Values
([],1) => 1
([],2) => 1
([(0,1)],2) => 2
([],3) => 1
([(1,2)],3) => 2
([(0,1),(0,2)],3) => 3
([(0,2),(2,1)],3) => 6
([(0,2),(1,2)],3) => 4
([],4) => 1
([(2,3)],4) => 2
([(1,2),(1,3)],4) => 3
([(0,1),(0,2),(0,3)],4) => 4
([(0,2),(0,3),(3,1)],4) => 8
([(0,1),(0,2),(1,3),(2,3)],4) => 16
([(1,2),(2,3)],4) => 6
([(0,3),(3,1),(3,2)],4) => 12
([(1,3),(2,3)],4) => 4
([(0,3),(1,3),(3,2)],4) => 18
([(0,3),(1,3),(2,3)],4) => 8
([(0,3),(1,2)],4) => 4
([(0,3),(1,2),(1,3)],4) => 6
([(0,2),(0,3),(1,2),(1,3)],4) => 9
([(0,3),(2,1),(3,2)],4) => 24
([(0,3),(1,2),(2,3)],4) => 12
([],5) => 1
([(3,4)],5) => 2
([(2,3),(2,4)],5) => 3
([(1,2),(1,3),(1,4)],5) => 4
([(0,1),(0,2),(0,3),(0,4)],5) => 5
([(0,2),(0,3),(0,4),(4,1)],5) => 10
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 20
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 40
([(1,3),(1,4),(4,2)],5) => 8
([(0,3),(0,4),(4,1),(4,2)],5) => 15
([(1,2),(1,3),(2,4),(3,4)],5) => 16
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 90
([(0,3),(0,4),(3,2),(4,1)],5) => 20
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 30
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 45
([(2,3),(3,4)],5) => 6
([(1,4),(4,2),(4,3)],5) => 12
([(0,4),(4,1),(4,2),(4,3)],5) => 20
([(2,4),(3,4)],5) => 4
([(1,4),(2,4),(4,3)],5) => 18
([(0,4),(1,4),(4,2),(4,3)],5) => 48
([(1,4),(2,4),(3,4)],5) => 8
([(0,4),(1,4),(2,4),(4,3)],5) => 54
([(0,4),(1,4),(2,4),(3,4)],5) => 16
([(0,4),(1,4),(2,3)],5) => 8
([(0,4),(1,3),(2,3),(2,4)],5) => 12
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 18
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 27
([(0,4),(1,4),(2,3),(4,2)],5) => 96
([(0,4),(1,3),(2,3),(3,4)],5) => 36
([(0,4),(1,4),(2,3),(2,4)],5) => 12
([(0,4),(1,4),(2,3),(3,4)],5) => 24
([(1,4),(2,3)],5) => 4
([(1,4),(2,3),(2,4)],5) => 6
([(0,4),(1,2),(1,4),(2,3)],5) => 16
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 48
([(1,3),(1,4),(2,3),(2,4)],5) => 9
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 32
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 64
([(0,4),(1,2),(1,4),(4,3)],5) => 24
([(0,4),(1,2),(1,3)],5) => 6
([(0,4),(1,2),(1,3),(1,4)],5) => 8
([(0,2),(0,4),(3,1),(4,3)],5) => 30
([(0,4),(1,2),(1,3),(3,4)],5) => 16
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 60
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 32
([(0,3),(0,4),(1,2),(1,4)],5) => 9
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 12
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 16
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 24
([(0,3),(1,2),(1,4),(3,4)],5) => 18
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 36
([(1,4),(3,2),(4,3)],5) => 24
([(0,3),(3,4),(4,1),(4,2)],5) => 60
([(1,4),(2,3),(3,4)],5) => 12
([(0,4),(1,2),(2,4),(4,3)],5) => 72
([(0,3),(1,4),(4,2)],5) => 12
([(0,4),(3,2),(4,1),(4,3)],5) => 40
([(0,4),(1,2),(2,3),(2,4)],5) => 24
([(0,4),(2,3),(3,1),(4,2)],5) => 120
([(0,3),(1,2),(2,4),(3,4)],5) => 36
([(0,4),(1,2),(2,3),(3,4)],5) => 48
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 80
([],6) => 1
([(4,5)],6) => 2
([(3,4),(3,5)],6) => 3
([(2,3),(2,4),(2,5)],6) => 4
([(1,2),(1,3),(1,4),(1,5)],6) => 5
([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 6
([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 12
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 24
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 48
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 96
([(1,3),(1,4),(1,5),(5,2)],6) => 10
([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 18
([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 20
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 40
>>> Load all 1200 entries. <<<([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 324
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => 48
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => 72
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 108
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 162
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 72
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 216
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 108
([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 24
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 36
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 54
([(2,3),(2,4),(4,5)],6) => 8
([(1,4),(1,5),(5,2),(5,3)],6) => 15
([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 24
([(2,3),(2,4),(3,5),(4,5)],6) => 16
([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 90
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 288
([(1,4),(1,5),(4,3),(5,2)],6) => 20
([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 30
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 45
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 192
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 384
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 144
([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 36
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 48
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 54
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 72
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 96
([(3,4),(4,5)],6) => 6
([(2,3),(3,4),(3,5)],6) => 12
([(1,5),(5,2),(5,3),(5,4)],6) => 20
([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 30
([(2,3),(3,5),(5,4)],6) => 24
([(1,4),(4,5),(5,2),(5,3)],6) => 60
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 120
([(3,5),(4,5)],6) => 4
([(2,5),(3,5),(5,4)],6) => 18
([(1,5),(2,5),(5,3),(5,4)],6) => 48
([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 100
([(2,5),(3,5),(4,5)],6) => 8
([(1,5),(2,5),(3,5),(5,4)],6) => 54
([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 192
([(1,5),(2,5),(3,5),(4,5)],6) => 16
([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 162
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 32
([(0,5),(1,5),(2,5),(3,4)],6) => 16
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 384
([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 108
([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 24
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 48
([(1,5),(2,5),(3,4)],6) => 8
([(1,5),(2,4),(3,4),(3,5)],6) => 12
([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 48
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 144
([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 18
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 64
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 192
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 27
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 128
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 256
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 96
([(1,5),(2,5),(3,4),(5,3)],6) => 96
([(1,5),(2,4),(3,4),(4,5)],6) => 36
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 288
([(0,5),(1,5),(2,3),(5,4)],6) => 36
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 200
([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => 96
([(1,5),(2,5),(3,4),(3,5)],6) => 12
([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => 72
([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => 32
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 144
([(0,5),(1,5),(2,3),(2,4)],6) => 12
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 300
([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => 54
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 144
([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 16
([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 60
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 96
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 216
([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 32
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 120
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 192
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 64
([(1,5),(2,5),(3,4),(4,5)],6) => 24
([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 216
([(0,5),(1,5),(2,3),(3,4)],6) => 24
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 600
([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 108
([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => 80
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 120
([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => 48
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 96
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 160
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 240
