Identifier
- St000040: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>1
[2,1]=>2
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>4
[3,1,2]=>4
[3,2,1]=>6
[1,2,3,4]=>1
[1,2,4,3]=>2
[1,3,2,4]=>2
[1,3,4,2]=>4
[1,4,2,3]=>4
[1,4,3,2]=>6
[2,1,3,4]=>2
[2,1,4,3]=>4
[2,3,1,4]=>4
[2,3,4,1]=>8
[2,4,1,3]=>8
[2,4,3,1]=>12
[3,1,2,4]=>4
[3,1,4,2]=>8
[3,2,1,4]=>6
[3,2,4,1]=>12
[3,4,1,2]=>14
[3,4,2,1]=>18
[4,1,2,3]=>8
[4,1,3,2]=>12
[4,2,1,3]=>12
[4,2,3,1]=>18
[4,3,1,2]=>18
[4,3,2,1]=>24
[1,2,3,4,5]=>1
[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]=>6
[1,3,2,4,5]=>2
[1,3,2,5,4]=>4
[1,3,4,2,5]=>4
[1,3,4,5,2]=>8
[1,3,5,2,4]=>8
[1,3,5,4,2]=>12
[1,4,2,3,5]=>4
[1,4,2,5,3]=>8
[1,4,3,2,5]=>6
[1,4,3,5,2]=>12
[1,4,5,2,3]=>14
[1,4,5,3,2]=>18
[1,5,2,3,4]=>8
[1,5,2,4,3]=>12
[1,5,3,2,4]=>12
[1,5,3,4,2]=>18
[1,5,4,2,3]=>18
[1,5,4,3,2]=>24
[2,1,3,4,5]=>2
[2,1,3,5,4]=>4
[2,1,4,3,5]=>4
[2,1,4,5,3]=>8
[2,1,5,3,4]=>8
[2,1,5,4,3]=>12
[2,3,1,4,5]=>4
[2,3,1,5,4]=>8
[2,3,4,1,5]=>8
[2,3,4,5,1]=>16
[2,3,5,1,4]=>16
[2,3,5,4,1]=>24
[2,4,1,3,5]=>8
[2,4,1,5,3]=>16
[2,4,3,1,5]=>12
[2,4,3,5,1]=>24
[2,4,5,1,3]=>28
[2,4,5,3,1]=>36
[2,5,1,3,4]=>16
[2,5,1,4,3]=>24
[2,5,3,1,4]=>24
[2,5,3,4,1]=>36
[2,5,4,1,3]=>36
[2,5,4,3,1]=>48
[3,1,2,4,5]=>4
[3,1,2,5,4]=>8
[3,1,4,2,5]=>8
[3,1,4,5,2]=>16
[3,1,5,2,4]=>16
[3,1,5,4,2]=>24
[3,2,1,4,5]=>6
[3,2,1,5,4]=>12
[3,2,4,1,5]=>12
[3,2,4,5,1]=>24
[3,2,5,1,4]=>24
[3,2,5,4,1]=>36
[3,4,1,2,5]=>14
[3,4,1,5,2]=>28
[3,4,2,1,5]=>18
[3,4,2,5,1]=>36
[3,4,5,1,2]=>46
[3,4,5,2,1]=>54
[3,5,1,2,4]=>28
[3,5,1,4,2]=>42
[3,5,2,1,4]=>36
[3,5,2,4,1]=>54
[3,5,4,1,2]=>60
[3,5,4,2,1]=>72
[4,1,2,3,5]=>8
[4,1,2,5,3]=>16
[4,1,3,2,5]=>12
[4,1,3,5,2]=>24
[4,1,5,2,3]=>28
[4,1,5,3,2]=>36
[4,2,1,3,5]=>12
[4,2,1,5,3]=>24
[4,2,3,1,5]=>18
[4,2,3,5,1]=>36
[4,2,5,1,3]=>42
[4,2,5,3,1]=>54
[4,3,1,2,5]=>18
[4,3,1,5,2]=>36
[4,3,2,1,5]=>24
[4,3,2,5,1]=>48
[4,3,5,1,2]=>60
[4,3,5,2,1]=>72
[4,5,1,2,3]=>46
[4,5,1,3,2]=>60
[4,5,2,1,3]=>60
[4,5,2,3,1]=>78
[4,5,3,1,2]=>78
[4,5,3,2,1]=>96
[5,1,2,3,4]=>16
[5,1,2,4,3]=>24
[5,1,3,2,4]=>24
[5,1,3,4,2]=>36
[5,1,4,2,3]=>36
[5,1,4,3,2]=>48
[5,2,1,3,4]=>24
[5,2,1,4,3]=>36
[5,2,3,1,4]=>36
[5,2,3,4,1]=>54
[5,2,4,1,3]=>54
[5,2,4,3,1]=>72
[5,3,1,2,4]=>36
[5,3,1,4,2]=>54
[5,3,2,1,4]=>48
[5,3,2,4,1]=>72
[5,3,4,1,2]=>78
[5,3,4,2,1]=>96
[5,4,1,2,3]=>54
[5,4,1,3,2]=>72
[5,4,2,1,3]=>72
[5,4,2,3,1]=>96
[5,4,3,1,2]=>96
[5,4,3,2,1]=>120
[1,2,3,4,5,6]=>1
[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]=>6
[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]=>8
[1,2,4,6,3,5]=>8
[1,2,4,6,5,3]=>12
[1,2,5,3,4,6]=>4
[1,2,5,3,6,4]=>8
[1,2,5,4,3,6]=>6
[1,2,5,4,6,3]=>12
[1,2,5,6,3,4]=>14
[1,2,5,6,4,3]=>18
[1,2,6,3,4,5]=>8
[1,2,6,3,5,4]=>12
[1,2,6,4,3,5]=>12
[1,2,6,4,5,3]=>18
[1,2,6,5,3,4]=>18
[1,2,6,5,4,3]=>24
[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]=>8
[1,3,2,6,4,5]=>8
[1,3,2,6,5,4]=>12
[1,3,4,2,5,6]=>4
[1,3,4,2,6,5]=>8
[1,3,4,5,2,6]=>8
[1,3,4,5,6,2]=>16
[1,3,4,6,2,5]=>16
[1,3,4,6,5,2]=>24
[1,3,5,2,4,6]=>8
[1,3,5,2,6,4]=>16
[1,3,5,4,2,6]=>12
[1,3,5,4,6,2]=>24
[1,3,5,6,2,4]=>28
[1,3,5,6,4,2]=>36
[1,3,6,2,4,5]=>16
[1,3,6,2,5,4]=>24
[1,3,6,4,2,5]=>24
[1,3,6,4,5,2]=>36
[1,3,6,5,2,4]=>36
[1,3,6,5,4,2]=>48
[1,4,2,3,5,6]=>4
[1,4,2,3,6,5]=>8
[1,4,2,5,3,6]=>8
[1,4,2,5,6,3]=>16
[1,4,2,6,3,5]=>16
[1,4,2,6,5,3]=>24
[1,4,3,2,5,6]=>6
[1,4,3,2,6,5]=>12
[1,4,3,5,2,6]=>12
[1,4,3,5,6,2]=>24
[1,4,3,6,2,5]=>24
[1,4,3,6,5,2]=>36
[1,4,5,2,3,6]=>14
[1,4,5,2,6,3]=>28
[1,4,5,3,2,6]=>18
[1,4,5,3,6,2]=>36
[1,4,5,6,2,3]=>46
[1,4,5,6,3,2]=>54
[1,4,6,2,3,5]=>28
[1,4,6,2,5,3]=>42
[1,4,6,3,2,5]=>36
[1,4,6,3,5,2]=>54
[1,4,6,5,2,3]=>60
[1,4,6,5,3,2]=>72
[1,5,2,3,4,6]=>8
[1,5,2,3,6,4]=>16
[1,5,2,4,3,6]=>12
[1,5,2,4,6,3]=>24
[1,5,2,6,3,4]=>28
[1,5,2,6,4,3]=>36
[1,5,3,2,4,6]=>12
[1,5,3,2,6,4]=>24
[1,5,3,4,2,6]=>18
[1,5,3,4,6,2]=>36
[1,5,3,6,2,4]=>42
[1,5,3,6,4,2]=>54
[1,5,4,2,3,6]=>18
[1,5,4,2,6,3]=>36
[1,5,4,3,2,6]=>24
[1,5,4,3,6,2]=>48
[1,5,4,6,2,3]=>60
[1,5,4,6,3,2]=>72
[1,5,6,2,3,4]=>46
[1,5,6,2,4,3]=>60
[1,5,6,3,2,4]=>60
[1,5,6,3,4,2]=>78
[1,5,6,4,2,3]=>78
[1,5,6,4,3,2]=>96
[1,6,2,3,4,5]=>16
[1,6,2,3,5,4]=>24
[1,6,2,4,3,5]=>24
[1,6,2,4,5,3]=>36
[1,6,2,5,3,4]=>36
[1,6,2,5,4,3]=>48
[1,6,3,2,4,5]=>24
[1,6,3,2,5,4]=>36
[1,6,3,4,2,5]=>36
[1,6,3,4,5,2]=>54
[1,6,3,5,2,4]=>54
[1,6,3,5,4,2]=>72
[1,6,4,2,3,5]=>36
[1,6,4,2,5,3]=>54
[1,6,4,3,2,5]=>48
[1,6,4,3,5,2]=>72
[1,6,4,5,2,3]=>78
[1,6,4,5,3,2]=>96
[1,6,5,2,3,4]=>54
[1,6,5,2,4,3]=>72
[1,6,5,3,2,4]=>72
[1,6,5,3,4,2]=>96
[1,6,5,4,2,3]=>96
[1,6,5,4,3,2]=>120
[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]=>8
[2,1,3,6,4,5]=>8
[2,1,3,6,5,4]=>12
[2,1,4,3,5,6]=>4
[2,1,4,3,6,5]=>8
[2,1,4,5,3,6]=>8
[2,1,4,5,6,3]=>16
[2,1,4,6,3,5]=>16
[2,1,4,6,5,3]=>24
[2,1,5,3,4,6]=>8
[2,1,5,3,6,4]=>16
[2,1,5,4,3,6]=>12
[2,1,5,4,6,3]=>24
[2,1,5,6,3,4]=>28
[2,1,5,6,4,3]=>36
[2,1,6,3,4,5]=>16
[2,1,6,3,5,4]=>24
[2,1,6,4,3,5]=>24
[2,1,6,4,5,3]=>36
[2,1,6,5,3,4]=>36
[2,1,6,5,4,3]=>48
[2,3,1,4,5,6]=>4
[2,3,1,4,6,5]=>8
[2,3,1,5,4,6]=>8
[2,3,1,5,6,4]=>16
[2,3,1,6,4,5]=>16
[2,3,1,6,5,4]=>24
[2,3,4,1,5,6]=>8
[2,3,4,1,6,5]=>16
[2,3,4,5,1,6]=>16
[2,3,4,5,6,1]=>32
[2,3,4,6,1,5]=>32
[2,3,4,6,5,1]=>48
[2,3,5,1,4,6]=>16
[2,3,5,1,6,4]=>32
[2,3,5,4,1,6]=>24
[2,3,5,4,6,1]=>48
[2,3,5,6,1,4]=>56
[2,3,5,6,4,1]=>72
[2,3,6,1,4,5]=>32
[2,3,6,1,5,4]=>48
[2,3,6,4,1,5]=>48
[2,3,6,4,5,1]=>72
[2,3,6,5,1,4]=>72
[2,3,6,5,4,1]=>96
[2,4,1,3,5,6]=>8
[2,4,1,3,6,5]=>16
[2,4,1,5,3,6]=>16
[2,4,1,5,6,3]=>32
[2,4,1,6,3,5]=>32
[2,4,1,6,5,3]=>48
[2,4,3,1,5,6]=>12
[2,4,3,1,6,5]=>24
[2,4,3,5,1,6]=>24
[2,4,3,5,6,1]=>48
[2,4,3,6,1,5]=>48
[2,4,3,6,5,1]=>72
[2,4,5,1,3,6]=>28
[2,4,5,1,6,3]=>56
[2,4,5,3,1,6]=>36
[2,4,5,3,6,1]=>72
[2,4,5,6,1,3]=>92
[2,4,5,6,3,1]=>108
[2,4,6,1,3,5]=>56
[2,4,6,1,5,3]=>84
[2,4,6,3,1,5]=>72
[2,4,6,3,5,1]=>108
[2,4,6,5,1,3]=>120
[2,4,6,5,3,1]=>144
[2,5,1,3,4,6]=>16
[2,5,1,3,6,4]=>32
[2,5,1,4,3,6]=>24
[2,5,1,4,6,3]=>48
[2,5,1,6,3,4]=>56
[2,5,1,6,4,3]=>72
[2,5,3,1,4,6]=>24
[2,5,3,1,6,4]=>48
[2,5,3,4,1,6]=>36
[2,5,3,4,6,1]=>72
[2,5,3,6,1,4]=>84
[2,5,3,6,4,1]=>108
[2,5,4,1,3,6]=>36
[2,5,4,1,6,3]=>72
[2,5,4,3,1,6]=>48
[2,5,4,3,6,1]=>96
[2,5,4,6,1,3]=>120
[2,5,4,6,3,1]=>144
[2,5,6,1,3,4]=>92
[2,5,6,1,4,3]=>120
[2,5,6,3,1,4]=>120
[2,5,6,3,4,1]=>156
[2,5,6,4,1,3]=>156
[2,5,6,4,3,1]=>192
[2,6,1,3,4,5]=>32
[2,6,1,3,5,4]=>48
[2,6,1,4,3,5]=>48
[2,6,1,4,5,3]=>72
[2,6,1,5,3,4]=>72
[2,6,1,5,4,3]=>96
[2,6,3,1,4,5]=>48
[2,6,3,1,5,4]=>72
[2,6,3,4,1,5]=>72
[2,6,3,4,5,1]=>108
[2,6,3,5,1,4]=>108
[2,6,3,5,4,1]=>144
[2,6,4,1,3,5]=>72
[2,6,4,1,5,3]=>108
[2,6,4,3,1,5]=>96
[2,6,4,3,5,1]=>144
[2,6,4,5,1,3]=>156
[2,6,4,5,3,1]=>192
[2,6,5,1,3,4]=>108
[2,6,5,1,4,3]=>144
[2,6,5,3,1,4]=>144
[2,6,5,3,4,1]=>192
[2,6,5,4,1,3]=>192
[2,6,5,4,3,1]=>240
[3,1,2,4,5,6]=>4
[3,1,2,4,6,5]=>8
[3,1,2,5,4,6]=>8
[3,1,2,5,6,4]=>16
[3,1,2,6,4,5]=>16
[3,1,2,6,5,4]=>24
[3,1,4,2,5,6]=>8
[3,1,4,2,6,5]=>16
[3,1,4,5,2,6]=>16
[3,1,4,5,6,2]=>32
[3,1,4,6,2,5]=>32
[3,1,4,6,5,2]=>48
[3,1,5,2,4,6]=>16
[3,1,5,2,6,4]=>32
[3,1,5,4,2,6]=>24
[3,1,5,4,6,2]=>48
[3,1,5,6,2,4]=>56
[3,1,5,6,4,2]=>72
[3,1,6,2,4,5]=>32
[3,1,6,2,5,4]=>48
[3,1,6,4,2,5]=>48
[3,1,6,4,5,2]=>72
[3,1,6,5,2,4]=>72
[3,1,6,5,4,2]=>96
[3,2,1,4,5,6]=>6
[3,2,1,4,6,5]=>12
[3,2,1,5,4,6]=>12
[3,2,1,5,6,4]=>24
[3,2,1,6,4,5]=>24
[3,2,1,6,5,4]=>36
[3,2,4,1,5,6]=>12
[3,2,4,1,6,5]=>24
[3,2,4,5,1,6]=>24
[3,2,4,5,6,1]=>48
[3,2,4,6,1,5]=>48
[3,2,4,6,5,1]=>72
[3,2,5,1,4,6]=>24
[3,2,5,1,6,4]=>48
[3,2,5,4,1,6]=>36
[3,2,5,4,6,1]=>72
[3,2,5,6,1,4]=>84
[3,2,5,6,4,1]=>108
[3,2,6,1,4,5]=>48
[3,2,6,1,5,4]=>72
[3,2,6,4,1,5]=>72
[3,2,6,4,5,1]=>108
[3,2,6,5,1,4]=>108
[3,2,6,5,4,1]=>144
[3,4,1,2,5,6]=>14
[3,4,1,2,6,5]=>28
[3,4,1,5,2,6]=>28
[3,4,1,5,6,2]=>56
[3,4,1,6,2,5]=>56
[3,4,1,6,5,2]=>84
[3,4,2,1,5,6]=>18
[3,4,2,1,6,5]=>36
