Identifier
- St000830: Permutations ⟶ ℤ
Values
=>
[1,2]=>0
[2,1]=>2
[1,2,3]=>0
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>4
[3,1,2]=>4
[3,2,1]=>4
[1,2,3,4]=>0
[1,2,4,3]=>2
[1,3,2,4]=>2
[1,3,4,2]=>4
[1,4,2,3]=>4
[1,4,3,2]=>4
[2,1,3,4]=>2
[2,1,4,3]=>4
[2,3,1,4]=>4
[2,3,4,1]=>6
[2,4,1,3]=>6
[2,4,3,1]=>6
[3,1,2,4]=>4
[3,1,4,2]=>6
[3,2,1,4]=>4
[3,2,4,1]=>6
[3,4,1,2]=>8
[3,4,2,1]=>8
[4,1,2,3]=>6
[4,1,3,2]=>6
[4,2,1,3]=>6
[4,2,3,1]=>6
[4,3,1,2]=>8
[4,3,2,1]=>8
[1,2,3,4,5]=>0
[1,2,3,5,4]=>2
[1,2,4,3,5]=>2
[1,2,4,5,3]=>4
[1,2,5,3,4]=>4
[1,2,5,4,3]=>4
[1,3,2,4,5]=>2
[1,3,2,5,4]=>4
[1,3,4,2,5]=>4
[1,3,4,5,2]=>6
[1,3,5,2,4]=>6
[1,3,5,4,2]=>6
[1,4,2,3,5]=>4
[1,4,2,5,3]=>6
[1,4,3,2,5]=>4
[1,4,3,5,2]=>6
[1,4,5,2,3]=>8
[1,4,5,3,2]=>8
[1,5,2,3,4]=>6
[1,5,2,4,3]=>6
[1,5,3,2,4]=>6
[1,5,3,4,2]=>6
[1,5,4,2,3]=>8
[1,5,4,3,2]=>8
[2,1,3,4,5]=>2
[2,1,3,5,4]=>4
[2,1,4,3,5]=>4
[2,1,4,5,3]=>6
[2,1,5,3,4]=>6
[2,1,5,4,3]=>6
[2,3,1,4,5]=>4
[2,3,1,5,4]=>6
[2,3,4,1,5]=>6
[2,3,4,5,1]=>8
[2,3,5,1,4]=>8
[2,3,5,4,1]=>8
[2,4,1,3,5]=>6
[2,4,1,5,3]=>8
[2,4,3,1,5]=>6
[2,4,3,5,1]=>8
[2,4,5,1,3]=>10
[2,4,5,3,1]=>10
[2,5,1,3,4]=>8
[2,5,1,4,3]=>8
[2,5,3,1,4]=>8
[2,5,3,4,1]=>8
[2,5,4,1,3]=>10
[2,5,4,3,1]=>10
[3,1,2,4,5]=>4
[3,1,2,5,4]=>6
[3,1,4,2,5]=>6
[3,1,4,5,2]=>8
[3,1,5,2,4]=>8
[3,1,5,4,2]=>8
[3,2,1,4,5]=>4
[3,2,1,5,4]=>6
[3,2,4,1,5]=>6
[3,2,4,5,1]=>8
[3,2,5,1,4]=>8
[3,2,5,4,1]=>8
[3,4,1,2,5]=>8
[3,4,1,5,2]=>10
[3,4,2,1,5]=>8
[3,4,2,5,1]=>10
[3,4,5,1,2]=>12
[3,4,5,2,1]=>12
[3,5,1,2,4]=>10
[3,5,1,4,2]=>10
[3,5,2,1,4]=>10
[3,5,2,4,1]=>10
[3,5,4,1,2]=>12
[3,5,4,2,1]=>12
[4,1,2,3,5]=>6
[4,1,2,5,3]=>8
[4,1,3,2,5]=>6
[4,1,3,5,2]=>8
[4,1,5,2,3]=>10
[4,1,5,3,2]=>10
[4,2,1,3,5]=>6
[4,2,1,5,3]=>8
[4,2,3,1,5]=>6
[4,2,3,5,1]=>8
[4,2,5,1,3]=>10
[4,2,5,3,1]=>10
[4,3,1,2,5]=>8
[4,3,1,5,2]=>10
[4,3,2,1,5]=>8
[4,3,2,5,1]=>10
[4,3,5,1,2]=>12
[4,3,5,2,1]=>12
[4,5,1,2,3]=>12
[4,5,1,3,2]=>12
[4,5,2,1,3]=>12
[4,5,2,3,1]=>12
[4,5,3,1,2]=>12
[4,5,3,2,1]=>12
[5,1,2,3,4]=>8
[5,1,2,4,3]=>8
[5,1,3,2,4]=>8
[5,1,3,4,2]=>8
[5,1,4,2,3]=>10
[5,1,4,3,2]=>10
[5,2,1,3,4]=>8
[5,2,1,4,3]=>8
[5,2,3,1,4]=>8
[5,2,3,4,1]=>8
[5,2,4,1,3]=>10
[5,2,4,3,1]=>10
[5,3,1,2,4]=>10
[5,3,1,4,2]=>10
[5,3,2,1,4]=>10
[5,3,2,4,1]=>10
[5,3,4,1,2]=>12
[5,3,4,2,1]=>12
[5,4,1,2,3]=>12
[5,4,1,3,2]=>12
[5,4,2,1,3]=>12
[5,4,2,3,1]=>12
[5,4,3,1,2]=>12
[5,4,3,2,1]=>12
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>2
[1,2,3,5,4,6]=>2
[1,2,3,5,6,4]=>4
[1,2,3,6,4,5]=>4
[1,2,3,6,5,4]=>4
[1,2,4,3,5,6]=>2
[1,2,4,3,6,5]=>4
[1,2,4,5,3,6]=>4
[1,2,4,5,6,3]=>6
[1,2,4,6,3,5]=>6
[1,2,4,6,5,3]=>6
[1,2,5,3,4,6]=>4
[1,2,5,3,6,4]=>6
[1,2,5,4,3,6]=>4
[1,2,5,4,6,3]=>6
[1,2,5,6,3,4]=>8
[1,2,5,6,4,3]=>8
[1,2,6,3,4,5]=>6
[1,2,6,3,5,4]=>6
[1,2,6,4,3,5]=>6
[1,2,6,4,5,3]=>6
[1,2,6,5,3,4]=>8
[1,2,6,5,4,3]=>8
[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>4
[1,3,2,5,4,6]=>4
[1,3,2,5,6,4]=>6
[1,3,2,6,4,5]=>6
