{[
[[[1, 25]], 1/143327232000],
[[[2, 25]], 1/143327232000],
[[[1, 1], [2, 24]], 1/3185049600],
[[[1, 2], [2, 23]], 49/7962624000],
[[[1, 3], [2, 22]], 4969/71663616000],
[[[1, 4], [2, 21]], 23893/47775744000],
[[[1, 5], [2, 20]], 4657/1911029760],
[[[1, 6], [2, 19]], 295927/35831808000],
[[[1, 7], [2, 18]], 235741/11943936000],
[[[1, 7], [3, 9]], 1/38880],
[[[1, 8], [2, 17]], 318641/9555148800],
[[[1, 9], [2, 16]], 126799/3185049600],
[[[1, 9], [3, 8]], 1/34560],
[[[1, 10], [2, 15]], 18239/530841600],
[[[1, 11], [2, 14]], 3941/176947200],
[[[1, 11], [3, 7]], 1/103680],
[[[1, 12], [2, 13]], 419/35389440],
[[[1, 13], [2, 12]], 419/35389440],
[[[1, 13], [3, 6]], 29/11197440],
[[[1, 13], [5, 3]], 1/10368000],
[[[1, 14], [2, 11]], 3941/176947200],
[[[1, 15], [2, 10]], 18239/530841600],
[[[1, 15], [3, 5]], 17/7464960],
[[[1, 16], [2, 9]], 126799/3185049600],
[[[1, 17], [2, 8]], 318641/9555148800],
[[[1, 17], [3, 4]], 49/49766400],
[[[1, 17], [5, 2]], 1/82944000],
[[[1, 18], [2, 7]], 235741/11943936000],
[[[1, 19], [2, 6]], 295927/35831808000],
[[[1, 19], [3, 3]], 1537/8957952000],
[[[1, 20], [2, 5]], 4657/1911029760],
[[[1, 21], [2, 4]], 23893/47775744000],
[[[1, 21], [3, 2]], 163/11943936000],
[[[1, 21], [5, 1]], 1/1990656000],
[[[1, 22], [2, 3]], 4969/71663616000],
[[[1, 23], [2, 2]], 49/7962624000],
[[[1, 23], [3, 1]], 1/1990656000],
[[[1, 24], [2, 1]], 1/3185049600],
[[[2, 7], [6, 9]], 1/38880],
[[[2, 9], [6, 8]], 1/34560],
[[[2, 11], [6, 7]], 1/103680],
[[[2, 13], [6, 6]], 29/11197440],
[[[2, 13], [10, 3]], 1/10368000],
[[[2, 15], [6, 5]], 17/7464960],
[[[2, 17], [6, 4]], 49/49766400],
[[[2, 17], [10, 2]], 1/82944000],
[[[2, 19], [6, 3]], 1537/8957952000],
[[[2, 21], [6, 2]], 163/11943936000],
[[[2, 21], [10, 1]], 1/1990656000],
[[[2, 23], [6, 1]], 1/1990656000],
[[[1, 1], [2, 8], [6, 8]], 1/10368],
[[[1, 1], [2, 10], [6, 7]], 7/103680],
[[[1, 1], [2, 12], [6, 6]], 19/933120],
[[[1, 1], [2, 12], [10, 3]], 1/691200],
[[[1, 1], [2, 14], [6, 5]], 17/746496],
[[[1, 1], [2, 16], [6, 4]], 2173/149299200],
[[[1, 1], [2, 16], [10, 2]], 1/3317760],
[[[1, 1], [2, 18], [6, 3]], 2713/746496000],
[[[1, 1], [2, 20], [6, 2]], 4669/11943936000],
[[[1, 1], [2, 20], [10, 1]], 7/398131200],
[[[1, 1], [2, 22], [4, 1]], 1/1492992000],
[[[1, 1], [2, 22], [6, 1]], 11/597196800],
[[[1, 2], [2, 7], [6, 8]], 1/103680],
[[[1, 2], [2, 9], [6, 7]], 13/103680],
[[[1, 2], [2, 11], [6, 6]], 61/933120],
[[[1, 2], [2, 11], [10, 3]], 29/3456000],
[[[1, 2], [2, 13], [6, 5]], 17/186624],
[[[1, 2], [2, 15], [6, 4]], 817/9331200],
[[[1, 2], [2, 15], [10, 2]], 7/2304000],
[[[1, 2], [2, 17], [6, 3]], 94027/2985984000],
[[[1, 2], [2, 19], [4, 2]], 1/44236800],
[[[1, 2], [2, 19], [6, 2]], 11153/2388787200],
[[[1, 2], [2, 19], [10, 1]], 517/1990656000],
[[[1, 2], [2, 21], [4, 1]], 47/1990656000],
[[[1, 2], [2, 21], [6, 1]], 1721/5971968000],
[[[1, 3], [2, 8], [6, 7]], 1/34560],
[[[1, 3], [2, 10], [6, 6]], 131/1399680],
[[[1, 3], [2, 10], [10, 3]], 253/10368000],
[[[1, 3], [2, 12], [6, 5]], 145/746496],
[[[1, 3], [2, 14], [6, 4]], 881/3110400],
[[[1, 3], [2, 14], [10, 2]], 337/20736000],
[[[1, 3], [2, 16], [4, 3]], 1/3317760],
[[[1, 3], [2, 16], [6, 3]], 332243/2239488000],
[[[1, 3], [2, 18], [4, 2]], 77/132710400],
[[[1, 3], [2, 18], [6, 2]], 367451/11943936000],
[[[1, 3], [2, 18], [10, 1]], 4243/1990656000],
[[[1, 3], [2, 20], [4, 1]], 7/19906560],
[[[1, 3], [2, 20], [6, 1]], 2527/995328000],
[[[1, 4], [2, 9], [6, 6]], 181/3732480],
[[[1, 4], [2, 9], [10, 3]], 133/3456000],
[[[1, 4], [2, 11], [6, 5]], 181/746496],
[[[1, 4], [2, 13], [4, 4]], 11/4423680],
[[[1, 4], [2, 13], [6, 4]], 40861/74649600],
[[[1, 4], [2, 13], [10, 2]], 2117/41472000],
[[[1, 4], [2, 15], [4, 3]], 11/2211840],
[[[1, 4], [2, 15], [6, 3]], 14063/33177600],
[[[1, 4], [2, 17], [4, 2]], 1/165888],
[[[1, 4], [2, 17], [6, 2]], 745579/5971968000],
[[[1, 4], [2, 17], [10, 1]], 10747/995328000],
[[[1, 4], [2, 19], [4, 1]], 17399/5971968000],
[[[1, 4], [2, 19], [6, 1]], 419/29859840],
[[[1, 5], [2, 8], [6, 6]], 1/93312],
[[[1, 5], [2, 8], [10, 3]], 23/691200],
[[[1, 5], [2, 10], [4, 5]], 1/20480],
[[[1, 5], [2, 10], [6, 5]], 671/3732480],
[[[1, 5], [2, 12], [4, 4]], 49/1474560],
[[[1, 5], [2, 12], [6, 4]], 1963/2985984],
[[[1, 5], [2, 12], [10, 2]], 271/2764800],
[[[1, 5], [2, 14], [4, 3]], 19/552960],
[[[1, 5], [2, 14], [6, 3]], 12803/16588800],
[[[1, 5], [2, 16], [4, 2]], 41/1228800],
[[[1, 5], [2, 16], [6, 2]], 1965853/5971968000],
[[[1, 5], [2, 16], [10, 1]], 7069/199065600],
[[[1, 5], [2, 18], [4, 1]], 3713/248832000],
[[[1, 5], [2, 18], [6, 1]], 19171/373248000],
[[[1, 5], [3, 7], [9, 1]], 1/1944],
[[[1, 6], [2, 7], [4, 6]], 1/2048],
[[[1, 6], [2, 7], [5, 3]], 1/384000],
[[[1, 6], [2, 7], [6, 6]], 1/559872],
[[[1, 6], [2, 7], [10, 3]], 17/1152000],
[[[1, 6], [2, 9], [4, 5]], 23/61440],
[[[1, 6], [2, 9], [6, 5]], 7/93312],
[[[1, 6], [2, 11], [4, 4]], 191/737280],
[[[1, 6], [2, 11], [6, 4]], 19/38880],
[[[1, 6], [2, 11], [10, 2]], 799/6912000],
[[[1, 6], [2, 13], [4, 3]], 983/6635520],
[[[1, 6], [2, 13], [6, 3]], 814957/895795200],
[[[1, 6], [2, 15], [4, 2]], 817/7372800],
[[[1, 6], [2, 15], [6, 2]], 690109/1194393600],
[[[1, 6], [2, 15], [10, 1]], 25733/331776000],
[[[1, 6], [2, 17], [4, 1]], 49481/995328000],
[[[1, 6], [2, 17], [6, 1]], 42473/331776000],
[[[1, 7], [2, 2], [3, 8]], 1/103680],
[[[1, 7], [2, 6], [3, 6]], 1/559872],
[[[1, 7], [2, 6], [4, 6]], 1/2048],
[[[1, 7], [2, 6], [5, 3]], 17/1152000],
[[[1, 7], [2, 6], [10, 3]], 1/384000],
[[[1, 7], [2, 8], [3, 5]], 1/1492992],
[[[1, 7], [2, 8], [4, 5]], 11/6144],
[[[1, 7], [2, 8], [6, 5]], 11/746496],
[[[1, 7], [2, 10], [4, 4]], 473/442368],
[[[1, 7], [2, 10], [6, 4]], 199/933120],
[[[1, 7], [2, 10], [10, 2]], 187/2304000],
[[[1, 7], [2, 12], [4, 3]], 307/614400],
[[[1, 7], [2, 12], [6, 3]], 20447/29859840],
[[[1, 7], [2, 14], [4, 2]], 16553/66355200],
[[[1, 7], [2, 14], [6, 2]], 161711/238878720],
[[[1, 7], [2, 14], [10, 1]], 37427/331776000],
[[[1, 7], [2, 16], [4, 1]], 1033/9331200],
[[[1, 7], [2, 16], [6, 1]], 32771/149299200],
[[[1, 7], [3, 3], [5, 3]], 1/324000],
[[[1, 7], [3, 6], [9, 1]], 1/1728],
[[[1, 8], [2, 1], [3, 8]], 1/10368],
[[[1, 8], [2, 3], [3, 7]], 1/34560],
[[[1, 8], [2, 5], [3, 6]], 1/93312],
[[[1, 8], [2, 5], [5, 3]], 23/691200],
[[[1, 8], [2, 7], [3, 5]], 11/746496],
[[[1, 8], [2, 7], [4, 5]], 11/6144],
[[[1, 8], [2, 7], [6, 5]], 1/1492992],
[[[1, 8], [2, 9], [3, 4]], 7/1990656],
[[[1, 8], [2, 9], [4, 4]], 1909/737280],
[[[1, 8], [2, 9], [5, 2]], 1/204800],
[[[1, 8], [2, 9], [6, 4]], 283/5971968],
[[[1, 8], [2, 9], [10, 2]], 19/614400],
[[[1, 8], [2, 11], [4, 3]], 4427/3686400],
[[[1, 8], [2, 11], [6, 3]], 37319/119439360],
[[[1, 8], [2, 13], [4, 2]], 3769/8294400],
[[[1, 8], [2, 13], [6, 2]], 250303/477757440],
[[[1, 8], [2, 13], [10, 1]], 4781/44236800],
[[[1, 8], [2, 15], [4, 1]], 33971/199065600],
[[[1, 8], [2, 15], [6, 1]], 12343/47775744],
[[[1, 9], [2, 2], [3, 7]], 13/103680],
[[[1, 9], [2, 4], [3, 6]], 181/3732480],
[[[1, 9], [2, 4], [5, 3]], 133/3456000],
[[[1, 9], [2, 6], [3, 5]], 7/93312],
[[[1, 9], [2, 6], [4, 5]], 23/61440],
[[[1, 9], [2, 8], [3, 4]], 283/5971968],
[[[1, 9], [2, 8], [4, 4]], 1909/737280],
[[[1, 9], [2, 8], [5, 2]], 19/614400],
[[[1, 9], [2, 8], [6, 4]], 7/1990656],
[[[1, 9], [2, 8], [10, 2]], 1/204800],
[[[1, 9], [2, 10], [3, 3]], 19/2654208],
[[[1, 9], [2, 10], [4, 3]], 4171/2211840],
[[[1, 9], [2, 10], [6, 3]], 19/248832],
[[[1, 9], [2, 12], [4, 2]], 7411/11059200],
[[[1, 9], [2, 12], [6, 2]], 4547/17694720],
[[[1, 9], [2, 12], [10, 1]], 3047/44236800],
[[[1, 9], [2, 14], [4, 1]], 6637/33177600],
[[[1, 9], [2, 14], [6, 1]], 41663/199065600],
[[[1, 9], [3, 2], [5, 3]], 1/288000],
[[[1, 9], [3, 4], [5, 2]], 1/129600],
[[[1, 9], [3, 5], [9, 1]], 1/5184],
[[[1, 10], [2, 1], [3, 7]], 7/103680],
[[[1, 10], [2, 3], [3, 6]], 131/1399680],
[[[1, 10], [2, 3], [5, 3]], 253/10368000],
[[[1, 10], [2, 5], [3, 5]], 671/3732480],
[[[1, 10], [2, 5], [4, 5]], 1/20480],
[[[1, 10], [2, 7], [3, 4]], 199/933120],
[[[1, 10], [2, 7], [4, 4]], 473/442368],
[[[1, 10], [2, 7], [5, 2]], 187/2304000],
[[[1, 10], [2, 9], [3, 3]], 19/248832],
[[[1, 10], [2, 9], [4, 3]], 4171/2211840],
[[[1, 10], [2, 9], [6, 3]], 19/2654208],
[[[1, 10], [2, 11], [3, 2]], 25/3538944],
[[[1, 10], [2, 11], [4, 2]], 1621/2211840],
[[[1, 10], [2, 11], [5, 1]], 77/14745600],
[[[1, 10], [2, 11], [6, 2]], 3721/53084160],
[[[1, 10], [2, 11], [10, 1]], 137/4915200],
[[[1, 10], [2, 13], [4, 1]], 931/4915200],
[[[1, 10], [2, 13], [6, 1]], 3077/26542080],
[[[1, 11], [2, 2], [3, 6]], 61/933120],
[[[1, 11], [2, 2], [5, 3]], 29/3456000],
[[[1, 11], [2, 4], [3, 5]], 181/746496],
[[[1, 11], [2, 6], [3, 4]], 19/38880],
[[[1, 11], [2, 6], [4, 4]], 191/737280],
[[[1, 11], [2, 6], [5, 2]], 799/6912000],
[[[1, 11], [2, 8], [3, 3]], 37319/119439360],
[[[1, 11], [2, 8], [4, 3]], 4427/3686400],
[[[1, 11], [2, 10], [3, 2]], 3721/53084160],
[[[1, 11], [2, 10], [4, 2]], 1621/2211840],
[[[1, 11], [2, 10], [5, 1]], 137/4915200],
[[[1, 11], [2, 10], [6, 2]], 25/3538944],
[[[1, 11], [2, 10], [10, 1]], 77/14745600],
[[[1, 11], [2, 12], [3, 1]], 23/4423680],
[[[1, 11], [2, 12], [4, 1]], 1289/8847360],
[[[1, 11], [2, 12], [6, 1]], 173/4423680],
[[[1, 11], [3, 1], [5, 3]], 1/864000],
[[[1, 11], [3, 3], [5, 2]], 47/5184000],
[[[1, 11], [3, 4], [9, 1]], 1/62208],
[[[1, 11], [3, 5], [5, 1]], 1/155520],
[[[1, 12], [2, 1], [3, 6]], 19/933120],
[[[1, 12], [2, 1], [5, 3]], 1/691200],
[[[1, 12], [2, 3], [3, 5]], 145/746496],
[[[1, 12], [2, 5], [3, 4]], 1963/2985984],
[[[1, 12], [2, 5], [4, 4]], 49/1474560],
[[[1, 12], [2, 5], [5, 2]], 271/2764800],
[[[1, 12], [2, 7], [3, 3]], 20447/29859840],
[[[1, 12], [2, 7], [4, 3]], 307/614400],
[[[1, 12], [2, 9], [3, 2]], 4547/17694720],
[[[1, 12], [2, 9], [4, 2]], 7411/11059200],
[[[1, 12], [2, 9], [5, 1]], 3047/44236800],
[[[1, 12], [2, 11], [3, 1]], 173/4423680],
[[[1, 12], [2, 11], [4, 1]], 1289/8847360],
[[[1, 12], [2, 11], [6, 1]], 23/4423680],
[[[1, 13], [2, 2], [3, 5]], 17/186624],
[[[1, 13], [2, 4], [3, 4]], 40861/74649600],
[[[1, 13], [2, 4], [4, 4]], 11/4423680],
[[[1, 13], [2, 4], [5, 2]], 2117/41472000],
[[[1, 13], [2, 6], [3, 3]], 814957/895795200],
[[[1, 13], [2, 6], [4, 3]], 983/6635520],
[[[1, 13], [2, 8], [3, 2]], 250303/477757440],
[[[1, 13], [2, 8], [4, 2]], 3769/8294400],
[[[1, 13], [2, 8], [5, 1]], 4781/44236800],
[[[1, 13], [2, 10], [3, 1]], 3077/26542080],
[[[1, 13], [2, 10], [4, 1]], 931/4915200],
[[[1, 13], [3, 2], [5, 2]], 23/6912000],
[[[1, 13], [3, 4], [5, 1]], 49/6220800],
[[[1, 14], [2, 1], [3, 5]], 17/746496],
[[[1, 14], [2, 3], [3, 4]], 881/3110400],
[[[1, 14], [2, 3], [5, 2]], 337/20736000],
[[[1, 14], [2, 5], [3, 3]], 12803/16588800],
[[[1, 14], [2, 5], [4, 3]], 19/552960],
[[[1, 14], [2, 7], [3, 2]], 161711/238878720],
[[[1, 14], [2, 7], [4, 2]], 16553/66355200],
[[[1, 14], [2, 7], [5, 1]], 37427/331776000],
[[[1, 14], [2, 9], [3, 1]], 41663/199065600],
[[[1, 14], [2, 9], [4, 1]], 6637/33177600],
[[[1, 15], [2, 2], [3, 4]], 817/9331200],
[[[1, 15], [2, 2], [5, 2]], 7/2304000],
[[[1, 15], [2, 4], [3, 3]], 14063/33177600],
[[[1, 15], [2, 4], [4, 3]], 11/2211840],
[[[1, 15], [2, 6], [3, 2]], 690109/1194393600],
[[[1, 15], [2, 6], [4, 2]], 817/7372800],
[[[1, 15], [2, 6], [5, 1]], 25733/331776000],
[[[1, 15], [2, 8], [3, 1]], 12343/47775744],
[[[1, 15], [2, 8], [4, 1]], 33971/199065600],
[[[1, 15], [3, 1], [5, 2]], 1/2592000],
[[[1, 15], [3, 3], [5, 1]], 49/15552000],
[[[1, 16], [2, 1], [3, 4]], 2173/149299200],
[[[1, 16], [2, 1], [5, 2]], 1/3317760],
[[[1, 16], [2, 3], [3, 3]], 332243/2239488000],
[[[1, 16], [2, 3], [4, 3]], 1/3317760],
[[[1, 16], [2, 5], [3, 2]], 1965853/5971968000],
[[[1, 16], [2, 5], [4, 2]], 41/1228800],
[[[1, 16], [2, 5], [5, 1]], 7069/199065600],
[[[1, 16], [2, 7], [3, 1]], 32771/149299200],
[[[1, 16], [2, 7], [4, 1]], 1033/9331200],
[[[1, 17], [2, 2], [3, 3]], 94027/2985984000],
[[[1, 17], [2, 4], [3, 2]], 745579/5971968000],
[[[1, 17], [2, 4], [4, 2]], 1/165888],
[[[1, 17], [2, 4], [5, 1]], 10747/995328000],
[[[1, 17], [2, 6], [3, 1]], 42473/331776000],
[[[1, 17], [2, 6], [4, 1]], 49481/995328000],
[[[1, 17], [3, 2], [5, 1]], 229/497664000],
[[[1, 18], [2, 1], [3, 3]], 2713/746496000],
[[[1, 18], [2, 3], [3, 2]], 367451/11943936000],
[[[1, 18], [2, 3], [4, 2]], 77/132710400],
[[[1, 18], [2, 3], [5, 1]], 4243/1990656000],
[[[1, 18], [2, 5], [3, 1]], 19171/373248000],
[[[1, 18], [2, 5], [4, 1]], 3713/248832000],
[[[1, 19], [2, 2], [3, 2]], 11153/2388787200],
[[[1, 19], [2, 2], [4, 2]], 1/44236800],
[[[1, 19], [2, 2], [5, 1]], 517/1990656000],
[[[1, 19], [2, 4], [3, 1]], 419/29859840],
[[[1, 19], [2, 4], [4, 1]], 17399/5971968000],
[[[1, 19], [3, 1], [5, 1]], 13/497664000],
[[[1, 20], [2, 1], [3, 2]], 4669/11943936000],
[[[1, 20], [2, 1], [5, 1]], 7/398131200],
[[[1, 20], [2, 3], [3, 1]], 2527/995328000],
[[[1, 20], [2, 3], [4, 1]], 7/19906560],
[[[1, 21], [2, 2], [3, 1]], 1721/5971968000],
[[[1, 21], [2, 2], [4, 1]], 47/1990656000],
[[[1, 22], [2, 1], [3, 1]], 11/597196800],
[[[1, 22], [2, 1], [4, 1]], 1/1492992000],
[[[2, 5], [6, 7], [18, 1]], 1/1944],
[[[2, 7], [6, 3], [10, 3]], 1/324000],
[[[2, 7], [6, 6], [18, 1]], 1/1728],
[[[2, 9], [6, 2], [10, 3]], 1/288000],
[[[2, 9], [6, 4], [10, 2]], 1/129600],
[[[2, 9], [6, 5], [18, 1]], 1/5184],
[[[2, 11], [6, 1], [10, 3]], 1/864000],
[[[2, 11], [6, 3], [10, 2]], 47/5184000],
[[[2, 11], [6, 4], [18, 1]], 1/62208],
[[[2, 11], [6, 5], [10, 1]], 1/155520],
[[[2, 13], [6, 2], [10, 2]], 23/6912000],
[[[2, 13], [6, 4], [10, 1]], 49/6220800],
[[[2, 15], [6, 1], [10, 2]], 1/2592000],
[[[2, 15], [6, 3], [10, 1]], 49/15552000],
[[[2, 17], [6, 2], [10, 1]], 229/497664000],
[[[2, 19], [6, 1], [10, 1]], 13/497664000],
[[[1, 1], [2, 6], [3, 1], [6, 8]], 11/38880],
[[[1, 1], [2, 6], [4, 1], [6, 8]], 1/51840],
[[[1, 1], [2, 6], [6, 3], [10, 3]], 1/108000],
[[[1, 1], [2, 6], [6, 6], [18, 1]], 5/2592],
[[[1, 1], [2, 8], [3, 1], [6, 7]], 11/34560],
[[[1, 1], [2, 8], [4, 1], [6, 7]], 1/51840],
