Identifier
- St000280: Permutations ⟶ ℤ
Values
=>
[1,2]=>2
[2,1]=>1
[1,2,3]=>5
[1,3,2]=>3
[2,1,3]=>2
[2,3,1]=>3
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>14
[1,2,4,3]=>9
[1,3,2,4]=>7
[1,3,4,2]=>9
[1,4,2,3]=>7
[1,4,3,2]=>4
[2,1,3,4]=>5
[2,1,4,3]=>3
[2,3,1,4]=>7
[2,3,4,1]=>9
[2,4,1,3]=>7
[2,4,3,1]=>4
[3,1,2,4]=>5
[3,1,4,2]=>3
[3,2,1,4]=>2
[3,2,4,1]=>3
[3,4,1,2]=>7
[3,4,2,1]=>4
[4,1,2,3]=>5
[4,1,3,2]=>3
[4,2,1,3]=>2
[4,2,3,1]=>3
[4,3,1,2]=>2
[4,3,2,1]=>1
[1,2,3,4,5]=>42
[1,2,3,5,4]=>28
[1,2,4,3,5]=>23
[1,2,4,5,3]=>28
[1,2,5,3,4]=>23
[1,2,5,4,3]=>14
[1,3,2,4,5]=>19
[1,3,2,5,4]=>12
[1,3,4,2,5]=>23
[1,3,4,5,2]=>28
[1,3,5,2,4]=>23
[1,3,5,4,2]=>14
[1,4,2,3,5]=>19
[1,4,2,5,3]=>12
[1,4,3,2,5]=>9
[1,4,3,5,2]=>12
[1,4,5,2,3]=>23
[1,4,5,3,2]=>14
[1,5,2,3,4]=>19
[1,5,2,4,3]=>12
[1,5,3,2,4]=>9
[1,5,3,4,2]=>12
[1,5,4,2,3]=>9
[1,5,4,3,2]=>5
[2,1,3,4,5]=>14
[2,1,3,5,4]=>9
[2,1,4,3,5]=>7
[2,1,4,5,3]=>9
[2,1,5,3,4]=>7
[2,1,5,4,3]=>4
[2,3,1,4,5]=>19
[2,3,1,5,4]=>12
[2,3,4,1,5]=>23
[2,3,4,5,1]=>28
[2,3,5,1,4]=>23
[2,3,5,4,1]=>14
[2,4,1,3,5]=>19
[2,4,1,5,3]=>12
[2,4,3,1,5]=>9
[2,4,3,5,1]=>12
[2,4,5,1,3]=>23
[2,4,5,3,1]=>14
[2,5,1,3,4]=>19
[2,5,1,4,3]=>12
[2,5,3,1,4]=>9
[2,5,3,4,1]=>12
[2,5,4,1,3]=>9
[2,5,4,3,1]=>5
[3,1,2,4,5]=>14
[3,1,2,5,4]=>9
[3,1,4,2,5]=>7
[3,1,4,5,2]=>9
[3,1,5,2,4]=>7
[3,1,5,4,2]=>4
[3,2,1,4,5]=>5
[3,2,1,5,4]=>3
[3,2,4,1,5]=>7
[3,2,4,5,1]=>9
[3,2,5,1,4]=>7
[3,2,5,4,1]=>4
[3,4,1,2,5]=>19
[3,4,1,5,2]=>12
[3,4,2,1,5]=>9
[3,4,2,5,1]=>12
[3,4,5,1,2]=>23
[3,4,5,2,1]=>14
[3,5,1,2,4]=>19
[3,5,1,4,2]=>12
[3,5,2,1,4]=>9
[3,5,2,4,1]=>12
[3,5,4,1,2]=>9
[3,5,4,2,1]=>5
[4,1,2,3,5]=>14
[4,1,2,5,3]=>9
[4,1,3,2,5]=>7
[4,1,3,5,2]=>9
[4,1,5,2,3]=>7
[4,1,5,3,2]=>4
[4,2,1,3,5]=>5
[4,2,1,5,3]=>3
[4,2,3,1,5]=>7
[4,2,3,5,1]=>9
[4,2,5,1,3]=>7
[4,2,5,3,1]=>4
[4,3,1,2,5]=>5
[4,3,1,5,2]=>3
[4,3,2,1,5]=>2
[4,3,2,5,1]=>3
[4,3,5,1,2]=>7
[4,3,5,2,1]=>4
[4,5,1,2,3]=>19
[4,5,1,3,2]=>12
[4,5,2,1,3]=>9
[4,5,2,3,1]=>12
[4,5,3,1,2]=>9
[4,5,3,2,1]=>5
[5,1,2,3,4]=>14
[5,1,2,4,3]=>9
[5,1,3,2,4]=>7
[5,1,3,4,2]=>9
[5,1,4,2,3]=>7
[5,1,4,3,2]=>4
[5,2,1,3,4]=>5
[5,2,1,4,3]=>3
[5,2,3,1,4]=>7
[5,2,3,4,1]=>9
[5,2,4,1,3]=>7
[5,2,4,3,1]=>4
[5,3,1,2,4]=>5
[5,3,1,4,2]=>3
[5,3,2,1,4]=>2
[5,3,2,4,1]=>3
[5,3,4,1,2]=>7
[5,3,4,2,1]=>4
[5,4,1,2,3]=>5
[5,4,1,3,2]=>3
[5,4,2,1,3]=>2
[5,4,2,3,1]=>3
[5,4,3,1,2]=>2
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>132
[1,2,3,4,6,5]=>90
[1,2,3,5,4,6]=>76
[1,2,3,5,6,4]=>90
[1,2,3,6,4,5]=>76
[1,2,3,6,5,4]=>48
[1,2,4,3,5,6]=>66
[1,2,4,3,6,5]=>43
[1,2,4,5,3,6]=>76
[1,2,4,5,6,3]=>90
[1,2,4,6,3,5]=>76
[1,2,4,6,5,3]=>48
[1,2,5,3,4,6]=>66
[1,2,5,3,6,4]=>43
[1,2,5,4,3,6]=>34
[1,2,5,4,6,3]=>43
[1,2,5,6,3,4]=>76
[1,2,5,6,4,3]=>48
[1,2,6,3,4,5]=>66
[1,2,6,3,5,4]=>43
[1,2,6,4,3,5]=>34
[1,2,6,4,5,3]=>43
[1,2,6,5,3,4]=>34
[1,2,6,5,4,3]=>20
[1,3,2,4,5,6]=>56
[1,3,2,4,6,5]=>37
[1,3,2,5,4,6]=>30
[1,3,2,5,6,4]=>37
[1,3,2,6,4,5]=>30
