{[
[[[1, 25]], 1/812665405440000],
[[[2, 25]], 1/812665405440000],
[[[1, 1], [2, 24]], 1/10032906240000],
[[[1, 2], [2, 23]], 13/3762339840000],
[[[1, 3], [2, 22]], 61/902961561600],
[[[1, 4], [2, 21]], 4967/6019743744000],
[[[1, 5], [2, 20]], 13217/2006581248000],
[[[1, 6], [2, 19]], 5261/150493593600],
[[[1, 7], [2, 18]], 3089/25082265600],
[[[1, 7], [3, 9]], 43/14171760],
[[[1, 8], [2, 17]], 37817/133772083200],
[[[1, 9], [2, 16]], 98101/240789749760],
[[[1, 9], [3, 8]], 1/196830],
[[[1, 9], [5, 4]], 1/90000],
[[[1, 10], [2, 15]], 583/1672151040],
[[[1, 11], [2, 14]], 53/318504960],
[[[1, 11], [3, 7]], 197/125971200],
[[[1, 12], [2, 13]], 17/382205952],
[[[1, 13], [2, 12]], 17/382205952],
[[[1, 13], [3, 6]], 11191/10581580800],
[[[1, 13], [5, 3]], 1/4252500],
[[[1, 14], [2, 11]], 53/318504960],
[[[1, 15], [2, 10]], 583/1672151040],
[[[1, 15], [3, 5]], 2531/7054387200],
[[[1, 16], [2, 9]], 98101/240789749760],
[[[1, 17], [2, 8]], 37817/133772083200],
[[[1, 17], [3, 4]], 2039/56435097600],
[[[1, 17], [5, 2]], 11/6531840000],
[[[1, 18], [2, 7]], 3089/25082265600],
[[[1, 19], [2, 6]], 5261/150493593600],
[[[1, 19], [3, 3]], 17/10581580800],
[[[1, 19], [7, 1]], 1/31352832000],
[[[1, 20], [2, 5]], 13217/2006581248000],
[[[1, 21], [2, 4]], 4967/6019743744000],
[[[1, 21], [3, 2]], 79/2257403904000],
[[[1, 21], [5, 1]], 1/235146240000],
[[[1, 22], [2, 3]], 61/902961561600],
[[[1, 23], [2, 2]], 13/3762339840000],
[[[1, 23], [3, 1]], 1/2821754880000],
[[[1, 24], [2, 1]], 1/10032906240000],
[[[2, 7], [6, 9]], 43/14171760],
[[[2, 9], [6, 8]], 1/196830],
[[[2, 9], [10, 4]], 1/90000],
[[[2, 11], [6, 7]], 197/125971200],
[[[2, 13], [6, 6]], 11191/10581580800],
[[[2, 13], [10, 3]], 1/4252500],
[[[2, 15], [6, 5]], 2531/7054387200],
[[[2, 17], [6, 4]], 2039/56435097600],
[[[2, 17], [10, 2]], 11/6531840000],
[[[2, 19], [6, 3]], 17/10581580800],
[[[2, 19], [14, 1]], 1/31352832000],
[[[2, 21], [6, 2]], 79/2257403904000],
[[[2, 21], [10, 1]], 1/235146240000],
[[[2, 23], [6, 1]], 1/2821754880000],
[[[1, 1], [2, 8], [6, 8]], 1/65610],
[[[1, 1], [2, 8], [10, 4]], 1/15000],
[[[1, 1], [2, 10], [6, 7]], 97/8398080],
[[[1, 1], [2, 12], [6, 6]], 253/24494400],
[[[1, 1], [2, 12], [10, 3]], 151/30240000],
[[[1, 1], [2, 14], [6, 5]], 2431/470292480],
[[[1, 1], [2, 16], [6, 4]], 16871/18811699200],
[[[1, 1], [2, 16], [10, 2]], 269/4354560000],
[[[1, 1], [2, 18], [6, 3]], 37/627056640],
[[[1, 1], [2, 18], [14, 1]], 23/15676416000],
[[[1, 1], [2, 20], [6, 2]], 653/376233984000],
[[[1, 1], [2, 20], [10, 1]], 47/209018880000],
[[[1, 1], [2, 22], [4, 1]], 19/15049359360000],
[[[1, 1], [2, 22], [6, 1]], 17/752467968000],
[[[1, 1], [3, 3], [9, 3]], 1/486],
[[[1, 2], [2, 7], [10, 4]], 1/30000],
[[[1, 2], [2, 9], [6, 7]], 191/8398080],
[[[1, 2], [2, 11], [6, 6]], 2893/83980800],
[[[1, 2], [2, 11], [10, 3]], 1/30000],
[[[1, 2], [2, 13], [6, 5]], 2207/78382080],
[[[1, 2], [2, 15], [6, 4]], 153007/18811699200],
[[[1, 2], [2, 15], [10, 2]], 47/53760000],
[[[1, 2], [2, 17], [6, 3]], 793/940584960],
[[[1, 2], [2, 17], [14, 1]], 19/696729600],
[[[1, 2], [2, 19], [4, 2]], 37/125411328000],
[[[1, 2], [2, 19], [6, 2]], 8819/250822656000],
[[[1, 2], [2, 19], [10, 1]], 1559/313528320000],
[[[1, 2], [2, 21], [4, 1]], 221/3009871872000],
[[[1, 2], [2, 21], [6, 1]], 457/752467968000],
[[[1, 3], [2, 8], [6, 7]], 91/25194240],
[[[1, 3], [2, 10], [6, 6]], 257/6298560],
[[[1, 3], [2, 10], [10, 3]], 7/86400],
[[[1, 3], [2, 12], [6, 5]], 2347/33592320],
[[[1, 3], [2, 14], [6, 4]], 57529/1612431360],
[[[1, 3], [2, 14], [10, 2]], 211/34836480],
[[[1, 3], [2, 16], [4, 3]], 19/696729600],
[[[1, 3], [2, 16], [6, 3]], 21361/3527193600],
[[[1, 3], [2, 16], [14, 1]], 23/87091200],
[[[1, 3], [2, 18], [4, 2]], 523/41803776000],
[[[1, 3], [2, 18], [6, 2]], 203/537477120],
[[[1, 3], [2, 18], [10, 1]], 1501/25082265600],
[[[1, 3], [2, 20], [4, 1]], 601/334430208000],
[[[1, 3], [2, 20], [6, 1]], 2903/322486272000],
[[[1, 3], [3, 5], [9, 2]], 19/8748],
[[[1, 4], [2, 9], [6, 6]], 173/33592320],
[[[1, 4], [2, 9], [10, 3]], 1/18000],
[[[1, 4], [2, 11], [6, 5]], 107/1492992],
[[[1, 4], [2, 13], [4, 4]], 1/983040],
[[[1, 4], [2, 13], [6, 4]], 99929/1254113280],
[[[1, 4], [2, 13], [10, 2]], 233/10752000],
[[[1, 4], [2, 15], [4, 3]], 59/77414400],
[[[1, 4], [2, 15], [6, 3]], 4489/188116992],
[[[1, 4], [2, 15], [14, 1]], 503/348364800],
[[[1, 4], [2, 17], [4, 2]], 221/1045094400],
[[[1, 4], [2, 17], [6, 2]], 6547/2786918400],
[[[1, 4], [2, 17], [10, 1]], 2237/5225472000],
[[[1, 4], [2, 19], [4, 1]], 24193/1003290624000],
[[[1, 4], [2, 19], [6, 1]], 4057/50164531200],
[[[1, 5], [2, 8], [10, 3]], 1/96000],
[[[1, 5], [2, 10], [4, 5]], 1/98304],
[[[1, 5], [2, 10], [6, 5]], 67/4478976],
[[[1, 5], [2, 12], [4, 4]], 43/2949120],
[[[1, 5], [2, 12], [6, 4]], 14821/179159040],
[[[1, 5], [2, 12], [10, 2]], 533/13824000],
[[[1, 5], [2, 14], [4, 3]], 887/116121600],
[[[1, 5], [2, 14], [6, 3]], 16267/313528320],
[[[1, 5], [2, 14], [14, 1]], 53/11612160],
[[[1, 5], [2, 16], [4, 2]], 91/49766400],
[[[1, 5], [2, 16], [6, 2]], 109301/12541132800],
[[[1, 5], [2, 16], [10, 1]], 13033/6967296000],
[[[1, 5], [2, 18], [4, 1]], 19477/100329062400],
[[[1, 5], [2, 18], [6, 1]], 11467/25082265600],
[[[1, 5], [3, 4], [9, 2]], 1/5832],
[[[1, 5], [3, 7], [9, 1]], 133/787320],
[[[1, 6], [2, 9], [4, 5]], 1/32768],
[[[1, 6], [2, 9], [6, 5]], 1/3359232],
[[[1, 6], [2, 11], [4, 4]], 43/737280],
[[[1, 6], [2, 11], [6, 4]], 2987/107495424],
[[[1, 6], [2, 11], [10, 2]], 83/2764800],
[[[1, 6], [2, 13], [4, 3]], 2389/69672960],
[[[1, 6], [2, 13], [6, 3]], 7777/134369280],
[[[1, 6], [2, 13], [14, 1]], 191/23224320],
[[[1, 6], [2, 15], [4, 2]], 607/69672960],
[[[1, 6], [2, 15], [6, 2]], 286949/15049359360],
[[[1, 6], [2, 15], [10, 1]], 1477/298598400],
[[[1, 6], [2, 17], [4, 1]], 32381/33443020800],
[[[1, 6], [2, 17], [6, 1]], 123289/75246796800],
[[[1, 7], [2, 2], [5, 4]], 1/30000],
[[[1, 7], [2, 8], [4, 5]], 1/24576],
[[[1, 7], [2, 10], [4, 4]], 17/184320],
[[[1, 7], [2, 10], [6, 4]], 71/35831808],
[[[1, 7], [2, 10], [10, 2]], 1/102400],
[[[1, 7], [2, 12], [4, 3]], 1/13440],
[[[1, 7], [2, 12], [6, 3]], 61/2239488],
[[[1, 7], [2, 12], [14, 1]], 47/5806080],
[[[1, 7], [2, 14], [4, 2]], 811/34836480],
[[[1, 7], [2, 14], [6, 2]], 9713/418037760],
[[[1, 7], [2, 14], [10, 1]], 3523/464486400],
[[[1, 7], [2, 16], [4, 1]], 100237/33443020800],
[[[1, 7], [2, 16], [6, 1]], 18353/5016453120],
[[[1, 7], [3, 1], [5, 4]], 1/11250],
[[[1, 7], [3, 3], [5, 3]], 1/12150],
[[[1, 7], [3, 3], [9, 2]], 1/116640],
[[[1, 7], [3, 5], [5, 2]], 1/36450],
[[[1, 7], [3, 6], [7, 1]], 43/1224720],
[[[1, 7], [3, 6], [9, 1]], 19/104976],
[[[1, 7], [3, 7], [5, 1]], 91/2624400],
[[[1, 7], [5, 3], [7, 1]], 1/10500],
[[[1, 8], [2, 1], [3, 8]], 1/65610],
[[[1, 8], [2, 1], [5, 4]], 1/15000],
[[[1, 8], [2, 3], [3, 7]], 91/25194240],
[[[1, 8], [2, 5], [5, 3]], 1/96000],
[[[1, 8], [2, 7], [4, 5]], 1/24576],
[[[1, 8], [2, 9], [4, 4]], 23/294912],
[[[1, 8], [2, 9], [10, 2]], 1/921600],
[[[1, 8], [2, 11], [4, 3]], 29/368640],
[[[1, 8], [2, 11], [6, 3]], 13/2985984],
[[[1, 8], [2, 11], [14, 1]], 13/3096576],
[[[1, 8], [2, 13], [4, 2]], 397/11612160],
[[[1, 8], [2, 13], [6, 2]], 2237/159252480],
[[[1, 8], [2, 13], [10, 1]], 13/2073600],
[[[1, 8], [2, 15], [4, 1]], 37643/6688604160],
[[[1, 8], [2, 15], [6, 1]], 2711/557383680],
[[[1, 9], [2, 2], [3, 7]], 191/8398080],
[[[1, 9], [2, 4], [3, 6]], 173/33592320],
[[[1, 9], [2, 4], [5, 3]], 1/18000],
[[[1, 9], [2, 6], [3, 5]], 1/3359232],
[[[1, 9], [2, 6], [4, 5]], 1/32768],
[[[1, 9], [2, 8], [4, 4]], 23/294912],
[[[1, 9], [2, 8], [5, 2]], 1/921600],
[[[1, 9], [2, 10], [4, 3]], 5/110592],
[[[1, 9], [2, 10], [6, 3]], 5/53747712],
[[[1, 9], [2, 10], [7, 1]], 1/9289728],
[[[1, 9], [2, 10], [14, 1]], 5/4644864],
[[[1, 9], [2, 12], [4, 2]], 29/1105920],
[[[1, 9], [2, 12], [6, 2]], 533/143327232],
[[[1, 9], [2, 12], [10, 1]], 211/79626240],
[[[1, 9], [2, 14], [4, 1]], 9083/1486356480],
[[[1, 9], [2, 14], [6, 1]], 5113/1433272320],
[[[1, 9], [3, 2], [5, 3]], 31/324000],
[[[1, 9], [3, 2], [9, 2]], 1/19595520],
[[[1, 9], [3, 4], [5, 2]], 71/1166400],
[[[1, 9], [3, 5], [7, 1]], 1/163296],
[[[1, 9], [3, 5], [9, 1]], 77/4199040],
[[[1, 9], [3, 6], [5, 1]], 173/10497600],
[[[1, 10], [2, 1], [3, 7]], 97/8398080],
[[[1, 10], [2, 3], [3, 6]], 257/6298560],
[[[1, 10], [2, 3], [5, 3]], 7/86400],
[[[1, 10], [2, 5], [3, 5]], 67/4478976],
[[[1, 10], [2, 5], [4, 5]], 1/98304],
[[[1, 10], [2, 7], [3, 4]], 71/35831808],
[[[1, 10], [2, 7], [4, 4]], 17/184320],
[[[1, 10], [2, 7], [5, 2]], 1/102400],
[[[1, 10], [2, 9], [3, 3]], 5/53747712],
[[[1, 10], [2, 9], [4, 3]], 5/110592],
[[[1, 10], [2, 9], [7, 1]], 5/4644864],
[[[1, 10], [2, 9], [14, 1]], 1/9289728],
[[[1, 10], [2, 11], [4, 2]], 29/2654208],
[[[1, 10], [2, 11], [5, 1]], 1/26542080],
[[[1, 10], [2, 11], [6, 2]], 31/95551488],
[[[1, 10], [2, 11], [10, 1]], 7/13271040],
[[[1, 10], [2, 13], [4, 1]], 457/127401984],
[[[1, 10], [2, 13], [6, 1]], 127/95551488],
[[[1, 11], [2, 2], [3, 6]], 2893/83980800],
[[[1, 11], [2, 2], [5, 3]], 1/30000],
[[[1, 11], [2, 4], [3, 5]], 107/1492992],
[[[1, 11], [2, 6], [3, 4]], 2987/107495424],
[[[1, 11], [2, 6], [4, 4]], 43/737280],
[[[1, 11], [2, 6], [5, 2]], 83/2764800],
[[[1, 11], [2, 8], [3, 3]], 13/2985984],
[[[1, 11], [2, 8], [4, 3]], 29/368640],
[[[1, 11], [2, 8], [7, 1]], 13/3096576],
[[[1, 11], [2, 10], [3, 2]], 31/95551488],
[[[1, 11], [2, 10], [4, 2]], 29/2654208],
[[[1, 11], [2, 10], [5, 1]], 7/13271040],
[[[1, 11], [2, 10], [10, 1]], 1/26542080],
[[[1, 11], [2, 12], [3, 1]], 1/95551488],
[[[1, 11], [2, 12], [4, 1]], 37/31850496],
[[[1, 11], [2, 12], [6, 1]], 7/31850496],
[[[1, 11], [3, 1], [5, 3]], 19/1620000],
[[[1, 11], [3, 3], [5, 2]], 11/291600],
[[[1, 11], [3, 4], [7, 1]], 41/6531840],
[[[1, 11], [3, 4], [9, 1]], 653/176359680],
[[[1, 11], [3, 5], [5, 1]], 101/6998400],
[[[1, 11], [5, 2], [7, 1]], 1/504000],
[[[1, 12], [2, 1], [3, 6]], 253/24494400],
[[[1, 12], [2, 1], [5, 3]], 151/30240000],
[[[1, 12], [2, 3], [3, 5]], 2347/33592320],
[[[1, 12], [2, 5], [3, 4]], 14821/179159040],
[[[1, 12], [2, 5], [4, 4]], 43/2949120],
[[[1, 12], [2, 5], [5, 2]], 533/13824000],
[[[1, 12], [2, 7], [3, 3]], 61/2239488],
[[[1, 12], [2, 7], [4, 3]], 1/13440],
[[[1, 12], [2, 7], [7, 1]], 47/5806080],
[[[1, 12], [2, 9], [3, 2]], 533/143327232],
[[[1, 12], [2, 9], [4, 2]], 29/1105920],
[[[1, 12], [2, 9], [5, 1]], 211/79626240],
[[[1, 12], [2, 11], [3, 1]], 7/31850496],
[[[1, 12], [2, 11], [4, 1]], 37/31850496],
[[[1, 12], [2, 11], [6, 1]], 1/95551488],
[[[1, 13], [2, 2], [3, 5]], 2207/78382080],
[[[1, 13], [2, 4], [3, 4]], 99929/1254113280],
[[[1, 13], [2, 4], [4, 4]], 1/983040],
[[[1, 13], [2, 4], [5, 2]], 233/10752000],
[[[1, 13], [2, 6], [3, 3]], 7777/134369280],
[[[1, 13], [2, 6], [4, 3]], 2389/69672960],
[[[1, 13], [2, 6], [7, 1]], 191/23224320],
[[[1, 13], [2, 8], [3, 2]], 2237/159252480],
[[[1, 13], [2, 8], [4, 2]], 397/11612160],
[[[1, 13], [2, 8], [5, 1]], 13/2073600],
[[[1, 13], [2, 10], [3, 1]], 127/95551488],
[[[1, 13], [2, 10], [4, 1]], 457/127401984],
[[[1, 13], [3, 2], [5, 2]], 1471/326592000],
[[[1, 13], [3, 3], [7, 1]], 23/9797760],
[[[1, 13], [3, 3], [9, 1]], 41/167961600],
[[[1, 13], [3, 4], [5, 1]], 3707/587865600],
[[[1, 14], [2, 1], [3, 5]], 2431/470292480],
[[[1, 14], [2, 3], [3, 4]], 57529/1612431360],
[[[1, 14], [2, 3], [5, 2]], 211/34836480],
[[[1, 14], [2, 5], [3, 3]], 16267/313528320],
[[[1, 14], [2, 5], [4, 3]], 887/116121600],
[[[1, 14], [2, 5], [7, 1]], 53/11612160],
[[[1, 14], [2, 7], [3, 2]], 9713/418037760],
[[[1, 14], [2, 7], [4, 2]], 811/34836480],
[[[1, 14], [2, 7], [5, 1]], 3523/464486400],
[[[1, 14], [2, 9], [3, 1]], 5113/1433272320],
[[[1, 14], [2, 9], [4, 1]], 9083/1486356480],
[[[1, 15], [2, 2], [3, 4]], 153007/18811699200],
[[[1, 15], [2, 2], [5, 2]], 47/53760000],
[[[1, 15], [2, 4], [3, 3]], 4489/188116992],
[[[1, 15], [2, 4], [4, 3]], 59/77414400],
[[[1, 15], [2, 4], [7, 1]], 503/348364800],
[[[1, 15], [2, 6], [3, 2]], 286949/15049359360],
[[[1, 15], [2, 6], [4, 2]], 607/69672960],
[[[1, 15], [2, 6], [5, 1]], 1477/298598400],
[[[1, 15], [2, 8], [3, 1]], 2711/557383680],
[[[1, 15], [2, 8], [4, 1]], 37643/6688604160],
[[[1, 15], [3, 1], [5, 2]], 257/1632960000],
[[[1, 15], [3, 2], [7, 1]], 41/261273600],
[[[1, 15], [3, 2], [9, 1]], 1/167961600],
[[[1, 15], [3, 3], [5, 1]], 421/587865600],
[[[1, 15], [5, 1], [7, 1]], 1/72576000],
[[[1, 16], [2, 1], [3, 4]], 16871/18811699200],
[[[1, 16], [2, 1], [5, 2]], 269/4354560000],
[[[1, 16], [2, 3], [3, 3]], 21361/3527193600],
[[[1, 16], [2, 3], [4, 3]], 19/696729600],
[[[1, 16], [2, 3], [7, 1]], 23/87091200],
[[[1, 16], [2, 5], [3, 2]], 109301/12541132800],
[[[1, 16], [2, 5], [4, 2]], 91/49766400],
[[[1, 16], [2, 5], [5, 1]], 13033/6967296000],
[[[1, 16], [2, 7], [3, 1]], 18353/5016453120],
[[[1, 16], [2, 7], [4, 1]], 100237/33443020800],
[[[1, 17], [2, 2], [3, 3]], 793/940584960],
[[[1, 17], [2, 2], [7, 1]], 19/696729600],
[[[1, 17], [2, 4], [3, 2]], 6547/2786918400],
[[[1, 17], [2, 4], [4, 2]], 221/1045094400],
[[[1, 17], [2, 4], [5, 1]], 2237/5225472000],
[[[1, 17], [2, 6], [3, 1]], 123289/75246796800],
[[[1, 17], [2, 6], [4, 1]], 32381/33443020800],
[[[1, 17], [3, 1], [7, 1]], 1/261273600],
[[[1, 17], [3, 1], [9, 1]], 1/20155392000],
[[[1, 17], [3, 2], [5, 1]], 71/2239488000],
[[[1, 18], [2, 1], [3, 3]], 37/627056640],
[[[1, 18], [2, 1], [7, 1]], 23/15676416000],
[[[1, 18], [2, 3], [3, 2]], 203/537477120],
[[[1, 18], [2, 3], [4, 2]], 523/41803776000],
[[[1, 18], [2, 3], [5, 1]], 1501/25082265600],
[[[1, 18], [2, 5], [3, 1]], 11467/25082265600],
[[[1, 18], [2, 5], [4, 1]], 19477/100329062400],
[[[1, 19], [2, 2], [3, 2]], 8819/250822656000],
[[[1, 19], [2, 2], [4, 2]], 37/125411328000],
[[[1, 19], [2, 2], [5, 1]], 1559/313528320000],
[[[1, 19], [2, 4], [3, 1]], 4057/50164531200],
[[[1, 19], [2, 4], [4, 1]], 24193/1003290624000],
[[[1, 19], [3, 1], [5, 1]], 143/235146240000],
[[[1, 20], [2, 1], [3, 2]], 653/376233984000],
[[[1, 20], [2, 1], [5, 1]], 47/209018880000],
[[[1, 20], [2, 3], [3, 1]], 2903/322486272000],
[[[1, 20], [2, 3], [4, 1]], 601/334430208000],
[[[1, 21], [2, 2], [3, 1]], 457/752467968000],
[[[1, 21], [2, 2], [4, 1]], 221/3009871872000],
[[[1, 22], [2, 1], [3, 1]], 17/752467968000],
[[[1, 22], [2, 1], [4, 1]], 19/15049359360000],
[[[2, 1], [6, 3], [18, 3]], 1/486],