[[[1, 1], [2, 8], [6, 2], [10, 3]], 19/864000],
[[[1, 1], [2, 8], [6, 4], [10, 2]], 1/32400],
[[[1, 1], [2, 8], [6, 5], [18, 1]], 7/5184],
[[[1, 1], [2, 10], [3, 1], [6, 6]], 11/103680],
[[[1, 1], [2, 10], [4, 1], [6, 6]], 1/207360],
[[[1, 1], [2, 10], [4, 1], [10, 3]], 1/1728000],
[[[1, 1], [2, 10], [6, 1], [10, 3]], 1/86400],
[[[1, 1], [2, 10], [6, 3], [10, 2]], 89/1296000],
[[[1, 1], [2, 10], [6, 4], [18, 1]], 1/5184],
[[[1, 1], [2, 10], [6, 5], [10, 1]], 1/31104],
[[[1, 1], [2, 12], [3, 1], [6, 5]], 11/1244160],
[[[1, 1], [2, 12], [4, 1], [6, 5]], 7/746496],
[[[1, 1], [2, 12], [6, 2], [10, 2]], 269/6912000],
[[[1, 1], [2, 12], [6, 4], [10, 1]], 431/6220800],
[[[1, 1], [2, 14], [4, 1], [6, 4]], 17/1492992],
[[[1, 1], [2, 14], [4, 1], [10, 2]], 1/2304000],
[[[1, 1], [2, 14], [6, 1], [10, 2]], 7/1036800],
[[[1, 1], [2, 14], [6, 3], [10, 1]], 2603/62208000],
[[[1, 1], [2, 16], [4, 1], [6, 3]], 1339/298598400],
[[[1, 1], [2, 16], [6, 2], [10, 1]], 4457/497664000],
[[[1, 1], [2, 18], [4, 1], [6, 2]], 949/1492992000],
[[[1, 1], [2, 18], [4, 1], [10, 1]], 11/331776000],
[[[1, 1], [2, 18], [6, 1], [10, 1]], 7/9953280],
[[[1, 1], [2, 20], [4, 1], [6, 1]], 211/5971968000],
[[[1, 2], [2, 5], [3, 2], [6, 7]], 5/7776],
[[[1, 2], [2, 5], [6, 3], [10, 3]], 1/108000],
[[[1, 2], [2, 5], [6, 6], [18, 1]], 1/5184],
[[[1, 2], [2, 7], [3, 1], [6, 7]], 11/10368],
[[[1, 2], [2, 7], [3, 2], [6, 6]], 5/6912],
[[[1, 2], [2, 7], [4, 1], [6, 7]], 1/17280],
[[[1, 2], [2, 7], [6, 2], [10, 3]], 1/21600],
[[[1, 2], [2, 7], [6, 4], [10, 2]], 1/21600],
[[[1, 2], [2, 7], [6, 5], [18, 1]], 13/5184],
[[[1, 2], [2, 9], [3, 1], [6, 6]], 77/103680],
[[[1, 2], [2, 9], [3, 2], [6, 5]], 5/20736],
[[[1, 2], [2, 9], [4, 1], [6, 6]], 1/34560],
[[[1, 2], [2, 9], [4, 1], [10, 3]], 1/192000],
[[[1, 2], [2, 9], [6, 1], [10, 3]], 37/864000],
[[[1, 2], [2, 9], [6, 3], [10, 2]], 109/576000],
[[[1, 2], [2, 9], [6, 4], [18, 1]], 1/1296],
[[[1, 2], [2, 9], [6, 5], [10, 1]], 1/15552],
[[[1, 2], [2, 11], [3, 1], [6, 5]], 11/103680],
[[[1, 2], [2, 11], [3, 2], [6, 4]], 5/248832],
[[[1, 2], [2, 11], [4, 1], [6, 5]], 1/20736],
[[[1, 2], [2, 11], [4, 2], [6, 4]], 1/55296],
[[[1, 2], [2, 11], [4, 2], [10, 2]], 1/460800],
[[[1, 2], [2, 11], [6, 2], [10, 2]], 9/51200],
[[[1, 2], [2, 11], [6, 4], [10, 1]], 1459/6220800],
[[[1, 2], [2, 13], [4, 1], [6, 4]], 253/2488320],
[[[1, 2], [2, 13], [4, 1], [10, 2]], 47/6912000],
[[[1, 2], [2, 13], [4, 2], [6, 3]], 23/1105920],
[[[1, 2], [2, 13], [6, 1], [10, 2]], 161/3456000],
[[[1, 2], [2, 13], [6, 3], [10, 1]], 13753/62208000],
[[[1, 2], [2, 15], [4, 1], [6, 3]], 599/9953280],
[[[1, 2], [2, 15], [4, 2], [6, 2]], 3/409600],
[[[1, 2], [2, 15], [4, 2], [10, 1]], 7/11059200],
[[[1, 2], [2, 15], [6, 2], [10, 1]], 3487/49766400],
[[[1, 2], [2, 17], [4, 1], [6, 2]], 1039/82944000],
[[[1, 2], [2, 17], [4, 1], [10, 1]], 31/36864000],
[[[1, 2], [2, 17], [4, 2], [6, 1]], 17/22118400],
[[[1, 2], [2, 17], [6, 1], [10, 1]], 3871/497664000],
[[[1, 2], [2, 19], [4, 1], [6, 1]], 239/248832000],
[[[1, 3], [2, 4], [3, 3], [6, 6]], 1/2592],
[[[1, 3], [2, 4], [6, 3], [10, 3]], 1/324000],
[[[1, 3], [2, 6], [3, 1], [6, 7]], 11/103680],
[[[1, 3], [2, 6], [3, 2], [6, 6]], 25/10368],
[[[1, 3], [2, 6], [3, 3], [6, 5]], 1/2304],
[[[1, 3], [2, 6], [6, 2], [10, 3]], 1/24000],
[[[1, 3], [2, 6], [6, 4], [10, 2]], 1/32400],
[[[1, 3], [2, 6], [6, 5], [18, 1]], 1/1728],
[[[1, 3], [2, 8], [3, 1], [6, 6]], 143/103680],
[[[1, 3], [2, 8], [3, 2], [6, 5]], 35/20736],
[[[1, 3], [2, 8], [3, 3], [6, 4]], 1/6912],
[[[1, 3], [2, 8], [4, 1], [6, 6]], 1/23040],
[[[1, 3], [2, 8], [4, 1], [10, 3]], 1/57600],
[[[1, 3], [2, 8], [6, 1], [10, 3]], 1/13500],
[[[1, 3], [2, 8], [6, 3], [10, 2]], 323/1296000],
[[[1, 3], [2, 8], [6, 4], [18, 1]], 1/864],
[[[1, 3], [2, 8], [6, 5], [10, 1]], 1/15552],
[[[1, 3], [2, 10], [3, 1], [6, 5]], 11/25920],
[[[1, 3], [2, 10], [3, 2], [6, 4]], 5/20736],
[[[1, 3], [2, 10], [3, 3], [6, 3]], 1/82944],
[[[1, 3], [2, 10], [4, 1], [6, 5]], 25/248832],
[[[1, 3], [2, 10], [4, 2], [6, 4]], 13/165888],
[[[1, 3], [2, 10], [4, 2], [10, 2]], 1/51200],
[[[1, 3], [2, 10], [4, 3], [6, 3]], 5/331776],
[[[1, 3], [2, 10], [6, 2], [10, 2]], 2741/6912000],
[[[1, 3], [2, 10], [6, 4], [10, 1]], 2521/6220800],
[[[1, 3], [2, 12], [4, 1], [6, 4]], 877/2488320],
[[[1, 3], [2, 12], [4, 1], [10, 2]], 19/460800],
[[[1, 3], [2, 12], [4, 2], [6, 3]], 17/103680],
[[[1, 3], [2, 12], [4, 3], [6, 2]], 1/61440],
[[[1, 3], [2, 12], [4, 3], [8, 1]], 1/368640],
[[[1, 3], [2, 12], [4, 3], [10, 1]], 1/368640],
[[[1, 3], [2, 12], [6, 1], [10, 2]], 863/5184000],
[[[1, 3], [2, 12], [6, 3], [10, 1]], 37891/62208000],
[[[1, 3], [2, 14], [4, 1], [6, 3]], 16061/49766400],
[[[1, 3], [2, 14], [4, 2], [6, 2]], 973/11059200],
[[[1, 3], [2, 14], [4, 2], [10, 1]], 113/11059200],
[[[1, 3], [2, 14], [4, 3], [6, 1]], 11/2211840],
[[[1, 3], [2, 14], [6, 2], [10, 1]], 72569/248832000],
[[[1, 3], [2, 16], [4, 1], [6, 2]], 24707/248832000],
[[[1, 3], [2, 16], [4, 1], [10, 1]], 143/16588800],
[[[1, 3], [2, 16], [4, 2], [6, 1]], 463/33177600],
[[[1, 3], [2, 16], [6, 1], [10, 1]], 5803/124416000],
[[[1, 3], [2, 18], [4, 1], [6, 1]], 21379/1990656000],
[[[1, 3], [3, 5], [5, 1], [15, 1]], 1/1620],
[[[1, 4], [2, 3], [3, 3], [5, 3]], 1/324000],
[[[1, 4], [2, 3], [3, 6], [6, 3]], 1/2592],
[[[1, 4], [2, 5], [3, 2], [5, 3]], 1/864000],
[[[1, 4], [2, 5], [3, 2], [6, 6]], 5/20736],
[[[1, 4], [2, 5], [3, 3], [6, 5]], 5/3456],
[[[1, 4], [2, 5], [3, 5], [6, 3]], 1/6912],
[[[1, 4], [2, 5], [6, 2], [10, 3]], 13/864000],
[[[1, 4], [2, 5], [6, 4], [10, 2]], 1/129600],
[[[1, 4], [2, 7], [3, 1], [6, 6]], 11/34560],
[[[1, 4], [2, 7], [3, 2], [6, 5]], 65/20736],
[[[1, 4], [2, 7], [3, 3], [6, 4]], 7/6912],
[[[1, 4], [2, 7], [4, 1], [10, 3]], 23/864000],
[[[1, 4], [2, 7], [6, 1], [10, 3]], 11/172800],
[[[1, 4], [2, 7], [6, 3], [10, 2]], 169/1036800],
[[[1, 4], [2, 7], [6, 4], [18, 1]], 1/2304],
[[[1, 4], [2, 7], [6, 5], [10, 1]], 1/31104],
[[[1, 4], [2, 9], [3, 1], [6, 5]], 11/17280],
[[[1, 4], [2, 9], [3, 2], [6, 4]], 1/864],
[[[1, 4], [2, 9], [3, 3], [6, 3]], 1/6912],
[[[1, 4], [2, 9], [4, 1], [6, 5]], 5/46656],
[[[1, 4], [2, 9], [4, 2], [6, 4]], 11/82944],
[[[1, 4], [2, 9], [4, 2], [10, 2]], 1/15360],
[[[1, 4], [2, 9], [4, 3], [6, 3]], 1/18432],
[[[1, 4], [2, 9], [4, 4], [6, 2]], 49/221184],
[[[1, 4], [2, 9], [4, 4], [8, 1]], 1/10240],
[[[1, 4], [2, 9], [4, 4], [10, 1]], 1/30720],
[[[1, 4], [2, 9], [5, 1], [10, 2]], 1/57600],
[[[1, 4], [2, 9], [6, 2], [10, 2]], 3353/6912000],
[[[1, 4], [2, 9], [6, 4], [10, 1]], 2399/6220800],
[[[1, 4], [2, 11], [3, 2], [6, 3]], 7/207360],
[[[1, 4], [2, 11], [4, 1], [6, 4]], 4709/7464960],
[[[1, 4], [2, 11], [4, 1], [10, 2]], 97/768000],
[[[1, 4], [2, 11], [4, 2], [6, 3]], 1603/3317760],
[[[1, 4], [2, 11], [4, 3], [6, 2]], 31/276480],
[[[1, 4], [2, 11], [4, 3], [8, 1]], 17/368640],
[[[1, 4], [2, 11], [4, 3], [10, 1]], 1/40960],
[[[1, 4], [2, 11], [4, 4], [6, 1]], 47/1105920],
[[[1, 4], [2, 11], [6, 1], [10, 2]], 701/2073600],
[[[1, 4], [2, 11], [6, 3], [10, 1]], 11989/12441600],
[[[1, 4], [2, 13], [3, 2], [6, 2]], 1/829440],
[[[1, 4], [2, 13], [4, 1], [6, 3]], 135589/149299200],
[[[1, 4], [2, 13], [4, 2], [6, 2]], 4573/11059200],
[[[1, 4], [2, 13], [4, 2], [8, 1]], 1/276480],
[[[1, 4], [2, 13], [4, 2], [10, 1]], 47/737280],
[[[1, 4], [2, 13], [4, 3], [6, 1]], 29/552960],
[[[1, 4], [2, 13], [5, 1], [10, 1]], 1/1382400],
[[[1, 4], [2, 13], [6, 2], [10, 1]], 89051/124416000],
[[[1, 4], [2, 15], [4, 1], [6, 2]], 313327/746496000],
[[[1, 4], [2, 15], [4, 1], [10, 1]], 3899/82944000],
[[[1, 4], [2, 15], [4, 2], [6, 1]], 829/8294400],
[[[1, 4], [2, 15], [6, 1], [10, 1]], 8393/49766400],
[[[1, 4], [2, 17], [4, 1], [6, 1]], 4867/74649600],
[[[1, 5], [2, 2], [3, 3], [5, 3]], 1/108000],
[[[1, 5], [2, 2], [3, 6], [9, 1]], 1/5184],
[[[1, 5], [2, 2], [3, 7], [6, 2]], 5/7776],
[[[1, 5], [2, 4], [3, 2], [5, 3]], 13/864000],
[[[1, 5], [2, 4], [3, 3], [6, 5]], 1/6912],
[[[1, 5], [2, 4], [3, 4], [5, 2]], 1/129600],
[[[1, 5], [2, 4], [3, 5], [6, 3]], 5/3456],
[[[1, 5], [2, 4], [3, 6], [6, 2]], 5/20736],
[[[1, 5], [2, 4], [6, 2], [10, 3]], 1/864000],
[[[1, 5], [2, 6], [3, 1], [5, 3]], 1/288000],
[[[1, 5], [2, 6], [3, 2], [6, 5]], 5/6912],
[[[1, 5], [2, 6], [3, 3], [5, 2]], 1/345600],
[[[1, 5], [2, 6], [3, 3], [6, 4]], 13/6912],
[[[1, 5], [2, 6], [3, 4], [6, 3]], 1/2304],
[[[1, 5], [2, 6], [4, 1], [5, 3]], 1/192000],
[[[1, 5], [2, 6], [4, 1], [10, 3]], 11/576000],
[[[1, 5], [2, 6], [4, 5], [5, 1]], 1/5120],
[[[1, 5], [2, 6], [4, 5], [8, 1]], 1/1024],
[[[1, 5], [2, 6], [4, 5], [10, 1]], 1/5120],
[[[1, 5], [2, 6], [6, 1], [10, 3]], 11/432000],
[[[1, 5], [2, 6], [6, 3], [10, 2]], 1/21600],
[[[1, 5], [2, 6], [6, 5], [10, 1]], 1/155520],
[[[1, 5], [2, 8], [3, 1], [6, 5]], 11/46080],
[[[1, 5], [2, 8], [3, 2], [6, 4]], 19/10368],
[[[1, 5], [2, 8], [3, 3], [6, 3]], 1/1728],
[[[1, 5], [2, 8], [4, 1], [6, 5]], 5/82944],
[[[1, 5], [2, 8], [4, 2], [6, 4]], 1/9216],
[[[1, 5], [2, 8], [4, 2], [10, 2]], 23/230400],
[[[1, 5], [2, 8], [4, 3], [6, 3]], 1/13824],
[[[1, 5], [2, 8], [4, 4], [6, 2]], 11/24576],
[[[1, 5], [2, 8], [4, 4], [8, 1]], 23/30720],
[[[1, 5], [2, 8], [4, 4], [10, 1]], 7/30720],
[[[1, 5], [2, 8], [4, 5], [6, 1]], 1/2048],
[[[1, 5], [2, 8], [5, 1], [10, 2]], 7/57600],
[[[1, 5], [2, 8], [6, 2], [10, 2]], 737/2304000],
[[[1, 5], [2, 8], [6, 4], [10, 1]], 49/248832],
[[[1, 5], [2, 10], [3, 2], [6, 3]], 31/103680],
[[[1, 5], [2, 10], [4, 1], [6, 4]], 1577/2488320],
[[[1, 5], [2, 10], [4, 1], [10, 2]], 1469/6912000],
[[[1, 5], [2, 10], [4, 2], [6, 3]], 13/18432],
[[[1, 5], [2, 10], [4, 3], [6, 2]], 49/69120],
[[[1, 5], [2, 10], [4, 3], [8, 1]], 71/184320],
[[[1, 5], [2, 10], [4, 3], [10, 1]], 3/20480],
[[[1, 5], [2, 10], [4, 4], [6, 1]], 67/184320],
[[[1, 5], [2, 10], [6, 1], [10, 2]], 77/192000],
[[[1, 5], [2, 10], [6, 3], [10, 1]], 11153/12441600],
[[[1, 5], [2, 12], [3, 2], [6, 2]], 17/829440],
[[[1, 5], [2, 12], [4, 1], [6, 3]], 9211/6220800],
[[[1, 5], [2, 12], [4, 2], [6, 2]], 3647/3686400],
[[[1, 5], [2, 12], [4, 2], [8, 1]], 17/276480],
[[[1, 5], [2, 12], [4, 2], [10, 1]], 2227/11059200],
[[[1, 5], [2, 12], [4, 3], [6, 1]], 127/442368],
[[[1, 5], [2, 12], [5, 1], [10, 1]], 17/1382400],
[[[1, 5], [2, 12], [6, 2], [10, 1]], 1049/972000],
[[[1, 5], [2, 14], [4, 1], [6, 2]], 4357/4147200],
[[[1, 5], [2, 14], [4, 1], [8, 1]], 1/1105920],
[[[1, 5], [2, 14], [4, 1], [10, 1]], 8353/55296000],
[[[1, 5], [2, 14], [4, 2], [6, 1]], 55/147456],
[[[1, 5], [2, 14], [6, 1], [10, 1]], 12001/31104000],
[[[1, 5], [2, 16], [4, 1], [6, 1]], 238063/995328000],
[[[1, 5], [3, 4], [5, 1], [15, 1]], 1/1440],
[[[1, 6], [2, 1], [3, 3], [5, 3]], 1/108000],
[[[1, 6], [2, 1], [3, 6], [9, 1]], 5/2592],
[[[1, 6], [2, 1], [3, 8], [4, 1]], 1/51840],
[[[1, 6], [2, 1], [3, 8], [6, 1]], 11/38880],
[[[1, 6], [2, 3], [3, 2], [5, 3]], 1/24000],
[[[1, 6], [2, 3], [3, 4], [5, 2]], 1/32400],
[[[1, 6], [2, 3], [3, 5], [6, 3]], 1/2304],
[[[1, 6], [2, 3], [3, 5], [9, 1]], 1/1728],
[[[1, 6], [2, 3], [3, 6], [6, 2]], 25/10368],
[[[1, 6], [2, 3], [3, 7], [6, 1]], 11/103680],
[[[1, 6], [2, 5], [3, 1], [5, 3]], 11/432000],
[[[1, 6], [2, 5], [3, 3], [5, 2]], 1/21600],
[[[1, 6], [2, 5], [3, 3], [6, 4]], 1/2304],
[[[1, 6], [2, 5], [3, 4], [6, 3]], 13/6912],
[[[1, 6], [2, 5], [3, 5], [5, 1]], 1/155520],
[[[1, 6], [2, 5], [3, 5], [6, 2]], 5/6912],
[[[1, 6], [2, 5], [4, 1], [5, 3]], 11/576000],
[[[1, 6], [2, 5], [4, 1], [10, 3]], 1/192000],
[[[1, 6], [2, 5], [4, 5], [5, 1]], 1/5120],
[[[1, 6], [2, 5], [4, 5], [8, 1]], 1/1024],
[[[1, 6], [2, 5], [4, 5], [10, 1]], 1/5120],
[[[1, 6], [2, 5], [6, 1], [10, 3]], 1/288000],
[[[1, 6], [2, 5], [6, 3], [10, 2]], 1/345600],
[[[1, 6], [2, 7], [3, 1], [4, 5]], 1/6144],
[[[1, 6], [2, 7], [3, 2], [4, 4]], 1/221184],
[[[1, 6], [2, 7], [3, 2], [5, 2]], 1/92160],
[[[1, 6], [2, 7], [3, 2], [6, 4]], 61/82944],
[[[1, 6], [2, 7], [3, 3], [4, 3]], 1/110592],
[[[1, 6], [2, 7], [3, 3], [6, 3]], 11/9216],
[[[1, 6], [2, 7], [3, 4], [4, 2]], 1/165888],
[[[1, 6], [2, 7], [3, 4], [5, 1]], 1/414720],
[[[1, 6], [2, 7], [3, 5], [4, 1]], 1/746496],
[[[1, 6], [2, 7], [4, 1], [6, 5]], 1/62208],
[[[1, 6], [2, 7], [4, 2], [5, 2]], 1/51200],
[[[1, 6], [2, 7], [4, 2], [6, 4]], 7/165888],
[[[1, 6], [2, 7], [4, 2], [10, 2]], 11/153600],
[[[1, 6], [2, 7], [4, 3], [6, 3]], 7/165888],
[[[1, 6], [2, 7], [4, 4], [5, 1]], 1/2048],
[[[1, 6], [2, 7], [4, 4], [6, 2]], 17/73728],
[[[1, 6], [2, 7], [4, 4], [8, 1]], 3/1024],
[[[1, 6], [2, 7], [4, 4], [10, 1]], 7/10240],
[[[1, 6], [2, 7], [4, 5], [6, 1]], 1/1536],
[[[1, 6], [2, 7], [5, 1], [10, 2]], 1/6400],
[[[1, 6], [2, 7], [5, 2], [10, 1]], 1/19200],
[[[1, 6], [2, 7], [6, 2], [10, 2]], 47/460800],
[[[1, 6], [2, 7], [6, 4], [10, 1]], 19/414720],
[[[1, 6], [2, 9], [3, 2], [6, 3]], 13/20736],
[[[1, 6], [2, 9], [4, 1], [6, 4]], 883/2488320],
[[[1, 6], [2, 9], [4, 1], [10, 2]], 51/256000],
[[[1, 6], [2, 9], [4, 2], [6, 3]], 1807/3317760],
[[[1, 6], [2, 9], [4, 3], [6, 2]], 109/92160],
[[[1, 6], [2, 9], [4, 3], [8, 1]], 283/184320],
[[[1, 6], [2, 9], [4, 3], [10, 1]], 107/184320],
[[[1, 6], [2, 9], [4, 4], [6, 1]], 1/576],
[[[1, 6], [2, 9], [6, 1], [10, 2]], 313/1152000],
[[[1, 6], [2, 9], [6, 3], [10, 1]], 1961/4147200],
[[[1, 6], [2, 11], [3, 1], [6, 3]], 11/103680],
[[[1, 6], [2, 11], [3, 2], [6, 2]], 47/414720],
[[[1, 6], [2, 11], [4, 1], [6, 3]], 14329/9953280],
[[[1, 6], [2, 11], [4, 2], [6, 2]], 10601/6635520],
[[[1, 6], [2, 11], [4, 2], [8, 1]], 103/276480],
[[[1, 6], [2, 11], [4, 2], [10, 1]], 869/2211840],
[[[1, 6], [2, 11], [4, 3], [6, 1]], 301/276480],
[[[1, 6], [2, 11], [5, 1], [10, 1]], 47/691200],
[[[1, 6], [2, 11], [6, 2], [10, 1]], 5537/5529600],
[[[1, 6], [2, 13], [3, 1], [6, 2]], 77/4147200],
[[[1, 6], [2, 13], [4, 1], [6, 2]], 80911/49766400],
[[[1, 6], [2, 13], [4, 1], [8, 1]], 17/1105920],
[[[1, 6], [2, 13], [4, 1], [10, 1]], 49487/165888000],
[[[1, 6], [2, 13], [4, 2], [6, 1]], 28163/33177600],
[[[1, 6], [2, 13], [6, 1], [10, 1]], 47089/82944000],
[[[1, 6], [2, 15], [3, 1], [6, 1]], 11/16588800],