[1,3,2,6,5,4]=>18
[1,3,4,2,5,6]=>66
[1,3,4,2,6,5]=>43
[1,3,4,5,2,6]=>76
[1,3,4,5,6,2]=>90
[1,3,4,6,2,5]=>76
[1,3,4,6,5,2]=>48
[1,3,5,2,4,6]=>66
[1,3,5,2,6,4]=>43
[1,3,5,4,2,6]=>34
[1,3,5,4,6,2]=>43
[1,3,5,6,2,4]=>76
[1,3,5,6,4,2]=>48
[1,3,6,2,4,5]=>66
[1,3,6,2,5,4]=>43
[1,3,6,4,2,5]=>34
[1,3,6,4,5,2]=>43
[1,3,6,5,2,4]=>34
[1,3,6,5,4,2]=>20
[1,4,2,3,5,6]=>56
[1,4,2,3,6,5]=>37
[1,4,2,5,3,6]=>30
[1,4,2,5,6,3]=>37
[1,4,2,6,3,5]=>30
[1,4,2,6,5,3]=>18
[1,4,3,2,5,6]=>24
[1,4,3,2,6,5]=>15
[1,4,3,5,2,6]=>30
[1,4,3,5,6,2]=>37
[1,4,3,6,2,5]=>30
[1,4,3,6,5,2]=>18
[1,4,5,2,3,6]=>66
[1,4,5,2,6,3]=>43
[1,4,5,3,2,6]=>34
[1,4,5,3,6,2]=>43
[1,4,5,6,2,3]=>76
[1,4,5,6,3,2]=>48
[1,4,6,2,3,5]=>66
[1,4,6,2,5,3]=>43
[1,4,6,3,2,5]=>34
[1,4,6,3,5,2]=>43
[1,4,6,5,2,3]=>34
[1,4,6,5,3,2]=>20
[1,5,2,3,4,6]=>56
[1,5,2,3,6,4]=>37
[1,5,2,4,3,6]=>30
[1,5,2,4,6,3]=>37
[1,5,2,6,3,4]=>30
[1,5,2,6,4,3]=>18
[1,5,3,2,4,6]=>24
[1,5,3,2,6,4]=>15
[1,5,3,4,2,6]=>30
[1,5,3,4,6,2]=>37
[1,5,3,6,2,4]=>30
[1,5,3,6,4,2]=>18
[1,5,4,2,3,6]=>24
[1,5,4,2,6,3]=>15
[1,5,4,3,2,6]=>11
[1,5,4,3,6,2]=>15
[1,5,4,6,2,3]=>30
[1,5,4,6,3,2]=>18
[1,5,6,2,3,4]=>66
[1,5,6,2,4,3]=>43
[1,5,6,3,2,4]=>34
[1,5,6,3,4,2]=>43
[1,5,6,4,2,3]=>34
[1,5,6,4,3,2]=>20
[1,6,2,3,4,5]=>56
[1,6,2,3,5,4]=>37
[1,6,2,4,3,5]=>30
[1,6,2,4,5,3]=>37
[1,6,2,5,3,4]=>30
[1,6,2,5,4,3]=>18
[1,6,3,2,4,5]=>24
[1,6,3,2,5,4]=>15
[1,6,3,4,2,5]=>30
[1,6,3,4,5,2]=>37
[1,6,3,5,2,4]=>30
[1,6,3,5,4,2]=>18
[1,6,4,2,3,5]=>24
[1,6,4,2,5,3]=>15
[1,6,4,3,2,5]=>11
[1,6,4,3,5,2]=>15
[1,6,4,5,2,3]=>30
[1,6,4,5,3,2]=>18
[1,6,5,2,3,4]=>24
[1,6,5,2,4,3]=>15
[1,6,5,3,2,4]=>11
[1,6,5,3,4,2]=>15
[1,6,5,4,2,3]=>11
[1,6,5,4,3,2]=>6
[2,1,3,4,5,6]=>42
[2,1,3,4,6,5]=>28
[2,1,3,5,4,6]=>23
[2,1,3,5,6,4]=>28
[2,1,3,6,4,5]=>23
[2,1,3,6,5,4]=>14
[2,1,4,3,5,6]=>19
[2,1,4,3,6,5]=>12
[2,1,4,5,3,6]=>23
[2,1,4,5,6,3]=>28
[2,1,4,6,3,5]=>23
[2,1,4,6,5,3]=>14
[2,1,5,3,4,6]=>19
[2,1,5,3,6,4]=>12
[2,1,5,4,3,6]=>9
[2,1,5,4,6,3]=>12
[2,1,5,6,3,4]=>23
[2,1,5,6,4,3]=>14
[2,1,6,3,4,5]=>19
[2,1,6,3,5,4]=>12
[2,1,6,4,3,5]=>9
[2,1,6,4,5,3]=>12
[2,1,6,5,3,4]=>9
[2,1,6,5,4,3]=>5
[2,3,1,4,5,6]=>56
[2,3,1,4,6,5]=>37
[2,3,1,5,4,6]=>30
[2,3,1,5,6,4]=>37
[2,3,1,6,4,5]=>30
[2,3,1,6,5,4]=>18
[2,3,4,1,5,6]=>66
[2,3,4,1,6,5]=>43
[2,3,4,5,1,6]=>76
[2,3,4,5,6,1]=>90
[2,3,4,6,1,5]=>76
[2,3,4,6,5,1]=>48
[2,3,5,1,4,6]=>66
[2,3,5,1,6,4]=>43
[2,3,5,4,1,6]=>34
[2,3,5,4,6,1]=>43
[2,3,5,6,1,4]=>76
[2,3,5,6,4,1]=>48
[2,3,6,1,4,5]=>66
[2,3,6,1,5,4]=>43
[2,3,6,4,1,5]=>34
[2,3,6,4,5,1]=>43
[2,3,6,5,1,4]=>34
[2,3,6,5,4,1]=>20
[2,4,1,3,5,6]=>56
[2,4,1,3,6,5]=>37
[2,4,1,5,3,6]=>30
[2,4,1,5,6,3]=>37
[2,4,1,6,3,5]=>30
[2,4,1,6,5,3]=>18
[2,4,3,1,5,6]=>24
[2,4,3,1,6,5]=>15
[2,4,3,5,1,6]=>30
[2,4,3,5,6,1]=>37
[2,4,3,6,1,5]=>30
[2,4,3,6,5,1]=>18
[2,4,5,1,3,6]=>66
[2,4,5,1,6,3]=>43
[2,4,5,3,1,6]=>34
[2,4,5,3,6,1]=>43
[2,4,5,6,1,3]=>76
[2,4,5,6,3,1]=>48
[2,4,6,1,3,5]=>66
[2,4,6,1,5,3]=>43
