((1, 2), (5, 1), (7, 1)):2/7
((2, 2), (4, 2), (6, 1), (10, 1)):-1/30
((1, 4), (5, 1), (12, 1)):1/600
((4, 2), (6, 4)):-1/622080
((1, 2), (2, 2), (4, 1), (9, 1)):5/36
((1, 4), (2, 4), (10, 1)):93/6400
((1, 2), (2, 2), (3, 1), (7, 1)):5/42
((14, 2),):-5/294
((42, 1),):10/21
((1, 2), (2, 6), (5, 1)):1/11520
((1, 2), (2, 2), (4, 1), (7, 1)):5/14
((1, 2), (3, 1), (15, 1)):1/9
((6, 2), (20, 1)):-1/120
((1, 2), (2, 2), (4, 1), (6, 3)):5/2592
((1, 2), (2, 6), (3, 1), (6, 1)):41/38880
((1, 2), (2, 2), (16, 1)):5/16
((12, 1), (20, 1)):1/20
((1, 2), (3, 1), (6, 4)):-1/25920
((1, 8), (3, 2)):-9283/6270566400
((1, 4), (20, 1)):1/480
((1, 4), (2, 2), (4, 1), (12, 1)):11/1152
((2, 2), (6, 1), (12, 2)):-1/432
((1, 10), (2, 2)):1/222953472
((2, 2), (4, 2), (18, 1)):1/216
((1, 2), (2, 4), (3, 1), (5, 1)):1/90
((3, 2), (4, 4)):-1/276480
((6, 2), (15, 1)):-1/180
((1, 2), (2, 4), (3, 3)):7/62208
((1, 4), (2, 2), (9, 1)):5/432
((2, 2), (10, 1), (14, 1)):2/7
((1, 2), (3, 1), (4, 4)):-1/7680
((1, 8), (5, 1)):1/725760
((2, 2), (3, 2), (14, 1)):-1/84
((1, 6), (2, 4), (3, 1)):13667/14929920
((3, 2), (6, 2), (12, 1)):359/15552
((2, 2), (6, 2), (18, 1)):137/972
((1, 4), (2, 2), (3, 2), (4, 1)):-43/6912
((1, 2), (2, 2), (4, 2), (12, 1)):-53/1536
((1, 2), (2, 4), (3, 2), (6, 1)):-53/10368
((1, 2), (2, 6), (8, 1)):1/3072
((1, 2), (4, 2), (9, 1)):1/216
((1, 12),):1/4635202682880
((1, 4), (2, 4), (12, 1)):1357/995328
((1, 8), (2, 2), (4, 1)):11/2322432
((1, 2), (2, 2), (6, 1), (14, 1)):5/42
((1, 2), (2, 2), (4, 1), (6, 1), (12, 1)):53/144
((4, 2), (6, 1), (18, 1)):-1/216
((8, 2), (12, 1)):1/192
((1, 4), (3, 1), (7, 1)):5/126
((2, 4), (3, 1), (9, 1)):1/1296
((1, 4), (6, 2), (12, 1)):1/62208
((2, 6), (14, 1)):1/1764
((1, 2), (4, 1), (8, 1), (12, 1)):11/192
((1, 2), (3, 2), (4, 1), (8, 1)):13/1152
((2, 4), (8, 2)):3/1024
((1, 2), (2, 2), (6, 4)):-157/622080
((3, 2), (10, 2)):-1/3600
((1, 2), (2, 2), (4, 2), (6, 2)):53/9216
((4, 2), (5, 2)):-1/2400
((2, 4), (3, 4)):1/3732480
((1, 2), (2, 2), (8, 1), (12, 1)):1/32
((1, 6), (2, 6)):871/26542080
((1, 2), (2, 4), (14, 1)):5/84
((1, 4), (4, 2), (12, 1)):17/9216
((1, 2), (3, 5)):1/139968
((1, 4), (30, 1)):1/720
((1, 2), (2, 4), (6, 1), (10, 1)):1/24