([(0,5),(1,5),(2,4),(3,4)],6) => 16
([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 24
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 36
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 36
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 54
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 81
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 192
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 400
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 72
([(2,5),(3,4)],6) => 4
([(2,5),(3,4),(3,5)],6) => 6
([(1,5),(2,3),(2,5),(3,4)],6) => 16
([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => 30
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 90
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 180
([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 48
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 360
([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 60
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 120
([(2,4),(2,5),(3,4),(3,5)],6) => 9
([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 32
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 75
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 64
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 100
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 150
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 225
([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 18
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 150
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 450
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 300
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 64
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 128
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 27
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 96
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 36
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 72
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 54
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 108
([(1,5),(2,3),(2,5),(5,4)],6) => 24
([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => 60
([(1,5),(2,3),(2,4)],6) => 6
([(1,5),(2,3),(2,4),(2,5)],6) => 8
([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => 20
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 60
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 40
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 120
([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => 30
([(0,5),(1,2),(1,3),(1,4)],6) => 8
([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 10
([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 36
([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 20
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 72
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 40
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 144
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 80
([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => 24
([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 48
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 80
([(1,3),(1,5),(4,2),(5,4)],6) => 30
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 72
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 72
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 96
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 288
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 108
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 144
([(1,5),(2,3),(2,4),(4,5)],6) => 16
([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => 90
([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 60
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 432
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 32
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 270
([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 40
([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 60
([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 90
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 180
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 96
([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 60
([(0,4),(1,3),(1,5),(5,2)],6) => 16
([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 48
([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => 30
([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 48
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 288
([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 32
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 96
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 576
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 180
([(1,4),(1,5),(2,3),(2,5)],6) => 9
([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12
([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 40
([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => 80
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 16
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 50
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 100
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 200
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 30
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 80
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 160
([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => 32
([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 24
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 80
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 120
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 240
([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 24
([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 64
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 45
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 120
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 64
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => 128
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 90
([(0,4),(0,5),(1,2),(1,3)],6) => 9
([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 12
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 15
([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 30
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 60
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 16
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 20
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 25
([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 40
([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 32
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 60
([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 24
([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 45
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 216
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 144
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => 48
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 60
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 90
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 135
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 64
([(1,4),(2,3),(2,5),(4,5)],6) => 18
([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 96
([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 36
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 160
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 320
([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 48
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 192
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 96
([(0,5),(1,3),(1,4),(5,2)],6) => 18
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 144
([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 90
([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => 36
([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 60
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 120
([(2,5),(3,4),(4,5)],6) => 12
([(1,5),(2,3),(3,5),(5,4)],6) => 72
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 240
([(1,3),(2,4),(4,5)],6) => 12
([(1,5),(4,3),(5,2),(5,4)],6) => 40
([(1,5),(2,3),(3,4),(3,5)],6) => 24
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 120
([(0,4),(1,5),(5,2),(5,3)],6) => 24
([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 60
([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => 40
([(1,5),(3,4),(4,2),(5,3)],6) => 120
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 360
([(1,4),(2,3),(3,5),(4,5)],6) => 36