[2,4,6,3,1,5]=>34
[2,4,6,3,5,1]=>43
[2,4,6,5,1,3]=>34
[2,4,6,5,3,1]=>20
[2,5,1,3,4,6]=>56
[2,5,1,3,6,4]=>37
[2,5,1,4,3,6]=>30
[2,5,1,4,6,3]=>37
[2,5,1,6,3,4]=>30
[2,5,1,6,4,3]=>18
[2,5,3,1,4,6]=>24
[2,5,3,1,6,4]=>15
[2,5,3,4,1,6]=>30
[2,5,3,4,6,1]=>37
[2,5,3,6,1,4]=>30
[2,5,3,6,4,1]=>18
[2,5,4,1,3,6]=>24
[2,5,4,1,6,3]=>15
[2,5,4,3,1,6]=>11
[2,5,4,3,6,1]=>15
[2,5,4,6,1,3]=>30
[2,5,4,6,3,1]=>18
[2,5,6,1,3,4]=>66
[2,5,6,1,4,3]=>43
[2,5,6,3,1,4]=>34
[2,5,6,3,4,1]=>43
[2,5,6,4,1,3]=>34
[2,5,6,4,3,1]=>20
[2,6,1,3,4,5]=>56
[2,6,1,3,5,4]=>37
[2,6,1,4,3,5]=>30
[2,6,1,4,5,3]=>37
[2,6,1,5,3,4]=>30
[2,6,1,5,4,3]=>18
[2,6,3,1,4,5]=>24
[2,6,3,1,5,4]=>15
[2,6,3,4,1,5]=>30
[2,6,3,4,5,1]=>37
[2,6,3,5,1,4]=>30
[2,6,3,5,4,1]=>18
[2,6,4,1,3,5]=>24
[2,6,4,1,5,3]=>15
[2,6,4,3,1,5]=>11
[2,6,4,3,5,1]=>15
[2,6,4,5,1,3]=>30
[2,6,4,5,3,1]=>18
[2,6,5,1,3,4]=>24
[2,6,5,1,4,3]=>15
[2,6,5,3,1,4]=>11
[2,6,5,3,4,1]=>15
[2,6,5,4,1,3]=>11
[2,6,5,4,3,1]=>6
[3,1,2,4,5,6]=>42
[3,1,2,4,6,5]=>28
[3,1,2,5,4,6]=>23
[3,1,2,5,6,4]=>28
[3,1,2,6,4,5]=>23
[3,1,2,6,5,4]=>14
[3,1,4,2,5,6]=>19
[3,1,4,2,6,5]=>12
[3,1,4,5,2,6]=>23
[3,1,4,5,6,2]=>28
[3,1,4,6,2,5]=>23
[3,1,4,6,5,2]=>14
[3,1,5,2,4,6]=>19
[3,1,5,2,6,4]=>12
[3,1,5,4,2,6]=>9
[3,1,5,4,6,2]=>12
[3,1,5,6,2,4]=>23
[3,1,5,6,4,2]=>14
[3,1,6,2,4,5]=>19
[3,1,6,2,5,4]=>12
[3,1,6,4,2,5]=>9
[3,1,6,4,5,2]=>12
[3,1,6,5,2,4]=>9
[3,1,6,5,4,2]=>5
[3,2,1,4,5,6]=>14
[3,2,1,4,6,5]=>9
[3,2,1,5,4,6]=>7
[3,2,1,5,6,4]=>9
[3,2,1,6,4,5]=>7
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>19
[3,2,4,1,6,5]=>12
[3,2,4,5,1,6]=>23
[3,2,4,5,6,1]=>28
[3,2,4,6,1,5]=>23
[3,2,4,6,5,1]=>14
[3,2,5,1,4,6]=>19
[3,2,5,1,6,4]=>12
[3,2,5,4,1,6]=>9
[3,2,5,4,6,1]=>12
[3,2,5,6,1,4]=>23
[3,2,5,6,4,1]=>14
[3,2,6,1,4,5]=>19
[3,2,6,1,5,4]=>12
[3,2,6,4,1,5]=>9
[3,2,6,4,5,1]=>12
[3,2,6,5,1,4]=>9
[3,2,6,5,4,1]=>5
[3,4,1,2,5,6]=>56
[3,4,1,2,6,5]=>37
[3,4,1,5,2,6]=>30
[3,4,1,5,6,2]=>37
[3,4,1,6,2,5]=>30
[3,4,1,6,5,2]=>18
[3,4,2,1,5,6]=>24
[3,4,2,1,6,5]=>15
[3,4,2,5,1,6]=>30
[3,4,2,5,6,1]=>37
[3,4,2,6,1,5]=>30
[3,4,2,6,5,1]=>18
[3,4,5,1,2,6]=>66
[3,4,5,1,6,2]=>43
[3,4,5,2,1,6]=>34
[3,4,5,2,6,1]=>43
[3,4,5,6,1,2]=>76
[3,4,5,6,2,1]=>48
[3,4,6,1,2,5]=>66
[3,4,6,1,5,2]=>43
[3,4,6,2,1,5]=>34
[3,4,6,2,5,1]=>43
[3,4,6,5,1,2]=>34
[3,4,6,5,2,1]=>20
[3,5,1,2,4,6]=>56
[3,5,1,2,6,4]=>37
[3,5,1,4,2,6]=>30
[3,5,1,4,6,2]=>37
[3,5,1,6,2,4]=>30
[3,5,1,6,4,2]=>18
[3,5,2,1,4,6]=>24
[3,5,2,1,6,4]=>15
[3,5,2,4,1,6]=>30
[3,5,2,4,6,1]=>37
[3,5,2,6,1,4]=>30
[3,5,2,6,4,1]=>18
[3,5,4,1,2,6]=>24
[3,5,4,1,6,2]=>15
[3,5,4,2,1,6]=>11
[3,5,4,2,6,1]=>15
[3,5,4,6,1,2]=>30
[3,5,4,6,2,1]=>18
[3,5,6,1,2,4]=>66
[3,5,6,1,4,2]=>43
[3,5,6,2,1,4]=>34
[3,5,6,2,4,1]=>43
[3,5,6,4,1,2]=>34
[3,5,6,4,2,1]=>20
[3,6,1,2,4,5]=>56
[3,6,1,2,5,4]=>37
[3,6,1,4,2,5]=>30
[3,6,1,4,5,2]=>37
[3,6,1,5,2,4]=>30
[3,6,1,5,4,2]=>18
[3,6,2,1,4,5]=>24
[3,6,2,1,5,4]=>15
[3,6,2,4,1,5]=>30
[3,6,2,4,5,1]=>37