[1,3,2,6,5,4]=>6
[1,3,4,2,5,6]=>4
[1,3,4,2,6,5]=>6
[1,3,4,5,2,6]=>6
[1,3,4,5,6,2]=>8
[1,3,4,6,2,5]=>8
[1,3,4,6,5,2]=>8
[1,3,5,2,4,6]=>6
[1,3,5,2,6,4]=>8
[1,3,5,4,2,6]=>6
[1,3,5,4,6,2]=>8
[1,3,5,6,2,4]=>10
[1,3,5,6,4,2]=>10
[1,3,6,2,4,5]=>8
[1,3,6,2,5,4]=>8
[1,3,6,4,2,5]=>8
[1,3,6,4,5,2]=>8
[1,3,6,5,2,4]=>10
[1,3,6,5,4,2]=>10
[1,4,2,3,5,6]=>4
[1,4,2,3,6,5]=>6
[1,4,2,5,3,6]=>6
[1,4,2,5,6,3]=>8
[1,4,2,6,3,5]=>8
[1,4,2,6,5,3]=>8
[1,4,3,2,5,6]=>4
[1,4,3,2,6,5]=>6
[1,4,3,5,2,6]=>6
[1,4,3,5,6,2]=>8
[1,4,3,6,2,5]=>8
[1,4,3,6,5,2]=>8
[1,4,5,2,3,6]=>8
[1,4,5,2,6,3]=>10
[1,4,5,3,2,6]=>8
[1,4,5,3,6,2]=>10
[1,4,5,6,2,3]=>12
[1,4,5,6,3,2]=>12
[1,4,6,2,3,5]=>10
[1,4,6,2,5,3]=>10
[1,4,6,3,2,5]=>10
[1,4,6,3,5,2]=>10
[1,4,6,5,2,3]=>12
[1,4,6,5,3,2]=>12
[1,5,2,3,4,6]=>6
[1,5,2,3,6,4]=>8
[1,5,2,4,3,6]=>6
[1,5,2,4,6,3]=>8
[1,5,2,6,3,4]=>10
[1,5,2,6,4,3]=>10
[1,5,3,2,4,6]=>6
[1,5,3,2,6,4]=>8
[1,5,3,4,2,6]=>6
[1,5,3,4,6,2]=>8
[1,5,3,6,2,4]=>10
[1,5,3,6,4,2]=>10
[1,5,4,2,3,6]=>8
[1,5,4,2,6,3]=>10
[1,5,4,3,2,6]=>8
[1,5,4,3,6,2]=>10
[1,5,4,6,2,3]=>12
[1,5,4,6,3,2]=>12
[1,5,6,2,3,4]=>12
[1,5,6,2,4,3]=>12
[1,5,6,3,2,4]=>12
[1,5,6,3,4,2]=>12
[1,5,6,4,2,3]=>12
[1,5,6,4,3,2]=>12
[1,6,2,3,4,5]=>8
[1,6,2,3,5,4]=>8
[1,6,2,4,3,5]=>8
[1,6,2,4,5,3]=>8
[1,6,2,5,3,4]=>10
[1,6,2,5,4,3]=>10
[1,6,3,2,4,5]=>8
[1,6,3,2,5,4]=>8
[1,6,3,4,2,5]=>8
[1,6,3,4,5,2]=>8
[1,6,3,5,2,4]=>10
[1,6,3,5,4,2]=>10
[1,6,4,2,3,5]=>10
[1,6,4,2,5,3]=>10
[1,6,4,3,2,5]=>10
[1,6,4,3,5,2]=>10
[1,6,4,5,2,3]=>12
[1,6,4,5,3,2]=>12
[1,6,5,2,3,4]=>12
[1,6,5,2,4,3]=>12
[1,6,5,3,2,4]=>12
[1,6,5,3,4,2]=>12
[1,6,5,4,2,3]=>12
[1,6,5,4,3,2]=>12
[2,1,3,4,5,6]=>2
[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>4
[2,1,3,5,6,4]=>6
[2,1,3,6,4,5]=>6
[2,1,3,6,5,4]=>6
[2,1,4,3,5,6]=>4
[2,1,4,3,6,5]=>6
[2,1,4,5,3,6]=>6
[2,1,4,5,6,3]=>8
[2,1,4,6,3,5]=>8
[2,1,4,6,5,3]=>8
[2,1,5,3,4,6]=>6
[2,1,5,3,6,4]=>8
[2,1,5,4,3,6]=>6
[2,1,5,4,6,3]=>8
[2,1,5,6,3,4]=>10
[2,1,5,6,4,3]=>10
[2,1,6,3,4,5]=>8
[2,1,6,3,5,4]=>8
[2,1,6,4,3,5]=>8
[2,1,6,4,5,3]=>8
[2,1,6,5,3,4]=>10
[2,1,6,5,4,3]=>10
[2,3,1,4,5,6]=>4
[2,3,1,4,6,5]=>6
[2,3,1,5,4,6]=>6
[2,3,1,5,6,4]=>8
[2,3,1,6,4,5]=>8
[2,3,1,6,5,4]=>8
[2,3,4,1,5,6]=>6
[2,3,4,1,6,5]=>8
[2,3,4,5,1,6]=>8
[2,3,4,5,6,1]=>10
[2,3,4,6,1,5]=>10
[2,3,4,6,5,1]=>10
[2,3,5,1,4,6]=>8
[2,3,5,1,6,4]=>10
[2,3,5,4,1,6]=>8
[2,3,5,4,6,1]=>10
[2,3,5,6,1,4]=>12
[2,3,5,6,4,1]=>12
[2,3,6,1,4,5]=>10
[2,3,6,1,5,4]=>10
[2,3,6,4,1,5]=>10
[2,3,6,4,5,1]=>10
[2,3,6,5,1,4]=>12
[2,3,6,5,4,1]=>12
[2,4,1,3,5,6]=>6
[2,4,1,3,6,5]=>8
[2,4,1,5,3,6]=>8
[2,4,1,5,6,3]=>10
[2,4,1,6,3,5]=>10
[2,4,1,6,5,3]=>10
[2,4,3,1,5,6]=>6
[2,4,3,1,6,5]=>8
[2,4,3,5,1,6]=>8
[2,4,3,5,6,1]=>10
[2,4,3,6,1,5]=>10
[2,4,3,6,5,1]=>10
[2,4,5,1,3,6]=>10
[2,4,5,1,6,3]=>12
[2,4,5,3,1,6]=>10
[2,4,5,3,6,1]=>12
[2,4,5,6,1,3]=>14
[2,4,5,6,3,1]=>14
[2,4,6,1,3,5]=>12
[2,4,6,1,5,3]=>12
[2,4,6,3,1,5]=>12
[2,4,6,3,5,1]=>12
[2,4,6,5,1,3]=>14