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 288
([(0,5),(1,4),(4,2),(5,3)],6) => 36
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 72
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 144
([(1,5),(2,3),(3,4),(4,5)],6) => 48
([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 80
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 540
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 360
([(0,5),(1,4),(2,3)],6) => 8
([(0,5),(1,3),(2,4),(2,5)],6) => 12
([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 16
([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 60
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 180
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 240
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 96
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 120
([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => 48
([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 18
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 24
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 32
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 27
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 36
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 48
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64
([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 72
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 24
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 48
([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 18
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 48
([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 36
([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 72
([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 72
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 180
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 270
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 180
([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => 36
([(0,5),(1,3),(4,2),(5,4)],6) => 48
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 120
([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 80
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 240
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 120
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
([(0,5),(1,3),(2,4),(4,5)],6) => 24
([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 48
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 480
([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 144
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 240
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 480
([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 144
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 360
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 72
([],7) => 1
([(5,6)],7) => 2
([(4,5),(4,6)],7) => 3
([(3,4),(3,5),(3,6)],7) => 4
([(2,3),(2,4),(2,5),(2,6)],7) => 5
([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 6
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 7
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 14
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => 28
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => 56
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => 112
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 224
([(1,3),(1,4),(1,5),(1,6),(6,2)],7) => 12
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 21
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 24
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 48
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 96
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 1134
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7) => 112
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7) => 168
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 756
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7) => 378
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7) => 56
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7) => 84
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 126
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 189
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7) => 84
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7) => 112
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 168
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 252
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 252
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 378
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 567
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 504
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7) => 252
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7) => 126
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => 28
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7) => 42
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => 63
([(2,4),(2,5),(2,6),(6,3)],7) => 10
([(1,4),(1,5),(1,6),(6,2),(6,3)],7) => 18
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 28
([(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 20
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 40
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 324
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => 1344
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 48
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 72
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 108
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 162
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 896
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 1792
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7) => 448
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 1344
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 672
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7) => 336
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 1008
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 72
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7) => 504
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7) => 84
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7) => 112
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7) => 378
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1008
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) => 216
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 2016
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7) => 252
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7) => 672
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 108
([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7) => 336
([(1,4),(1,5),(1,6),(5,3),(6,2)],7) => 24
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 36
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7) => 54
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7) => 126
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7) => 189
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 252
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 672
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 448
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 896
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 224
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 448
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7) => 168
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => 42
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7) => 56
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7) => 63
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 84
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 112
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => 56
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7) => 84
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7) => 112
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7) => 126
([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 168
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 224
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 189
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 252
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 336
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 448
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 168
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 504
([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7) => 126
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 336
