,4,8,7,1,5,2,3]=>14
[7,6,4,1,3,8,2,5]=>8
[1,7,5,6,3,2,8,4]=>12
[4,2,1,7,8,5,3,6]=>7
[2,7,4,6,3,1,8,5]=>12
[2,6,8,4,3,7,5,1]=>14
[6,2,4,8,3,7,5,1]=>13
[7,2,6,3,4,1,8,5]=>9
[2,6,7,3,1,4,8,5]=>10
[2,7,1,8,3,5,4,6]=>11
[2,1,7,3,5,8,4,6]=>7
[8,7,1,3,6,2,4,5]=>4
[8,2,1,7,3,5,6,4]=>6
[7,8,2,6,3,1,5,4]=>18
[8,7,2,6,3,5,4,1]=>8
[1,2,8,7,4,5,6,3]=>8
[8,3,7,1,5,6,2,4]=>11
[8,6,1,2,7,5,3,4]=>6
[8,1,6,2,7,4,5,3]=>9
[1,8,5,2,6,7,4,3]=>12
[5,2,1,8,6,7,4,3]=>10
[2,8,5,7,6,4,3,1]=>14
[1,7,8,5,2,6,4,3]=>14
[7,8,1,6,4,2,5,3]=>18
[7,8,6,1,5,3,2,4]=>15
[7,3,8,6,1,5,2,4]=>14
[8,7,6,1,5,3,4,2]=>5
[8,7,1,6,4,5,3,2]=>8
[8,1,7,5,6,4,3,2]=>11
[1,8,6,7,5,4,3,2]=>14
[9,1,2,3,4,5,6,7,8]=>0
[8,1,2,3,4,5,6,9,7]=>2
[2,9,1,3,4,5,6,7,8]=>8
[9,3,1,2,4,5,6,7,8]=>0
[8,9,1,2,3,4,5,6,7]=>14
[9,7,8,1,2,3,4,5,6]=>12
[2,3,4,5,6,7,9,1,8]=>8
[2,3,4,5,6,7,8,9,1]=>8
[2,3,4,5,6,7,8,1,9]=>7
[2,3,4,5,6,7,1,8,9]=>6
[1,2,3,4,5,6,7,9,8]=>1
[2,1,3,4,5,6,7,8,9]=>0
[1,8,2,3,4,5,6,9,7]=>7
[7,1,2,3,4,5,6,9,8]=>1
[2,1,9,3,4,5,6,7,8]=>6
[2,8,1,3,4,5,6,7,9]=>7
[1,2,3,4,5,6,7,8,9]=>0
[3,2,4,5,6,7,8,9,1]=>8
[9,8,7,6,5,4,3,2,1]=>0
[8,7,6,5,4,3,2,1,9]=>0
[1,9,8,7,6,5,4,3,2]=>7
[8,7,6,4,5,3,2,1,9]=>6
[1,9,8,7,5,6,4,3,2]=>13
[8,7,5,4,6,3,2,1,9]=>9
[8,7,4,6,5,3,2,1,9]=>7
[1,9,8,6,5,7,4,3,2]=>16
[1,9,8,5,7,6,4,3,2]=>14
[9,2,1,3,4,5,6,7,8]=>0
[9,2,3,1,4,5,6,7,8]=>2
[4,2,3,5,6,7,8,9,1]=>8
[3,4,2,5,6,7,8,9,1]=>10
[9,8,1,2,3,4,5,6,7]=>0
[7,8,9,1,2,3,4,5,6]=>18
[9,8,7,1,2,3,4,5,6]=>0
[6,7,8,9,1,2,3,4,5]=>20
[9,6,7,8,1,2,3,4,5]=>15
[8,9,6,7,1,2,3,4,5]=>24
[9,8,6,7,1,2,3,4,5]=>10
[9,8,7,6,1,2,3,4,5]=>0
[9,5,6,7,8,1,2,3,4]=>16
[8,9,5,6,7,1,2,3,4]=>26
[9,8,5,6,7,1,2,3,4]=>12
[9,7,8,5,6,1,2,3,4]=>20
[9,8,7,5,6,1,2,3,4]=>8
[9,8,7,6,5,1,2,3,4]=>0
[7,8,9,4,5,6,1,2,3]=>27
[9,7,8,4,5,6,1,2,3]=>21
[9,8,7,4,5,6,1,2,3]=>9
[8,9,6,7,4,5,1,2,3]=>30
[9,8,6,7,4,5,1,2,3]=>16
[9,8,7,6,4,5,1,2,3]=>6
[9,8,7,6,5,4,1,2,3]=>0
[9,7,8,5,6,3,4,1,2]=>24
[9,8,7,5,6,3,4,1,2]=>12
[9,8,7,6,5,3,4,1,2]=>4
[9,8,7,6,5,4,3,1,2]=>0
[7,8,6,5,4,3,2,1,9]=>12
[1,8,9,7,6,5,4,3,2]=>12
[7,6,8,5,4,3,2,1,9]=>15
[6,8,7,5,4,3,2,1,9]=>11
[1,8,7,9,6,5,4,3,2]=>16
[1,7,9,8,6,5,4,3,2]=>11
[8,1,2,3,4,5,6,7,9]=>0
[1,9,2,3,4,5,6,7,8]=>7
[7,8,1,2,3,4,5,6,9]=>12
[1,8,9,2,3,4,5,6,7]=>12
[7,1,8,2,3,4,5,6,9]=>10
[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