[2,4,6,5,3,1]=>14
[2,5,1,3,4,6]=>8
[2,5,1,3,6,4]=>10
[2,5,1,4,3,6]=>8
[2,5,1,4,6,3]=>10
[2,5,1,6,3,4]=>12
[2,5,1,6,4,3]=>12
[2,5,3,1,4,6]=>8
[2,5,3,1,6,4]=>10
[2,5,3,4,1,6]=>8
[2,5,3,4,6,1]=>10
[2,5,3,6,1,4]=>12
[2,5,3,6,4,1]=>12
[2,5,4,1,3,6]=>10
[2,5,4,1,6,3]=>12
[2,5,4,3,1,6]=>10
[2,5,4,3,6,1]=>12
[2,5,4,6,1,3]=>14
[2,5,4,6,3,1]=>14
[2,5,6,1,3,4]=>14
[2,5,6,1,4,3]=>14
[2,5,6,3,1,4]=>14
[2,5,6,3,4,1]=>14
[2,5,6,4,1,3]=>14
[2,5,6,4,3,1]=>14
[2,6,1,3,4,5]=>10
[2,6,1,3,5,4]=>10
[2,6,1,4,3,5]=>10
[2,6,1,4,5,3]=>10
[2,6,1,5,3,4]=>12
[2,6,1,5,4,3]=>12
[2,6,3,1,4,5]=>10
[2,6,3,1,5,4]=>10
[2,6,3,4,1,5]=>10
[2,6,3,4,5,1]=>10
[2,6,3,5,1,4]=>12
[2,6,3,5,4,1]=>12
[2,6,4,1,3,5]=>12
[2,6,4,1,5,3]=>12
[2,6,4,3,1,5]=>12
[2,6,4,3,5,1]=>12
[2,6,4,5,1,3]=>14
[2,6,4,5,3,1]=>14
[2,6,5,1,3,4]=>14
[2,6,5,1,4,3]=>14
[2,6,5,3,1,4]=>14
[2,6,5,3,4,1]=>14
[2,6,5,4,1,3]=>14
[2,6,5,4,3,1]=>14
[3,1,2,4,5,6]=>4
[3,1,2,4,6,5]=>6
[3,1,2,5,4,6]=>6
[3,1,2,5,6,4]=>8
[3,1,2,6,4,5]=>8
[3,1,2,6,5,4]=>8
[3,1,4,2,5,6]=>6
[3,1,4,2,6,5]=>8
[3,1,4,5,2,6]=>8
[3,1,4,5,6,2]=>10
[3,1,4,6,2,5]=>10
[3,1,4,6,5,2]=>10
[3,1,5,2,4,6]=>8
[3,1,5,2,6,4]=>10
[3,1,5,4,2,6]=>8
[3,1,5,4,6,2]=>10
[3,1,5,6,2,4]=>12
[3,1,5,6,4,2]=>12
[3,1,6,2,4,5]=>10
[3,1,6,2,5,4]=>10
[3,1,6,4,2,5]=>10
[3,1,6,4,5,2]=>10
[3,1,6,5,2,4]=>12
[3,1,6,5,4,2]=>12
[3,2,1,4,5,6]=>4
[3,2,1,4,6,5]=>6
[3,2,1,5,4,6]=>6
[3,2,1,5,6,4]=>8
[3,2,1,6,4,5]=>8
[3,2,1,6,5,4]=>8
[3,2,4,1,5,6]=>6
[3,2,4,1,6,5]=>8
[3,2,4,5,1,6]=>8
[3,2,4,5,6,1]=>10
[3,2,4,6,1,5]=>10
[3,2,4,6,5,1]=>10
[3,2,5,1,4,6]=>8
[3,2,5,1,6,4]=>10
[3,2,5,4,1,6]=>8
[3,2,5,4,6,1]=>10
[3,2,5,6,1,4]=>12
[3,2,5,6,4,1]=>12
[3,2,6,1,4,5]=>10
[3,2,6,1,5,4]=>10
[3,2,6,4,1,5]=>10
[3,2,6,4,5,1]=>10
[3,2,6,5,1,4]=>12
[3,2,6,5,4,1]=>12
[3,4,1,2,5,6]=>8
[3,4,1,2,6,5]=>10
[3,4,1,5,2,6]=>10
[3,4,1,5,6,2]=>12
[3,4,1,6,2,5]=>12
[3,4,1,6,5,2]=>12
[3,4,2,1,5,6]=>8
[3,4,2,1,6,5]=>10
[3,4,2,5,1,6]=>10
[3,4,2,5,6,1]=>12
[3,4,2,6,1,5]=>12
[3,4,2,6,5,1]=>12
[3,4,5,1,2,6]=>12
[3,4,5,1,6,2]=>14
[3,4,5,2,1,6]=>12
[3,4,5,2,6,1]=>14
[3,4,5,6,1,2]=>16
[3,4,5,6,2,1]=>16
[3,4,6,1,2,5]=>14
[3,4,6,1,5,2]=>14
[3,4,6,2,1,5]=>14
[3,4,6,2,5,1]=>14
[3,4,6,5,1,2]=>16
[3,4,6,5,2,1]=>16
[3,5,1,2,4,6]=>10
[3,5,1,2,6,4]=>12
[3,5,1,4,2,6]=>10
[3,5,1,4,6,2]=>12
[3,5,1,6,2,4]=>14
[3,5,1,6,4,2]=>14
[3,5,2,1,4,6]=>10
[3,5,2,1,6,4]=>12
[3,5,2,4,1,6]=>10
[3,5,2,4,6,1]=>12
[3,5,2,6,1,4]=>14
[3,5,2,6,4,1]=>14
[3,5,4,1,2,6]=>12
[3,5,4,1,6,2]=>14
[3,5,4,2,1,6]=>12
[3,5,4,2,6,1]=>14
[3,5,4,6,1,2]=>16
[3,5,4,6,2,1]=>16
[3,5,6,1,2,4]=>16
[3,5,6,1,4,2]=>16
[3,5,6,2,1,4]=>16
[3,5,6,2,4,1]=>16
[3,5,6,4,1,2]=>16
[3,5,6,4,2,1]=>16
[3,6,1,2,4,5]=>12
[3,6,1,2,5,4]=>12
[3,6,1,4,2,5]=>12
[3,6,1,4,5,2]=>12
[3,6,1,5,2,4]=>14
[3,6,1,5,4,2]=>14
[3,6,2,1,4,5]=>12
[3,6,2,1,5,4]=>12
[3,6,2,4,1,5]=>12
[3,6,2,4,5,1]=>12
[3,6,2,5,1,4]=>14
[3,6,2,5,4,1]=>14
[3,6,4,1,2,5]=>14
[3,6,4,1,5,2]=>14
[3,6,4,2,1,5]=>14