((1, 2), (7, 1), (12, 1)):1/14
((1, 2), (2, 6), (4, 2)):-19/245760
((1, 2), (6, 2), (7, 1)):-1/84
((2, 4), (30, 1)):1/720
((1, 2), (2, 2), (12, 2)):1/384
((1, 4), (5, 1), (6, 2)):-1/3600
((1, 2), (2, 6), (4, 1), (6, 1)):23/13824
((1, 2), (2, 2), (4, 1), (6, 1), (10, 1)):1/12
((1, 2), (3, 1), (24, 1)):1/12
((2, 8), (12, 1)):1/348364800
((1, 2), (2, 4), (4, 3)):35/9216
((1, 4), (2, 2), (3, 1), (5, 1)):1/24
((4, 4), (6, 2)):-1/276480
((1, 4), (2, 2), (5, 1), (6, 1)):41/1800
((2, 4), (5, 2)):1/14400
((1, 6), (2, 2), (5, 1)):1/768
((1, 4), (2, 2), (3, 2), (6, 1)):259/62208
((1, 2), (2, 2), (3, 2), (10, 1)):13/720
((2, 4), (24, 1)):1/576
((1, 6), (3, 3)):241/1679616
((2, 2), (4, 1), (6, 2), (8, 1)):13/1152
((1, 2), (2, 4), (3, 1), (4, 1), (6, 1)):5/72
((2, 2), (4, 1), (16, 1)):5/32
((1, 2), (3, 1), (4, 2), (5, 1)):-1/30
((6, 2), (12, 2)):-7/576
((3, 4), (4, 2)):-1/622080
((2, 6), (4, 1), (8, 1)):1/18432
((1, 6), (3, 1), (4, 2)):-53/1244160
((1, 4), (3, 2), (4, 2)):13/2048
((1, 8), (2, 2), (6, 1)):431/1045094400
((1, 2), (2, 2), (3, 1), (6, 1), (10, 1)):2/15
((1, 2), (2, 2), (10, 1), (12, 1)):1/40
((2, 4), (6, 1), (18, 1)):283/3888
((2, 4), (4, 2), (12, 1)):17/9216
((1, 4), (3, 1), (9, 1)):283/3888
((1, 2), (2, 2), (8, 2)):27/512
((2, 2), (4, 2), (14, 1)):-1/14
((2, 2), (6, 3), (12, 1)):7/3888
((12, 3),):5/2592
((1, 4), (2, 4), (3, 1), (6, 1)):35/1296
((1, 4), (3, 1), (4, 1), (8, 1)):5/576
((1, 2), (3, 1), (5, 1), (6, 2)):1/180
((1, 2), (2, 4), (4, 1), (6, 2)):-43/6912
((8, 1), (16, 1)):5/16
((1, 4), (2, 4), (6, 2)):-25487/1990656
((3, 2), (4, 2), (12, 1)):5/3456
((2, 2), (6, 5)):1/139968
((1, 2), (2, 4), (7, 1)):1/42
((3, 2), (6, 4)):-281/933120
((1, 2), (2, 2), (3, 2), (8, 1)):-3/64
((10, 2), (12, 1)):1/600
((9, 2),):-5/162
((1, 2), (2, 2), (3, 1), (18, 1)):7/81
((1, 2), (5, 1), (9, 1)):2/9
((3, 1), (4, 2), (9, 1)):-1/216
((2, 2), (3, 4), (6, 1)):-1/25920
((1, 2), (2, 4), (5, 1), (6, 1)):1/72
((1, 4), (2, 4), (4, 1), (6, 1)):35/2304
((1, 2), (3, 3), (6, 2)):-49/23328
((1, 2), (2, 2), (6, 1), (18, 1)):47/216
((3, 6),):-1/11757312
((36, 1),):5/9
((1, 2), (2, 2), (4, 1), (6, 1), (8, 1)):41/192
((5, 2), (6, 2)):-1/3600
((2, 4), (4, 1), (6, 1), (8, 1)):5/576