([(3,4),(3,5),(5,6)],7) => 8
([(2,5),(2,6),(6,3),(6,4)],7) => 15
([(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 24
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => 35
([(3,4),(3,5),(4,6),(5,6)],7) => 16
([(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 90
([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) => 288
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => 700
([(2,5),(2,6),(5,4),(6,3)],7) => 20
([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 30
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 45
([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => 192
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7) => 525
([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 384
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => 3150
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => 700
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => 1050
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 1575
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7) => 144
([(0,4),(0,5),(4,6),(5,1),(5,6),(6,2),(6,3)],7) => 420
([(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 36
([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7) => 48
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,6),(6,3)],7) => 210
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => 56
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7) => 70
([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => 54
([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7) => 72
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 96
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => 350
([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 700
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1400
([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7) => 280
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => 560
([(0,4),(0,5),(4,2),(4,6),(5,1),(5,6),(6,3)],7) => 224
([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => 63
([(0,4),(0,5),(4,3),(4,6),(5,1),(5,2),(5,6)],7) => 84
([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7) => 105
([(0,3),(0,4),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 112
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7) => 140
([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 175
([(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 60
([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) => 432
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => 1680
([(4,5),(5,6)],7) => 6
([(3,4),(4,5),(4,6)],7) => 12
([(2,6),(6,3),(6,4),(6,5)],7) => 20
([(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 30
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => 42
([(3,4),(4,6),(6,5)],7) => 24
([(2,5),(5,6),(6,3),(6,4)],7) => 60
([(1,5),(5,6),(6,2),(6,3),(6,4)],7) => 120
([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => 210
([(4,6),(5,6)],7) => 4
([(3,6),(4,6),(6,5)],7) => 18
([(2,6),(3,6),(6,4),(6,5)],7) => 48
([(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 100
([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 180
([(3,6),(4,6),(5,6)],7) => 8
([(2,6),(3,6),(4,6),(6,5)],7) => 54
([(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 192
([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 500
([(2,6),(3,6),(4,6),(5,6)],7) => 16
([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 162
([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 768
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 32
([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 486
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 64
([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 32
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 1536
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 324
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 48
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 96
([(1,6),(2,6),(3,6),(4,5)],7) => 16
([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 384
([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 108
([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 108
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 1000
([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 384
([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 24
([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 216
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 64
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 432
([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => 24
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 1500
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,5)],7) => 162
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 576
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 32
([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 64
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 128
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 48
([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 648
([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 48
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 3000
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 1152
([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 324
([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 96
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 480
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 960
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 1680
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 192
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 32
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 48
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 72
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 108
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 108
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 162
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 243
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 768
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2000
([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 216
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 48
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 72
([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 384
([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 800
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 1440
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 144
([(2,6),(3,6),(4,5)],7) => 8
([(2,6),(3,5),(4,5),(4,6)],7) => 12
([(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 48
([(0,6),(1,5),(2,5),(2,6),(6,3),(6,4)],7) => 120
([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 144
([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 1440
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7) => 180
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 360
([(0,6),(1,5),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 720
([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18
([(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 64
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7) => 150
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,4)],7) => 450
([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 900
([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 192
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 300
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 600
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 27
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 128
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 375
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 256
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 500
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7) => 750
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 1125
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 54
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 750
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 2250
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7) => 256
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => 1500
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 512
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 81
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7) => 384
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 108
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 216
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 162