[7,1,2,3,4,5,6,8,9]=>0
[3,4,1,2,5,6,7,8,9]=>4
[3,2,1,4,5,6,7,8,9]=>0
[4,5,6,1,2,3,7,8,9]=>9
[4,2,5,1,3,6,7,8,9]=>5
[4,3,2,1,5,6,7,8,9]=>0
[5,6,7,8,1,2,3,4,9]=>16
[5,2,6,7,1,3,4,8,9]=>10
[5,6,3,4,1,2,7,8,9]=>12
[5,3,2,6,1,4,7,8,9]=>6
[5,4,3,2,1,6,7,8,9]=>0
[6,2,7,8,9,1,3,4,5]=>17
[6,7,3,4,8,1,2,5,9]=>17
[6,3,2,7,8,1,4,5,9]=>11
[6,4,7,2,5,1,3,8,9]=>14
[6,4,3,2,7,1,5,8,9]=>7
[6,5,4,3,2,1,7,8,9]=>0
[7,4,8,2,5,9,1,3,6]=>19
[7,4,3,2,8,9,1,5,6]=>12
[7,8,5,6,3,4,1,2,9]=>24
[7,5,3,8,2,6,1,4,9]=>16
[7,5,4,3,2,8,1,6,9]=>8
[7,6,5,4,3,2,1,8,9]=>0
[8,6,9,4,7,2,5,1,3]=>27
[8,6,4,3,9,2,7,1,5]=>18
[8,6,5,4,3,2,9,1,7]=>9
[2,1,4,3,6,5,8,7,10,9]=>4
[4,3,2,1,6,5,8,7,10,9]=>3
[6,3,2,5,4,1,8,7,10,9]=>6
[8,3,2,5,4,7,6,1,10,9]=>8
[10,3,2,5,4,7,6,9,8,1]=>10
[2,1,6,5,4,3,8,7,10,9]=>5
[6,5,4,3,2,1,8,7,10,9]=>2
[8,5,4,3,2,7,6,1,10,9]=>7
[10,5,4,3,2,7,6,9,8,1]=>9
[2,1,8,5,4,7,6,3,10,9]=>10
[8,7,4,3,6,5,2,1,10,9]=>8
[10,7,4,3,6,5,2,9,8,1]=>12
[2,1,10,5,4,7,6,9,8,3]=>14
[10,9,4,3,6,5,8,7,2,1]=>12
[8,9,5,6,3,4,10,1,2,7]=>29
[2,1,4,3,8,7,6,5,10,9]=>5
[4,3,2,1,8,7,6,5,10,9]=>4
[8,3,2,7,6,5,4,1,10,9]=>7
[10,3,2,7,6,5,4,9,8,1]=>11
[2,1,8,7,6,5,4,3,10,9]=>6
[8,7,6,5,4,3,2,1,10,9]=>1
[9,7,6,5,4,3,2,10,1,8]=>10
[10,7,6,5,4,3,2,9,8,1]=>8
[2,1,10,7,6,5,4,9,8,3]=>13
[10,9,6,5,4,3,8,7,2,1]=>11
[2,1,4,3,10,7,6,9,8,5]=>10
[4,3,2,1,10,7,6,9,8,5]=>9
[10,3,2,9,6,5,8,7,4,1]=>15
[2,1,10,9,6,5,8,7,4,3]=>14
[10,9,8,5,4,7,6,3,2,1]=>10
[6,7,8,9,10,1,2,3,4,5]=>25
[7,3,2,8,9,10,1,4,5,6]=>18
[8,5,4,3,2,9,10,1,6,7]=>13
[2,1,4,3,6,5,10,9,8,7]=>5
[4,3,2,1,6,5,10,9,8,7]=>4
[6,3,2,5,4,1,10,9,8,7]=>7
[10,3,2,5,4,9,8,7,6,1]=>9
[2,1,6,5,4,3,10,9,8,7]=>6
[6,5,4,3,2,1,10,9,8,7]=>3
[10,5,4,3,2,9,8,7,6,1]=>8
[2,1,10,5,4,9,8,7,6,3]=>13
[10,9,4,3,8,7,6,5,2,1]=>9
[9,7,5,10,3,8,2,6,1,4]=>30
[2,1,4,3,10,9,8,7,6,5]=>6
[4,3,2,1,10,9,8,7,6,5]=>5
[10,3,2,9,8,7,6,5,4,1]=>8
[2,1,10,9,8,7,6,5,4,3]=>7
[10,9,8,7,6,5,4,3,2,1]=>0
[2,3,4,5,6,7,8,9,10,1]=>9
[2,3,4,5,6,7,8,9,1,10]=>8
[10,8,9,5,6,7,1,2,3,4]=>26
[10,8,9,4,5,6,1,2,3,7]=>23
[10,7,8,5,6,9,1,2,3,4]=>24
[10,7,8,4,5,9,1,2,3,6]=>22
[10,6,7,4,5,8,1,2,3,9]=>19
[10,7,8,3,4,9,1,2,5,6]=>20
[10,6,7,3,4,8,1,2,5,9]=>17
[9,8,10,5,6,7,1,2,3,4]=>33
[9,8,10,4,5,6,1,2,3,7]=>30
[9,7,10,5,6,8,1,2,3,4]=>32
[9,7,10,4,5,8,1,2,3,6]=>30