[[[1, 6], [2, 15], [4, 1], [6, 1]], 13859/24883200],
[[[1, 7], [2, 2], [3, 2], [5, 3]], 1/21600],
[[[1, 7], [2, 2], [3, 4], [5, 2]], 1/21600],
[[[1, 7], [2, 2], [3, 5], [9, 1]], 13/5184],
[[[1, 7], [2, 2], [3, 6], [6, 2]], 5/6912],
[[[1, 7], [2, 2], [3, 7], [4, 1]], 1/17280],
[[[1, 7], [2, 2], [3, 7], [6, 1]], 11/10368],
[[[1, 7], [2, 4], [3, 1], [5, 3]], 11/172800],
[[[1, 7], [2, 4], [3, 3], [5, 2]], 169/1036800],
[[[1, 7], [2, 4], [3, 4], [6, 3]], 7/6912],
[[[1, 7], [2, 4], [3, 4], [9, 1]], 1/2304],
[[[1, 7], [2, 4], [3, 5], [5, 1]], 1/31104],
[[[1, 7], [2, 4], [3, 5], [6, 2]], 65/20736],
[[[1, 7], [2, 4], [3, 6], [6, 1]], 11/34560],
[[[1, 7], [2, 4], [4, 1], [5, 3]], 23/864000],
[[[1, 7], [2, 6], [3, 1], [4, 5]], 1/1536],
[[[1, 7], [2, 6], [3, 2], [4, 4]], 17/73728],
[[[1, 7], [2, 6], [3, 2], [5, 2]], 47/460800],
[[[1, 7], [2, 6], [3, 3], [4, 3]], 7/165888],
[[[1, 7], [2, 6], [3, 3], [6, 3]], 11/9216],
[[[1, 7], [2, 6], [3, 4], [4, 2]], 7/165888],
[[[1, 7], [2, 6], [3, 4], [5, 1]], 19/414720],
[[[1, 7], [2, 6], [3, 4], [6, 2]], 61/82944],
[[[1, 7], [2, 6], [3, 5], [4, 1]], 1/62208],
[[[1, 7], [2, 6], [4, 1], [6, 5]], 1/746496],
[[[1, 7], [2, 6], [4, 2], [5, 2]], 11/153600],
[[[1, 7], [2, 6], [4, 2], [6, 4]], 1/165888],
[[[1, 7], [2, 6], [4, 2], [10, 2]], 1/51200],
[[[1, 7], [2, 6], [4, 3], [6, 3]], 1/110592],
[[[1, 7], [2, 6], [4, 4], [5, 1]], 7/10240],
[[[1, 7], [2, 6], [4, 4], [6, 2]], 1/221184],
[[[1, 7], [2, 6], [4, 4], [8, 1]], 3/1024],
[[[1, 7], [2, 6], [4, 4], [10, 1]], 1/2048],
[[[1, 7], [2, 6], [4, 5], [6, 1]], 1/6144],
[[[1, 7], [2, 6], [5, 1], [10, 2]], 1/19200],
[[[1, 7], [2, 6], [5, 2], [10, 1]], 1/6400],
[[[1, 7], [2, 6], [6, 2], [10, 2]], 1/92160],
[[[1, 7], [2, 6], [6, 4], [10, 1]], 1/414720],
[[[1, 7], [2, 8], [3, 1], [4, 4]], 31/73728],
[[[1, 7], [2, 8], [3, 1], [5, 2]], 1/76800],
[[[1, 7], [2, 8], [3, 2], [4, 3]], 1/27648],
[[[1, 7], [2, 8], [3, 2], [6, 3]], 1/2304],
[[[1, 7], [2, 8], [3, 3], [4, 2]], 7/221184],
[[[1, 7], [2, 8], [3, 3], [5, 1]], 1/92160],
[[[1, 7], [2, 8], [3, 3], [6, 2]], 1/13824],
[[[1, 7], [2, 8], [3, 4], [4, 1]], 5/497664],
[[[1, 7], [2, 8], [4, 1], [5, 2]], 1/51200],
[[[1, 7], [2, 8], [4, 1], [6, 4]], 149/1492992],
[[[1, 7], [2, 8], [4, 1], [10, 2]], 1/10240],
[[[1, 7], [2, 8], [4, 2], [6, 3]], 35/165888],
[[[1, 7], [2, 8], [4, 3], [5, 1]], 869/1843200],
[[[1, 7], [2, 8], [4, 3], [6, 2]], 67/110592],
[[[1, 7], [2, 8], [4, 3], [8, 1]], 113/36864],
[[[1, 7], [2, 8], [4, 3], [10, 1]], 1709/1843200],
[[[1, 7], [2, 8], [4, 4], [6, 1]], 203/110592],
[[[1, 7], [2, 8], [6, 1], [10, 2]], 11/115200],
[[[1, 7], [2, 8], [6, 3], [10, 1]], 103/829440],
[[[1, 7], [2, 10], [3, 1], [6, 3]], 11/51840],
[[[1, 7], [2, 10], [3, 2], [6, 2]], 11/46080],
[[[1, 7], [2, 10], [4, 1], [6, 3]], 24301/29859840],
[[[1, 7], [2, 10], [4, 2], [6, 2]], 10261/6635520],
[[[1, 7], [2, 10], [4, 2], [8, 1]], 89/92160],
[[[1, 7], [2, 10], [4, 2], [10, 1]], 7031/11059200],
[[[1, 7], [2, 10], [4, 3], [6, 1]], 1093/442368],
[[[1, 7], [2, 10], [5, 1], [10, 1]], 11/76800],
[[[1, 7], [2, 10], [6, 2], [10, 1]], 607/1105920],
[[[1, 7], [2, 12], [3, 1], [6, 2]], 341/2073600],
[[[1, 7], [2, 12], [4, 1], [6, 2]], 9739/5971968],
[[[1, 7], [2, 12], [4, 1], [8, 1]], 47/552960],
[[[1, 7], [2, 12], [4, 1], [10, 1]], 2071/5529600],
[[[1, 7], [2, 12], [4, 2], [6, 1]], 16063/11059200],
[[[1, 7], [2, 12], [6, 1], [10, 1]], 4411/8294400],
[[[1, 7], [2, 14], [3, 1], [6, 1]], 187/16588800],
[[[1, 7], [2, 14], [4, 1], [6, 1]], 507499/597196800],
[[[1, 7], [3, 3], [5, 1], [15, 1]], 1/4320],
[[[1, 8], [2, 1], [3, 2], [5, 3]], 19/864000],
[[[1, 8], [2, 1], [3, 4], [5, 2]], 1/32400],
[[[1, 8], [2, 1], [3, 5], [9, 1]], 7/5184],
[[[1, 8], [2, 1], [3, 7], [4, 1]], 1/51840],
[[[1, 8], [2, 1], [3, 7], [6, 1]], 11/34560],
[[[1, 8], [2, 3], [3, 1], [5, 3]], 1/13500],
[[[1, 8], [2, 3], [3, 3], [5, 2]], 323/1296000],
[[[1, 8], [2, 3], [3, 4], [6, 3]], 1/6912],
[[[1, 8], [2, 3], [3, 4], [9, 1]], 1/864],
[[[1, 8], [2, 3], [3, 5], [5, 1]], 1/15552],
[[[1, 8], [2, 3], [3, 5], [6, 2]], 35/20736],
[[[1, 8], [2, 3], [3, 6], [4, 1]], 1/23040],
[[[1, 8], [2, 3], [3, 6], [6, 1]], 143/103680],
[[[1, 8], [2, 3], [4, 1], [5, 3]], 1/57600],
[[[1, 8], [2, 5], [3, 1], [4, 5]], 1/2048],
[[[1, 8], [2, 5], [3, 2], [4, 4]], 11/24576],
[[[1, 8], [2, 5], [3, 2], [5, 2]], 737/2304000],
[[[1, 8], [2, 5], [3, 3], [4, 3]], 1/13824],
[[[1, 8], [2, 5], [3, 3], [6, 3]], 1/1728],
[[[1, 8], [2, 5], [3, 4], [4, 2]], 1/9216],
[[[1, 8], [2, 5], [3, 4], [5, 1]], 49/248832],
[[[1, 8], [2, 5], [3, 4], [6, 2]], 19/10368],
[[[1, 8], [2, 5], [3, 5], [4, 1]], 5/82944],
[[[1, 8], [2, 5], [3, 5], [6, 1]], 11/46080],
[[[1, 8], [2, 5], [4, 2], [5, 2]], 23/230400],
[[[1, 8], [2, 5], [4, 4], [5, 1]], 7/30720],
[[[1, 8], [2, 5], [4, 4], [8, 1]], 23/30720],
[[[1, 8], [2, 5], [5, 2], [10, 1]], 7/57600],
[[[1, 8], [2, 7], [3, 1], [4, 4]], 203/110592],
[[[1, 8], [2, 7], [3, 1], [5, 2]], 11/115200],
[[[1, 8], [2, 7], [3, 2], [4, 3]], 67/110592],
[[[1, 8], [2, 7], [3, 2], [6, 3]], 1/13824],
[[[1, 8], [2, 7], [3, 3], [4, 2]], 35/165888],
[[[1, 8], [2, 7], [3, 3], [5, 1]], 103/829440],
[[[1, 8], [2, 7], [3, 3], [6, 2]], 1/2304],
[[[1, 8], [2, 7], [3, 4], [4, 1]], 149/1492992],
[[[1, 8], [2, 7], [4, 1], [5, 2]], 1/10240],
[[[1, 8], [2, 7], [4, 1], [6, 4]], 5/497664],
[[[1, 8], [2, 7], [4, 1], [10, 2]], 1/51200],
[[[1, 8], [2, 7], [4, 2], [6, 3]], 7/221184],
[[[1, 8], [2, 7], [4, 3], [5, 1]], 1709/1843200],
[[[1, 8], [2, 7], [4, 3], [6, 2]], 1/27648],
[[[1, 8], [2, 7], [4, 3], [8, 1]], 113/36864],
[[[1, 8], [2, 7], [4, 3], [10, 1]], 869/1843200],
[[[1, 8], [2, 7], [4, 4], [6, 1]], 31/73728],
[[[1, 8], [2, 7], [6, 1], [10, 2]], 1/76800],
[[[1, 8], [2, 7], [6, 3], [10, 1]], 1/92160],
[[[1, 8], [2, 9], [3, 1], [4, 3]], 929/2211840],
[[[1, 8], [2, 9], [3, 1], [6, 3]], 11/103680],
[[[1, 8], [2, 9], [3, 2], [4, 2]], 1/16384],
[[[1, 8], [2, 9], [3, 2], [5, 1]], 13/737280],
[[[1, 8], [2, 9], [3, 2], [6, 2]], 7/27648],
[[[1, 8], [2, 9], [3, 3], [4, 1]], 37/1327104],
[[[1, 8], [2, 9], [4, 1], [6, 3]], 481/1990656],
[[[1, 8], [2, 9], [4, 2], [5, 1]], 823/3686400],
[[[1, 8], [2, 9], [4, 2], [6, 2]], 4421/6635520],
[[[1, 8], [2, 9], [4, 2], [8, 1]], 1/768],
[[[1, 8], [2, 9], [4, 2], [10, 1]], 2261/3686400],
[[[1, 8], [2, 9], [4, 3], [6, 1]], 1129/552960],
[[[1, 8], [2, 9], [5, 1], [10, 1]], 7/46080],
[[[1, 8], [2, 9], [6, 2], [10, 1]], 13/81920],
[[[1, 8], [2, 11], [3, 1], [6, 2]], 143/414720],
[[[1, 8], [2, 11], [4, 1], [6, 2]], 1147/1105920],
[[[1, 8], [2, 11], [4, 1], [8, 1]], 11/61440],
[[[1, 8], [2, 11], [4, 1], [10, 1]], 1871/5529600],
[[[1, 8], [2, 11], [4, 2], [6, 1]], 151/82944],
[[[1, 8], [2, 11], [6, 1], [10, 1]], 3421/11059200],
[[[1, 8], [2, 13], [3, 1], [6, 1]], 517/8294400],
[[[1, 8], [2, 13], [4, 1], [6, 1]], 22709/24883200],
[[[1, 9], [2, 2], [3, 1], [5, 3]], 37/864000],
[[[1, 9], [2, 2], [3, 3], [5, 2]], 109/576000],
[[[1, 9], [2, 2], [3, 4], [9, 1]], 1/1296],
[[[1, 9], [2, 2], [3, 5], [5, 1]], 1/15552],
[[[1, 9], [2, 2], [3, 5], [6, 2]], 5/20736],
[[[1, 9], [2, 2], [3, 6], [4, 1]], 1/34560],
[[[1, 9], [2, 2], [3, 6], [6, 1]], 77/103680],
[[[1, 9], [2, 2], [4, 1], [5, 3]], 1/192000],
[[[1, 9], [2, 4], [3, 2], [4, 4]], 49/221184],
[[[1, 9], [2, 4], [3, 2], [5, 2]], 3353/6912000],
[[[1, 9], [2, 4], [3, 3], [4, 3]], 1/18432],
[[[1, 9], [2, 4], [3, 3], [6, 3]], 1/6912],
[[[1, 9], [2, 4], [3, 4], [4, 2]], 11/82944],
[[[1, 9], [2, 4], [3, 4], [5, 1]], 2399/6220800],
[[[1, 9], [2, 4], [3, 4], [6, 2]], 1/864],
[[[1, 9], [2, 4], [3, 5], [4, 1]], 5/46656],
[[[1, 9], [2, 4], [3, 5], [6, 1]], 11/17280],
[[[1, 9], [2, 4], [4, 2], [5, 2]], 1/15360],
[[[1, 9], [2, 4], [4, 4], [5, 1]], 1/30720],
[[[1, 9], [2, 4], [4, 4], [8, 1]], 1/10240],
[[[1, 9], [2, 4], [5, 2], [10, 1]], 1/57600],
[[[1, 9], [2, 6], [3, 1], [4, 4]], 1/576],
[[[1, 9], [2, 6], [3, 1], [5, 2]], 313/1152000],
[[[1, 9], [2, 6], [3, 2], [4, 3]], 109/92160],
[[[1, 9], [2, 6], [3, 3], [4, 2]], 1807/3317760],
[[[1, 9], [2, 6], [3, 3], [5, 1]], 1961/4147200],
[[[1, 9], [2, 6], [3, 3], [6, 2]], 13/20736],
[[[1, 9], [2, 6], [3, 4], [4, 1]], 883/2488320],
[[[1, 9], [2, 6], [4, 1], [5, 2]], 51/256000],
[[[1, 9], [2, 6], [4, 3], [5, 1]], 107/184320],
[[[1, 9], [2, 6], [4, 3], [8, 1]], 283/184320],
[[[1, 9], [2, 8], [3, 1], [4, 3]], 1129/552960],
[[[1, 9], [2, 8], [3, 2], [4, 2]], 4421/6635520],
[[[1, 9], [2, 8], [3, 2], [5, 1]], 13/81920],
[[[1, 9], [2, 8], [3, 2], [6, 2]], 7/27648],
[[[1, 9], [2, 8], [3, 3], [4, 1]], 481/1990656],
[[[1, 9], [2, 8], [3, 3], [6, 1]], 11/103680],
[[[1, 9], [2, 8], [4, 1], [6, 3]], 37/1327104],
[[[1, 9], [2, 8], [4, 2], [5, 1]], 2261/3686400],
[[[1, 9], [2, 8], [4, 2], [6, 2]], 1/16384],
[[[1, 9], [2, 8], [4, 2], [8, 1]], 1/768],
[[[1, 9], [2, 8], [4, 2], [10, 1]], 823/3686400],
[[[1, 9], [2, 8], [4, 3], [6, 1]], 929/2211840],
[[[1, 9], [2, 8], [5, 1], [10, 1]], 7/46080],
[[[1, 9], [2, 8], [6, 2], [10, 1]], 13/737280],
[[[1, 9], [2, 10], [3, 1], [4, 2]], 913/4423680],
[[[1, 9], [2, 10], [3, 1], [5, 1]], 1/81920],
[[[1, 9], [2, 10], [3, 1], [6, 2]], 11/46080],
[[[1, 9], [2, 10], [3, 2], [4, 1]], 1/27648],
[[[1, 9], [2, 10], [3, 2], [6, 1]], 11/276480],
[[[1, 9], [2, 10], [4, 1], [5, 1]], 391/7372800],
[[[1, 9], [2, 10], [4, 1], [6, 2]], 2323/6635520],
[[[1, 9], [2, 10], [4, 1], [8, 1]], 7/36864],
[[[1, 9], [2, 10], [4, 1], [10, 1]], 1499/7372800],
[[[1, 9], [2, 10], [4, 2], [6, 1]], 503/442368],
[[[1, 9], [2, 10], [6, 1], [10, 1]], 557/5529600],
[[[1, 9], [2, 12], [3, 1], [6, 1]], 121/921600],
[[[1, 9], [2, 12], [4, 1], [6, 1]], 3767/5308416],
[[[1, 9], [3, 2], [5, 1], [15, 1]], 1/51840],
[[[1, 10], [2, 1], [3, 1], [5, 3]], 1/86400],
[[[1, 10], [2, 1], [3, 3], [5, 2]], 89/1296000],
[[[1, 10], [2, 1], [3, 4], [9, 1]], 1/5184],
[[[1, 10], [2, 1], [3, 5], [5, 1]], 1/31104],
[[[1, 10], [2, 1], [3, 6], [4, 1]], 1/207360],
[[[1, 10], [2, 1], [3, 6], [6, 1]], 11/103680],
[[[1, 10], [2, 1], [4, 1], [5, 3]], 1/1728000],
[[[1, 10], [2, 3], [3, 2], [5, 2]], 2741/6912000],
[[[1, 10], [2, 3], [3, 3], [4, 3]], 5/331776],
[[[1, 10], [2, 3], [3, 3], [6, 3]], 1/82944],
[[[1, 10], [2, 3], [3, 4], [4, 2]], 13/165888],
[[[1, 10], [2, 3], [3, 4], [5, 1]], 2521/6220800],
[[[1, 10], [2, 3], [3, 4], [6, 2]], 5/20736],
[[[1, 10], [2, 3], [3, 5], [4, 1]], 25/248832],
[[[1, 10], [2, 3], [3, 5], [6, 1]], 11/25920],
[[[1, 10], [2, 3], [4, 2], [5, 2]], 1/51200],
[[[1, 10], [2, 5], [3, 1], [4, 4]], 67/184320],
[[[1, 10], [2, 5], [3, 1], [5, 2]], 77/192000],
[[[1, 10], [2, 5], [3, 2], [4, 3]], 49/69120],
[[[1, 10], [2, 5], [3, 3], [4, 2]], 13/18432],
[[[1, 10], [2, 5], [3, 3], [5, 1]], 11153/12441600],
[[[1, 10], [2, 5], [3, 3], [6, 2]], 31/103680],
[[[1, 10], [2, 5], [3, 4], [4, 1]], 1577/2488320],
[[[1, 10], [2, 5], [4, 1], [5, 2]], 1469/6912000],
[[[1, 10], [2, 5], [4, 3], [5, 1]], 3/20480],
[[[1, 10], [2, 5], [4, 3], [8, 1]], 71/184320],
[[[1, 10], [2, 7], [3, 1], [4, 3]], 1093/442368],
[[[1, 10], [2, 7], [3, 2], [4, 2]], 10261/6635520],
[[[1, 10], [2, 7], [3, 2], [5, 1]], 607/1105920],
[[[1, 10], [2, 7], [3, 2], [6, 2]], 11/46080],
[[[1, 10], [2, 7], [3, 3], [4, 1]], 24301/29859840],
[[[1, 10], [2, 7], [3, 3], [6, 1]], 11/51840],
[[[1, 10], [2, 7], [4, 2], [5, 1]], 7031/11059200],
[[[1, 10], [2, 7], [4, 2], [8, 1]], 89/92160],
[[[1, 10], [2, 7], [5, 1], [10, 1]], 11/76800],
[[[1, 10], [2, 9], [3, 1], [4, 2]], 503/442368],
[[[1, 10], [2, 9], [3, 1], [5, 1]], 557/5529600],
[[[1, 10], [2, 9], [3, 1], [6, 2]], 11/276480],
[[[1, 10], [2, 9], [3, 2], [4, 1]], 2323/6635520],
[[[1, 10], [2, 9], [3, 2], [6, 1]], 11/46080],
[[[1, 10], [2, 9], [4, 1], [5, 1]], 1499/7372800],
[[[1, 10], [2, 9], [4, 1], [6, 2]], 1/27648],
[[[1, 10], [2, 9], [4, 1], [8, 1]], 7/36864],
[[[1, 10], [2, 9], [4, 1], [10, 1]], 391/7372800],
[[[1, 10], [2, 9], [4, 2], [6, 1]], 913/4423680],
[[[1, 10], [2, 9], [6, 1], [10, 1]], 1/81920],
[[[1, 10], [2, 11], [3, 1], [4, 1]], 451/8847360],
[[[1, 10], [2, 11], [3, 1], [6, 1]], 77/552960],
[[[1, 10], [2, 11], [4, 1], [6, 1]], 359/1105920],
[[[1, 11], [2, 2], [3, 2], [5, 2]], 9/51200],
[[[1, 11], [2, 2], [3, 4], [4, 2]], 1/55296],
[[[1, 11], [2, 2], [3, 4], [5, 1]], 1459/6220800],
[[[1, 11], [2, 2], [3, 4], [6, 2]], 5/248832],
[[[1, 11], [2, 2], [3, 5], [4, 1]], 1/20736],
[[[1, 11], [2, 2], [3, 5], [6, 1]], 11/103680],
[[[1, 11], [2, 2], [4, 2], [5, 2]], 1/460800],
[[[1, 11], [2, 4], [3, 1], [4, 4]], 47/1105920],
[[[1, 11], [2, 4], [3, 1], [5, 2]], 701/2073600],
[[[1, 11], [2, 4], [3, 2], [4, 3]], 31/276480],
[[[1, 11], [2, 4], [3, 3], [4, 2]], 1603/3317760],
[[[1, 11], [2, 4], [3, 3], [5, 1]], 11989/12441600],
[[[1, 11], [2, 4], [3, 3], [6, 2]], 7/207360],
[[[1, 11], [2, 4], [3, 4], [4, 1]], 4709/7464960],
[[[1, 11], [2, 4], [4, 1], [5, 2]], 97/768000],
[[[1, 11], [2, 4], [4, 3], [5, 1]], 1/40960],
[[[1, 11], [2, 4], [4, 3], [8, 1]], 17/368640],
[[[1, 11], [2, 6], [3, 1], [4, 3]], 301/276480],
[[[1, 11], [2, 6], [3, 2], [4, 2]], 10601/6635520],
[[[1, 11], [2, 6], [3, 2], [5, 1]], 5537/5529600],
[[[1, 11], [2, 6], [3, 2], [6, 2]], 47/414720],
[[[1, 11], [2, 6], [3, 3], [4, 1]], 14329/9953280],
[[[1, 11], [2, 6], [3, 3], [6, 1]], 11/103680],
[[[1, 11], [2, 6], [4, 2], [5, 1]], 869/2211840],
[[[1, 11], [2, 6], [4, 2], [8, 1]], 103/276480],
[[[1, 11], [2, 6], [5, 1], [10, 1]], 47/691200],
[[[1, 11], [2, 8], [3, 1], [4, 2]], 151/82944],
[[[1, 11], [2, 8], [3, 1], [5, 1]], 3421/11059200],
[[[1, 11], [2, 8], [3, 2], [4, 1]], 1147/1105920],
[[[1, 11], [2, 8], [3, 2], [6, 1]], 143/414720],
[[[1, 11], [2, 8], [4, 1], [5, 1]], 1871/5529600],
[[[1, 11], [2, 8], [4, 1], [8, 1]], 11/61440],
[[[1, 11], [2, 10], [3, 1], [4, 1]], 359/1105920],
[[[1, 11], [2, 10], [3, 1], [6, 1]], 77/552960],
[[[1, 11], [2, 10], [4, 1], [6, 1]], 451/8847360],
[[[1, 12], [2, 1], [3, 2], [5, 2]], 269/6912000],
[[[1, 12], [2, 1], [3, 4], [5, 1]], 431/6220800],
[[[1, 12], [2, 1], [3, 5], [4, 1]], 7/746496],
[[[1, 12], [2, 1], [3, 5], [6, 1]], 11/1244160],
[[[1, 12], [2, 3], [3, 1], [5, 2]], 863/5184000],