((1, 6), (2, 2), (3, 1), (6, 1)):41/38880
((1, 2), (2, 4), (4, 1), (5, 1)):1/96
((1, 2), (4, 1), (5, 1), (8, 1)):1/8
((2, 2), (4, 2), (6, 3)):1/15552
((1, 2), (2, 4), (6, 1), (8, 1)):5/192
((1, 2), (2, 6), (12, 1)):1/92160
((1, 2), (2, 4), (3, 2), (4, 1)):-1/256
((1, 4), (2, 2), (4, 1), (5, 1)):7/96
((1, 2), (3, 2), (7, 1)):13/252
((1, 4), (2, 4), (3, 2)):-25487/1990656
((1, 2), (2, 4), (3, 1), (10, 1)):41/1800
((7, 2),):-5/294
((2, 8), (4, 2)):-337/2786918400
((3, 1), (6, 2), (9, 1)):1/324
((1, 2), (2, 2), (6, 1), (9, 1)):7/81
((2, 2), (4, 3), (8, 1)):5/1536
((2, 2), (4, 4), (6, 1)):-1/7680
((1, 2), (3, 1), (4, 2), (12, 1)):-43/864
((2, 6), (6, 3)):241/1679616
((1, 2), (9, 1), (12, 1)):1/54
((1, 2), (4, 1), (6, 2), (8, 1)):-1/384
((1, 4), (2, 2), (3, 1), (4, 2)):-73/4608
((1, 4), (2, 2), (3, 1), (4, 1), (6, 1)):5/72
((4, 2), (30, 1)):-1/120
((1, 2), (2, 2), (5, 1), (12, 1)):1/40
((1, 2), (2, 8), (4, 1)):11/2322432
((1, 6), (3, 1), (12, 1)):1/51840
((1, 8), (12, 1)):1/348364800
((6, 2), (30, 1)):1/12
((1, 4), (2, 2), (4, 1), (6, 2)):-1/256
((12, 1), (24, 1)):3/8
((1, 6), (2, 2), (12, 1)):1/92160
((2, 2), (3, 2), (6, 1), (12, 1)):-89/3888
((4, 2), (6, 2), (12, 1)):5/3456
((1, 2), (4, 2), (7, 1)):-1/14
((3, 2), (5, 2)):-1/3600
((1, 2), (2, 2), (30, 1)):1/40
((2, 4), (4, 4)):487/2211840
((2, 4), (20, 1)):1/480
((1, 4), (2, 4), (5, 1)):93/6400
((1, 2), (2, 2), (6, 2), (10, 1)):-3/80
((1, 2), (2, 2), (10, 2)):1/32
((2, 2), (6, 1), (10, 1), (12, 1)):1/10
((1, 6), (2, 2), (3, 1), (4, 1)):23/13824
((1, 6), (2, 4), (4, 1)):31/36864
((1, 2), (2, 2), (20, 1)):3/80
((1, 4), (2, 4), (3, 1), (4, 1)):35/2304
((2, 2), (4, 2), (6, 1), (12, 1)):-43/864
((2, 6), (3, 2), (6, 1)):1/933120
((1, 2), (2, 2), (4, 1), (14, 1)):5/14
((1, 2), (2, 2), (3, 1), (6, 1), (12, 1)):82/243
((1, 4), (4, 2), (5, 1)):-7/4800
((2, 4), (6, 2), (12, 1)):11/20736
((2, 2), (3, 2), (6, 1), (10, 1)):1/180
((1, 10), (3, 1)):1/627056640
((1, 2), (2, 6), (3, 1), (4, 1)):1/4608
((3, 2), (4, 2), (6, 2)):-41/62208
((2, 2), (6, 1), (20, 1)):1/30
((2, 10), (6, 1)):1/627056640
((1, 2), (2, 2), (4, 4)):-313/122880
((3, 2), (15, 1)):1/12
((1, 2), (3, 3), (12, 1)):7/3888
((3, 3), (9, 1)):5/2916