[[[2, 3], [6, 5], [18, 2]], 19/8748],
[[[2, 5], [6, 4], [18, 2]], 1/5832],
[[[2, 5], [6, 7], [18, 1]], 133/787320],
[[[2, 7], [6, 1], [10, 4]], 1/11250],
[[[2, 7], [6, 3], [10, 3]], 1/12150],
[[[2, 7], [6, 3], [18, 2]], 1/116640],
[[[2, 7], [6, 5], [10, 2]], 1/36450],
[[[2, 7], [6, 6], [14, 1]], 43/1224720],
[[[2, 7], [6, 6], [18, 1]], 19/104976],
[[[2, 7], [6, 7], [10, 1]], 91/2624400],
[[[2, 7], [10, 3], [14, 1]], 1/10500],
[[[2, 9], [6, 2], [10, 3]], 31/324000],
[[[2, 9], [6, 2], [18, 2]], 1/19595520],
[[[2, 9], [6, 4], [10, 2]], 71/1166400],
[[[2, 9], [6, 5], [14, 1]], 1/163296],
[[[2, 9], [6, 5], [18, 1]], 77/4199040],
[[[2, 9], [6, 6], [10, 1]], 173/10497600],
[[[2, 11], [6, 1], [10, 3]], 19/1620000],
[[[2, 11], [6, 3], [10, 2]], 11/291600],
[[[2, 11], [6, 4], [14, 1]], 41/6531840],
[[[2, 11], [6, 4], [18, 1]], 653/176359680],
[[[2, 11], [6, 5], [10, 1]], 101/6998400],
[[[2, 11], [10, 2], [14, 1]], 1/504000],
[[[2, 13], [6, 2], [10, 2]], 1471/326592000],
[[[2, 13], [6, 3], [14, 1]], 23/9797760],
[[[2, 13], [6, 3], [18, 1]], 41/167961600],
[[[2, 13], [6, 4], [10, 1]], 3707/587865600],
[[[2, 15], [6, 1], [10, 2]], 257/1632960000],
[[[2, 15], [6, 2], [14, 1]], 41/261273600],
[[[2, 15], [6, 2], [18, 1]], 1/167961600],
[[[2, 15], [6, 3], [10, 1]], 421/587865600],
[[[2, 15], [10, 1], [14, 1]], 1/72576000],
[[[2, 17], [6, 1], [14, 1]], 1/261273600],
[[[2, 17], [6, 1], [18, 1]], 1/20155392000],
[[[2, 17], [6, 2], [10, 1]], 71/2239488000],
[[[2, 19], [6, 1], [10, 1]], 143/235146240000],
[[[1, 1], [2, 4], [6, 4], [18, 2]], 1/1944],
[[[1, 1], [2, 6], [3, 1], [6, 8]], 113/1574640],
[[[1, 1], [2, 6], [4, 1], [10, 4]], 1/15000],
[[[1, 1], [2, 6], [6, 3], [18, 2]], 1/7776],
[[[1, 1], [2, 6], [6, 6], [14, 1]], 43/1224720],
[[[1, 1], [2, 6], [6, 6], [18, 1]], 19/34992],
[[[1, 1], [2, 6], [10, 3], [14, 1]], 1/10500],
[[[1, 1], [2, 8], [3, 1], [6, 7]], 139/1574640],
[[[1, 1], [2, 8], [4, 1], [6, 7]], 91/4199040],
[[[1, 1], [2, 8], [6, 2], [10, 3]], 17/54000],
[[[1, 1], [2, 8], [6, 2], [18, 2]], 1/544320],
[[[1, 1], [2, 8], [6, 4], [10, 2]], 37/194400],
[[[1, 1], [2, 8], [6, 5], [14, 1]], 1/40824],
[[[1, 1], [2, 8], [6, 5], [18, 1]], 53/279936],
[[[1, 1], [2, 8], [6, 6], [10, 1]], 1/16200],
[[[1, 1], [2, 10], [3, 1], [6, 6]], 143/8398080],
[[[1, 1], [2, 10], [4, 1], [6, 6]], 23/2624400],
[[[1, 1], [2, 10], [4, 1], [10, 3]], 1/40000],
[[[1, 1], [2, 10], [6, 1], [10, 3]], 13/108000],
[[[1, 1], [2, 10], [6, 3], [10, 2]], 1/3888],
[[[1, 1], [2, 10], [6, 4], [14, 1]], 37/816480],
[[[1, 1], [2, 10], [6, 4], [18, 1]], 191/4898880],
[[[1, 1], [2, 10], [6, 5], [10, 1]], 43/466560],
[[[1, 1], [2, 10], [10, 2], [14, 1]], 1/31500],
[[[1, 1], [2, 12], [3, 1], [6, 5]], 179/25194240],
[[[1, 1], [2, 12], [4, 1], [6, 5]], 49/5598720],
[[[1, 1], [2, 12], [6, 2], [10, 2]], 1199/18144000],
[[[1, 1], [2, 12], [6, 3], [14, 1]], 257/9797760],
[[[1, 1], [2, 12], [6, 3], [18, 1]], 29/5598720],
[[[1, 1], [2, 12], [6, 4], [10, 1]], 8677/130636800],
[[[1, 1], [2, 14], [3, 1], [6, 4]], 113/88179840],
[[[1, 1], [2, 14], [4, 1], [6, 4]], 34487/9405849600],
[[[1, 1], [2, 14], [4, 1], [10, 2]], 11/30240000],
[[[1, 1], [2, 14], [6, 1], [10, 2]], 433/108864000],
[[[1, 1], [2, 14], [6, 2], [14, 1]], 911/261273600],
[[[1, 1], [2, 14], [6, 2], [18, 1]], 11/55987200],
[[[1, 1], [2, 14], [6, 3], [10, 1]], 181/13063680],
[[[1, 1], [2, 14], [10, 1], [14, 1]], 31/72576000],
[[[1, 1], [2, 16], [3, 1], [6, 3]], 97/1343692800],
[[[1, 1], [2, 16], [4, 1], [6, 3]], 811/2351462400],
[[[1, 1], [2, 16], [4, 1], [14, 1]], 1/116121600],
[[[1, 1], [2, 16], [6, 1], [14, 1]], 17/130636800],
[[[1, 1], [2, 16], [6, 1], [18, 1]], 1/447897600],
[[[1, 1], [2, 16], [6, 2], [10, 1]], 2479/2612736000],
[[[1, 1], [2, 18], [3, 1], [6, 2]], 229/141087744000],
[[[1, 1], [2, 18], [4, 1], [6, 2]], 29/2239488000],
[[[1, 1], [2, 18], [4, 1], [8, 1]], 1/17915904000],
[[[1, 1], [2, 18], [4, 1], [10, 1]], 239/156764160000],
[[[1, 1], [2, 18], [6, 1], [10, 1]], 131/5225472000],
[[[1, 1], [2, 20], [3, 1], [6, 1]], 29/2257403904000],
[[[1, 1], [2, 20], [4, 1], [6, 1]], 1/4702924800],
[[[1, 2], [2, 5], [3, 2], [6, 7]], 7/13122],
[[[1, 2], [2, 5], [6, 3], [18, 2]], 1/2592],
[[[1, 2], [2, 7], [3, 1], [6, 7]], 139/524880],
[[[1, 2], [2, 7], [3, 2], [6, 6]], 91/209952],
[[[1, 2], [2, 7], [4, 1], [6, 7]], 91/4199040],
[[[1, 2], [2, 7], [4, 2], [6, 6]], 43/2799360],
[[[1, 2], [2, 7], [4, 2], [10, 3]], 1/6000],
[[[1, 2], [2, 7], [6, 2], [10, 3]], 1/36000],
[[[1, 2], [2, 7], [6, 2], [18, 2]], 1/51840],
[[[1, 2], [2, 7], [6, 4], [10, 2]], 1/129600],
[[[1, 2], [2, 7], [6, 5], [14, 1]], 1/54432],
[[[1, 2], [2, 7], [6, 5], [18, 1]], 5/10368],
[[[1, 2], [2, 7], [6, 6], [10, 1]], 43/3499200],
[[[1, 2], [2, 9], [3, 1], [6, 6]], 25/186624],
[[[1, 2], [2, 9], [3, 2], [6, 5]], 391/8398080],
[[[1, 2], [2, 9], [4, 1], [6, 6]], 173/4199040],
[[[1, 2], [2, 9], [4, 1], [10, 3]], 7/36000],
[[[1, 2], [2, 9], [4, 2], [6, 5]], 5/373248],
[[[1, 2], [2, 9], [6, 1], [10, 3]], 11/36000],
[[[1, 2], [2, 9], [6, 3], [10, 2]], 1/2160],
[[[1, 2], [2, 9], [6, 4], [14, 1]], 11/108864],
[[[1, 2], [2, 9], [6, 4], [18, 1]], 23/155520],
[[[1, 2], [2, 9], [6, 5], [10, 1]], 71/466560],
[[[1, 2], [2, 9], [10, 2], [14, 1]], 1/8400],
[[[1, 2], [2, 11], [3, 1], [6, 5]], 199/2799360],
[[[1, 2], [2, 11], [3, 2], [6, 4]], 37/4199040],
[[[1, 2], [2, 11], [4, 1], [6, 5]], 361/5598720],
[[[1, 2], [2, 11], [4, 2], [6, 4]], 43/1658880],
[[[1, 2], [2, 11], [4, 2], [10, 2]], 1/48000],
[[[1, 2], [2, 11], [6, 2], [10, 2]], 263/864000],
[[[1, 2], [2, 11], [6, 3], [14, 1]], 29/272160],
[[[1, 2], [2, 11], [6, 3], [18, 1]], 1/27648],
[[[1, 2], [2, 11], [6, 4], [10, 1]], 371/1555200],
[[[1, 2], [2, 13], [3, 1], [6, 4]], 935/47029248],
[[[1, 2], [2, 13], [3, 2], [6, 3]], 887/2351462400],
[[[1, 2], [2, 13], [4, 1], [6, 4]], 79711/1881169920],
[[[1, 2], [2, 13], [4, 1], [10, 2]], 1213/145152000],
[[[1, 2], [2, 13], [4, 2], [6, 3]], 163/11197440],
[[[1, 2], [2, 13], [4, 2], [14, 1]], 1/1290240],
[[[1, 2], [2, 13], [6, 1], [10, 2]], 643/18144000],
[[[1, 2], [2, 13], [6, 2], [14, 1]], 463/17418240],
[[[1, 2], [2, 13], [6, 2], [18, 1]], 1/414720],
[[[1, 2], [2, 13], [6, 3], [10, 1]], 229/2449440],
[[[1, 2], [2, 13], [10, 1], [14, 1]], 23/4838400],
[[[1, 2], [2, 15], [3, 1], [6, 3]], 1937/1045094400],
[[[1, 2], [2, 15], [3, 2], [6, 2]], 17/3762339840],
[[[1, 2], [2, 15], [4, 1], [6, 3]], 35501/4702924800],
[[[1, 2], [2, 15], [4, 1], [14, 1]], 1/3628800],
[[[1, 2], [2, 15], [4, 2], [6, 2]], 1249/1045094400],
[[[1, 2], [2, 15], [4, 2], [8, 1]], 1/66355200],
[[[1, 2], [2, 15], [4, 2], [10, 1]], 13/72576000],
[[[1, 2], [2, 15], [6, 1], [14, 1]], 73/43545600],
[[[1, 2], [2, 15], [6, 1], [18, 1]], 1/24883200],
[[[1, 2], [2, 15], [6, 2], [10, 1]], 13999/1306368000],
[[[1, 2], [2, 17], [3, 1], [6, 2]], 47/783820800],
[[[1, 2], [2, 17], [4, 1], [6, 2]], 1357/3135283200],
[[[1, 2], [2, 17], [4, 1], [8, 1]], 1/398131200],
[[[1, 2], [2, 17], [4, 1], [10, 1]], 619/10450944000],
[[[1, 2], [2, 17], [4, 2], [6, 1]], 23/696729600],
[[[1, 2], [2, 17], [6, 1], [10, 1]], 361/870912000],
[[[1, 2], [2, 19], [3, 1], [6, 1]], 47/75246796800],
[[[1, 2], [2, 19], [4, 1], [6, 1]], 911/94058496000],
[[[1, 3], [2, 4], [3, 3], [6, 6]], 131/104976],
[[[1, 3], [2, 4], [3, 5], [6, 4]], 5/11664],
[[[1, 3], [2, 4], [6, 3], [18, 2]], 1/7776],
[[[1, 3], [2, 6], [3, 2], [6, 6]], 91/69984],
[[[1, 3], [2, 6], [3, 3], [6, 5]], 25/34992],
[[[1, 3], [2, 6], [4, 2], [10, 3]], 1/8000],
[[[1, 3], [2, 6], [6, 2], [18, 2]], 1/15552],
[[[1, 3], [2, 6], [6, 5], [18, 1]], 37/279936],
[[[1, 3], [2, 8], [3, 1], [6, 6]], 157/559872],
[[[1, 3], [2, 8], [3, 2], [6, 5]], 211/559872],
[[[1, 3], [2, 8], [3, 3], [6, 4]], 73/2799360],
[[[1, 3], [2, 8], [4, 1], [6, 6]], 1/25920],
[[[1, 3], [2, 8], [4, 1], [10, 3]], 7/24000],
[[[1, 3], [2, 8], [4, 2], [6, 5]], 11/373248],
[[[1, 3], [2, 8], [4, 3], [6, 4]], 1/165888],
[[[1, 3], [2, 8], [4, 3], [10, 2]], 1/6400],
[[[1, 3], [2, 8], [6, 1], [10, 3]], 13/108000],
[[[1, 3], [2, 8], [6, 3], [10, 2]], 7/97200],
[[[1, 3], [2, 8], [6, 4], [14, 1]], 1/15552],
[[[1, 3], [2, 8], [6, 4], [18, 1]], 31/139968],
[[[1, 3], [2, 8], [6, 5], [10, 1]], 17/1399680],
[[[1, 3], [2, 8], [10, 2], [14, 1]], 1/8400],
[[[1, 3], [2, 10], [3, 1], [6, 5]], 343/1399680],
[[[1, 3], [2, 10], [3, 2], [6, 4]], 89/933120],
[[[1, 3], [2, 10], [3, 3], [6, 3]], 131/235146240],
[[[1, 3], [2, 10], [4, 1], [6, 5]], 55/373248],
[[[1, 3], [2, 10], [4, 2], [6, 4]], 2021/14929920],
[[[1, 3], [2, 10], [4, 2], [10, 2]], 233/1152000],
[[[1, 3], [2, 10], [4, 3], [6, 3]], 1/31104],
[[[1, 3], [2, 10], [4, 3], [14, 1]], 1/43008],
[[[1, 3], [2, 10], [6, 2], [10, 2]], 13/25920],
[[[1, 3], [2, 10], [6, 3], [14, 1]], 5/27216],
[[[1, 3], [2, 10], [6, 3], [18, 1]], 101/933120],
[[[1, 3], [2, 10], [6, 4], [10, 1]], 1727/5598720],
[[[1, 3], [2, 12], [3, 1], [6, 4]], 1807/15676416],
[[[1, 3], [2, 12], [3, 2], [6, 3]], 1273/156764160],
[[[1, 3], [2, 12], [4, 1], [6, 4]], 18601/104509440],
[[[1, 3], [2, 12], [4, 1], [10, 2]], 1033/16128000],
[[[1, 3], [2, 12], [4, 2], [6, 3]], 967/7464960],
[[[1, 3], [2, 12], [4, 2], [14, 1]], 1/71680],
[[[1, 3], [2, 12], [4, 3], [6, 2]], 47/1658880],
[[[1, 3], [2, 12], [4, 3], [8, 1]], 1/737280],
[[[1, 3], [2, 12], [4, 3], [10, 1]], 7/921600],
[[[1, 3], [2, 12], [6, 1], [10, 2]], 359/2592000],
[[[1, 3], [2, 12], [6, 2], [14, 1]], 77/829440],
[[[1, 3], [2, 12], [6, 2], [18, 1]], 31/2239488],
[[[1, 3], [2, 12], [6, 3], [10, 1]], 3899/13996800],
[[[1, 3], [2, 12], [10, 1], [14, 1]], 113/4838400],
[[[1, 3], [2, 14], [3, 1], [6, 3]], 55207/3135283200],
[[[1, 3], [2, 14], [3, 2], [6, 2]], 941/6270566400],
[[[1, 3], [2, 14], [4, 1], [6, 3]], 431/7464960],
[[[1, 3], [2, 14], [4, 1], [14, 1]], 47/14515200],
[[[1, 3], [2, 14], [4, 2], [6, 2]], 5989/261273600],
[[[1, 3], [2, 14], [4, 2], [8, 1]], 31/66355200],
[[[1, 3], [2, 14], [4, 2], [10, 1]], 163/36288000],
[[[1, 3], [2, 14], [4, 3], [6, 1]], 1/552960],
[[[1, 3], [2, 14], [6, 1], [14, 1]], 13/1244160],
[[[1, 3], [2, 14], [6, 1], [18, 1]], 83/223948800],
[[[1, 3], [2, 14], [6, 2], [10, 1]], 18269/313528320],
[[[1, 3], [2, 16], [3, 1], [6, 2]], 341/391910400],
[[[1, 3], [2, 16], [4, 1], [6, 2]], 5759/1045094400],
[[[1, 3], [2, 16], [4, 1], [8, 1]], 1/22118400],
[[[1, 3], [2, 16], [4, 1], [10, 1]], 197/217728000],
[[[1, 3], [2, 16], [4, 2], [6, 1]], 527/522547200],
[[[1, 3], [2, 16], [6, 1], [10, 1]], 27779/7838208000],
[[[1, 3], [2, 18], [3, 1], [6, 1]], 3137/250822656000],
[[[1, 3], [2, 18], [4, 1], [6, 1]], 373/2090188800],
[[[1, 3], [3, 2], [7, 1], [9, 2]], 1/756],
[[[1, 3], [3, 3], [5, 1], [9, 2]], 1/810],
[[[1, 3], [3, 3], [5, 2], [15, 1]], 1/225],
[[[1, 3], [3, 5], [5, 1], [15, 1]], 1/2430],
[[[1, 4], [2, 1], [3, 4], [9, 2]], 1/1944],
[[[1, 4], [2, 3], [3, 3], [9, 2]], 1/7776],
[[[1, 4], [2, 3], [3, 4], [6, 5]], 5/11664],
[[[1, 4], [2, 3], [3, 6], [6, 3]], 131/104976],
[[[1, 4], [2, 5], [3, 3], [6, 5]], 25/11664],
[[[1, 4], [2, 5], [3, 4], [6, 4]], 5/5832],
[[[1, 4], [2, 5], [6, 2], [18, 2]], 1/20736],
[[[1, 4], [2, 7], [3, 1], [6, 6]], 89/1679616],
[[[1, 4], [2, 7], [3, 2], [6, 5]], 151/186624],
[[[1, 4], [2, 7], [3, 3], [6, 4]], 37/186624],
[[[1, 4], [2, 7], [4, 1], [10, 3]], 1/12000],
[[[1, 4], [2, 7], [4, 2], [6, 5]], 1/93312],
[[[1, 4], [2, 7], [4, 3], [6, 4]], 1/165888],
[[[1, 4], [2, 7], [4, 3], [10, 2]], 3/12800],
[[[1, 4], [2, 7], [6, 4], [14, 1]], 1/435456],
[[[1, 4], [2, 7], [6, 4], [18, 1]], 13/186624],
[[[1, 4], [2, 7], [10, 2], [14, 1]], 1/33600],
[[[1, 4], [2, 9], [3, 1], [6, 5]], 515/1679616],
[[[1, 4], [2, 9], [3, 2], [6, 4]], 7/19440],
[[[1, 4], [2, 9], [3, 3], [6, 3]], 17/1632960],
[[[1, 4], [2, 9], [4, 1], [6, 5]], 109/1119744],
[[[1, 4], [2, 9], [4, 2], [6, 4]], 587/2985984],
[[[1, 4], [2, 9], [4, 2], [10, 2]], 37/76800],
[[[1, 4], [2, 9], [4, 3], [6, 3]], 1/9216],
[[[1, 4], [2, 9], [4, 3], [14, 1]], 1/10752],
[[[1, 4], [2, 9], [4, 4], [6, 2]], 1/73728],
[[[1, 4], [2, 9], [4, 4], [8, 1]], 1/24576],
[[[1, 4], [2, 9], [4, 4], [10, 1]], 1/15360],
[[[1, 4], [2, 9], [6, 2], [10, 2]], 7/38400],
[[[1, 4], [2, 9], [6, 3], [14, 1]], 25/217728],
[[[1, 4], [2, 9], [6, 3], [18, 1]], 11/82944],
[[[1, 4], [2, 9], [6, 4], [10, 1]], 113/1866240],
[[[1, 4], [2, 11], [3, 1], [6, 4]], 5087/16796160],
[[[1, 4], [2, 11], [3, 2], [6, 3]], 253/4354560],
[[[1, 4], [2, 11], [4, 1], [6, 4]], 14257/44789760],
[[[1, 4], [2, 11], [4, 1], [10, 2]], 691/3456000],
[[[1, 4], [2, 11], [4, 2], [6, 3]], 1489/3732480],
[[[1, 4], [2, 11], [4, 2], [14, 1]], 31/430080],
[[[1, 4], [2, 11], [4, 3], [6, 2]], 17/92160],
[[[1, 4], [2, 11], [4, 3], [8, 1]], 17/737280],
[[[1, 4], [2, 11], [4, 3], [10, 1]], 83/921600],
[[[1, 4], [2, 11], [4, 4], [6, 1]], 1/36864],
[[[1, 4], [2, 11], [6, 1], [10, 2]], 3/12800],
[[[1, 4], [2, 11], [6, 2], [14, 1]], 899/5806080],
[[[1, 4], [2, 11], [6, 2], [18, 1]], 49/1244160],
[[[1, 4], [2, 11], [6, 3], [10, 1]], 131/373248],
[[[1, 4], [2, 11], [10, 1], [14, 1]], 257/4838400],
[[[1, 4], [2, 13], [3, 1], [6, 3]], 153211/1881169920],
[[[1, 4], [2, 13], [3, 2], [6, 2]], 3887/2090188800],
[[[1, 4], [2, 13], [4, 1], [6, 3]], 64051/313528320],
[[[1, 4], [2, 13], [4, 1], [14, 1]], 17/967680],
[[[1, 4], [2, 13], [4, 2], [6, 2]], 6059/41803776],
[[[1, 4], [2, 13], [4, 2], [8, 1]], 23/4423680],
[[[1, 4], [2, 13], [4, 2], [10, 1]], 2281/58060800],
[[[1, 4], [2, 13], [4, 3], [6, 1]], 5/165888],
[[[1, 4], [2, 13], [6, 1], [14, 1]], 149/4354560],
[[[1, 4], [2, 13], [6, 1], [18, 1]], 7/3732480],
[[[1, 4], [2, 13], [6, 2], [10, 1]], 28081/174182400],
[[[1, 4], [2, 15], [3, 1], [6, 2]], 1207/188116992],
[[[1, 4], [2, 15], [4, 1], [6, 2]], 107297/3135283200],
[[[1, 4], [2, 15], [4, 1], [8, 1]], 83/199065600],
[[[1, 4], [2, 15], [4, 1], [10, 1]], 3029/435456000],
[[[1, 4], [2, 15], [4, 2], [6, 1]], 373/32659200],
[[[1, 4], [2, 15], [6, 1], [10, 1]], 2209/130636800],
[[[1, 4], [2, 17], [3, 1], [6, 1]], 2521/18811699200],
[[[1, 4], [2, 17], [4, 1], [6, 1]], 673/391910400],
[[[1, 5], [2, 2], [3, 3], [9, 2]], 1/2592],
[[[1, 5], [2, 2], [3, 7], [6, 2]], 7/13122],
[[[1, 5], [2, 4], [3, 2], [9, 2]], 1/20736],
[[[1, 5], [2, 4], [3, 4], [6, 4]], 5/5832],
[[[1, 5], [2, 4], [3, 5], [6, 3]], 25/11664],
[[[1, 5], [2, 6], [3, 2], [6, 5]], 91/559872],
[[[1, 5], [2, 6], [3, 3], [6, 4]], 25/62208],
[[[1, 5], [2, 6], [3, 4], [6, 3]], 13/186624],
[[[1, 5], [2, 6], [4, 3], [10, 2]], 1/12800],