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 324
([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 96
([(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 300
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 36
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7) => 300
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => 1800
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3),(6,5)],7) => 900
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 128
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7) => 1200
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 384
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 600
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7) => 192
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 54
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(6,4)],7) => 288
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 72
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 144
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 54
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 192
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 144
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 108
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 216
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 108
([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 24
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7) => 32
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7) => 240
([(0,6),(1,4),(2,5),(3,4),(3,5),(5,6)],7) => 96
([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 720
([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 288
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7) => 36
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 54
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 72
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 96
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 72
([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7) => 144
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 48
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 96
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,6)],7) => 72
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 144
([(2,6),(3,6),(4,5),(6,4)],7) => 96
([(2,6),(3,5),(4,5),(5,6)],7) => 36
([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 288
([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => 1200
([(1,6),(2,6),(3,4),(6,5)],7) => 36
([(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 200
([(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 96
([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7) => 600
([(0,6),(1,6),(2,3),(6,4),(6,5)],7) => 96
([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => 360
([(0,6),(1,6),(2,5),(6,3),(6,4),(6,5)],7) => 200
([(2,6),(3,6),(4,5),(4,6)],7) => 12
([(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 72
([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 240
([(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 32
([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 144
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 180
([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 480
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 60
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7) => 270
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 720
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 120
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => 1440
([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7) => 540
([(1,6),(2,6),(3,4),(3,5)],7) => 12
([(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 300
([(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 54
([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 144
([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 800
([(0,5),(1,5),(2,4),(2,6),(5,6),(6,3)],7) => 384
([(0,6),(1,6),(2,3),(2,4),(6,5)],7) => 54
([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7) => 540
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,5)],7) => 144
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 300
([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 16
([(0,6),(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 90
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 40
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 180
([(0,6),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 80
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 360
([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => 16
([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => 720
([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7) => 72
([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7) => 192
([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 400
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 20
([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7) => 72
([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7) => 112
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7) => 252
([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 40
([(0,6),(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 144
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7) => 224
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 504
([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 80
([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 288
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 448
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 160
([(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 32
([(0,6),(1,6),(2,3),(2,4),(4,6),(6,5)],7) => 270
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 64
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 810
([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => 32
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => 1440
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7) => 144
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 384
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 768
([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => 1600
([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7) => 144
([(0,6),(1,3),(1,5),(4,6),(5,2),(5,4)],7) => 96
([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 140
([(0,6),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 60
([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => 144
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => 864
([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) => 216
([(0,4),(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3)],7) => 336
([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7) => 420
([(0,6),(1,3),(1,4),(2,6),(3,5),(3,6),(4,2),(4,5)],7) => 288
([(0,4),(0,5),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 336
([(0,3),(0,4),(1,5),(2,5),(3,2),(3,6),(4,1),(4,6)],7) => 448
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 896
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7) => 224
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 1260
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6)],7) => 280
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 840
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => 192
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => 576
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 1680
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6)],7) => 80
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => 540
([(0,6),(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7) => 192
([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 280
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 120
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 240
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 384
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 560
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => 64
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => 2880
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 288
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7) => 120
([(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 180
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) => 1152
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2800
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 360
([(0,6),(1,6),(2,3),(2,4),(4,5),(5,6)],7) => 120
([(0,6),(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7) => 192