[3,6,2,5,1,4]=>30
[3,6,2,5,4,1]=>18
[3,6,4,1,2,5]=>24
[3,6,4,1,5,2]=>15
[3,6,4,2,1,5]=>11
[3,6,4,2,5,1]=>15
[3,6,4,5,1,2]=>30
[3,6,4,5,2,1]=>18
[3,6,5,1,2,4]=>24
[3,6,5,1,4,2]=>15
[3,6,5,2,1,4]=>11
[3,6,5,2,4,1]=>15
[3,6,5,4,1,2]=>11
[3,6,5,4,2,1]=>6
[4,1,2,3,5,6]=>42
[4,1,2,3,6,5]=>28
[4,1,2,5,3,6]=>23
[4,1,2,5,6,3]=>28
[4,1,2,6,3,5]=>23
[4,1,2,6,5,3]=>14
[4,1,3,2,5,6]=>19
[4,1,3,2,6,5]=>12
[4,1,3,5,2,6]=>23
[4,1,3,5,6,2]=>28
[4,1,3,6,2,5]=>23
[4,1,3,6,5,2]=>14
[4,1,5,2,3,6]=>19
[4,1,5,2,6,3]=>12
[4,1,5,3,2,6]=>9
[4,1,5,3,6,2]=>12
[4,1,5,6,2,3]=>23
[4,1,5,6,3,2]=>14
[4,1,6,2,3,5]=>19
[4,1,6,2,5,3]=>12
[4,1,6,3,2,5]=>9
[4,1,6,3,5,2]=>12
[4,1,6,5,2,3]=>9
[4,1,6,5,3,2]=>5
[4,2,1,3,5,6]=>14
[4,2,1,3,6,5]=>9
[4,2,1,5,3,6]=>7
[4,2,1,5,6,3]=>9
[4,2,1,6,3,5]=>7
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>19
[4,2,3,1,6,5]=>12
[4,2,3,5,1,6]=>23
[4,2,3,5,6,1]=>28
[4,2,3,6,1,5]=>23
[4,2,3,6,5,1]=>14
[4,2,5,1,3,6]=>19
[4,2,5,1,6,3]=>12
[4,2,5,3,1,6]=>9
[4,2,5,3,6,1]=>12
[4,2,5,6,1,3]=>23
[4,2,5,6,3,1]=>14
[4,2,6,1,3,5]=>19
[4,2,6,1,5,3]=>12
[4,2,6,3,1,5]=>9
[4,2,6,3,5,1]=>12
[4,2,6,5,1,3]=>9
[4,2,6,5,3,1]=>5
[4,3,1,2,5,6]=>14
[4,3,1,2,6,5]=>9
[4,3,1,5,2,6]=>7
[4,3,1,5,6,2]=>9
[4,3,1,6,2,5]=>7
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>5
[4,3,2,1,6,5]=>3
[4,3,2,5,1,6]=>7
[4,3,2,5,6,1]=>9
[4,3,2,6,1,5]=>7
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>19
[4,3,5,1,6,2]=>12
[4,3,5,2,1,6]=>9
[4,3,5,2,6,1]=>12
[4,3,5,6,1,2]=>23
[4,3,5,6,2,1]=>14
[4,3,6,1,2,5]=>19
[4,3,6,1,5,2]=>12
[4,3,6,2,1,5]=>9
[4,3,6,2,5,1]=>12
[4,3,6,5,1,2]=>9
[4,3,6,5,2,1]=>5
[4,5,1,2,3,6]=>56
[4,5,1,2,6,3]=>37
[4,5,1,3,2,6]=>30
[4,5,1,3,6,2]=>37
[4,5,1,6,2,3]=>30
[4,5,1,6,3,2]=>18
[4,5,2,1,3,6]=>24
[4,5,2,1,6,3]=>15
[4,5,2,3,1,6]=>30
[4,5,2,3,6,1]=>37
[4,5,2,6,1,3]=>30
[4,5,2,6,3,1]=>18
[4,5,3,1,2,6]=>24
[4,5,3,1,6,2]=>15
[4,5,3,2,1,6]=>11
[4,5,3,2,6,1]=>15
[4,5,3,6,1,2]=>30
[4,5,3,6,2,1]=>18
[4,5,6,1,2,3]=>66
[4,5,6,1,3,2]=>43
[4,5,6,2,1,3]=>34
[4,5,6,2,3,1]=>43
[4,5,6,3,1,2]=>34
[4,5,6,3,2,1]=>20
[4,6,1,2,3,5]=>56
[4,6,1,2,5,3]=>37
[4,6,1,3,2,5]=>30
[4,6,1,3,5,2]=>37
[4,6,1,5,2,3]=>30
[4,6,1,5,3,2]=>18
[4,6,2,1,3,5]=>24
[4,6,2,1,5,3]=>15
[4,6,2,3,1,5]=>30
[4,6,2,3,5,1]=>37
[4,6,2,5,1,3]=>30
[4,6,2,5,3,1]=>18
[4,6,3,1,2,5]=>24
[4,6,3,1,5,2]=>15
[4,6,3,2,1,5]=>11
[4,6,3,2,5,1]=>15
[4,6,3,5,1,2]=>30
[4,6,3,5,2,1]=>18
[4,6,5,1,2,3]=>24
[4,6,5,1,3,2]=>15
[4,6,5,2,1,3]=>11
[4,6,5,2,3,1]=>15
[4,6,5,3,1,2]=>11
[4,6,5,3,2,1]=>6
[5,1,2,3,4,6]=>42
[5,1,2,3,6,4]=>28
[5,1,2,4,3,6]=>23
[5,1,2,4,6,3]=>28
[5,1,2,6,3,4]=>23
[5,1,2,6,4,3]=>14
[5,1,3,2,4,6]=>19
[5,1,3,2,6,4]=>12
[5,1,3,4,2,6]=>23
[5,1,3,4,6,2]=>28
[5,1,3,6,2,4]=>23
[5,1,3,6,4,2]=>14
[5,1,4,2,3,6]=>19
[5,1,4,2,6,3]=>12
[5,1,4,3,2,6]=>9
[5,1,4,3,6,2]=>12
[5,1,4,6,2,3]=>23
[5,1,4,6,3,2]=>14
[5,1,6,2,3,4]=>19
[5,1,6,2,4,3]=>12
[5,1,6,3,2,4]=>9
[5,1,6,3,4,2]=>12
[5,1,6,4,2,3]=>9