[[[1, 5], [2, 8], [3, 1], [6, 5]], 29/559872],
[[[1, 5], [2, 8], [3, 2], [6, 4]], 95/186624],
[[[1, 5], [2, 8], [3, 3], [6, 3]], 7/124416],
[[[1, 5], [2, 8], [4, 1], [6, 5]], 1/279936],
[[[1, 5], [2, 8], [4, 2], [6, 4]], 25/331776],
[[[1, 5], [2, 8], [4, 2], [10, 2]], 9/25600],
[[[1, 5], [2, 8], [4, 3], [6, 3]], 1/10368],
[[[1, 5], [2, 8], [4, 3], [14, 1]], 1/7168],
[[[1, 5], [2, 8], [4, 4], [6, 2]], 1/36864],
[[[1, 5], [2, 8], [4, 4], [8, 1]], 1/8192],
[[[1, 5], [2, 8], [4, 4], [10, 1]], 3/20480],
[[[1, 5], [2, 8], [6, 2], [10, 2]], 1/172800],
[[[1, 5], [2, 8], [6, 3], [14, 1]], 1/72576],
[[[1, 5], [2, 8], [6, 3], [18, 1]], 5/124416],
[[[1, 5], [2, 8], [6, 4], [10, 1]], 1/1244160],
[[[1, 5], [2, 10], [3, 1], [6, 4]], 371/1119744],
[[[1, 5], [2, 10], [3, 2], [6, 3]], 671/3732480],
[[[1, 5], [2, 10], [4, 1], [6, 4]], 3727/17915904],
[[[1, 5], [2, 10], [4, 1], [10, 2]], 19/76800],
[[[1, 5], [2, 10], [4, 2], [6, 3]], 121/248832],
[[[1, 5], [2, 10], [4, 2], [14, 1]], 7/46080],
[[[1, 5], [2, 10], [4, 3], [6, 2]], 109/276480],
[[[1, 5], [2, 10], [4, 3], [8, 1]], 19/184320],
[[[1, 5], [2, 10], [4, 3], [10, 1]], 133/460800],
[[[1, 5], [2, 10], [4, 4], [6, 1]], 1/8192],
[[[1, 5], [2, 10], [6, 1], [10, 2]], 47/345600],
[[[1, 5], [2, 10], [6, 2], [14, 1]], 43/387072],
[[[1, 5], [2, 10], [6, 2], [18, 1]], 13/248832],
[[[1, 5], [2, 10], [6, 3], [10, 1]], 77/622080],
[[[1, 5], [2, 10], [10, 1], [14, 1]], 17/322560],
[[[1, 5], [2, 12], [3, 1], [6, 3]], 8069/41803776],
[[[1, 5], [2, 12], [3, 2], [6, 2]], 13591/1254113280],
[[[1, 5], [2, 12], [4, 1], [6, 3]], 7781/22394880],
[[[1, 5], [2, 12], [4, 1], [14, 1]], 37/774144],
[[[1, 5], [2, 12], [4, 2], [6, 2]], 2333/5806080],
[[[1, 5], [2, 12], [4, 2], [8, 1]], 113/4423680],
[[[1, 5], [2, 12], [4, 2], [10, 1]], 2887/19353600],
[[[1, 5], [2, 12], [4, 3], [6, 1]], 17/110592],
[[[1, 5], [2, 12], [6, 1], [14, 1]], 19/322560],
[[[1, 5], [2, 12], [6, 1], [18, 1]], 13/2488320],
[[[1, 5], [2, 12], [6, 2], [10, 1]], 593/2764800],
[[[1, 5], [2, 14], [3, 1], [6, 2]], 8219/313528320],
[[[1, 5], [2, 14], [4, 1], [6, 2]], 70489/627056640],
[[[1, 5], [2, 14], [4, 1], [8, 1]], 7/3317760],
[[[1, 5], [2, 14], [4, 1], [10, 1]], 10037/348364800],
[[[1, 5], [2, 14], [4, 2], [6, 1]], 47/774144],
[[[1, 5], [2, 14], [6, 1], [10, 1]], 3947/87091200],
[[[1, 5], [2, 16], [3, 1], [6, 1]], 4213/5016453120],
[[[1, 5], [2, 16], [4, 1], [6, 1]], 14677/1567641600],
[[[1, 5], [3, 1], [5, 3], [9, 1]], 1/6750],
[[[1, 5], [3, 2], [5, 1], [9, 2]], 1/6480],
[[[1, 5], [3, 2], [5, 2], [15, 1]], 1/1800],
[[[1, 5], [3, 3], [5, 2], [9, 1]], 1/8100],
[[[1, 5], [3, 4], [5, 1], [15, 1]], 1/1620],
[[[1, 5], [3, 4], [7, 1], [9, 1]], 1/756],
[[[1, 5], [3, 5], [5, 1], [9, 1]], 37/29160],
[[[1, 6], [2, 1], [3, 3], [9, 2]], 1/7776],
[[[1, 6], [2, 1], [3, 6], [7, 1]], 43/1224720],
[[[1, 6], [2, 1], [3, 6], [9, 1]], 19/34992],
[[[1, 6], [2, 1], [3, 8], [6, 1]], 113/1574640],
[[[1, 6], [2, 1], [4, 1], [5, 4]], 1/15000],
[[[1, 6], [2, 1], [5, 3], [7, 1]], 1/10500],
[[[1, 6], [2, 3], [3, 2], [9, 2]], 1/15552],
[[[1, 6], [2, 3], [3, 5], [6, 3]], 25/34992],
[[[1, 6], [2, 3], [3, 5], [9, 1]], 37/279936],
[[[1, 6], [2, 3], [3, 6], [6, 2]], 91/69984],
[[[1, 6], [2, 3], [4, 2], [5, 3]], 1/8000],
[[[1, 6], [2, 5], [3, 3], [6, 4]], 13/186624],
[[[1, 6], [2, 5], [3, 4], [6, 3]], 25/62208],
[[[1, 6], [2, 5], [3, 5], [6, 2]], 91/559872],
[[[1, 6], [2, 5], [4, 3], [5, 2]], 1/12800],
[[[1, 6], [2, 7], [3, 2], [6, 4]], 1/7776],
[[[1, 6], [2, 7], [3, 3], [6, 3]], 113/746496],
[[[1, 6], [2, 7], [4, 2], [10, 2]], 1/15360],
[[[1, 6], [2, 7], [4, 3], [6, 3]], 5/248832],
[[[1, 6], [2, 7], [4, 3], [7, 1]], 1/43008],
[[[1, 6], [2, 7], [4, 3], [14, 1]], 1/10752],
[[[1, 6], [2, 7], [4, 4], [5, 1]], 1/61440],
[[[1, 6], [2, 7], [4, 4], [6, 2]], 1/73728],
[[[1, 6], [2, 7], [4, 4], [8, 1]], 1/6144],
[[[1, 6], [2, 7], [4, 4], [10, 1]], 1/10240],
[[[1, 6], [2, 7], [6, 3], [18, 1]], 1/746496],
[[[1, 6], [2, 9], [3, 1], [6, 4]], 61/746496],
[[[1, 6], [2, 9], [3, 2], [6, 3]], 115/497664],
[[[1, 6], [2, 9], [4, 1], [6, 4]], 145/5971968],
[[[1, 6], [2, 9], [4, 1], [10, 2]], 17/153600],
[[[1, 6], [2, 9], [4, 2], [6, 3]], 25/124416],
[[[1, 6], [2, 9], [4, 2], [14, 1]], 13/86016],
[[[1, 6], [2, 9], [4, 3], [6, 2]], 53/165888],
[[[1, 6], [2, 9], [4, 3], [8, 1]], 1/6144],
[[[1, 6], [2, 9], [4, 3], [10, 1]], 31/92160],
[[[1, 6], [2, 9], [4, 4], [6, 1]], 13/73728],
[[[1, 6], [2, 9], [6, 1], [10, 2]], 1/43200],
[[[1, 6], [2, 9], [6, 2], [14, 1]], 31/1161216],
[[[1, 6], [2, 9], [6, 2], [18, 1]], 19/746496],
[[[1, 6], [2, 9], [6, 3], [10, 1]], 7/933120],
[[[1, 6], [2, 9], [10, 1], [14, 1]], 1/46080],
[[[1, 6], [2, 11], [3, 1], [6, 3]], 2147/9953280],
[[[1, 6], [2, 11], [3, 2], [6, 2]], 4393/139345920],
[[[1, 6], [2, 11], [4, 1], [6, 3]], 757/2985984],
[[[1, 6], [2, 11], [4, 1], [14, 1]], 1/15120],
[[[1, 6], [2, 11], [4, 2], [6, 2]], 335/663552],
[[[1, 6], [2, 11], [4, 2], [8, 1]], 257/4423680],
[[[1, 6], [2, 11], [4, 2], [10, 1]], 71/276480],
[[[1, 6], [2, 11], [4, 3], [6, 1]], 269/829440],
[[[1, 6], [2, 11], [6, 1], [14, 1]], 29/580608],
[[[1, 6], [2, 11], [6, 1], [18, 1]], 113/14929920],
[[[1, 6], [2, 11], [6, 2], [10, 1]], 277/2488320],
[[[1, 6], [2, 13], [3, 1], [6, 2]], 2081/34836480],
[[[1, 6], [2, 13], [4, 1], [6, 2]], 13567/69672960],
[[[1, 6], [2, 13], [4, 1], [8, 1]], 13/2211840],
[[[1, 6], [2, 13], [4, 1], [10, 1]], 829/12902400],
[[[1, 6], [2, 13], [4, 2], [6, 1]], 3797/23224320],
[[[1, 6], [2, 13], [6, 1], [10, 1]], 1613/24883200],
[[[1, 6], [2, 15], [3, 1], [6, 1]], 13261/4180377600],
[[[1, 6], [2, 15], [4, 1], [6, 1]], 6187/209018880],
[[[1, 7], [2, 2], [3, 2], [5, 3]], 1/36000],
[[[1, 7], [2, 2], [3, 2], [9, 2]], 1/51840],
[[[1, 7], [2, 2], [3, 4], [5, 2]], 1/129600],
[[[1, 7], [2, 2], [3, 5], [7, 1]], 1/54432],
[[[1, 7], [2, 2], [3, 5], [9, 1]], 5/10368],
[[[1, 7], [2, 2], [3, 6], [4, 2]], 43/2799360],
[[[1, 7], [2, 2], [3, 6], [5, 1]], 43/3499200],
[[[1, 7], [2, 2], [3, 6], [6, 2]], 91/209952],
[[[1, 7], [2, 2], [3, 7], [4, 1]], 91/4199040],
[[[1, 7], [2, 2], [3, 7], [6, 1]], 139/524880],
[[[1, 7], [2, 2], [4, 2], [5, 3]], 1/6000],
[[[1, 7], [2, 4], [3, 4], [4, 3]], 1/165888],
[[[1, 7], [2, 4], [3, 4], [6, 3]], 37/186624],
[[[1, 7], [2, 4], [3, 4], [7, 1]], 1/435456],
[[[1, 7], [2, 4], [3, 4], [9, 1]], 13/186624],
[[[1, 7], [2, 4], [3, 5], [4, 2]], 1/93312],
[[[1, 7], [2, 4], [3, 5], [6, 2]], 151/186624],
[[[1, 7], [2, 4], [3, 6], [6, 1]], 89/1679616],
[[[1, 7], [2, 4], [4, 1], [5, 3]], 1/12000],
[[[1, 7], [2, 4], [4, 3], [5, 2]], 3/12800],
[[[1, 7], [2, 4], [5, 2], [7, 1]], 1/33600],
[[[1, 7], [2, 6], [3, 2], [4, 4]], 1/73728],
[[[1, 7], [2, 6], [3, 3], [4, 3]], 5/248832],
[[[1, 7], [2, 6], [3, 3], [6, 3]], 113/746496],
[[[1, 7], [2, 6], [3, 3], [9, 1]], 1/746496],
[[[1, 7], [2, 6], [3, 4], [6, 2]], 1/7776],
[[[1, 7], [2, 6], [4, 2], [5, 2]], 1/15360],
[[[1, 7], [2, 6], [4, 3], [7, 1]], 1/10752],
[[[1, 7], [2, 6], [4, 3], [14, 1]], 1/43008],
[[[1, 7], [2, 6], [4, 4], [5, 1]], 1/10240],
[[[1, 7], [2, 6], [4, 4], [8, 1]], 1/6144],
[[[1, 7], [2, 6], [4, 4], [10, 1]], 1/61440],
[[[1, 7], [2, 8], [3, 1], [4, 4]], 1/73728],
[[[1, 7], [2, 8], [3, 1], [6, 4]], 5/2239488],
[[[1, 7], [2, 8], [3, 2], [6, 3]], 13/165888],
[[[1, 7], [2, 8], [3, 3], [6, 2]], 1/248832],
[[[1, 7], [2, 8], [4, 1], [10, 2]], 7/460800],
[[[1, 7], [2, 8], [4, 2], [6, 3]], 5/497664],
[[[1, 7], [2, 8], [4, 2], [7, 1]], 1/86016],
[[[1, 7], [2, 8], [4, 2], [14, 1]], 1/14336],
[[[1, 7], [2, 8], [4, 3], [5, 1]], 1/61440],
[[[1, 7], [2, 8], [4, 3], [6, 2]], 1/12288],
[[[1, 7], [2, 8], [4, 3], [8, 1]], 1/8192],
[[[1, 7], [2, 8], [4, 3], [10, 1]], 3/20480],
[[[1, 7], [2, 8], [4, 4], [6, 1]], 7/73728],
[[[1, 7], [2, 8], [6, 2], [14, 1]], 1/1161216],
[[[1, 7], [2, 8], [6, 2], [18, 1]], 1/248832],
[[[1, 7], [2, 8], [10, 1], [14, 1]], 1/322560],
[[[1, 7], [2, 10], [3, 1], [6, 3]], 497/5971968],
[[[1, 7], [2, 10], [3, 2], [6, 2]], 287/6635520],
[[[1, 7], [2, 10], [4, 1], [6, 3]], 85/1492992],
[[[1, 7], [2, 10], [4, 1], [14, 1]], 1/21504],
[[[1, 7], [2, 10], [4, 2], [6, 2]], 43/165888],
[[[1, 7], [2, 10], [4, 2], [8, 1]], 17/294912],
[[[1, 7], [2, 10], [4, 2], [10, 1]], 1/5120],
[[[1, 7], [2, 10], [4, 3], [6, 1]], 11/36864],
[[[1, 7], [2, 10], [6, 1], [14, 1]], 11/580608],
[[[1, 7], [2, 10], [6, 1], [18, 1]], 5/995328],
[[[1, 7], [2, 10], [6, 2], [10, 1]], 31/1658880],
[[[1, 7], [2, 12], [3, 1], [6, 2]], 53/746496],
[[[1, 7], [2, 12], [4, 1], [6, 2]], 1633/9953280],
[[[1, 7], [2, 12], [4, 1], [8, 1]], 113/13271040],
[[[1, 7], [2, 12], [4, 1], [10, 1]], 19/259200],
[[[1, 7], [2, 12], [4, 2], [6, 1]], 23/103680],
[[[1, 7], [2, 12], [6, 1], [10, 1]], 73/1658880],
[[[1, 7], [2, 14], [3, 1], [6, 1]], 5123/716636160],
[[[1, 7], [2, 14], [4, 1], [6, 1]], 3713/69672960],
[[[1, 7], [3, 2], [5, 2], [7, 1]], 1/12600],
[[[1, 7], [3, 2], [5, 2], [9, 1]], 1/8100],
[[[1, 7], [3, 3], [5, 1], [15, 1]], 1/32400],
[[[1, 7], [3, 4], [5, 1], [7, 1]], 1/45360],
[[[1, 7], [3, 4], [5, 1], [9, 1]], 13/58320],
[[[1, 8], [2, 1], [3, 2], [5, 3]], 17/54000],
[[[1, 8], [2, 1], [3, 2], [9, 2]], 1/544320],
[[[1, 8], [2, 1], [3, 4], [5, 2]], 37/194400],
[[[1, 8], [2, 1], [3, 5], [7, 1]], 1/40824],
[[[1, 8], [2, 1], [3, 5], [9, 1]], 53/279936],
[[[1, 8], [2, 1], [3, 6], [5, 1]], 1/16200],
[[[1, 8], [2, 1], [3, 7], [4, 1]], 91/4199040],
[[[1, 8], [2, 1], [3, 7], [6, 1]], 139/1574640],
[[[1, 8], [2, 3], [3, 1], [5, 3]], 13/108000],
[[[1, 8], [2, 3], [3, 3], [5, 2]], 7/97200],
[[[1, 8], [2, 3], [3, 4], [4, 3]], 1/165888],
[[[1, 8], [2, 3], [3, 4], [6, 3]], 73/2799360],
[[[1, 8], [2, 3], [3, 4], [7, 1]], 1/15552],
[[[1, 8], [2, 3], [3, 4], [9, 1]], 31/139968],
[[[1, 8], [2, 3], [3, 5], [4, 2]], 11/373248],
[[[1, 8], [2, 3], [3, 5], [5, 1]], 17/1399680],
[[[1, 8], [2, 3], [3, 5], [6, 2]], 211/559872],
[[[1, 8], [2, 3], [3, 6], [4, 1]], 1/25920],
[[[1, 8], [2, 3], [3, 6], [6, 1]], 157/559872],
[[[1, 8], [2, 3], [4, 1], [5, 3]], 7/24000],
[[[1, 8], [2, 3], [4, 3], [5, 2]], 1/6400],
[[[1, 8], [2, 3], [5, 2], [7, 1]], 1/8400],
[[[1, 8], [2, 5], [3, 2], [4, 4]], 1/36864],
[[[1, 8], [2, 5], [3, 2], [5, 2]], 1/172800],
[[[1, 8], [2, 5], [3, 3], [4, 3]], 1/10368],
[[[1, 8], [2, 5], [3, 3], [6, 3]], 7/124416],
[[[1, 8], [2, 5], [3, 3], [7, 1]], 1/72576],
[[[1, 8], [2, 5], [3, 3], [9, 1]], 5/124416],
[[[1, 8], [2, 5], [3, 4], [4, 2]], 25/331776],
[[[1, 8], [2, 5], [3, 4], [5, 1]], 1/1244160],
[[[1, 8], [2, 5], [3, 4], [6, 2]], 95/186624],
[[[1, 8], [2, 5], [3, 5], [4, 1]], 1/279936],
[[[1, 8], [2, 5], [3, 5], [6, 1]], 29/559872],
[[[1, 8], [2, 5], [4, 2], [5, 2]], 9/25600],
[[[1, 8], [2, 5], [4, 3], [7, 1]], 1/7168],
[[[1, 8], [2, 5], [4, 4], [5, 1]], 3/20480],
[[[1, 8], [2, 5], [4, 4], [8, 1]], 1/8192],
[[[1, 8], [2, 7], [3, 1], [4, 4]], 7/73728],
[[[1, 8], [2, 7], [3, 2], [4, 3]], 1/12288],
[[[1, 8], [2, 7], [3, 2], [6, 3]], 1/248832],
[[[1, 8], [2, 7], [3, 2], [7, 1]], 1/1161216],
[[[1, 8], [2, 7], [3, 2], [9, 1]], 1/248832],
[[[1, 8], [2, 7], [3, 3], [4, 2]], 5/497664],
[[[1, 8], [2, 7], [3, 3], [6, 2]], 13/165888],
[[[1, 8], [2, 7], [3, 4], [6, 1]], 5/2239488],
[[[1, 8], [2, 7], [4, 1], [5, 2]], 7/460800],
[[[1, 8], [2, 7], [4, 2], [7, 1]], 1/14336],
[[[1, 8], [2, 7], [4, 2], [14, 1]], 1/86016],
[[[1, 8], [2, 7], [4, 3], [5, 1]], 3/20480],
[[[1, 8], [2, 7], [4, 3], [8, 1]], 1/8192],
[[[1, 8], [2, 7], [4, 3], [10, 1]], 1/61440],
[[[1, 8], [2, 7], [4, 4], [6, 1]], 1/73728],
[[[1, 8], [2, 7], [5, 1], [7, 1]], 1/322560],
[[[1, 8], [2, 9], [3, 1], [4, 3]], 1/110592],
[[[1, 8], [2, 9], [3, 1], [6, 3]], 17/1990656],
[[[1, 8], [2, 9], [3, 1], [9, 1]], 1/5971968],
[[[1, 8], [2, 9], [3, 2], [6, 2]], 13/497664],
[[[1, 8], [2, 9], [4, 1], [6, 3]], 5/2985984],
[[[1, 8], [2, 9], [4, 1], [7, 1]], 1/516096],
[[[1, 8], [2, 9], [4, 1], [14, 1]], 1/64512],
[[[1, 8], [2, 9], [4, 2], [5, 1]], 1/184320],
[[[1, 8], [2, 9], [4, 2], [6, 2]], 25/663552],
[[[1, 8], [2, 9], [4, 2], [8, 1]], 1/36864],
[[[1, 8], [2, 9], [4, 2], [10, 1]], 11/184320],
[[[1, 8], [2, 9], [4, 3], [6, 1]], 1/9216],
[[[1, 8], [2, 9], [6, 1], [14, 1]], 1/387072],
[[[1, 8], [2, 9], [6, 1], [18, 1]], 1/663552],
[[[1, 8], [2, 9], [6, 2], [10, 1]], 1/3317760],
[[[1, 8], [2, 11], [3, 1], [6, 2]], 37/995328],
[[[1, 8], [2, 11], [4, 1], [6, 2]], 113/1990656],
[[[1, 8], [2, 11], [4, 1], [8, 1]], 5/884736],
[[[1, 8], [2, 11], [4, 1], [10, 1]], 11/276480],
[[[1, 8], [2, 11], [4, 2], [6, 1]], 47/331776],
[[[1, 8], [2, 11], [6, 1], [10, 1]], 43/3317760],
[[[1, 8], [2, 13], [3, 1], [6, 1]], 1271/139345920],
[[[1, 8], [2, 13], [4, 1], [6, 1]], 1/19440],
[[[1, 9], [2, 2], [3, 1], [5, 3]], 11/36000],
[[[1, 9], [2, 2], [3, 3], [5, 2]], 1/2160],
[[[1, 9], [2, 2], [3, 4], [7, 1]], 11/108864],
[[[1, 9], [2, 2], [3, 4], [9, 1]], 23/155520],
[[[1, 9], [2, 2], [3, 5], [4, 2]], 5/373248],
[[[1, 9], [2, 2], [3, 5], [5, 1]], 71/466560],
[[[1, 9], [2, 2], [3, 5], [6, 2]], 391/8398080],
[[[1, 9], [2, 2], [3, 6], [4, 1]], 173/4199040],
[[[1, 9], [2, 2], [3, 6], [6, 1]], 25/186624],
[[[1, 9], [2, 2], [4, 1], [5, 3]], 7/36000],
[[[1, 9], [2, 2], [5, 2], [7, 1]], 1/8400],
[[[1, 9], [2, 4], [3, 2], [4, 4]], 1/73728],
[[[1, 9], [2, 4], [3, 2], [5, 2]], 7/38400],
[[[1, 9], [2, 4], [3, 3], [4, 3]], 1/9216],
[[[1, 9], [2, 4], [3, 3], [6, 3]], 17/1632960],
[[[1, 9], [2, 4], [3, 3], [7, 1]], 25/217728],
[[[1, 9], [2, 4], [3, 3], [9, 1]], 11/82944],
[[[1, 9], [2, 4], [3, 4], [4, 2]], 587/2985984],
[[[1, 9], [2, 4], [3, 4], [5, 1]], 113/1866240],
[[[1, 9], [2, 4], [3, 4], [6, 2]], 7/19440],
[[[1, 9], [2, 4], [3, 5], [4, 1]], 109/1119744],
[[[1, 9], [2, 4], [3, 5], [6, 1]], 515/1679616],
[[[1, 9], [2, 4], [4, 2], [5, 2]], 37/76800],
[[[1, 9], [2, 4], [4, 3], [7, 1]], 1/10752],
[[[1, 9], [2, 4], [4, 4], [5, 1]], 1/15360],
[[[1, 9], [2, 4], [4, 4], [8, 1]], 1/24576],
[[[1, 9], [2, 6], [3, 1], [4, 4]], 13/73728],
[[[1, 9], [2, 6], [3, 1], [5, 2]], 1/43200],
[[[1, 9], [2, 6], [3, 2], [4, 3]], 53/165888],
[[[1, 9], [2, 6], [3, 2], [7, 1]], 31/1161216],
[[[1, 9], [2, 6], [3, 2], [9, 1]], 19/746496],
[[[1, 9], [2, 6], [3, 3], [4, 2]], 25/124416],
[[[1, 9], [2, 6], [3, 3], [5, 1]], 7/933120],
[[[1, 9], [2, 6], [3, 3], [6, 2]], 115/497664],
[[[1, 9], [2, 6], [3, 4], [4, 1]], 145/5971968],
[[[1, 9], [2, 6], [3, 4], [6, 1]], 61/746496],
[[[1, 9], [2, 6], [4, 1], [5, 2]], 17/153600],
[[[1, 9], [2, 6], [4, 2], [7, 1]], 13/86016],
[[[1, 9], [2, 6], [4, 3], [5, 1]], 31/92160],