((1, 2), (3, 1), (6, 2), (12, 1)):-89/3888
((2, 8), (10, 1)):1/725760
((1, 4), (12, 2)):1/6912
((5, 2), (12, 1)):1/600
((1, 2), (3, 2), (9, 1)):137/972
((4, 4), (12, 1)):-157/138240
((1, 4), (3, 2), (5, 1)):-43/10800
((1, 2), (2, 2), (3, 4)):-157/622080
((18, 2),):-5/162
((2, 8), (6, 2)):-9283/6270566400
((2, 2), (6, 1), (30, 1)):1/9
((1, 4), (3, 2), (12, 1)):11/20736
((1, 4), (10, 2)):1/14400
((1, 8), (4, 2)):-337/2786918400
((1, 4), (4, 2), (6, 2)):55/497664
((1, 2), (2, 4), (4, 2), (6, 1)):-73/4608
((1, 2), (2, 6), (10, 1)):1/768
((1, 2), (2, 2), (4, 2), (5, 1)):-27/320
((1, 2), (2, 2), (3, 1), (9, 1)):47/216
((3, 2), (30, 1)):-1/180
((1, 2), (2, 2), (3, 1), (5, 1), (6, 1)):2/15
((28, 1),):5/7
((6, 2), (10, 2)):-1/3600
((1, 2), (2, 2), (4, 2), (10, 1)):-27/320
((2, 2), (3, 1), (6, 1), (9, 1)):1/27
((1, 2), (3, 1), (10, 2)):1/900
((6, 2), (24, 1)):1/144
((1, 2), (3, 1), (8, 2)):-1/288
((1, 8), (6, 2)):-1/2090188800
((2, 2), (5, 2), (6, 1)):1/900
((1, 4), (2, 2), (3, 1), (8, 1)):5/192
((3, 4), (6, 2)):-281/933120
((1, 2), (2, 2), (3, 2), (12, 1)):-5/1152
((4, 2), (8, 2)):-37/1536
((4, 2), (24, 1)):-1/96
((6, 4), (12, 1)):-1/17280
((3, 2), (20, 1)):-1/120
((2, 2), (12, 1), (14, 1)):1/14
((2, 2), (12, 1), (18, 1)):1/54
((1, 2), (3, 1), (20, 1)):1/30
((2, 2), (6, 1), (10, 2)):-1/60
((1, 4), (2, 6), (6, 1)):13667/14929920
((1, 2), (2, 4), (18, 1)):5/432
((1, 6), (2, 2), (3, 2)):-787/1658880
((2, 2), (3, 2), (6, 3)):-49/23328
((4, 2), (12, 2)):-323/3456
((1, 6), (2, 2), (4, 1), (6, 1)):1/4608
((1, 2), (3, 1), (30, 1)):1/45
((1, 2), (2, 8), (6, 1)):23/3483648
((1, 4), (2, 2), (3, 1), (12, 1)):1/192
((1, 2), (2, 2), (24, 1)):1/32
((1, 2), (2, 4), (4, 1), (12, 1)):11/1152
((2, 2), (22, 1)):10/11
((1, 4), (2, 8)):7661/1238630400
((1, 4), (2, 4), (8, 1)):35/4608
((2, 4), (6, 2), (10, 1)):-43/10800
((4, 2), (10, 2)):-1/2400
((1, 2), (2, 2), (3, 2), (6, 2)):1289/20736
((4, 2), (15, 1)):-1/120
((1, 2), (2, 2), (3, 1), (4, 1), (5, 1)):1/12
((1, 4), (2, 2), (6, 1), (12, 1)):107/31104
((3, 2), (6, 1), (18, 1)):1/324
((1, 2), (3, 1), (5, 1), (12, 1)):1/10
((2, 4), (3, 2), (10, 1)):-1/3600
((3, 2), (8, 2)):-1/1152
((1, 6), (4, 1), (8, 1)):1/18432