[5,1,6,4,3,2]=>5
[5,2,1,3,4,6]=>14
[5,2,1,3,6,4]=>9
[5,2,1,4,3,6]=>7
[5,2,1,4,6,3]=>9
[5,2,1,6,3,4]=>7
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>19
[5,2,3,1,6,4]=>12
[5,2,3,4,1,6]=>23
[5,2,3,4,6,1]=>28
[5,2,3,6,1,4]=>23
[5,2,3,6,4,1]=>14
[5,2,4,1,3,6]=>19
[5,2,4,1,6,3]=>12
[5,2,4,3,1,6]=>9
[5,2,4,3,6,1]=>12
[5,2,4,6,1,3]=>23
[5,2,4,6,3,1]=>14
[5,2,6,1,3,4]=>19
[5,2,6,1,4,3]=>12
[5,2,6,3,1,4]=>9
[5,2,6,3,4,1]=>12
[5,2,6,4,1,3]=>9
[5,2,6,4,3,1]=>5
[5,3,1,2,4,6]=>14
[5,3,1,2,6,4]=>9
[5,3,1,4,2,6]=>7
[5,3,1,4,6,2]=>9
[5,3,1,6,2,4]=>7
[5,3,1,6,4,2]=>4
[5,3,2,1,4,6]=>5
[5,3,2,1,6,4]=>3
[5,3,2,4,1,6]=>7
[5,3,2,4,6,1]=>9
[5,3,2,6,1,4]=>7
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>19
[5,3,4,1,6,2]=>12
[5,3,4,2,1,6]=>9
[5,3,4,2,6,1]=>12
[5,3,4,6,1,2]=>23
[5,3,4,6,2,1]=>14
[5,3,6,1,2,4]=>19
[5,3,6,1,4,2]=>12
[5,3,6,2,1,4]=>9
[5,3,6,2,4,1]=>12
[5,3,6,4,1,2]=>9
[5,3,6,4,2,1]=>5
[5,4,1,2,3,6]=>14
[5,4,1,2,6,3]=>9
[5,4,1,3,2,6]=>7
[5,4,1,3,6,2]=>9
[5,4,1,6,2,3]=>7
[5,4,1,6,3,2]=>4
[5,4,2,1,3,6]=>5
[5,4,2,1,6,3]=>3
[5,4,2,3,1,6]=>7
[5,4,2,3,6,1]=>9
[5,4,2,6,1,3]=>7
[5,4,2,6,3,1]=>4
[5,4,3,1,2,6]=>5
[5,4,3,1,6,2]=>3
[5,4,3,2,1,6]=>2
[5,4,3,2,6,1]=>3
[5,4,3,6,1,2]=>7
[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>19
[5,4,6,1,3,2]=>12
[5,4,6,2,1,3]=>9
[5,4,6,2,3,1]=>12
[5,4,6,3,1,2]=>9
[5,4,6,3,2,1]=>5
[5,6,1,2,3,4]=>56
[5,6,1,2,4,3]=>37
[5,6,1,3,2,4]=>30
[5,6,1,3,4,2]=>37
[5,6,1,4,2,3]=>30
[5,6,1,4,3,2]=>18
[5,6,2,1,3,4]=>24
[5,6,2,1,4,3]=>15
[5,6,2,3,1,4]=>30
[5,6,2,3,4,1]=>37
[5,6,2,4,1,3]=>30
[5,6,2,4,3,1]=>18
[5,6,3,1,2,4]=>24
[5,6,3,1,4,2]=>15
[5,6,3,2,1,4]=>11
[5,6,3,2,4,1]=>15
[5,6,3,4,1,2]=>30
[5,6,3,4,2,1]=>18
[5,6,4,1,2,3]=>24
[5,6,4,1,3,2]=>15
[5,6,4,2,1,3]=>11
[5,6,4,2,3,1]=>15
[5,6,4,3,1,2]=>11
[5,6,4,3,2,1]=>6
[6,1,2,3,4,5]=>42
[6,1,2,3,5,4]=>28
[6,1,2,4,3,5]=>23
[6,1,2,4,5,3]=>28
[6,1,2,5,3,4]=>23
[6,1,2,5,4,3]=>14
[6,1,3,2,4,5]=>19
[6,1,3,2,5,4]=>12
[6,1,3,4,2,5]=>23
[6,1,3,4,5,2]=>28
[6,1,3,5,2,4]=>23
[6,1,3,5,4,2]=>14
[6,1,4,2,3,5]=>19
[6,1,4,2,5,3]=>12
[6,1,4,3,2,5]=>9
[6,1,4,3,5,2]=>12
[6,1,4,5,2,3]=>23
[6,1,4,5,3,2]=>14
[6,1,5,2,3,4]=>19
[6,1,5,2,4,3]=>12
[6,1,5,3,2,4]=>9
[6,1,5,3,4,2]=>12
[6,1,5,4,2,3]=>9
[6,1,5,4,3,2]=>5
[6,2,1,3,4,5]=>14
[6,2,1,3,5,4]=>9
[6,2,1,4,3,5]=>7
[6,2,1,4,5,3]=>9
[6,2,1,5,3,4]=>7
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>19
[6,2,3,1,5,4]=>12
[6,2,3,4,1,5]=>23
[6,2,3,4,5,1]=>28
[6,2,3,5,1,4]=>23
[6,2,3,5,4,1]=>14
[6,2,4,1,3,5]=>19
[6,2,4,1,5,3]=>12
[6,2,4,3,1,5]=>9
[6,2,4,3,5,1]=>12
[6,2,4,5,1,3]=>23
[6,2,4,5,3,1]=>14
[6,2,5,1,3,4]=>19
[6,2,5,1,4,3]=>12
[6,2,5,3,1,4]=>9
[6,2,5,3,4,1]=>12
[6,2,5,4,1,3]=>9
[6,2,5,4,3,1]=>5
[6,3,1,2,4,5]=>14
[6,3,1,2,5,4]=>9
[6,3,1,4,2,5]=>7
[6,3,1,4,5,2]=>9
[6,3,1,5,2,4]=>7
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>5
[6,3,2,1,5,4]=>3
[6,3,2,4,1,5]=>7
[6,3,2,4,5,1]=>9
[6,3,2,5,1,4]=>7