[[[1, 9], [2, 6], [4, 3], [8, 1]], 1/6144],
[[[1, 9], [2, 6], [5, 1], [7, 1]], 1/46080],
[[[1, 9], [2, 8], [3, 1], [4, 3]], 1/9216],
[[[1, 9], [2, 8], [3, 1], [7, 1]], 1/387072],
[[[1, 9], [2, 8], [3, 1], [9, 1]], 1/663552],
[[[1, 9], [2, 8], [3, 2], [4, 2]], 25/663552],
[[[1, 9], [2, 8], [3, 2], [5, 1]], 1/3317760],
[[[1, 9], [2, 8], [3, 2], [6, 2]], 13/497664],
[[[1, 9], [2, 8], [3, 3], [4, 1]], 5/2985984],
[[[1, 9], [2, 8], [3, 3], [6, 1]], 17/1990656],
[[[1, 9], [2, 8], [4, 1], [7, 1]], 1/64512],
[[[1, 9], [2, 8], [4, 1], [14, 1]], 1/516096],
[[[1, 9], [2, 8], [4, 2], [5, 1]], 11/184320],
[[[1, 9], [2, 8], [4, 2], [8, 1]], 1/36864],
[[[1, 9], [2, 8], [4, 2], [10, 1]], 1/184320],
[[[1, 9], [2, 8], [4, 3], [6, 1]], 1/110592],
[[[1, 9], [2, 8], [6, 1], [18, 1]], 1/5971968],
[[[1, 9], [2, 10], [3, 1], [4, 2]], 1/442368],
[[[1, 9], [2, 10], [3, 1], [6, 2]], 5/663552],
[[[1, 9], [2, 10], [3, 2], [6, 1]], 1/2985984],
[[[1, 9], [2, 10], [4, 1], [5, 1]], 1/1327104],
[[[1, 9], [2, 10], [4, 1], [6, 2]], 1/165888],
[[[1, 9], [2, 10], [4, 1], [8, 1]], 5/2654208],
[[[1, 9], [2, 10], [4, 1], [10, 1]], 7/737280],
[[[1, 9], [2, 10], [4, 2], [6, 1]], 1/27648],
[[[1, 9], [2, 10], [6, 1], [10, 1]], 13/9953280],
[[[1, 9], [2, 12], [3, 1], [6, 1]], 317/53084160],
[[[1, 9], [2, 12], [4, 1], [6, 1]], 1/41472],
[[[1, 9], [3, 1], [5, 2], [7, 1]], 1/12600],
[[[1, 9], [3, 1], [5, 2], [9, 1]], 1/324000],
[[[1, 9], [3, 2], [5, 1], [15, 1]], 1/5443200],
[[[1, 9], [3, 3], [5, 1], [7, 1]], 1/22680],
[[[1, 9], [3, 3], [5, 1], [9, 1]], 7/194400],
[[[1, 10], [2, 1], [3, 1], [5, 3]], 13/108000],
[[[1, 10], [2, 1], [3, 3], [5, 2]], 1/3888],
[[[1, 10], [2, 1], [3, 4], [7, 1]], 37/816480],
[[[1, 10], [2, 1], [3, 4], [9, 1]], 191/4898880],
[[[1, 10], [2, 1], [3, 5], [5, 1]], 43/466560],
[[[1, 10], [2, 1], [3, 6], [4, 1]], 23/2624400],
[[[1, 10], [2, 1], [3, 6], [6, 1]], 143/8398080],
[[[1, 10], [2, 1], [4, 1], [5, 3]], 1/40000],
[[[1, 10], [2, 1], [5, 2], [7, 1]], 1/31500],
[[[1, 10], [2, 3], [3, 2], [5, 2]], 13/25920],
[[[1, 10], [2, 3], [3, 3], [4, 3]], 1/31104],
[[[1, 10], [2, 3], [3, 3], [6, 3]], 131/235146240],
[[[1, 10], [2, 3], [3, 3], [7, 1]], 5/27216],
[[[1, 10], [2, 3], [3, 3], [9, 1]], 101/933120],
[[[1, 10], [2, 3], [3, 4], [4, 2]], 2021/14929920],
[[[1, 10], [2, 3], [3, 4], [5, 1]], 1727/5598720],
[[[1, 10], [2, 3], [3, 4], [6, 2]], 89/933120],
[[[1, 10], [2, 3], [3, 5], [4, 1]], 55/373248],
[[[1, 10], [2, 3], [3, 5], [6, 1]], 343/1399680],
[[[1, 10], [2, 3], [4, 2], [5, 2]], 233/1152000],
[[[1, 10], [2, 3], [4, 3], [7, 1]], 1/43008],
[[[1, 10], [2, 5], [3, 1], [4, 4]], 1/8192],
[[[1, 10], [2, 5], [3, 1], [5, 2]], 47/345600],
[[[1, 10], [2, 5], [3, 2], [4, 3]], 109/276480],
[[[1, 10], [2, 5], [3, 2], [7, 1]], 43/387072],
[[[1, 10], [2, 5], [3, 2], [9, 1]], 13/248832],
[[[1, 10], [2, 5], [3, 3], [4, 2]], 121/248832],
[[[1, 10], [2, 5], [3, 3], [5, 1]], 77/622080],
[[[1, 10], [2, 5], [3, 3], [6, 2]], 671/3732480],
[[[1, 10], [2, 5], [3, 4], [4, 1]], 3727/17915904],
[[[1, 10], [2, 5], [3, 4], [6, 1]], 371/1119744],
[[[1, 10], [2, 5], [4, 1], [5, 2]], 19/76800],
[[[1, 10], [2, 5], [4, 2], [7, 1]], 7/46080],
[[[1, 10], [2, 5], [4, 3], [5, 1]], 133/460800],
[[[1, 10], [2, 5], [4, 3], [8, 1]], 19/184320],
[[[1, 10], [2, 5], [5, 1], [7, 1]], 17/322560],
[[[1, 10], [2, 7], [3, 1], [4, 3]], 11/36864],
[[[1, 10], [2, 7], [3, 1], [7, 1]], 11/580608],
[[[1, 10], [2, 7], [3, 1], [9, 1]], 5/995328],
[[[1, 10], [2, 7], [3, 2], [4, 2]], 43/165888],
[[[1, 10], [2, 7], [3, 2], [5, 1]], 31/1658880],
[[[1, 10], [2, 7], [3, 2], [6, 2]], 287/6635520],
[[[1, 10], [2, 7], [3, 3], [4, 1]], 85/1492992],
[[[1, 10], [2, 7], [3, 3], [6, 1]], 497/5971968],
[[[1, 10], [2, 7], [4, 1], [7, 1]], 1/21504],
[[[1, 10], [2, 7], [4, 2], [5, 1]], 1/5120],
[[[1, 10], [2, 7], [4, 2], [8, 1]], 17/294912],
[[[1, 10], [2, 9], [3, 1], [4, 2]], 1/27648],
[[[1, 10], [2, 9], [3, 1], [5, 1]], 13/9953280],
[[[1, 10], [2, 9], [3, 1], [6, 2]], 1/2985984],
[[[1, 10], [2, 9], [3, 2], [4, 1]], 1/165888],
[[[1, 10], [2, 9], [3, 2], [6, 1]], 5/663552],
[[[1, 10], [2, 9], [4, 1], [5, 1]], 7/737280],
[[[1, 10], [2, 9], [4, 1], [8, 1]], 5/2654208],
[[[1, 10], [2, 9], [4, 1], [10, 1]], 1/1327104],
[[[1, 10], [2, 9], [4, 2], [6, 1]], 1/442368],
[[[1, 10], [2, 11], [3, 1], [4, 1]], 1/3981312],
[[[1, 10], [2, 11], [3, 1], [6, 1]], 199/95551488],
[[[1, 10], [2, 11], [4, 1], [6, 1]], 19/3981312],
[[[1, 11], [2, 2], [3, 2], [5, 2]], 263/864000],
[[[1, 11], [2, 2], [3, 3], [7, 1]], 29/272160],
[[[1, 11], [2, 2], [3, 3], [9, 1]], 1/27648],
[[[1, 11], [2, 2], [3, 4], [4, 2]], 43/1658880],
[[[1, 11], [2, 2], [3, 4], [5, 1]], 371/1555200],
[[[1, 11], [2, 2], [3, 4], [6, 2]], 37/4199040],
[[[1, 11], [2, 2], [3, 5], [4, 1]], 361/5598720],
[[[1, 11], [2, 2], [3, 5], [6, 1]], 199/2799360],
[[[1, 11], [2, 2], [4, 2], [5, 2]], 1/48000],
[[[1, 11], [2, 4], [3, 1], [4, 4]], 1/36864],
[[[1, 11], [2, 4], [3, 1], [5, 2]], 3/12800],
[[[1, 11], [2, 4], [3, 2], [4, 3]], 17/92160],
[[[1, 11], [2, 4], [3, 2], [7, 1]], 899/5806080],
[[[1, 11], [2, 4], [3, 2], [9, 1]], 49/1244160],
[[[1, 11], [2, 4], [3, 3], [4, 2]], 1489/3732480],
[[[1, 11], [2, 4], [3, 3], [5, 1]], 131/373248],
[[[1, 11], [2, 4], [3, 3], [6, 2]], 253/4354560],
[[[1, 11], [2, 4], [3, 4], [4, 1]], 14257/44789760],
[[[1, 11], [2, 4], [3, 4], [6, 1]], 5087/16796160],
[[[1, 11], [2, 4], [4, 1], [5, 2]], 691/3456000],
[[[1, 11], [2, 4], [4, 2], [7, 1]], 31/430080],
[[[1, 11], [2, 4], [4, 3], [5, 1]], 83/921600],
[[[1, 11], [2, 4], [4, 3], [8, 1]], 17/737280],
[[[1, 11], [2, 4], [5, 1], [7, 1]], 257/4838400],
[[[1, 11], [2, 6], [3, 1], [4, 3]], 269/829440],
[[[1, 11], [2, 6], [3, 1], [7, 1]], 29/580608],
[[[1, 11], [2, 6], [3, 1], [9, 1]], 113/14929920],
[[[1, 11], [2, 6], [3, 2], [4, 2]], 335/663552],
[[[1, 11], [2, 6], [3, 2], [5, 1]], 277/2488320],
[[[1, 11], [2, 6], [3, 2], [6, 2]], 4393/139345920],
[[[1, 11], [2, 6], [3, 3], [4, 1]], 757/2985984],
[[[1, 11], [2, 6], [3, 3], [6, 1]], 2147/9953280],
[[[1, 11], [2, 6], [4, 1], [7, 1]], 1/15120],
[[[1, 11], [2, 6], [4, 2], [5, 1]], 71/276480],
[[[1, 11], [2, 6], [4, 2], [8, 1]], 257/4423680],
[[[1, 11], [2, 8], [3, 1], [4, 2]], 47/331776],
[[[1, 11], [2, 8], [3, 1], [5, 1]], 43/3317760],
[[[1, 11], [2, 8], [3, 2], [4, 1]], 113/1990656],
[[[1, 11], [2, 8], [3, 2], [6, 1]], 37/995328],
[[[1, 11], [2, 8], [4, 1], [5, 1]], 11/276480],
[[[1, 11], [2, 8], [4, 1], [8, 1]], 5/884736],
[[[1, 11], [2, 10], [3, 1], [4, 1]], 19/3981312],
[[[1, 11], [2, 10], [3, 1], [6, 1]], 199/95551488],
[[[1, 11], [2, 10], [4, 1], [6, 1]], 1/3981312],
[[[1, 11], [3, 2], [5, 1], [7, 1]], 1/43200],
[[[1, 11], [3, 2], [5, 1], [9, 1]], 1/583200],
[[[1, 12], [2, 1], [3, 2], [5, 2]], 1199/18144000],
[[[1, 12], [2, 1], [3, 3], [7, 1]], 257/9797760],
[[[1, 12], [2, 1], [3, 3], [9, 1]], 29/5598720],
[[[1, 12], [2, 1], [3, 4], [5, 1]], 8677/130636800],
[[[1, 12], [2, 1], [3, 5], [4, 1]], 49/5598720],
[[[1, 12], [2, 1], [3, 5], [6, 1]], 179/25194240],
[[[1, 12], [2, 3], [3, 1], [5, 2]], 359/2592000],
[[[1, 12], [2, 3], [3, 2], [4, 3]], 47/1658880],
[[[1, 12], [2, 3], [3, 2], [7, 1]], 77/829440],
[[[1, 12], [2, 3], [3, 2], [9, 1]], 31/2239488],
[[[1, 12], [2, 3], [3, 3], [4, 2]], 967/7464960],
[[[1, 12], [2, 3], [3, 3], [5, 1]], 3899/13996800],
[[[1, 12], [2, 3], [3, 3], [6, 2]], 1273/156764160],
[[[1, 12], [2, 3], [3, 4], [4, 1]], 18601/104509440],
[[[1, 12], [2, 3], [3, 4], [6, 1]], 1807/15676416],
[[[1, 12], [2, 3], [4, 1], [5, 2]], 1033/16128000],
[[[1, 12], [2, 3], [4, 2], [7, 1]], 1/71680],
[[[1, 12], [2, 3], [4, 3], [5, 1]], 7/921600],
[[[1, 12], [2, 3], [4, 3], [8, 1]], 1/737280],
[[[1, 12], [2, 3], [5, 1], [7, 1]], 113/4838400],
[[[1, 12], [2, 5], [3, 1], [4, 3]], 17/110592],
[[[1, 12], [2, 5], [3, 1], [7, 1]], 19/322560],
[[[1, 12], [2, 5], [3, 1], [9, 1]], 13/2488320],
[[[1, 12], [2, 5], [3, 2], [4, 2]], 2333/5806080],
[[[1, 12], [2, 5], [3, 2], [5, 1]], 593/2764800],
[[[1, 12], [2, 5], [3, 2], [6, 2]], 13591/1254113280],
[[[1, 12], [2, 5], [3, 3], [4, 1]], 7781/22394880],
[[[1, 12], [2, 5], [3, 3], [6, 1]], 8069/41803776],
[[[1, 12], [2, 5], [4, 1], [7, 1]], 37/774144],
[[[1, 12], [2, 5], [4, 2], [5, 1]], 2887/19353600],
[[[1, 12], [2, 5], [4, 2], [8, 1]], 113/4423680],
[[[1, 12], [2, 7], [3, 1], [4, 2]], 23/103680],
[[[1, 12], [2, 7], [3, 1], [5, 1]], 73/1658880],
[[[1, 12], [2, 7], [3, 2], [4, 1]], 1633/9953280],
[[[1, 12], [2, 7], [3, 2], [6, 1]], 53/746496],
[[[1, 12], [2, 7], [4, 1], [5, 1]], 19/259200],
[[[1, 12], [2, 7], [4, 1], [8, 1]], 113/13271040],
[[[1, 12], [2, 9], [3, 1], [4, 1]], 1/41472],
[[[1, 12], [2, 9], [3, 1], [6, 1]], 317/53084160],
[[[1, 13], [2, 2], [3, 1], [5, 2]], 643/18144000],
[[[1, 13], [2, 2], [3, 2], [7, 1]], 463/17418240],
[[[1, 13], [2, 2], [3, 2], [9, 1]], 1/414720],
[[[1, 13], [2, 2], [3, 3], [4, 2]], 163/11197440],
[[[1, 13], [2, 2], [3, 3], [5, 1]], 229/2449440],
[[[1, 13], [2, 2], [3, 3], [6, 2]], 887/2351462400],
[[[1, 13], [2, 2], [3, 4], [4, 1]], 79711/1881169920],
[[[1, 13], [2, 2], [3, 4], [6, 1]], 935/47029248],
[[[1, 13], [2, 2], [4, 1], [5, 2]], 1213/145152000],
[[[1, 13], [2, 2], [4, 2], [7, 1]], 1/1290240],
[[[1, 13], [2, 2], [5, 1], [7, 1]], 23/4838400],
[[[1, 13], [2, 4], [3, 1], [4, 3]], 5/165888],
[[[1, 13], [2, 4], [3, 1], [7, 1]], 149/4354560],
[[[1, 13], [2, 4], [3, 1], [9, 1]], 7/3732480],
[[[1, 13], [2, 4], [3, 2], [4, 2]], 6059/41803776],
[[[1, 13], [2, 4], [3, 2], [5, 1]], 28081/174182400],
[[[1, 13], [2, 4], [3, 2], [6, 2]], 3887/2090188800],
[[[1, 13], [2, 4], [3, 3], [4, 1]], 64051/313528320],
[[[1, 13], [2, 4], [3, 3], [6, 1]], 153211/1881169920],
[[[1, 13], [2, 4], [4, 1], [7, 1]], 17/967680],
[[[1, 13], [2, 4], [4, 2], [5, 1]], 2281/58060800],
[[[1, 13], [2, 4], [4, 2], [8, 1]], 23/4423680],
[[[1, 13], [2, 6], [3, 1], [4, 2]], 3797/23224320],
[[[1, 13], [2, 6], [3, 1], [5, 1]], 1613/24883200],
[[[1, 13], [2, 6], [3, 2], [4, 1]], 13567/69672960],
[[[1, 13], [2, 6], [3, 2], [6, 1]], 2081/34836480],
[[[1, 13], [2, 6], [4, 1], [5, 1]], 829/12902400],
[[[1, 13], [2, 6], [4, 1], [8, 1]], 13/2211840],
[[[1, 13], [2, 8], [3, 1], [4, 1]], 1/19440],
[[[1, 13], [2, 8], [3, 1], [6, 1]], 1271/139345920],
[[[1, 13], [3, 1], [5, 1], [7, 1]], 1/907200],
[[[1, 13], [3, 1], [5, 1], [9, 1]], 1/46656000],
[[[1, 14], [2, 1], [3, 1], [5, 2]], 433/108864000],
[[[1, 14], [2, 1], [3, 2], [7, 1]], 911/261273600],
[[[1, 14], [2, 1], [3, 2], [9, 1]], 11/55987200],
[[[1, 14], [2, 1], [3, 3], [5, 1]], 181/13063680],
[[[1, 14], [2, 1], [3, 4], [4, 1]], 34487/9405849600],
[[[1, 14], [2, 1], [3, 4], [6, 1]], 113/88179840],
[[[1, 14], [2, 1], [4, 1], [5, 2]], 11/30240000],
[[[1, 14], [2, 1], [5, 1], [7, 1]], 31/72576000],
[[[1, 14], [2, 3], [3, 1], [4, 3]], 1/552960],
[[[1, 14], [2, 3], [3, 1], [7, 1]], 13/1244160],
[[[1, 14], [2, 3], [3, 1], [9, 1]], 83/223948800],
[[[1, 14], [2, 3], [3, 2], [4, 2]], 5989/261273600],
[[[1, 14], [2, 3], [3, 2], [5, 1]], 18269/313528320],
[[[1, 14], [2, 3], [3, 2], [6, 2]], 941/6270566400],
[[[1, 14], [2, 3], [3, 3], [4, 1]], 431/7464960],
[[[1, 14], [2, 3], [3, 3], [6, 1]], 55207/3135283200],
[[[1, 14], [2, 3], [4, 1], [7, 1]], 47/14515200],
[[[1, 14], [2, 3], [4, 2], [5, 1]], 163/36288000],
[[[1, 14], [2, 3], [4, 2], [8, 1]], 31/66355200],
[[[1, 14], [2, 5], [3, 1], [4, 2]], 47/774144],
[[[1, 14], [2, 5], [3, 1], [5, 1]], 3947/87091200],
[[[1, 14], [2, 5], [3, 2], [4, 1]], 70489/627056640],
[[[1, 14], [2, 5], [3, 2], [6, 1]], 8219/313528320],
[[[1, 14], [2, 5], [4, 1], [5, 1]], 10037/348364800],
[[[1, 14], [2, 5], [4, 1], [8, 1]], 7/3317760],
[[[1, 14], [2, 7], [3, 1], [4, 1]], 3713/69672960],
[[[1, 14], [2, 7], [3, 1], [6, 1]], 5123/716636160],
[[[1, 15], [2, 2], [3, 1], [7, 1]], 73/43545600],
[[[1, 15], [2, 2], [3, 1], [9, 1]], 1/24883200],
[[[1, 15], [2, 2], [3, 2], [4, 2]], 1249/1045094400],
[[[1, 15], [2, 2], [3, 2], [5, 1]], 13999/1306368000],
[[[1, 15], [2, 2], [3, 2], [6, 2]], 17/3762339840],
[[[1, 15], [2, 2], [3, 3], [4, 1]], 35501/4702924800],
[[[1, 15], [2, 2], [3, 3], [6, 1]], 1937/1045094400],
[[[1, 15], [2, 2], [4, 1], [7, 1]], 1/3628800],
[[[1, 15], [2, 2], [4, 2], [5, 1]], 13/72576000],
[[[1, 15], [2, 2], [4, 2], [8, 1]], 1/66355200],
[[[1, 15], [2, 4], [3, 1], [4, 2]], 373/32659200],
[[[1, 15], [2, 4], [3, 1], [5, 1]], 2209/130636800],
[[[1, 15], [2, 4], [3, 2], [4, 1]], 107297/3135283200],
[[[1, 15], [2, 4], [3, 2], [6, 1]], 1207/188116992],
[[[1, 15], [2, 4], [4, 1], [5, 1]], 3029/435456000],
[[[1, 15], [2, 4], [4, 1], [8, 1]], 83/199065600],
[[[1, 15], [2, 6], [3, 1], [4, 1]], 6187/209018880],
[[[1, 15], [2, 6], [3, 1], [6, 1]], 13261/4180377600],
[[[1, 16], [2, 1], [3, 1], [7, 1]], 17/130636800],
[[[1, 16], [2, 1], [3, 1], [9, 1]], 1/447897600],
[[[1, 16], [2, 1], [3, 2], [5, 1]], 2479/2612736000],
[[[1, 16], [2, 1], [3, 3], [4, 1]], 811/2351462400],
[[[1, 16], [2, 1], [3, 3], [6, 1]], 97/1343692800],
[[[1, 16], [2, 1], [4, 1], [7, 1]], 1/116121600],
[[[1, 16], [2, 3], [3, 1], [4, 2]], 527/522547200],
[[[1, 16], [2, 3], [3, 1], [5, 1]], 27779/7838208000],
[[[1, 16], [2, 3], [3, 2], [4, 1]], 5759/1045094400],
[[[1, 16], [2, 3], [3, 2], [6, 1]], 341/391910400],
[[[1, 16], [2, 3], [4, 1], [5, 1]], 197/217728000],
[[[1, 16], [2, 3], [4, 1], [8, 1]], 1/22118400],
[[[1, 16], [2, 5], [3, 1], [4, 1]], 14677/1567641600],
[[[1, 16], [2, 5], [3, 1], [6, 1]], 4213/5016453120],
[[[1, 17], [2, 2], [3, 1], [4, 2]], 23/696729600],
[[[1, 17], [2, 2], [3, 1], [5, 1]], 361/870912000],
[[[1, 17], [2, 2], [3, 2], [4, 1]], 1357/3135283200],
[[[1, 17], [2, 2], [3, 2], [6, 1]], 47/783820800],
[[[1, 17], [2, 2], [4, 1], [5, 1]], 619/10450944000],
[[[1, 17], [2, 2], [4, 1], [8, 1]], 1/398131200],
[[[1, 17], [2, 4], [3, 1], [4, 1]], 673/391910400],
[[[1, 17], [2, 4], [3, 1], [6, 1]], 2521/18811699200],
[[[1, 18], [2, 1], [3, 1], [5, 1]], 131/5225472000],
[[[1, 18], [2, 1], [3, 2], [4, 1]], 29/2239488000],
[[[1, 18], [2, 1], [3, 2], [6, 1]], 229/141087744000],
[[[1, 18], [2, 1], [4, 1], [5, 1]], 239/156764160000],
[[[1, 18], [2, 1], [4, 1], [8, 1]], 1/17915904000],
[[[1, 18], [2, 3], [3, 1], [4, 1]], 373/2090188800],
[[[1, 18], [2, 3], [3, 1], [6, 1]], 3137/250822656000],
[[[1, 19], [2, 2], [3, 1], [4, 1]], 911/94058496000],
[[[1, 19], [2, 2], [3, 1], [6, 1]], 47/75246796800],
[[[1, 20], [2, 1], [3, 1], [4, 1]], 1/4702924800],
[[[1, 20], [2, 1], [3, 1], [6, 1]], 29/2257403904000],