[[[1, 12], [2, 3], [3, 2], [4, 3]], 1/61440],
[[[1, 12], [2, 3], [3, 3], [4, 2]], 17/103680],
[[[1, 12], [2, 3], [3, 3], [5, 1]], 37891/62208000],
[[[1, 12], [2, 3], [3, 4], [4, 1]], 877/2488320],
[[[1, 12], [2, 3], [4, 1], [5, 2]], 19/460800],
[[[1, 12], [2, 3], [4, 3], [5, 1]], 1/368640],
[[[1, 12], [2, 3], [4, 3], [8, 1]], 1/368640],
[[[1, 12], [2, 5], [3, 1], [4, 3]], 127/442368],
[[[1, 12], [2, 5], [3, 2], [4, 2]], 3647/3686400],
[[[1, 12], [2, 5], [3, 2], [5, 1]], 1049/972000],
[[[1, 12], [2, 5], [3, 2], [6, 2]], 17/829440],
[[[1, 12], [2, 5], [3, 3], [4, 1]], 9211/6220800],
[[[1, 12], [2, 5], [4, 2], [5, 1]], 2227/11059200],
[[[1, 12], [2, 5], [4, 2], [8, 1]], 17/276480],
[[[1, 12], [2, 5], [5, 1], [10, 1]], 17/1382400],
[[[1, 12], [2, 7], [3, 1], [4, 2]], 16063/11059200],
[[[1, 12], [2, 7], [3, 1], [5, 1]], 4411/8294400],
[[[1, 12], [2, 7], [3, 2], [4, 1]], 9739/5971968],
[[[1, 12], [2, 7], [3, 2], [6, 1]], 341/2073600],
[[[1, 12], [2, 7], [4, 1], [5, 1]], 2071/5529600],
[[[1, 12], [2, 7], [4, 1], [8, 1]], 47/552960],
[[[1, 12], [2, 9], [3, 1], [4, 1]], 3767/5308416],
[[[1, 12], [2, 9], [3, 1], [6, 1]], 121/921600],
[[[1, 13], [2, 2], [3, 1], [5, 2]], 161/3456000],
[[[1, 13], [2, 2], [3, 3], [4, 2]], 23/1105920],
[[[1, 13], [2, 2], [3, 3], [5, 1]], 13753/62208000],
[[[1, 13], [2, 2], [3, 4], [4, 1]], 253/2488320],
[[[1, 13], [2, 2], [4, 1], [5, 2]], 47/6912000],
[[[1, 13], [2, 4], [3, 1], [4, 3]], 29/552960],
[[[1, 13], [2, 4], [3, 2], [4, 2]], 4573/11059200],
[[[1, 13], [2, 4], [3, 2], [5, 1]], 89051/124416000],
[[[1, 13], [2, 4], [3, 2], [6, 2]], 1/829440],
[[[1, 13], [2, 4], [3, 3], [4, 1]], 135589/149299200],
[[[1, 13], [2, 4], [4, 2], [5, 1]], 47/737280],
[[[1, 13], [2, 4], [4, 2], [8, 1]], 1/276480],
[[[1, 13], [2, 4], [5, 1], [10, 1]], 1/1382400],
[[[1, 13], [2, 6], [3, 1], [4, 2]], 28163/33177600],
[[[1, 13], [2, 6], [3, 1], [5, 1]], 47089/82944000],
[[[1, 13], [2, 6], [3, 2], [4, 1]], 80911/49766400],
[[[1, 13], [2, 6], [3, 2], [6, 1]], 77/4147200],
[[[1, 13], [2, 6], [4, 1], [5, 1]], 49487/165888000],
[[[1, 13], [2, 6], [4, 1], [8, 1]], 17/1105920],
[[[1, 13], [2, 8], [3, 1], [4, 1]], 22709/24883200],
[[[1, 13], [2, 8], [3, 1], [6, 1]], 517/8294400],
[[[1, 14], [2, 1], [3, 1], [5, 2]], 7/1036800],
[[[1, 14], [2, 1], [3, 3], [5, 1]], 2603/62208000],
[[[1, 14], [2, 1], [3, 4], [4, 1]], 17/1492992],
[[[1, 14], [2, 1], [4, 1], [5, 2]], 1/2304000],
[[[1, 14], [2, 3], [3, 1], [4, 3]], 11/2211840],
[[[1, 14], [2, 3], [3, 2], [4, 2]], 973/11059200],
[[[1, 14], [2, 3], [3, 2], [5, 1]], 72569/248832000],
[[[1, 14], [2, 3], [3, 3], [4, 1]], 16061/49766400],
[[[1, 14], [2, 3], [4, 2], [5, 1]], 113/11059200],
[[[1, 14], [2, 5], [3, 1], [4, 2]], 55/147456],
[[[1, 14], [2, 5], [3, 1], [5, 1]], 12001/31104000],
[[[1, 14], [2, 5], [3, 2], [4, 1]], 4357/4147200],
[[[1, 14], [2, 5], [4, 1], [5, 1]], 8353/55296000],
[[[1, 14], [2, 5], [4, 1], [8, 1]], 1/1105920],
[[[1, 14], [2, 7], [3, 1], [4, 1]], 507499/597196800],
[[[1, 14], [2, 7], [3, 1], [6, 1]], 187/16588800],
[[[1, 15], [2, 2], [3, 2], [4, 2]], 3/409600],
[[[1, 15], [2, 2], [3, 2], [5, 1]], 3487/49766400],
[[[1, 15], [2, 2], [3, 3], [4, 1]], 599/9953280],
[[[1, 15], [2, 2], [4, 2], [5, 1]], 7/11059200],
[[[1, 15], [2, 4], [3, 1], [4, 2]], 829/8294400],
[[[1, 15], [2, 4], [3, 1], [5, 1]], 8393/49766400],
[[[1, 15], [2, 4], [3, 2], [4, 1]], 313327/746496000],
[[[1, 15], [2, 4], [4, 1], [5, 1]], 3899/82944000],
[[[1, 15], [2, 6], [3, 1], [4, 1]], 13859/24883200],
[[[1, 15], [2, 6], [3, 1], [6, 1]], 11/16588800],
[[[1, 16], [2, 1], [3, 2], [5, 1]], 4457/497664000],
[[[1, 16], [2, 1], [3, 3], [4, 1]], 1339/298598400],
[[[1, 16], [2, 3], [3, 1], [4, 2]], 463/33177600],
[[[1, 16], [2, 3], [3, 1], [5, 1]], 5803/124416000],
[[[1, 16], [2, 3], [3, 2], [4, 1]], 24707/248832000],
[[[1, 16], [2, 3], [4, 1], [5, 1]], 143/16588800],
[[[1, 16], [2, 5], [3, 1], [4, 1]], 238063/995328000],
[[[1, 17], [2, 2], [3, 1], [4, 2]], 17/22118400],
[[[1, 17], [2, 2], [3, 1], [5, 1]], 3871/497664000],
[[[1, 17], [2, 2], [3, 2], [4, 1]], 1039/82944000],
[[[1, 17], [2, 2], [4, 1], [5, 1]], 31/36864000],
[[[1, 17], [2, 4], [3, 1], [4, 1]], 4867/74649600],
[[[1, 18], [2, 1], [3, 1], [5, 1]], 7/9953280],
[[[1, 18], [2, 1], [3, 2], [4, 1]], 949/1492992000],
[[[1, 18], [2, 1], [4, 1], [5, 1]], 11/331776000],
[[[1, 18], [2, 3], [3, 1], [4, 1]], 21379/1990656000],
[[[1, 19], [2, 2], [3, 1], [4, 1]], 239/248832000],
[[[1, 20], [2, 1], [3, 1], [4, 1]], 211/5971968000],
[[[2, 3], [6, 5], [10, 1], [30, 1]], 1/1620],
[[[2, 5], [6, 4], [10, 1], [30, 1]], 1/1440],
[[[2, 7], [6, 3], [10, 1], [30, 1]], 1/4320],
[[[2, 9], [6, 2], [10, 1], [30, 1]], 1/51840],
[[[1, 1], [2, 4], [3, 1], [6, 6], [18, 1]], 1/972],
[[[1, 1], [2, 4], [4, 1], [6, 6], [18, 1]], 1/2592],
[[[1, 1], [2, 4], [6, 4], [10, 1], [30, 1]], 1/432],
[[[1, 1], [2, 6], [3, 1], [6, 5], [18, 1]], 1/864],
[[[1, 1], [2, 6], [4, 1], [6, 2], [10, 3]], 1/432000],
[[[1, 1], [2, 6], [4, 1], [6, 5], [18, 1]], 1/2592],
[[[1, 1], [2, 6], [6, 3], [10, 1], [30, 1]], 7/4320],
[[[1, 1], [2, 8], [3, 1], [6, 4], [18, 1]], 1/2592],
[[[1, 1], [2, 8], [4, 1], [6, 1], [10, 3]], 1/432000],
[[[1, 1], [2, 8], [4, 1], [6, 3], [10, 2]], 1/57600],
[[[1, 1], [2, 8], [4, 1], [6, 4], [18, 1]], 1/10368],
[[[1, 1], [2, 8], [6, 2], [10, 1], [30, 1]], 1/4320],
[[[1, 1], [2, 10], [3, 1], [6, 3], [18, 1]], 1/31104],
[[[1, 1], [2, 10], [4, 1], [6, 2], [10, 2]], 11/576000],
[[[1, 1], [2, 10], [4, 1], [6, 4], [10, 1]], 1/41472],
[[[1, 1], [2, 12], [4, 1], [6, 1], [10, 2]], 7/1152000],
[[[1, 1], [2, 12], [4, 1], [6, 3], [10, 1]], 29/1036800],
[[[1, 1], [2, 14], [4, 1], [6, 2], [10, 1]], 277/27648000],
[[[1, 1], [2, 16], [4, 1], [6, 1], [10, 1]], 91/82944000],
[[[1, 2], [2, 3], [3, 2], [6, 5], [18, 1]], 1/1944],
[[[1, 2], [2, 3], [6, 4], [10, 1], [30, 1]], 1/4320],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 7]], 11/51840],
[[[1, 2], [2, 5], [3, 1], [6, 5], [18, 1]], 5/1296],
[[[1, 2], [2, 5], [3, 2], [6, 4], [18, 1]], 1/1728],
[[[1, 2], [2, 5], [4, 1], [6, 2], [10, 3]], 1/144000],
[[[1, 2], [2, 5], [4, 1], [6, 5], [18, 1]], 1/864],
[[[1, 2], [2, 5], [6, 3], [10, 1], [30, 1]], 13/4320],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 6]], 11/51840],
[[[1, 2], [2, 7], [3, 1], [6, 4], [18, 1]], 7/2592],
[[[1, 2], [2, 7], [3, 2], [4, 2], [6, 4]], 1/5184],
[[[1, 2], [2, 7], [3, 2], [6, 3], [18, 1]], 1/5184],
[[[1, 2], [2, 7], [4, 1], [6, 1], [10, 3]], 1/72000],
[[[1, 2], [2, 7], [4, 1], [6, 3], [10, 2]], 1/17280],
[[[1, 2], [2, 7], [4, 1], [6, 4], [18, 1]], 1/1728],
[[[1, 2], [2, 7], [4, 2], [5, 1], [10, 2]], 1/19200],
[[[1, 2], [2, 7], [4, 2], [6, 2], [10, 2]], 1/115200],
[[[1, 2], [2, 7], [6, 2], [10, 1], [30, 1]], 1/1080],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 5]], 11/207360],
[[[1, 2], [2, 9], [3, 1], [6, 3], [18, 1]], 1/2592],
[[[1, 2], [2, 9], [3, 2], [4, 2], [6, 3]], 7/207360],
[[[1, 2], [2, 9], [3, 2], [6, 2], [18, 1]], 1/62208],
[[[1, 2], [2, 9], [4, 1], [6, 2], [10, 2]], 73/576000],
[[[1, 2], [2, 9], [4, 1], [6, 4], [10, 1]], 7/69120],
[[[1, 2], [2, 9], [4, 2], [6, 1], [10, 2]], 1/115200],
[[[1, 2], [2, 9], [4, 2], [6, 3], [10, 1]], 1/34560],
[[[1, 2], [2, 11], [3, 2], [4, 2], [6, 2]], 1/829440],
[[[1, 2], [2, 11], [4, 1], [6, 1], [10, 2]], 1/16000],
[[[1, 2], [2, 11], [4, 1], [6, 3], [10, 1]], 1/4608],
[[[1, 2], [2, 11], [4, 2], [5, 1], [10, 1]], 1/460800],
[[[1, 2], [2, 11], [4, 2], [6, 2], [10, 1]], 29/921600],
[[[1, 2], [2, 13], [4, 1], [6, 2], [10, 1]], 1097/9216000],
[[[1, 2], [2, 13], [4, 2], [6, 1], [10, 1]], 1/102400],
[[[1, 2], [2, 15], [4, 1], [6, 1], [10, 1]], 271/13824000],
[[[1, 3], [2, 2], [3, 4], [5, 1], [15, 1]], 1/4320],
[[[1, 3], [2, 2], [3, 5], [6, 2], [9, 1]], 1/1944],
[[[1, 3], [2, 4], [3, 1], [6, 5], [18, 1]], 1/2592],
[[[1, 3], [2, 4], [3, 2], [4, 1], [5, 3]], 1/432000],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 6]], 5/10368],
[[[1, 3], [2, 4], [3, 2], [6, 4], [18, 1]], 5/2592],
[[[1, 3], [2, 4], [3, 4], [6, 2], [9, 1]], 1/5184],
[[[1, 3], [2, 4], [3, 5], [4, 1], [6, 3]], 1/3456],
[[[1, 3], [2, 4], [4, 1], [6, 2], [10, 3]], 1/144000],
[[[1, 3], [2, 4], [4, 3], [5, 1], [10, 2]], 1/3200],
[[[1, 3], [2, 4], [4, 3], [5, 2], [10, 1]], 1/3200],
[[[1, 3], [2, 4], [6, 3], [10, 1], [30, 1]], 1/1440],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 6]], 11/17280],
[[[1, 3], [2, 6], [3, 1], [6, 4], [18, 1]], 13/2592],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 5]], 5/10368],
[[[1, 3], [2, 6], [3, 2], [4, 2], [6, 4]], 1/2592],
[[[1, 3], [2, 6], [3, 2], [4, 3], [6, 3]], 1/2304],
[[[1, 3], [2, 6], [3, 2], [6, 3], [18, 1]], 7/5184],
[[[1, 3], [2, 6], [4, 1], [6, 1], [10, 3]], 1/36000],
[[[1, 3], [2, 6], [4, 1], [6, 3], [10, 2]], 1/14400],
[[[1, 3], [2, 6], [4, 1], [6, 4], [18, 1]], 1/1152],
[[[1, 3], [2, 6], [4, 2], [5, 1], [10, 2]], 7/19200],
[[[1, 3], [2, 6], [4, 2], [6, 2], [10, 2]], 1/38400],
[[[1, 3], [2, 6], [6, 2], [10, 1], [30, 1]], 1/720],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 5]], 11/34560],
[[[1, 3], [2, 8], [3, 1], [4, 3], [6, 3]], 1/2304],
[[[1, 3], [2, 8], [3, 1], [6, 3], [18, 1]], 1/648],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 4]], 7/13824],
[[[1, 3], [2, 8], [3, 2], [4, 2], [6, 3]], 31/103680],
[[[1, 3], [2, 8], [3, 2], [4, 3], [6, 2]], 1/23040],
[[[1, 3], [2, 8], [3, 2], [6, 2], [18, 1]], 1/5184],
[[[1, 3], [2, 8], [4, 1], [5, 1], [10, 2]], 1/14400],
[[[1, 3], [2, 8], [4, 1], [6, 2], [10, 2]], 7/24000],
[[[1, 3], [2, 8], [4, 1], [6, 4], [10, 1]], 17/103680],
[[[1, 3], [2, 8], [4, 2], [6, 1], [10, 2]], 1/19200],
[[[1, 3], [2, 8], [4, 2], [6, 3], [10, 1]], 7/69120],
[[[1, 3], [2, 8], [4, 3], [5, 1], [10, 1]], 1/12800],
[[[1, 3], [2, 8], [4, 3], [6, 2], [8, 1]], 1/2304],
[[[1, 3], [2, 8], [4, 3], [6, 2], [10, 1]], 1/92160],
[[[1, 3], [2, 8], [4, 3], [8, 1], [10, 1]], 1/15360],
[[[1, 3], [2, 10], [3, 1], [4, 3], [6, 2]], 7/92160],
[[[1, 3], [2, 10], [3, 2], [4, 1], [6, 3]], 7/103680],
[[[1, 3], [2, 10], [3, 2], [4, 2], [6, 2]], 17/829440],
[[[1, 3], [2, 10], [4, 1], [6, 1], [10, 2]], 31/128000],
[[[1, 3], [2, 10], [4, 1], [6, 3], [10, 1]], 323/518400],
[[[1, 3], [2, 10], [4, 2], [5, 1], [10, 1]], 17/460800],
[[[1, 3], [2, 10], [4, 2], [6, 2], [10, 1]], 197/921600],
[[[1, 3], [2, 10], [4, 3], [6, 1], [8, 1]], 7/92160],
[[[1, 3], [2, 10], [4, 3], [6, 1], [10, 1]], 1/92160],
[[[1, 3], [2, 12], [3, 1], [4, 3], [6, 1]], 1/368640],
[[[1, 3], [2, 12], [3, 2], [4, 1], [6, 2]], 1/414720],
[[[1, 3], [2, 12], [4, 1], [5, 1], [10, 1]], 1/345600],
[[[1, 3], [2, 12], [4, 1], [6, 2], [10, 1]], 15221/27648000],
[[[1, 3], [2, 12], [4, 2], [6, 1], [10, 1]], 47/460800],
[[[1, 3], [2, 14], [4, 1], [6, 1], [10, 1]], 5731/41472000],
[[[1, 4], [2, 1], [3, 4], [5, 1], [15, 1]], 1/432],
[[[1, 4], [2, 1], [3, 6], [4, 1], [9, 1]], 1/2592],
[[[1, 4], [2, 1], [3, 6], [6, 1], [9, 1]], 1/972],
[[[1, 4], [2, 3], [3, 2], [4, 1], [5, 3]], 1/144000],
[[[1, 4], [2, 3], [3, 2], [6, 4], [18, 1]], 1/5184],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 5]], 1/3456],
[[[1, 4], [2, 3], [3, 3], [5, 1], [15, 1]], 1/1440],
[[[1, 4], [2, 3], [3, 4], [6, 2], [9, 1]], 5/2592],
[[[1, 4], [2, 3], [3, 5], [6, 1], [9, 1]], 1/2592],
[[[1, 4], [2, 3], [3, 6], [4, 1], [6, 2]], 5/10368],
[[[1, 4], [2, 3], [4, 1], [6, 2], [10, 3]], 1/432000],
[[[1, 4], [2, 3], [4, 3], [5, 1], [10, 2]], 1/3200],
[[[1, 4], [2, 3], [4, 3], [5, 2], [10, 1]], 1/3200],
[[[1, 4], [2, 5], [3, 1], [4, 1], [5, 3]], 1/144000],
[[[1, 4], [2, 5], [3, 1], [6, 4], [18, 1]], 1/864],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 5]], 5/3456],
[[[1, 4], [2, 5], [3, 2], [4, 2], [5, 2]], 1/115200],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 4]], 1/5184],
[[[1, 4], [2, 5], [3, 2], [4, 3], [6, 3]], 1/1728],
[[[1, 4], [2, 5], [3, 2], [4, 4], [6, 2]], 1/2304],
[[[1, 4], [2, 5], [3, 2], [6, 3], [18, 1]], 13/5184],
[[[1, 4], [2, 5], [3, 3], [4, 1], [5, 2]], 1/172800],
[[[1, 4], [2, 5], [3, 3], [4, 1], [6, 4]], 1/3456],
[[[1, 4], [2, 5], [3, 3], [4, 3], [6, 2]], 1/6912],
[[[1, 4], [2, 5], [3, 3], [6, 2], [9, 1]], 1/1728],
[[[1, 4], [2, 5], [3, 4], [4, 1], [6, 3]], 1/1152],
[[[1, 4], [2, 5], [4, 1], [6, 1], [10, 3]], 1/43200],
[[[1, 4], [2, 5], [4, 1], [6, 3], [10, 2]], 1/28800],
[[[1, 4], [2, 5], [4, 2], [5, 1], [10, 2]], 17/19200],
[[[1, 4], [2, 5], [4, 2], [5, 2], [10, 1]], 11/19200],
[[[1, 4], [2, 5], [4, 2], [6, 2], [10, 2]], 1/38400],
[[[1, 4], [2, 5], [4, 4], [5, 1], [8, 1]], 1/2560],
[[[1, 4], [2, 5], [4, 4], [5, 1], [10, 1]], 1/1280],
[[[1, 4], [2, 5], [4, 4], [8, 1], [10, 1]], 1/2560],
[[[1, 4], [2, 5], [6, 2], [10, 1], [30, 1]], 1/1920],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 5]], 11/23040],
[[[1, 4], [2, 7], [3, 1], [4, 3], [6, 3]], 1/1152],
[[[1, 4], [2, 7], [3, 1], [4, 4], [6, 2]], 1/1024],
[[[1, 4], [2, 7], [3, 1], [6, 3], [18, 1]], 1/432],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 4]], 31/20736],
[[[1, 4], [2, 7], [3, 2], [4, 2], [6, 3]], 31/20736],
[[[1, 4], [2, 7], [3, 2], [4, 3], [6, 2]], 23/69120],
[[[1, 4], [2, 7], [3, 2], [6, 2], [18, 1]], 1/1296],
[[[1, 4], [2, 7], [3, 2], [6, 3], [10, 1]], 1/4320],
[[[1, 4], [2, 7], [3, 3], [4, 1], [6, 3]], 1/13824],
[[[1, 4], [2, 7], [4, 1], [5, 1], [10, 2]], 7/14400],
[[[1, 4], [2, 7], [4, 1], [6, 2], [10, 2]], 11/36000],
[[[1, 4], [2, 7], [4, 1], [6, 4], [10, 1]], 13/103680],
[[[1, 4], [2, 7], [4, 2], [6, 1], [10, 2]], 1/9600],
[[[1, 4], [2, 7], [4, 2], [6, 3], [10, 1]], 1/7680],
[[[1, 4], [2, 7], [4, 3], [5, 1], [10, 1]], 23/38400],
[[[1, 4], [2, 7], [4, 3], [6, 2], [8, 1]], 1/1152],
[[[1, 4], [2, 7], [4, 3], [6, 2], [10, 1]], 1/30720],
[[[1, 4], [2, 7], [4, 3], [8, 1], [10, 1]], 7/15360],
[[[1, 4], [2, 7], [4, 4], [6, 1], [8, 1]], 1/1024],
[[[1, 4], [2, 7], [4, 4], [6, 1], [10, 1]], 1/3840],
[[[1, 4], [2, 7], [5, 1], [6, 1], [10, 2]], 1/7200],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 3]], 19/20736],
[[[1, 4], [2, 9], [3, 1], [4, 3], [6, 2]], 31/46080],
[[[1, 4], [2, 9], [3, 1], [4, 4], [6, 1]], 1/10240],