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>19
[6,3,4,1,5,2]=>12
[6,3,4,2,1,5]=>9
[6,3,4,2,5,1]=>12
[6,3,4,5,1,2]=>23
[6,3,4,5,2,1]=>14
[6,3,5,1,2,4]=>19
[6,3,5,1,4,2]=>12
[6,3,5,2,1,4]=>9
[6,3,5,2,4,1]=>12
[6,3,5,4,1,2]=>9
[6,3,5,4,2,1]=>5
[6,4,1,2,3,5]=>14
[6,4,1,2,5,3]=>9
[6,4,1,3,2,5]=>7
[6,4,1,3,5,2]=>9
[6,4,1,5,2,3]=>7
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>5
[6,4,2,1,5,3]=>3
[6,4,2,3,1,5]=>7
[6,4,2,3,5,1]=>9
[6,4,2,5,1,3]=>7
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>5
[6,4,3,1,5,2]=>3
[6,4,3,2,1,5]=>2
[6,4,3,2,5,1]=>3
[6,4,3,5,1,2]=>7
[6,4,3,5,2,1]=>4
[6,4,5,1,2,3]=>19
[6,4,5,1,3,2]=>12
[6,4,5,2,1,3]=>9
[6,4,5,2,3,1]=>12
[6,4,5,3,1,2]=>9
[6,4,5,3,2,1]=>5
[6,5,1,2,3,4]=>14
[6,5,1,2,4,3]=>9
[6,5,1,3,2,4]=>7
[6,5,1,3,4,2]=>9
[6,5,1,4,2,3]=>7
[6,5,1,4,3,2]=>4
[6,5,2,1,3,4]=>5
[6,5,2,1,4,3]=>3
[6,5,2,3,1,4]=>7
[6,5,2,3,4,1]=>9
[6,5,2,4,1,3]=>7
[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>5
[6,5,3,1,4,2]=>3
[6,5,3,2,1,4]=>2
[6,5,3,2,4,1]=>3
[6,5,3,4,1,2]=>7
[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>5
[6,5,4,1,3,2]=>3
[6,5,4,2,1,3]=>2
[6,5,4,2,3,1]=>3
[6,5,4,3,1,2]=>2
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>429
[1,2,3,4,5,7,6]=>297
[1,2,3,4,6,5,7]=>255
[1,2,3,4,6,7,5]=>297
[1,2,3,4,7,5,6]=>255
[1,2,3,4,7,6,5]=>165
[1,2,3,5,4,6,7]=>227
[1,2,3,5,4,7,6]=>151
[1,2,3,5,6,4,7]=>255
[1,2,3,5,6,7,4]=>297
[1,2,3,5,7,4,6]=>255
[1,2,3,5,7,6,4]=>165
[1,2,3,6,4,5,7]=>227
[1,2,3,6,4,7,5]=>151
[1,2,3,6,5,4,7]=>123
[1,2,3,6,5,7,4]=>151
[1,2,3,6,7,4,5]=>255
[1,2,3,6,7,5,4]=>165
[1,2,3,7,4,5,6]=>227
[1,2,3,7,4,6,5]=>151
[1,2,3,7,5,4,6]=>123
[1,2,3,7,5,6,4]=>151
[1,2,3,7,6,4,5]=>123
[1,2,3,7,6,5,4]=>75
[1,2,4,3,5,6,7]=>202
[1,2,4,3,5,7,6]=>136
[1,2,4,3,6,5,7]=>113
[1,2,4,3,6,7,5]=>136
[1,2,4,3,7,5,6]=>113
[1,2,4,3,7,6,5]=>70
[1,2,4,5,3,6,7]=>227
[1,2,4,5,3,7,6]=>151
[1,2,4,5,6,3,7]=>255
[1,2,4,5,6,7,3]=>297
[1,2,4,5,7,3,6]=>255
[1,2,4,5,7,6,3]=>165
[1,2,4,6,3,5,7]=>227
[1,2,4,6,3,7,5]=>151
[1,2,4,6,5,3,7]=>123
[1,2,4,6,5,7,3]=>151
[1,2,4,6,7,3,5]=>255
[1,2,4,6,7,5,3]=>165
[1,2,4,7,3,5,6]=>227
[1,2,4,7,3,6,5]=>151
[1,2,4,7,5,3,6]=>123
[1,2,4,7,5,6,3]=>151
[1,2,4,7,6,3,5]=>123
[1,2,4,7,6,5,3]=>75
[1,2,5,3,4,6,7]=>202
[1,2,5,3,4,7,6]=>136
[1,2,5,3,6,4,7]=>113
[1,2,5,3,6,7,4]=>136
[1,2,5,3,7,4,6]=>113
[1,2,5,3,7,6,4]=>70
[1,2,5,4,3,6,7]=>95
[1,2,5,4,3,7,6]=>61
[1,2,5,4,6,3,7]=>113
[1,2,5,4,6,7,3]=>136
[1,2,5,4,7,3,6]=>113
[1,2,5,4,7,6,3]=>70
[1,2,5,6,3,4,7]=>227
[1,2,5,6,3,7,4]=>151
[1,2,5,6,4,3,7]=>123
[1,2,5,6,4,7,3]=>151
[1,2,5,6,7,3,4]=>255
[1,2,5,6,7,4,3]=>165
[1,2,5,7,3,4,6]=>227
[1,2,5,7,3,6,4]=>151
[1,2,5,7,4,3,6]=>123
[1,2,5,7,4,6,3]=>151
[1,2,5,7,6,3,4]=>123
[1,2,5,7,6,4,3]=>75
[1,2,6,3,4,5,7]=>202
[1,2,6,3,4,7,5]=>136
[1,2,6,3,5,4,7]=>113
[1,2,6,3,5,7,4]=>136
[1,2,6,3,7,4,5]=>113
[1,2,6,3,7,5,4]=>70
[1,2,6,4,3,5,7]=>95
[1,2,6,4,3,7,5]=>61