[[[2, 3], [6, 2], [14, 1], [18, 2]], 1/756],
[[[2, 3], [6, 3], [10, 1], [18, 2]], 1/810],
[[[2, 3], [6, 3], [10, 2], [30, 1]], 1/225],
[[[2, 3], [6, 5], [10, 1], [30, 1]], 1/2430],
[[[2, 5], [6, 1], [10, 3], [18, 1]], 1/6750],
[[[2, 5], [6, 2], [10, 1], [18, 2]], 1/6480],
[[[2, 5], [6, 2], [10, 2], [30, 1]], 1/1800],
[[[2, 5], [6, 3], [10, 2], [18, 1]], 1/8100],
[[[2, 5], [6, 4], [10, 1], [30, 1]], 1/1620],
[[[2, 5], [6, 4], [14, 1], [18, 1]], 1/756],
[[[2, 5], [6, 5], [10, 1], [18, 1]], 37/29160],
[[[2, 7], [6, 2], [10, 2], [14, 1]], 1/12600],
[[[2, 7], [6, 2], [10, 2], [18, 1]], 1/8100],
[[[2, 7], [6, 3], [10, 1], [30, 1]], 1/32400],
[[[2, 7], [6, 4], [10, 1], [14, 1]], 1/45360],
[[[2, 7], [6, 4], [10, 1], [18, 1]], 13/58320],
[[[2, 9], [6, 1], [10, 2], [14, 1]], 1/12600],
[[[2, 9], [6, 1], [10, 2], [18, 1]], 1/324000],
[[[2, 9], [6, 2], [10, 1], [30, 1]], 1/5443200],
[[[2, 9], [6, 3], [10, 1], [14, 1]], 1/22680],
[[[2, 9], [6, 3], [10, 1], [18, 1]], 7/194400],
[[[2, 11], [6, 2], [10, 1], [14, 1]], 1/43200],
[[[2, 11], [6, 2], [10, 1], [18, 1]], 1/583200],
[[[2, 13], [6, 1], [10, 1], [14, 1]], 1/907200],
[[[2, 13], [6, 1], [10, 1], [18, 1]], 1/46656000],
[[[1, 1], [2, 2], [3, 1], [6, 4], [18, 2]], 7/972],
[[[1, 1], [2, 2], [6, 2], [14, 1], [18, 2]], 1/756],
[[[1, 1], [2, 4], [3, 1], [6, 3], [18, 2]], 1/1944],
[[[1, 1], [2, 4], [3, 1], [6, 6], [18, 1]], 19/8748],
[[[1, 1], [2, 4], [4, 1], [6, 3], [18, 2]], 1/1296],
[[[1, 1], [2, 4], [6, 2], [10, 1], [18, 2]], 1/1080],
[[[1, 1], [2, 4], [6, 2], [10, 2], [30, 1]], 1/300],
[[[1, 1], [2, 4], [6, 4], [10, 1], [30, 1]], 1/540],
[[[1, 1], [2, 4], [6, 4], [14, 1], [18, 1]], 1/756],
[[[1, 1], [2, 6], [3, 1], [6, 2], [10, 3]], 1/3375],
[[[1, 1], [2, 6], [3, 1], [6, 4], [10, 2]], 1/4860],
[[[1, 1], [2, 6], [3, 1], [6, 5], [14, 1]], 1/1944],
[[[1, 1], [2, 6], [3, 1], [6, 5], [18, 1]], 19/17496],
[[[1, 1], [2, 6], [3, 1], [6, 6], [10, 1]], 89/174960],
[[[1, 1], [2, 6], [4, 1], [6, 2], [10, 3]], 1/18000],
[[[1, 1], [2, 6], [4, 1], [6, 2], [18, 2]], 1/25920],
[[[1, 1], [2, 6], [4, 1], [6, 4], [10, 2]], 1/64800],
[[[1, 1], [2, 6], [4, 1], [6, 5], [18, 1]], 37/46656],
[[[1, 1], [2, 6], [4, 1], [6, 6], [8, 1]], 43/699840],
[[[1, 1], [2, 6], [4, 1], [6, 6], [10, 1]], 43/1749600],
[[[1, 1], [2, 6], [4, 1], [8, 1], [10, 3]], 1/6000],
[[[1, 1], [2, 6], [6, 2], [10, 2], [14, 1]], 1/12600],
[[[1, 1], [2, 6], [6, 2], [10, 2], [18, 1]], 1/2700],
[[[1, 1], [2, 6], [6, 3], [10, 1], [30, 1]], 1/2160],
[[[1, 1], [2, 6], [6, 4], [10, 1], [14, 1]], 1/45360],
[[[1, 1], [2, 6], [6, 4], [10, 1], [18, 1]], 11/9720],
[[[1, 1], [2, 8], [3, 1], [6, 1], [10, 3]], 7/108000],
[[[1, 1], [2, 8], [3, 1], [6, 3], [10, 2]], 17/64800],
[[[1, 1], [2, 8], [3, 1], [6, 4], [14, 1]], 1/27216],
[[[1, 1], [2, 8], [3, 1], [6, 4], [18, 1]], 13/233280],
[[[1, 1], [2, 8], [3, 1], [6, 5], [10, 1]], 29/174960],
[[[1, 1], [2, 8], [4, 1], [6, 1], [10, 3]], 1/3600],
[[[1, 1], [2, 8], [4, 1], [6, 3], [10, 2]], 1/5400],
[[[1, 1], [2, 8], [4, 1], [6, 4], [14, 1]], 1/72576],
[[[1, 1], [2, 8], [4, 1], [6, 4], [18, 1]], 19/233280],
[[[1, 1], [2, 8], [4, 1], [6, 5], [8, 1]], 1/93312],
[[[1, 1], [2, 8], [4, 1], [6, 5], [10, 1]], 1/25920],
[[[1, 1], [2, 8], [4, 1], [10, 2], [14, 1]], 1/5600],
[[[1, 1], [2, 8], [6, 1], [10, 2], [14, 1]], 1/3150],
[[[1, 1], [2, 8], [6, 1], [10, 2], [18, 1]], 1/21600],
[[[1, 1], [2, 8], [6, 2], [10, 1], [30, 1]], 1/151200],
[[[1, 1], [2, 8], [6, 3], [10, 1], [14, 1]], 1/5670],
[[[1, 1], [2, 8], [6, 3], [10, 1], [18, 1]], 1/4320],
[[[1, 1], [2, 10], [3, 1], [6, 2], [10, 2]], 17/324000],
[[[1, 1], [2, 10], [3, 1], [6, 3], [14, 1]], 1/51840],
[[[1, 1], [2, 10], [3, 1], [6, 3], [18, 1]], 31/19595520],
[[[1, 1], [2, 10], [3, 1], [6, 4], [10, 1]], 53/699840],
[[[1, 1], [2, 10], [4, 1], [6, 2], [10, 2]], 83/432000],
[[[1, 1], [2, 10], [4, 1], [6, 3], [14, 1]], 1/36288],
[[[1, 1], [2, 10], [4, 1], [6, 3], [18, 1]], 7/311040],
[[[1, 1], [2, 10], [4, 1], [6, 4], [8, 1]], 41/3732480],
[[[1, 1], [2, 10], [4, 1], [6, 4], [10, 1]], 371/4665600],
[[[1, 1], [2, 10], [4, 1], [8, 1], [10, 2]], 1/288000],
[[[1, 1], [2, 10], [6, 2], [10, 1], [14, 1]], 13/75600],
[[[1, 1], [2, 10], [6, 2], [10, 1], [18, 1]], 1/32400],
[[[1, 1], [2, 12], [3, 1], [6, 1], [10, 2]], 127/108864000],
[[[1, 1], [2, 12], [3, 1], [6, 2], [14, 1]], 1/1088640],
[[[1, 1], [2, 12], [3, 1], [6, 2], [18, 1]], 1/55987200],
[[[1, 1], [2, 12], [3, 1], [6, 3], [10, 1]], 1397/97977600],
[[[1, 1], [2, 12], [4, 1], [6, 1], [10, 2]], 1/51840],
[[[1, 1], [2, 12], [4, 1], [6, 2], [14, 1]], 1/69120],
[[[1, 1], [2, 12], [4, 1], [6, 2], [18, 1]], 1/933120],
[[[1, 1], [2, 12], [4, 1], [6, 3], [8, 1]], 23/5598720],
[[[1, 1], [2, 12], [4, 1], [6, 3], [10, 1]], 41/874800],
[[[1, 1], [2, 12], [4, 1], [10, 1], [14, 1]], 1/403200],
[[[1, 1], [2, 12], [6, 1], [10, 1], [14, 1]], 19/907200],
[[[1, 1], [2, 12], [6, 1], [10, 1], [18, 1]], 1/1555200],
[[[1, 1], [2, 14], [3, 1], [6, 1], [14, 1]], 1/87091200],
[[[1, 1], [2, 14], [3, 1], [6, 2], [10, 1]], 143/244944000],
[[[1, 1], [2, 14], [4, 1], [6, 1], [14, 1]], 1/1451520],
[[[1, 1], [2, 14], [4, 1], [6, 1], [18, 1]], 1/74649600],
[[[1, 1], [2, 14], [4, 1], [6, 2], [8, 1]], 41/149299200],
[[[1, 1], [2, 14], [4, 1], [6, 2], [10, 1]], 4117/870912000],
[[[1, 1], [2, 14], [4, 1], [8, 1], [10, 1]], 1/41472000],
[[[1, 1], [2, 16], [3, 1], [6, 1], [10, 1]], 107/15676416000],
[[[1, 1], [2, 16], [4, 1], [6, 1], [8, 1]], 1/149299200],
[[[1, 1], [2, 16], [4, 1], [6, 1], [10, 1]], 79/522547200],
[[[1, 1], [3, 1], [6, 2], [9, 1], [18, 2]], 1/162],
[[[1, 1], [3, 3], [5, 1], [9, 1], [15, 1]], 1/135],
[[[1, 2], [2, 1], [3, 2], [7, 1], [9, 2]], 1/756],
[[[1, 2], [2, 1], [3, 4], [6, 1], [9, 2]], 7/972],
[[[1, 2], [2, 3], [3, 1], [6, 3], [18, 2]], 1/648],
[[[1, 2], [2, 3], [3, 2], [6, 5], [18, 1]], 4/729],
[[[1, 2], [2, 3], [3, 4], [6, 3], [9, 1]], 5/5832],
[[[1, 2], [2, 3], [4, 1], [6, 3], [18, 2]], 1/1296],
[[[1, 2], [2, 3], [4, 2], [6, 2], [18, 2]], 1/1728],
[[[1, 2], [2, 3], [6, 2], [10, 1], [18, 2]], 1/2160],
[[[1, 2], [2, 3], [6, 2], [10, 2], [30, 1]], 1/600],
[[[1, 2], [2, 5], [3, 1], [6, 5], [14, 1]], 1/1944],
[[[1, 2], [2, 5], [3, 1], [6, 5], [18, 1]], 19/5832],
[[[1, 2], [2, 5], [3, 2], [6, 3], [10, 2]], 1/2700],
[[[1, 2], [2, 5], [3, 2], [6, 4], [14, 1]], 1/648],
[[[1, 2], [2, 5], [3, 2], [6, 4], [18, 1]], 19/11664],
[[[1, 2], [2, 5], [3, 2], [6, 5], [10, 1]], 91/58320],
[[[1, 2], [2, 5], [4, 1], [6, 2], [18, 2]], 1/2592],
[[[1, 2], [2, 5], [4, 1], [6, 5], [18, 1]], 37/46656],
[[[1, 2], [2, 5], [4, 2], [6, 4], [18, 1]], 1/1728],
[[[1, 2], [2, 5], [6, 3], [10, 1], [30, 1]], 1/720],
[[[1, 2], [2, 5], [6, 4], [10, 1], [18, 1]], 1/2160],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 6]], 89/279936],
[[[1, 2], [2, 7], [3, 1], [6, 1], [10, 3]], 1/3600],
[[[1, 2], [2, 7], [3, 1], [6, 3], [10, 2]], 1/1200],
[[[1, 2], [2, 7], [3, 1], [6, 4], [14, 1]], 1/6804],
[[[1, 2], [2, 7], [3, 1], [6, 4], [18, 1]], 1/1728],
[[[1, 2], [2, 7], [3, 1], [6, 5], [10, 1]], 79/116640],
[[[1, 2], [2, 7], [3, 2], [6, 2], [10, 2]], 1/8640],
[[[1, 2], [2, 7], [3, 2], [6, 3], [14, 1]], 1/18144],
[[[1, 2], [2, 7], [3, 2], [6, 3], [18, 1]], 1/466560],
[[[1, 2], [2, 7], [3, 2], [6, 4], [10, 1]], 1/2430],
[[[1, 2], [2, 7], [4, 1], [6, 1], [10, 3]], 7/18000],
[[[1, 2], [2, 7], [4, 1], [6, 3], [10, 2]], 1/4050],
[[[1, 2], [2, 7], [4, 1], [6, 4], [14, 1]], 1/36288],
[[[1, 2], [2, 7], [4, 1], [6, 4], [18, 1]], 13/23328],
[[[1, 2], [2, 7], [4, 1], [6, 5], [8, 1]], 1/31104],
[[[1, 2], [2, 7], [4, 1], [6, 5], [10, 1]], 11/233280],
[[[1, 2], [2, 7], [4, 1], [10, 2], [14, 1]], 1/2800],
[[[1, 2], [2, 7], [4, 2], [6, 2], [10, 2]], 1/9600],
[[[1, 2], [2, 7], [4, 2], [6, 3], [18, 1]], 1/20736],
[[[1, 2], [2, 7], [4, 2], [6, 4], [8, 1]], 1/41472],
[[[1, 2], [2, 7], [4, 2], [6, 4], [10, 1]], 1/51840],
[[[1, 2], [2, 7], [4, 2], [8, 1], [10, 2]], 1/3200],
[[[1, 2], [2, 7], [6, 1], [10, 2], [14, 1]], 1/4200],
[[[1, 2], [2, 7], [6, 1], [10, 2], [18, 1]], 1/7200],
[[[1, 2], [2, 7], [6, 2], [10, 1], [30, 1]], 1/14400],
[[[1, 2], [2, 7], [6, 3], [10, 1], [14, 1]], 1/7560],
[[[1, 2], [2, 7], [6, 3], [10, 1], [18, 1]], 1/2592],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 5]], 227/2799360],
[[[1, 2], [2, 9], [3, 1], [6, 2], [10, 2]], 1/2400],
[[[1, 2], [2, 9], [3, 1], [6, 3], [14, 1]], 13/90720],
[[[1, 2], [2, 9], [3, 1], [6, 3], [18, 1]], 17/544320],
[[[1, 2], [2, 9], [3, 1], [6, 4], [10, 1]], 23/46656],
[[[1, 2], [2, 9], [3, 2], [6, 2], [14, 1]], 1/725760],
[[[1, 2], [2, 9], [3, 2], [6, 3], [10, 1]], 49/777600],
[[[1, 2], [2, 9], [4, 1], [6, 2], [10, 2]], 37/43200],
[[[1, 2], [2, 9], [4, 1], [6, 3], [14, 1]], 5/36288],
[[[1, 2], [2, 9], [4, 1], [6, 3], [18, 1]], 13/77760],
[[[1, 2], [2, 9], [4, 1], [6, 4], [8, 1]], 17/248832],
[[[1, 2], [2, 9], [4, 1], [6, 4], [10, 1]], 157/466560],
[[[1, 2], [2, 9], [4, 1], [8, 1], [10, 2]], 1/19200],
[[[1, 2], [2, 9], [4, 2], [6, 1], [10, 2]], 1/3200],
[[[1, 2], [2, 9], [4, 2], [6, 2], [14, 1]], 1/32256],
[[[1, 2], [2, 9], [4, 2], [6, 2], [18, 1]], 1/20736],
[[[1, 2], [2, 9], [4, 2], [6, 3], [8, 1]], 1/20736],
[[[1, 2], [2, 9], [4, 2], [6, 3], [10, 1]], 7/51840],
[[[1, 2], [2, 9], [4, 2], [10, 1], [14, 1]], 1/8960],
[[[1, 2], [2, 9], [6, 2], [10, 1], [14, 1]], 1/2520],
[[[1, 2], [2, 9], [6, 2], [10, 1], [18, 1]], 1/6480],
[[[1, 2], [2, 11], [3, 1], [4, 1], [6, 4]], 1/21870],
[[[1, 2], [2, 11], [3, 1], [6, 1], [10, 2]], 1/44800],
[[[1, 2], [2, 11], [3, 1], [6, 2], [14, 1]], 19/1088640],
[[[1, 2], [2, 11], [3, 1], [6, 2], [18, 1]], 1/1866240],
[[[1, 2], [2, 11], [3, 1], [6, 3], [10, 1]], 3637/21772800],
[[[1, 2], [2, 11], [3, 2], [6, 2], [10, 1]], 19/13063680],
[[[1, 2], [2, 11], [4, 1], [6, 1], [10, 2]], 101/432000],
[[[1, 2], [2, 11], [4, 1], [6, 2], [14, 1]], 59/483840],
[[[1, 2], [2, 11], [4, 1], [6, 2], [18, 1]], 19/933120],
[[[1, 2], [2, 11], [4, 1], [6, 3], [8, 1]], 13/311040],
[[[1, 2], [2, 11], [4, 1], [6, 3], [10, 1]], 863/2332800],
[[[1, 2], [2, 11], [4, 1], [10, 1], [14, 1]], 17/403200],
[[[1, 2], [2, 11], [4, 2], [6, 1], [14, 1]], 1/32256],
[[[1, 2], [2, 11], [4, 2], [6, 1], [18, 1]], 1/829440],
[[[1, 2], [2, 11], [4, 2], [6, 2], [8, 1]], 7/276480],
[[[1, 2], [2, 11], [4, 2], [6, 2], [10, 1]], 59/460800],
[[[1, 2], [2, 11], [4, 2], [8, 1], [10, 1]], 1/230400],
[[[1, 2], [2, 11], [6, 1], [10, 1], [14, 1]], 1/8400],
[[[1, 2], [2, 11], [6, 1], [10, 1], [18, 1]], 7/1036800],
[[[1, 2], [2, 13], [3, 1], [4, 1], [6, 3]], 12647/1567641600],
[[[1, 2], [2, 13], [3, 1], [6, 1], [14, 1]], 31/87091200],
[[[1, 2], [2, 13], [3, 1], [6, 2], [10, 1]], 853/65318400],
[[[1, 2], [2, 13], [4, 1], [6, 1], [14, 1]], 1/72576],
[[[1, 2], [2, 13], [4, 1], [6, 1], [18, 1]], 31/74649600],
[[[1, 2], [2, 13], [4, 1], [6, 2], [8, 1]], 29/4976640],
[[[1, 2], [2, 13], [4, 1], [6, 2], [10, 1]], 10319/130636800],
[[[1, 2], [2, 13], [4, 1], [8, 1], [10, 1]], 1/1382400],
[[[1, 2], [2, 13], [4, 2], [6, 1], [8, 1]], 1/829440],
[[[1, 2], [2, 13], [4, 2], [6, 1], [10, 1]], 43/4147200],
[[[1, 2], [2, 15], [3, 1], [4, 1], [6, 2]], 509/1567641600],
[[[1, 2], [2, 15], [3, 1], [6, 1], [10, 1]], 121/522547200],
[[[1, 2], [2, 15], [4, 1], [6, 1], [8, 1]], 11/49766400],
[[[1, 2], [2, 15], [4, 1], [6, 1], [10, 1]], 10837/2612736000],
[[[1, 2], [2, 17], [3, 1], [4, 1], [6, 1]], 59/15676416000],
[[[1, 3], [2, 2], [3, 2], [4, 2], [9, 2]], 1/1728],
[[[1, 3], [2, 2], [3, 2], [5, 1], [9, 2]], 1/2160],
[[[1, 3], [2, 2], [3, 2], [5, 2], [15, 1]], 1/600],
[[[1, 3], [2, 2], [3, 3], [4, 1], [9, 2]], 1/1296],
[[[1, 3], [2, 2], [3, 3], [6, 1], [9, 2]], 1/648],
[[[1, 3], [2, 2], [3, 3], [6, 4], [18, 1]], 5/5832],
[[[1, 3], [2, 2], [3, 5], [6, 2], [9, 1]], 4/729],
[[[1, 3], [2, 4], [3, 2], [6, 4], [14, 1]], 1/648],
[[[1, 3], [2, 4], [3, 2], [6, 4], [18, 1]], 19/3888],
[[[1, 3], [2, 4], [3, 3], [6, 3], [7, 1]], 5/9072],
[[[1, 3], [2, 4], [3, 3], [6, 3], [14, 1]], 5/9072],
[[[1, 3], [2, 4], [3, 3], [6, 4], [10, 1]], 13/19440],
[[[1, 3], [2, 4], [4, 1], [6, 2], [18, 2]], 1/1728],
[[[1, 3], [2, 4], [6, 3], [10, 1], [30, 1]], 1/2160],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 6]], 89/279936],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 5]], 7/31104],
[[[1, 3], [2, 6], [3, 1], [6, 1], [10, 3]], 1/12000],
[[[1, 3], [2, 6], [3, 1], [6, 3], [10, 2]], 1/21600],
[[[1, 3], [2, 6], [3, 1], [6, 4], [14, 1]], 1/9072],
[[[1, 3], [2, 6], [3, 1], [6, 4], [18, 1]], 23/15552],
[[[1, 3], [2, 6], [3, 1], [6, 5], [10, 1]], 7/38880],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 5]], 91/93312],
[[[1, 3], [2, 6], [3, 2], [6, 2], [10, 2]], 1/2400],
[[[1, 3], [2, 6], [3, 2], [6, 3], [14, 1]], 1/4536],
[[[1, 3], [2, 6], [3, 2], [6, 3], [18, 1]], 1/31104],
[[[1, 3], [2, 6], [3, 2], [6, 4], [10, 1]], 23/12960],
[[[1, 3], [2, 6], [3, 3], [6, 3], [10, 1]], 11/77760],
[[[1, 3], [2, 6], [4, 1], [6, 4], [14, 1]], 1/72576],
[[[1, 3], [2, 6], [4, 1], [6, 4], [18, 1]], 11/15552],
[[[1, 3], [2, 6], [4, 1], [10, 2], [14, 1]], 1/5600],
[[[1, 3], [2, 6], [4, 2], [6, 2], [10, 2]], 1/14400],
[[[1, 3], [2, 6], [4, 2], [6, 3], [18, 1]], 1/10368],
[[[1, 3], [2, 6], [4, 2], [6, 4], [8, 1]], 1/41472],
[[[1, 3], [2, 6], [4, 2], [6, 4], [10, 1]], 1/103680],
[[[1, 3], [2, 6], [4, 2], [8, 1], [10, 2]], 1/3200],
[[[1, 3], [2, 6], [6, 1], [10, 2], [18, 1]], 1/21600],
[[[1, 3], [2, 6], [6, 2], [10, 1], [30, 1]], 1/4320],
[[[1, 3], [2, 6], [6, 3], [10, 1], [18, 1]], 1/38880],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 5]], 29/69984],
[[[1, 3], [2, 8], [3, 1], [4, 2], [6, 4]], 1/10368],
[[[1, 3], [2, 8], [3, 1], [6, 2], [10, 2]], 19/21600],
[[[1, 3], [2, 8], [3, 1], [6, 3], [14, 1]], 1/3024],
[[[1, 3], [2, 8], [3, 1], [6, 3], [18, 1]], 29/155520],
[[[1, 3], [2, 8], [3, 1], [6, 4], [10, 1]], 13/15552],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 4]], 59/311040],
[[[1, 3], [2, 8], [3, 2], [6, 2], [14, 1]], 1/45360],
[[[1, 3], [2, 8], [3, 2], [6, 3], [10, 1]], 23/51840],
[[[1, 3], [2, 8], [4, 1], [6, 2], [10, 2]], 23/28800],
[[[1, 3], [2, 8], [4, 1], [6, 3], [14, 1]], 1/5184],
[[[1, 3], [2, 8], [4, 1], [6, 3], [18, 1]], 1/2592],
[[[1, 3], [2, 8], [4, 1], [6, 4], [8, 1]], 1/9216],
[[[1, 3], [2, 8], [4, 1], [6, 4], [10, 1]], 89/311040],
[[[1, 3], [2, 8], [4, 1], [8, 1], [10, 2]], 1/6400],
[[[1, 3], [2, 8], [4, 2], [6, 1], [10, 2]], 23/28800],
[[[1, 3], [2, 8], [4, 2], [6, 2], [14, 1]], 1/10752],