([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 280
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) => 432
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 672
([(2,6),(3,6),(4,5),(5,6)],7) => 24
([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 216
([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => 960
([(1,6),(2,6),(3,4),(4,5)],7) => 24
([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 600
([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 108
([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 1152
([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 108
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => 1080
([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7) => 288
([(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 48
([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7) => 360
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7) => 160
([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) => 720
([(0,3),(1,6),(2,6),(3,4),(3,5)],7) => 48
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => 2160
([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7) => 216
([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) => 576
([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7) => 120
([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 168
([(0,3),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 80
([(0,3),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 160
([(0,6),(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 240
([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 336
([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 320
([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 480
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 672
([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 240
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2160
([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 480
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 3780
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 96
([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 1080
([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 96
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 4320
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 432
([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7) => 480
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 840
([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7) => 240
([(1,6),(2,6),(3,5),(4,5)],7) => 16
([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 24
([(0,6),(1,6),(2,5),(3,5),(3,6),(5,4)],7) => 96
([(0,6),(1,6),(2,4),(3,4),(3,6),(4,5),(6,5)],7) => 432
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 128
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 576
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 288
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 36
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 192
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 576
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 54
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 256
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 768
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 384
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 81
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 512
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 1024
([(0,6),(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 144
([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 192
([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 400
([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 1800
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => 3240
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 72
([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 864
([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 72
([(0,6),(1,5),(2,5),(4,6),(5,3),(5,4)],7) => 400
([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => 720
([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7) => 192
([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 324
([(0,6),(1,6),(2,5),(3,4)],7) => 16
([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 192
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => 720
([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7) => 400
([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 72
([(0,4),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 192
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 2400
([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 576
([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => 24
([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) => 480
([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7) => 144
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5)],7) => 64
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7) => 960
([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 288
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 36
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 96
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => 36
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 216
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 48
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 96
([(0,6),(1,6),(2,5),(3,4),(3,6),(5,6)],7) => 72
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5)],7) => 72
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 144
([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 24
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => 36
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 48
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 64
([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7) => 360
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 144
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7) => 600
([(0,4),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 108
([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 288
([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7) => 288
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => 1080
([(0,5),(1,5),(2,4),(2,6),(3,6),(5,3),(5,4)],7) => 600
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 108
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7) => 32
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 64
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) => 480
([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7) => 960
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 192
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => 36
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7) => 54
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7) => 72
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 96
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 128
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(4,6)],7) => 216
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6)],7) => 81
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 288
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 81
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 108
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 144
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 108
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 144
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 192
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 256
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => 192
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3)],7) => 450
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7) => 900
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => 1620
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,6),(5,6)],7) => 162
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 432
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 48
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 64
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(5,3)],7) => 300
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7) => 576
([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 900
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => 1296
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => 1728
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 2304
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 128
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 600