[1,2,6,4,5,3,7]=>113
[1,2,6,4,5,7,3]=>136
[1,2,6,4,7,3,5]=>113
[1,2,6,4,7,5,3]=>70
[1,2,6,5,3,4,7]=>95
[1,2,6,5,3,7,4]=>61
[1,2,6,5,4,3,7]=>47
[1,2,6,5,4,7,3]=>61
[1,2,6,5,7,3,4]=>113
[1,2,6,5,7,4,3]=>70
[1,2,6,7,3,4,5]=>227
[1,2,6,7,3,5,4]=>151
[1,2,6,7,4,3,5]=>123
[1,2,6,7,4,5,3]=>151
[1,2,6,7,5,3,4]=>123
[1,2,6,7,5,4,3]=>75
[1,2,7,3,4,5,6]=>202
[1,2,7,3,4,6,5]=>136
[1,2,7,3,5,4,6]=>113
[1,2,7,3,5,6,4]=>136
[1,2,7,3,6,4,5]=>113
[1,2,7,3,6,5,4]=>70
[1,2,7,4,3,5,6]=>95
[1,2,7,4,3,6,5]=>61
[1,2,7,4,5,3,6]=>113
[1,2,7,4,5,6,3]=>136
[1,2,7,4,6,3,5]=>113
[1,2,7,4,6,5,3]=>70
[1,2,7,5,3,4,6]=>95
[1,2,7,5,3,6,4]=>61
[1,2,7,5,4,3,6]=>47
[1,2,7,5,4,6,3]=>61
[1,2,7,5,6,3,4]=>113
[1,2,7,5,6,4,3]=>70
[1,2,7,6,3,4,5]=>95
[1,2,7,6,3,5,4]=>61
[1,2,7,6,4,3,5]=>47
[1,2,7,6,4,5,3]=>61
[1,2,7,6,5,3,4]=>47
[1,2,7,6,5,4,3]=>27
[1,3,2,4,5,6,7]=>174
[1,3,2,4,5,7,6]=>118
[1,3,2,4,6,5,7]=>99
[1,3,2,4,6,7,5]=>118
[1,3,2,4,7,5,6]=>99
[1,3,2,4,7,6,5]=>62
[1,3,2,5,4,6,7]=>85
[1,3,2,5,4,7,6]=>55
[1,3,2,5,6,4,7]=>99
[1,3,2,5,6,7,4]=>118
[1,3,2,5,7,4,6]=>99
[1,3,2,5,7,6,4]=>62
[1,3,2,6,4,5,7]=>85
[1,3,2,6,4,7,5]=>55
[1,3,2,6,5,4,7]=>43
[1,3,2,6,5,7,4]=>55
[1,3,2,6,7,4,5]=>99
[1,3,2,6,7,5,4]=>62
[1,3,2,7,4,5,6]=>85
[1,3,2,7,4,6,5]=>55
[1,3,2,7,5,4,6]=>43
[1,3,2,7,5,6,4]=>55
[1,3,2,7,6,4,5]=>43
[1,3,2,7,6,5,4]=>25
[1,3,4,2,5,6,7]=>202
[1,3,4,2,5,7,6]=>136
[1,3,4,2,6,5,7]=>113
[1,3,4,2,6,7,5]=>136
[1,3,4,2,7,5,6]=>113
[1,3,4,2,7,6,5]=>70
[1,3,4,5,2,6,7]=>227
[1,3,4,5,2,7,6]=>151
[1,3,4,5,6,2,7]=>255
[1,3,4,5,6,7,2]=>297
[1,3,4,5,7,2,6]=>255
[1,3,4,5,7,6,2]=>165
[1,3,4,6,2,5,7]=>227
[1,3,4,6,2,7,5]=>151
[1,3,4,6,5,2,7]=>123
[1,3,4,6,5,7,2]=>151
[1,3,4,6,7,2,5]=>255
[1,3,4,6,7,5,2]=>165
[1,3,4,7,2,5,6]=>227
[1,3,4,7,2,6,5]=>151
[1,3,4,7,5,2,6]=>123
[1,3,4,7,5,6,2]=>151
[1,3,4,7,6,2,5]=>123
[1,3,4,7,6,5,2]=>75
[1,3,5,2,4,6,7]=>202
[1,3,5,2,4,7,6]=>136
[1,3,5,2,6,4,7]=>113
[1,3,5,2,6,7,4]=>136
[1,3,5,2,7,4,6]=>113
[1,3,5,2,7,6,4]=>70
[1,3,5,4,2,6,7]=>95
[1,3,5,4,2,7,6]=>61
[1,3,5,4,6,2,7]=>113
[1,3,5,4,6,7,2]=>136
[1,3,5,4,7,2,6]=>113
[1,3,5,4,7,6,2]=>70
[1,3,5,6,2,4,7]=>227
[1,3,5,6,2,7,4]=>151
[1,3,5,6,4,2,7]=>123
[1,3,5,6,4,7,2]=>151
[1,3,5,6,7,2,4]=>255
[1,3,5,6,7,4,2]=>165
[1,3,5,7,2,4,6]=>227
[1,3,5,7,2,6,4]=>151
[1,3,5,7,4,2,6]=>123
[1,3,5,7,4,6,2]=>151
[1,3,5,7,6,2,4]=>123
[1,3,5,7,6,4,2]=>75
[1,3,6,2,4,5,7]=>202
[1,3,6,2,4,7,5]=>136
[1,3,6,2,5,4,7]=>113
[1,3,6,2,5,7,4]=>136
[1,3,6,2,7,4,5]=>113
[1,3,6,2,7,5,4]=>70
[1,3,6,4,2,5,7]=>95
[1,3,6,4,2,7,5]=>61
[1,3,6,4,5,2,7]=>113
[1,3,6,4,5,7,2]=>136
[1,3,6,4,7,2,5]=>113
[1,3,6,4,7,5,2]=>70
[1,3,6,5,2,4,7]=>95
[1,3,6,5,2,7,4]=>61
[1,3,6,5,4,2,7]=>47
[1,3,6,5,4,7,2]=>61
[1,3,6,5,7,2,4]=>113
[1,3,6,5,7,4,2]=>70
[1,3,6,7,2,4,5]=>227
[1,3,6,7,2,5,4]=>151
[1,3,6,7,4,2,5]=>123
[1,3,6,7,4,5,2]=>151
[1,3,6,7,5,2,4]=>123
[1,3,6,7,5,4,2]=>75
[1,3,7,2,4,5,6]=>202
[1,3,7,2,4,6,5]=>136
[1,3,7,2,5,4,6]=>113