[[[1, 3], [2, 8], [4, 2], [6, 2], [18, 1]], 5/20736],
[[[1, 3], [2, 8], [4, 2], [6, 3], [8, 1]], 1/5184],
[[[1, 3], [2, 8], [4, 2], [6, 3], [10, 1]], 17/51840],
[[[1, 3], [2, 8], [4, 2], [10, 1], [14, 1]], 3/8960],
[[[1, 3], [2, 8], [4, 3], [6, 1], [18, 1]], 1/27648],
[[[1, 3], [2, 8], [4, 3], [6, 2], [8, 1]], 1/18432],
[[[1, 3], [2, 8], [4, 3], [6, 2], [10, 1]], 1/15360],
[[[1, 3], [2, 8], [4, 3], [8, 1], [10, 1]], 1/5120],
[[[1, 3], [2, 8], [6, 2], [10, 1], [14, 1]], 1/3780],
[[[1, 3], [2, 8], [6, 2], [10, 1], [18, 1]], 1/3888],
[[[1, 3], [2, 10], [3, 1], [4, 1], [6, 4]], 959/2799360],
[[[1, 3], [2, 10], [3, 1], [4, 2], [6, 3]], 89/829440],
[[[1, 3], [2, 10], [3, 1], [6, 1], [10, 2]], 109/864000],
[[[1, 3], [2, 10], [3, 1], [6, 2], [14, 1]], 1/10080],
[[[1, 3], [2, 10], [3, 1], [6, 2], [18, 1]], 7/1244160],
[[[1, 3], [2, 10], [3, 1], [6, 3], [10, 1]], 19/28800],
[[[1, 3], [2, 10], [3, 2], [4, 1], [6, 3]], 23/622080],
[[[1, 3], [2, 10], [3, 2], [6, 2], [10, 1]], 389/14515200],
[[[1, 3], [2, 10], [4, 1], [6, 1], [10, 2]], 23/28800],
[[[1, 3], [2, 10], [4, 1], [6, 2], [14, 1]], 43/120960],
[[[1, 3], [2, 10], [4, 1], [6, 2], [18, 1]], 1/8640],
[[[1, 3], [2, 10], [4, 1], [6, 3], [8, 1]], 1/6912],
[[[1, 3], [2, 10], [4, 1], [6, 3], [10, 1]], 143/155520],
[[[1, 3], [2, 10], [4, 1], [10, 1], [14, 1]], 19/100800],
[[[1, 3], [2, 10], [4, 2], [6, 1], [14, 1]], 1/5376],
[[[1, 3], [2, 10], [4, 2], [6, 1], [18, 1]], 17/829440],
[[[1, 3], [2, 10], [4, 2], [6, 2], [8, 1]], 13/69120],
[[[1, 3], [2, 10], [4, 2], [6, 2], [10, 1]], 163/230400],
[[[1, 3], [2, 10], [4, 2], [8, 1], [10, 1]], 1/14400],
[[[1, 3], [2, 10], [4, 3], [6, 1], [8, 1]], 1/18432],
[[[1, 3], [2, 10], [4, 3], [6, 1], [10, 1]], 7/46080],
[[[1, 3], [2, 10], [6, 1], [10, 1], [14, 1]], 1/3780],
[[[1, 3], [2, 10], [6, 1], [10, 1], [18, 1]], 23/777600],
[[[1, 3], [2, 12], [3, 1], [4, 1], [6, 3]], 32503/313528320],
[[[1, 3], [2, 12], [3, 1], [4, 2], [6, 2]], 43/2488320],
[[[1, 3], [2, 12], [3, 1], [6, 1], [14, 1]], 23/5806080],
[[[1, 3], [2, 12], [3, 1], [6, 2], [10, 1]], 2161/21772800],
[[[1, 3], [2, 12], [3, 2], [4, 1], [6, 2]], 887/1045094400],
[[[1, 3], [2, 12], [4, 1], [6, 1], [14, 1]], 127/1451520],
[[[1, 3], [2, 12], [4, 1], [6, 1], [18, 1]], 23/4976640],
[[[1, 3], [2, 12], [4, 1], [6, 2], [8, 1]], 1/24576],
[[[1, 3], [2, 12], [4, 1], [6, 2], [10, 1]], 25019/58060800],
[[[1, 3], [2, 12], [4, 1], [8, 1], [10, 1]], 7/921600],
[[[1, 3], [2, 12], [4, 2], [6, 1], [8, 1]], 19/829440],
[[[1, 3], [2, 12], [4, 2], [6, 1], [10, 1]], 611/4147200],
[[[1, 3], [2, 14], [3, 1], [4, 1], [6, 2]], 5959/783820800],
[[[1, 3], [2, 14], [3, 1], [4, 2], [6, 1]], 43/116121600],
[[[1, 3], [2, 14], [3, 1], [6, 1], [10, 1]], 1289/435456000],
[[[1, 3], [2, 14], [4, 1], [6, 1], [8, 1]], 1/368640],
[[[1, 3], [2, 14], [4, 1], [6, 1], [10, 1]], 1031/24883200],
[[[1, 3], [2, 16], [3, 1], [4, 1], [6, 1]], 103/783820800],
[[[1, 3], [3, 2], [5, 1], [7, 1], [15, 1]], 1/210],
[[[1, 4], [2, 1], [3, 2], [5, 1], [9, 2]], 1/1080],
[[[1, 4], [2, 1], [3, 2], [5, 2], [15, 1]], 1/300],
[[[1, 4], [2, 1], [3, 3], [4, 1], [9, 2]], 1/1296],
[[[1, 4], [2, 1], [3, 3], [6, 1], [9, 2]], 1/1944],
[[[1, 4], [2, 1], [3, 4], [5, 1], [15, 1]], 1/540],
[[[1, 4], [2, 1], [3, 4], [7, 1], [9, 1]], 1/756],
[[[1, 4], [2, 1], [3, 6], [6, 1], [9, 1]], 19/8748],
[[[1, 4], [2, 3], [3, 2], [4, 1], [9, 2]], 1/1728],
[[[1, 4], [2, 3], [3, 3], [5, 1], [15, 1]], 1/2160],
[[[1, 4], [2, 3], [3, 3], [6, 3], [7, 1]], 5/9072],
[[[1, 4], [2, 3], [3, 3], [6, 3], [14, 1]], 5/9072],
[[[1, 4], [2, 3], [3, 4], [5, 1], [6, 3]], 13/19440],
[[[1, 4], [2, 3], [3, 4], [6, 2], [7, 1]], 1/648],
[[[1, 4], [2, 3], [3, 4], [6, 2], [9, 1]], 19/3888],
[[[1, 4], [2, 5], [3, 1], [6, 4], [18, 1]], 19/46656],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 5]], 91/93312],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 4]], 7/10368],
[[[1, 4], [2, 5], [3, 2], [6, 2], [10, 2]], 1/14400],
[[[1, 4], [2, 5], [3, 2], [6, 3], [14, 1]], 1/6048],
[[[1, 4], [2, 5], [3, 2], [6, 3], [18, 1]], 1/10368],
[[[1, 4], [2, 5], [3, 2], [6, 4], [10, 1]], 7/12960],
[[[1, 4], [2, 5], [3, 3], [4, 1], [6, 4]], 13/31104],
[[[1, 4], [2, 5], [3, 3], [4, 2], [6, 3]], 5/20736],
[[[1, 4], [2, 5], [3, 3], [5, 1], [6, 3]], 1/5184],
[[[1, 4], [2, 5], [3, 3], [6, 2], [9, 1]], 1/31104],
[[[1, 4], [2, 5], [3, 3], [6, 3], [10, 1]], 1/1620],
[[[1, 4], [2, 5], [3, 4], [4, 1], [6, 3]], 13/31104],
[[[1, 4], [2, 5], [4, 2], [6, 3], [18, 1]], 1/20736],
[[[1, 4], [2, 5], [6, 2], [10, 1], [30, 1]], 1/5760],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 5]], 79/186624],
[[[1, 4], [2, 7], [3, 1], [4, 2], [6, 4]], 13/62208],
[[[1, 4], [2, 7], [3, 1], [4, 3], [6, 3]], 1/27648],
[[[1, 4], [2, 7], [3, 1], [6, 2], [10, 2]], 1/4320],
[[[1, 4], [2, 7], [3, 1], [6, 3], [14, 1]], 1/4536],
[[[1, 4], [2, 7], [3, 1], [6, 3], [18, 1]], 19/46656],
[[[1, 4], [2, 7], [3, 1], [6, 4], [10, 1]], 19/233280],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 4]], 1/972],
[[[1, 4], [2, 7], [3, 2], [4, 2], [6, 3]], 7/41472],
[[[1, 4], [2, 7], [3, 2], [6, 2], [14, 1]], 1/12096],
[[[1, 4], [2, 7], [3, 2], [6, 3], [10, 1]], 43/51840],
[[[1, 4], [2, 7], [3, 3], [4, 1], [6, 3]], 1/15552],
[[[1, 4], [2, 7], [4, 1], [6, 2], [10, 2]], 1/21600],
[[[1, 4], [2, 7], [4, 1], [6, 3], [14, 1]], 1/12096],
[[[1, 4], [2, 7], [4, 1], [6, 3], [18, 1]], 1/3888],
[[[1, 4], [2, 7], [4, 1], [6, 4], [8, 1]], 1/248832],
[[[1, 4], [2, 7], [4, 1], [6, 4], [10, 1]], 1/155520],
[[[1, 4], [2, 7], [4, 1], [8, 1], [10, 2]], 1/19200],
[[[1, 4], [2, 7], [4, 2], [6, 1], [10, 2]], 1/2400],
[[[1, 4], [2, 7], [4, 2], [6, 2], [14, 1]], 1/10752],
[[[1, 4], [2, 7], [4, 2], [6, 2], [18, 1]], 7/20736],
[[[1, 4], [2, 7], [4, 2], [6, 3], [8, 1]], 1/6912],
[[[1, 4], [2, 7], [4, 2], [6, 3], [10, 1]], 1/6480],
[[[1, 4], [2, 7], [4, 2], [10, 1], [14, 1]], 3/8960],
[[[1, 4], [2, 7], [4, 3], [6, 1], [18, 1]], 1/9216],
[[[1, 4], [2, 7], [4, 3], [6, 2], [8, 1]], 1/9216],
[[[1, 4], [2, 7], [4, 3], [6, 2], [10, 1]], 1/11520],
[[[1, 4], [2, 7], [4, 3], [8, 1], [10, 1]], 1/2560],
[[[1, 4], [2, 7], [6, 2], [10, 1], [14, 1]], 1/60480],
[[[1, 4], [2, 7], [6, 2], [10, 1], [18, 1]], 1/12960],
[[[1, 4], [2, 9], [3, 1], [4, 1], [6, 4]], 149/186624],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 3]], 467/829440],
[[[1, 4], [2, 9], [3, 1], [4, 3], [6, 2]], 1/9216],
[[[1, 4], [2, 9], [3, 1], [6, 1], [10, 2]], 11/43200],
[[[1, 4], [2, 9], [3, 1], [6, 2], [14, 1]], 1/4536],
[[[1, 4], [2, 9], [3, 1], [6, 2], [18, 1]], 23/933120],
[[[1, 4], [2, 9], [3, 1], [6, 3], [10, 1]], 293/311040],
[[[1, 4], [2, 9], [3, 2], [4, 1], [6, 3]], 37/124416],
[[[1, 4], [2, 9], [3, 2], [4, 2], [6, 2]], 67/1658880],
[[[1, 4], [2, 9], [3, 2], [6, 2], [10, 1]], 73/518400],
[[[1, 4], [2, 9], [4, 1], [6, 1], [10, 2]], 73/86400],
[[[1, 4], [2, 9], [4, 1], [6, 2], [14, 1]], 5/12096],
[[[1, 4], [2, 9], [4, 1], [6, 2], [18, 1]], 1/3888],
[[[1, 4], [2, 9], [4, 1], [6, 3], [8, 1]], 11/62208],
[[[1, 4], [2, 9], [4, 1], [6, 3], [10, 1]], 109/155520],
[[[1, 4], [2, 9], [4, 1], [10, 1], [14, 1]], 1/3360],
[[[1, 4], [2, 9], [4, 2], [6, 1], [14, 1]], 1/2688],
[[[1, 4], [2, 9], [4, 2], [6, 1], [18, 1]], 19/207360],
[[[1, 4], [2, 9], [4, 2], [6, 2], [8, 1]], 1/2304],
[[[1, 4], [2, 9], [4, 2], [6, 2], [10, 1]], 31/27648],
[[[1, 4], [2, 9], [4, 2], [8, 1], [10, 1]], 1/3840],
[[[1, 4], [2, 9], [4, 3], [6, 1], [8, 1]], 5/18432],
[[[1, 4], [2, 9], [4, 3], [6, 1], [10, 1]], 5/9216],
[[[1, 4], [2, 9], [6, 1], [10, 1], [14, 1]], 13/60480],
[[[1, 4], [2, 9], [6, 1], [10, 1], [18, 1]], 11/207360],
[[[1, 4], [2, 11], [3, 1], [4, 1], [6, 3]], 8297/17418240],
[[[1, 4], [2, 11], [3, 1], [4, 2], [6, 2]], 37/207360],
[[[1, 4], [2, 11], [3, 1], [4, 3], [6, 1]], 7/552960],
[[[1, 4], [2, 11], [3, 1], [6, 1], [14, 1]], 113/5806080],
[[[1, 4], [2, 11], [3, 1], [6, 2], [10, 1]], 103/311040],
[[[1, 4], [2, 11], [3, 2], [4, 1], [6, 2]], 3439/209018880],
[[[1, 4], [2, 11], [4, 1], [6, 1], [14, 1]], 29/120960],
[[[1, 4], [2, 11], [4, 1], [6, 1], [18, 1]], 113/4976640],
[[[1, 4], [2, 11], [4, 1], [6, 2], [8, 1]], 101/829440],
[[[1, 4], [2, 11], [4, 1], [6, 2], [10, 1]], 37/38400],
[[[1, 4], [2, 11], [4, 1], [8, 1], [10, 1]], 23/691200],
[[[1, 4], [2, 11], [4, 2], [6, 1], [8, 1]], 1/7680],
[[[1, 4], [2, 11], [4, 2], [6, 1], [10, 1]], 217/345600],
[[[1, 4], [2, 13], [3, 1], [4, 1], [6, 2]], 937/14929920],
[[[1, 4], [2, 13], [3, 1], [4, 2], [6, 1]], 1373/174182400],
[[[1, 4], [2, 13], [3, 1], [6, 1], [10, 1]], 9433/522547200],
[[[1, 4], [2, 13], [4, 1], [6, 1], [8, 1]], 31/1990656],
[[[1, 4], [2, 13], [4, 1], [6, 1], [10, 1]], 33119/174182400],
[[[1, 4], [2, 15], [3, 1], [4, 1], [6, 1]], 919/522547200],
[[[1, 5], [2, 2], [3, 2], [4, 1], [9, 2]], 1/2592],
[[[1, 5], [2, 2], [3, 3], [5, 1], [15, 1]], 1/720],
[[[1, 5], [2, 2], [3, 3], [5, 2], [6, 2]], 1/2700],
[[[1, 5], [2, 2], [3, 4], [4, 2], [9, 1]], 1/1728],
[[[1, 5], [2, 2], [3, 4], [5, 1], [9, 1]], 1/2160],
[[[1, 5], [2, 2], [3, 4], [6, 2], [7, 1]], 1/648],
[[[1, 5], [2, 2], [3, 4], [6, 2], [9, 1]], 19/11664],
[[[1, 5], [2, 2], [3, 5], [4, 1], [9, 1]], 37/46656],
[[[1, 5], [2, 2], [3, 5], [5, 1], [6, 2]], 91/58320],
[[[1, 5], [2, 2], [3, 5], [6, 1], [7, 1]], 1/1944],
[[[1, 5], [2, 2], [3, 5], [6, 1], [9, 1]], 19/5832],
[[[1, 5], [2, 4], [3, 2], [5, 1], [15, 1]], 1/5760],
[[[1, 5], [2, 4], [3, 2], [5, 2], [6, 2]], 1/14400],
[[[1, 5], [2, 4], [3, 2], [6, 3], [18, 1]], 1/31104],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 4]], 13/31104],
[[[1, 5], [2, 4], [3, 3], [4, 2], [6, 3]], 5/20736],
[[[1, 5], [2, 4], [3, 3], [4, 2], [9, 1]], 1/20736],
[[[1, 5], [2, 4], [3, 3], [5, 1], [6, 3]], 1/1620],
[[[1, 5], [2, 4], [3, 3], [6, 2], [7, 1]], 1/6048],
[[[1, 5], [2, 4], [3, 3], [6, 2], [9, 1]], 1/10368],
[[[1, 5], [2, 4], [3, 3], [6, 3], [10, 1]], 1/5184],
[[[1, 5], [2, 4], [3, 4], [4, 1], [6, 3]], 13/31104],
[[[1, 5], [2, 4], [3, 4], [4, 2], [6, 2]], 7/10368],
[[[1, 5], [2, 4], [3, 4], [5, 1], [6, 2]], 7/12960],
[[[1, 5], [2, 4], [3, 4], [6, 1], [9, 1]], 19/46656],
[[[1, 5], [2, 4], [3, 5], [4, 1], [6, 2]], 91/93312],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 4]], 5/62208],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 3]], 1/27648],
[[[1, 5], [2, 6], [3, 1], [4, 3], [9, 1]], 1/27648],
[[[1, 5], [2, 6], [3, 1], [6, 3], [14, 1]], 1/72576],
[[[1, 5], [2, 6], [3, 1], [6, 3], [18, 1]], 13/62208],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 4]], 23/20736],
[[[1, 5], [2, 6], [3, 2], [4, 2], [6, 3]], 5/13824],
[[[1, 5], [2, 6], [3, 2], [4, 3], [6, 2]], 1/9216],
[[[1, 5], [2, 6], [3, 2], [6, 2], [7, 1]], 1/48384],
[[[1, 5], [2, 6], [3, 2], [6, 2], [14, 1]], 1/12096],
[[[1, 5], [2, 6], [3, 2], [6, 3], [10, 1]], 7/51840],
[[[1, 5], [2, 6], [3, 3], [4, 1], [6, 3]], 23/31104],
[[[1, 5], [2, 6], [3, 3], [4, 2], [6, 2]], 1/6912],
[[[1, 5], [2, 6], [4, 1], [6, 3], [18, 1]], 1/62208],
[[[1, 5], [2, 6], [4, 2], [6, 2], [14, 1]], 1/32256],
[[[1, 5], [2, 6], [4, 2], [6, 2], [18, 1]], 1/6912],
[[[1, 5], [2, 6], [4, 2], [10, 1], [14, 1]], 1/8960],
[[[1, 5], [2, 6], [4, 3], [6, 1], [18, 1]], 1/9216],
[[[1, 5], [2, 6], [4, 3], [6, 2], [8, 1]], 1/18432],
[[[1, 5], [2, 6], [4, 3], [6, 2], [10, 1]], 1/46080],
[[[1, 5], [2, 6], [4, 3], [8, 1], [10, 1]], 1/5120],
[[[1, 5], [2, 8], [3, 1], [4, 1], [6, 4]], 101/186624],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 3]], 137/165888],
[[[1, 5], [2, 8], [3, 1], [4, 3], [6, 2]], 5/13824],
[[[1, 5], [2, 8], [3, 1], [4, 4], [6, 1]], 1/24576],
[[[1, 5], [2, 8], [3, 1], [6, 1], [10, 2]], 1/7680],
[[[1, 5], [2, 8], [3, 1], [6, 2], [14, 1]], 13/72576],
[[[1, 5], [2, 8], [3, 1], [6, 2], [18, 1]], 11/248832],
[[[1, 5], [2, 8], [3, 1], [6, 3], [10, 1]], 5/20736],
[[[1, 5], [2, 8], [3, 2], [4, 1], [6, 3]], 31/41472],
[[[1, 5], [2, 8], [3, 2], [4, 2], [6, 2]], 127/552960],
[[[1, 5], [2, 8], [3, 2], [6, 2], [10, 1]], 53/207360],
[[[1, 5], [2, 8], [4, 1], [6, 1], [10, 2]], 1/4800],
[[[1, 5], [2, 8], [4, 1], [6, 2], [14, 1]], 17/96768],
[[[1, 5], [2, 8], [4, 1], [6, 2], [18, 1]], 13/62208],
[[[1, 5], [2, 8], [4, 1], [6, 3], [8, 1]], 1/41472],
[[[1, 5], [2, 8], [4, 1], [6, 3], [10, 1]], 11/155520],
[[[1, 5], [2, 8], [4, 1], [10, 1], [14, 1]], 1/5376],
[[[1, 5], [2, 8], [4, 2], [6, 1], [14, 1]], 5/16128],
[[[1, 5], [2, 8], [4, 2], [6, 1], [18, 1]], 1/6912],
[[[1, 5], [2, 8], [4, 2], [6, 2], [8, 1]], 1/3456],
[[[1, 5], [2, 8], [4, 2], [6, 2], [10, 1]], 71/138240],
[[[1, 5], [2, 8], [4, 2], [8, 1], [10, 1]], 1/3840],
[[[1, 5], [2, 8], [4, 3], [6, 1], [8, 1]], 7/18432],
[[[1, 5], [2, 8], [4, 3], [6, 1], [10, 1]], 5/9216],
[[[1, 5], [2, 8], [6, 1], [10, 1], [14, 1]], 1/20160],
[[[1, 5], [2, 8], [6, 1], [10, 1], [18, 1]], 1/34560],
[[[1, 5], [2, 10], [3, 1], [4, 1], [6, 3]], 2299/2488320],
[[[1, 5], [2, 10], [3, 1], [4, 2], [6, 2]], 259/414720],
[[[1, 5], [2, 10], [3, 1], [4, 3], [6, 1]], 7/69120],
[[[1, 5], [2, 10], [3, 1], [6, 1], [14, 1]], 257/5806080],
[[[1, 5], [2, 10], [3, 1], [6, 2], [10, 1]], 49/103680],
[[[1, 5], [2, 10], [3, 2], [4, 1], [6, 2]], 1129/11612160],
[[[1, 5], [2, 10], [4, 1], [6, 1], [14, 1]], 29/96768],
[[[1, 5], [2, 10], [4, 1], [6, 1], [18, 1]], 257/4976640],
[[[1, 5], [2, 10], [4, 1], [6, 2], [8, 1]], 11/73728],
[[[1, 5], [2, 10], [4, 1], [6, 2], [10, 1]], 1367/1658880],
[[[1, 5], [2, 10], [4, 1], [8, 1], [10, 1]], 11/184320],
[[[1, 5], [2, 10], [4, 2], [6, 1], [8, 1]], 1/3456],
[[[1, 5], [2, 10], [4, 2], [6, 1], [10, 1]], 7/6912],
[[[1, 5], [2, 12], [3, 1], [4, 1], [6, 2]], 4199/17418240],
[[[1, 5], [2, 12], [3, 1], [4, 2], [6, 1]], 3877/69672960],
[[[1, 5], [2, 12], [3, 1], [6, 1], [10, 1]], 649/11612160],
[[[1, 5], [2, 12], [4, 1], [6, 1], [8, 1]], 49/1105920],
[[[1, 5], [2, 12], [4, 1], [6, 1], [10, 1]], 3479/8294400],
[[[1, 5], [2, 14], [3, 1], [4, 1], [6, 1]], 3023/261273600],
[[[1, 6], [2, 1], [3, 2], [4, 1], [5, 3]], 1/18000],
[[[1, 6], [2, 1], [3, 2], [4, 1], [9, 2]], 1/25920],
[[[1, 6], [2, 1], [3, 2], [5, 2], [7, 1]], 1/12600],
[[[1, 6], [2, 1], [3, 2], [5, 2], [9, 1]], 1/2700],
[[[1, 6], [2, 1], [3, 2], [5, 3], [6, 1]], 1/3375],
[[[1, 6], [2, 1], [3, 3], [5, 1], [15, 1]], 1/2160],
[[[1, 6], [2, 1], [3, 4], [4, 1], [5, 2]], 1/64800],
[[[1, 6], [2, 1], [3, 4], [5, 1], [7, 1]], 1/45360],
[[[1, 6], [2, 1], [3, 4], [5, 1], [9, 1]], 11/9720],
[[[1, 6], [2, 1], [3, 4], [5, 2], [6, 1]], 1/4860],