[9,6,10,4,5,7,1,2,3,8]=>28
[9,7,10,3,4,8,1,2,5,6]=>28
[9,6,10,3,4,7,1,2,5,8]=>26
[8,7,9,5,6,10,1,2,3,4]=>30
[8,7,9,4,5,10,1,2,3,6]=>28
[8,6,9,4,5,10,1,2,3,7]=>27
[7,6,8,4,5,9,1,2,3,10]=>24
[8,7,9,3,4,10,1,2,5,6]=>26
[8,6,9,3,4,10,1,2,5,7]=>25
[7,6,8,3,4,9,1,2,5,10]=>22
[9,6,10,5,7,8,1,2,3,4]=>31
[9,6,10,4,7,8,1,2,3,5]=>30
[9,5,10,4,6,7,1,2,3,8]=>27
[9,6,10,3,7,8,1,2,4,5]=>29
[9,5,10,3,6,7,1,2,4,8]=>26
[8,6,9,5,7,10,1,2,3,4]=>29
[8,6,9,4,7,10,1,2,3,5]=>28
[8,5,9,4,6,10,1,2,3,7]=>26
[7,5,8,4,6,9,1,2,3,10]=>23
[8,6,9,3,7,10,1,2,4,5]=>27
[8,5,9,3,6,10,1,2,4,7]=>25
[7,5,8,3,6,9,1,2,4,10]=>22
[8,4,9,3,5,10,1,2,6,7]=>23
[7,4,8,3,5,9,1,2,6,10]=>20
[9,6,10,2,7,8,1,3,4,5]=>28
[9,5,10,2,6,7,1,3,4,8]=>25
[8,6,9,2,7,10,1,3,4,5]=>26
[8,5,9,2,6,10,1,3,4,7]=>24
[7,5,8,2,6,9,1,3,4,10]=>21
[8,4,9,2,5,10,1,3,6,7]=>22
[7,4,8,2,5,9,1,3,6,10]=>19
[1,2,3,4,5,6,7,8,10,9]=>1
[2,1,3,4,5,6,7,8,9,10]=>0
[9,1,2,3,4,5,6,7,10,8]=>2
[2,10,1,3,4,5,6,7,8,9]=>9
[1,2,3,4,5,6,7,8,9,10]=>0
[9,8,7,6,5,4,3,2,1,10]=>0
[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,1,2,3,4,5,6,7,8]=>0
[1,10,9,8,7,6,5,4,3,2]=>8
[9,8,7,5,6,4,3,2,1,10]=>8
[1,10,9,8,6,7,5,4,3,2]=>16
[10,2,1,3,4,5,6,7,8,9]=>0
[3,2,4,5,6,7,8,9,10,1]=>9
[2,4,6,8,10,1,3,5,7,9]=>15
[2,4,6,9,10,1,3,5,7,8]=>16
[2,4,7,8,10,1,3,5,6,9]=>16
[2,4,7,9,10,1,3,5,6,8]=>17
[2,4,8,9,10,1,3,5,6,7]=>18
[2,5,6,8,10,1,3,4,7,9]=>16
[2,5,6,9,10,1,3,4,7,8]=>17
[2,5,7,8,10,1,3,4,6,9]=>17
[2,5,7,9,10,1,3,4,6,8]=>18
[2,5,8,9,10,1,3,4,6,7]=>19
[2,6,7,8,10,1,3,4,5,9]=>18
[2,6,7,9,10,1,3,4,5,8]=>19
[2,6,8,9,10,1,3,4,5,7]=>20
[2,7,8,9,10,1,3,4,5,6]=>21
[3,4,6,8,10,1,2,5,7,9]=>16
[3,4,6,9,10,1,2,5,7,8]=>17
[3,4,7,8,10,1,2,5,6,9]=>17
[3,4,7,9,10,1,2,5,6,8]=>18
[3,4,8,9,10,1,2,5,6,7]=>19
[3,5,6,8,10,1,2,4,7,9]=>17
[3,5,6,9,10,1,2,4,7,8]=>18
[3,5,7,8,10,1,2,4,6,9]=>18
[3,5,7,9,10,1,2,4,6,8]=>19
[3,5,8,9,10,1,2,4,6,7]=>20
[3,6,7,8,10,1,2,4,5,9]=>19
[3,6,7,9,10,1,2,4,5,8]=>20
[3,6,8,9,10,1,2,4,5,7]=>21
[3,7,8,9,10,1,2,4,5,6]=>22
[4,5,6,8,10,1,2,3,7,9]=>18
[4,5,6,9,10,1,2,3,7,8]=>19
[4,5,7,8,10,1,2,3,6,9]=>19
[4,5,7,9,10,1,2,3,6,8]=>20
[4,5,8,9,10,1,2,3,6,7]=>21
[4,6,7,8,10,1,2,3,5,9]=>20
[4,6,7,9,10,1,2,3,5,8]=>21
[4,6,8,9,10,1,2,3,5,7]=>22
[4,7,8,9,10,1,2,3,5,6]=>23
[5,6,7,8,10,1,2,3,4,9]=>21
[5,6,7,9,10,1,2,3,4,8]=>22