[3,6,4,2,5,1]=>14
[3,6,4,5,1,2]=>16
[3,6,4,5,2,1]=>16
[3,6,5,1,2,4]=>16
[3,6,5,1,4,2]=>16
[3,6,5,2,1,4]=>16
[3,6,5,2,4,1]=>16
[3,6,5,4,1,2]=>16
[3,6,5,4,2,1]=>16
[4,1,2,3,5,6]=>6
[4,1,2,3,6,5]=>8
[4,1,2,5,3,6]=>8
[4,1,2,5,6,3]=>10
[4,1,2,6,3,5]=>10
[4,1,2,6,5,3]=>10
[4,1,3,2,5,6]=>6
[4,1,3,2,6,5]=>8
[4,1,3,5,2,6]=>8
[4,1,3,5,6,2]=>10
[4,1,3,6,2,5]=>10
[4,1,3,6,5,2]=>10
[4,1,5,2,3,6]=>10
[4,1,5,2,6,3]=>12
[4,1,5,3,2,6]=>10
[4,1,5,3,6,2]=>12
[4,1,5,6,2,3]=>14
[4,1,5,6,3,2]=>14
[4,1,6,2,3,5]=>12
[4,1,6,2,5,3]=>12
[4,1,6,3,2,5]=>12
[4,1,6,3,5,2]=>12
[4,1,6,5,2,3]=>14
[4,1,6,5,3,2]=>14
[4,2,1,3,5,6]=>6
[4,2,1,3,6,5]=>8
[4,2,1,5,3,6]=>8
[4,2,1,5,6,3]=>10
[4,2,1,6,3,5]=>10
[4,2,1,6,5,3]=>10
[4,2,3,1,5,6]=>6
[4,2,3,1,6,5]=>8
[4,2,3,5,1,6]=>8
[4,2,3,5,6,1]=>10
[4,2,3,6,1,5]=>10
[4,2,3,6,5,1]=>10
[4,2,5,1,3,6]=>10
[4,2,5,1,6,3]=>12
[4,2,5,3,1,6]=>10
[4,2,5,3,6,1]=>12
[4,2,5,6,1,3]=>14
[4,2,5,6,3,1]=>14
[4,2,6,1,3,5]=>12
[4,2,6,1,5,3]=>12
[4,2,6,3,1,5]=>12
[4,2,6,3,5,1]=>12
[4,2,6,5,1,3]=>14
[4,2,6,5,3,1]=>14
[4,3,1,2,5,6]=>8
[4,3,1,2,6,5]=>10
[4,3,1,5,2,6]=>10
[4,3,1,5,6,2]=>12
[4,3,1,6,2,5]=>12
[4,3,1,6,5,2]=>12
[4,3,2,1,5,6]=>8
[4,3,2,1,6,5]=>10
[4,3,2,5,1,6]=>10
[4,3,2,5,6,1]=>12
[4,3,2,6,1,5]=>12
[4,3,2,6,5,1]=>12
[4,3,5,1,2,6]=>12
[4,3,5,1,6,2]=>14
[4,3,5,2,1,6]=>12
[4,3,5,2,6,1]=>14
[4,3,5,6,1,2]=>16
[4,3,5,6,2,1]=>16
[4,3,6,1,2,5]=>14
[4,3,6,1,5,2]=>14
[4,3,6,2,1,5]=>14
[4,3,6,2,5,1]=>14
[4,3,6,5,1,2]=>16
[4,3,6,5,2,1]=>16
[4,5,1,2,3,6]=>12
[4,5,1,2,6,3]=>14
[4,5,1,3,2,6]=>12
[4,5,1,3,6,2]=>14
[4,5,1,6,2,3]=>16
[4,5,1,6,3,2]=>16
[4,5,2,1,3,6]=>12
[4,5,2,1,6,3]=>14
[4,5,2,3,1,6]=>12
[4,5,2,3,6,1]=>14
[4,5,2,6,1,3]=>16
[4,5,2,6,3,1]=>16
[4,5,3,1,2,6]=>12
[4,5,3,1,6,2]=>14
[4,5,3,2,1,6]=>12
[4,5,3,2,6,1]=>14
[4,5,3,6,1,2]=>16
[4,5,3,6,2,1]=>16
[4,5,6,1,2,3]=>18
[4,5,6,1,3,2]=>18
[4,5,6,2,1,3]=>18
[4,5,6,2,3,1]=>18
[4,5,6,3,1,2]=>18
[4,5,6,3,2,1]=>18
[4,6,1,2,3,5]=>14
[4,6,1,2,5,3]=>14
[4,6,1,3,2,5]=>14
[4,6,1,3,5,2]=>14
[4,6,1,5,2,3]=>16
[4,6,1,5,3,2]=>16
[4,6,2,1,3,5]=>14
[4,6,2,1,5,3]=>14
[4,6,2,3,1,5]=>14
[4,6,2,3,5,1]=>14
[4,6,2,5,1,3]=>16
[4,6,2,5,3,1]=>16
[4,6,3,1,2,5]=>14
[4,6,3,1,5,2]=>14
[4,6,3,2,1,5]=>14
[4,6,3,2,5,1]=>14
[4,6,3,5,1,2]=>16
[4,6,3,5,2,1]=>16
[4,6,5,1,2,3]=>18
[4,6,5,1,3,2]=>18
[4,6,5,2,1,3]=>18
[4,6,5,2,3,1]=>18
[4,6,5,3,1,2]=>18
[4,6,5,3,2,1]=>18
[5,1,2,3,4,6]=>8
[5,1,2,3,6,4]=>10
[5,1,2,4,3,6]=>8
[5,1,2,4,6,3]=>10
[5,1,2,6,3,4]=>12
[5,1,2,6,4,3]=>12
[5,1,3,2,4,6]=>8
[5,1,3,2,6,4]=>10
[5,1,3,4,2,6]=>8
[5,1,3,4,6,2]=>10
[5,1,3,6,2,4]=>12
[5,1,3,6,4,2]=>12
[5,1,4,2,3,6]=>10
[5,1,4,2,6,3]=>12
[5,1,4,3,2,6]=>10
[5,1,4,3,6,2]=>12
[5,1,4,6,2,3]=>14
[5,1,4,6,3,2]=>14
[5,1,6,2,3,4]=>14
[5,1,6,2,4,3]=>14
[5,1,6,3,2,4]=>14
[5,1,6,3,4,2]=>14
[5,1,6,4,2,3]=>14
[5,1,6,4,3,2]=>14
[5,2,1,3,4,6]=>8
[5,2,1,3,6,4]=>10
[5,2,1,4,3,6]=>8
[5,2,1,4,6,3]=>10
[5,2,1,6,3,4]=>12
[5,2,1,6,4,3]=>12
[5,2,3,1,4,6]=>8