[3,4,2,5,1,6]=>36
[3,4,2,5,6,1]=>72
[3,4,2,6,1,5]=>72
[3,4,2,6,5,1]=>108
[3,4,5,1,2,6]=>46
[3,4,5,1,6,2]=>92
[3,4,5,2,1,6]=>54
[3,4,5,2,6,1]=>108
[3,4,5,6,1,2]=>146
[3,4,5,6,2,1]=>162
[3,4,6,1,2,5]=>92
[3,4,6,1,5,2]=>138
[3,4,6,2,1,5]=>108
[3,4,6,2,5,1]=>162
[3,4,6,5,1,2]=>192
[3,4,6,5,2,1]=>216
[3,5,1,2,4,6]=>28
[3,5,1,2,6,4]=>56
[3,5,1,4,2,6]=>42
[3,5,1,4,6,2]=>84
[3,5,1,6,2,4]=>98
[3,5,1,6,4,2]=>126
[3,5,2,1,4,6]=>36
[3,5,2,1,6,4]=>72
[3,5,2,4,1,6]=>54
[3,5,2,4,6,1]=>108
[3,5,2,6,1,4]=>126
[3,5,2,6,4,1]=>162
[3,5,4,1,2,6]=>60
[3,5,4,1,6,2]=>120
[3,5,4,2,1,6]=>72
[3,5,4,2,6,1]=>144
[3,5,4,6,1,2]=>192
[3,5,4,6,2,1]=>216
[3,5,6,1,2,4]=>152
[3,5,6,1,4,2]=>198
[3,5,6,2,1,4]=>180
[3,5,6,2,4,1]=>234
[3,5,6,4,1,2]=>252
[3,5,6,4,2,1]=>288
[3,6,1,2,4,5]=>56
[3,6,1,2,5,4]=>84
[3,6,1,4,2,5]=>84
[3,6,1,4,5,2]=>126
[3,6,1,5,2,4]=>126
[3,6,1,5,4,2]=>168
[3,6,2,1,4,5]=>72
[3,6,2,1,5,4]=>108
[3,6,2,4,1,5]=>108
[3,6,2,4,5,1]=>162
[3,6,2,5,1,4]=>162
[3,6,2,5,4,1]=>216
[3,6,4,1,2,5]=>120
[3,6,4,1,5,2]=>180
[3,6,4,2,1,5]=>144
[3,6,4,2,5,1]=>216
[3,6,4,5,1,2]=>252
[3,6,4,5,2,1]=>288
[3,6,5,1,2,4]=>180
[3,6,5,1,4,2]=>240
[3,6,5,2,1,4]=>216
[3,6,5,2,4,1]=>288
[3,6,5,4,1,2]=>312
[3,6,5,4,2,1]=>360
[4,1,2,3,5,6]=>8
[4,1,2,3,6,5]=>16
[4,1,2,5,3,6]=>16
[4,1,2,5,6,3]=>32
[4,1,2,6,3,5]=>32
[4,1,2,6,5,3]=>48
[4,1,3,2,5,6]=>12
[4,1,3,2,6,5]=>24
[4,1,3,5,2,6]=>24
[4,1,3,5,6,2]=>48
[4,1,3,6,2,5]=>48
[4,1,3,6,5,2]=>72
[4,1,5,2,3,6]=>28
[4,1,5,2,6,3]=>56
[4,1,5,3,2,6]=>36
[4,1,5,3,6,2]=>72
[4,1,5,6,2,3]=>92
[4,1,5,6,3,2]=>108
[4,1,6,2,3,5]=>56
[4,1,6,2,5,3]=>84
[4,1,6,3,2,5]=>72
[4,1,6,3,5,2]=>108
[4,1,6,5,2,3]=>120
[4,1,6,5,3,2]=>144
[4,2,1,3,5,6]=>12
[4,2,1,3,6,5]=>24
[4,2,1,5,3,6]=>24
[4,2,1,5,6,3]=>48
[4,2,1,6,3,5]=>48
[4,2,1,6,5,3]=>72
[4,2,3,1,5,6]=>18
[4,2,3,1,6,5]=>36
[4,2,3,5,1,6]=>36
[4,2,3,5,6,1]=>72
[4,2,3,6,1,5]=>72
[4,2,3,6,5,1]=>108
[4,2,5,1,3,6]=>42
[4,2,5,1,6,3]=>84
[4,2,5,3,1,6]=>54
[4,2,5,3,6,1]=>108
[4,2,5,6,1,3]=>138
[4,2,5,6,3,1]=>162
[4,2,6,1,3,5]=>84
[4,2,6,1,5,3]=>126
[4,2,6,3,1,5]=>108
[4,2,6,3,5,1]=>162
[4,2,6,5,1,3]=>180
[4,2,6,5,3,1]=>216
[4,3,1,2,5,6]=>18
[4,3,1,2,6,5]=>36
[4,3,1,5,2,6]=>36
[4,3,1,5,6,2]=>72
[4,3,1,6,2,5]=>72
[4,3,1,6,5,2]=>108
[4,3,2,1,5,6]=>24
[4,3,2,1,6,5]=>48
[4,3,2,5,1,6]=>48
[4,3,2,5,6,1]=>96
[4,3,2,6,1,5]=>96
[4,3,2,6,5,1]=>144
[4,3,5,1,2,6]=>60
[4,3,5,1,6,2]=>120
[4,3,5,2,1,6]=>72
[4,3,5,2,6,1]=>144
[4,3,5,6,1,2]=>192
[4,3,5,6,2,1]=>216
[4,3,6,1,2,5]=>120
[4,3,6,1,5,2]=>180
[4,3,6,2,1,5]=>144
[4,3,6,2,5,1]=>216
[4,3,6,5,1,2]=>252
[4,3,6,5,2,1]=>288
[4,5,1,2,3,6]=>46
[4,5,1,2,6,3]=>92
[4,5,1,3,2,6]=>60
[4,5,1,3,6,2]=>120
[4,5,1,6,2,3]=>152
[4,5,1,6,3,2]=>180
[4,5,2,1,3,6]=>60
[4,5,2,1,6,3]=>120
[4,5,2,3,1,6]=>78
[4,5,2,3,6,1]=>156
[4,5,2,6,1,3]=>198
[4,5,2,6,3,1]=>234
[4,5,3,1,2,6]=>78
[4,5,3,1,6,2]=>156
[4,5,3,2,1,6]=>96
[4,5,3,2,6,1]=>192
[4,5,3,6,1,2]=>252
[4,5,3,6,2,1]=>288
[4,5,6,1,2,3]=>230
[4,5,6,1,3,2]=>276
[4,5,6,2,1,3]=>276
[4,5,6,2,3,1]=>330
[4,5,6,3,1,2]=>330
[4,5,6,3,2,1]=>384
[4,6,1,2,3,5]=>92
[4,6,1,2,5,3]=>138
[4,6,1,3,5,2]=>180
[4,6,1,5,2,3]=>198
[4,6,1,5,3,2]=>240
[4,6,2,1,3,5]=>120
[4,6,2,1,5,3]=>180
[4,6,2,3,1,5]=>156
[4,6,2,3,5,1]=>234
[4,6,2,5,1,3]=>258
[4,6,2,5,3,1]=>312
[4,6,3,1,2,5]=>156
[4,6,3,1,5,2]=>234
[4,6,3,2,1,5]=>192
[4,6,3,2,5,1]=>288
[4,6,3,5,1,2]=>330
[4,6,3,5,2,1]=>384
[4,6,5,1,2,3]=>276
[4,6,5,1,3,2]=>336
[4,6,5,2,1,3]=>336
[4,6,5,2,3,1]=>408
[4,6,5,3,1,2]=>408
[4,6,5,3,2,1]=>480
[5,1,2,3,4,6]=>16
[5,1,2,3,6,4]=>32
[5,1,2,4,3,6]=>24
[5,1,2,4,6,3]=>48
[5,1,2,6,3,4]=>56
[5,1,2,6,4,3]=>72
[5,1,3,2,4,6]=>24
[5,1,3,2,6,4]=>48
[5,1,3,4,2,6]=>36
[5,1,3,4,6,2]=>72
[5,1,3,6,2,4]=>84
[5,1,3,6,4,2]=>108
[5,1,4,2,3,6]=>36
[5,1,4,2,6,3]=>72
[5,1,4,3,2,6]=>48
[5,1,4,6,2,3]=>120
[5,1,4,6,3,2]=>144
[5,1,6,2,3,4]=>92
[5,1,6,2,4,3]=>120
[5,1,6,3,2,4]=>120
[5,1,6,3,4,2]=>156
[5,1,6,4,2,3]=>156
[5,1,6,4,3,2]=>192
[5,2,1,3,4,6]=>24
[5,2,1,3,6,4]=>48
[5,2,1,4,3,6]=>36
[5,2,1,4,6,3]=>72
[5,2,1,6,3,4]=>84
[5,2,1,6,4,3]=>108
[5,2,3,1,4,6]=>36
[5,2,3,1,6,4]=>72
[5,2,3,4,1,6]=>54
[5,2,3,4,6,1]=>108
[5,2,3,6,1,4]=>126
[5,2,3,6,4,1]=>162
[5,2,4,1,3,6]=>54
[5,2,4,1,6,3]=>108
[5,2,4,3,1,6]=>72
[5,2,4,3,6,1]=>144
[5,2,4,6,1,3]=>180
[5,2,4,6,3,1]=>216
[5,2,6,1,3,4]=>138
[5,2,6,1,4,3]=>180
[5,2,6,3,1,4]=>180
[5,2,6,3,4,1]=>234
[5,2,6,4,1,3]=>234
[5,2,6,4,3,1]=>288
[5,3,1,2,4,6]=>36
[5,3,1,2,6,4]=>72
[5,3,1,4,2,6]=>54
[5,3,1,4,6,2]=>108
[5,3,1,6,2,4]=>126
[5,3,1,6,4,2]=>162
[5,3,2,1,4,6]=>48
[5,3,2,1,6,4]=>96
[5,3,2,4,1,6]=>72
[5,3,2,4,6,1]=>144
[5,3,2,6,1,4]=>168
[5,3,2,6,4,1]=>216
[5,3,4,1,2,6]=>78
[5,3,4,1,6,2]=>156
[5,3,4,2,1,6]=>96
[5,3,4,2,6,1]=>192
[5,3,4,6,1,2]=>252
[5,3,4,6,2,1]=>288
[5,3,6,1,2,4]=>198
[5,3,6,1,4,2]=>258
[5,3,6,2,1,4]=>240
[5,3,6,2,4,1]=>312
[5,3,6,4,1,2]=>330
[5,3,6,4,2,1]=>384
[5,4,1,2,3,6]=>54
[5,4,1,2,6,3]=>108
[5,4,1,3,2,6]=>72
[5,4,1,3,6,2]=>144
[5,4,1,6,2,3]=>180
[5,4,1,6,3,2]=>216
[5,4,2,1,3,6]=>72
[5,4,2,1,6,3]=>144
[5,4,2,3,1,6]=>96
[5,4,2,3,6,1]=>192
[5,4,2,6,1,3]=>240
[5,4,2,6,3,1]=>288
[5,4,3,1,2,6]=>96
[5,4,3,1,6,2]=>192
[5,4,3,2,1,6]=>120
[5,4,3,2,6,1]=>240
[5,4,3,6,1,2]=>312
[5,4,3,6,2,1]=>360
[5,4,6,1,2,3]=>276
[5,4,6,1,3,2]=>336
[5,4,6,2,1,3]=>336
[5,4,6,2,3,1]=>408
[5,4,6,3,1,2]=>408
[5,4,6,3,2,1]=>480
[5,6,1,2,3,4]=>146
[5,6,1,2,4,3]=>192
[5,6,1,3,2,4]=>192
[5,6,1,3,4,2]=>252
[5,6,1,4,2,3]=>252
[5,6,1,4,3,2]=>312
[5,6,2,1,3,4]=>192
[5,6,2,1,4,3]=>252
[5,6,2,3,1,4]=>252
[5,6,2,3,4,1]=>330
[5,6,2,4,1,3]=>330
[5,6,2,4,3,1]=>408
[5,6,3,1,2,4]=>252
[5,6,3,1,4,2]=>330
[5,6,3,2,1,4]=>312
[5,6,3,2,4,1]=>408
[5,6,3,4,1,2]=>426
[5,6,3,4,2,1]=>504
[5,6,4,1,2,3]=>330
[5,6,4,1,3,2]=>408
[5,6,4,2,1,3]=>408
[5,6,4,2,3,1]=>504
[5,6,4,3,1,2]=>504
[5,6,4,3,2,1]=>600
[6,1,2,3,4,5]=>32
[6,1,2,3,5,4]=>48
[6,1,2,4,3,5]=>48
[6,1,2,4,5,3]=>72
[6,1,2,5,3,4]=>72
[6,1,2,5,4,3]=>96
[6,1,3,2,4,5]=>48
[6,1,3,2,5,4]=>72
[6,1,3,4,2,5]=>72
[6,1,3,4,5,2]=>108
[6,1,3,5,2,4]=>108
[6,1,3,5,4,2]=>144
[6,1,4,2,3,5]=>72
[6,1,4,2,5,3]=>108
[6,1,4,3,2,5]=>96
[6,1,4,3,5,2]=>144
[6,1,4,5,2,3]=>156
[6,1,4,5,3,2]=>192
[6,1,5,2,3,4]=>108
[6,1,5,2,4,3]=>144
[6,1,5,3,2,4]=>144
[6,1,5,3,4,2]=>192
[6,1,5,4,2,3]=>192
[6,1,5,4,3,2]=>240
[6,2,1,3,4,5]=>48
[6,2,1,3,5,4]=>72
[6,2,1,4,3,5]=>72
[6,2,1,4,5,3]=>108
[6,2,1,5,3,4]=>108
[6,2,1,5,4,3]=>144
[6,2,3,1,4,5]=>72
[6,2,3,1,5,4]=>108
[6,2,3,4,1,5]=>108
[6,2,3,4,5,1]=>162
[6,2,3,5,1,4]=>162
[6,2,3,5,4,1]=>216
[6,2,4,1,3,5]=>108
[6,2,4,1,5,3]=>162
[6,2,4,3,1,5]=>144
[6,2,4,3,5,1]=>216
[6,2,4,5,1,3]=>234
[6,2,4,5,3,1]=>288
[6,2,5,1,3,4]=>162
[6,2,5,1,4,3]=>216
[6,2,5,3,1,4]=>216
[6,2,5,3,4,1]=>288
[6,2,5,4,1,3]=>288
[6,2,5,4,3,1]=>360
[6,3,1,2,4,5]=>72
[6,3,1,2,5,4]=>108
[6,3,1,4,2,5]=>108
[6,3,1,4,5,2]=>162
[6,3,1,5,2,4]=>162
[6,3,1,5,4,2]=>216
[6,3,2,1,4,5]=>96
[6,3,2,1,5,4]=>144
[6,3,2,4,1,5]=>144
[6,3,2,4,5,1]=>216
[6,3,2,5,1,4]=>216
[6,3,2,5,4,1]=>288
[6,3,4,1,2,5]=>156
[6,3,4,1,5,2]=>234
[6,3,4,2,1,5]=>192
[6,3,4,2,5,1]=>288
[6,3,4,5,1,2]=>330
[6,3,4,5,2,1]=>384
[6,3,5,1,2,4]=>234
[6,3,5,1,4,2]=>312
[6,3,5,2,1,4]=>288
[6,3,5,2,4,1]=>384
[6,3,5,4,1,2]=>408
[6,3,5,4,2,1]=>480
[6,4,1,2,3,5]=>108
[6,4,1,2,5,3]=>162
[6,4,1,3,2,5]=>144
[6,4,1,3,5,2]=>216
[6,4,1,5,2,3]=>234
[6,4,1,5,3,2]=>288
[6,4,2,1,3,5]=>144
[6,4,2,1,5,3]=>216
[6,4,2,3,1,5]=>192
[6,4,2,3,5,1]=>288
[6,4,2,5,1,3]=>312
[6,4,2,5,3,1]=>384
[6,4,3,1,2,5]=>192
[6,4,3,1,5,2]=>288
[6,4,3,2,1,5]=>240
[6,4,3,2,5,1]=>360
[6,4,3,5,1,2]=>408
[6,4,3,5,2,1]=>480
[6,4,5,1,2,3]=>330
[6,4,5,1,3,2]=>408
[6,4,5,2,1,3]=>408
[6,4,5,2,3,1]=>504
[6,4,5,3,1,2]=>504
[6,4,5,3,2,1]=>600
[6,5,1,2,3,4]=>162
[6,5,1,2,4,3]=>216
[6,5,1,3,2,4]=>216
[6,5,1,3,4,2]=>288
[6,5,1,4,2,3]=>288
[6,5,1,4,3,2]=>360
[6,5,2,1,3,4]=>216
[6,5,2,1,4,3]=>288
[6,5,2,3,1,4]=>288
[6,5,2,3,4,1]=>384
[6,5,2,4,1,3]=>384