[5,6,8,9,10,1,2,3,4,7]=>23
[5,7,8,9,10,1,2,3,4,6]=>24
[9,10,1,2,3,4,5,6,7,8]=>16
[8,9,10,1,2,3,4,5,6,7]=>21
[10,8,9,1,2,3,4,5,6,7]=>14
[10,9,8,1,2,3,4,5,6,7]=>0
[7,8,9,10,1,2,3,4,5,6]=>24
[10,7,8,9,1,2,3,4,5,6]=>18
[9,10,7,8,1,2,3,4,5,6]=>28
[10,9,7,8,1,2,3,4,5,6]=>12
[10,9,8,7,1,2,3,4,5,6]=>0
[10,6,7,8,9,1,2,3,4,5]=>20
[9,10,6,7,8,1,2,3,4,5]=>31
[10,9,6,7,8,1,2,3,4,5]=>15
[10,8,9,6,7,1,2,3,4,5]=>24
[10,9,8,6,7,1,2,3,4,5]=>10
[10,9,8,7,6,1,2,3,4,5]=>0
[9,10,5,6,7,8,1,2,3,4]=>32
[10,9,5,6,7,8,1,2,3,4]=>16
[8,9,10,5,6,7,1,2,3,4]=>33
[10,9,8,5,6,7,1,2,3,4]=>12
[9,10,7,8,5,6,1,2,3,4]=>36
[10,9,7,8,5,6,1,2,3,4]=>20
[10,9,8,7,5,6,1,2,3,4]=>8
[10,9,8,7,6,5,1,2,3,4]=>0
[10,7,8,9,4,5,6,1,2,3]=>27
[9,10,7,8,4,5,6,1,2,3]=>37
[10,9,7,8,4,5,6,1,2,3]=>21
[10,9,8,7,4,5,6,1,2,3]=>9
[10,8,9,6,7,4,5,1,2,3]=>30
[10,9,8,6,7,4,5,1,2,3]=>16
[10,9,8,7,6,4,5,1,2,3]=>6
[10,9,8,7,6,5,4,1,2,3]=>0
[9,10,7,8,5,6,3,4,1,2]=>40
[10,9,7,8,5,6,3,4,1,2]=>24
[10,9,8,7,5,6,3,4,1,2]=>12
[10,9,8,7,6,5,3,4,1,2]=>4
[10,9,8,7,6,5,4,3,1,2]=>0
[8,9,7,6,5,4,3,2,1,10]=>14
[1,9,10,8,7,6,5,4,3,2]=>14
[9,1,2,3,4,5,6,7,8,10]=>0
[1,10,2,3,4,5,6,7,8,9]=>8
[8,9,1,2,3,4,5,6,7,10]=>14
[1,9,10,2,3,4,5,6,7,8]=>14
[3,4,1,2,5,6,7,8,9,10]=>4
[3,2,1,4,5,6,7,8,9,10]=>0
[4,5,6,1,2,3,7,8,9,10]=>9
[4,2,5,1,3,6,7,8,9,10]=>5
[4,3,2,1,5,6,7,8,9,10]=>0
[5,6,7,8,1,2,3,4,9,10]=>16
[5,2,6,7,1,3,4,8,9,10]=>10
[5,6,3,4,1,2,7,8,9,10]=>12
[5,3,2,6,1,4,7,8,9,10]=>6
[5,4,3,2,1,6,7,8,9,10]=>0
[6,2,7,8,9,1,3,4,5,10]=>17
[6,7,3,4,8,1,2,5,9,10]=>17
[6,3,2,7,8,1,4,5,9,10]=>11
[6,4,7,2,5,1,3,8,9,10]=>14
[6,4,3,2,7,1,5,8,9,10]=>7
[6,5,4,3,2,1,7,8,9,10]=>0
[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]=>12
[7,8,5,6,3,4,1,2,9,10]=>24
[7,5,3,8,2,6,1,4,9,10]=>16
[7,5,4,3,2,8,1,6,9,10]=>8
[7,6,5,4,3,2,1,8,9,10]=>0
[8,5,9,10,2,6,7,1,3,4]=>29
[8,5,3,9,2,6,10,1,4,7]=>21
[8,6,9,4,7,2,5,1,3,10]=>27
[8,6,4,3,9,2,7,1,5,10]=>18
[8,6,5,4,3,2,9,1,7,10]=>9
[8,7,6,5,4,3,2,1,9,10]=>0
[9,7,5,4,3,10,2,8,1,6]=>20
[1,2,3,4,5,6,7,8,9,11,10]=>1
[2,1,3,4,5,6,7,8,9,10,11]=>0
[11,1,2,3,4,5,6,7,8,9,10]=>0
[10,9,8,7,6,5,4,3,2,1,11]=>0
[1,11,10,9,8,7,6,5,4,3,2]=>9
[2,3,4,5,6,7,8,9,10,11,1]=>10
[10,1,2,3,4,5,6,7,8,9,11]=>0
[1,11,2,3,4,5,6,7,8,9,10]=>9
[2,1,4,3,6,5,8,7,12,11,10,9]=>6
[2,1,4,3,6,5,12,9,8,11,10,7]=>11