((2, 6), (4, 2), (6, 1)):-53/1244160
((2, 4), (12, 2)):1/6912
((6, 2), (8, 2)):-1/1152
((1, 8), (2, 2), (3, 1)):23/3483648
((1, 2), (2, 2), (15, 1)):1/40
((1, 2), (2, 2), (3, 1), (4, 1), (6, 2)):1/32
((1, 2), (2, 2), (3, 1), (6, 1), (8, 1)):5/18
((1, 2), (2, 2), (3, 3), (4, 1)):5/2592
((3, 4), (12, 1)):-1/17280
((1, 2), (2, 2), (3, 1), (4, 1), (12, 1)):53/144
((1, 4), (2, 2), (7, 1)):5/84
((1, 4), (2, 2), (18, 1)):7/864
((2, 4), (10, 2)):61/2880
((1, 4), (24, 1)):1/576
((1, 4), (6, 1), (18, 1)):1/1296
((1, 4), (2, 2), (4, 1), (8, 1)):219/2048
((1, 2), (2, 2), (5, 1), (6, 2)):13/720
((1, 2), (2, 2), (3, 1), (4, 2), (6, 1)):-377/1944
((1, 2), (3, 3), (4, 2)):1/15552
((1, 2), (2, 2), (5, 1), (10, 1)):6/5
((1, 2), (2, 2), (4, 2), (8, 1)):-103/256
((1, 6), (3, 1), (6, 2)):1/933120
((2, 4), (6, 4)):18883/11197440
((4, 6),):-5/4644864
((2, 2), (3, 2), (4, 1), (8, 1)):-1/384
((1, 4), (3, 2), (6, 2)):257/41472
((2, 2), (10, 1), (18, 1)):2/9
((1, 6), (2, 4), (6, 1)):31/165888
((1, 2), (3, 1), (4, 2), (6, 2)):5/15552
((1, 2), (2, 2), (4, 1), (5, 1), (6, 1)):1/12
((2, 4), (15, 1)):1/720
((1, 2), (2, 2), (3, 2), (4, 2)):53/9216
((1, 4), (2, 2), (4, 1), (10, 1)):1/96
((2, 6), (18, 1)):1/23328
((1, 6), (9, 1)):1/23328
((1, 2), (2, 2), (3, 1), (4, 3)):5/1152
((1, 2), (2, 4), (6, 1), (12, 1)):1/192
((1, 4), (2, 2), (6, 3)):7/62208
((1, 2), (2, 2), (3, 1), (4, 1), (8, 1)):41/192
((12, 1), (15, 1)):1/30
((2, 2), (3, 2), (18, 1)):-1/324
((1, 2), (2, 10)):1/222953472
((2, 6), (6, 1), (12, 1)):1/51840
((6, 1), (12, 1), (18, 1)):1/18
((1, 4), (2, 2), (4, 3)):35/9216
((1, 4), (2, 4), (4, 2)):-476093/7962624
((2, 2), (6, 1), (24, 1)):1/12
((2, 4), (4, 2), (10, 1)):-7/4800
((12, 1), (30, 1)):1/30
((1, 2), (2, 6), (3, 2)):13/1658880
((1, 2), (3, 1), (5, 2)):-1/60
((1, 4), (3, 4)):18883/11197440
((1, 2), (2, 2), (6, 1), (7, 1)):2/21
((1, 2), (2, 2), (3, 1), (4, 1), (10, 1)):1/12
((1, 2), (3, 1), (6, 1), (18, 1)):1/27
((6, 6),):-1/11757312
((1, 2), (6, 2), (9, 1)):-1/324
((1, 2), (2, 4), (6, 3)):125/31104
((1, 2), (2, 4), (3, 1), (4, 2)):-469/248832
((1, 2), (2, 2), (5, 1), (8, 1)):1/8
((1, 2), (2, 4), (4, 1), (8, 1)):219/2048
((1, 4), (2, 2), (3, 1), (10, 1)):1/72