[6,5,2,4,3,1]=>480
[6,5,3,1,2,4]=>288
[6,5,3,1,4,2]=>384
[6,5,3,2,1,4]=>360
[6,5,3,2,4,1]=>480
[6,5,3,4,1,2]=>504
[6,5,3,4,2,1]=>600
[6,5,4,1,2,3]=>384
[6,5,4,1,3,2]=>480
[6,5,4,2,1,3]=>480
[6,5,4,2,3,1]=>600
[6,5,4,3,1,2]=>600
[6,5,4,3,2,1]=>720
[1,2,3,4,5,6,7]=>1
[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]=>6
[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]=>8
[1,2,3,5,7,4,6]=>8
[1,2,3,5,7,6,4]=>12
[1,2,3,6,4,5,7]=>4
[1,2,3,6,4,7,5]=>8
[1,2,3,6,7,4,5]=>14
[1,2,3,6,7,5,4]=>18
[1,2,3,7,4,5,6]=>8
[1,2,3,7,4,6,5]=>12
[1,2,3,7,5,4,6]=>12
[1,2,3,7,5,6,4]=>18
[1,2,3,7,6,4,5]=>18
[1,2,3,7,6,5,4]=>24
[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]=>8
[1,2,4,3,7,5,6]=>8
[1,2,4,3,7,6,5]=>12
[1,2,4,5,3,6,7]=>4
[1,2,4,5,3,7,6]=>8
[1,2,4,5,6,3,7]=>8
[1,2,4,5,6,7,3]=>16
[1,2,4,5,7,3,6]=>16
[1,2,4,5,7,6,3]=>24
[1,2,4,6,3,5,7]=>8
[1,2,4,6,3,7,5]=>16
[1,2,4,6,7,3,5]=>28
[1,2,4,6,7,5,3]=>36
[1,2,4,7,3,5,6]=>16
[1,2,4,7,5,6,3]=>36
[1,2,4,7,6,5,3]=>48
[1,2,5,3,4,6,7]=>4
[1,2,5,3,4,7,6]=>8
[1,2,5,3,6,4,7]=>8
[1,2,5,3,6,7,4]=>16
[1,2,5,3,7,4,6]=>16
[1,2,5,4,3,7,6]=>12
[1,2,5,4,6,7,3]=>24
[1,2,5,6,3,4,7]=>14
[1,2,5,6,3,7,4]=>28
[1,2,5,6,7,3,4]=>46
[1,2,5,6,7,4,3]=>54
[1,2,5,7,3,4,6]=>28
[1,2,5,7,3,6,4]=>42
[1,2,5,7,4,3,6]=>36
[1,2,5,7,6,3,4]=>60
[1,2,5,7,6,4,3]=>72
[1,2,6,3,4,5,7]=>8
[1,2,6,3,4,7,5]=>16
[1,2,6,3,5,7,4]=>24
[1,2,6,3,7,4,5]=>28
[1,2,6,3,7,5,4]=>36
[1,2,6,4,3,7,5]=>24
[1,2,6,4,7,3,5]=>42
[1,2,6,5,3,7,4]=>36
[1,2,6,5,4,7,3]=>48
[1,2,6,5,7,3,4]=>60
[1,2,6,7,3,4,5]=>46
[1,2,6,7,4,3,5]=>60
[1,2,6,7,4,5,3]=>78
[1,2,6,7,5,3,4]=>78
[1,2,6,7,5,4,3]=>96
[1,2,7,3,4,5,6]=>16
[1,2,7,3,4,6,5]=>24
[1,2,7,3,5,4,6]=>24
[1,2,7,3,5,6,4]=>36
[1,2,7,3,6,5,4]=>48
[1,2,7,4,3,5,6]=>24
[1,2,7,4,3,6,5]=>36
[1,2,7,4,5,3,6]=>36
[1,2,7,4,5,6,3]=>54
[1,2,7,5,3,4,6]=>36
[1,2,7,5,6,3,4]=>78
[1,2,7,5,6,4,3]=>96
[1,2,7,6,3,4,5]=>54
[1,2,7,6,3,5,4]=>72
[1,2,7,6,4,3,5]=>72
[1,2,7,6,4,5,3]=>96
[1,2,7,6,5,3,4]=>96
[1,2,7,6,5,4,3]=>120
[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]=>8
[1,3,2,4,7,5,6]=>8
[1,3,2,4,7,6,5]=>12
[1,3,2,5,4,6,7]=>4
[1,3,2,5,4,7,6]=>8
[1,3,2,5,6,4,7]=>8
[1,3,2,5,6,7,4]=>16
[1,3,2,5,7,4,6]=>16
[1,3,2,6,4,5,7]=>8
[1,3,2,6,4,7,5]=>16
[1,3,2,6,7,4,5]=>28
[1,3,2,7,4,5,6]=>16
[1,3,4,2,5,6,7]=>4
[1,3,4,2,5,7,6]=>8
[1,3,4,2,6,5,7]=>8
[1,3,4,2,6,7,5]=>16
[1,3,4,2,7,5,6]=>16
[1,3,4,2,7,6,5]=>24
[1,3,4,5,2,6,7]=>8
[1,3,4,5,2,7,6]=>16
[1,3,4,5,6,2,7]=>16
[1,3,4,5,6,7,2]=>32
[1,3,4,5,7,2,6]=>32
[1,3,4,5,7,6,2]=>48
[1,3,4,6,2,5,7]=>16
[1,3,4,6,2,7,5]=>32
[1,3,4,6,7,2,5]=>56
[1,3,4,6,7,5,2]=>72
[1,3,4,7,2,5,6]=>32
[1,3,4,7,2,6,5]=>48
[1,3,4,7,5,6,2]=>72
[1,3,4,7,6,5,2]=>96
[1,3,5,2,4,6,7]=>8
[1,3,5,2,4,7,6]=>16
[1,3,5,2,6,4,7]=>16
[1,3,5,2,6,7,4]=>32
[1,3,5,2,7,4,6]=>32
[1,3,5,2,7,6,4]=>48
[1,3,5,6,2,4,7]=>28
[1,3,5,6,2,7,4]=>56
[1,3,5,6,7,2,4]=>92
[1,3,5,6,7,4,2]=>108
[1,3,5,7,2,4,6]=>56
[1,3,5,7,2,6,4]=>84
[1,3,5,7,6,4,2]=>144
[1,3,6,2,4,5,7]=>16
[1,3,6,2,4,7,5]=>32
[1,3,6,2,5,7,4]=>48
[1,3,6,2,7,4,5]=>56
[1,3,6,4,2,7,5]=>48
[1,3,6,4,5,7,2]=>72
[1,3,6,7,2,4,5]=>92
[1,3,6,7,2,5,4]=>120
[1,3,6,7,4,5,2]=>156
[1,3,6,7,5,4,2]=>192
[1,3,7,2,4,5,6]=>32
[1,3,7,2,6,5,4]=>96
[1,3,7,4,2,6,5]=>72
[1,3,7,4,5,6,2]=>108
[1,3,7,5,2,4,6]=>72
[1,3,7,5,2,6,4]=>108
[1,3,7,5,6,4,2]=>192
[1,3,7,6,2,5,4]=>144
[1,3,7,6,4,5,2]=>192
[1,3,7,6,5,4,2]=>240
[1,4,2,3,5,6,7]=>4
[1,4,2,3,5,7,6]=>8
[1,4,2,3,6,5,7]=>8
[1,4,2,3,6,7,5]=>16
[1,4,2,3,7,5,6]=>16
[1,4,2,3,7,6,5]=>24
[1,4,2,5,3,6,7]=>8
[1,4,2,5,3,7,6]=>16
[1,4,2,5,6,3,7]=>16
[1,4,2,5,6,7,3]=>32
[1,4,2,5,7,3,6]=>32
[1,4,2,5,7,6,3]=>48
[1,4,2,6,3,5,7]=>16
[1,4,2,6,3,7,5]=>32
[1,4,2,6,7,3,5]=>56
[1,4,2,7,3,5,6]=>32
[1,4,2,7,3,6,5]=>48
[1,4,2,7,6,3,5]=>72
[1,4,2,7,6,5,3]=>96
[1,4,3,2,7,6,5]=>36
[1,4,3,5,6,7,2]=>48
[1,4,5,2,3,6,7]=>14
[1,4,5,2,3,7,6]=>28
[1,4,5,2,6,3,7]=>28
[1,4,5,2,6,7,3]=>56
[1,4,5,2,7,3,6]=>56
[1,4,5,2,7,6,3]=>84
[1,4,5,3,7,6,2]=>108
[1,4,5,6,2,3,7]=>46
[1,4,5,6,2,7,3]=>92
[1,4,5,6,7,2,3]=>146
[1,4,5,6,7,3,2]=>162
[1,4,5,7,2,3,6]=>92
[1,4,5,7,2,6,3]=>138
[1,4,5,7,6,2,3]=>192
[1,4,5,7,6,3,2]=>216
[1,4,6,2,3,5,7]=>28
[1,4,6,2,3,7,5]=>56
[1,4,6,2,7,3,5]=>98
[1,4,6,2,7,5,3]=>126
[1,4,6,7,2,3,5]=>152
[1,4,6,7,5,2,3]=>252
[1,4,6,7,5,3,2]=>288
[1,4,7,2,3,5,6]=>56
[1,4,7,2,3,6,5]=>84
[1,4,7,2,5,6,3]=>126
[1,4,7,2,6,5,3]=>168
[1,4,7,3,2,6,5]=>108
[1,4,7,3,5,2,6]=>108
[1,4,7,3,6,5,2]=>216
[1,4,7,5,6,2,3]=>252
[1,4,7,5,6,3,2]=>288
[1,4,7,6,2,5,3]=>240
[1,4,7,6,5,2,3]=>312
[1,4,7,6,5,3,2]=>360
[1,5,2,3,4,6,7]=>8
[1,5,2,3,4,7,6]=>16
[1,5,2,3,6,4,7]=>16
[1,5,2,3,6,7,4]=>32
[1,5,2,3,7,4,6]=>32
[1,5,2,3,7,6,4]=>48
[1,5,2,4,6,7,3]=>48
[1,5,2,4,7,6,3]=>72
[1,5,2,6,3,4,7]=>28
[1,5,2,6,3,7,4]=>56
[1,5,2,6,7,3,4]=>92
[1,5,2,6,7,4,3]=>108
[1,5,2,7,3,4,6]=>56
[1,5,2,7,3,6,4]=>84
[1,5,2,7,4,6,3]=>108
[1,5,2,7,6,4,3]=>144
[1,5,3,2,4,7,6]=>24
[1,5,3,2,6,7,4]=>48
[1,5,3,2,7,6,4]=>72
[1,5,3,4,2,7,6]=>36
[1,5,3,4,6,7,2]=>72
[1,5,3,4,7,6,2]=>108
[1,5,3,6,7,2,4]=>138
[1,5,3,7,2,4,6]=>84
[1,5,3,7,2,6,4]=>126
[1,5,3,7,4,6,2]=>162
[1,5,3,7,6,4,2]=>216
[1,5,4,2,7,6,3]=>108
[1,5,4,3,2,7,6]=>48
[1,5,4,3,7,6,2]=>144
[1,5,4,7,2,6,3]=>180
[1,5,4,7,6,3,2]=>288
[1,5,6,2,3,4,7]=>46
[1,5,6,2,3,7,4]=>92
[1,5,6,2,4,7,3]=>120
[1,5,6,2,7,3,4]=>152
[1,5,6,3,2,7,4]=>120
[1,5,6,3,4,7,2]=>156
[1,5,6,3,7,2,4]=>198
[1,5,6,4,7,2,3]=>252
[1,5,6,4,7,3,2]=>288
[1,5,6,7,2,3,4]=>230
[1,5,6,7,2,4,3]=>276
[1,5,6,7,3,2,4]=>276
[1,5,6,7,3,4,2]=>330
[1,5,6,7,4,2,3]=>330
[1,5,6,7,4,3,2]=>384
[1,5,7,2,3,4,6]=>92
[1,5,7,2,6,4,3]=>240
[1,5,7,3,2,6,4]=>180
[1,5,7,3,4,6,2]=>234
[1,5,7,3,6,4,2]=>312
[1,5,7,4,2,6,3]=>234
[1,5,7,4,6,2,3]=>330
[1,5,7,6,2,3,4]=>276
[1,5,7,6,2,4,3]=>336
[1,5,7,6,3,2,4]=>336
[1,5,7,6,3,4,2]=>408
[1,5,7,6,4,2,3]=>408
[1,5,7,6,4,3,2]=>480
[1,6,2,3,4,5,7]=>16
[1,6,2,3,4,7,5]=>32
[1,6,2,3,5,7,4]=>48
[1,6,2,3,7,4,5]=>56
[1,6,2,3,7,5,4]=>72
[1,6,2,4,7,5,3]=>108
[1,6,2,7,3,4,5]=>92
[1,6,2,7,5,4,3]=>192
[1,6,3,2,4,7,5]=>48
[1,6,3,2,5,7,4]=>72
[1,6,3,2,7,4,5]=>84
[1,6,3,2,7,5,4]=>108
[1,6,3,4,2,7,5]=>72
[1,6,3,4,5,7,2]=>108
[1,6,3,4,7,2,5]=>126
[1,6,3,5,2,7,4]=>108
[1,6,3,7,2,4,5]=>138
[1,6,3,7,2,5,4]=>180
[1,6,3,7,4,2,5]=>180
[1,6,3,7,4,5,2]=>234
[1,6,3,7,5,2,4]=>234
[1,6,4,2,3,7,5]=>72
[1,6,5,4,3,7,2]=>240
[1,6,5,4,7,3,2]=>360
[1,6,5,7,4,3,2]=>480
[1,6,7,2,3,4,5]=>146
[1,6,7,3,2,4,5]=>192
[1,6,7,3,4,2,5]=>252
[1,6,7,3,4,5,2]=>330
[1,6,7,3,5,2,4]=>330
[1,6,7,4,2,3,5]=>252
[1,6,7,4,3,2,5]=>312
[1,6,7,4,5,2,3]=>426
[1,6,7,4,5,3,2]=>504
[1,6,7,5,2,3,4]=>330
[1,6,7,5,3,2,4]=>408
[1,6,7,5,3,4,2]=>504
[1,6,7,5,4,2,3]=>504
[1,6,7,5,4,3,2]=>600
[1,7,2,3,4,5,6]=>32
[1,7,2,3,4,6,5]=>48
[1,7,2,3,6,5,4]=>96
[1,7,2,4,5,6,3]=>108
[1,7,2,5,6,3,4]=>156
[1,7,3,2,4,5,6]=>48
[1,7,3,2,4,6,5]=>72
[1,7,3,2,5,6,4]=>108
[1,7,3,2,6,4,5]=>108
[1,7,3,4,2,5,6]=>72
[1,7,3,4,2,6,5]=>108
[1,7,3,4,5,2,6]=>108
[1,7,3,4,5,6,2]=>162
[1,7,3,5,2,4,6]=>108
[1,7,3,5,6,4,2]=>288
[1,7,3,6,2,5,4]=>216
[1,7,3,6,5,4,2]=>360
[1,7,4,2,3,5,6]=>72
[1,7,4,2,3,6,5]=>108
[1,7,4,2,6,3,5]=>162
[1,7,4,2,6,5,3]=>216
[1,7,4,3,2,6,5]=>144
[1,7,4,3,6,5,2]=>288
[1,7,4,5,2,3,6]=>156
[1,7,4,5,2,6,3]=>234
[1,7,4,5,3,6,2]=>288
[1,7,4,5,6,2,3]=>330
[1,7,4,5,6,3,2]=>384
[1,7,4,6,2,5,3]=>312
[1,7,4,6,5,3,2]=>480
[1,7,5,2,3,4,6]=>108
[1,7,5,2,4,6,3]=>216
[1,7,5,3,2,4,6]=>144
[1,7,5,3,2,6,4]=>216
[1,7,5,4,3,6,2]=>360
[1,7,5,4,6,3,2]=>480
[1,7,5,6,2,3,4]=>330
[1,7,5,6,3,2,4]=>408
[1,7,5,6,3,4,2]=>504
[1,7,5,6,4,2,3]=>504
[1,7,5,6,4,3,2]=>600
[1,7,6,2,3,4,5]=>162
[1,7,6,2,5,4,3]=>360
[1,7,6,3,2,4,5]=>216
[1,7,6,3,2,5,4]=>288
[1,7,6,3,4,2,5]=>288
[1,7,6,3,4,5,2]=>384
[1,7,6,3,5,4,2]=>480
[1,7,6,4,2,3,5]=>288
[1,7,6,4,5,2,3]=>504
[1,7,6,4,5,3,2]=>600
[1,7,6,5,2,3,4]=>384
[1,7,6,5,2,4,3]=>480
[1,7,6,5,3,2,4]=>480
[1,7,6,5,3,4,2]=>600
[1,7,6,5,4,2,3]=>600