[2,1,4,3,6,5,12,11,10,9,8,7]=>7
[2,1,4,3,8,7,6,5,12,11,10,9]=>7
[2,1,4,3,12,7,6,9,8,11,10,5]=>15
[2,1,4,3,12,7,6,11,10,9,8,5]=>14
[2,1,4,3,10,9,8,7,6,5,12,11]=>7
[2,1,4,3,12,9,8,7,6,11,10,5]=>14
[2,1,4,3,12,11,8,7,10,9,6,5]=>15
[2,1,4,3,12,11,10,9,8,7,6,5]=>8
[2,1,6,5,4,3,8,7,12,11,10,9]=>7
[2,1,6,5,4,3,10,9,8,7,12,11]=>7
[2,1,6,5,4,3,12,9,8,11,10,7]=>12
[2,1,6,5,4,3,12,11,10,9,8,7]=>8
[2,1,8,5,4,7,6,3,12,11,10,9]=>12
[2,1,12,5,4,7,6,9,8,11,10,3]=>19
[2,1,12,5,4,7,6,11,10,9,8,3]=>18
[2,1,10,5,4,9,8,7,6,3,12,11]=>14
[2,1,12,5,4,9,8,7,6,11,10,3]=>20
[2,1,12,5,4,11,8,7,10,9,6,3]=>24
[2,1,12,5,4,11,10,9,8,7,6,3]=>17
[2,1,8,7,6,5,4,3,10,9,12,11]=>7
[2,1,8,7,6,5,4,3,12,11,10,9]=>8
[2,1,12,7,6,5,4,9,8,11,10,3]=>18
[2,1,12,7,6,5,4,11,10,9,8,3]=>17
[2,1,10,9,6,5,8,7,4,3,12,11]=>15
[2,1,12,9,6,5,8,7,4,11,10,3]=>21
[2,1,12,11,6,5,8,7,10,9,4,3]=>21
[2,1,12,11,6,5,10,9,8,7,4,3]=>18
[2,1,10,9,8,7,6,5,4,3,12,11]=>8
[2,1,12,9,8,7,6,5,4,11,10,3]=>17
[2,1,12,11,8,7,6,5,10,9,4,3]=>20
[2,1,12,11,10,7,6,9,8,5,4,3]=>19
[2,1,12,11,10,9,8,7,6,5,4,3]=>9
[4,3,2,1,6,5,8,7,10,9,12,11]=>4
[4,3,2,1,6,5,8,7,12,11,10,9]=>5
[4,3,2,1,6,5,10,9,8,7,12,11]=>5
[4,3,2,1,6,5,12,9,8,11,10,7]=>10
[4,3,2,1,6,5,12,11,10,9,8,7]=>6
[4,3,2,1,8,7,6,5,10,9,12,11]=>5
[4,3,2,1,8,7,6,5,12,11,10,9]=>6
[4,3,2,1,10,7,6,9,8,5,12,11]=>10
[4,3,2,1,12,7,6,9,8,11,10,5]=>14
[4,3,2,1,12,7,6,11,10,9,8,5]=>13
[4,3,2,1,10,9,8,7,6,5,12,11]=>6
[4,3,2,1,12,9,8,7,6,11,10,5]=>13
[4,3,2,1,12,11,8,7,10,9,6,5]=>14
[4,3,2,1,12,11,10,9,8,7,6,5]=>7
[6,3,2,5,4,1,8,7,10,9,12,11]=>7
[6,3,2,5,4,1,8,7,12,11,10,9]=>8
[6,3,2,5,4,1,10,9,8,7,12,11]=>8
[6,3,2,5,4,1,12,9,8,11,10,7]=>13
[6,3,2,5,4,1,12,11,10,9,8,7]=>9
[8,3,2,5,4,7,6,1,10,9,12,11]=>9
[8,3,2,5,4,7,6,1,12,11,10,9]=>10
[10,3,2,5,4,7,6,9,8,1,12,11]=>11
[12,3,2,5,4,7,6,9,8,11,10,1]=>13
[12,3,2,5,4,7,6,11,10,9,8,1]=>12
[10,3,2,5,4,9,8,7,6,1,12,11]=>10
[12,3,2,5,4,9,8,7,6,11,10,1]=>14
[12,3,2,5,4,11,8,7,10,9,6,1]=>18
[12,3,2,5,4,11,10,9,8,7,6,1]=>11
[8,3,2,7,6,5,4,1,10,9,12,11]=>8
[8,3,2,7,6,5,4,1,12,11,10,9]=>9
[10,3,2,7,6,5,4,9,8,1,12,11]=>12
[12,3,2,7,6,5,4,9,8,11,10,1]=>14
[12,3,2,7,6,5,4,11,10,9,8,1]=>13
[10,3,2,9,6,5,8,7,4,1,12,11]=>16
[12,3,2,9,6,5,8,7,4,11,10,1]=>19
[12,3,2,11,6,5,8,7,10,9,4,1]=>22
[12,3,2,11,6,5,10,9,8,7,4,1]=>19