((1, 2), (2, 6), (6, 2)):-787/1658880
((1, 2), (4, 1), (16, 1)):5/32
((1, 2), (2, 8), (3, 1)):431/1045094400
((1, 2), (2, 2), (5, 2)):1/32
((3, 1), (9, 1), (12, 1)):1/18
((1, 4), (4, 4)):487/2211840
((2, 12),):1/4635202682880
((2, 2), (3, 2), (4, 2), (6, 1)):5/15552
((1, 6), (2, 2), (6, 2)):13/1658880
((1, 6), (2, 2), (4, 2)):-19/245760
((1, 2), (3, 3), (5, 1)):1/324
((1, 6), (2, 2), (8, 1)):1/3072
((2, 2), (4, 1), (8, 1), (10, 1)):1/8
((1, 4), (5, 2)):61/2880
((1, 4), (8, 2)):3/1024
((2, 8), (3, 2)):-1/2090188800
((1, 2), (2, 4), (3, 1), (12, 1)):107/31104
((1, 2), (11, 1)):10/11
((2, 2), (6, 2), (14, 1)):13/252
((21, 1),):10/21
((1, 4), (6, 4)):1/3732480
((1, 2), (2, 4), (9, 1)):7/864
((1, 2), (2, 2), (3, 2), (5, 1)):-3/80
((1, 2), (2, 2), (3, 2), (4, 1), (6, 1)):1/32
((1, 2), (2, 2), (3, 1), (6, 3)):8/729
((1, 6), (7, 1)):1/1764
((2, 4), (3, 2), (12, 1)):1/62208
((1, 6), (2, 2), (10, 1)):1/11520
((1, 6), (3, 1), (5, 1)):1/1080
((2, 4), (10, 1), (12, 1)):1/600
((1, 4), (2, 6), (4, 1)):31/36864
((1, 2), (2, 2), (3, 1), (14, 1)):2/21
((1, 2), (3, 1), (12, 2)):-1/432
((1, 4), (2, 2), (6, 1), (8, 1)):5/576
((3, 2), (24, 1)):1/144
((1, 2), (2, 2), (3, 3), (6, 1)):8/729
((2, 4), (4, 2), (6, 2)):13/2048
((1, 2), (2, 2), (4, 1), (18, 1)):5/36
((4, 2), (20, 1)):-5/16
((1, 4), (15, 1)):1/720
((1, 2), (4, 3), (8, 1)):5/1536
((1, 2), (2, 4), (3, 1), (8, 1)):5/576
((1, 2), (2, 4), (3, 1), (6, 2)):259/62208
((2, 2), (4, 1), (8, 1), (12, 1)):11/192
((3, 2), (12, 2)):-7/576
((1, 4), (2, 6), (3, 1)):31/165888
((1, 2), (2, 4), (4, 1), (10, 1)):7/96
((1, 8), (2, 4)):7661/1238630400
((1, 4), (2, 2), (4, 2), (6, 1)):-469/248832
((1, 4), (2, 2), (3, 3)):125/31104
((1, 4), (2, 2), (3, 1), (6, 2)):-53/10368
((2, 2), (6, 1), (8, 2)):-1/288
((2, 2), (6, 1), (15, 1)):1/45
((1, 2), (2, 2), (6, 2), (12, 1)):-5/1152
((1, 2), (2, 2), (8, 1), (10, 1)):1/8
((1, 2), (2, 2), (6, 2), (8, 1)):-3/64
((1, 4), (2, 2), (14, 1)):1/42
((2, 2), (6, 3), (10, 1)):1/324
((6, 3), (18, 1)):5/2916
((1, 2), (2, 2), (4, 3), (6, 1)):5/1152
((2, 4), (3, 2), (4, 2)):55/497664
((2, 6), (6, 1), (10, 1)):1/1080
((2, 4), (3, 2), (6, 2)):257/41472
((2, 4), (6, 1), (14, 1)):5/126
((1, 4), (2, 2), (6, 1), (10, 1)):1/90