[1,7,6,5,4,3,2]=>720
[2,1,3,4,5,6,7]=>2
[2,1,3,4,5,7,6]=>4
[2,1,3,4,6,7,5]=>8
[2,1,3,4,7,5,6]=>8
[2,1,3,5,4,6,7]=>4
[2,1,3,5,7,6,4]=>24
[2,1,3,6,4,7,5]=>16
[2,1,3,6,7,4,5]=>28
[2,1,3,7,4,5,6]=>16
[2,1,3,7,5,4,6]=>24
[2,1,3,7,6,4,5]=>36
[2,1,3,7,6,5,4]=>48
[2,1,4,3,6,5,7]=>8
[2,1,4,5,6,3,7]=>16
[2,1,4,7,3,5,6]=>32
[2,1,4,7,3,6,5]=>48
[2,1,4,7,5,3,6]=>48
[2,1,4,7,5,6,3]=>72
[2,1,4,7,6,5,3]=>96
[2,1,5,3,4,7,6]=>16
[2,1,5,6,4,3,7]=>36
[2,1,5,6,7,3,4]=>92
[2,1,6,3,4,5,7]=>16
[2,1,6,3,4,7,5]=>32
[2,1,6,3,7,4,5]=>56
[2,1,6,4,5,3,7]=>36
[2,1,6,5,3,4,7]=>36
[2,1,6,5,4,3,7]=>48
[2,1,6,5,7,3,4]=>120
[2,1,6,7,3,4,5]=>92
[2,1,6,7,4,3,5]=>120
[2,1,6,7,5,3,4]=>156
[2,1,7,3,4,5,6]=>32
[2,1,7,3,4,6,5]=>48
[2,1,7,3,5,4,6]=>48
[2,1,7,3,6,4,5]=>72
[2,1,7,3,6,5,4]=>96
[2,1,7,5,3,4,6]=>72
[2,1,7,6,3,5,4]=>144
[2,1,7,6,5,3,4]=>192
[2,1,7,6,5,4,3]=>240
[2,3,1,4,5,6,7]=>4
[2,3,1,4,5,7,6]=>8
[2,3,1,4,7,6,5]=>24
[2,3,1,5,7,4,6]=>32
[2,3,1,6,4,7,5]=>32
[2,3,1,7,4,5,6]=>32
[2,3,1,7,4,6,5]=>48
[2,3,1,7,5,6,4]=>72
[2,3,4,1,5,6,7]=>8
[2,3,4,1,5,7,6]=>16
[2,3,4,1,7,6,5]=>48
[2,3,4,5,1,6,7]=>16
[2,3,4,5,1,7,6]=>32
[2,3,4,5,6,1,7]=>32
[2,3,4,5,6,7,1]=>64
[2,3,4,5,7,1,6]=>64
[2,3,4,5,7,6,1]=>96
[2,3,4,6,1,7,5]=>64
[2,3,4,6,5,7,1]=>96
[2,3,4,6,7,1,5]=>112
[2,3,4,6,7,5,1]=>144
[2,3,4,7,1,5,6]=>64
[2,3,4,7,1,6,5]=>96
[2,3,4,7,5,6,1]=>144
[2,3,4,7,6,1,5]=>144
[2,3,4,7,6,5,1]=>192
[2,3,5,1,6,7,4]=>64
[2,3,5,1,7,4,6]=>64
[2,3,5,1,7,6,4]=>96
[2,3,5,4,6,7,1]=>96
[2,3,5,4,7,6,1]=>144
[2,3,5,6,1,7,4]=>112
[2,3,5,6,4,7,1]=>144
[2,3,5,6,7,1,4]=>184
[2,3,5,6,7,4,1]=>216
[2,3,5,7,1,4,6]=>112
[2,3,5,7,1,6,4]=>168
[2,3,5,7,4,1,6]=>144
[2,3,5,7,6,1,4]=>240
[2,3,5,7,6,4,1]=>288
[2,3,6,1,4,7,5]=>64
[2,3,6,1,7,4,5]=>112
[2,3,6,1,7,5,4]=>144
[2,3,6,4,5,7,1]=>144
[2,3,6,4,7,5,1]=>216
[2,3,6,5,1,7,4]=>144
[2,3,6,5,4,7,1]=>192
[2,3,6,5,7,1,4]=>240
[2,3,6,5,7,4,1]=>288
[2,3,6,7,1,4,5]=>184
[2,3,6,7,4,5,1]=>312
[2,3,6,7,5,1,4]=>312
[2,3,6,7,5,4,1]=>384
[2,3,7,1,4,5,6]=>64
[2,3,7,1,4,6,5]=>96
[2,3,7,1,5,4,6]=>96
[2,3,7,1,5,6,4]=>144
[2,3,7,1,6,4,5]=>144
[2,3,7,4,5,6,1]=>216
[2,3,7,4,6,1,5]=>216
[2,3,7,4,6,5,1]=>288
[2,3,7,5,1,4,6]=>144
[2,3,7,5,4,1,6]=>192
[2,3,7,5,4,6,1]=>288
[2,3,7,5,6,1,4]=>312
[2,3,7,5,6,4,1]=>384
[2,3,7,6,1,4,5]=>216
[2,3,7,6,5,1,4]=>384
[2,3,7,6,5,4,1]=>480
[2,4,1,3,5,6,7]=>8
[2,4,1,3,7,5,6]=>32
[2,4,1,3,7,6,5]=>48
[2,4,1,5,3,7,6]=>32
[2,4,1,5,6,7,3]=>64
[2,4,1,5,7,3,6]=>64
[2,4,1,6,3,7,5]=>64
[2,4,1,6,7,3,5]=>112
[2,4,1,6,7,5,3]=>144
[2,4,1,7,3,5,6]=>64
[2,4,1,7,3,6,5]=>96
[2,4,1,7,6,3,5]=>144
[2,4,3,1,7,6,5]=>72
[2,4,3,5,6,7,1]=>96
[2,4,3,5,7,6,1]=>144
[2,4,3,6,5,7,1]=>144
[2,4,3,6,7,1,5]=>168
[2,4,3,6,7,5,1]=>216
[2,4,3,7,5,6,1]=>216
[2,4,3,7,6,5,1]=>288
[2,4,5,1,6,7,3]=>112
[2,4,5,1,7,3,6]=>112
[2,4,5,1,7,6,3]=>168
[2,4,5,3,6,7,1]=>144
[2,4,5,3,7,1,6]=>144
[2,4,5,3,7,6,1]=>216
[2,4,5,6,1,7,3]=>184
[2,4,5,6,3,7,1]=>216
[2,4,5,6,7,1,3]=>292
[2,4,5,6,7,3,1]=>324
[2,4,5,7,1,3,6]=>184
[2,4,5,7,3,1,6]=>216
[2,4,5,7,6,1,3]=>384
[2,4,5,7,6,3,1]=>432
[2,4,6,1,3,7,5]=>112
[2,4,6,1,5,7,3]=>168
[2,4,6,1,7,3,5]=>196
[2,4,6,3,1,7,5]=>144
[2,4,6,3,7,5,1]=>324
[2,4,6,5,3,7,1]=>288
[2,4,6,5,7,3,1]=>432
[2,4,6,7,1,3,5]=>304
[2,4,6,7,1,5,3]=>396
[2,4,6,7,3,5,1]=>468
[2,4,6,7,5,3,1]=>576
[2,4,7,1,3,5,6]=>112
[2,4,7,1,5,3,6]=>168
[2,4,7,1,5,6,3]=>252
[2,4,7,1,6,3,5]=>252
[2,4,7,3,1,5,6]=>144
[2,4,7,3,6,1,5]=>324
[2,4,7,6,5,1,3]=>624
[2,4,7,6,5,3,1]=>720
[2,5,1,3,4,6,7]=>16
[2,5,1,3,6,7,4]=>64
[2,5,1,3,7,4,6]=>64
[2,5,1,3,7,6,4]=>96
[2,5,1,4,7,6,3]=>144
[2,5,1,6,3,7,4]=>112
[2,5,1,6,4,7,3]=>144
[2,5,1,6,7,3,4]=>184
[2,5,1,6,7,4,3]=>216
[2,5,1,7,3,4,6]=>112
[2,5,1,7,3,6,4]=>168
[2,5,1,7,4,3,6]=>144
[2,5,1,7,6,3,4]=>240
[2,5,1,7,6,4,3]=>288
[2,5,3,1,7,4,6]=>96
[2,5,3,1,7,6,4]=>144
[2,5,3,4,6,7,1]=>144
[2,5,3,4,7,6,1]=>216
[2,5,3,6,4,7,1]=>216
[2,5,3,6,7,1,4]=>276
[2,5,3,6,7,4,1]=>324
[2,5,3,7,6,1,4]=>360
[2,5,4,1,6,7,3]=>144
[2,5,4,1,7,3,6]=>144
[2,5,4,3,6,7,1]=>192
[2,5,4,3,7,1,6]=>192
[2,5,4,3,7,6,1]=>288
[2,5,4,6,3,7,1]=>288
[2,5,4,6,7,1,3]=>384
[2,5,4,6,7,3,1]=>432
[2,5,4,7,1,3,6]=>240
[2,5,4,7,6,1,3]=>504
[2,5,4,7,6,3,1]=>576
[2,5,6,1,3,7,4]=>184
[2,5,6,1,4,7,3]=>240
[2,5,6,1,7,3,4]=>304
[2,5,6,3,4,7,1]=>312
[2,5,6,3,7,4,1]=>468
[2,5,6,4,3,7,1]=>384
[2,5,6,4,7,1,3]=>504
[2,5,6,4,7,3,1]=>576
[2,5,6,7,1,3,4]=>460
[2,5,6,7,3,1,4]=>552
[2,5,6,7,4,3,1]=>768
[2,5,7,1,3,4,6]=>184
[2,5,7,1,4,6,3]=>360
[2,5,7,3,1,4,6]=>240
[2,5,7,3,4,1,6]=>312
[2,5,7,3,6,1,4]=>516
[2,5,7,6,4,1,3]=>816
[2,5,7,6,4,3,1]=>960
[2,6,1,3,4,5,7]=>32
[2,6,1,3,4,7,5]=>64
[2,6,1,3,7,4,5]=>112
[2,6,1,3,7,5,4]=>144
[2,6,1,5,3,7,4]=>144
[2,6,1,5,7,4,3]=>288
[2,6,1,7,3,4,5]=>184
[2,6,1,7,4,5,3]=>312
[2,6,3,1,7,4,5]=>168
[2,6,3,4,5,7,1]=>216
[2,6,3,5,4,7,1]=>288
[2,6,3,5,7,1,4]=>360
[2,6,3,7,1,4,5]=>276
[2,6,3,7,4,1,5]=>360
[2,6,3,7,4,5,1]=>468
[2,6,4,1,3,7,5]=>144
[2,6,4,1,7,3,5]=>252
[2,6,4,3,5,7,1]=>288
[2,6,4,5,1,7,3]=>312
[2,6,4,5,3,7,1]=>384
[2,6,4,5,7,3,1]=>576
[2,6,4,7,3,5,1]=>624
[2,6,4,7,5,3,1]=>768
[2,6,5,1,3,7,4]=>216
[2,6,5,1,7,3,4]=>360
[2,6,5,4,3,1,7]=>240
[2,6,5,4,3,7,1]=>480
[2,6,5,4,7,3,1]=>720
[2,6,5,7,1,3,4]=>552
[2,6,5,7,4,3,1]=>960
[2,6,7,1,3,4,5]=>292
[2,6,7,1,4,5,3]=>504
[2,6,7,1,5,3,4]=>504
[2,6,7,3,4,5,1]=>660
[2,6,7,4,3,1,5]=>624
[2,6,7,4,3,5,1]=>816
[2,6,7,5,4,3,1]=>1200
[2,7,1,3,4,5,6]=>64
[2,7,1,3,4,6,5]=>96
[2,7,1,3,6,4,5]=>144
[2,7,1,4,5,3,6]=>144
[2,7,1,5,3,4,6]=>144
[2,7,1,5,4,3,6]=>192
[2,7,1,5,6,3,4]=>312
[2,7,1,6,3,4,5]=>216
[2,7,1,6,5,4,3]=>480
[2,7,3,1,4,6,5]=>144
[2,7,3,4,1,5,6]=>144
[2,7,3,4,1,6,5]=>216
[2,7,3,4,5,6,1]=>324
[2,7,3,4,6,1,5]=>324
[2,7,3,4,6,5,1]=>432
[2,7,3,5,4,6,1]=>432
[2,7,3,5,6,4,1]=>576
[2,7,3,6,1,4,5]=>324
[2,7,3,6,5,1,4]=>576
[2,7,3,6,5,4,1]=>720
[2,7,4,1,3,5,6]=>144
[2,7,4,1,5,3,6]=>216
[2,7,4,1,6,3,5]=>324
[2,7,4,3,5,1,6]=>288
[2,7,4,3,5,6,1]=>432
[2,7,4,3,6,1,5]=>432
[2,7,4,3,6,5,1]=>576
[2,7,4,5,1,3,6]=>312
[2,7,4,5,3,1,6]=>384
[2,7,4,5,3,6,1]=>576
[2,7,4,5,6,1,3]=>660
[2,7,4,5,6,3,1]=>768
[2,7,4,6,1,3,5]=>468
[2,7,4,6,5,1,3]=>816
[2,7,4,6,5,3,1]=>960
[2,7,5,1,3,4,6]=>216
[2,7,5,1,6,3,4]=>468
[2,7,5,3,4,1,6]=>384
[2,7,5,4,3,6,1]=>720
[2,7,5,4,6,3,1]=>960
[2,7,6,1,3,4,5]=>324
[2,7,6,1,4,3,5]=>432
[2,7,6,1,5,4,3]=>720
[2,7,6,3,1,4,5]=>432
[2,7,6,3,5,1,4]=>768
[2,7,6,4,5,3,1]=>1200
[2,7,6,5,1,3,4]=>768
[2,7,6,5,1,4,3]=>960
[2,7,6,5,4,1,3]=>1200
[2,7,6,5,4,3,1]=>1440
[3,1,2,4,5,6,7]=>4
[3,1,2,4,5,7,6]=>8
[3,1,2,4,6,7,5]=>16
[3,1,2,4,7,5,6]=>16
[3,1,2,6,4,5,7]=>16
[3,1,2,6,4,7,5]=>32
[3,1,2,6,7,4,5]=>56
[3,1,2,7,4,5,6]=>32
[3,1,2,7,6,4,5]=>72
[3,1,2,7,6,5,4]=>96
[3,1,4,2,5,7,6]=>16
[3,1,4,2,6,7,5]=>32
[3,1,4,5,2,7,6]=>32
[3,1,4,5,6,7,2]=>64
[3,1,4,5,7,2,6]=>64
[3,1,4,6,2,7,5]=>64
[3,1,4,6,7,2,5]=>112
[3,1,4,6,7,5,2]=>144
[3,1,4,7,2,5,6]=>64
[3,1,4,7,2,6,5]=>96
[3,1,4,7,5,6,2]=>144
[3,1,4,7,6,2,5]=>144
[3,1,5,2,4,6,7]=>16
[3,1,5,2,4,7,6]=>32
[3,1,5,2,6,7,4]=>64
[3,1,5,2,7,4,6]=>64
[3,1,5,4,6,7,2]=>96
[3,1,5,6,2,4,7]=>56
[3,1,5,6,2,7,4]=>112
[3,1,5,6,4,7,2]=>144
[3,1,5,6,7,2,4]=>184
[3,1,5,6,7,4,2]=>216
[3,1,5,7,2,4,6]=>112
[3,1,5,7,4,2,6]=>144
[3,1,5,7,6,2,4]=>240
[3,1,6,2,4,5,7]=>32
[3,1,6,2,4,7,5]=>64
[3,1,6,2,5,7,4]=>96
[3,1,6,2,7,4,5]=>112
[3,1,6,2,7,5,4]=>144
[3,1,6,4,2,7,5]=>96
[3,1,6,4,5,7,2]=>144
[3,1,6,5,2,7,4]=>144
[3,1,6,5,4,7,2]=>192
[3,1,6,7,2,4,5]=>184
[3,1,6,7,2,5,4]=>240
[3,1,6,7,4,5,2]=>312
[3,1,7,2,4,5,6]=>64
[3,1,7,2,4,6,5]=>96
[3,1,7,2,5,6,4]=>144
[3,1,7,2,6,4,5]=>144
[3,1,7,4,2,6,5]=>144
[3,1,7,4,5,6,2]=>216
[3,1,7,5,2,4,6]=>144
[3,1,7,5,2,6,4]=>216
[3,1,7,5,6,2,4]=>312
[3,1,7,6,2,4,5]=>216
[3,1,7,6,2,5,4]=>288
[3,1,7,6,5,4,2]=>480
[3,2,1,4,5,6,7]=>6
[3,2,1,5,4,6,7]=>12
[3,2,4,1,5,6,7]=>12
[3,2,4,5,1,6,7]=>24
[3,2,4,5,6,1,7]=>48
[3,2,4,5,6,7,1]=>96
[3,2,4,5,7,6,1]=>144
[3,2,4,6,1,7,5]=>96