[5,2,3,1,6,4]=>10
[5,2,3,4,1,6]=>8
[5,2,3,4,6,1]=>10
[5,2,3,6,1,4]=>12
[5,2,3,6,4,1]=>12
[5,2,4,1,3,6]=>10
[5,2,4,1,6,3]=>12
[5,2,4,3,1,6]=>10
[5,2,4,3,6,1]=>12
[5,2,4,6,1,3]=>14
[5,2,4,6,3,1]=>14
[5,2,6,1,3,4]=>14
[5,2,6,1,4,3]=>14
[5,2,6,3,1,4]=>14
[5,2,6,3,4,1]=>14
[5,2,6,4,1,3]=>14
[5,2,6,4,3,1]=>14
[5,3,1,2,4,6]=>10
[5,3,1,2,6,4]=>12
[5,3,1,4,2,6]=>10
[5,3,1,4,6,2]=>12
[5,3,1,6,2,4]=>14
[5,3,1,6,4,2]=>14
[5,3,2,1,4,6]=>10
[5,3,2,1,6,4]=>12
[5,3,2,4,1,6]=>10
[5,3,2,4,6,1]=>12
[5,3,2,6,1,4]=>14
[5,3,2,6,4,1]=>14
[5,3,4,1,2,6]=>12
[5,3,4,1,6,2]=>14
[5,3,4,2,1,6]=>12
[5,3,4,2,6,1]=>14
[5,3,4,6,1,2]=>16
[5,3,4,6,2,1]=>16
[5,3,6,1,2,4]=>16
[5,3,6,1,4,2]=>16
[5,3,6,2,1,4]=>16
[5,3,6,2,4,1]=>16
[5,3,6,4,1,2]=>16
[5,3,6,4,2,1]=>16
[5,4,1,2,3,6]=>12
[5,4,1,2,6,3]=>14
[5,4,1,3,2,6]=>12
[5,4,1,3,6,2]=>14
[5,4,1,6,2,3]=>16
[5,4,1,6,3,2]=>16
[5,4,2,1,3,6]=>12
[5,4,2,1,6,3]=>14
[5,4,2,3,1,6]=>12
[5,4,2,3,6,1]=>14
[5,4,2,6,1,3]=>16
[5,4,2,6,3,1]=>16
[5,4,3,1,2,6]=>12
[5,4,3,1,6,2]=>14
[5,4,3,2,1,6]=>12
[5,4,3,2,6,1]=>14
[5,4,3,6,1,2]=>16
[5,4,3,6,2,1]=>16
[5,4,6,1,2,3]=>18
[5,4,6,1,3,2]=>18
[5,4,6,2,1,3]=>18
[5,4,6,2,3,1]=>18
[5,4,6,3,1,2]=>18
[5,4,6,3,2,1]=>18
[5,6,1,2,3,4]=>16
[5,6,1,2,4,3]=>16
[5,6,1,3,2,4]=>16
[5,6,1,3,4,2]=>16
[5,6,1,4,2,3]=>16
[5,6,1,4,3,2]=>16
[5,6,2,1,3,4]=>16
[5,6,2,1,4,3]=>16
[5,6,2,3,1,4]=>16
[5,6,2,3,4,1]=>16
[5,6,2,4,1,3]=>16
[5,6,2,4,3,1]=>16
[5,6,3,1,2,4]=>16
[5,6,3,1,4,2]=>16
[5,6,3,2,1,4]=>16
[5,6,3,2,4,1]=>16
[5,6,3,4,1,2]=>16
[5,6,3,4,2,1]=>16
[5,6,4,1,2,3]=>18
[5,6,4,1,3,2]=>18
[5,6,4,2,1,3]=>18
[5,6,4,2,3,1]=>18
[5,6,4,3,1,2]=>18
[5,6,4,3,2,1]=>18
[6,1,2,3,4,5]=>10
[6,1,2,3,5,4]=>10
[6,1,2,4,3,5]=>10
[6,1,2,4,5,3]=>10
[6,1,2,5,3,4]=>12
[6,1,2,5,4,3]=>12
[6,1,3,2,4,5]=>10
[6,1,3,2,5,4]=>10
[6,1,3,4,2,5]=>10
[6,1,3,4,5,2]=>10
[6,1,3,5,2,4]=>12
[6,1,3,5,4,2]=>12
[6,1,4,2,3,5]=>12
[6,1,4,2,5,3]=>12
[6,1,4,3,2,5]=>12
[6,1,4,3,5,2]=>12
[6,1,4,5,2,3]=>14
[6,1,4,5,3,2]=>14
[6,1,5,2,3,4]=>14
[6,1,5,2,4,3]=>14
[6,1,5,3,2,4]=>14
[6,1,5,3,4,2]=>14
[6,1,5,4,2,3]=>14
[6,1,5,4,3,2]=>14
[6,2,1,3,4,5]=>10
[6,2,1,3,5,4]=>10
[6,2,1,4,3,5]=>10
[6,2,1,4,5,3]=>10
[6,2,1,5,3,4]=>12
[6,2,1,5,4,3]=>12
[6,2,3,1,4,5]=>10
[6,2,3,1,5,4]=>10
[6,2,3,4,1,5]=>10
[6,2,3,4,5,1]=>10
[6,2,3,5,1,4]=>12
[6,2,3,5,4,1]=>12
[6,2,4,1,3,5]=>12
[6,2,4,1,5,3]=>12
[6,2,4,3,1,5]=>12
[6,2,4,3,5,1]=>12
[6,2,4,5,1,3]=>14
[6,2,4,5,3,1]=>14
[6,2,5,1,3,4]=>14
[6,2,5,1,4,3]=>14
[6,2,5,3,1,4]=>14
[6,2,5,3,4,1]=>14
[6,2,5,4,1,3]=>14
[6,2,5,4,3,1]=>14
[6,3,1,2,4,5]=>12
[6,3,1,2,5,4]=>12
[6,3,1,4,2,5]=>12
[6,3,1,4,5,2]=>12
[6,3,1,5,2,4]=>14
[6,3,1,5,4,2]=>14
[6,3,2,1,4,5]=>12
[6,3,2,1,5,4]=>12
[6,3,2,4,1,5]=>12
[6,3,2,4,5,1]=>12
[6,3,2,5,1,4]=>14
[6,3,2,5,4,1]=>14
[6,3,4,1,2,5]=>14
[6,3,4,1,5,2]=>14
[6,3,4,2,1,5]=>14
[6,3,4,2,5,1]=>14
[6,3,4,5,1,2]=>16
[6,3,4,5,2,1]=>16
[6,3,5,1,2,4]=>16
[6,3,5,1,4,2]=>16
[6,3,5,2,1,4]=>16
[6,3,5,2,4,1]=>16