([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 1152
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 256
([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7) => 240
([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7) => 480
([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7) => 96
([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 48
([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 1920
([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 432
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 144
([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 48
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 1200
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 576
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => 2160
([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7) => 1200
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 216
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6)],7) => 96
([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 960
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2400
([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 288
([(3,6),(4,5)],7) => 4
([(3,6),(4,5),(4,6)],7) => 6
([(2,6),(3,4),(3,6),(4,5)],7) => 16
([(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 30
([(0,6),(1,5),(1,6),(5,2),(5,3),(5,4)],7) => 48
([(0,6),(1,4),(1,6),(4,2),(4,3),(4,5),(6,5)],7) => 144
([(0,6),(1,3),(1,6),(3,2),(3,4),(3,5),(6,4),(6,5)],7) => 288
([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 480
([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => 90
([(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 180
([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => 576
([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7) => 108
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7) => 216
([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7) => 360
([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 48
([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => 360
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => 1440
([(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 60
([(1,5),(2,3),(2,5),(3,6),(5,4),(5,6)],7) => 120
([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7) => 144
([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7) => 240
([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 60
([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 180
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => 1728
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => 216
([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => 720
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => 432
([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7) => 144
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => 432
([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => 864
([(3,5),(3,6),(4,5),(4,6)],7) => 9
([(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 32
([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 75
([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 144
([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 64
([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 450
([(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 100
([(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 150
([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 225
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 216
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7) => 288
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,4)],7) => 324
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 432
([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 576
([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 18
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 24
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 80
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 160
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 240
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 480
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 32
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7) => 100
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 200
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 600
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 300
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 150
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(6,3)],7) => 90
([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 150
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 432
([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => 576
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 1152
([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => 864
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => 864
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => 648
([(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 64
([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 300
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 128
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 1350
([(0,5),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 200
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,3),(5,6)],7) => 300
([(0,6),(1,4),(1,5),(2,4),(2,5),(5,6),(6,3)],7) => 450
([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7) => 900
([(0,5),(0,6),(1,5),(1,6),(2,4),(6,3)],7) => 64
([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7) => 288
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7) => 576
([(0,5),(1,4),(1,6),(2,4),(2,6),(6,3),(6,5)],7) => 150
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7) => 128
([(0,4),(1,5),(1,6),(2,5),(2,6),(5,3),(6,3),(6,4)],7) => 300
([(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 450
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 27
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(6,4)],7) => 128
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 96
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 400
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3)],7) => 600
([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7) => 1200
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(5,4)],7) => 96
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(4,5),(6,5)],7) => 256
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7) => 225
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 600
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 36
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 160
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(5,4),(6,4)],7) => 320
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7) => 90
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => 320
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 640
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 72
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7) => 320
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7) => 960
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7) => 480
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => 72
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(6,5)],7) => 256
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5)],7) => 256
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,6),(4,6),(5,6)],7) => 512
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6)],7) => 135
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7) => 480
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => 270
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7) => 27
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7) => 432
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => 1728
([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => 864
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => 1296
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(5,6)],7) => 96
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 225
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7) => 192
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 300
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 450
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 675
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7) => 36
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(4,5)],7) => 128
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7) => 300
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 45
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7) => 90
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 180