[3,2,4,6,5,7,1]=>144
[3,2,4,6,7,1,5]=>168
[3,2,4,6,7,5,1]=>216
[3,2,4,7,1,5,6]=>96
[3,2,4,7,5,6,1]=>216
[3,2,4,7,6,5,1]=>288
[3,2,5,1,6,7,4]=>96
[3,2,5,4,6,7,1]=>144
[3,2,5,4,7,6,1]=>216
[3,2,5,6,1,7,4]=>168
[3,2,5,6,4,7,1]=>216
[3,2,5,6,7,1,4]=>276
[3,2,5,6,7,4,1]=>324
[3,2,5,7,1,6,4]=>252
[3,2,5,7,6,4,1]=>432
[3,2,6,1,4,5,7]=>48
[3,2,6,1,7,4,5]=>168
[3,2,6,4,5,7,1]=>216
[3,2,6,5,1,4,7]=>108
[3,2,6,5,1,7,4]=>216
[3,2,6,5,4,1,7]=>144
[3,2,6,5,4,7,1]=>288
[3,2,6,5,7,1,4]=>360
[3,2,6,5,7,4,1]=>432
[3,2,6,7,1,5,4]=>360
[3,2,6,7,4,1,5]=>360
[3,2,6,7,5,4,1]=>576
[3,2,7,4,5,6,1]=>324
[3,2,7,4,6,5,1]=>432
[3,2,7,5,4,6,1]=>432
[3,2,7,5,6,1,4]=>468
[3,2,7,5,6,4,1]=>576
[3,2,7,6,5,1,4]=>576
[3,2,7,6,5,4,1]=>720
[3,4,1,2,5,6,7]=>14
[3,4,1,2,5,7,6]=>28
[3,4,1,2,6,7,5]=>56
[3,4,1,2,7,5,6]=>56
[3,4,1,5,2,7,6]=>56
[3,4,1,5,6,7,2]=>112
[3,4,1,5,7,2,6]=>112
[3,4,1,6,2,5,7]=>56
[3,4,1,6,2,7,5]=>112
[3,4,1,6,5,7,2]=>168
[3,4,1,6,7,2,5]=>196
[3,4,1,7,2,5,6]=>112
[3,4,1,7,2,6,5]=>168
[3,4,1,7,5,6,2]=>252
[3,4,1,7,6,2,5]=>252
[3,4,2,1,5,6,7]=>18
[3,4,2,5,1,6,7]=>36
[3,4,2,5,6,1,7]=>72
[3,4,2,5,6,7,1]=>144
[3,4,2,5,7,1,6]=>144
[3,4,2,5,7,6,1]=>216
[3,4,2,6,1,7,5]=>144
[3,4,2,6,5,7,1]=>216
[3,4,2,6,7,5,1]=>324
[3,4,2,7,1,5,6]=>144
[3,4,2,7,6,5,1]=>432
[3,4,5,1,2,6,7]=>46
[3,4,5,1,2,7,6]=>92
[3,4,5,1,6,7,2]=>184
[3,4,5,1,7,2,6]=>184
[3,4,5,1,7,6,2]=>276
[3,4,5,2,1,6,7]=>54
[3,4,5,2,6,1,7]=>108
[3,4,5,2,6,7,1]=>216
[3,4,5,2,7,1,6]=>216
[3,4,5,2,7,6,1]=>324
[3,4,5,6,1,2,7]=>146
[3,4,5,6,1,7,2]=>292
[3,4,5,6,2,1,7]=>162
[3,4,5,6,2,7,1]=>324
[3,4,5,6,7,1,2]=>454
[3,4,5,6,7,2,1]=>486
[3,4,5,7,1,2,6]=>292
[3,4,5,7,1,6,2]=>438
[3,4,5,7,2,1,6]=>324
[3,4,5,7,6,2,1]=>648
[3,4,6,1,2,5,7]=>92
[3,4,6,1,2,7,5]=>184
[3,4,6,1,5,2,7]=>138
[3,4,6,1,7,2,5]=>322
[3,4,6,1,7,5,2]=>414
[3,4,6,2,1,5,7]=>108
[3,4,6,2,1,7,5]=>216
[3,4,6,2,7,1,5]=>378
[3,4,6,2,7,5,1]=>486
[3,4,6,5,2,7,1]=>432
[3,4,6,5,7,1,2]=>600
[3,4,6,5,7,2,1]=>648
[3,4,6,7,1,2,5]=>484
[3,4,6,7,1,5,2]=>630
[3,4,6,7,2,1,5]=>540
[3,4,6,7,2,5,1]=>702
[3,4,6,7,5,1,2]=>792
[3,4,6,7,5,2,1]=>864
[3,4,7,1,2,5,6]=>184
[3,4,7,1,2,6,5]=>276
[3,4,7,1,5,6,2]=>414
[3,4,7,2,1,5,6]=>216
[3,4,7,2,1,6,5]=>324
[3,4,7,2,5,1,6]=>324
[3,4,7,6,1,5,2]=>768
[3,4,7,6,2,1,5]=>648
[3,4,7,6,5,2,1]=>1080
[3,5,1,2,4,6,7]=>28
[3,5,1,2,6,7,4]=>112
[3,5,1,2,7,4,6]=>112
[3,5,1,2,7,6,4]=>168
[3,5,1,4,2,6,7]=>42
[3,5,1,4,6,7,2]=>168
[3,5,1,4,7,2,6]=>168
[3,5,1,4,7,6,2]=>252
[3,5,1,6,2,4,7]=>98
[3,5,1,6,2,7,4]=>196
[3,5,1,6,4,7,2]=>252
[3,5,1,6,7,2,4]=>322
[3,5,1,6,7,4,2]=>378
[3,5,1,7,2,4,6]=>196
[3,5,1,7,2,6,4]=>294
[3,5,1,7,4,6,2]=>378
[3,5,2,1,4,6,7]=>36
[3,5,2,1,4,7,6]=>72
[3,5,2,1,6,7,4]=>144
[3,5,2,1,7,4,6]=>144
[3,5,2,6,1,4,7]=>126
[3,5,2,6,1,7,4]=>252
[3,5,2,6,4,7,1]=>324
[3,5,2,6,7,1,4]=>414
[3,5,2,6,7,4,1]=>486
[3,5,2,7,1,6,4]=>378
[3,5,2,7,4,1,6]=>324
[3,5,4,1,7,2,6]=>240
[3,5,4,2,6,7,1]=>288
[3,5,4,2,7,6,1]=>432
[3,5,4,6,1,7,2]=>384
[3,5,4,6,2,7,1]=>432
[3,5,4,6,7,2,1]=>648
[3,5,4,7,1,6,2]=>576
[3,5,4,7,2,1,6]=>432
[3,5,4,7,6,2,1]=>864
[3,5,6,1,2,4,7]=>152
[3,5,6,1,2,7,4]=>304
[3,5,6,1,4,2,7]=>198
[3,5,6,1,7,2,4]=>502
[3,5,6,2,4,7,1]=>468
[3,5,6,2,7,1,4]=>594
[3,5,6,2,7,4,1]=>702
[3,5,6,4,1,2,7]=>252
[3,5,6,4,2,1,7]=>288
[3,5,6,4,2,7,1]=>576
[3,5,6,4,7,1,2]=>792
[3,5,6,4,7,2,1]=>864
[3,5,6,7,1,2,4]=>736
[3,5,6,7,2,1,4]=>828
[3,5,6,7,4,1,2]=>1044
[3,5,6,7,4,2,1]=>1152
[3,5,7,1,2,4,6]=>304
[3,5,7,1,4,6,2]=>594
[3,5,7,2,1,4,6]=>360
[3,5,7,2,4,1,6]=>468
[3,5,7,2,6,1,4]=>774
[3,5,7,4,1,6,2]=>756
[3,5,7,4,2,1,6]=>576
[3,5,7,6,1,4,2]=>1080
[3,5,7,6,2,1,4]=>1008
[3,5,7,6,4,2,1]=>1440
[3,6,1,2,4,5,7]=>56
[3,6,1,2,4,7,5]=>112
[3,6,1,2,7,4,5]=>196
[3,6,1,4,5,2,7]=>126
[3,6,1,4,5,7,2]=>252
[3,6,1,4,7,2,5]=>294
[3,6,1,4,7,5,2]=>378
[3,6,1,5,7,4,2]=>504
[3,6,1,7,2,4,5]=>322
[3,6,1,7,2,5,4]=>420
[3,6,1,7,5,4,2]=>672
[3,6,2,1,4,7,5]=>144
[3,6,2,1,5,4,7]=>108
[3,6,2,1,7,5,4]=>324
[3,6,2,4,1,5,7]=>108
[3,6,2,4,1,7,5]=>216
[3,6,2,4,7,1,5]=>378
[3,6,2,7,1,5,4]=>540
[3,6,2,7,4,5,1]=>702
[3,6,2,7,5,1,4]=>702
[3,6,4,7,1,5,2]=>828
[3,6,4,7,2,5,1]=>936
[3,6,5,2,1,7,4]=>432
[3,6,5,2,7,1,4]=>720
[3,6,5,4,2,1,7]=>360
[3,6,5,4,2,7,1]=>720
[3,6,5,4,7,2,1]=>1080
[3,6,5,7,4,2,1]=>1440
[3,6,7,1,2,4,5]=>484
[3,6,7,1,4,2,5]=>636
[3,6,7,1,5,4,2]=>1032
[3,6,7,2,1,5,4]=>756
[3,6,7,2,4,5,1]=>990
[3,6,7,2,5,4,1]=>1224
[3,6,7,4,1,5,2]=>1068
[3,6,7,4,5,1,2]=>1356
[3,6,7,5,4,2,1]=>1800
[3,7,1,2,4,5,6]=>112
[3,7,1,2,6,4,5]=>252
[3,7,1,4,2,5,6]=>168
[3,7,1,4,5,6,2]=>378
[3,7,1,5,2,6,4]=>378
[3,7,1,5,4,6,2]=>504
[3,7,2,1,4,5,6]=>144
[3,7,2,1,5,6,4]=>324
[3,7,2,4,1,6,5]=>324
[3,7,2,4,5,1,6]=>324
[3,7,2,5,1,4,6]=>324
[3,7,2,5,4,1,6]=>432
[3,7,2,6,4,1,5]=>648
[3,7,4,1,2,6,5]=>360
[3,7,4,6,1,5,2]=>1008
[3,7,4,6,2,1,5]=>864
[3,7,5,1,4,2,6]=>480
[3,7,5,1,6,2,4]=>780
[3,7,5,2,4,1,6]=>576
[3,7,5,6,2,1,4]=>1224
[3,7,6,1,4,5,2]=>960
[3,7,6,2,1,4,5]=>648
[3,7,6,2,4,1,5]=>864
[3,7,6,5,1,4,2]=>1560
[3,7,6,5,2,1,4]=>1440
[3,7,6,5,4,2,1]=>2160
[4,1,2,3,5,6,7]=>8
[4,1,2,3,5,7,6]=>16
[4,1,2,3,7,5,6]=>32
[4,1,2,5,3,7,6]=>32
[4,1,2,5,6,7,3]=>64
[4,1,2,5,7,3,6]=>64
[4,1,2,5,7,6,3]=>96
[4,1,2,6,3,5,7]=>32
[4,1,2,6,3,7,5]=>64
[4,1,2,6,5,7,3]=>96
[4,1,2,6,7,3,5]=>112
[4,1,2,6,7,5,3]=>144
[4,1,2,7,3,5,6]=>64
[4,1,2,7,3,6,5]=>96
[4,1,2,7,6,3,5]=>144
[4,1,3,2,5,6,7]=>12
[4,1,3,2,7,6,5]=>72
[4,1,3,6,2,7,5]=>96
[4,1,3,7,2,6,5]=>144
[4,1,5,2,3,6,7]=>28
[4,1,5,2,3,7,6]=>56
[4,1,5,2,6,7,3]=>112
[4,1,5,2,7,3,6]=>112
[4,1,5,2,7,6,3]=>168
[4,1,5,3,2,7,6]=>72
[4,1,5,3,6,7,2]=>144
[4,1,5,3,7,2,6]=>144
[4,1,5,6,2,3,7]=>92
[4,1,5,6,2,7,3]=>184
[4,1,5,6,3,7,2]=>216
[4,1,5,6,7,2,3]=>292
[4,1,5,6,7,3,2]=>324
[4,1,5,7,2,3,6]=>184
[4,1,5,7,2,6,3]=>276
[4,1,5,7,3,2,6]=>216
[4,1,5,7,3,6,2]=>324
[4,1,6,2,3,5,7]=>56
[4,1,6,2,3,7,5]=>112
[4,1,6,2,5,7,3]=>168
[4,1,6,2,7,3,5]=>196
[4,1,6,2,7,5,3]=>252
[4,1,6,3,2,7,5]=>144
[4,1,6,3,7,5,2]=>324
[4,1,6,5,7,3,2]=>432
[4,1,6,7,2,3,5]=>304
[4,1,6,7,3,5,2]=>468
[4,1,6,7,5,3,2]=>576
[4,1,7,2,3,5,6]=>112
[4,1,7,2,3,6,5]=>168
[4,1,7,3,2,5,6]=>144
[4,1,7,3,5,6,2]=>324
[4,1,7,6,5,3,2]=>720
[4,2,1,3,5,6,7]=>12
[4,2,1,3,6,7,5]=>48
[4,2,1,3,7,5,6]=>48
[4,2,1,5,3,7,6]=>48
[4,2,1,5,6,3,7]=>48
[4,2,1,5,6,7,3]=>96
[4,2,1,5,7,3,6]=>96
[4,2,1,6,7,3,5]=>168
[4,2,1,7,3,6,5]=>144
[4,2,1,7,5,6,3]=>216
[4,2,3,1,5,6,7]=>18
[4,2,3,5,1,6,7]=>36
[4,2,3,5,6,1,7]=>72
[4,2,3,5,6,7,1]=>144
[4,2,3,5,7,1,6]=>144
[4,2,3,5,7,6,1]=>216
[4,2,3,6,1,7,5]=>144
[4,2,3,6,5,7,1]=>216
[4,2,3,6,7,1,5]=>252
[4,2,3,7,5,6,1]=>324
[4,2,3,7,6,1,5]=>324
[4,2,3,7,6,5,1]=>432
[4,2,5,1,3,6,7]=>42
[4,2,5,1,3,7,6]=>84
[4,2,5,1,6,7,3]=>168
[4,2,5,1,7,3,6]=>168
[4,2,5,1,7,6,3]=>252
[4,2,5,3,6,7,1]=>216
[4,2,5,6,1,3,7]=>138
[4,2,5,6,1,7,3]=>276
[4,2,5,6,3,7,1]=>324
[4,2,5,6,7,1,3]=>438
[4,2,5,7,1,6,3]=>414
[4,2,5,7,3,1,6]=>324
[4,2,6,1,5,3,7]=>126
[4,2,6,1,5,7,3]=>252
[4,2,6,1,7,3,5]=>294
[4,2,6,1,7,5,3]=>378
[4,2,6,3,1,5,7]=>108
[4,2,6,3,1,7,5]=>216
[4,2,6,3,7,1,5]=>378
[4,2,6,5,1,3,7]=>180
[4,2,6,5,7,1,3]=>576
[4,2,6,7,1,5,3]=>594
[4,2,6,7,5,1,3]=>756
[4,2,7,1,3,5,6]=>168
[4,2,7,1,5,6,3]=>378
[4,2,7,3,1,5,6]=>216
[4,2,7,3,1,6,5]=>324
[4,2,7,3,5,1,6]=>324
[4,2,7,5,3,1,6]=>432
[4,2,7,5,6,3,1]=>864
[4,2,7,6,3,1,5]=>648
[4,2,7,6,5,3,1]=>1080
[4,3,1,2,5,6,7]=>18
[4,3,1,2,7,5,6]=>72
[4,3,1,5,6,7,2]=>144
[4,3,1,5,7,2,6]=>144
[4,3,1,6,2,7,5]=>144
[4,3,1,6,7,2,5]=>252
[4,3,1,7,2,5,6]=>144
[4,3,1,7,6,2,5]=>324
[4,3,1,7,6,5,2]=>432
[4,3,2,1,5,6,7]=>24
[4,3,2,1,5,7,6]=>48
[4,3,2,5,1,6,7]=>48
[4,3,2,5,1,7,6]=>96
[4,3,2,5,6,1,7]=>96
[4,3,2,5,6,7,1]=>192
[4,3,2,5,7,6,1]=>288
[4,3,2,6,5,7,1]=>288
[4,3,2,6,7,5,1]=>432
[4,3,2,7,5,6,1]=>432
[4,3,2,7,6,5,1]=>576
[4,3,5,1,2,6,7]=>60
[4,3,5,1,2,7,6]=>120
[4,3,5,1,6,7,2]=>240
[4,3,5,2,1,6,7]=>72
[4,3,5,2,6,1,7]=>144
[4,3,5,2,6,7,1]=>288
[4,3,5,2,7,6,1]=>432
[4,3,5,6,1,2,7]=>192