[6,3,5,4,1,2]=>16
[6,3,5,4,2,1]=>16
[6,4,1,2,3,5]=>14
[6,4,1,2,5,3]=>14
[6,4,1,3,2,5]=>14
[6,4,1,3,5,2]=>14
[6,4,1,5,2,3]=>16
[6,4,1,5,3,2]=>16
[6,4,2,1,3,5]=>14
[6,4,2,1,5,3]=>14
[6,4,2,3,1,5]=>14
[6,4,2,3,5,1]=>14
[6,4,2,5,1,3]=>16
[6,4,2,5,3,1]=>16
[6,4,3,1,2,5]=>14
[6,4,3,1,5,2]=>14
[6,4,3,2,1,5]=>14
[6,4,3,2,5,1]=>14
[6,4,3,5,1,2]=>16
[6,4,3,5,2,1]=>16
[6,4,5,1,2,3]=>18
[6,4,5,1,3,2]=>18
[6,4,5,2,1,3]=>18
[6,4,5,2,3,1]=>18
[6,4,5,3,1,2]=>18
[6,4,5,3,2,1]=>18
[6,5,1,2,3,4]=>16
[6,5,1,2,4,3]=>16
[6,5,1,3,2,4]=>16
[6,5,1,3,4,2]=>16
[6,5,1,4,2,3]=>16
[6,5,1,4,3,2]=>16
[6,5,2,1,3,4]=>16
[6,5,2,1,4,3]=>16
[6,5,2,3,1,4]=>16
[6,5,2,3,4,1]=>16
[6,5,2,4,1,3]=>16
[6,5,2,4,3,1]=>16
[6,5,3,1,2,4]=>16
[6,5,3,1,4,2]=>16
[6,5,3,2,1,4]=>16
[6,5,3,2,4,1]=>16
[6,5,3,4,1,2]=>16
[6,5,3,4,2,1]=>16
[6,5,4,1,2,3]=>18
[6,5,4,1,3,2]=>18
[6,5,4,2,1,3]=>18
[6,5,4,2,3,1]=>18
[6,5,4,3,1,2]=>18
[6,5,4,3,2,1]=>18
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>2
[1,2,3,4,6,5,7]=>2
[1,2,3,4,6,7,5]=>4
[1,2,3,4,7,5,6]=>4
[1,2,3,4,7,6,5]=>4
[1,2,3,5,4,6,7]=>2
[1,2,3,5,4,7,6]=>4
[1,2,3,5,6,4,7]=>4
[1,2,3,5,6,7,4]=>6
[1,2,3,5,7,4,6]=>6
[1,2,3,5,7,6,4]=>6
[1,2,3,6,4,5,7]=>4
[1,2,3,6,4,7,5]=>6
[1,2,3,6,5,4,7]=>4
[1,2,3,6,5,7,4]=>6
[1,2,3,6,7,4,5]=>8
[1,2,3,6,7,5,4]=>8
[1,2,3,7,4,5,6]=>6
[1,2,3,7,4,6,5]=>6
[1,2,3,7,5,4,6]=>6
[1,2,3,7,5,6,4]=>6
[1,2,3,7,6,4,5]=>8
[1,2,3,7,6,5,4]=>8
[1,2,4,3,5,6,7]=>2
[1,2,4,3,5,7,6]=>4
[1,2,4,3,6,5,7]=>4
[1,2,4,3,6,7,5]=>6
[1,2,4,3,7,5,6]=>6
[1,2,4,3,7,6,5]=>6
[1,2,4,5,3,6,7]=>4
[1,2,4,5,3,7,6]=>6
[1,2,4,5,6,3,7]=>6
[1,2,4,5,6,7,3]=>8
[1,2,4,5,7,3,6]=>8
[1,2,4,5,7,6,3]=>8
[1,2,4,6,3,5,7]=>6
[1,2,4,6,3,7,5]=>8
[1,2,4,6,5,3,7]=>6
[1,2,4,6,5,7,3]=>8
[1,2,4,6,7,3,5]=>10
[1,2,4,6,7,5,3]=>10
[1,2,4,7,3,5,6]=>8
[1,2,4,7,3,6,5]=>8
[1,2,4,7,5,3,6]=>8
[1,2,4,7,5,6,3]=>8
[1,2,4,7,6,3,5]=>10
[1,2,4,7,6,5,3]=>10
[1,2,5,3,4,6,7]=>4
[1,2,5,3,4,7,6]=>6
[1,2,5,3,6,4,7]=>6
[1,2,5,3,6,7,4]=>8
[1,2,5,3,7,4,6]=>8
[1,2,5,3,7,6,4]=>8
[1,2,5,4,3,6,7]=>4
[1,2,5,4,3,7,6]=>6
[1,2,5,4,6,3,7]=>6
[1,2,5,4,6,7,3]=>8
[1,2,5,4,7,3,6]=>8
[1,2,5,4,7,6,3]=>8
[1,2,5,6,3,4,7]=>8
[1,2,5,6,3,7,4]=>10
[1,2,5,6,4,3,7]=>8
[1,2,5,6,4,7,3]=>10
[1,2,5,6,7,3,4]=>12
[1,2,5,6,7,4,3]=>12
[1,2,5,7,3,4,6]=>10
[1,2,5,7,3,6,4]=>10
[1,2,5,7,4,3,6]=>10
[1,2,5,7,4,6,3]=>10
[1,2,5,7,6,3,4]=>12
[1,2,5,7,6,4,3]=>12
[1,2,6,3,4,5,7]=>6
[1,2,6,3,4,7,5]=>8
[1,2,6,3,5,4,7]=>6
[1,2,6,3,5,7,4]=>8
[1,2,6,3,7,4,5]=>10
[1,2,6,3,7,5,4]=>10
[1,2,6,4,3,5,7]=>6
[1,2,6,4,3,7,5]=>8
[1,2,6,4,5,3,7]=>6
[1,2,6,4,5,7,3]=>8
[1,2,6,4,7,3,5]=>10
[1,2,6,4,7,5,3]=>10
[1,2,6,5,3,4,7]=>8
[1,2,6,5,3,7,4]=>10
[1,2,6,5,4,3,7]=>8
[1,2,6,5,4,7,3]=>10
[1,2,6,5,7,3,4]=>12
[1,2,6,5,7,4,3]=>12
[1,2,6,7,3,4,5]=>12
[1,2,6,7,3,5,4]=>12
[1,2,6,7,4,3,5]=>12
[1,2,6,7,4,5,3]=>12
[1,2,6,7,5,3,4]=>12
[1,2,6,7,5,4,3]=>12
[1,2,7,3,4,5,6]=>8
[1,2,7,3,4,6,5]=>8
[1,2,7,3,5,4,6]=>8
[1,2,7,3,5,6,4]=>8