[10,3,2,9,8,7,6,5,4,1,12,11]=>9
[12,3,2,9,8,7,6,5,4,11,10,1]=>15
[12,3,2,11,8,7,6,5,10,9,4,1]=>21
[6,5,4,3,2,1,8,7,10,9,12,11]=>3
[6,5,4,3,2,1,8,7,12,11,10,9]=>4
[6,5,4,3,2,1,10,9,8,7,12,11]=>4
[6,5,4,3,2,1,12,9,8,11,10,7]=>9
[6,5,4,3,2,1,12,11,10,9,8,7]=>5
[8,5,4,3,2,7,6,1,12,11,10,9]=>9
[10,5,4,3,2,7,6,9,8,1,12,11]=>10
[12,5,4,3,2,7,6,9,8,11,10,1]=>12
[12,5,4,3,2,7,6,11,10,9,8,1]=>11
[10,5,4,3,2,9,8,7,6,1,12,11]=>9
[12,5,4,3,2,9,8,7,6,11,10,1]=>13
[12,5,4,3,2,11,8,7,10,9,6,1]=>17
[8,7,4,3,6,5,2,1,10,9,12,11]=>9
[8,7,4,3,6,5,2,1,12,11,10,9]=>10
[10,7,4,3,6,5,2,9,8,1,12,11]=>13
[12,7,4,3,6,5,2,9,8,11,10,1]=>15
[12,7,4,3,6,5,2,11,10,9,8,1]=>14
[10,9,4,3,6,5,8,7,2,1,12,11]=>13
[12,9,4,3,6,5,8,7,2,11,10,1]=>17
[12,11,4,3,6,5,8,7,10,9,2,1]=>17
[10,9,4,3,8,7,6,5,2,1,12,11]=>10
[12,9,4,3,8,7,6,5,2,11,10,1]=>16
[8,7,6,5,4,3,2,1,10,9,12,11]=>2
[8,7,6,5,4,3,2,1,12,11,10,9]=>3
[10,7,6,5,4,3,2,9,8,1,12,11]=>9
[12,7,6,5,4,3,2,9,8,11,10,1]=>11
[10,9,6,5,4,3,8,7,2,1,12,11]=>12
[12,9,6,5,4,3,8,7,2,11,10,1]=>16
[12,11,6,5,4,3,8,7,10,9,2,1]=>16
[10,9,8,5,4,7,6,3,2,1,12,11]=>11
[10,9,8,7,6,5,4,3,2,1,12,11]=>1
[2,4,6,8,10,12,1,3,5,7,9,11]=>21
[2,4,6,8,11,12,1,3,5,7,9,10]=>22
[2,4,6,9,10,12,1,3,5,7,8,11]=>22
[2,4,6,9,11,12,1,3,5,7,8,10]=>23
[2,4,6,10,11,12,1,3,5,7,8,9]=>24
[2,4,7,8,10,12,1,3,5,6,9,11]=>22
[2,4,7,8,11,12,1,3,5,6,9,10]=>23
[2,4,7,9,10,12,1,3,5,6,8,11]=>23
[2,4,7,9,11,12,1,3,5,6,8,10]=>24
[2,4,7,10,11,12,1,3,5,6,8,9]=>25
[2,4,8,9,10,12,1,3,5,6,7,11]=>24
[2,4,8,9,11,12,1,3,5,6,7,10]=>25
[2,4,8,10,11,12,1,3,5,6,7,9]=>26
[2,4,9,10,11,12,1,3,5,6,7,8]=>27
[2,5,6,8,10,12,1,3,4,7,9,11]=>22
[2,5,6,8,11,12,1,3,4,7,9,10]=>23
[2,5,6,9,10,12,1,3,4,7,8,11]=>23
[2,5,6,9,11,12,1,3,4,7,8,10]=>24
[2,5,6,10,11,12,1,3,4,7,8,9]=>25
[2,5,7,8,10,12,1,3,4,6,9,11]=>23
[2,5,7,8,11,12,1,3,4,6,9,10]=>24
[2,5,7,9,11,12,1,3,4,6,8,10]=>25
[2,5,7,10,11,12,1,3,4,6,8,9]=>26
[2,5,8,9,10,12,1,3,4,6,7,11]=>25
[2,5,8,9,11,12,1,3,4,6,7,10]=>26
[2,5,8,10,11,12,1,3,4,6,7,9]=>27
[2,5,9,10,11,12,1,3,4,6,7,8]=>28
[2,6,7,8,10,12,1,3,4,5,9,11]=>24
[2,6,7,8,11,12,1,3,4,5,9,10]=>25
[2,6,7,9,10,12,1,3,4,5,8,11]=>25
[2,6,7,9,11,12,1,3,4,5,8,10]=>26
[2,6,7,10,11,12,1,3,4,5,8,9]=>27
[2,6,8,9,10,12,1,3,4,5,7,11]=>26
[2,6,8,9,11,12,1,3,4,5,7,10]=>27
[2,6,8,10,11,12,1,3,4,5,7,9]=>28