[4,3,5,6,2,1,7]=>216
[4,3,5,6,2,7,1]=>432
[4,3,5,6,7,2,1]=>648
[4,3,5,7,6,1,2]=>792
[4,3,5,7,6,2,1]=>864
[4,3,6,1,5,7,2]=>360
[4,3,6,2,1,7,5]=>288
[4,3,6,2,5,1,7]=>216
[4,3,6,2,7,1,5]=>504
[4,3,6,5,1,7,2]=>504
[4,3,6,5,2,1,7]=>288
[4,3,6,5,2,7,1]=>576
[4,3,6,5,7,2,1]=>864
[4,3,6,7,1,5,2]=>828
[4,3,6,7,5,2,1]=>1152
[4,3,7,5,6,2,1]=>1152
[4,3,7,6,1,2,5]=>756
[4,3,7,6,5,2,1]=>1440
[4,5,1,2,3,6,7]=>46
[4,5,1,2,3,7,6]=>92
[4,5,1,2,6,7,3]=>184
[4,5,1,2,7,3,6]=>184
[4,5,1,2,7,6,3]=>276
[4,5,1,3,2,6,7]=>60
[4,5,1,3,6,7,2]=>240
[4,5,1,3,7,2,6]=>240
[4,5,1,3,7,6,2]=>360
[4,5,1,6,2,3,7]=>152
[4,5,1,6,2,7,3]=>304
[4,5,1,6,7,2,3]=>484
[4,5,1,7,2,3,6]=>304
[4,5,2,1,3,6,7]=>60
[4,5,2,1,6,7,3]=>240
[4,5,2,3,1,6,7]=>78
[4,5,2,3,6,1,7]=>156
[4,5,2,3,6,7,1]=>312
[4,5,2,3,7,1,6]=>312
[4,5,2,6,3,7,1]=>468
[4,5,2,6,7,1,3]=>630
[4,5,2,6,7,3,1]=>702
[4,5,2,7,1,3,6]=>396
[4,5,2,7,1,6,3]=>594
[4,5,2,7,3,1,6]=>468
[4,5,2,7,6,1,3]=>828
[4,5,3,1,2,6,7]=>78
[4,5,3,2,1,6,7]=>96
[4,5,3,2,6,1,7]=>192
[4,5,3,2,6,7,1]=>384
[4,5,3,2,7,6,1]=>576
[4,5,3,6,1,2,7]=>252
[4,5,3,6,2,1,7]=>288
[4,5,3,6,2,7,1]=>576
[4,5,3,6,7,1,2]=>792
[4,5,3,6,7,2,1]=>864
[4,5,3,7,1,6,2]=>756
[4,5,3,7,2,1,6]=>576
[4,5,3,7,6,2,1]=>1152
[4,5,6,1,2,3,7]=>230
[4,5,6,1,2,7,3]=>460
[4,5,6,1,3,7,2]=>552
[4,5,6,1,7,2,3]=>736
[4,5,6,1,7,3,2]=>828
[4,5,6,2,1,3,7]=>276
[4,5,6,2,1,7,3]=>552
[4,5,6,2,3,1,7]=>330
[4,5,6,2,3,7,1]=>660
[4,5,6,3,1,2,7]=>330
[4,5,6,3,1,7,2]=>660
[4,5,6,3,2,1,7]=>384
[4,5,6,3,2,7,1]=>768
[4,5,6,3,7,1,2]=>1044
[4,5,6,3,7,2,1]=>1152
[4,5,6,7,1,2,3]=>1066
[4,5,6,7,1,3,2]=>1212
[4,5,6,7,2,1,3]=>1212
[4,5,6,7,3,1,2]=>1374
[4,5,6,7,3,2,1]=>1536
[4,5,7,1,2,3,6]=>460
[4,5,7,1,2,6,3]=>690
[4,5,7,1,6,3,2]=>1104
[4,5,7,2,1,6,3]=>828
[4,5,7,2,6,1,3]=>1158
[4,5,7,3,1,6,2]=>990
[4,5,7,3,2,1,6]=>768
[4,5,7,3,6,2,1]=>1536
[4,5,7,6,2,1,3]=>1488
[4,5,7,6,3,2,1]=>1920
[4,6,1,2,3,5,7]=>92
[4,6,1,2,3,7,5]=>184
[4,6,1,2,7,3,5]=>322
[4,6,1,3,5,2,7]=>180
[4,6,1,3,5,7,2]=>360
[4,6,1,3,7,2,5]=>420
[4,6,1,5,7,2,3]=>636
[4,6,1,7,2,3,5]=>502
[4,6,2,1,7,5,3]=>540
[4,6,2,3,1,7,5]=>312
[4,6,2,3,7,1,5]=>546
[4,6,2,3,7,5,1]=>702
[4,6,2,7,1,3,5]=>654
[4,6,2,7,1,5,3]=>852
[4,6,2,7,3,5,1]=>1014
[4,6,2,7,5,1,3]=>1086
[4,6,2,7,5,3,1]=>1248
[4,6,3,1,5,2,7]=>234
[4,6,3,1,7,5,2]=>702
[4,6,3,2,1,5,7]=>192
[4,6,3,2,7,1,5]=>672
[4,6,3,7,1,5,2]=>1086
[4,6,3,7,2,5,1]=>1248
[4,6,3,7,5,1,2]=>1374
[4,6,3,7,5,2,1]=>1536
[4,6,5,2,7,1,3]=>1080
[4,6,5,2,7,3,1]=>1224
[4,6,5,3,2,1,7]=>480
[4,6,5,3,2,7,1]=>960
[4,6,5,3,7,2,1]=>1440
[4,6,5,7,1,2,3]=>1296
[4,6,5,7,3,2,1]=>1920
[4,6,7,1,2,3,5]=>736
[4,6,7,1,5,2,3]=>1242
[4,6,7,3,1,5,2]=>1398
[4,6,7,3,2,5,1]=>1632
[4,6,7,3,5,1,2]=>1782
[4,6,7,3,5,2,1]=>2016
[4,6,7,5,2,1,3]=>1824
[4,6,7,5,3,2,1]=>2400
[4,7,1,2,3,5,6]=>184
[4,7,1,2,5,6,3]=>414
[4,7,1,2,6,3,5]=>414
[4,7,1,3,5,6,2]=>540
[4,7,1,5,6,3,2]=>960
[4,7,2,1,3,5,6]=>240
[4,7,2,1,5,3,6]=>360
[4,7,2,1,5,6,3]=>540
[4,7,2,1,6,3,5]=>540
[4,7,2,3,1,5,6]=>312
[4,7,2,5,1,3,6]=>516
[4,7,2,5,6,1,3]=>1086
[4,7,2,6,1,3,5]=>774
[4,7,3,1,5,6,2]=>702
[4,7,3,1,6,2,5]=>702
[4,7,3,2,1,6,5]=>576
[4,7,3,2,5,1,6]=>576
[4,7,3,5,1,6,2]=>990
[4,7,3,5,2,1,6]=>768
[4,7,3,6,2,1,5]=>1152
[4,7,5,6,3,2,1]=>2400
[4,7,6,1,2,5,3]=>1104
[4,7,6,1,5,3,2]=>1680
[4,7,6,2,1,3,5]=>1008
[4,7,6,2,5,1,3]=>1752
[4,7,6,3,1,5,2]=>1632
[4,7,6,3,2,1,5]=>1440
[4,7,6,5,3,2,1]=>2880
[5,1,2,3,4,6,7]=>16
[5,1,2,3,4,7,6]=>32
[5,1,2,3,6,4,7]=>32
[5,1,2,3,6,7,4]=>64
[5,1,2,3,7,4,6]=>64
[5,1,2,6,3,4,7]=>56
[5,1,2,6,3,7,4]=>112
[5,1,2,6,4,7,3]=>144
[5,1,2,6,7,3,4]=>184
[5,1,2,6,7,4,3]=>216
[5,1,2,7,3,4,6]=>112
[5,1,2,7,3,6,4]=>168
[5,1,2,7,4,3,6]=>144
[5,1,3,4,2,6,7]=>36
[5,1,3,4,7,6,2]=>216
[5,1,3,6,4,7,2]=>216
[5,1,3,6,7,4,2]=>324
[5,1,3,7,2,4,6]=>168
[5,1,3,7,2,6,4]=>252
[5,1,3,7,4,6,2]=>324
[5,1,4,2,6,7,3]=>144
[5,1,4,2,7,3,6]=>144
[5,1,4,2,7,6,3]=>216
[5,1,4,6,2,7,3]=>240
[5,1,6,2,3,4,7]=>92
[5,1,6,2,3,7,4]=>184
[5,1,6,2,7,3,4]=>304
[5,1,6,3,2,7,4]=>240
[5,1,6,3,4,7,2]=>312
[5,1,6,3,7,4,2]=>468
[5,1,6,4,7,3,2]=>576
[5,1,6,7,2,3,4]=>460
[5,1,6,7,4,3,2]=>768
[5,1,7,2,3,4,6]=>184
[5,1,7,3,4,2,6]=>312
[5,1,7,4,2,6,3]=>468
[5,1,7,4,3,6,2]=>576
[5,1,7,6,4,3,2]=>960
[5,2,1,3,4,6,7]=>24
[5,2,1,3,7,4,6]=>96
[5,2,1,4,3,6,7]=>36
[5,2,1,6,3,7,4]=>168
[5,2,1,6,4,3,7]=>108
[5,2,1,6,7,3,4]=>276
[5,2,1,6,7,4,3]=>324
[5,2,1,7,4,6,3]=>324
[5,2,3,1,4,6,7]=>36
[5,2,3,1,4,7,6]=>72
[5,2,3,1,6,7,4]=>144
[5,2,3,1,7,4,6]=>144
[5,2,3,4,1,6,7]=>54
[5,2,3,4,6,1,7]=>108
[5,2,3,4,6,7,1]=>216
[5,2,3,4,7,1,6]=>216
[5,2,3,4,7,6,1]=>324
[5,2,3,6,1,4,7]=>126
[5,2,3,6,1,7,4]=>252
[5,2,3,6,7,1,4]=>414
[5,2,3,7,1,4,6]=>252
[5,2,3,7,1,6,4]=>378
[5,2,3,7,4,1,6]=>324
[5,2,3,7,6,4,1]=>648
[5,2,4,3,6,7,1]=>288
[5,2,4,3,7,6,1]=>432
[5,2,4,6,3,7,1]=>432
[5,2,4,7,3,1,6]=>432
[5,2,4,7,6,3,1]=>864
[5,2,6,1,4,3,7]=>180
[5,2,6,1,4,7,3]=>360
[5,2,6,3,4,7,1]=>468
[5,2,6,3,7,1,4]=>594
[5,2,6,4,1,3,7]=>234
[5,2,6,4,7,1,3]=>756
[5,2,6,7,1,3,4]=>690
[5,2,6,7,3,1,4]=>828
[5,2,6,7,3,4,1]=>990
[5,2,6,7,4,1,3]=>990
[5,2,7,1,4,6,3]=>540
[5,2,7,3,1,4,6]=>360
[5,2,7,3,1,6,4]=>540
[5,2,7,3,4,1,6]=>468
[5,2,7,4,1,6,3]=>702
[5,2,7,4,3,1,6]=>576
[5,2,7,6,3,4,1]=>1224
[5,3,1,2,4,6,7]=>36
[5,3,1,2,6,7,4]=>144
[5,3,1,2,7,4,6]=>144
[5,3,1,4,7,6,2]=>324
[5,3,1,6,4,7,2]=>324
[5,3,1,6,7,4,2]=>486
[5,3,1,7,2,4,6]=>252
[5,3,1,7,2,6,4]=>378
[5,3,1,7,4,2,6]=>324
[5,3,1,7,6,4,2]=>648
[5,3,2,1,4,6,7]=>48
[5,3,2,1,4,7,6]=>96
[5,3,2,4,1,6,7]=>72
[5,3,2,4,6,1,7]=>144
[5,3,2,4,6,7,1]=>288
[5,3,2,4,7,6,1]=>432
[5,3,2,6,1,4,7]=>168
[5,3,2,6,4,1,7]=>216
[5,3,4,1,2,6,7]=>78
[5,3,4,1,6,7,2]=>312
[5,3,4,1,7,2,6]=>312
[5,3,4,2,1,6,7]=>96
[5,3,4,2,6,1,7]=>192
[5,3,4,2,6,7,1]=>384
[5,3,4,2,7,6,1]=>576
[5,3,4,6,1,2,7]=>252
[5,3,4,6,2,1,7]=>288
[5,3,4,6,2,7,1]=>576
[5,3,4,7,2,6,1]=>864
[5,3,6,1,2,7,4]=>396
[5,3,6,1,4,7,2]=>516
[5,3,6,1,7,4,2]=>774
[5,3,6,2,1,4,7]=>240
[5,3,6,2,4,1,7]=>312
[5,3,6,2,4,7,1]=>624
[5,3,6,2,7,1,4]=>792
[5,3,6,7,1,4,2]=>1158
[5,3,6,7,2,1,4]=>1104
[5,3,6,7,2,4,1]=>1320
[5,3,6,7,4,2,1]=>1536
[5,3,7,1,6,2,4]=>852
[5,3,7,1,6,4,2]=>1032
[5,3,7,2,1,4,6]=>480
[5,3,7,4,1,2,6]=>660
[5,3,7,4,2,1,6]=>768
[5,3,7,6,4,1,2]=>1704
[5,3,7,6,4,2,1]=>1920
[5,4,1,2,3,6,7]=>54
[5,4,1,2,6,7,3]=>216
[5,4,1,2,7,3,6]=>216
[5,4,1,6,2,7,3]=>360
[5,4,1,6,7,3,2]=>648
[5,4,1,7,6,2,3]=>756
[5,4,1,7,6,3,2]=>864
[5,4,2,1,3,6,7]=>72
[5,4,2,1,3,7,6]=>144
[5,4,2,1,6,7,3]=>288
[5,4,2,1,7,3,6]=>288
[5,4,2,3,1,6,7]=>96
[5,4,2,3,6,1,7]=>192
[5,4,2,6,1,3,7]=>240
[5,4,2,6,1,7,3]=>480
[5,4,2,6,7,1,3]=>768
[5,4,2,7,3,1,6]=>576
[5,4,3,1,2,6,7]=>96
[5,4,3,1,7,6,2]=>576
[5,4,3,2,1,6,7]=>120
[5,4,3,2,1,7,6]=>240
[5,4,3,2,6,1,7]=>240
[5,4,3,2,6,7,1]=>480
[5,4,3,2,7,1,6]=>480
[5,4,3,2,7,6,1]=>720
[5,4,3,6,1,2,7]=>312
[5,4,3,6,1,7,2]=>624
[5,4,3,6,2,1,7]=>360
[5,4,3,6,2,7,1]=>720
[5,4,3,6,7,2,1]=>1080
[5,4,3,7,6,2,1]=>1440
[5,4,6,1,2,3,7]=>276
[5,4,6,1,7,3,2]=>1008
[5,4,6,2,1,3,7]=>336
[5,4,6,2,3,1,7]=>408
[5,4,6,2,7,1,3]=>1080
[5,4,6,3,1,2,7]=>408
[5,4,6,3,1,7,2]=>816
[5,4,6,3,2,1,7]=>480
[5,4,6,3,2,7,1]=>960
[5,4,6,3,7,2,1]=>1440
[5,4,6,7,3,2,1]=>1920
[5,4,7,2,1,3,6]=>672
[5,4,7,3,6,1,2]=>1704
[5,4,7,3,6,2,1]=>1920
[5,4,7,6,3,2,1]=>2400
[5,6,1,2,3,4,7]=>146
[5,6,1,2,3,7,4]=>292
[5,6,1,2,4,7,3]=>384
[5,6,1,2,7,3,4]=>484
[5,6,1,3,4,7,2]=>504
[5,6,1,4,3,2,7]=>312
[5,6,1,7,2,3,4]=>736
[5,6,2,1,3,4,7]=>192
[5,6,2,1,7,4,3]=>756
[5,6,2,3,1,4,7]=>252
[5,6,2,3,4,1,7]=>330
[5,6,2,3,4,7,1]=>660
[5,6,2,3,7,4,1]=>990
[5,6,2,4,7,1,3]=>1068
[5,6,2,7,3,1,4]=>1164
[5,6,2,7,3,4,1]=>1398
[5,6,2,7,4,1,3]=>1398
[5,6,2,7,4,3,1]=>1632
[5,6,3,1,2,4,7]=>252
[5,6,3,1,4,2,7]=>330
[5,6,3,2,1,4,7]=>312
[5,6,3,2,4,1,7]=>408
[5,6,3,2,4,7,1]=>816
[5,6,3,2,7,1,4]=>1032
[5,6,3,2,7,4,1]=>1224
[5,6,3,4,1,2,7]=>426
[5,6,3,4,2,1,7]=>504
[5,6,3,4,7,1,2]=>1356
[5,6,3,7,1,2,4]=>1242