[1,2,7,3,6,4,5]=>10
[1,2,7,3,6,5,4]=>10
[1,2,7,4,3,5,6]=>8
[1,2,7,4,3,6,5]=>8
[1,2,7,4,5,3,6]=>8
[1,2,7,4,5,6,3]=>8
[1,2,7,4,6,3,5]=>10
[1,2,7,4,6,5,3]=>10
[1,2,7,5,3,4,6]=>10
[1,2,7,5,3,6,4]=>10
[1,2,7,5,4,3,6]=>10
[1,2,7,5,4,6,3]=>10
[1,2,7,5,6,3,4]=>12
[1,2,7,5,6,4,3]=>12
[1,2,7,6,3,4,5]=>12
[1,2,7,6,3,5,4]=>12
[1,2,7,6,4,3,5]=>12
[1,2,7,6,4,5,3]=>12
[1,2,7,6,5,3,4]=>12
[1,2,7,6,5,4,3]=>12
[1,3,2,4,5,6,7]=>2
[1,3,2,4,5,7,6]=>4
[1,3,2,4,6,5,7]=>4
[1,3,2,4,6,7,5]=>6
[1,3,2,4,7,5,6]=>6
[1,3,2,4,7,6,5]=>6
[1,3,2,5,4,6,7]=>4
[1,3,2,5,4,7,6]=>6
[1,3,2,5,6,4,7]=>6
[1,3,2,5,6,7,4]=>8
[1,3,2,5,7,4,6]=>8
[1,3,2,5,7,6,4]=>8
[1,3,2,6,4,5,7]=>6
[1,3,2,6,4,7,5]=>8
[1,3,2,6,5,4,7]=>6
[1,3,2,6,5,7,4]=>8
[1,3,2,6,7,4,5]=>10
[1,3,2,6,7,5,4]=>10
[1,3,2,7,4,5,6]=>8
[1,3,2,7,4,6,5]=>8
[1,3,2,7,5,4,6]=>8
[1,3,2,7,5,6,4]=>8
[1,3,2,7,6,4,5]=>10
[1,3,2,7,6,5,4]=>10
[1,3,4,2,5,6,7]=>4
[1,3,4,2,5,7,6]=>6
[1,3,4,2,6,5,7]=>6
[1,3,4,2,6,7,5]=>8
[1,3,4,2,7,5,6]=>8
[1,3,4,2,7,6,5]=>8
[1,3,4,5,2,6,7]=>6
[1,3,4,5,2,7,6]=>8
[1,3,4,5,6,2,7]=>8
[1,3,4,5,6,7,2]=>10
[1,3,4,5,7,2,6]=>10
[1,3,4,5,7,6,2]=>10
[1,3,4,6,2,5,7]=>8
[1,3,4,6,2,7,5]=>10
[1,3,4,6,5,2,7]=>8
[1,3,4,6,5,7,2]=>10
[1,3,4,6,7,2,5]=>12
[1,3,4,6,7,5,2]=>12
[1,3,4,7,2,5,6]=>10
[1,3,4,7,2,6,5]=>10
[1,3,4,7,5,2,6]=>10
[1,3,4,7,5,6,2]=>10
[1,3,4,7,6,2,5]=>12
[1,3,4,7,6,5,2]=>12
[1,3,5,2,4,6,7]=>6
[1,3,5,2,4,7,6]=>8
[1,3,5,2,6,4,7]=>8
[1,3,5,2,6,7,4]=>10
[1,3,5,2,7,4,6]=>10
[1,3,5,2,7,6,4]=>10
[1,3,5,4,2,6,7]=>6
[1,3,5,4,2,7,6]=>8
[1,3,5,4,6,2,7]=>8
[1,3,5,4,6,7,2]=>10
[1,3,5,4,7,2,6]=>10
[1,3,5,4,7,6,2]=>10
[1,3,5,6,2,4,7]=>10
[1,3,5,6,2,7,4]=>12
[1,3,5,6,4,2,7]=>10
[1,3,5,6,4,7,2]=>12
[1,3,5,6,7,2,4]=>14
[1,3,5,6,7,4,2]=>14
[1,3,5,7,2,4,6]=>12
[1,3,5,7,2,6,4]=>12
[1,3,5,7,4,2,6]=>12
[1,3,5,7,4,6,2]=>12
[1,3,5,7,6,2,4]=>14
[1,3,5,7,6,4,2]=>14
[1,3,6,2,4,5,7]=>8
[1,3,6,2,4,7,5]=>10
[1,3,6,2,5,4,7]=>8
[1,3,6,2,5,7,4]=>10
[1,3,6,2,7,4,5]=>12
[1,3,6,2,7,5,4]=>12
[1,3,6,4,2,5,7]=>8
[1,3,6,4,2,7,5]=>10
[1,3,6,4,5,2,7]=>8
[1,3,6,4,5,7,2]=>10
[1,3,6,4,7,2,5]=>12
[1,3,6,4,7,5,2]=>12
[1,3,6,5,2,4,7]=>10
[1,3,6,5,2,7,4]=>12
[1,3,6,5,4,2,7]=>10
[1,3,6,5,4,7,2]=>12
[1,3,6,5,7,2,4]=>14
[1,3,6,5,7,4,2]=>14
[1,3,6,7,2,4,5]=>14
[1,3,6,7,2,5,4]=>14
[1,3,6,7,4,2,5]=>14
[1,3,6,7,4,5,2]=>14
[1,3,6,7,5,2,4]=>14
[1,3,6,7,5,4,2]=>14
[1,3,7,2,4,5,6]=>10
[1,3,7,2,4,6,5]=>10
[1,3,7,2,5,4,6]=>10
[1,3,7,2,5,6,4]=>10
[1,3,7,2,6,4,5]=>12
[1,3,7,2,6,5,4]=>12
[1,3,7,4,2,5,6]=>10
[1,3,7,4,2,6,5]=>10
[1,3,7,4,5,2,6]=>10
[1,3,7,4,5,6,2]=>10
[1,3,7,4,6,2,5]=>12
[1,3,7,4,6,5,2]=>12
[1,3,7,5,2,4,6]=>12
[1,3,7,5,2,6,4]=>12
[1,3,7,5,4,2,6]=>12
[1,3,7,5,4,6,2]=>12
[1,3,7,5,6,2,4]=>14
[1,3,7,5,6,4,2]=>14
[1,3,7,6,2,4,5]=>14
[1,3,7,6,2,5,4]=>14
[1,3,7,6,4,2,5]=>14
[1,3,7,6,4,5,2]=>14
[1,3,7,6,5,2,4]=>14
[1,3,7,6,5,4,2]=>14
[1,4,2,3,5,6,7]=>4
[1,4,2,3,5,7,6]=>6
[1,4,2,3,6,5,7]=>6
[1,4,2,3,6,7,5]=>8
[1,4,2,3,7,5,6]=>8