[2,6,9,10,11,12,1,3,4,5,7,8]=>29
[2,7,8,9,10,12,1,3,4,5,6,11]=>27
[2,7,8,9,11,12,1,3,4,5,6,10]=>28
[2,7,8,10,11,12,1,3,4,5,6,9]=>29
[2,7,9,10,11,12,1,3,4,5,6,8]=>30
[2,8,9,10,11,12,1,3,4,5,6,7]=>31
[3,4,6,8,10,12,1,2,5,7,9,11]=>22
[3,4,6,8,11,12,1,2,5,7,9,10]=>23
[3,4,6,9,10,12,1,2,5,7,8,11]=>23
[3,4,6,9,11,12,1,2,5,7,8,10]=>24
[3,4,6,10,11,12,1,2,5,7,8,9]=>25
[3,4,7,8,10,12,1,2,5,6,9,11]=>23
[3,4,7,8,11,12,1,2,5,6,9,10]=>24
[3,4,7,9,10,12,1,2,5,6,8,11]=>24
[3,4,7,9,11,12,1,2,5,6,8,10]=>25
[3,4,7,10,11,12,1,2,5,6,8,9]=>26
[3,4,8,9,10,12,1,2,5,6,7,11]=>25
[3,4,8,9,11,12,1,2,5,6,7,10]=>26
[3,4,8,10,11,12,1,2,5,6,7,9]=>27
[3,4,9,10,11,12,1,2,5,6,7,8]=>28
[3,5,6,8,10,12,1,2,4,7,9,11]=>23
[3,5,6,8,11,12,1,2,4,7,9,10]=>24
[3,5,6,9,10,12,1,2,4,7,8,11]=>24
[3,5,6,9,11,12,1,2,4,7,8,10]=>25
[3,5,6,10,11,12,1,2,4,7,8,9]=>26
[3,5,7,8,10,12,1,2,4,6,9,11]=>24
[3,5,7,8,11,12,1,2,4,6,9,10]=>25
[3,5,7,9,10,12,1,2,4,6,8,11]=>25
[3,5,7,9,11,12,1,2,4,6,8,10]=>26
[3,5,7,10,11,12,1,2,4,6,8,9]=>27
[3,5,8,9,10,12,1,2,4,6,7,11]=>26
[3,5,8,9,11,12,1,2,4,6,7,10]=>27
[3,5,8,10,11,12,1,2,4,6,7,9]=>28
[3,5,9,10,11,12,1,2,4,6,7,8]=>29
[3,6,7,8,10,12,1,2,4,5,9,11]=>25
[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
[3,6,7,9,11,12,1,2,4,5,8,10]=>27
[3,6,7,10,11,12,1,2,4,5,8,9]=>28
[3,6,8,9,10,12,1,2,4,5,7,11]=>27
[3,6,8,9,11,12,1,2,4,5,7,10]=>28
[3,6,8,10,11,12,1,2,4,5,7,9]=>29
[3,6,9,10,11,12,1,2,4,5,7,8]=>30
[3,7,8,9,10,12,1,2,4,5,6,11]=>28
[3,7,8,9,11,12,1,2,4,5,6,10]=>29
[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
[3,8,9,10,11,12,1,2,4,5,6,7]=>32
[4,5,6,8,10,12,1,2,3,7,9,11]=>24
[4,5,6,8,11,12,1,2,3,7,9,10]=>25
[4,5,6,9,10,12,1,2,3,7,8,11]=>25
[4,5,6,9,11,12,1,2,3,7,8,10]=>26
[4,5,6,10,11,12,1,2,3,7,8,9]=>27
[4,5,7,8,10,12,1,2,3,6,9,11]=>25
[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
[4,5,7,9,11,12,1,2,3,6,8,10]=>27
[4,5,7,10,11,12,1,2,3,6,8,9]=>28
[4,5,8,9,10,12,1,2,3,6,7,11]=>27
[4,5,8,9,11,12,1,2,3,6,7,10]=>28
[4,5,8,10,11,12,1,2,3,6,7,9]=>29
[4,5,9,10,11,12,1,2,3,6,7,8]=>30
[4,6,7,8,10,12,1,2,3,5,9,11]=>26
[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
[4,6,7,9,11,12,1,2,3,5,8,10]=>28
[4,6,7,10,11,12,1,2,3,5,8,9]=>29
[4,6,8,9,10,12,1,2,3,5,7,11]=>28
[4,6,8,9,11,12,1,2,3,5,7,10]=>29
[4,6,8,10,11,12,1,2,3,5,7,9]=>30