[[[1, 6], [2, 1], [3, 5], [4, 1], [9, 1]], 37/46656],
[[[1, 6], [2, 1], [3, 5], [6, 1], [7, 1]], 1/1944],
[[[1, 6], [2, 1], [3, 5], [6, 1], [9, 1]], 19/17496],
[[[1, 6], [2, 1], [3, 6], [4, 1], [5, 1]], 43/1749600],
[[[1, 6], [2, 1], [3, 6], [4, 1], [8, 1]], 43/699840],
[[[1, 6], [2, 1], [3, 6], [5, 1], [6, 1]], 89/174960],
[[[1, 6], [2, 1], [4, 1], [5, 3], [8, 1]], 1/6000],
[[[1, 6], [2, 3], [3, 1], [5, 2], [9, 1]], 1/21600],
[[[1, 6], [2, 3], [3, 1], [5, 3], [6, 1]], 1/12000],
[[[1, 6], [2, 3], [3, 2], [4, 2], [5, 2]], 1/14400],
[[[1, 6], [2, 3], [3, 2], [5, 1], [15, 1]], 1/4320],
[[[1, 6], [2, 3], [3, 2], [5, 2], [6, 2]], 1/2400],
[[[1, 6], [2, 3], [3, 3], [4, 2], [9, 1]], 1/10368],
[[[1, 6], [2, 3], [3, 3], [5, 1], [6, 3]], 11/77760],
[[[1, 6], [2, 3], [3, 3], [5, 1], [9, 1]], 1/38880],
[[[1, 6], [2, 3], [3, 3], [5, 2], [6, 1]], 1/21600],
[[[1, 6], [2, 3], [3, 3], [6, 2], [7, 1]], 1/4536],
[[[1, 6], [2, 3], [3, 3], [6, 2], [9, 1]], 1/31104],
[[[1, 6], [2, 3], [3, 4], [4, 1], [7, 1]], 1/72576],
[[[1, 6], [2, 3], [3, 4], [4, 1], [9, 1]], 11/15552],
[[[1, 6], [2, 3], [3, 4], [4, 2], [5, 1]], 1/103680],
[[[1, 6], [2, 3], [3, 4], [4, 2], [8, 1]], 1/41472],
[[[1, 6], [2, 3], [3, 4], [5, 1], [6, 2]], 23/12960],
[[[1, 6], [2, 3], [3, 4], [6, 1], [7, 1]], 1/9072],
[[[1, 6], [2, 3], [3, 4], [6, 1], [9, 1]], 23/15552],
[[[1, 6], [2, 3], [3, 5], [4, 1], [6, 2]], 91/93312],
[[[1, 6], [2, 3], [3, 5], [4, 2], [6, 1]], 7/31104],
[[[1, 6], [2, 3], [3, 5], [5, 1], [6, 1]], 7/38880],
[[[1, 6], [2, 3], [3, 6], [4, 1], [6, 1]], 89/279936],
[[[1, 6], [2, 3], [4, 1], [5, 2], [7, 1]], 1/5600],
[[[1, 6], [2, 3], [4, 2], [5, 2], [8, 1]], 1/3200],
[[[1, 6], [2, 5], [3, 1], [4, 3], [9, 1]], 1/9216],
[[[1, 6], [2, 5], [3, 2], [4, 2], [6, 3]], 1/6912],
[[[1, 6], [2, 5], [3, 2], [4, 2], [7, 1]], 1/32256],
[[[1, 6], [2, 5], [3, 2], [4, 2], [9, 1]], 1/6912],
[[[1, 6], [2, 5], [3, 2], [4, 3], [5, 1]], 1/46080],
[[[1, 6], [2, 5], [3, 2], [4, 3], [6, 2]], 1/9216],
[[[1, 6], [2, 5], [3, 2], [4, 3], [8, 1]], 1/18432],
[[[1, 6], [2, 5], [3, 2], [6, 2], [7, 1]], 1/12096],
[[[1, 6], [2, 5], [3, 2], [6, 2], [14, 1]], 1/48384],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 3]], 23/31104],
[[[1, 6], [2, 5], [3, 3], [4, 1], [9, 1]], 1/62208],
[[[1, 6], [2, 5], [3, 3], [4, 2], [6, 2]], 5/13824],
[[[1, 6], [2, 5], [3, 3], [4, 3], [6, 1]], 1/27648],
[[[1, 6], [2, 5], [3, 3], [5, 1], [6, 2]], 7/51840],
[[[1, 6], [2, 5], [3, 3], [6, 1], [7, 1]], 1/72576],
[[[1, 6], [2, 5], [3, 3], [6, 1], [9, 1]], 13/62208],
[[[1, 6], [2, 5], [3, 4], [4, 1], [6, 2]], 23/20736],
[[[1, 6], [2, 5], [3, 4], [4, 2], [6, 1]], 5/62208],
[[[1, 6], [2, 5], [4, 2], [5, 1], [7, 1]], 1/8960],
[[[1, 6], [2, 5], [4, 3], [5, 1], [8, 1]], 1/5120],
[[[1, 6], [2, 5], [4, 3], [6, 1], [18, 1]], 1/27648],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 4]], 5/186624],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 3]], 55/165888],
[[[1, 6], [2, 7], [3, 1], [4, 2], [9, 1]], 1/55296],
[[[1, 6], [2, 7], [3, 1], [4, 3], [6, 2]], 1/3072],
[[[1, 6], [2, 7], [3, 1], [4, 4], [6, 1]], 1/8192],
[[[1, 6], [2, 7], [3, 1], [6, 1], [10, 2]], 1/57600],
[[[1, 6], [2, 7], [3, 1], [6, 2], [14, 1]], 1/24192],
[[[1, 6], [2, 7], [3, 1], [6, 2], [18, 1]], 1/41472],
[[[1, 6], [2, 7], [3, 1], [6, 3], [10, 1]], 1/207360],
[[[1, 6], [2, 7], [3, 2], [4, 1], [6, 3]], 23/41472],
[[[1, 6], [2, 7], [3, 2], [4, 2], [6, 2]], 5/9216],
[[[1, 6], [2, 7], [3, 2], [4, 3], [6, 1]], 1/13824],
[[[1, 6], [2, 7], [3, 2], [5, 1], [6, 2]], 1/138240],
[[[1, 6], [2, 7], [3, 2], [6, 1], [9, 1]], 1/248832],
[[[1, 6], [2, 7], [3, 2], [6, 2], [10, 1]], 7/69120],
[[[1, 6], [2, 7], [3, 3], [4, 1], [6, 2]], 1/20736],
[[[1, 6], [2, 7], [4, 1], [6, 2], [14, 1]], 1/96768],
[[[1, 6], [2, 7], [4, 1], [6, 2], [18, 1]], 1/20736],
[[[1, 6], [2, 7], [4, 1], [10, 1], [14, 1]], 1/26880],
[[[1, 6], [2, 7], [4, 2], [6, 1], [14, 1]], 1/10752],
[[[1, 6], [2, 7], [4, 2], [6, 1], [18, 1]], 5/55296],
[[[1, 6], [2, 7], [4, 2], [6, 2], [8, 1]], 1/55296],
[[[1, 6], [2, 7], [4, 2], [6, 2], [10, 1]], 1/55296],
[[[1, 6], [2, 7], [4, 2], [8, 1], [10, 1]], 1/15360],
[[[1, 6], [2, 7], [4, 3], [6, 1], [8, 1]], 1/6144],
[[[1, 6], [2, 7], [4, 3], [6, 1], [10, 1]], 7/46080],
[[[1, 6], [2, 7], [6, 1], [10, 1], [18, 1]], 1/207360],
[[[1, 6], [2, 9], [3, 1], [4, 1], [6, 3]], 661/995328],
[[[1, 6], [2, 9], [3, 1], [4, 2], [6, 2]], 71/82944],
[[[1, 6], [2, 9], [3, 1], [4, 3], [6, 1]], 1/3840],
[[[1, 6], [2, 9], [3, 1], [6, 1], [14, 1]], 17/387072],
[[[1, 6], [2, 9], [3, 1], [6, 2], [10, 1]], 43/207360],
[[[1, 6], [2, 9], [3, 2], [4, 1], [6, 2]], 379/1658880],
[[[1, 6], [2, 9], [4, 1], [6, 1], [14, 1]], 1/6048],
[[[1, 6], [2, 9], [4, 1], [6, 1], [18, 1]], 17/331776],
[[[1, 6], [2, 9], [4, 1], [6, 2], [8, 1]], 5/110592],
[[[1, 6], [2, 9], [4, 1], [6, 2], [10, 1]], 1/5120],
[[[1, 6], [2, 9], [4, 1], [8, 1], [10, 1]], 1/30720],
[[[1, 6], [2, 9], [4, 2], [6, 1], [8, 1]], 13/55296],
[[[1, 6], [2, 9], [4, 2], [6, 1], [10, 1]], 167/276480],
[[[1, 6], [2, 11], [3, 1], [4, 1], [6, 2]], 2233/4976640],
[[[1, 6], [2, 11], [3, 1], [4, 2], [6, 1]], 1007/5806080],
[[[1, 6], [2, 11], [3, 1], [6, 1], [10, 1]], 697/8294400],
[[[1, 6], [2, 11], [4, 1], [6, 1], [8, 1]], 13/221184],
[[[1, 6], [2, 11], [4, 1], [6, 1], [10, 1]], 77/184320],
[[[1, 6], [2, 13], [3, 1], [4, 1], [6, 1]], 4247/104509440],
[[[1, 7], [2, 2], [3, 1], [4, 1], [5, 3]], 7/18000],
[[[1, 7], [2, 2], [3, 1], [5, 2], [7, 1]], 1/4200],
[[[1, 7], [2, 2], [3, 1], [5, 2], [9, 1]], 1/7200],
[[[1, 7], [2, 2], [3, 1], [5, 3], [6, 1]], 1/3600],
[[[1, 7], [2, 2], [3, 2], [4, 2], [5, 2]], 1/9600],
[[[1, 7], [2, 2], [3, 2], [5, 1], [15, 1]], 1/14400],
[[[1, 7], [2, 2], [3, 2], [5, 2], [6, 2]], 1/8640],
[[[1, 7], [2, 2], [3, 3], [4, 1], [5, 2]], 1/4050],
[[[1, 7], [2, 2], [3, 3], [4, 2], [9, 1]], 1/20736],
[[[1, 7], [2, 2], [3, 3], [5, 1], [7, 1]], 1/7560],
[[[1, 7], [2, 2], [3, 3], [5, 1], [9, 1]], 1/2592],
[[[1, 7], [2, 2], [3, 3], [5, 2], [6, 1]], 1/1200],
[[[1, 7], [2, 2], [3, 3], [6, 2], [7, 1]], 1/18144],
[[[1, 7], [2, 2], [3, 3], [6, 2], [9, 1]], 1/466560],
[[[1, 7], [2, 2], [3, 4], [4, 1], [7, 1]], 1/36288],
[[[1, 7], [2, 2], [3, 4], [4, 1], [9, 1]], 13/23328],
[[[1, 7], [2, 2], [3, 4], [4, 2], [5, 1]], 1/51840],
[[[1, 7], [2, 2], [3, 4], [4, 2], [8, 1]], 1/41472],
[[[1, 7], [2, 2], [3, 4], [5, 1], [6, 2]], 1/2430],
[[[1, 7], [2, 2], [3, 4], [6, 1], [7, 1]], 1/6804],
[[[1, 7], [2, 2], [3, 4], [6, 1], [9, 1]], 1/1728],
[[[1, 7], [2, 2], [3, 5], [4, 1], [5, 1]], 11/233280],
[[[1, 7], [2, 2], [3, 5], [4, 1], [8, 1]], 1/31104],
[[[1, 7], [2, 2], [3, 5], [5, 1], [6, 1]], 79/116640],
[[[1, 7], [2, 2], [3, 6], [4, 1], [6, 1]], 89/279936],
[[[1, 7], [2, 2], [4, 1], [5, 2], [7, 1]], 1/2800],
[[[1, 7], [2, 2], [4, 2], [5, 2], [8, 1]], 1/3200],
[[[1, 7], [2, 4], [3, 1], [4, 2], [5, 2]], 1/2400],
[[[1, 7], [2, 4], [3, 1], [4, 3], [9, 1]], 1/9216],
[[[1, 7], [2, 4], [3, 2], [4, 1], [5, 2]], 1/21600],
[[[1, 7], [2, 4], [3, 2], [4, 2], [7, 1]], 1/10752],
[[[1, 7], [2, 4], [3, 2], [4, 2], [9, 1]], 7/20736],
[[[1, 7], [2, 4], [3, 2], [4, 3], [5, 1]], 1/11520],
[[[1, 7], [2, 4], [3, 2], [4, 3], [8, 1]], 1/9216],
[[[1, 7], [2, 4], [3, 2], [5, 1], [7, 1]], 1/60480],
[[[1, 7], [2, 4], [3, 2], [5, 1], [9, 1]], 1/12960],
[[[1, 7], [2, 4], [3, 2], [5, 2], [6, 1]], 1/4320],
[[[1, 7], [2, 4], [3, 2], [6, 2], [7, 1]], 1/12096],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 3]], 1/15552],
[[[1, 7], [2, 4], [3, 3], [4, 1], [7, 1]], 1/12096],
[[[1, 7], [2, 4], [3, 3], [4, 1], [9, 1]], 1/3888],
[[[1, 7], [2, 4], [3, 3], [4, 2], [5, 1]], 1/6480],
[[[1, 7], [2, 4], [3, 3], [4, 2], [6, 2]], 7/41472],
[[[1, 7], [2, 4], [3, 3], [4, 2], [8, 1]], 1/6912],
[[[1, 7], [2, 4], [3, 3], [4, 3], [6, 1]], 1/27648],
[[[1, 7], [2, 4], [3, 3], [5, 1], [6, 2]], 43/51840],
[[[1, 7], [2, 4], [3, 3], [6, 1], [7, 1]], 1/4536],
[[[1, 7], [2, 4], [3, 3], [6, 1], [9, 1]], 19/46656],
[[[1, 7], [2, 4], [3, 4], [4, 1], [5, 1]], 1/155520],
[[[1, 7], [2, 4], [3, 4], [4, 1], [6, 2]], 1/972],
[[[1, 7], [2, 4], [3, 4], [4, 1], [8, 1]], 1/248832],
[[[1, 7], [2, 4], [3, 4], [4, 2], [6, 1]], 13/62208],
[[[1, 7], [2, 4], [3, 4], [5, 1], [6, 1]], 19/233280],
[[[1, 7], [2, 4], [3, 5], [4, 1], [6, 1]], 79/186624],
[[[1, 7], [2, 4], [4, 1], [5, 2], [8, 1]], 1/19200],
[[[1, 7], [2, 4], [4, 2], [5, 1], [7, 1]], 3/8960],
[[[1, 7], [2, 4], [4, 3], [5, 1], [8, 1]], 1/2560],
[[[1, 7], [2, 6], [3, 1], [4, 2], [7, 1]], 1/10752],
[[[1, 7], [2, 6], [3, 1], [4, 2], [9, 1]], 5/55296],
[[[1, 7], [2, 6], [3, 1], [4, 3], [5, 1]], 7/46080],
[[[1, 7], [2, 6], [3, 1], [4, 3], [6, 2]], 1/13824],
[[[1, 7], [2, 6], [3, 1], [4, 3], [8, 1]], 1/6144],
[[[1, 7], [2, 6], [3, 1], [4, 4], [6, 1]], 1/8192],
[[[1, 7], [2, 6], [3, 1], [5, 1], [9, 1]], 1/207360],
[[[1, 7], [2, 6], [3, 1], [5, 2], [6, 1]], 1/57600],
[[[1, 7], [2, 6], [3, 1], [6, 2], [18, 1]], 1/248832],
[[[1, 7], [2, 6], [3, 2], [4, 1], [6, 3]], 1/20736],
[[[1, 7], [2, 6], [3, 2], [4, 1], [7, 1]], 1/96768],
[[[1, 7], [2, 6], [3, 2], [4, 1], [9, 1]], 1/20736],
[[[1, 7], [2, 6], [3, 2], [4, 2], [5, 1]], 1/55296],
[[[1, 7], [2, 6], [3, 2], [4, 2], [6, 2]], 5/9216],
[[[1, 7], [2, 6], [3, 2], [4, 2], [8, 1]], 1/55296],
[[[1, 7], [2, 6], [3, 2], [4, 3], [6, 1]], 1/3072],
[[[1, 7], [2, 6], [3, 2], [5, 1], [6, 2]], 7/69120],
[[[1, 7], [2, 6], [3, 2], [6, 1], [7, 1]], 1/24192],
[[[1, 7], [2, 6], [3, 2], [6, 1], [9, 1]], 1/41472],
[[[1, 7], [2, 6], [3, 2], [6, 2], [10, 1]], 1/138240],
[[[1, 7], [2, 6], [3, 3], [4, 1], [6, 2]], 23/41472],
[[[1, 7], [2, 6], [3, 3], [4, 2], [6, 1]], 55/165888],
[[[1, 7], [2, 6], [3, 3], [5, 1], [6, 1]], 1/207360],
[[[1, 7], [2, 6], [3, 4], [4, 1], [6, 1]], 5/186624],
[[[1, 7], [2, 6], [4, 1], [5, 1], [7, 1]], 1/26880],
[[[1, 7], [2, 6], [4, 2], [5, 1], [8, 1]], 1/15360],
[[[1, 7], [2, 6], [4, 2], [6, 1], [18, 1]], 1/55296],
[[[1, 7], [2, 8], [3, 1], [4, 1], [6, 3]], 35/331776],
[[[1, 7], [2, 8], [3, 1], [4, 1], [9, 1]], 1/331776],
[[[1, 7], [2, 8], [3, 1], [4, 2], [6, 2]], 23/55296],
[[[1, 7], [2, 8], [3, 1], [4, 3], [6, 1]], 37/110592],
[[[1, 7], [2, 8], [3, 1], [6, 1], [7, 1]], 1/387072],
[[[1, 7], [2, 8], [3, 1], [6, 1], [14, 1]], 1/55296],
[[[1, 7], [2, 8], [3, 1], [6, 2], [10, 1]], 1/41472],
[[[1, 7], [2, 8], [3, 2], [4, 1], [6, 2]], 83/331776],
[[[1, 7], [2, 8], [3, 2], [4, 2], [6, 1]], 1/27648],
[[[1, 7], [2, 8], [4, 1], [6, 1], [14, 1]], 1/32256],
[[[1, 7], [2, 8], [4, 1], [6, 1], [18, 1]], 7/331776],
[[[1, 7], [2, 8], [4, 1], [6, 2], [8, 1]], 1/663552],
[[[1, 7], [2, 8], [4, 1], [6, 2], [10, 1]], 7/1658880],
[[[1, 7], [2, 8], [4, 1], [8, 1], [10, 1]], 1/184320],
[[[1, 7], [2, 8], [4, 2], [6, 1], [8, 1]], 1/18432],
[[[1, 7], [2, 8], [4, 2], [6, 1], [10, 1]], 1/10240],
[[[1, 7], [2, 10], [3, 1], [4, 1], [6, 2]], 61/165888],
[[[1, 7], [2, 10], [3, 1], [4, 2], [6, 1]], 55/221184],
[[[1, 7], [2, 10], [3, 1], [6, 1], [10, 1]], 43/829440],
[[[1, 7], [2, 10], [4, 1], [6, 1], [8, 1]], 19/663552],
[[[1, 7], [2, 10], [4, 1], [6, 1], [10, 1]], 271/1658880],
[[[1, 7], [2, 12], [3, 1], [4, 1], [6, 1]], 443/5806080],
[[[1, 8], [2, 1], [3, 1], [4, 1], [5, 3]], 1/3600],
[[[1, 8], [2, 1], [3, 1], [5, 2], [7, 1]], 1/3150],
[[[1, 8], [2, 1], [3, 1], [5, 2], [9, 1]], 1/21600],
[[[1, 8], [2, 1], [3, 1], [5, 3], [6, 1]], 7/108000],
[[[1, 8], [2, 1], [3, 2], [5, 1], [15, 1]], 1/151200],
[[[1, 8], [2, 1], [3, 3], [4, 1], [5, 2]], 1/5400],
[[[1, 8], [2, 1], [3, 3], [5, 1], [7, 1]], 1/5670],
[[[1, 8], [2, 1], [3, 3], [5, 1], [9, 1]], 1/4320],
[[[1, 8], [2, 1], [3, 3], [5, 2], [6, 1]], 17/64800],
[[[1, 8], [2, 1], [3, 4], [4, 1], [7, 1]], 1/72576],
[[[1, 8], [2, 1], [3, 4], [4, 1], [9, 1]], 19/233280],
[[[1, 8], [2, 1], [3, 4], [6, 1], [7, 1]], 1/27216],
[[[1, 8], [2, 1], [3, 4], [6, 1], [9, 1]], 13/233280],
[[[1, 8], [2, 1], [3, 5], [4, 1], [5, 1]], 1/25920],
[[[1, 8], [2, 1], [3, 5], [4, 1], [8, 1]], 1/93312],
[[[1, 8], [2, 1], [3, 5], [5, 1], [6, 1]], 29/174960],
[[[1, 8], [2, 1], [4, 1], [5, 2], [7, 1]], 1/5600],
[[[1, 8], [2, 3], [3, 1], [4, 2], [5, 2]], 23/28800],
[[[1, 8], [2, 3], [3, 1], [4, 3], [9, 1]], 1/27648],
[[[1, 8], [2, 3], [3, 2], [4, 1], [5, 2]], 23/28800],
[[[1, 8], [2, 3], [3, 2], [4, 2], [7, 1]], 1/10752],
[[[1, 8], [2, 3], [3, 2], [4, 2], [9, 1]], 5/20736],
[[[1, 8], [2, 3], [3, 2], [4, 3], [5, 1]], 1/15360],
[[[1, 8], [2, 3], [3, 2], [4, 3], [8, 1]], 1/18432],
[[[1, 8], [2, 3], [3, 2], [5, 1], [7, 1]], 1/3780],
[[[1, 8], [2, 3], [3, 2], [5, 1], [9, 1]], 1/3888],
[[[1, 8], [2, 3], [3, 2], [5, 2], [6, 1]], 19/21600],
[[[1, 8], [2, 3], [3, 2], [6, 2], [7, 1]], 1/45360],
[[[1, 8], [2, 3], [3, 3], [4, 1], [7, 1]], 1/5184],
[[[1, 8], [2, 3], [3, 3], [4, 1], [9, 1]], 1/2592],
[[[1, 8], [2, 3], [3, 3], [4, 2], [5, 1]], 17/51840],
[[[1, 8], [2, 3], [3, 3], [4, 2], [8, 1]], 1/5184],
[[[1, 8], [2, 3], [3, 3], [5, 1], [6, 2]], 23/51840],
[[[1, 8], [2, 3], [3, 3], [6, 1], [7, 1]], 1/3024],
[[[1, 8], [2, 3], [3, 3], [6, 1], [9, 1]], 29/155520],
[[[1, 8], [2, 3], [3, 4], [4, 1], [5, 1]], 89/311040],
[[[1, 8], [2, 3], [3, 4], [4, 1], [6, 2]], 59/311040],
[[[1, 8], [2, 3], [3, 4], [4, 1], [8, 1]], 1/9216],
[[[1, 8], [2, 3], [3, 4], [4, 2], [6, 1]], 1/10368],
[[[1, 8], [2, 3], [3, 4], [5, 1], [6, 1]], 13/15552],
[[[1, 8], [2, 3], [3, 5], [4, 1], [6, 1]], 29/69984],
[[[1, 8], [2, 3], [4, 1], [5, 2], [8, 1]], 1/6400],
[[[1, 8], [2, 3], [4, 2], [5, 1], [7, 1]], 3/8960],
[[[1, 8], [2, 3], [4, 3], [5, 1], [8, 1]], 1/5120],
[[[1, 8], [2, 5], [3, 1], [4, 1], [5, 2]], 1/4800],
[[[1, 8], [2, 5], [3, 1], [4, 2], [7, 1]], 5/16128],
[[[1, 8], [2, 5], [3, 1], [4, 2], [9, 1]], 1/6912],
[[[1, 8], [2, 5], [3, 1], [4, 3], [5, 1]], 5/9216],
[[[1, 8], [2, 5], [3, 1], [4, 3], [8, 1]], 7/18432],
[[[1, 8], [2, 5], [3, 1], [4, 4], [6, 1]], 1/24576],
[[[1, 8], [2, 5], [3, 1], [5, 1], [7, 1]], 1/20160],
[[[1, 8], [2, 5], [3, 1], [5, 1], [9, 1]], 1/34560],
[[[1, 8], [2, 5], [3, 1], [5, 2], [6, 1]], 1/7680],
[[[1, 8], [2, 5], [3, 2], [4, 1], [7, 1]], 17/96768],
[[[1, 8], [2, 5], [3, 2], [4, 1], [9, 1]], 13/62208],
[[[1, 8], [2, 5], [3, 2], [4, 2], [5, 1]], 71/138240],
[[[1, 8], [2, 5], [3, 2], [4, 2], [6, 2]], 127/552960],
[[[1, 8], [2, 5], [3, 2], [4, 2], [8, 1]], 1/3456],
[[[1, 8], [2, 5], [3, 2], [4, 3], [6, 1]], 5/13824],
[[[1, 8], [2, 5], [3, 2], [5, 1], [6, 2]], 53/207360],
[[[1, 8], [2, 5], [3, 2], [6, 1], [7, 1]], 13/72576],
[[[1, 8], [2, 5], [3, 2], [6, 1], [9, 1]], 11/248832],