[5,6,3,7,2,1,4]=>1440
[5,6,3,7,4,1,2]=>1782
[5,6,3,7,4,2,1]=>2016
[5,6,4,1,2,3,7]=>330
[5,6,4,1,3,7,2]=>816
[5,6,4,2,1,3,7]=>408
[5,6,4,2,3,1,7]=>504
[5,6,4,3,1,2,7]=>504
[5,6,4,3,2,1,7]=>600
[5,6,4,3,2,7,1]=>1200
[5,6,4,3,7,2,1]=>1800
[5,6,4,7,2,3,1]=>2112
[5,6,4,7,3,2,1]=>2400
[5,6,7,1,2,3,4]=>1066
[5,6,7,1,2,4,3]=>1296
[5,6,7,1,3,2,4]=>1296
[5,6,7,1,3,4,2]=>1572
[5,6,7,1,4,2,3]=>1572
[5,6,7,2,3,4,1]=>1902
[5,6,7,3,1,2,4]=>1572
[5,6,7,3,1,4,2]=>1902
[5,6,7,3,4,2,1]=>2616
[5,6,7,4,1,2,3]=>1902
[5,6,7,4,1,3,2]=>2232
[5,6,7,4,2,3,1]=>2616
[5,6,7,4,3,1,2]=>2616
[5,6,7,4,3,2,1]=>3000
[5,7,1,2,3,4,6]=>292
[5,7,1,2,3,6,4]=>438
[5,7,1,2,6,3,4]=>630
[5,7,1,2,6,4,3]=>768
[5,7,1,3,2,4,6]=>384
[5,7,1,3,2,6,4]=>576
[5,7,1,3,6,4,2]=>1008
[5,7,1,4,3,6,2]=>936
[5,7,1,6,2,4,3]=>1080
[5,7,1,6,4,3,2]=>1560
[5,7,2,1,4,3,6]=>504
[5,7,2,1,6,3,4]=>828
[5,7,2,3,1,4,6]=>504
[5,7,2,3,4,1,6]=>660
[5,7,2,3,6,1,4]=>1086
[5,7,2,4,1,6,3]=>990
[5,7,2,6,1,3,4]=>1158
[5,7,2,6,4,1,3]=>1728
[5,7,2,6,4,3,1]=>2040
[5,7,3,1,4,6,2]=>990
[5,7,3,2,1,4,6]=>624
[5,7,3,2,1,6,4]=>936
[5,7,3,2,4,1,6]=>816
[5,7,3,2,6,1,4]=>1344
[5,7,3,4,1,6,2]=>1278
[5,7,3,4,2,1,6]=>1008
[5,7,3,6,1,4,2]=>1824
[5,7,3,6,2,1,4]=>1752
[5,7,3,6,4,2,1]=>2520
[5,7,4,1,2,6,3]=>990
[5,7,4,1,3,6,2]=>1224
[5,7,4,1,6,3,2]=>1632
[5,7,4,2,1,3,6]=>816
[5,7,4,2,6,1,3]=>1728
[5,7,4,3,1,6,2]=>1512
[5,7,4,3,2,1,6]=>1200
[5,7,4,3,6,2,1]=>2400
[5,7,4,6,3,1,2]=>2616
[5,7,6,2,3,1,4]=>1824
[5,7,6,4,3,2,1]=>3600
[6,1,2,3,4,5,7]=>32
[6,1,2,3,4,7,5]=>64
[6,1,2,3,7,4,5]=>112
[6,1,2,3,7,5,4]=>144
[6,1,2,4,7,5,3]=>216
[6,1,2,5,3,7,4]=>144
[6,1,2,7,3,4,5]=>184
[6,1,2,7,3,5,4]=>240
[6,1,2,7,4,3,5]=>240
[6,1,2,7,4,5,3]=>312
[6,1,2,7,5,4,3]=>384
[6,1,3,4,2,7,5]=>144
[6,1,3,4,5,2,7]=>108
[6,1,3,4,5,7,2]=>216
[6,1,3,4,7,2,5]=>252
[6,1,3,4,7,5,2]=>324
[6,1,3,5,7,2,4]=>360
[6,1,3,7,2,4,5]=>276
[6,1,3,7,2,5,4]=>360
[6,1,3,7,4,2,5]=>360
[6,1,3,7,5,4,2]=>576
[6,1,4,2,3,7,5]=>144
[6,1,4,2,5,7,3]=>216
[6,1,4,2,7,5,3]=>324
[6,1,4,3,2,7,5]=>192
[6,1,4,3,7,5,2]=>432
[6,1,4,5,2,7,3]=>312
[6,1,4,7,2,5,3]=>516
[6,1,4,7,5,2,3]=>660
[6,1,4,7,5,3,2]=>768
[6,1,5,2,3,7,4]=>216
[6,1,5,2,7,3,4]=>360
[6,1,5,4,7,2,3]=>624
[6,1,7,2,3,4,5]=>292
[6,1,7,2,3,5,4]=>384
[6,1,7,2,4,3,5]=>384
[6,1,7,2,5,4,3]=>624
[6,1,7,3,2,5,4]=>504
[6,1,7,3,4,5,2]=>660
[6,1,7,3,5,4,2]=>816
[6,1,7,4,5,3,2]=>1008
[6,1,7,5,2,3,4]=>660
[6,1,7,5,2,4,3]=>816
[6,1,7,5,4,3,2]=>1200
[6,2,1,3,4,5,7]=>48
[6,2,1,3,7,4,5]=>168
[6,2,1,4,5,3,7]=>108
[6,2,1,4,7,3,5]=>252
[6,2,1,4,7,5,3]=>324
[6,2,1,5,4,3,7]=>144
[6,2,1,5,7,3,4]=>360
[6,2,1,7,5,4,3]=>576
[6,2,3,1,4,5,7]=>72
[6,2,3,1,5,4,7]=>108
[6,2,3,1,7,4,5]=>252
[6,2,3,1,7,5,4]=>324
[6,2,3,4,1,5,7]=>108
[6,2,3,4,1,7,5]=>216
[6,2,3,4,5,1,7]=>162
[6,2,3,4,5,7,1]=>324
[6,2,3,4,7,1,5]=>378
[6,2,3,4,7,5,1]=>486
[6,2,3,5,4,7,1]=>432
[6,2,3,5,7,4,1]=>648
[6,2,3,7,1,5,4]=>540
[6,2,3,7,4,1,5]=>540
[6,2,3,7,4,5,1]=>702
[6,2,3,7,5,1,4]=>702
[6,2,4,3,5,7,1]=>432
[6,2,4,3,7,1,5]=>504
[6,2,4,5,3,1,7]=>288
[6,2,4,5,3,7,1]=>576
[6,2,4,5,7,1,3]=>756
[6,2,4,5,7,3,1]=>864
[6,2,4,7,1,3,5]=>594
[6,2,4,7,5,1,3]=>990
[6,2,5,1,7,3,4]=>540
[6,2,5,3,1,7,4]=>432
[6,2,5,3,7,1,4]=>720
[6,2,5,4,3,1,7]=>360
[6,2,5,4,3,7,1]=>720
[6,2,5,7,3,4,1]=>1224
[6,2,7,1,4,3,5]=>576
[6,2,7,1,5,4,3]=>936
[6,2,7,3,1,4,5]=>576
[6,2,7,3,4,5,1]=>990
[6,2,7,3,5,1,4]=>990
[6,2,7,4,1,5,3]=>990
[6,2,7,4,3,1,5]=>936
[6,2,7,4,5,1,3]=>1278
[6,2,7,5,1,3,4]=>990
[6,2,7,5,1,4,3]=>1224
[6,2,7,5,4,1,3]=>1512
[6,3,1,2,4,5,7]=>72
[6,3,1,2,4,7,5]=>144
[6,3,1,2,7,4,5]=>252
[6,3,1,5,2,7,4]=>324
[6,3,1,5,4,7,2]=>432
[6,3,1,5,7,2,4]=>540
[6,3,1,5,7,4,2]=>648
[6,3,1,7,2,4,5]=>414
[6,3,1,7,4,5,2]=>702
[6,3,1,7,5,4,2]=>864
[6,3,2,1,4,5,7]=>96
[6,3,2,4,1,5,7]=>144
[6,3,2,4,5,1,7]=>216
[6,3,2,4,5,7,1]=>432
[6,3,2,5,1,4,7]=>216
[6,3,2,5,4,1,7]=>288
[6,3,2,5,4,7,1]=>576
[6,3,4,1,2,5,7]=>156
[6,3,4,1,2,7,5]=>312
[6,3,4,1,7,2,5]=>546
[6,3,4,1,7,5,2]=>702
[6,3,4,2,1,5,7]=>192
[6,3,4,2,5,1,7]=>288
[6,3,4,2,5,7,1]=>576
[6,3,4,5,1,2,7]=>330
[6,3,4,5,1,7,2]=>660
[6,3,4,5,2,1,7]=>384
[6,3,4,5,2,7,1]=>768
[6,3,4,5,7,1,2]=>1044
[6,3,4,7,1,5,2]=>1086
[6,3,4,7,2,1,5]=>960
[6,3,4,7,2,5,1]=>1248
[6,3,4,7,5,1,2]=>1374
[6,3,4,7,5,2,1]=>1536
[6,3,5,1,2,7,4]=>468
[6,3,5,1,7,2,4]=>780
[6,3,5,4,2,1,7]=>480
[6,3,5,4,2,7,1]=>960
[6,3,5,7,1,2,4]=>1164
[6,3,5,7,4,1,2]=>1704
[6,3,5,7,4,2,1]=>1920
[6,3,7,1,2,4,5]=>630
[6,3,7,1,2,5,4]=>828
[6,3,7,1,4,2,5]=>828
[6,3,7,1,4,5,2]=>1086
[6,3,7,1,5,4,2]=>1344
[6,3,7,2,1,4,5]=>768
[6,3,7,2,4,1,5]=>1008
[6,3,7,2,4,5,1]=>1320
[6,3,7,4,5,1,2]=>1782
[6,3,7,4,5,2,1]=>2016
[6,3,7,5,1,4,2]=>1728
[6,3,7,5,2,1,4]=>1632
[6,3,7,5,4,2,1]=>2400
[6,4,1,2,3,5,7]=>108
[6,4,1,2,3,7,5]=>216
[6,4,1,2,7,5,3]=>486
[6,4,1,5,2,7,3]=>468
[6,4,1,5,7,2,3]=>756
[6,4,1,5,7,3,2]=>864
[6,4,1,7,2,3,5]=>594
[6,4,1,7,2,5,3]=>774
[6,4,1,7,5,2,3]=>990
[6,4,1,7,5,3,2]=>1152
[6,4,2,1,3,5,7]=>144
[6,4,2,1,5,3,7]=>216
[6,4,2,1,7,5,3]=>648
[6,4,2,3,1,5,7]=>192
[6,4,2,3,1,7,5]=>384
[6,4,2,3,5,1,7]=>288
[6,4,2,3,7,1,5]=>672
[6,4,2,5,1,3,7]=>312
[6,4,2,5,7,1,3]=>1008
[6,4,2,7,1,3,5]=>792
[6,4,2,7,3,5,1]=>1248
[6,4,2,7,5,3,1]=>1536
[6,4,3,1,2,5,7]=>192
[6,4,3,1,5,7,2]=>576
[6,4,3,2,1,5,7]=>240
[6,4,3,2,1,7,5]=>480
[6,4,3,2,5,1,7]=>360
[6,4,3,2,5,7,1]=>720
[6,4,3,2,7,1,5]=>840
[6,4,3,5,1,2,7]=>408
[6,4,3,5,1,7,2]=>816
[6,4,3,5,2,1,7]=>480
[6,4,3,5,2,7,1]=>960
[6,4,3,7,1,2,5]=>1032
[6,4,5,1,2,3,7]=>330
[6,4,5,2,1,3,7]=>408
[6,4,5,2,1,7,3]=>816
[6,4,5,2,3,1,7]=>504
[6,4,5,2,7,1,3]=>1320
[6,4,5,3,1,2,7]=>504
[6,4,5,3,2,1,7]=>600
[6,4,5,7,1,2,3]=>1572
[6,4,5,7,3,2,1]=>2400
[6,4,7,1,2,5,3]=>1158
[6,4,7,1,3,5,2]=>1416
[6,4,7,1,5,3,2]=>1752
[6,4,7,2,1,3,5]=>1080
[6,4,7,2,3,5,1]=>1728
[6,4,7,2,5,1,3]=>1824
[6,4,7,3,1,5,2]=>1728
[6,4,7,3,2,1,5]=>1560
[6,4,7,3,2,5,1]=>2040
[6,4,7,3,5,2,1]=>2520
[6,4,7,5,1,2,3]=>1902
[6,4,7,5,2,1,3]=>2232
[6,4,7,5,2,3,1]=>2616
[6,4,7,5,3,1,2]=>2616
[6,4,7,5,3,2,1]=>3000
[6,5,1,2,3,4,7]=>162
[6,5,1,2,7,3,4]=>540
[6,5,1,2,7,4,3]=>648
[6,5,1,3,2,7,4]=>432
[6,5,1,3,7,4,2]=>864
[6,5,1,7,2,4,3]=>1008
[6,5,1,7,4,3,2]=>1440
[6,5,2,1,3,4,7]=>216
[6,5,2,1,4,3,7]=>288
[6,5,2,1,7,3,4]=>720
[6,5,2,3,1,4,7]=>288
[6,5,2,3,1,7,4]=>576
[6,5,2,3,4,1,7]=>384
[6,5,2,3,7,1,4]=>960
[6,5,2,7,1,3,4]=>1104
[6,5,2,7,4,1,3]=>1632
[6,5,3,1,2,4,7]=>288
[6,5,3,1,4,7,2]=>768
[6,5,3,2,1,4,7]=>360
[6,5,3,2,4,1,7]=>480
[6,5,3,4,1,2,7]=>504
[6,5,3,4,2,1,7]=>600
[6,5,3,4,2,7,1]=>1200
[6,5,3,7,1,2,4]=>1440
[6,5,3,7,1,4,2]=>1752
[6,5,3,7,2,1,4]=>1680
[6,5,4,1,2,3,7]=>384
[6,5,4,1,2,7,3]=>768
[6,5,4,1,7,2,3]=>1248
[6,5,4,1,7,3,2]=>1440
[6,5,4,2,1,3,7]=>480
[6,5,4,2,3,1,7]=>600
[6,5,4,2,7,1,3]=>1560
[6,5,4,3,1,2,7]=>600
[6,5,4,3,1,7,2]=>1200
[6,5,4,3,2,1,7]=>720
[6,5,4,3,2,7,1]=>1440
[6,5,4,3,7,2,1]=>2160
[6,5,4,7,3,2,1]=>2880
[6,5,7,4,3,2,1]=>3600
[6,7,1,2,3,4,5]=>454
[6,7,1,2,3,5,4]=>600
[6,7,1,2,4,3,5]=>600
[6,7,1,2,4,5,3]=>792
[6,7,1,3,2,4,5]=>600
[6,7,1,3,4,5,2]=>1044
[6,7,1,4,5,3,2]=>1608
[6,7,1,5,2,3,4]=>1044
[6,7,1,5,4,3,2]=>1920
[6,7,2,1,3,5,4]=>792
[6,7,2,1,5,4,3]=>1296
[6,7,2,3,1,4,5]=>792
[6,7,2,3,4,1,5]=>1044
[6,7,2,3,4,5,1]=>1374
[6,7,2,4,5,1,3]=>1782
[6,7,2,5,4,3,1]=>2520
[6,7,3,1,4,5,2]=>1374
[6,7,3,1,5,4,2]=>1704
[6,7,3,2,1,4,5]=>984
[6,7,3,2,1,5,4]=>1296
[6,7,3,2,4,5,1]=>1704
[6,7,3,2,5,1,4]=>1704
[6,7,3,2,5,4,1]=>2112
[6,7,3,4,1,5,2]=>1782
[6,7,3,4,2,1,5]=>1608
[6,7,3,4,5,1,2]=>2286
[6,7,3,5,4,2,1]=>3120
[6,7,4,1,2,3,5]=>1044
[6,7,4,1,3,5,2]=>1704
[6,7,4,1,5,3,2]=>2112
[6,7,4,2,3,5,1]=>2112
[6,7,4,3,2,5,1]=>2520
[6,7,4,3,5,2,1]=>3120
[6,7,4,5,1,2,3]=>2286
[6,7,4,5,1,3,2]=>2712
[6,7,5,1,2,3,4]=>1374
[6,7,5,1,4,3,2]=>2520
[6,7,5,4,3,2,1]=>4320
[7,1,2,3,4,5,6]=>64
[7,1,2,3,5,4,6]=>96
[7,1,2,3,6,4,5]=>144
[7,1,2,4,5,3,6]=>144
[7,1,2,4,5,6,3]=>216
[7,1,2,5,3,4,6]=>144
[7,1,2,5,3,6,4]=>216