[1,4,2,3,7,6,5]=>8
[1,4,2,5,3,6,7]=>6
[1,4,2,5,3,7,6]=>8
[1,4,2,5,6,3,7]=>8
[1,4,2,5,6,7,3]=>10
[1,4,2,5,7,3,6]=>10
[1,4,2,5,7,6,3]=>10
[1,4,2,6,3,5,7]=>8
[1,4,2,6,3,7,5]=>10
[1,4,2,6,5,3,7]=>8
[1,4,2,6,5,7,3]=>10
[1,4,2,6,7,3,5]=>12
[1,4,2,6,7,5,3]=>12
[1,4,2,7,3,5,6]=>10
[1,4,2,7,3,6,5]=>10
[1,4,2,7,5,3,6]=>10
[1,4,2,7,5,6,3]=>10
[1,4,2,7,6,3,5]=>12
[1,4,2,7,6,5,3]=>12
[1,4,3,2,5,6,7]=>4
[1,4,3,2,5,7,6]=>6
[1,4,3,2,6,5,7]=>6
[1,4,3,2,6,7,5]=>8
[1,4,3,2,7,5,6]=>8
[1,4,3,2,7,6,5]=>8
[1,4,3,5,2,6,7]=>6
[1,4,3,5,2,7,6]=>8
[1,4,3,5,6,2,7]=>8
[1,4,3,5,6,7,2]=>10
[1,4,3,5,7,2,6]=>10
[1,4,3,5,7,6,2]=>10
[1,4,3,6,2,5,7]=>8
[1,4,3,6,2,7,5]=>10
[1,4,3,6,5,2,7]=>8
[1,4,3,6,5,7,2]=>10
[1,4,3,6,7,2,5]=>12
[1,4,3,6,7,5,2]=>12
[1,4,3,7,2,5,6]=>10
[1,4,3,7,2,6,5]=>10
[1,4,3,7,5,2,6]=>10
[1,4,3,7,5,6,2]=>10
[1,4,3,7,6,2,5]=>12
[1,4,3,7,6,5,2]=>12
[1,4,5,2,3,6,7]=>8
[1,4,5,2,3,7,6]=>10
[1,4,5,2,6,3,7]=>10
[1,4,5,2,6,7,3]=>12
[1,4,5,2,7,3,6]=>12
[1,4,5,2,7,6,3]=>12
[1,4,5,3,2,6,7]=>8
[1,4,5,3,2,7,6]=>10
[1,4,5,3,6,2,7]=>10
[1,4,5,3,6,7,2]=>12
[1,4,5,3,7,2,6]=>12
[1,4,5,3,7,6,2]=>12
[1,4,5,6,2,3,7]=>12
[1,4,5,6,2,7,3]=>14
[1,4,5,6,3,2,7]=>12
[1,4,5,6,3,7,2]=>14
[1,4,5,6,7,2,3]=>16
[1,4,5,6,7,3,2]=>16
[1,4,5,7,2,3,6]=>14
[1,4,5,7,2,6,3]=>14
[1,4,5,7,3,2,6]=>14
[1,4,5,7,3,6,2]=>14
[1,4,5,7,6,2,3]=>16
[1,4,5,7,6,3,2]=>16
[1,4,6,2,3,5,7]=>10
[1,4,6,2,3,7,5]=>12
[1,4,6,2,5,3,7]=>10
[1,4,6,2,5,7,3]=>12
[1,4,6,2,7,3,5]=>14
[1,4,6,2,7,5,3]=>14
[1,4,6,3,2,5,7]=>10
[1,4,6,3,2,7,5]=>12
[1,4,6,3,5,2,7]=>10
[1,4,6,3,5,7,2]=>12
[1,4,6,3,7,2,5]=>14
[1,4,6,3,7,5,2]=>14
[1,4,6,5,2,3,7]=>12
[1,4,6,5,2,7,3]=>14
[1,4,6,5,3,2,7]=>12
[1,4,6,5,3,7,2]=>14
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Description
The total displacement of a permutation.
This is, for a permutation $\pi$ of $n$, given by $\sum_{i = 1}^n | \pi(i) - i |.$
This is twice the statistic St000029The depth of a permutation. and can be found in [3, Problem 5.1.1.28] and also in [1, 2].
This is, for a permutation $\pi$ of $n$, given by $\sum_{i = 1}^n | \pi(i) - i |.$
This is twice the statistic St000029The depth of a permutation. and can be found in [3, Problem 5.1.1.28] and also in [1, 2].
References
[1] Chatterjee, S., Diaconis, P. A central limit theorem for a new statistic on permutations arXiv:1608.01666
[2] Diaconis, P., Graham, R. L. Spearman's footrule as a measure of disarray MathSciNet:0652736
[3] Knuth, D. E. The art of computer programming. Vol. 3 MathSciNet:3077154
[2] Diaconis, P., Graham, R. L. Spearman's footrule as a measure of disarray MathSciNet:0652736
[3] Knuth, D. E. The art of computer programming. Vol. 3 MathSciNet:3077154
Code
def statistic(pi):
return sum( abs(pi(i) - i) for i in [ 1 .. len(pi) ] )
Created
May 31, 2017 at 10:42 by Christian Stump
Updated
May 31, 2017 at 13:53 by Christian Stump
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