[1,3,7,2,5,6,4]=>136
[1,3,7,2,6,4,5]=>113
[1,3,7,2,6,5,4]=>70
[1,3,7,4,2,5,6]=>95
[1,3,7,4,2,6,5]=>61
[1,3,7,4,5,2,6]=>113
[1,3,7,4,5,6,2]=>136
[1,3,7,4,6,2,5]=>113
[1,3,7,4,6,5,2]=>70
[1,3,7,5,2,4,6]=>95
[1,3,7,5,2,6,4]=>61
[1,3,7,5,4,2,6]=>47
[1,3,7,5,4,6,2]=>61
[1,3,7,5,6,2,4]=>113
[1,3,7,5,6,4,2]=>70
[1,3,7,6,2,4,5]=>95
[1,3,7,6,2,5,4]=>61
[1,3,7,6,4,2,5]=>47
[1,3,7,6,4,5,2]=>61
[1,3,7,6,5,2,4]=>47
[1,3,7,6,5,4,2]=>27
[1,4,2,3,5,6,7]=>174
[1,4,2,3,5,7,6]=>118
[1,4,2,3,6,5,7]=>99
[1,4,2,3,6,7,5]=>118
[1,4,2,3,7,5,6]=>99
[1,4,2,3,7,6,5]=>62
[1,4,2,5,3,6,7]=>85
[1,4,2,5,3,7,6]=>55
[1,4,2,5,6,3,7]=>99
[1,4,2,5,6,7,3]=>118
[1,4,2,5,7,3,6]=>99
[1,4,2,5,7,6,3]=>62
[1,4,2,6,3,5,7]=>85
[1,4,2,6,3,7,5]=>55
[1,4,2,6,5,3,7]=>43
[1,4,2,6,5,7,3]=>55
[1,4,2,6,7,3,5]=>99
[1,4,2,6,7,5,3]=>62
[1,4,2,7,3,5,6]=>85
[1,4,2,7,3,6,5]=>55
[1,4,2,7,5,3,6]=>43
[1,4,2,7,5,6,3]=>55
[1,4,2,7,6,3,5]=>43
[1,4,2,7,6,5,3]=>25
[1,4,3,2,5,6,7]=>70
[1,4,3,2,5,7,6]=>46
[1,4,3,2,6,5,7]=>37
[1,4,3,2,6,7,5]=>46
[1,4,3,2,7,5,6]=>37
[1,4,3,2,7,6,5]=>22
[1,4,3,5,2,6,7]=>85
[1,4,3,5,2,7,6]=>55
[1,4,3,5,6,2,7]=>99
[1,4,3,5,6,7,2]=>118
[1,4,3,5,7,2,6]=>99
[1,4,3,5,7,6,2]=>62
[1,4,3,6,2,5,7]=>85
[1,4,3,6,2,7,5]=>55
[1,4,3,6,5,2,7]=>43
[1,4,3,6,5,7,2]=>55
[1,4,3,6,7,2,5]=>99
[1,4,3,6,7,5,2]=>62
[1,4,3,7,2,5,6]=>85
[1,4,3,7,2,6,5]=>55
[1,4,3,7,5,2,6]=>43
[1,4,3,7,5,6,2]=>55
[1,4,3,7,6,2,5]=>43
[1,4,3,7,6,5,2]=>25
[1,4,5,2,3,6,7]=>202
[1,4,5,2,3,7,6]=>136
[1,4,5,2,6,3,7]=>113
[1,4,5,2,6,7,3]=>136
[1,4,5,2,7,3,6]=>113
[1,4,5,2,7,6,3]=>70
[1,4,5,3,2,6,7]=>95
[1,4,5,3,2,7,6]=>61
[1,4,5,3,6,2,7]=>113
[1,4,5,3,6,7,2]=>136
[1,4,5,3,7,2,6]=>113
[1,4,5,3,7,6,2]=>70
[1,4,5,6,2,3,7]=>227
[1,4,5,6,2,7,3]=>151
[1,4,5,6,3,2,7]=>123
[1,4,5,6,3,7,2]=>151
[1,4,5,6,7,2,3]=>255
[1,4,5,6,7,3,2]=>165
[1,4,5,7,2,3,6]=>227
[1,4,5,7,2,6,3]=>151
[1,4,5,7,3,2,6]=>123
[1,4,5,7,3,6,2]=>151
[1,4,5,7,6,2,3]=>123
[1,4,5,7,6,3,2]=>75
[1,4,6,2,3,5,7]=>202
[1,4,6,2,3,7,5]=>136
[1,4,6,2,5,3,7]=>113
[1,4,6,2,5,7,3]=>136
[1,4,6,2,7,3,5]=>113
[1,4,6,2,7,5,3]=>70
[1,4,6,3,2,5,7]=>95
[1,4,6,3,2,7,5]=>61
[1,4,6,3,5,2,7]=>113
[1,4,6,3,5,7,2]=>136
[1,4,6,3,7,2,5]=>113
[1,4,6,3,7,5,2]=>70
[1,4,6,5,2,3,7]=>95
[1,4,6,5,2,7,3]=>61
[1,4,6,5,3,2,7]=>47
[1,4,6,5,3,7,2]=>61
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Description
The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations.
Code
def to_labelling_permutation(elt):
from sage.combinat.words.word import Word
return Word(elt).standard_permutation().inverse()
@cached_function
def preimages(level):
result = dict()
for el in ParkingFunctions(level):
image = to_labelling_permutation(el)
result[image] = result.get(image, 0) + 1
return result
def statistic(x):
return preimages(x.size()).get(x, 0)
Created
Sep 11, 2015 at 22:08 by Martin Rubey
Updated
Feb 09, 2021 at 14:35 by Martin Rubey
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