[4,6,9,10,11,12,1,2,3,5,7,8]=>31
[4,7,8,9,10,12,1,2,3,5,6,11]=>29
[4,7,8,9,11,12,1,2,3,5,6,10]=>30
[4,7,8,10,11,12,1,2,3,5,6,9]=>31
[4,7,9,10,11,12,1,2,3,5,6,8]=>32
[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]=>27
[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
[5,6,7,9,11,12,1,2,3,4,8,10]=>29
[5,6,7,10,11,12,1,2,3,4,8,9]=>30
[5,6,8,9,10,12,1,2,3,4,7,11]=>29
[5,6,8,9,11,12,1,2,3,4,7,10]=>30
[5,6,8,10,11,12,1,2,3,4,7,9]=>31
[5,6,9,10,11,12,1,2,3,4,7,8]=>32
[5,7,8,9,10,12,1,2,3,4,6,11]=>30
[5,7,8,9,11,12,1,2,3,4,6,10]=>31
[5,7,8,10,11,12,1,2,3,4,6,9]=>32
[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]=>34
[6,7,8,9,10,12,1,2,3,4,5,11]=>31
[6,7,8,9,11,12,1,2,3,4,5,10]=>32
[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]=>34
[6,8,9,10,11,12,1,2,3,4,5,7]=>35
[7,8,9,10,11,12,1,2,3,4,5,6]=>36
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Description
The number of admissible inversions of a permutation.
Let $w = w_1,w_2,\dots,w_k$ be a word of length $k$ with distinct letters from $[n]$.
An admissible inversion of $w$ is a pair $(w_i,w_j)$ such that $1\leq i < j\leq k$ and $w_i > w_j$ that satisfies either of the following conditions:
$1 < i$ and $w_{i−1} < w_i$ or there is some $l$ such that $i < l < j$ and $w_i < w_l$.
Let $w = w_1,w_2,\dots,w_k$ be a word of length $k$ with distinct letters from $[n]$.
An admissible inversion of $w$ is a pair $(w_i,w_j)$ such that $1\leq i < j\leq k$ and $w_i > w_j$ that satisfies either of the following conditions:
$1 < i$ and $w_{i−1} < w_i$ or there is some $l$ such that $i < l < j$ and $w_i < w_l$.
References
[1] Lin, Z., Zeng, J. The γ-positivity of basic Eulerian polynomials via group actions arXiv:1411.3397
Code
def statistic(w):
return len(admissible_inversions(w))
def admissible_inversions(w):
"""
sage: len(admissible_inversions([2,9,1,7,5,3,4,6,8]))
12
"""
return [(i,j) for (i,j) in Permutation(w).inversions()
if admissible_inversion(w, i, j)]
def admissible_inversion(w, i, j):
return (w[i-1] > w[j-1] and
((1 < i and w[i-2] < w[i-1]) or
any(w[i-1] < w[l-1] for l in range(i+1, j))))
Created
Apr 07, 2016 at 12:05 by Martin Rubey
Updated
Jan 12, 2018 at 22:07 by Martin Rubey
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