[[[1, 4], [2, 9], [3, 2], [4, 1], [6, 3]], 31/51840],
[[[1, 4], [2, 9], [3, 2], [4, 2], [6, 2]], 83/414720],
[[[1, 4], [2, 9], [3, 2], [6, 2], [10, 1]], 1/34560],
[[[1, 4], [2, 9], [4, 1], [6, 1], [10, 2]], 13/28800],
[[[1, 4], [2, 9], [4, 1], [6, 3], [10, 1]], 227/259200],
[[[1, 4], [2, 9], [4, 2], [5, 1], [10, 1]], 71/230400],
[[[1, 4], [2, 9], [4, 2], [6, 2], [8, 1]], 1/1728],
[[[1, 4], [2, 9], [4, 2], [6, 2], [10, 1]], 59/115200],
[[[1, 4], [2, 9], [4, 2], [8, 1], [10, 1]], 1/11520],
[[[1, 4], [2, 9], [4, 3], [6, 1], [8, 1]], 31/46080],
[[[1, 4], [2, 9], [4, 3], [6, 1], [10, 1]], 1/15360],
[[[1, 4], [2, 9], [5, 1], [6, 2], [10, 1]], 1/8640],
[[[1, 4], [2, 11], [3, 1], [4, 2], [6, 2]], 133/829440],
[[[1, 4], [2, 11], [3, 1], [4, 3], [6, 1]], 17/368640],
[[[1, 4], [2, 11], [3, 2], [4, 1], [6, 2]], 17/414720],
[[[1, 4], [2, 11], [4, 1], [5, 1], [10, 1]], 17/345600],
[[[1, 4], [2, 11], [4, 1], [6, 2], [10, 1]], 35587/27648000],
[[[1, 4], [2, 11], [4, 2], [6, 1], [8, 1]], 7/69120],
[[[1, 4], [2, 11], [4, 2], [6, 1], [10, 1]], 373/921600],
[[[1, 4], [2, 11], [5, 1], [6, 1], [10, 1]], 7/345600],
[[[1, 4], [2, 13], [3, 1], [4, 2], [6, 1]], 19/3317760],
[[[1, 4], [2, 13], [4, 1], [6, 1], [10, 1]], 4201/8294400],
[[[1, 5], [2, 2], [3, 2], [4, 1], [5, 3]], 1/144000],
[[[1, 5], [2, 2], [3, 3], [5, 1], [15, 1]], 13/4320],
[[[1, 5], [2, 2], [3, 4], [6, 2], [9, 1]], 1/1728],
[[[1, 5], [2, 2], [3, 5], [4, 1], [9, 1]], 1/864],
[[[1, 5], [2, 2], [3, 5], [6, 1], [9, 1]], 5/1296],
[[[1, 5], [2, 2], [3, 7], [4, 1], [6, 1]], 11/51840],
[[[1, 5], [2, 4], [3, 1], [4, 1], [5, 3]], 1/43200],
[[[1, 5], [2, 4], [3, 2], [4, 2], [5, 2]], 1/38400],
[[[1, 5], [2, 4], [3, 2], [4, 3], [6, 3]], 1/6912],
[[[1, 5], [2, 4], [3, 2], [4, 4], [6, 2]], 1/2304],
[[[1, 5], [2, 4], [3, 2], [5, 1], [15, 1]], 1/1920],
[[[1, 5], [2, 4], [3, 2], [6, 3], [18, 1]], 1/1728],
[[[1, 5], [2, 4], [3, 3], [4, 1], [5, 2]], 1/28800],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 4]], 1/1152],
[[[1, 5], [2, 4], [3, 3], [4, 3], [6, 2]], 1/1728],
[[[1, 5], [2, 4], [3, 3], [6, 2], [9, 1]], 13/5184],
[[[1, 5], [2, 4], [3, 4], [4, 1], [6, 3]], 1/3456],
[[[1, 5], [2, 4], [3, 4], [4, 2], [6, 2]], 1/5184],
[[[1, 5], [2, 4], [3, 4], [6, 1], [9, 1]], 1/864],
[[[1, 5], [2, 4], [3, 5], [4, 1], [6, 2]], 5/3456],
[[[1, 5], [2, 4], [4, 1], [6, 1], [10, 3]], 1/144000],
[[[1, 5], [2, 4], [4, 1], [6, 3], [10, 2]], 1/172800],
[[[1, 5], [2, 4], [4, 2], [5, 1], [10, 2]], 11/19200],
[[[1, 5], [2, 4], [4, 2], [5, 2], [10, 1]], 17/19200],
[[[1, 5], [2, 4], [4, 2], [6, 2], [10, 2]], 1/115200],
[[[1, 5], [2, 4], [4, 4], [5, 1], [8, 1]], 1/2560],
[[[1, 5], [2, 4], [4, 4], [5, 1], [10, 1]], 1/1280],
[[[1, 5], [2, 4], [4, 4], [8, 1], [10, 1]], 1/2560],
[[[1, 5], [2, 6], [3, 1], [4, 2], [5, 2]], 1/38400],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 3]], 1/2304],
[[[1, 5], [2, 6], [3, 1], [4, 4], [6, 2]], 1/768],
[[[1, 5], [2, 6], [3, 1], [4, 4], [8, 1]], 1/3072],
[[[1, 5], [2, 6], [3, 1], [4, 5], [6, 1]], 1/1024],
[[[1, 5], [2, 6], [3, 1], [6, 3], [18, 1]], 1/1152],
[[[1, 5], [2, 6], [3, 2], [4, 1], [5, 2]], 1/38400],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 4]], 61/41472],
[[[1, 5], [2, 6], [3, 2], [4, 2], [6, 3]], 11/6912],
[[[1, 5], [2, 6], [3, 2], [4, 3], [5, 1]], 1/92160],
[[[1, 5], [2, 6], [3, 2], [4, 3], [6, 2]], 11/6912],
[[[1, 5], [2, 6], [3, 2], [4, 4], [6, 1]], 1/3072],
[[[1, 5], [2, 6], [3, 2], [6, 2], [9, 1]], 1/2304],
[[[1, 5], [2, 6], [3, 2], [6, 2], [18, 1]], 1/864],
[[[1, 5], [2, 6], [3, 2], [6, 3], [10, 1]], 1/4320],
[[[1, 5], [2, 6], [3, 3], [4, 1], [6, 3]], 5/4608],
[[[1, 5], [2, 6], [3, 3], [4, 2], [5, 1]], 1/69120],
[[[1, 5], [2, 6], [3, 3], [4, 2], [6, 2]], 5/13824],
[[[1, 5], [2, 6], [3, 4], [4, 1], [5, 1]], 1/207360],
[[[1, 5], [2, 6], [4, 1], [5, 1], [10, 2]], 7/9600],
[[[1, 5], [2, 6], [4, 1], [5, 2], [10, 1]], 1/3200],
[[[1, 5], [2, 6], [4, 1], [6, 2], [10, 2]], 17/115200],
[[[1, 5], [2, 6], [4, 1], [6, 4], [10, 1]], 1/23040],
[[[1, 5], [2, 6], [4, 2], [6, 1], [10, 2]], 1/11520],
[[[1, 5], [2, 6], [4, 2], [6, 3], [10, 1]], 1/13824],
[[[1, 5], [2, 6], [4, 3], [5, 1], [8, 1]], 11/15360],
[[[1, 5], [2, 6], [4, 3], [5, 1], [10, 1]], 3/1280],
[[[1, 5], [2, 6], [4, 3], [6, 2], [8, 1]], 1/2304],
[[[1, 5], [2, 6], [4, 3], [6, 2], [10, 1]], 1/30720],
[[[1, 5], [2, 6], [4, 3], [8, 1], [10, 1]], 17/15360],
[[[1, 5], [2, 6], [4, 4], [6, 1], [8, 1]], 1/768],
[[[1, 5], [2, 6], [4, 4], [6, 1], [10, 1]], 1/3840],
[[[1, 5], [2, 6], [5, 1], [6, 1], [10, 2]], 1/7200],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 3]], 19/10368],
[[[1, 5], [2, 8], [3, 1], [4, 3], [6, 2]], 1/288],
[[[1, 5], [2, 8], [3, 1], [4, 4], [6, 1]], 23/30720],
[[[1, 5], [2, 8], [3, 2], [4, 1], [6, 3]], 35/20736],
[[[1, 5], [2, 8], [3, 2], [4, 2], [6, 2]], 25/27648],
[[[1, 5], [2, 8], [3, 2], [6, 2], [10, 1]], 7/34560],
[[[1, 5], [2, 8], [4, 1], [6, 1], [10, 2]], 167/384000],
[[[1, 5], [2, 8], [4, 1], [6, 3], [10, 1]], 221/345600],
[[[1, 5], [2, 8], [4, 2], [5, 1], [10, 1]], 283/230400],
[[[1, 5], [2, 8], [4, 2], [6, 2], [8, 1]], 1/864],
[[[1, 5], [2, 8], [4, 2], [6, 2], [10, 1]], 131/230400],
[[[1, 5], [2, 8], [4, 2], [8, 1], [10, 1]], 7/11520],
[[[1, 5], [2, 8], [4, 3], [6, 1], [8, 1]], 25/9216],
[[[1, 5], [2, 8], [4, 3], [6, 1], [10, 1]], 1/1536],
[[[1, 5], [2, 8], [5, 1], [6, 2], [10, 1]], 1/4320],
[[[1, 5], [2, 10], [3, 1], [4, 1], [6, 3]], 61/103680],
[[[1, 5], [2, 10], [3, 1], [4, 2], [6, 2]], 589/414720],
[[[1, 5], [2, 10], [3, 1], [4, 3], [6, 1]], 17/36864],
[[[1, 5], [2, 10], [3, 2], [4, 1], [6, 2]], 7/25920],
[[[1, 5], [2, 10], [4, 1], [5, 1], [10, 1]], 103/345600],
[[[1, 5], [2, 10], [4, 1], [6, 2], [8, 1]], 1/6912],
[[[1, 5], [2, 10], [4, 1], [6, 2], [10, 1]], 3061/1843200],
[[[1, 5], [2, 10], [4, 1], [8, 1], [10, 1]], 1/46080],
[[[1, 5], [2, 10], [4, 2], [6, 1], [8, 1]], 31/34560],
[[[1, 5], [2, 10], [4, 2], [6, 1], [10, 1]], 1/1280],
[[[1, 5], [2, 10], [5, 1], [6, 1], [10, 1]], 31/172800],
[[[1, 5], [2, 12], [3, 1], [4, 1], [6, 2]], 427/4147200],
[[[1, 5], [2, 12], [3, 1], [4, 2], [6, 1]], 323/3317760],
[[[1, 5], [2, 12], [4, 1], [6, 1], [8, 1]], 7/276480],
[[[1, 5], [2, 12], [4, 1], [6, 1], [10, 1]], 17/16000],
[[[1, 5], [2, 14], [3, 1], [4, 1], [6, 1]], 61/16588800],
[[[1, 6], [2, 1], [3, 2], [4, 1], [5, 3]], 1/432000],
[[[1, 6], [2, 1], [3, 3], [5, 1], [15, 1]], 7/4320],
[[[1, 6], [2, 1], [3, 5], [4, 1], [9, 1]], 1/2592],
[[[1, 6], [2, 1], [3, 5], [6, 1], [9, 1]], 1/864],
[[[1, 6], [2, 3], [3, 1], [4, 1], [5, 3]], 1/36000],
[[[1, 6], [2, 3], [3, 2], [4, 2], [5, 2]], 1/38400],
[[[1, 6], [2, 3], [3, 2], [5, 1], [15, 1]], 1/720],
[[[1, 6], [2, 3], [3, 3], [4, 1], [5, 2]], 1/14400],
[[[1, 6], [2, 3], [3, 3], [4, 3], [6, 2]], 1/2304],
[[[1, 6], [2, 3], [3, 3], [6, 2], [9, 1]], 7/5184],
[[[1, 6], [2, 3], [3, 4], [4, 1], [9, 1]], 1/1152],
[[[1, 6], [2, 3], [3, 4], [4, 2], [6, 2]], 1/2592],
[[[1, 6], [2, 3], [3, 4], [6, 1], [9, 1]], 13/2592],
[[[1, 6], [2, 3], [3, 5], [4, 1], [6, 2]], 5/10368],
[[[1, 6], [2, 3], [3, 6], [4, 1], [6, 1]], 11/17280],
[[[1, 6], [2, 3], [4, 2], [5, 2], [10, 1]], 7/19200],
[[[1, 6], [2, 5], [3, 1], [4, 2], [5, 2]], 1/11520],
[[[1, 6], [2, 5], [3, 1], [4, 4], [5, 1]], 1/3840],
[[[1, 6], [2, 5], [3, 1], [4, 4], [6, 2]], 1/3072],
[[[1, 6], [2, 5], [3, 1], [4, 4], [8, 1]], 1/768],
[[[1, 6], [2, 5], [3, 1], [4, 5], [6, 1]], 1/1024],
[[[1, 6], [2, 5], [3, 1], [5, 2], [10, 1]], 1/7200],
[[[1, 6], [2, 5], [3, 2], [4, 1], [5, 2]], 17/115200],
[[[1, 6], [2, 5], [3, 2], [4, 2], [6, 3]], 5/13824],
[[[1, 6], [2, 5], [3, 2], [4, 3], [5, 1]], 1/30720],
[[[1, 6], [2, 5], [3, 2], [4, 3], [6, 2]], 11/6912],
[[[1, 6], [2, 5], [3, 2], [4, 3], [8, 1]], 1/2304],
[[[1, 6], [2, 5], [3, 2], [4, 4], [6, 1]], 1/768],
[[[1, 6], [2, 5], [3, 2], [6, 2], [9, 1]], 1/864],
[[[1, 6], [2, 5], [3, 2], [6, 2], [18, 1]], 1/2304],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 3]], 5/4608],
[[[1, 6], [2, 5], [3, 3], [4, 2], [5, 1]], 1/13824],
[[[1, 6], [2, 5], [3, 3], [4, 2], [6, 2]], 11/6912],
[[[1, 6], [2, 5], [3, 3], [4, 3], [6, 1]], 1/2304],
[[[1, 6], [2, 5], [3, 3], [5, 1], [6, 2]], 1/4320],
[[[1, 6], [2, 5], [3, 3], [6, 1], [9, 1]], 1/1152],
[[[1, 6], [2, 5], [3, 4], [4, 1], [5, 1]], 1/23040],
[[[1, 6], [2, 5], [3, 4], [4, 1], [6, 2]], 61/41472],
[[[1, 6], [2, 5], [4, 1], [5, 1], [10, 2]], 1/3200],
[[[1, 6], [2, 5], [4, 1], [5, 2], [10, 1]], 7/9600],
[[[1, 6], [2, 5], [4, 1], [6, 2], [10, 2]], 1/38400],
[[[1, 6], [2, 5], [4, 1], [6, 4], [10, 1]], 1/207360],
[[[1, 6], [2, 5], [4, 2], [6, 1], [10, 2]], 1/38400],
[[[1, 6], [2, 5], [4, 2], [6, 3], [10, 1]], 1/69120],
[[[1, 6], [2, 5], [4, 3], [5, 1], [8, 1]], 17/15360],
[[[1, 6], [2, 5], [4, 3], [5, 1], [10, 1]], 3/1280],
[[[1, 6], [2, 5], [4, 3], [6, 2], [10, 1]], 1/92160],
[[[1, 6], [2, 5], [4, 3], [8, 1], [10, 1]], 11/15360],
[[[1, 6], [2, 5], [4, 4], [6, 1], [8, 1]], 1/3072],
[[[1, 6], [2, 7], [3, 1], [4, 1], [5, 2]], 1/25600],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 3]], 19/20736],
[[[1, 6], [2, 7], [3, 1], [4, 3], [5, 1]], 1/30720],
[[[1, 6], [2, 7], [3, 1], [4, 3], [6, 2]], 103/27648],
[[[1, 6], [2, 7], [3, 1], [4, 3], [8, 1]], 11/18432],
[[[1, 6], [2, 7], [3, 1], [4, 4], [6, 1]], 17/4608],
[[[1, 6], [2, 7], [3, 2], [4, 1], [6, 3]], 5/3456],
[[[1, 6], [2, 7], [3, 2], [4, 2], [5, 1]], 11/184320],
[[[1, 6], [2, 7], [3, 2], [4, 2], [6, 2]], 59/27648],
[[[1, 6], [2, 7], [3, 2], [4, 3], [6, 1]], 47/55296],
[[[1, 6], [2, 7], [3, 2], [5, 1], [6, 2]], 1/11520],
[[[1, 6], [2, 7], [3, 2], [6, 2], [10, 1]], 1/3840],
[[[1, 6], [2, 7], [3, 3], [4, 1], [5, 1]], 1/34560],
[[[1, 6], [2, 7], [3, 3], [4, 1], [6, 2]], 1/3456],
[[[1, 6], [2, 7], [4, 1], [6, 1], [10, 2]], 1/4800],
[[[1, 6], [2, 7], [4, 1], [6, 3], [10, 1]], 47/207360],
[[[1, 6], [2, 7], [4, 2], [5, 1], [8, 1]], 1/2560],
[[[1, 6], [2, 7], [4, 2], [5, 1], [10, 1]], 113/46080],
[[[1, 6], [2, 7], [4, 2], [6, 2], [8, 1]], 1/1728],
[[[1, 6], [2, 7], [4, 2], [6, 2], [10, 1]], 11/36864],
[[[1, 6], [2, 7], [4, 2], [8, 1], [10, 1]], 7/7680],
[[[1, 6], [2, 7], [4, 3], [6, 1], [8, 1]], 25/9216],
[[[1, 6], [2, 7], [4, 3], [6, 1], [10, 1]], 29/46080],
[[[1, 6], [2, 7], [5, 1], [6, 2], [10, 1]], 1/8640],
[[[1, 6], [2, 9], [3, 1], [4, 1], [6, 3]], 61/51840],
[[[1, 6], [2, 9], [3, 1], [4, 2], [6, 2]], 223/51840],
[[[1, 6], [2, 9], [3, 1], [4, 3], [6, 1]], 1171/552960],
[[[1, 6], [2, 9], [3, 1], [6, 2], [10, 1]], 11/86400],
[[[1, 6], [2, 9], [3, 2], [4, 1], [6, 2]], 7/8640],
[[[1, 6], [2, 9], [4, 1], [5, 1], [10, 1]], 89/115200],
[[[1, 6], [2, 9], [4, 1], [6, 2], [8, 1]], 1/3456],
[[[1, 6], [2, 9], [4, 1], [6, 2], [10, 1]], 6577/5529600],
[[[1, 6], [2, 9], [4, 1], [8, 1], [10, 1]], 7/46080],
[[[1, 6], [2, 9], [4, 2], [6, 1], [8, 1]], 61/27648],
[[[1, 6], [2, 9], [4, 2], [6, 1], [10, 1]], 3109/2764800],
[[[1, 6], [2, 9], [5, 1], [6, 1], [10, 1]], 13/34560],
[[[1, 6], [2, 11], [3, 1], [4, 1], [6, 2]], 1891/2073600],
[[[1, 6], [2, 11], [3, 1], [4, 2], [6, 1]], 5563/8294400],
[[[1, 6], [2, 11], [3, 1], [6, 1], [10, 1]], 11/691200],
[[[1, 6], [2, 11], [4, 1], [6, 1], [8, 1]], 31/138240],
[[[1, 6], [2, 11], [4, 1], [6, 1], [10, 1]], 10919/8294400],
[[[1, 6], [2, 13], [3, 1], [4, 1], [6, 1]], 1037/16588800],
[[[1, 7], [2, 2], [3, 1], [4, 1], [5, 3]], 1/72000],
[[[1, 7], [2, 2], [3, 2], [4, 2], [5, 2]], 1/115200],
[[[1, 7], [2, 2], [3, 2], [5, 1], [15, 1]], 1/1080],
[[[1, 7], [2, 2], [3, 3], [4, 1], [5, 2]], 1/17280],
[[[1, 7], [2, 2], [3, 3], [6, 2], [9, 1]], 1/5184],
[[[1, 7], [2, 2], [3, 4], [4, 1], [9, 1]], 1/1728],
[[[1, 7], [2, 2], [3, 4], [4, 2], [6, 2]], 1/5184],
[[[1, 7], [2, 2], [3, 4], [6, 1], [9, 1]], 7/2592],
[[[1, 7], [2, 2], [3, 6], [4, 1], [6, 1]], 11/51840],
[[[1, 7], [2, 2], [4, 2], [5, 2], [10, 1]], 1/19200],
[[[1, 7], [2, 4], [3, 1], [4, 2], [5, 2]], 1/9600],
[[[1, 7], [2, 4], [3, 1], [4, 4], [5, 1]], 1/3840],
[[[1, 7], [2, 4], [3, 1], [4, 4], [8, 1]], 1/1024],
[[[1, 7], [2, 4], [3, 1], [5, 2], [10, 1]], 1/7200],
[[[1, 7], [2, 4], [3, 2], [4, 1], [5, 2]], 11/36000],
[[[1, 7], [2, 4], [3, 2], [4, 3], [5, 1]], 1/30720],
[[[1, 7], [2, 4], [3, 2], [4, 3], [6, 2]], 23/69120],
[[[1, 7], [2, 4], [3, 2], [4, 3], [8, 1]], 1/1152],
[[[1, 7], [2, 4], [3, 2], [4, 4], [6, 1]], 1/1024],
[[[1, 7], [2, 4], [3, 2], [6, 2], [9, 1]], 1/1296],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 3]], 1/13824],
[[[1, 7], [2, 4], [3, 3], [4, 2], [5, 1]], 1/7680],
[[[1, 7], [2, 4], [3, 3], [4, 2], [6, 2]], 31/20736],
[[[1, 7], [2, 4], [3, 3], [4, 3], [6, 1]], 1/1152],
[[[1, 7], [2, 4], [3, 3], [5, 1], [6, 2]], 1/4320],
[[[1, 7], [2, 4], [3, 3], [6, 1], [9, 1]], 1/432],
[[[1, 7], [2, 4], [3, 4], [4, 1], [5, 1]], 13/103680],
[[[1, 7], [2, 4], [3, 4], [4, 1], [6, 2]], 31/20736],
[[[1, 7], [2, 4], [3, 5], [4, 1], [6, 1]], 11/23040],
[[[1, 7], [2, 4], [4, 1], [5, 2], [10, 1]], 7/14400],
[[[1, 7], [2, 4], [4, 3], [5, 1], [8, 1]], 7/15360],
[[[1, 7], [2, 4], [4, 3], [5, 1], [10, 1]], 23/38400],
[[[1, 7], [2, 6], [3, 1], [4, 1], [5, 2]], 1/4800],
[[[1, 7], [2, 6], [3, 1], [4, 3], [5, 1]], 29/46080],
[[[1, 7], [2, 6], [3, 1], [4, 3], [6, 2]], 47/55296],
[[[1, 7], [2, 6], [3, 1], [4, 3], [8, 1]], 25/9216],
[[[1, 7], [2, 6], [3, 1], [4, 4], [6, 1]], 17/4608],
[[[1, 7], [2, 6], [3, 2], [4, 1], [6, 3]], 1/3456],
[[[1, 7], [2, 6], [3, 2], [4, 2], [5, 1]], 11/36864],
[[[1, 7], [2, 6], [3, 2], [4, 2], [6, 2]], 59/27648],
[[[1, 7], [2, 6], [3, 2], [4, 2], [8, 1]], 1/1728],
[[[1, 7], [2, 6], [3, 2], [4, 3], [6, 1]], 103/27648],
[[[1, 7], [2, 6], [3, 2], [5, 1], [6, 2]], 1/3840],
[[[1, 7], [2, 6], [3, 2], [5, 1], [10, 1]], 1/8640],
[[[1, 7], [2, 6], [3, 2], [6, 2], [10, 1]], 1/11520],
[[[1, 7], [2, 6], [3, 3], [4, 1], [5, 1]], 47/207360],
[[[1, 7], [2, 6], [3, 3], [4, 1], [6, 2]], 5/3456],
[[[1, 7], [2, 6], [3, 3], [4, 2], [6, 1]], 19/20736],
[[[1, 7], [2, 6], [4, 1], [6, 1], [10, 2]], 1/25600],
[[[1, 7], [2, 6], [4, 1], [6, 3], [10, 1]], 1/34560],
[[[1, 7], [2, 6], [4, 2], [5, 1], [8, 1]], 7/7680],
[[[1, 7], [2, 6], [4, 2], [5, 1], [10, 1]], 113/46080],