[7,1,2,5,6,3,4]=>312
[7,1,2,6,3,4,5]=>216
[7,1,3,2,5,6,4]=>216
[7,1,3,4,5,2,6]=>216
[7,1,3,4,5,6,2]=>324
[7,1,4,2,3,5,6]=>144
[7,1,4,2,6,3,5]=>324
[7,1,4,5,2,3,6]=>312
[7,1,4,5,6,2,3]=>660
[7,1,4,6,2,3,5]=>468
[7,1,5,2,3,4,6]=>216
[7,1,5,2,3,6,4]=>324
[7,1,5,2,6,3,4]=>468
[7,1,5,4,2,3,6]=>384
[7,1,6,3,4,5,2]=>768
[7,1,6,5,2,3,4]=>768
[7,1,6,5,4,3,2]=>1440
[7,2,1,3,4,5,6]=>96
[7,2,1,3,5,4,6]=>144
[7,2,1,3,6,4,5]=>216
[7,2,1,4,5,6,3]=>324
[7,2,3,1,4,5,6]=>144
[7,2,3,1,5,6,4]=>324
[7,2,3,4,1,5,6]=>216
[7,2,3,4,1,6,5]=>324
[7,2,3,4,5,1,6]=>324
[7,2,3,4,5,6,1]=>486
[7,2,3,4,6,5,1]=>648
[7,2,3,5,4,6,1]=>648
[7,2,3,5,6,4,1]=>864
[7,2,3,6,4,1,5]=>648
[7,2,3,6,5,4,1]=>1080
[7,2,4,3,5,6,1]=>648
[7,2,4,3,6,5,1]=>864
[7,2,4,5,3,6,1]=>864
[7,2,4,5,6,3,1]=>1152
[7,2,4,6,5,3,1]=>1440
[7,2,5,3,1,4,6]=>432
[7,2,5,3,4,1,6]=>576
[7,2,5,4,3,6,1]=>1080
[7,2,5,4,6,3,1]=>1440
[7,2,5,6,3,1,4]=>1224
[7,2,6,3,1,4,5]=>648
[7,2,6,3,4,1,5]=>864
[7,2,6,4,5,3,1]=>1800
[7,2,6,5,4,3,1]=>2160
[7,3,1,2,4,5,6]=>144
[7,3,1,2,6,4,5]=>324
[7,3,1,4,2,6,5]=>324
[7,3,1,5,2,4,6]=>324
[7,3,1,5,6,2,4]=>702
[7,3,1,6,2,4,5]=>486
[7,3,1,6,5,4,2]=>1080
[7,3,2,1,4,5,6]=>192
[7,3,2,4,1,5,6]=>288
[7,3,2,4,5,1,6]=>432
[7,3,2,4,5,6,1]=>648
[7,3,2,4,6,5,1]=>864
[7,3,2,5,4,6,1]=>864
[7,3,2,5,6,4,1]=>1152
[7,3,2,6,5,4,1]=>1440
[7,3,4,1,2,5,6]=>312
[7,3,4,1,5,2,6]=>468
[7,3,4,1,6,2,5]=>702
[7,3,4,2,1,5,6]=>384
[7,3,4,2,5,1,6]=>576
[7,3,4,2,5,6,1]=>864
[7,3,4,2,6,5,1]=>1152
[7,3,4,5,1,2,6]=>660
[7,3,4,5,2,1,6]=>768
[7,3,4,5,2,6,1]=>1152
[7,3,4,5,6,1,2]=>1374
[7,3,4,5,6,2,1]=>1536
[7,3,4,6,1,2,5]=>990
[7,3,4,6,5,2,1]=>1920
[7,3,5,1,2,4,6]=>468
[7,3,5,1,6,2,4]=>1014
[7,3,5,4,2,6,1]=>1440
[7,3,5,4,6,2,1]=>1920
[7,3,6,1,2,4,5]=>702
[7,3,6,1,5,4,2]=>1560
[7,3,6,4,5,2,1]=>2400
[7,3,6,5,1,2,4]=>1632
[7,3,6,5,1,4,2]=>2040
[7,3,6,5,4,1,2]=>2520
[7,3,6,5,4,2,1]=>2880
[7,4,1,2,3,5,6]=>216
[7,4,1,2,6,3,5]=>486
[7,4,1,3,5,2,6]=>432
[7,4,1,3,5,6,2]=>648
[7,4,1,5,2,3,6]=>468
[7,4,1,5,6,2,3]=>990
[7,4,1,6,2,3,5]=>702
[7,4,1,6,3,5,2]=>1152
[7,4,1,6,5,3,2]=>1440
[7,4,2,1,3,5,6]=>288
[7,4,2,3,1,5,6]=>384
[7,4,2,3,5,1,6]=>576
[7,4,2,6,3,1,5]=>1152
[7,4,3,1,2,5,6]=>384
[7,4,3,2,1,5,6]=>480
[7,4,3,2,5,6,1]=>1080
[7,4,3,2,6,5,1]=>1440
[7,4,3,5,2,6,1]=>1440
[7,4,3,5,6,2,1]=>1920
[7,4,3,6,5,2,1]=>2400
[7,4,5,1,2,3,6]=>660
[7,4,5,1,3,2,6]=>816
[7,4,5,2,1,3,6]=>816
[7,4,5,2,3,1,6]=>1008
[7,4,5,3,1,2,6]=>1008
[7,4,5,3,2,1,6]=>1200
[7,4,5,6,1,2,3]=>1902
[7,4,5,6,2,1,3]=>2232
[7,4,5,6,2,3,1]=>2616
[7,4,5,6,3,1,2]=>2616
[7,4,5,6,3,2,1]=>3000
[7,4,6,2,1,3,5]=>1224
[7,4,6,2,3,1,5]=>1512
[7,4,6,3,1,2,5]=>1512
[7,4,6,3,2,1,5]=>1800
[7,4,6,5,3,2,1]=>3600
[7,5,1,2,3,4,6]=>324
[7,5,1,2,4,3,6]=>432
[7,5,1,2,6,3,4]=>702
[7,5,1,3,4,2,6]=>576
[7,5,1,6,4,2,3]=>1512
[7,5,1,6,4,3,2]=>1800
[7,5,2,1,3,4,6]=>432
[7,5,2,3,1,4,6]=>576
[7,5,2,3,4,1,6]=>768
[7,5,2,4,6,3,1]=>1920
[7,5,2,6,3,1,4]=>1632
[7,5,3,1,2,4,6]=>576
[7,5,3,2,1,4,6]=>720
[7,5,3,2,4,1,6]=>960
[7,5,3,4,1,2,6]=>1008
[7,5,3,4,2,1,6]=>1200
[7,5,3,4,2,6,1]=>1800
[7,5,3,4,6,2,1]=>2400
[7,5,4,1,2,3,6]=>768
[7,5,4,1,6,2,3]=>1632
[7,5,4,1,6,3,2]=>1920
[7,5,4,2,1,3,6]=>960
[7,5,4,2,3,1,6]=>1200
[7,5,4,3,1,2,6]=>1200
[7,5,4,3,2,1,6]=>1440
[7,5,4,3,2,6,1]=>2160
[7,5,4,3,6,2,1]=>2880
[7,5,4,6,3,2,1]=>3600
[7,5,6,1,2,3,4]=>1374
[7,5,6,2,1,3,4]=>1704
[7,5,6,2,3,1,4]=>2112
[7,5,6,2,3,4,1]=>2616
[7,5,6,3,1,2,4]=>2112
[7,5,6,3,2,1,4]=>2520
[7,5,6,3,4,1,2]=>3216
[7,5,6,3,4,2,1]=>3720
[7,5,6,4,1,2,3]=>2616
[7,5,6,4,2,1,3]=>3120
[7,5,6,4,2,3,1]=>3720
[7,5,6,4,3,1,2]=>3720
[7,5,6,4,3,2,1]=>4320
[7,6,1,2,3,4,5]=>486
[7,6,1,2,3,5,4]=>648
[7,6,1,2,5,4,3]=>1080
[7,6,1,3,4,2,5]=>864
[7,6,1,5,4,3,2]=>2160
[7,6,2,1,3,4,5]=>648
[7,6,2,1,4,3,5]=>864
[7,6,2,3,1,4,5]=>864
[7,6,2,3,4,1,5]=>1152
[7,6,2,3,4,5,1]=>1536
[7,6,3,1,2,4,5]=>864
[7,6,3,2,1,4,5]=>1080
[7,6,3,4,1,2,5]=>1512
[7,6,3,4,2,1,5]=>1800
[7,6,3,4,5,1,2]=>2616
[7,6,3,4,5,2,1]=>3000
[7,6,3,5,4,2,1]=>3600
[7,6,4,1,2,3,5]=>1152
[7,6,4,2,1,3,5]=>1440
[7,6,4,2,3,1,5]=>1800
[7,6,4,3,1,2,5]=>1800
[7,6,4,3,2,1,5]=>2160
[7,6,4,3,5,2,1]=>3600
[7,6,4,5,1,2,3]=>2616
[7,6,4,5,1,3,2]=>3120
[7,6,4,5,2,1,3]=>3120
[7,6,4,5,2,3,1]=>3720
[7,6,4,5,3,1,2]=>3720
[7,6,4,5,3,2,1]=>4320
[7,6,5,1,2,3,4]=>1536
[7,6,5,2,1,3,4]=>1920
[7,6,5,2,3,1,4]=>2400
[7,6,5,2,3,4,1]=>3000
[7,6,5,3,1,2,4]=>2400
[7,6,5,3,2,1,4]=>2880
[7,6,5,3,4,1,2]=>3720
[7,6,5,3,4,2,1]=>4320
[7,6,5,4,1,2,3]=>3000
[7,6,5,4,2,1,3]=>3600
[7,6,5,4,2,3,1]=>4320
[7,6,5,4,3,1,2]=>4320
[7,6,5,4,3,2,1]=>5040
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Description
The number of regions of the inversion arrangement of a permutation.
The inversion arrangement $\mathcal{A}_w$ consists of the hyperplanes $x_i-x_j=0$ such that $(i,j)$ is an inversion of $w$.
Postnikov [4] conjectured that the number of regions in $\mathcal{A}_w$ equals the number of permutations in the interval $[id,w]$ in the strong Bruhat order if and only if $w$ avoids $4231$, $35142$, $42513$, $351624$. This conjecture was proved by Hultman-Linusson-Shareshian-Sjöstrand [1].
Oh-Postnikov-Yoo [3] showed that the number of regions of $\mathcal{A}_w$ is $|\chi_{G_w}(-1)|$ where $\chi_{G_w}$ is the chromatic polynomial of the inversion graph $G_w$. This is the graph with vertices ${1,2,\ldots,n}$ and edges $(i,j)$ for $i\lneq j$ $w_i\gneq w_j$.
For a permutation $w=w_1\cdots w_n$, Lewis-Morales [2] and Hultman (see appendix in [2]) showed that this number equals the number of placements of $n$ non-attacking rooks on the south-west Rothe diagram of $w$.
The inversion arrangement $\mathcal{A}_w$ consists of the hyperplanes $x_i-x_j=0$ such that $(i,j)$ is an inversion of $w$.
Postnikov [4] conjectured that the number of regions in $\mathcal{A}_w$ equals the number of permutations in the interval $[id,w]$ in the strong Bruhat order if and only if $w$ avoids $4231$, $35142$, $42513$, $351624$. This conjecture was proved by Hultman-Linusson-Shareshian-Sjöstrand [1].
Oh-Postnikov-Yoo [3] showed that the number of regions of $\mathcal{A}_w$ is $|\chi_{G_w}(-1)|$ where $\chi_{G_w}$ is the chromatic polynomial of the inversion graph $G_w$. This is the graph with vertices ${1,2,\ldots,n}$ and edges $(i,j)$ for $i\lneq j$ $w_i\gneq w_j$.
For a permutation $w=w_1\cdots w_n$, Lewis-Morales [2] and Hultman (see appendix in [2]) showed that this number equals the number of placements of $n$ non-attacking rooks on the south-west Rothe diagram of $w$.
References
[1] Hultman, A., Linusson, S., Shareshian, J., Sjöstrand, J. From Bruhat intervals to intersection lattices and a conjecture of Postnikov MathSciNet:2500158
[2] Brewster Lewis, J., Morales, A. H. Combinatorics of diagrams of permutations arXiv:1405.1608
[3] Oh, S., Postnikov, A., Yoo, H. Bruhat order, smooth Schubert varieties, and hyperplane arrangements MathSciNet:2450335
[4] Postnikov, A. Total positivity, Grassmannians, and networks arXiv:math/0609764
[2] Brewster Lewis, J., Morales, A. H. Combinatorics of diagrams of permutations arXiv:1405.1608
[3] Oh, S., Postnikov, A., Yoo, H. Bruhat order, smooth Schubert varieties, and hyperplane arrangements MathSciNet:2450335
[4] Postnikov, A. Total positivity, Grassmannians, and networks arXiv:math/0609764
Code
def statistic(x):
# create inversion graph of the permutation
g = Graph(len(x))
for inv in x.inversions():
g.add_edge((inv[0]-1,inv[1]-1))
# chromatic polynomial of inversion graph
chrompoly = g.chromatic_polynomial()
# number of regions of inversion arrangement is the number of
# acyclic orientations of the inversion graph
return abs(chrompoly(-1))
Created
Feb 26, 2013 at 06:31 by Alejandro Morales
Updated
Feb 09, 2021 at 14:31 by Martin Rubey
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