([(0,5),(0,6),(1,2),(1,4),(3,5),(3,6),(4,3)],7) => 216
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7) => 315
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => 1008
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => 72
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) => 256
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 135
([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => 648
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => 945
([(0,5),(0,6),(1,2),(1,4),(2,6),(3,5),(3,6),(4,3)],7) => 432
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,6),(4,1),(4,2)],7) => 630
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,6)],7) => 144
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 180
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 270
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 405
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 54
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(6,4)],7) => 384
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7) => 192
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => 768
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 108
([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 640
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => 1280
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4)],7) => 54
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => 864
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => 3456
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => 2592
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => 1728
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7) => 192
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7) => 384
([(0,5),(0,6),(1,4),(3,5),(3,6),(4,2),(4,3)],7) => 270
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 378
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6)],7) => 108
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(4,5)],7) => 384
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) => 180
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7) => 360
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 216
([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 540
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 756
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => 540
([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 810
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 1134
([(2,6),(3,4),(3,6),(6,5)],7) => 24
([(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 60
([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7) => 120
([(2,6),(3,4),(3,5)],7) => 6
([(2,6),(3,4),(3,5),(3,6)],7) => 8
([(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 20
([(0,6),(1,4),(1,5),(1,6),(5,2),(5,3)],7) => 36
([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => 108
([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7) => 216
([(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 60
([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7) => 432
([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7) => 72
([(0,6),(1,3),(1,4),(1,6),(4,5),(6,2),(6,5)],7) => 144
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 40
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 120
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => 1296
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,5),(6,2)],7) => 144
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7) => 288
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7) => 216
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(5,4),(6,4)],7) => 648
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7) => 48
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(4,5)],7) => 72
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7) => 216
([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 432
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,6)],7) => 216
([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 108
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 324
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 648
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => 144
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(6,4),(6,5)],7) => 288
([(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 30
([(0,6),(1,2),(1,3),(1,6),(6,4),(6,5)],7) => 72
([(1,6),(2,3),(2,4),(2,5)],7) => 8
([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 10
([(0,6),(1,3),(1,4),(1,5),(1,6),(5,2)],7) => 24
([(0,6),(1,2),(1,3),(1,4),(1,6),(4,5),(6,5)],7) => 72
([(0,6),(1,2),(1,3),(1,4),(1,6),(3,5),(4,5)],7) => 48
([(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 144
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7) => 96
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 288
([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7) => 36
([(0,6),(1,2),(1,3),(1,4),(1,5)],7) => 10
([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 12
([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 42
([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7) => 24
([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7) => 84
([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 48
([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7) => 168
([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 96
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 336
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 192
([(0,5),(1,2),(1,3),(1,4),(1,6),(5,6)],7) => 30
([(0,4),(1,2),(1,3),(1,5),(1,6),(4,5),(4,6)],7) => 60
([(0,3),(1,2),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7) => 100
([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 150
([(1,3),(1,4),(1,6),(5,2),(6,5)],7) => 36
([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => 84
([(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 20
([(0,6),(1,2),(1,3),(1,4),(4,6),(6,5)],7) => 108
([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 72
([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => 504
([(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 40
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 324
([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 144
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 1512
([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 80
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 972
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 96
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) => 648
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 224
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 144
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2)],7) => 48
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7) => 216
([(0,3),(0,4),(0,5),(2,6),(4,6),(5,1),(5,2)],7) => 112
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 72
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,1,1,0,1 1,1,1,3,0,2,0,2,1,0,0,2,0,0,0,1,0,1,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + q^{2} + q^{3} + q^{4} + q^{6}$
$F_{4} = q + q^{2} + q^{3} + 3\ q^{4} + 2\ q^{6} + 2\ q^{8} + q^{9} + 2\ q^{12} + q^{16} + q^{18} + q^{24}$
$F_{5} = q + q^{2} + q^{3} + 3\ q^{4} + q^{5} + 3\ q^{6} + 4\ q^{8} + 2\ q^{9} + q^{10} + 6\ q^{12} + q^{15} + 5\ q^{16} + 3\ q^{18} + 3\ q^{20} + 5\ q^{24} + q^{27} + 2\ q^{30} + 2\ q^{32} + 3\ q^{36} + 2\ q^{40} + q^{45} + 3\ q^{48} + q^{54} + 2\ q^{60} + q^{64} + q^{72} + q^{80} + q^{90} + q^{96} + q^{120}$
$F_{6} = q + q^{2} + q^{3} + 3\ q^{4} + q^{5} + 4\ q^{6} + 6\ q^{8} + 3\ q^{9} + 2\ q^{10} + 10\ q^{12} + 2\ q^{15} + 11\ q^{16} + 8\ q^{18} + 6\ q^{20} + 18\ q^{24} + q^{25} + 3\ q^{27} + 8\ q^{30} + 10\ q^{32} + 15\ q^{36} + 8\ q^{40} + 3\ q^{45} + 20\ q^{48} + q^{50} + 6\ q^{54} + 14\ q^{60} + 8\ q^{64} + 15\ q^{72} + q^{75} + 8\ q^{80} + q^{81} + 7\ q^{90} + 14\ q^{96} + 3\ q^{100} + 6\ q^{108} + 13\ q^{120} + 3\ q^{128} + q^{135} + 11\ q^{144} + 2\ q^{150} + 3\ q^{160} + 2\ q^{162} + 7\ q^{180} + 6\ q^{192} + 2\ q^{200} + 4\ q^{216} + q^{225} + 7\ q^{240} + q^{256} + 2\ q^{270} + 5\ q^{288} + 2\ q^{300} + q^{320} + q^{324} + 4\ q^{360} + 2\ q^{384} + q^{400} + q^{432} + q^{450} + 2\ q^{480} + q^{540} + q^{576} + q^{600} + q^{720}$
Description
The product of the sizes of the principal order filters in a poset.
Code
def statistic(P):
return prod(len(P.principal_order_filter(x)) for x in P)
Created
Jul 07, 2022 at 23:30 by Martin Rubey
Updated
Jul 07, 2022 at 23:30 by Martin Rubey
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