[[[1, 7], [2, 6], [4, 2], [6, 2], [10, 1]], 11/184320],
[[[1, 7], [2, 6], [4, 2], [8, 1], [10, 1]], 1/2560],
[[[1, 7], [2, 6], [4, 3], [6, 1], [8, 1]], 11/18432],
[[[1, 7], [2, 6], [4, 3], [6, 1], [10, 1]], 1/30720],
[[[1, 7], [2, 8], [3, 1], [4, 1], [6, 3]], 61/103680],
[[[1, 7], [2, 8], [3, 1], [4, 2], [5, 1]], 1/12288],
[[[1, 7], [2, 8], [3, 1], [4, 2], [6, 2]], 529/138240],
[[[1, 7], [2, 8], [3, 1], [4, 2], [8, 1]], 1/3072],
[[[1, 7], [2, 8], [3, 1], [4, 3], [6, 1]], 2947/552960],
[[[1, 7], [2, 8], [3, 1], [5, 1], [10, 1]], 1/23040],
[[[1, 7], [2, 8], [3, 1], [6, 2], [10, 1]], 11/86400],
[[[1, 7], [2, 8], [3, 2], [4, 1], [5, 1]], 23/368640],
[[[1, 7], [2, 8], [3, 2], [4, 1], [6, 2]], 17/13824],
[[[1, 7], [2, 8], [3, 2], [4, 2], [6, 1]], 217/276480],
[[[1, 7], [2, 8], [4, 1], [5, 1], [8, 1]], 1/15360],
[[[1, 7], [2, 8], [4, 1], [5, 1], [10, 1]], 1/960],
[[[1, 7], [2, 8], [4, 1], [6, 2], [8, 1]], 1/6912],
[[[1, 7], [2, 8], [4, 1], [6, 2], [10, 1]], 161/368640],
[[[1, 7], [2, 8], [4, 1], [8, 1], [10, 1]], 1/5120],
[[[1, 7], [2, 8], [4, 2], [6, 1], [8, 1]], 1/576],
[[[1, 7], [2, 8], [4, 2], [6, 1], [10, 1]], 1019/1382400],
[[[1, 7], [2, 8], [5, 1], [6, 1], [10, 1]], 1/3840],
[[[1, 7], [2, 10], [3, 1], [4, 1], [6, 2]], 223/103680],
[[[1, 7], [2, 10], [3, 1], [4, 2], [6, 1]], 5941/2764800],
[[[1, 7], [2, 10], [3, 1], [6, 1], [10, 1]], 77/691200],
[[[1, 7], [2, 10], [4, 1], [6, 1], [8, 1]], 13/27648],
[[[1, 7], [2, 10], [4, 1], [6, 1], [10, 1]], 2843/2764800],
[[[1, 7], [2, 12], [3, 1], [4, 1], [6, 1]], 613/1658880],
[[[1, 8], [2, 1], [3, 1], [4, 1], [5, 3]], 1/432000],
[[[1, 8], [2, 1], [3, 2], [5, 1], [15, 1]], 1/4320],
[[[1, 8], [2, 1], [3, 3], [4, 1], [5, 2]], 1/57600],
[[[1, 8], [2, 1], [3, 4], [4, 1], [9, 1]], 1/10368],
[[[1, 8], [2, 1], [3, 4], [6, 1], [9, 1]], 1/2592],
[[[1, 8], [2, 3], [3, 1], [4, 2], [5, 2]], 1/19200],
[[[1, 8], [2, 3], [3, 2], [4, 1], [5, 2]], 7/24000],
[[[1, 8], [2, 3], [3, 2], [4, 3], [5, 1]], 1/92160],
[[[1, 8], [2, 3], [3, 2], [4, 3], [6, 2]], 1/23040],
[[[1, 8], [2, 3], [3, 2], [4, 3], [8, 1]], 1/2304],
[[[1, 8], [2, 3], [3, 2], [6, 2], [9, 1]], 1/5184],
[[[1, 8], [2, 3], [3, 3], [4, 2], [5, 1]], 7/69120],
[[[1, 8], [2, 3], [3, 3], [4, 2], [6, 2]], 31/103680],
[[[1, 8], [2, 3], [3, 3], [4, 3], [6, 1]], 1/2304],
[[[1, 8], [2, 3], [3, 3], [6, 1], [9, 1]], 1/648],
[[[1, 8], [2, 3], [3, 4], [4, 1], [5, 1]], 17/103680],
[[[1, 8], [2, 3], [3, 4], [4, 1], [6, 2]], 7/13824],
[[[1, 8], [2, 3], [3, 5], [4, 1], [6, 1]], 11/34560],
[[[1, 8], [2, 3], [4, 1], [5, 2], [10, 1]], 1/14400],
[[[1, 8], [2, 3], [4, 3], [5, 1], [8, 1]], 1/15360],
[[[1, 8], [2, 3], [4, 3], [5, 1], [10, 1]], 1/12800],
[[[1, 8], [2, 5], [3, 1], [4, 1], [5, 2]], 167/384000],
[[[1, 8], [2, 5], [3, 1], [4, 3], [5, 1]], 1/1536],
[[[1, 8], [2, 5], [3, 1], [4, 3], [8, 1]], 25/9216],
[[[1, 8], [2, 5], [3, 1], [4, 4], [6, 1]], 23/30720],
[[[1, 8], [2, 5], [3, 2], [4, 2], [5, 1]], 131/230400],
[[[1, 8], [2, 5], [3, 2], [4, 2], [6, 2]], 25/27648],
[[[1, 8], [2, 5], [3, 2], [4, 2], [8, 1]], 1/864],
[[[1, 8], [2, 5], [3, 2], [4, 3], [6, 1]], 1/288],
[[[1, 8], [2, 5], [3, 2], [5, 1], [6, 2]], 7/34560],
[[[1, 8], [2, 5], [3, 2], [5, 1], [10, 1]], 1/4320],
[[[1, 8], [2, 5], [3, 3], [4, 1], [5, 1]], 221/345600],
[[[1, 8], [2, 5], [3, 3], [4, 1], [6, 2]], 35/20736],
[[[1, 8], [2, 5], [3, 3], [4, 2], [6, 1]], 19/10368],
[[[1, 8], [2, 5], [4, 2], [5, 1], [8, 1]], 7/11520],
[[[1, 8], [2, 5], [4, 2], [5, 1], [10, 1]], 283/230400],
[[[1, 8], [2, 7], [3, 1], [4, 2], [5, 1]], 1019/1382400],
[[[1, 8], [2, 7], [3, 1], [4, 2], [6, 2]], 217/276480],
[[[1, 8], [2, 7], [3, 1], [4, 2], [8, 1]], 1/576],
[[[1, 8], [2, 7], [3, 1], [4, 3], [6, 1]], 2947/552960],
[[[1, 8], [2, 7], [3, 1], [5, 1], [10, 1]], 1/3840],
[[[1, 8], [2, 7], [3, 2], [4, 1], [5, 1]], 161/368640],
[[[1, 8], [2, 7], [3, 2], [4, 1], [6, 2]], 17/13824],
[[[1, 8], [2, 7], [3, 2], [4, 1], [8, 1]], 1/6912],
[[[1, 8], [2, 7], [3, 2], [4, 2], [6, 1]], 529/138240],
[[[1, 8], [2, 7], [3, 2], [5, 1], [6, 1]], 11/86400],
[[[1, 8], [2, 7], [3, 3], [4, 1], [6, 1]], 61/103680],
[[[1, 8], [2, 7], [4, 1], [5, 1], [8, 1]], 1/5120],
[[[1, 8], [2, 7], [4, 1], [5, 1], [10, 1]], 1/960],
[[[1, 8], [2, 7], [4, 1], [6, 2], [10, 1]], 23/368640],
[[[1, 8], [2, 7], [4, 1], [8, 1], [10, 1]], 1/15360],
[[[1, 8], [2, 7], [4, 2], [6, 1], [8, 1]], 1/3072],
[[[1, 8], [2, 7], [4, 2], [6, 1], [10, 1]], 1/12288],
[[[1, 8], [2, 7], [5, 1], [6, 1], [10, 1]], 1/23040],
[[[1, 8], [2, 9], [3, 1], [4, 1], [5, 1]], 7/122880],
[[[1, 8], [2, 9], [3, 1], [4, 1], [6, 2]], 227/138240],
[[[1, 8], [2, 9], [3, 1], [4, 1], [8, 1]], 1/18432],
[[[1, 8], [2, 9], [3, 1], [4, 2], [6, 1]], 2017/552960],
[[[1, 8], [2, 9], [3, 1], [5, 1], [6, 1]], 11/230400],
[[[1, 8], [2, 9], [3, 1], [6, 1], [10, 1]], 11/76800],
[[[1, 8], [2, 9], [3, 2], [4, 1], [6, 1]], 83/276480],
[[[1, 8], [2, 9], [4, 1], [6, 1], [8, 1]], 1/3072],
[[[1, 8], [2, 9], [4, 1], [6, 1], [10, 1]], 1229/2764800],
[[[1, 8], [2, 11], [3, 1], [4, 1], [6, 1]], 2519/2764800],
[[[1, 9], [2, 2], [3, 1], [4, 2], [5, 2]], 1/115200],
[[[1, 9], [2, 2], [3, 2], [4, 1], [5, 2]], 73/576000],
[[[1, 9], [2, 2], [3, 2], [6, 2], [9, 1]], 1/62208],
[[[1, 9], [2, 2], [3, 3], [4, 2], [5, 1]], 1/34560],
[[[1, 9], [2, 2], [3, 3], [4, 2], [6, 2]], 7/207360],
[[[1, 9], [2, 2], [3, 3], [6, 1], [9, 1]], 1/2592],
[[[1, 9], [2, 2], [3, 4], [4, 1], [5, 1]], 7/69120],
[[[1, 9], [2, 2], [3, 5], [4, 1], [6, 1]], 11/207360],
[[[1, 9], [2, 4], [3, 1], [4, 1], [5, 2]], 13/28800],
[[[1, 9], [2, 4], [3, 1], [4, 3], [5, 1]], 1/15360],
[[[1, 9], [2, 4], [3, 1], [4, 3], [8, 1]], 31/46080],
[[[1, 9], [2, 4], [3, 1], [4, 4], [6, 1]], 1/10240],
[[[1, 9], [2, 4], [3, 2], [4, 2], [5, 1]], 59/115200],
[[[1, 9], [2, 4], [3, 2], [4, 2], [6, 2]], 83/414720],
[[[1, 9], [2, 4], [3, 2], [4, 2], [8, 1]], 1/1728],
[[[1, 9], [2, 4], [3, 2], [4, 3], [6, 1]], 31/46080],
[[[1, 9], [2, 4], [3, 2], [5, 1], [6, 2]], 1/34560],
[[[1, 9], [2, 4], [3, 2], [5, 1], [10, 1]], 1/8640],
[[[1, 9], [2, 4], [3, 3], [4, 1], [5, 1]], 227/259200],
[[[1, 9], [2, 4], [3, 3], [4, 1], [6, 2]], 31/51840],
[[[1, 9], [2, 4], [3, 3], [4, 2], [6, 1]], 19/20736],
[[[1, 9], [2, 4], [4, 2], [5, 1], [8, 1]], 1/11520],
[[[1, 9], [2, 4], [4, 2], [5, 1], [10, 1]], 71/230400],
[[[1, 9], [2, 6], [3, 1], [4, 2], [5, 1]], 3109/2764800],
[[[1, 9], [2, 6], [3, 1], [4, 2], [8, 1]], 61/27648],
[[[1, 9], [2, 6], [3, 1], [4, 3], [6, 1]], 1171/552960],
[[[1, 9], [2, 6], [3, 1], [5, 1], [10, 1]], 13/34560],
[[[1, 9], [2, 6], [3, 2], [4, 1], [5, 1]], 6577/5529600],
[[[1, 9], [2, 6], [3, 2], [4, 1], [6, 2]], 7/8640],
[[[1, 9], [2, 6], [3, 2], [4, 1], [8, 1]], 1/3456],
[[[1, 9], [2, 6], [3, 2], [4, 2], [6, 1]], 223/51840],
[[[1, 9], [2, 6], [3, 2], [5, 1], [6, 1]], 11/86400],
[[[1, 9], [2, 6], [3, 3], [4, 1], [6, 1]], 61/51840],
[[[1, 9], [2, 6], [4, 1], [5, 1], [8, 1]], 7/46080],
[[[1, 9], [2, 6], [4, 1], [5, 1], [10, 1]], 89/115200],
[[[1, 9], [2, 8], [3, 1], [4, 1], [5, 1]], 1229/2764800],
[[[1, 9], [2, 8], [3, 1], [4, 1], [6, 2]], 83/276480],
[[[1, 9], [2, 8], [3, 1], [4, 1], [8, 1]], 1/3072],
[[[1, 9], [2, 8], [3, 1], [4, 2], [6, 1]], 2017/552960],
[[[1, 9], [2, 8], [3, 1], [5, 1], [6, 1]], 11/76800],
[[[1, 9], [2, 8], [3, 1], [6, 1], [10, 1]], 11/230400],
[[[1, 9], [2, 8], [3, 2], [4, 1], [6, 1]], 227/138240],
[[[1, 9], [2, 8], [4, 1], [6, 1], [8, 1]], 1/18432],
[[[1, 9], [2, 8], [4, 1], [6, 1], [10, 1]], 7/122880],
[[[1, 9], [2, 10], [3, 1], [4, 1], [6, 1]], 647/552960],
[[[1, 10], [2, 1], [3, 2], [4, 1], [5, 2]], 11/576000],
[[[1, 10], [2, 1], [3, 3], [6, 1], [9, 1]], 1/31104],
[[[1, 10], [2, 1], [3, 4], [4, 1], [5, 1]], 1/41472],
[[[1, 10], [2, 3], [3, 1], [4, 1], [5, 2]], 31/128000],
[[[1, 10], [2, 3], [3, 1], [4, 3], [5, 1]], 1/92160],
[[[1, 10], [2, 3], [3, 1], [4, 3], [8, 1]], 7/92160],
[[[1, 10], [2, 3], [3, 2], [4, 2], [5, 1]], 197/921600],
[[[1, 10], [2, 3], [3, 2], [4, 2], [6, 2]], 17/829440],
[[[1, 10], [2, 3], [3, 2], [4, 3], [6, 1]], 7/92160],
[[[1, 10], [2, 3], [3, 3], [4, 1], [5, 1]], 323/518400],
[[[1, 10], [2, 3], [3, 3], [4, 1], [6, 2]], 7/103680],
[[[1, 10], [2, 3], [4, 2], [5, 1], [10, 1]], 17/460800],
[[[1, 10], [2, 5], [3, 1], [4, 2], [5, 1]], 1/1280],
[[[1, 10], [2, 5], [3, 1], [4, 2], [8, 1]], 31/34560],
[[[1, 10], [2, 5], [3, 1], [4, 3], [6, 1]], 17/36864],
[[[1, 10], [2, 5], [3, 1], [5, 1], [10, 1]], 31/172800],
[[[1, 10], [2, 5], [3, 2], [4, 1], [5, 1]], 3061/1843200],
[[[1, 10], [2, 5], [3, 2], [4, 1], [6, 2]], 7/25920],
[[[1, 10], [2, 5], [3, 2], [4, 1], [8, 1]], 1/6912],
[[[1, 10], [2, 5], [3, 2], [4, 2], [6, 1]], 589/414720],
[[[1, 10], [2, 5], [3, 3], [4, 1], [6, 1]], 61/103680],
[[[1, 10], [2, 5], [4, 1], [5, 1], [8, 1]], 1/46080],
[[[1, 10], [2, 5], [4, 1], [5, 1], [10, 1]], 103/345600],
[[[1, 10], [2, 7], [3, 1], [4, 1], [5, 1]], 2843/2764800],
[[[1, 10], [2, 7], [3, 1], [4, 1], [8, 1]], 13/27648],
[[[1, 10], [2, 7], [3, 1], [4, 2], [6, 1]], 5941/2764800],
[[[1, 10], [2, 7], [3, 1], [5, 1], [6, 1]], 77/691200],
[[[1, 10], [2, 7], [3, 2], [4, 1], [6, 1]], 223/103680],
[[[1, 10], [2, 9], [3, 1], [4, 1], [6, 1]], 647/552960],
[[[1, 11], [2, 2], [3, 1], [4, 1], [5, 2]], 1/16000],
[[[1, 11], [2, 2], [3, 2], [4, 2], [5, 1]], 29/921600],
[[[1, 11], [2, 2], [3, 2], [4, 2], [6, 2]], 1/829440],
[[[1, 11], [2, 2], [3, 3], [4, 1], [5, 1]], 1/4608],
[[[1, 11], [2, 2], [4, 2], [5, 1], [10, 1]], 1/460800],
[[[1, 11], [2, 4], [3, 1], [4, 2], [5, 1]], 373/921600],
[[[1, 11], [2, 4], [3, 1], [4, 2], [8, 1]], 7/69120],
[[[1, 11], [2, 4], [3, 1], [4, 3], [6, 1]], 17/368640],
[[[1, 11], [2, 4], [3, 1], [5, 1], [10, 1]], 7/345600],
[[[1, 11], [2, 4], [3, 2], [4, 1], [5, 1]], 35587/27648000],
[[[1, 11], [2, 4], [3, 2], [4, 1], [6, 2]], 17/414720],
[[[1, 11], [2, 4], [3, 2], [4, 2], [6, 1]], 133/829440],
[[[1, 11], [2, 4], [4, 1], [5, 1], [10, 1]], 17/345600],
[[[1, 11], [2, 6], [3, 1], [4, 1], [5, 1]], 10919/8294400],
[[[1, 11], [2, 6], [3, 1], [4, 1], [8, 1]], 31/138240],
[[[1, 11], [2, 6], [3, 1], [4, 2], [6, 1]], 5563/8294400],
[[[1, 11], [2, 6], [3, 1], [5, 1], [6, 1]], 11/691200],
[[[1, 11], [2, 6], [3, 2], [4, 1], [6, 1]], 1891/2073600],
[[[1, 11], [2, 8], [3, 1], [4, 1], [6, 1]], 2519/2764800],
[[[1, 12], [2, 1], [3, 1], [4, 1], [5, 2]], 7/1152000],
[[[1, 12], [2, 1], [3, 3], [4, 1], [5, 1]], 29/1036800],
[[[1, 12], [2, 3], [3, 1], [4, 2], [5, 1]], 47/460800],
[[[1, 12], [2, 3], [3, 1], [4, 3], [6, 1]], 1/368640],
[[[1, 12], [2, 3], [3, 2], [4, 1], [5, 1]], 15221/27648000],
[[[1, 12], [2, 3], [3, 2], [4, 1], [6, 2]], 1/414720],
[[[1, 12], [2, 3], [4, 1], [5, 1], [10, 1]], 1/345600],
[[[1, 12], [2, 5], [3, 1], [4, 1], [5, 1]], 17/16000],
[[[1, 12], [2, 5], [3, 1], [4, 1], [8, 1]], 7/276480],
[[[1, 12], [2, 5], [3, 1], [4, 2], [6, 1]], 323/3317760],
[[[1, 12], [2, 5], [3, 2], [4, 1], [6, 1]], 427/4147200],
[[[1, 12], [2, 7], [3, 1], [4, 1], [6, 1]], 613/1658880],
[[[1, 13], [2, 2], [3, 1], [4, 2], [5, 1]], 1/102400],
[[[1, 13], [2, 2], [3, 2], [4, 1], [5, 1]], 1097/9216000],
[[[1, 13], [2, 4], [3, 1], [4, 1], [5, 1]], 4201/8294400],
[[[1, 13], [2, 4], [3, 1], [4, 2], [6, 1]], 19/3317760],
[[[1, 13], [2, 6], [3, 1], [4, 1], [6, 1]], 1037/16588800],
[[[1, 14], [2, 1], [3, 2], [4, 1], [5, 1]], 277/27648000],
[[[1, 14], [2, 3], [3, 1], [4, 1], [5, 1]], 5731/41472000],
[[[1, 14], [2, 5], [3, 1], [4, 1], [6, 1]], 61/16588800],
[[[1, 15], [2, 2], [3, 1], [4, 1], [5, 1]], 271/13824000],
[[[1, 16], [2, 1], [3, 1], [4, 1], [5, 1]], 91/82944000],
[[[1, 1], [2, 2], [3, 1], [6, 4], [10, 1], [30, 1]], 1/1620],
[[[1, 1], [2, 2], [4, 1], [6, 4], [10, 1], [30, 1]], 1/2160],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 6], [12, 1]], 1/1296],
[[[1, 1], [2, 4], [3, 1], [6, 3], [10, 1], [30, 1]], 1/1440],
[[[1, 1], [2, 4], [4, 1], [6, 3], [10, 1], [30, 1]], 1/2160],
[[[1, 1], [2, 6], [3, 1], [4, 1], [6, 5], [12, 1]], 1/1152],
[[[1, 1], [2, 6], [3, 1], [6, 2], [10, 1], [30, 1]], 1/4320],
[[[1, 1], [2, 6], [4, 1], [6, 2], [10, 1], [30, 1]], 1/8640],
[[[1, 1], [2, 8], [3, 1], [4, 1], [6, 4], [12, 1]], 1/3456],
[[[1, 1], [2, 8], [3, 1], [6, 1], [10, 1], [30, 1]], 1/51840],
[[[1, 1], [2, 10], [3, 1], [4, 1], [6, 3], [12, 1]], 1/41472],
[[[1, 2], [2, 1], [3, 4], [4, 1], [5, 1], [15, 1]], 1/2160],
[[[1, 2], [2, 1], [3, 4], [5, 1], [6, 1], [15, 1]], 1/1620],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 5], [18, 1]], 1/1296],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 5], [12, 1]], 1/1728],
[[[1, 2], [2, 3], [3, 1], [6, 3], [10, 1], [30, 1]], 1/432],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 5], [12, 1]], 1/1296],
[[[1, 2], [2, 3], [3, 3], [5, 1], [6, 1], [15, 1]], 1/4320],
[[[1, 2], [2, 3], [3, 4], [4, 1], [6, 2], [9, 1]], 1/2592],
[[[1, 2], [2, 3], [3, 4], [4, 2], [6, 2], [12, 1]], 1/1728],
[[[1, 2], [2, 3], [4, 1], [6, 3], [10, 1], [30, 1]], 1/720],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 4], [18, 1]], 1/1296],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 5], [12, 1]], 5/1728],
[[[1, 2], [2, 5], [3, 1], [4, 2], [6, 4], [12, 1]], 1/1728],
[[[1, 2], [2, 5], [3, 1], [5, 1], [6, 2], [10, 2]], 1/3600],
[[[1, 2], [2, 5], [3, 1], [6, 2], [10, 1], [30, 1]], 7/4320],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 4], [12, 1]], 1/1152],
[[[1, 2], [2, 5], [3, 2], [4, 2], [6, 3], [10, 1]], 1/4320],
[[[1, 2], [2, 5], [4, 1], [6, 2], [10, 1], [30, 1]], 1/1440],
[[[1, 2], [2, 5], [4, 2], [5, 1], [6, 1], [10, 2]], 1/2400],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 3], [18, 1]], 1/5184],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 4], [12, 1]], 7/3456],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 3], [8, 1]], 1/3456],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 3], [12, 1]], 1/6912],
[[[1, 2], [2, 7], [3, 1], [5, 1], [6, 1], [10, 2]], 1/28800],
[[[1, 2], [2, 7], [3, 1], [5, 1], [6, 3], [10, 1]], 1/4320],
[[[1, 2], [2, 7], [3, 1], [6, 1], [10, 1], [30, 1]], 1/4320],
[[[1, 2], [2, 7], [3, 2], [4, 1], [6, 3], [12, 1]], 1/3456],
[[[1, 2], [2, 7], [3, 2], [4, 2], [6, 2], [10, 1]], 1/34560],
[[[1, 2], [2, 7], [4, 2], [5, 1], [6, 2], [10, 1]], 1/2880],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 3], [12, 1]], 1/3456],
[[[1, 2], [2, 9], [3, 1], [4, 2], [6, 2], [8, 1]], 7/138240],
[[[1, 2], [2, 9], [3, 1], [5, 1], [6, 2], [10, 1]], 7/172800],
[[[1, 2], [2, 9], [3, 2], [4, 1], [6, 2], [12, 1]], 1/41472],
[[[1, 2], [2, 9], [4, 2], [5, 1], [6, 1], [10, 1]], 7/115200],
[[[1, 2], [2, 11], [3, 1], [4, 2], [6, 1], [8, 1]], 1/552960],
[[[1, 2], [2, 11], [3, 1], [5, 1], [6, 1], [10, 1]], 1/691200],
[[[1, 3], [2, 2], [3, 1], [6, 3], [10, 1], [30, 1]], 1/4320],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 4], [18, 1]], 1/2592],
[[[1, 3], [2, 2], [3, 2], [4, 2], [6, 4], [12, 1]], 1/1728],
[[[1, 3], [2, 2], [3, 3], [4, 1], [5, 1], [15, 1]], 1/720],
[[[1, 3], [2, 2], [3, 3], [5, 1], [6, 1], [15, 1]], 1/432],
[[[1, 3], [2, 2], [3, 5], [4, 1], [6, 1], [9, 1]], 1/1296],
[[[1, 3], [2, 2], [3, 5], [4, 1], [6, 2], [12, 1]], 1/1296],
[[[1, 3], [2, 2], [3, 5], [4, 2], [6, 1], [12, 1]], 1/1728],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 4], [18, 1]], 1/432],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 5], [12, 1]], 1/3456],
[[[1, 3], [2, 4], [3, 1], [4, 2], [6, 4], [12, 1]], 1/576],
[[[1, 3], [2, 4], [3, 1], [5, 1], [6, 2], [10, 2]], 1/3600],
[[[1, 3], [2, 4], [3, 1], [6, 2], [10, 1], [30, 1]], 13/4320],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 3], [18, 1]], 1/2592],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 4], [12, 1]], 5/1728],
[[[1, 3], [2, 4], [3, 2], [4, 2], [6, 3], [10, 1]], 1/4320],
[[[1, 3], [2, 4], [3, 2], [4, 2], [6, 3], [12, 1]], 1/1728],
[[[1, 3], [2, 4], [3, 2], [4, 3], [5, 1], [6, 2]], 1/5760],
[[[1, 3], [2, 4], [3, 2], [4, 3], [6, 2], [10, 1]], 1/5760],
[[[1, 3], [2, 4], [3, 2], [5, 1], [6, 1], [15, 1]], 1/1440],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 2], [9, 1]], 1/864],
[[[1, 3], [2, 4], [3, 3], [4, 2], [6, 2], [12, 1]], 1/576],
[[[1, 3], [2, 4], [3, 4], [4, 1], [6, 2], [12, 1]], 1/3456],
[[[1, 3], [2, 4], [4, 1], [6, 2], [10, 1], [30, 1]], 1/960],
[[[1, 3], [2, 4], [4, 2], [5, 1], [6, 1], [10, 2]], 1/2400],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 3], [18, 1]], 1/864],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 4], [12, 1]], 13/3456],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 3], [8, 1]], 1/1728],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 3], [12, 1]], 1/1152],
[[[1, 3], [2, 6], [3, 1], [4, 3], [6, 2], [8, 1]], 1/1536],
[[[1, 3], [2, 6], [3, 1], [4, 3], [6, 2], [10, 1]], 1/1920],
[[[1, 3], [2, 6], [3, 1], [5, 1], [6, 1], [10, 2]], 7/28800],
[[[1, 3], [2, 6], [3, 1], [5, 1], [6, 3], [10, 1]], 1/2160],
[[[1, 3], [2, 6], [3, 1], [6, 1], [10, 1], [30, 1]], 1/1080],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 2], [18, 1]], 1/10368],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 3], [10, 1]], 1/2160],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 3], [12, 1]], 7/3456],
[[[1, 3], [2, 6], [3, 2], [4, 2], [6, 2], [10, 1]], 7/34560],
[[[1, 3], [2, 6], [3, 2], [4, 2], [6, 2], [12, 1]], 1/6912],
[[[1, 3], [2, 6], [4, 1], [5, 1], [6, 1], [10, 2]], 1/1800],
[[[1, 3], [2, 6], [4, 2], [5, 1], [6, 2], [10, 1]], 1/1440],
[[[1, 3], [2, 6], [4, 3], [5, 1], [6, 1], [10, 1]], 1/1280],
[[[1, 3], [2, 6], [4, 3], [6, 1], [8, 1], [10, 1]], 1/1920],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 3], [8, 1]], 1/3456],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 3], [12, 1]], 1/864],
[[[1, 3], [2, 8], [3, 1], [4, 2], [6, 2], [8, 1]], 31/69120],
[[[1, 3], [2, 8], [3, 1], [4, 3], [6, 1], [8, 1]], 1/15360],
[[[1, 3], [2, 8], [3, 1], [4, 3], [6, 1], [10, 1]], 1/15360],
[[[1, 3], [2, 8], [3, 1], [5, 1], [6, 2], [10, 1]], 31/86400],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 2], [10, 1]], 1/17280],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 2], [12, 1]], 1/3456],
[[[1, 3], [2, 8], [4, 1], [5, 1], [6, 2], [10, 1]], 1/2160],
[[[1, 3], [2, 8], [4, 2], [5, 1], [6, 1], [10, 1]], 31/57600],
[[[1, 3], [2, 10], [3, 1], [4, 1], [6, 2], [8, 1]], 7/138240],
[[[1, 3], [2, 10], [3, 1], [4, 2], [6, 1], [8, 1]], 17/552960],
[[[1, 3], [2, 10], [3, 1], [5, 1], [6, 1], [10, 1]], 17/691200],
[[[1, 3], [2, 10], [4, 1], [5, 1], [6, 1], [10, 1]], 7/86400],
[[[1, 3], [2, 12], [3, 1], [4, 1], [6, 1], [8, 1]], 1/552960],
[[[1, 4], [2, 1], [3, 3], [4, 1], [5, 1], [15, 1]], 1/2160],
[[[1, 4], [2, 1], [3, 3], [5, 1], [6, 1], [15, 1]], 1/1440],
[[[1, 4], [2, 1], [3, 6], [4, 1], [6, 1], [12, 1]], 1/1296],
[[[1, 4], [2, 3], [3, 1], [4, 2], [5, 2], [10, 1]], 1/2400],
[[[1, 4], [2, 3], [3, 1], [6, 2], [10, 1], [30, 1]], 1/1440],
[[[1, 4], [2, 3], [3, 2], [4, 1], [5, 1], [15, 1]], 1/960],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 3], [18, 1]], 1/864],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 4], [12, 1]], 1/3456],
[[[1, 4], [2, 3], [3, 2], [4, 2], [6, 3], [12, 1]], 1/576],
[[[1, 4], [2, 3], [3, 2], [4, 3], [5, 1], [6, 2]], 1/5760],
[[[1, 4], [2, 3], [3, 2], [4, 3], [6, 2], [10, 1]], 1/5760],
[[[1, 4], [2, 3], [3, 2], [5, 1], [6, 1], [15, 1]], 13/4320],
[[[1, 4], [2, 3], [3, 2], [5, 2], [6, 1], [10, 1]], 1/3600],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 2], [9, 1]], 1/2592],
[[[1, 4], [2, 3], [3, 3], [4, 2], [5, 1], [6, 2]], 1/4320],
[[[1, 4], [2, 3], [3, 3], [4, 2], [6, 2], [12, 1]], 1/1728],
[[[1, 4], [2, 3], [3, 4], [4, 1], [6, 1], [9, 1]], 1/432],
[[[1, 4], [2, 3], [3, 4], [4, 1], [6, 2], [12, 1]], 5/1728],
[[[1, 4], [2, 3], [3, 4], [4, 2], [6, 1], [12, 1]], 1/576],
[[[1, 4], [2, 3], [3, 5], [4, 1], [6, 1], [12, 1]], 1/3456],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 3], [18, 1]], 1/576],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 4], [12, 1]], 1/1152],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 3], [8, 1]], 1/3456],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 3], [12, 1]], 1/768],
[[[1, 4], [2, 5], [3, 1], [4, 3], [5, 1], [10, 1]], 1/3840],
[[[1, 4], [2, 5], [3, 1], [4, 3], [6, 2], [8, 1]], 1/1152],
[[[1, 4], [2, 5], [3, 1], [4, 3], [6, 2], [10, 1]], 1/1920],
[[[1, 4], [2, 5], [3, 1], [4, 4], [5, 1], [6, 1]], 1/2560],
[[[1, 4], [2, 5], [3, 1], [4, 4], [6, 1], [8, 1]], 1/1536],
[[[1, 4], [2, 5], [3, 1], [4, 4], [6, 1], [10, 1]], 1/2560],
[[[1, 4], [2, 5], [3, 1], [5, 1], [6, 1], [10, 2]], 1/3200],
[[[1, 4], [2, 5], [3, 1], [5, 1], [6, 1], [15, 1]], 1/1920],
[[[1, 4], [2, 5], [3, 1], [5, 1], [6, 3], [10, 1]], 1/4320],
[[[1, 4], [2, 5], [3, 1], [5, 2], [6, 1], [10, 1]], 1/9600],
[[[1, 4], [2, 5], [3, 1], [6, 1], [10, 1], [30, 1]], 1/720],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 2], [9, 1]], 1/1152],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 2], [18, 1]], 1/1728],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 3], [10, 1]], 1/2160],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 3], [12, 1]], 13/3456],
[[[1, 4], [2, 5], [3, 2], [4, 2], [5, 1], [6, 2]], 1/2304],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 2], [10, 1]], 7/11520],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 2], [12, 1]], 5/2304],
[[[1, 4], [2, 5], [3, 2], [4, 3], [6, 1], [8, 1]], 1/4608],
[[[1, 4], [2, 5], [3, 3], [4, 1], [6, 2], [12, 1]], 1/1152],
[[[1, 4], [2, 5], [4, 1], [5, 1], [6, 1], [10, 2]], 1/1800],
[[[1, 4], [2, 5], [4, 2], [5, 1], [6, 2], [10, 1]], 1/2880],
[[[1, 4], [2, 5], [4, 3], [5, 1], [6, 1], [10, 1]], 1/960],
[[[1, 4], [2, 5], [4, 3], [6, 1], [8, 1], [10, 1]], 1/1920],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 3], [8, 1]], 1/1728],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 3], [12, 1]], 1/576],
[[[1, 4], [2, 7], [3, 1], [4, 2], [6, 2], [8, 1]], 11/6912],
[[[1, 4], [2, 7], [3, 1], [4, 2], [6, 2], [10, 1]], 19/17280],
[[[1, 4], [2, 7], [3, 1], [4, 3], [6, 1], [8, 1]], 23/46080],
[[[1, 4], [2, 7], [3, 1], [4, 3], [6, 1], [10, 1]], 7/15360],
[[[1, 4], [2, 7], [3, 1], [5, 1], [6, 2], [10, 1]], 13/17280],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 2], [10, 1]], 7/17280],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 2], [12, 1]], 1/864],
[[[1, 4], [2, 7], [4, 1], [5, 1], [6, 2], [10, 1]], 1/1080],
[[[1, 4], [2, 7], [4, 2], [5, 1], [6, 1], [10, 1]], 5/2304],
[[[1, 4], [2, 7], [4, 2], [6, 1], [8, 1], [10, 1]], 1/1440],
[[[1, 4], [2, 9], [3, 1], [4, 1], [6, 2], [8, 1]], 31/69120],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 1], [8, 1]], 13/55296],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 1], [10, 1]], 19/138240],
[[[1, 4], [2, 9], [3, 1], [5, 1], [6, 1], [10, 1]], 47/345600],
[[[1, 4], [2, 9], [4, 1], [5, 1], [6, 1], [10, 1]], 31/43200],
[[[1, 4], [2, 11], [3, 1], [4, 1], [6, 1], [8, 1]], 17/552960],
[[[1, 5], [2, 2], [3, 1], [4, 2], [5, 2], [10, 1]], 1/2400],
[[[1, 5], [2, 2], [3, 2], [4, 1], [5, 1], [15, 1]], 1/1440],
[[[1, 5], [2, 2], [3, 2], [5, 1], [6, 1], [15, 1]], 7/4320],
[[[1, 5], [2, 2], [3, 2], [5, 2], [6, 1], [10, 1]], 1/3600],
[[[1, 5], [2, 2], [3, 3], [4, 2], [5, 1], [6, 2]], 1/4320],
[[[1, 5], [2, 2], [3, 4], [4, 1], [6, 1], [9, 1]], 1/1296],
[[[1, 5], [2, 2], [3, 4], [4, 1], [6, 2], [12, 1]], 1/1152],
[[[1, 5], [2, 2], [3, 4], [4, 2], [6, 1], [12, 1]], 1/1728],
[[[1, 5], [2, 2], [3, 5], [4, 1], [6, 1], [12, 1]], 5/1728],
[[[1, 5], [2, 4], [3, 1], [4, 1], [5, 2], [10, 1]], 1/1800],
[[[1, 5], [2, 4], [3, 1], [4, 3], [5, 1], [8, 1]], 1/1920],
[[[1, 5], [2, 4], [3, 1], [4, 3], [5, 1], [10, 1]], 1/960],
[[[1, 5], [2, 4], [3, 1], [4, 3], [6, 2], [8, 1]], 1/4608],
[[[1, 5], [2, 4], [3, 1], [4, 4], [5, 1], [6, 1]], 1/2560],
[[[1, 5], [2, 4], [3, 1], [4, 4], [6, 1], [8, 1]], 1/1536],
[[[1, 5], [2, 4], [3, 1], [4, 4], [6, 1], [10, 1]], 1/2560],
[[[1, 5], [2, 4], [3, 1], [5, 1], [6, 1], [10, 2]], 1/9600],
[[[1, 5], [2, 4], [3, 1], [5, 1], [6, 1], [15, 1]], 1/720],
[[[1, 5], [2, 4], [3, 1], [5, 2], [6, 1], [10, 1]], 1/3200],
[[[1, 5], [2, 4], [3, 1], [6, 1], [10, 1], [30, 1]], 1/1920],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 2], [9, 1]], 1/1728],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 2], [18, 1]], 1/1152],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 3], [12, 1]], 1/1152],
[[[1, 5], [2, 4], [3, 2], [4, 2], [5, 1], [6, 2]], 7/11520],
[[[1, 5], [2, 4], [3, 2], [4, 2], [5, 1], [10, 1]], 1/2880],
[[[1, 5], [2, 4], [3, 2], [4, 2], [6, 2], [10, 1]], 1/2304],
[[[1, 5], [2, 4], [3, 2], [4, 2], [6, 2], [12, 1]], 5/2304],
[[[1, 5], [2, 4], [3, 2], [4, 3], [5, 1], [6, 1]], 1/1920],
[[[1, 5], [2, 4], [3, 2], [4, 3], [6, 1], [8, 1]], 1/1152],
[[[1, 5], [2, 4], [3, 3], [4, 1], [5, 1], [6, 2]], 1/2160],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 1], [9, 1]], 1/576],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 2], [12, 1]], 13/3456],
[[[1, 5], [2, 4], [3, 3], [4, 2], [6, 1], [8, 1]], 1/3456],
[[[1, 5], [2, 4], [3, 3], [4, 2], [6, 1], [12, 1]], 1/768],
[[[1, 5], [2, 4], [3, 3], [5, 1], [6, 1], [10, 1]], 1/4320],
[[[1, 5], [2, 4], [3, 4], [4, 1], [6, 1], [12, 1]], 1/1152],
[[[1, 5], [2, 4], [4, 3], [5, 1], [6, 1], [10, 1]], 1/3840],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 3], [8, 1]], 1/3456],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 3], [12, 1]], 1/1536],
[[[1, 5], [2, 6], [3, 1], [4, 2], [5, 1], [10, 1]], 11/23040],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 2], [8, 1]], 7/4608],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 2], [10, 1]], 19/17280],
[[[1, 5], [2, 6], [3, 1], [4, 3], [5, 1], [6, 1]], 47/46080],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 1], [8, 1]], 1/576],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 1], [10, 1]], 13/9216],
[[[1, 5], [2, 6], [3, 1], [5, 1], [6, 2], [10, 1]], 1/1920],
[[[1, 5], [2, 6], [3, 2], [4, 1], [5, 1], [6, 2]], 1/2880],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 2], [10, 1]], 1/1440],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 2], [12, 1]], 11/4608],
[[[1, 5], [2, 6], [3, 2], [4, 2], [6, 1], [8, 1]], 1/3072],
[[[1, 5], [2, 6], [3, 2], [5, 1], [6, 1], [10, 1]], 1/11520],
[[[1, 5], [2, 6], [4, 1], [5, 1], [6, 2], [10, 1]], 1/2160],
[[[1, 5], [2, 6], [4, 2], [5, 1], [6, 1], [10, 1]], 5/2304],
[[[1, 5], [2, 6], [4, 2], [6, 1], [8, 1], [10, 1]], 1/1440],
[[[1, 5], [2, 8], [3, 1], [4, 1], [6, 2], [8, 1]], 13/13824],
[[[1, 5], [2, 8], [3, 1], [4, 1], [6, 2], [10, 1]], 61/86400],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 1], [8, 1]], 79/92160],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 1], [10, 1]], 133/138240],
[[[1, 5], [2, 8], [3, 1], [5, 1], [6, 1], [10, 1]], 11/38400],
[[[1, 5], [2, 8], [4, 1], [5, 1], [6, 1], [10, 1]], 61/34560],
[[[1, 5], [2, 8], [4, 1], [6, 1], [8, 1], [10, 1]], 1/5760],
[[[1, 5], [2, 10], [3, 1], [4, 1], [6, 1], [8, 1]], 47/276480],
[[[1, 5], [2, 10], [3, 1], [4, 1], [6, 1], [10, 1]], 61/691200],
[[[1, 6], [2, 1], [3, 2], [4, 1], [5, 1], [15, 1]], 1/8640],
[[[1, 6], [2, 1], [3, 2], [5, 1], [6, 1], [15, 1]], 1/4320],
[[[1, 6], [2, 1], [3, 5], [4, 1], [6, 1], [12, 1]], 1/1152],
[[[1, 6], [2, 3], [3, 1], [4, 1], [5, 2], [10, 1]], 1/1800],
[[[1, 6], [2, 3], [3, 1], [4, 3], [5, 1], [8, 1]], 1/1920],
[[[1, 6], [2, 3], [3, 1], [4, 3], [5, 1], [10, 1]], 1/1280],
[[[1, 6], [2, 3], [3, 1], [5, 1], [6, 1], [15, 1]], 1/1080],
[[[1, 6], [2, 3], [3, 1], [5, 2], [6, 1], [10, 1]], 7/28800],
[[[1, 6], [2, 3], [3, 2], [4, 1], [6, 2], [9, 1]], 1/10368],
[[[1, 6], [2, 3], [3, 2], [4, 2], [5, 1], [6, 2]], 7/34560],
[[[1, 6], [2, 3], [3, 2], [4, 2], [5, 1], [10, 1]], 1/1440],
[[[1, 6], [2, 3], [3, 2], [4, 2], [6, 2], [12, 1]], 1/6912],
[[[1, 6], [2, 3], [3, 2], [4, 3], [5, 1], [6, 1]], 1/1920],
[[[1, 6], [2, 3], [3, 2], [4, 3], [6, 1], [8, 1]], 1/1536],
[[[1, 6], [2, 3], [3, 3], [4, 1], [5, 1], [6, 2]], 1/2160],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 1], [9, 1]], 1/864],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 2], [12, 1]], 7/3456],
[[[1, 6], [2, 3], [3, 3], [4, 2], [6, 1], [8, 1]], 1/1728],
[[[1, 6], [2, 3], [3, 3], [4, 2], [6, 1], [12, 1]], 1/1152],
[[[1, 6], [2, 3], [3, 3], [5, 1], [6, 1], [10, 1]], 1/2160],
[[[1, 6], [2, 3], [3, 4], [4, 1], [6, 1], [12, 1]], 13/3456],
[[[1, 6], [2, 5], [3, 1], [4, 2], [5, 1], [8, 1]], 1/1440],
[[[1, 6], [2, 5], [3, 1], [4, 2], [5, 1], [10, 1]], 5/2304],
[[[1, 6], [2, 5], [3, 1], [4, 2], [6, 2], [8, 1]], 1/3072],
[[[1, 6], [2, 5], [3, 1], [4, 3], [5, 1], [6, 1]], 13/9216],
[[[1, 6], [2, 5], [3, 1], [4, 3], [6, 1], [8, 1]], 1/576],
[[[1, 6], [2, 5], [3, 1], [4, 3], [6, 1], [10, 1]], 47/46080],
[[[1, 6], [2, 5], [3, 1], [5, 1], [6, 2], [10, 1]], 1/11520],
[[[1, 6], [2, 5], [3, 2], [4, 1], [5, 1], [6, 2]], 1/1440],
[[[1, 6], [2, 5], [3, 2], [4, 1], [5, 1], [10, 1]], 1/2160],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 2], [10, 1]], 1/2880],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 2], [12, 1]], 11/4608],
[[[1, 6], [2, 5], [3, 2], [4, 2], [5, 1], [6, 1]], 19/17280],
[[[1, 6], [2, 5], [3, 2], [4, 2], [6, 1], [8, 1]], 7/4608],
[[[1, 6], [2, 5], [3, 2], [5, 1], [6, 1], [10, 1]], 1/1920],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 1], [8, 1]], 1/3456],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 1], [12, 1]], 1/1536],
[[[1, 6], [2, 5], [4, 2], [5, 1], [6, 1], [10, 1]], 11/23040],
[[[1, 6], [2, 7], [3, 1], [4, 1], [5, 1], [10, 1]], 1/3840],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 2], [8, 1]], 1/1536],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 2], [10, 1]], 61/86400],
[[[1, 6], [2, 7], [3, 1], [4, 2], [5, 1], [6, 1]], 217/230400],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 1], [8, 1]], 3/2048],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 1], [10, 1]], 407/230400],
[[[1, 6], [2, 7], [3, 1], [5, 1], [6, 1], [10, 1]], 7/23040],
[[[1, 6], [2, 7], [3, 2], [4, 1], [6, 1], [8, 1]], 1/9216],
[[[1, 6], [2, 7], [4, 1], [5, 1], [6, 1], [10, 1]], 1/720],
[[[1, 6], [2, 7], [4, 1], [6, 1], [8, 1], [10, 1]], 1/5760],
[[[1, 6], [2, 9], [3, 1], [4, 1], [6, 1], [8, 1]], 11/30720],
[[[1, 6], [2, 9], [3, 1], [4, 1], [6, 1], [10, 1]], 427/691200],
[[[1, 7], [2, 2], [3, 1], [5, 1], [6, 1], [15, 1]], 1/4320],
[[[1, 7], [2, 2], [3, 1], [5, 2], [6, 1], [10, 1]], 1/28800],
[[[1, 7], [2, 2], [3, 2], [4, 2], [5, 1], [6, 2]], 1/34560],
[[[1, 7], [2, 2], [3, 2], [4, 2], [5, 1], [10, 1]], 1/2880],
[[[1, 7], [2, 2], [3, 3], [4, 1], [6, 1], [9, 1]], 1/5184],
[[[1, 7], [2, 2], [3, 3], [4, 1], [6, 2], [12, 1]], 1/3456],
[[[1, 7], [2, 2], [3, 3], [4, 2], [6, 1], [8, 1]], 1/3456],
[[[1, 7], [2, 2], [3, 3], [4, 2], [6, 1], [12, 1]], 1/6912],
[[[1, 7], [2, 2], [3, 3], [5, 1], [6, 1], [10, 1]], 1/4320],
[[[1, 7], [2, 2], [3, 4], [4, 1], [6, 1], [12, 1]], 7/3456],
[[[1, 7], [2, 4], [3, 1], [4, 2], [5, 1], [8, 1]], 1/1440],
[[[1, 7], [2, 4], [3, 1], [4, 2], [5, 1], [10, 1]], 5/2304],
[[[1, 7], [2, 4], [3, 1], [4, 3], [5, 1], [6, 1]], 7/15360],
[[[1, 7], [2, 4], [3, 1], [4, 3], [6, 1], [8, 1]], 23/46080],
[[[1, 7], [2, 4], [3, 2], [4, 1], [5, 1], [6, 2]], 7/17280],
[[[1, 7], [2, 4], [3, 2], [4, 1], [5, 1], [10, 1]], 1/1080],
[[[1, 7], [2, 4], [3, 2], [4, 1], [6, 2], [12, 1]], 1/864],
[[[1, 7], [2, 4], [3, 2], [4, 2], [5, 1], [6, 1]], 19/17280],
[[[1, 7], [2, 4], [3, 2], [4, 2], [6, 1], [8, 1]], 11/6912],
[[[1, 7], [2, 4], [3, 2], [5, 1], [6, 1], [10, 1]], 13/17280],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 1], [8, 1]], 1/1728],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 1], [12, 1]], 1/576],
[[[1, 7], [2, 6], [3, 1], [4, 1], [5, 1], [8, 1]], 1/5760],
[[[1, 7], [2, 6], [3, 1], [4, 1], [5, 1], [10, 1]], 1/720],
[[[1, 7], [2, 6], [3, 1], [4, 1], [6, 2], [8, 1]], 1/9216],
[[[1, 7], [2, 6], [3, 1], [4, 2], [5, 1], [6, 1]], 407/230400],
[[[1, 7], [2, 6], [3, 1], [4, 2], [6, 1], [8, 1]], 3/2048],
[[[1, 7], [2, 6], [3, 1], [4, 2], [6, 1], [10, 1]], 217/230400],
[[[1, 7], [2, 6], [3, 1], [5, 1], [6, 1], [10, 1]], 7/23040],
[[[1, 7], [2, 6], [3, 2], [4, 1], [5, 1], [6, 1]], 61/86400],
[[[1, 7], [2, 6], [3, 2], [4, 1], [6, 1], [8, 1]], 1/1536],
[[[1, 7], [2, 6], [4, 1], [5, 1], [6, 1], [10, 1]], 1/3840],
[[[1, 7], [2, 8], [3, 1], [4, 1], [5, 1], [6, 1]], 83/230400],
[[[1, 7], [2, 8], [3, 1], [4, 1], [6, 1], [8, 1]], 7/18432],
[[[1, 7], [2, 8], [3, 1], [4, 1], [6, 1], [10, 1]], 41/46080],
[[[1, 8], [2, 1], [3, 1], [5, 1], [6, 1], [15, 1]], 1/51840],
[[[1, 8], [2, 1], [3, 4], [4, 1], [6, 1], [12, 1]], 1/3456],
[[[1, 8], [2, 3], [3, 1], [4, 2], [5, 1], [10, 1]], 31/57600],
[[[1, 8], [2, 3], [3, 1], [4, 3], [5, 1], [6, 1]], 1/15360],
[[[1, 8], [2, 3], [3, 1], [4, 3], [6, 1], [8, 1]], 1/15360],
[[[1, 8], [2, 3], [3, 2], [4, 1], [5, 1], [6, 2]], 1/17280],
[[[1, 8], [2, 3], [3, 2], [4, 1], [5, 1], [10, 1]], 1/2160],
[[[1, 8], [2, 3], [3, 2], [4, 1], [6, 2], [12, 1]], 1/3456],
[[[1, 8], [2, 3], [3, 2], [4, 2], [6, 1], [8, 1]], 31/69120],
[[[1, 8], [2, 3], [3, 2], [5, 1], [6, 1], [10, 1]], 31/86400],
[[[1, 8], [2, 3], [3, 3], [4, 1], [6, 1], [8, 1]], 1/3456],
[[[1, 8], [2, 3], [3, 3], [4, 1], [6, 1], [12, 1]], 1/864],
[[[1, 8], [2, 5], [3, 1], [4, 1], [5, 1], [8, 1]], 1/5760],
[[[1, 8], [2, 5], [3, 1], [4, 1], [5, 1], [10, 1]], 61/34560],
[[[1, 8], [2, 5], [3, 1], [4, 2], [5, 1], [6, 1]], 133/138240],
[[[1, 8], [2, 5], [3, 1], [4, 2], [6, 1], [8, 1]], 79/92160],
[[[1, 8], [2, 5], [3, 1], [5, 1], [6, 1], [10, 1]], 11/38400],
[[[1, 8], [2, 5], [3, 2], [4, 1], [5, 1], [6, 1]], 61/86400],
[[[1, 8], [2, 5], [3, 2], [4, 1], [6, 1], [8, 1]], 13/13824],
[[[1, 8], [2, 7], [3, 1], [4, 1], [5, 1], [6, 1]], 41/46080],
[[[1, 8], [2, 7], [3, 1], [4, 1], [6, 1], [8, 1]], 7/18432],
[[[1, 8], [2, 7], [3, 1], [4, 1], [6, 1], [10, 1]], 83/230400],
[[[1, 9], [2, 2], [3, 1], [4, 2], [5, 1], [10, 1]], 7/115200],
[[[1, 9], [2, 2], [3, 2], [4, 1], [6, 2], [12, 1]], 1/41472],
[[[1, 9], [2, 2], [3, 2], [4, 2], [6, 1], [8, 1]], 7/138240],
[[[1, 9], [2, 2], [3, 2], [5, 1], [6, 1], [10, 1]], 7/172800],
[[[1, 9], [2, 2], [3, 3], [4, 1], [6, 1], [12, 1]], 1/3456],
[[[1, 9], [2, 4], [3, 1], [4, 1], [5, 1], [10, 1]], 31/43200],
[[[1, 9], [2, 4], [3, 1], [4, 2], [5, 1], [6, 1]], 19/138240],
[[[1, 9], [2, 4], [3, 1], [4, 2], [6, 1], [8, 1]], 13/55296],
[[[1, 9], [2, 4], [3, 1], [5, 1], [6, 1], [10, 1]], 47/345600],
[[[1, 9], [2, 4], [3, 2], [4, 1], [6, 1], [8, 1]], 31/69120],
[[[1, 9], [2, 6], [3, 1], [4, 1], [5, 1], [6, 1]], 427/691200],
[[[1, 9], [2, 6], [3, 1], [4, 1], [6, 1], [8, 1]], 11/30720],
[[[1, 10], [2, 1], [3, 3], [4, 1], [6, 1], [12, 1]], 1/41472],
[[[1, 10], [2, 3], [3, 1], [4, 1], [5, 1], [10, 1]], 7/86400],
[[[1, 10], [2, 3], [3, 1], [4, 2], [6, 1], [8, 1]], 17/552960],
[[[1, 10], [2, 3], [3, 1], [5, 1], [6, 1], [10, 1]], 17/691200],
[[[1, 10], [2, 3], [3, 2], [4, 1], [6, 1], [8, 1]], 7/138240],
[[[1, 10], [2, 5], [3, 1], [4, 1], [5, 1], [6, 1]], 61/691200],
[[[1, 10], [2, 5], [3, 1], [4, 1], [6, 1], [8, 1]], 47/276480],
[[[1, 11], [2, 2], [3, 1], [4, 2], [6, 1], [8, 1]], 1/552960],
[[[1, 11], [2, 2], [3, 1], [5, 1], [6, 1], [10, 1]], 1/691200],
[[[1, 11], [2, 4], [3, 1], [4, 1], [6, 1], [8, 1]], 17/552960],
[[[1, 12], [2, 3], [3, 1], [4, 1], [6, 1], [8, 1]], 1/552960],
[[[1, 1], [2, 2], [3, 3], [4, 1], [5, 1], [6, 1], [15, 1]], 1/2160],
[[[1, 1], [2, 4], [3, 1], [4, 1], [5, 1], [6, 2], [10, 2]], 1/3600],
[[[1, 1], [2, 6], [3, 1], [4, 1], [5, 1], [6, 1], [10, 2]], 1/28800],
[[[1, 1], [2, 6], [3, 1], [4, 1], [5, 1], [6, 3], [10, 1]], 1/4320],
[[[1, 1], [2, 8], [3, 1], [4, 1], [5, 1], [6, 2], [10, 1]], 7/172800],
[[[1, 1], [2, 10], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 1/691200],
[[[1, 2], [2, 1], [3, 1], [4, 1], [6, 3], [10, 1], [30, 1]], 1/2160],
[[[1, 2], [2, 3], [3, 1], [4, 1], [5, 1], [6, 2], [10, 2]], 1/3600],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 2], [10, 1], [30, 1]], 1/2160],
[[[1, 2], [2, 3], [3, 1], [4, 2], [5, 1], [6, 1], [10, 2]], 1/4800],
[[[1, 2], [2, 3], [3, 1], [4, 2], [5, 2], [6, 1], [10, 1]], 1/4800],
[[[1, 2], [2, 3], [3, 2], [4, 1], [5, 1], [6, 1], [15, 1]], 1/720],
[[[1, 2], [2, 5], [3, 1], [4, 1], [5, 1], [6, 1], [10, 2]], 7/28800],
[[[1, 2], [2, 5], [3, 1], [4, 1], [5, 1], [6, 3], [10, 1]], 1/2160],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 1], [10, 1], [30, 1]], 1/8640],
[[[1, 2], [2, 5], [3, 1], [4, 2], [5, 1], [6, 2], [10, 1]], 1/1920],
[[[1, 2], [2, 5], [3, 1], [4, 2], [6, 2], [8, 1], [10, 1]], 1/2880],
[[[1, 2], [2, 7], [3, 1], [4, 1], [5, 1], [6, 2], [10, 1]], 31/86400],
[[[1, 2], [2, 7], [3, 1], [4, 2], [5, 1], [6, 1], [10, 1]], 1/19200],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 1/23040],
[[[1, 2], [2, 9], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 17/691200],
[[[1, 3], [2, 2], [3, 1], [4, 1], [6, 2], [10, 1], [30, 1]], 1/720],
[[[1, 3], [2, 2], [3, 1], [4, 2], [5, 1], [6, 1], [10, 2]], 1/4800],
[[[1, 3], [2, 2], [3, 1], [4, 2], [5, 2], [6, 1], [10, 1]], 1/4800],
[[[1, 3], [2, 2], [3, 2], [4, 1], [5, 1], [6, 1], [15, 1]], 1/2160],
[[[1, 3], [2, 2], [3, 2], [4, 1], [5, 2], [6, 1], [10, 1]], 1/3600],
[[[1, 3], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1], [10, 2]], 1/1920],
[[[1, 3], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1], [15, 1]], 1/960],
[[[1, 3], [2, 4], [3, 1], [4, 1], [5, 1], [6, 3], [10, 1]], 1/4320],
[[[1, 3], [2, 4], [3, 1], [4, 1], [5, 2], [6, 1], [10, 1]], 1/3200],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 1], [10, 1], [30, 1]], 1/1440],
[[[1, 3], [2, 4], [3, 1], [4, 2], [5, 1], [6, 2], [10, 1]], 1/1440],
[[[1, 3], [2, 4], [3, 1], [4, 2], [6, 2], [8, 1], [10, 1]], 1/2880],
[[[1, 3], [2, 4], [3, 1], [4, 3], [5, 1], [6, 1], [8, 1]], 1/3840],
[[[1, 3], [2, 4], [3, 1], [4, 3], [5, 1], [6, 1], [10, 1]], 1/1920],
[[[1, 3], [2, 4], [3, 1], [4, 3], [6, 1], [8, 1], [10, 1]], 1/3840],
[[[1, 3], [2, 4], [3, 2], [4, 2], [5, 1], [6, 1], [10, 1]], 1/5760],
[[[1, 3], [2, 6], [3, 1], [4, 1], [5, 1], [6, 2], [10, 1]], 11/8640],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 2], [8, 1], [10, 1]], 1/2880],
[[[1, 3], [2, 6], [3, 1], [4, 2], [5, 1], [6, 1], [10, 1]], 23/57600],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 7/23040],
[[[1, 3], [2, 8], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 13/69120],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/23040],
[[[1, 4], [2, 1], [3, 2], [4, 1], [5, 2], [6, 1], [10, 1]], 1/3600],
[[[1, 4], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1], [10, 2]], 1/3200],
[[[1, 4], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1], [15, 1]], 1/1440],
[[[1, 4], [2, 3], [3, 1], [4, 1], [5, 2], [6, 1], [10, 1]], 1/1920],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 1], [10, 1], [30, 1]], 1/960],
[[[1, 4], [2, 3], [3, 1], [4, 2], [5, 1], [6, 2], [10, 1]], 1/5760],
[[[1, 4], [2, 3], [3, 1], [4, 3], [5, 1], [6, 1], [8, 1]], 1/3840],
[[[1, 4], [2, 3], [3, 1], [4, 3], [5, 1], [6, 1], [10, 1]], 1/1920],
[[[1, 4], [2, 3], [3, 1], [4, 3], [6, 1], [8, 1], [10, 1]], 1/3840],
[[[1, 4], [2, 3], [3, 2], [4, 2], [5, 1], [6, 1], [8, 1]], 1/2880],
[[[1, 4], [2, 3], [3, 2], [4, 2], [5, 1], [6, 1], [10, 1]], 1/1440],
[[[1, 4], [2, 3], [3, 3], [4, 1], [5, 1], [6, 1], [10, 1]], 1/4320],
[[[1, 4], [2, 5], [3, 1], [4, 1], [5, 1], [6, 2], [10, 1]], 7/5760],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 2], [8, 1], [10, 1]], 1/2880],
[[[1, 4], [2, 5], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 1/2560],
[[[1, 4], [2, 5], [3, 1], [4, 2], [5, 1], [6, 1], [10, 1]], 1/720],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 1/1536],
[[[1, 4], [2, 5], [3, 2], [4, 1], [5, 1], [6, 1], [10, 1]], 1/3840],
[[[1, 4], [2, 7], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 79/115200],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 7/23040],
[[[1, 5], [2, 2], [3, 1], [4, 1], [5, 1], [6, 1], [15, 1]], 1/8640],
[[[1, 5], [2, 2], [3, 1], [4, 1], [5, 2], [6, 1], [10, 1]], 7/28800],
[[[1, 5], [2, 2], [3, 2], [4, 2], [5, 1], [6, 1], [8, 1]], 1/2880],
[[[1, 5], [2, 2], [3, 2], [4, 2], [5, 1], [6, 1], [10, 1]], 1/1920],
[[[1, 5], [2, 2], [3, 3], [4, 1], [5, 1], [6, 1], [10, 1]], 1/2160],
[[[1, 5], [2, 4], [3, 1], [4, 1], [5, 1], [6, 2], [10, 1]], 1/3840],
[[[1, 5], [2, 4], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 1/1536],
[[[1, 5], [2, 4], [3, 1], [4, 2], [5, 1], [6, 1], [10, 1]], 1/720],
[[[1, 5], [2, 4], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 1/2560],
[[[1, 5], [2, 4], [3, 2], [4, 1], [5, 1], [6, 1], [8, 1]], 1/2880],
[[[1, 5], [2, 4], [3, 2], [4, 1], [5, 1], [6, 1], [10, 1]], 7/5760],
[[[1, 5], [2, 6], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/7680],
[[[1, 5], [2, 6], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 3/2560],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/2560],
[[[1, 6], [2, 1], [3, 1], [4, 1], [5, 2], [6, 1], [10, 1]], 1/28800],
[[[1, 6], [2, 1], [3, 3], [4, 1], [5, 1], [6, 1], [10, 1]], 1/4320],
[[[1, 6], [2, 3], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 7/23040],
[[[1, 6], [2, 3], [3, 1], [4, 2], [5, 1], [6, 1], [10, 1]], 23/57600],
[[[1, 6], [2, 3], [3, 2], [4, 1], [5, 1], [6, 1], [8, 1]], 1/2880],
[[[1, 6], [2, 3], [3, 2], [4, 1], [5, 1], [6, 1], [10, 1]], 11/8640],
[[[1, 6], [2, 5], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/2560],
[[[1, 6], [2, 5], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 3/2560],
[[[1, 6], [2, 5], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/7680],
[[[1, 7], [2, 2], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 1/23040],
[[[1, 7], [2, 2], [3, 1], [4, 2], [5, 1], [6, 1], [10, 1]], 1/19200],
[[[1, 7], [2, 2], [3, 2], [4, 1], [5, 1], [6, 1], [10, 1]], 31/86400],
[[[1, 7], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 7/23040],
[[[1, 7], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 79/115200],
[[[1, 8], [2, 1], [3, 2], [4, 1], [5, 1], [6, 1], [10, 1]], 7/172800],
[[[1, 8], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/23040],
[[[1, 8], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 13/69120],
[[[1, 9], [2, 2], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 17/691200],
[[[1, 10], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [10, 1]], 1/691200]
]}