[[[1, 8], [2, 5], [3, 3], [4, 1], [5, 1]], 11/155520],
[[[1, 8], [2, 5], [3, 3], [4, 1], [6, 2]], 31/41472],
[[[1, 8], [2, 5], [3, 3], [4, 1], [8, 1]], 1/41472],
[[[1, 8], [2, 5], [3, 3], [4, 2], [6, 1]], 137/165888],
[[[1, 8], [2, 5], [3, 3], [5, 1], [6, 1]], 5/20736],
[[[1, 8], [2, 5], [3, 4], [4, 1], [6, 1]], 101/186624],
[[[1, 8], [2, 5], [4, 1], [5, 1], [7, 1]], 1/5376],
[[[1, 8], [2, 5], [4, 2], [5, 1], [8, 1]], 1/3840],
[[[1, 8], [2, 7], [3, 1], [4, 1], [7, 1]], 1/32256],
[[[1, 8], [2, 7], [3, 1], [4, 1], [9, 1]], 7/331776],
[[[1, 8], [2, 7], [3, 1], [4, 2], [5, 1]], 1/10240],
[[[1, 8], [2, 7], [3, 1], [4, 2], [6, 2]], 1/27648],
[[[1, 8], [2, 7], [3, 1], [4, 2], [8, 1]], 1/18432],
[[[1, 8], [2, 7], [3, 1], [4, 3], [6, 1]], 37/110592],
[[[1, 8], [2, 7], [3, 1], [6, 1], [7, 1]], 1/55296],
[[[1, 8], [2, 7], [3, 1], [6, 1], [14, 1]], 1/387072],
[[[1, 8], [2, 7], [3, 2], [4, 1], [5, 1]], 7/1658880],
[[[1, 8], [2, 7], [3, 2], [4, 1], [6, 2]], 83/331776],
[[[1, 8], [2, 7], [3, 2], [4, 1], [8, 1]], 1/663552],
[[[1, 8], [2, 7], [3, 2], [4, 2], [6, 1]], 23/55296],
[[[1, 8], [2, 7], [3, 2], [5, 1], [6, 1]], 1/41472],
[[[1, 8], [2, 7], [3, 3], [4, 1], [6, 1]], 35/331776],
[[[1, 8], [2, 7], [4, 1], [5, 1], [8, 1]], 1/184320],
[[[1, 8], [2, 7], [4, 1], [6, 1], [18, 1]], 1/331776],
[[[1, 8], [2, 9], [3, 1], [4, 1], [6, 2]], 35/331776],
[[[1, 8], [2, 9], [3, 1], [4, 2], [6, 1]], 41/221184],
[[[1, 8], [2, 9], [3, 1], [5, 1], [6, 1]], 1/1105920],
[[[1, 8], [2, 9], [3, 1], [6, 1], [10, 1]], 7/552960],
[[[1, 8], [2, 9], [3, 2], [4, 1], [6, 1]], 1/165888],
[[[1, 8], [2, 9], [4, 1], [6, 1], [8, 1]], 1/221184],
[[[1, 8], [2, 9], [4, 1], [6, 1], [10, 1]], 11/552960],
[[[1, 8], [2, 11], [3, 1], [4, 1], [6, 1]], 119/1658880],
[[[1, 9], [2, 2], [3, 1], [4, 2], [5, 2]], 1/3200],
[[[1, 9], [2, 2], [3, 2], [4, 1], [5, 2]], 37/43200],
[[[1, 9], [2, 2], [3, 2], [4, 2], [7, 1]], 1/32256],
[[[1, 9], [2, 2], [3, 2], [4, 2], [9, 1]], 1/20736],
[[[1, 9], [2, 2], [3, 2], [5, 1], [7, 1]], 1/2520],
[[[1, 9], [2, 2], [3, 2], [5, 1], [9, 1]], 1/6480],
[[[1, 9], [2, 2], [3, 2], [5, 2], [6, 1]], 1/2400],
[[[1, 9], [2, 2], [3, 2], [6, 2], [7, 1]], 1/725760],
[[[1, 9], [2, 2], [3, 3], [4, 1], [7, 1]], 5/36288],
[[[1, 9], [2, 2], [3, 3], [4, 1], [9, 1]], 13/77760],
[[[1, 9], [2, 2], [3, 3], [4, 2], [5, 1]], 7/51840],
[[[1, 9], [2, 2], [3, 3], [4, 2], [8, 1]], 1/20736],
[[[1, 9], [2, 2], [3, 3], [5, 1], [6, 2]], 49/777600],
[[[1, 9], [2, 2], [3, 3], [6, 1], [7, 1]], 13/90720],
[[[1, 9], [2, 2], [3, 3], [6, 1], [9, 1]], 17/544320],
[[[1, 9], [2, 2], [3, 4], [4, 1], [5, 1]], 157/466560],
[[[1, 9], [2, 2], [3, 4], [4, 1], [8, 1]], 17/248832],
[[[1, 9], [2, 2], [3, 4], [5, 1], [6, 1]], 23/46656],
[[[1, 9], [2, 2], [3, 5], [4, 1], [6, 1]], 227/2799360],
[[[1, 9], [2, 2], [4, 1], [5, 2], [8, 1]], 1/19200],
[[[1, 9], [2, 2], [4, 2], [5, 1], [7, 1]], 1/8960],
[[[1, 9], [2, 4], [3, 1], [4, 1], [5, 2]], 73/86400],
[[[1, 9], [2, 4], [3, 1], [4, 2], [7, 1]], 1/2688],
[[[1, 9], [2, 4], [3, 1], [4, 2], [9, 1]], 19/207360],
[[[1, 9], [2, 4], [3, 1], [4, 3], [5, 1]], 5/9216],
[[[1, 9], [2, 4], [3, 1], [4, 3], [8, 1]], 5/18432],
[[[1, 9], [2, 4], [3, 1], [5, 1], [7, 1]], 13/60480],
[[[1, 9], [2, 4], [3, 1], [5, 1], [9, 1]], 11/207360],
[[[1, 9], [2, 4], [3, 1], [5, 2], [6, 1]], 11/43200],
[[[1, 9], [2, 4], [3, 2], [4, 1], [7, 1]], 5/12096],
[[[1, 9], [2, 4], [3, 2], [4, 1], [9, 1]], 1/3888],
[[[1, 9], [2, 4], [3, 2], [4, 2], [5, 1]], 31/27648],
[[[1, 9], [2, 4], [3, 2], [4, 2], [6, 2]], 67/1658880],
[[[1, 9], [2, 4], [3, 2], [4, 2], [8, 1]], 1/2304],
[[[1, 9], [2, 4], [3, 2], [4, 3], [6, 1]], 1/9216],
[[[1, 9], [2, 4], [3, 2], [5, 1], [6, 2]], 73/518400],
[[[1, 9], [2, 4], [3, 2], [6, 1], [7, 1]], 1/4536],
[[[1, 9], [2, 4], [3, 2], [6, 1], [9, 1]], 23/933120],
[[[1, 9], [2, 4], [3, 3], [4, 1], [5, 1]], 109/155520],
[[[1, 9], [2, 4], [3, 3], [4, 1], [6, 2]], 37/124416],
[[[1, 9], [2, 4], [3, 3], [4, 1], [8, 1]], 11/62208],
[[[1, 9], [2, 4], [3, 3], [4, 2], [6, 1]], 467/829440],
[[[1, 9], [2, 4], [3, 3], [5, 1], [6, 1]], 293/311040],
[[[1, 9], [2, 4], [3, 4], [4, 1], [6, 1]], 149/186624],
[[[1, 9], [2, 4], [4, 1], [5, 1], [7, 1]], 1/3360],
[[[1, 9], [2, 4], [4, 2], [5, 1], [8, 1]], 1/3840],
[[[1, 9], [2, 6], [3, 1], [4, 1], [7, 1]], 1/6048],
[[[1, 9], [2, 6], [3, 1], [4, 1], [9, 1]], 17/331776],
[[[1, 9], [2, 6], [3, 1], [4, 2], [5, 1]], 167/276480],
[[[1, 9], [2, 6], [3, 1], [4, 2], [8, 1]], 13/55296],
[[[1, 9], [2, 6], [3, 1], [4, 3], [6, 1]], 1/3840],
[[[1, 9], [2, 6], [3, 1], [6, 1], [7, 1]], 17/387072],
[[[1, 9], [2, 6], [3, 2], [4, 1], [5, 1]], 1/5120],
[[[1, 9], [2, 6], [3, 2], [4, 1], [6, 2]], 379/1658880],
[[[1, 9], [2, 6], [3, 2], [4, 1], [8, 1]], 5/110592],
[[[1, 9], [2, 6], [3, 2], [4, 2], [6, 1]], 71/82944],
[[[1, 9], [2, 6], [3, 2], [5, 1], [6, 1]], 43/207360],
[[[1, 9], [2, 6], [3, 3], [4, 1], [6, 1]], 661/995328],
[[[1, 9], [2, 6], [4, 1], [5, 1], [8, 1]], 1/30720],
[[[1, 9], [2, 8], [3, 1], [4, 1], [5, 1]], 11/552960],
[[[1, 9], [2, 8], [3, 1], [4, 1], [6, 2]], 1/165888],
[[[1, 9], [2, 8], [3, 1], [4, 1], [8, 1]], 1/221184],
[[[1, 9], [2, 8], [3, 1], [4, 2], [6, 1]], 41/221184],
[[[1, 9], [2, 8], [3, 1], [5, 1], [6, 1]], 7/552960],
[[[1, 9], [2, 8], [3, 1], [6, 1], [10, 1]], 1/1105920],
[[[1, 9], [2, 8], [3, 2], [4, 1], [6, 1]], 35/331776],
[[[1, 9], [2, 10], [3, 1], [4, 1], [6, 1]], 23/663552],
[[[1, 10], [2, 1], [3, 2], [4, 1], [5, 2]], 83/432000],
[[[1, 10], [2, 1], [3, 2], [5, 1], [7, 1]], 13/75600],
[[[1, 10], [2, 1], [3, 2], [5, 1], [9, 1]], 1/32400],
[[[1, 10], [2, 1], [3, 2], [5, 2], [6, 1]], 17/324000],
[[[1, 10], [2, 1], [3, 3], [4, 1], [7, 1]], 1/36288],
[[[1, 10], [2, 1], [3, 3], [4, 1], [9, 1]], 7/311040],
[[[1, 10], [2, 1], [3, 3], [6, 1], [7, 1]], 1/51840],
[[[1, 10], [2, 1], [3, 3], [6, 1], [9, 1]], 31/19595520],
[[[1, 10], [2, 1], [3, 4], [4, 1], [5, 1]], 371/4665600],
[[[1, 10], [2, 1], [3, 4], [4, 1], [8, 1]], 41/3732480],
[[[1, 10], [2, 1], [3, 4], [5, 1], [6, 1]], 53/699840],
[[[1, 10], [2, 1], [4, 1], [5, 2], [8, 1]], 1/288000],
[[[1, 10], [2, 3], [3, 1], [4, 1], [5, 2]], 23/28800],
[[[1, 10], [2, 3], [3, 1], [4, 2], [7, 1]], 1/5376],
[[[1, 10], [2, 3], [3, 1], [4, 2], [9, 1]], 17/829440],
[[[1, 10], [2, 3], [3, 1], [4, 3], [5, 1]], 7/46080],
[[[1, 10], [2, 3], [3, 1], [4, 3], [8, 1]], 1/18432],
[[[1, 10], [2, 3], [3, 1], [5, 1], [7, 1]], 1/3780],
[[[1, 10], [2, 3], [3, 1], [5, 1], [9, 1]], 23/777600],
[[[1, 10], [2, 3], [3, 1], [5, 2], [6, 1]], 109/864000],
[[[1, 10], [2, 3], [3, 2], [4, 1], [7, 1]], 43/120960],
[[[1, 10], [2, 3], [3, 2], [4, 1], [9, 1]], 1/8640],
[[[1, 10], [2, 3], [3, 2], [4, 2], [5, 1]], 163/230400],
[[[1, 10], [2, 3], [3, 2], [4, 2], [8, 1]], 13/69120],
[[[1, 10], [2, 3], [3, 2], [5, 1], [6, 2]], 389/14515200],
[[[1, 10], [2, 3], [3, 2], [6, 1], [7, 1]], 1/10080],
[[[1, 10], [2, 3], [3, 2], [6, 1], [9, 1]], 7/1244160],
[[[1, 10], [2, 3], [3, 3], [4, 1], [5, 1]], 143/155520],
[[[1, 10], [2, 3], [3, 3], [4, 1], [6, 2]], 23/622080],
[[[1, 10], [2, 3], [3, 3], [4, 1], [8, 1]], 1/6912],
[[[1, 10], [2, 3], [3, 3], [4, 2], [6, 1]], 89/829440],
[[[1, 10], [2, 3], [3, 3], [5, 1], [6, 1]], 19/28800],
[[[1, 10], [2, 3], [3, 4], [4, 1], [6, 1]], 959/2799360],
[[[1, 10], [2, 3], [4, 1], [5, 1], [7, 1]], 19/100800],
[[[1, 10], [2, 3], [4, 2], [5, 1], [8, 1]], 1/14400],
[[[1, 10], [2, 5], [3, 1], [4, 1], [7, 1]], 29/96768],
[[[1, 10], [2, 5], [3, 1], [4, 1], [9, 1]], 257/4976640],
[[[1, 10], [2, 5], [3, 1], [4, 2], [5, 1]], 7/6912],
[[[1, 10], [2, 5], [3, 1], [4, 2], [8, 1]], 1/3456],
[[[1, 10], [2, 5], [3, 1], [4, 3], [6, 1]], 7/69120],
[[[1, 10], [2, 5], [3, 1], [6, 1], [7, 1]], 257/5806080],
[[[1, 10], [2, 5], [3, 2], [4, 1], [5, 1]], 1367/1658880],
[[[1, 10], [2, 5], [3, 2], [4, 1], [6, 2]], 1129/11612160],
[[[1, 10], [2, 5], [3, 2], [4, 1], [8, 1]], 11/73728],
[[[1, 10], [2, 5], [3, 2], [4, 2], [6, 1]], 259/414720],
[[[1, 10], [2, 5], [3, 2], [5, 1], [6, 1]], 49/103680],
[[[1, 10], [2, 5], [3, 3], [4, 1], [6, 1]], 2299/2488320],
[[[1, 10], [2, 5], [4, 1], [5, 1], [8, 1]], 11/184320],
[[[1, 10], [2, 7], [3, 1], [4, 1], [5, 1]], 271/1658880],
[[[1, 10], [2, 7], [3, 1], [4, 1], [8, 1]], 19/663552],
[[[1, 10], [2, 7], [3, 1], [4, 2], [6, 1]], 55/221184],
[[[1, 10], [2, 7], [3, 1], [5, 1], [6, 1]], 43/829440],
[[[1, 10], [2, 7], [3, 2], [4, 1], [6, 1]], 61/165888],
[[[1, 10], [2, 9], [3, 1], [4, 1], [6, 1]], 23/663552],
[[[1, 11], [2, 2], [3, 1], [4, 1], [5, 2]], 101/432000],
[[[1, 11], [2, 2], [3, 1], [4, 2], [7, 1]], 1/32256],
[[[1, 11], [2, 2], [3, 1], [4, 2], [9, 1]], 1/829440],
[[[1, 11], [2, 2], [3, 1], [5, 1], [7, 1]], 1/8400],
[[[1, 11], [2, 2], [3, 1], [5, 1], [9, 1]], 7/1036800],
[[[1, 11], [2, 2], [3, 1], [5, 2], [6, 1]], 1/44800],
[[[1, 11], [2, 2], [3, 2], [4, 1], [7, 1]], 59/483840],
[[[1, 11], [2, 2], [3, 2], [4, 1], [9, 1]], 19/933120],
[[[1, 11], [2, 2], [3, 2], [4, 2], [5, 1]], 59/460800],
[[[1, 11], [2, 2], [3, 2], [4, 2], [8, 1]], 7/276480],
[[[1, 11], [2, 2], [3, 2], [5, 1], [6, 2]], 19/13063680],
[[[1, 11], [2, 2], [3, 2], [6, 1], [7, 1]], 19/1088640],
[[[1, 11], [2, 2], [3, 2], [6, 1], [9, 1]], 1/1866240],
[[[1, 11], [2, 2], [3, 3], [4, 1], [5, 1]], 863/2332800],
[[[1, 11], [2, 2], [3, 3], [4, 1], [8, 1]], 13/311040],
[[[1, 11], [2, 2], [3, 3], [5, 1], [6, 1]], 3637/21772800],
[[[1, 11], [2, 2], [3, 4], [4, 1], [6, 1]], 1/21870],
[[[1, 11], [2, 2], [4, 1], [5, 1], [7, 1]], 17/403200],
[[[1, 11], [2, 2], [4, 2], [5, 1], [8, 1]], 1/230400],
[[[1, 11], [2, 4], [3, 1], [4, 1], [7, 1]], 29/120960],
[[[1, 11], [2, 4], [3, 1], [4, 1], [9, 1]], 113/4976640],
[[[1, 11], [2, 4], [3, 1], [4, 2], [5, 1]], 217/345600],
[[[1, 11], [2, 4], [3, 1], [4, 2], [8, 1]], 1/7680],
[[[1, 11], [2, 4], [3, 1], [4, 3], [6, 1]], 7/552960],
[[[1, 11], [2, 4], [3, 1], [6, 1], [7, 1]], 113/5806080],
[[[1, 11], [2, 4], [3, 2], [4, 1], [5, 1]], 37/38400],
[[[1, 11], [2, 4], [3, 2], [4, 1], [6, 2]], 3439/209018880],
[[[1, 11], [2, 4], [3, 2], [4, 1], [8, 1]], 101/829440],
[[[1, 11], [2, 4], [3, 2], [4, 2], [6, 1]], 37/207360],
[[[1, 11], [2, 4], [3, 2], [5, 1], [6, 1]], 103/311040],
[[[1, 11], [2, 4], [3, 3], [4, 1], [6, 1]], 8297/17418240],
[[[1, 11], [2, 4], [4, 1], [5, 1], [8, 1]], 23/691200],
[[[1, 11], [2, 6], [3, 1], [4, 1], [5, 1]], 77/184320],
[[[1, 11], [2, 6], [3, 1], [4, 1], [8, 1]], 13/221184],
[[[1, 11], [2, 6], [3, 1], [4, 2], [6, 1]], 1007/5806080],
[[[1, 11], [2, 6], [3, 1], [5, 1], [6, 1]], 697/8294400],
[[[1, 11], [2, 6], [3, 2], [4, 1], [6, 1]], 2233/4976640],
[[[1, 11], [2, 8], [3, 1], [4, 1], [6, 1]], 119/1658880],
[[[1, 12], [2, 1], [3, 1], [4, 1], [5, 2]], 1/51840],
[[[1, 12], [2, 1], [3, 1], [5, 1], [7, 1]], 19/907200],
[[[1, 12], [2, 1], [3, 1], [5, 1], [9, 1]], 1/1555200],
[[[1, 12], [2, 1], [3, 1], [5, 2], [6, 1]], 127/108864000],
[[[1, 12], [2, 1], [3, 2], [4, 1], [7, 1]], 1/69120],
[[[1, 12], [2, 1], [3, 2], [4, 1], [9, 1]], 1/933120],
[[[1, 12], [2, 1], [3, 2], [6, 1], [7, 1]], 1/1088640],
[[[1, 12], [2, 1], [3, 2], [6, 1], [9, 1]], 1/55987200],
[[[1, 12], [2, 1], [3, 3], [4, 1], [5, 1]], 41/874800],
[[[1, 12], [2, 1], [3, 3], [4, 1], [8, 1]], 23/5598720],
[[[1, 12], [2, 1], [3, 3], [5, 1], [6, 1]], 1397/97977600],
[[[1, 12], [2, 1], [4, 1], [5, 1], [7, 1]], 1/403200],
[[[1, 12], [2, 3], [3, 1], [4, 1], [7, 1]], 127/1451520],
[[[1, 12], [2, 3], [3, 1], [4, 1], [9, 1]], 23/4976640],
[[[1, 12], [2, 3], [3, 1], [4, 2], [5, 1]], 611/4147200],
[[[1, 12], [2, 3], [3, 1], [4, 2], [8, 1]], 19/829440],
[[[1, 12], [2, 3], [3, 1], [6, 1], [7, 1]], 23/5806080],
[[[1, 12], [2, 3], [3, 2], [4, 1], [5, 1]], 25019/58060800],
[[[1, 12], [2, 3], [3, 2], [4, 1], [6, 2]], 887/1045094400],
[[[1, 12], [2, 3], [3, 2], [4, 1], [8, 1]], 1/24576],
[[[1, 12], [2, 3], [3, 2], [4, 2], [6, 1]], 43/2488320],
[[[1, 12], [2, 3], [3, 2], [5, 1], [6, 1]], 2161/21772800],
[[[1, 12], [2, 3], [3, 3], [4, 1], [6, 1]], 32503/313528320],
[[[1, 12], [2, 3], [4, 1], [5, 1], [8, 1]], 7/921600],
[[[1, 12], [2, 5], [3, 1], [4, 1], [5, 1]], 3479/8294400],
[[[1, 12], [2, 5], [3, 1], [4, 1], [8, 1]], 49/1105920],
[[[1, 12], [2, 5], [3, 1], [4, 2], [6, 1]], 3877/69672960],
[[[1, 12], [2, 5], [3, 1], [5, 1], [6, 1]], 649/11612160],
[[[1, 12], [2, 5], [3, 2], [4, 1], [6, 1]], 4199/17418240],
[[[1, 12], [2, 7], [3, 1], [4, 1], [6, 1]], 443/5806080],
[[[1, 13], [2, 2], [3, 1], [4, 1], [7, 1]], 1/72576],
[[[1, 13], [2, 2], [3, 1], [4, 1], [9, 1]], 31/74649600],
[[[1, 13], [2, 2], [3, 1], [4, 2], [5, 1]], 43/4147200],
[[[1, 13], [2, 2], [3, 1], [4, 2], [8, 1]], 1/829440],
[[[1, 13], [2, 2], [3, 1], [6, 1], [7, 1]], 31/87091200],
[[[1, 13], [2, 2], [3, 2], [4, 1], [5, 1]], 10319/130636800],
[[[1, 13], [2, 2], [3, 2], [4, 1], [8, 1]], 29/4976640],
[[[1, 13], [2, 2], [3, 2], [5, 1], [6, 1]], 853/65318400],
[[[1, 13], [2, 2], [3, 3], [4, 1], [6, 1]], 12647/1567641600],
[[[1, 13], [2, 2], [4, 1], [5, 1], [8, 1]], 1/1382400],
[[[1, 13], [2, 4], [3, 1], [4, 1], [5, 1]], 33119/174182400],
[[[1, 13], [2, 4], [3, 1], [4, 1], [8, 1]], 31/1990656],
[[[1, 13], [2, 4], [3, 1], [4, 2], [6, 1]], 1373/174182400],
[[[1, 13], [2, 4], [3, 1], [5, 1], [6, 1]], 9433/522547200],
[[[1, 13], [2, 4], [3, 2], [4, 1], [6, 1]], 937/14929920],
[[[1, 13], [2, 6], [3, 1], [4, 1], [6, 1]], 4247/104509440],
[[[1, 14], [2, 1], [3, 1], [4, 1], [7, 1]], 1/1451520],
[[[1, 14], [2, 1], [3, 1], [4, 1], [9, 1]], 1/74649600],
[[[1, 14], [2, 1], [3, 1], [6, 1], [7, 1]], 1/87091200],
[[[1, 14], [2, 1], [3, 2], [4, 1], [5, 1]], 4117/870912000],
[[[1, 14], [2, 1], [3, 2], [4, 1], [8, 1]], 41/149299200],
[[[1, 14], [2, 1], [3, 2], [5, 1], [6, 1]], 143/244944000],
[[[1, 14], [2, 1], [4, 1], [5, 1], [8, 1]], 1/41472000],
[[[1, 14], [2, 3], [3, 1], [4, 1], [5, 1]], 1031/24883200],
[[[1, 14], [2, 3], [3, 1], [4, 1], [8, 1]], 1/368640],
[[[1, 14], [2, 3], [3, 1], [4, 2], [6, 1]], 43/116121600],
[[[1, 14], [2, 3], [3, 1], [5, 1], [6, 1]], 1289/435456000],
[[[1, 14], [2, 3], [3, 2], [4, 1], [6, 1]], 5959/783820800],
[[[1, 14], [2, 5], [3, 1], [4, 1], [6, 1]], 3023/261273600],
[[[1, 15], [2, 2], [3, 1], [4, 1], [5, 1]], 10837/2612736000],
[[[1, 15], [2, 2], [3, 1], [4, 1], [8, 1]], 11/49766400],
[[[1, 15], [2, 2], [3, 1], [5, 1], [6, 1]], 121/522547200],
[[[1, 15], [2, 2], [3, 2], [4, 1], [6, 1]], 509/1567641600],
[[[1, 15], [2, 4], [3, 1], [4, 1], [6, 1]], 919/522547200],
[[[1, 16], [2, 1], [3, 1], [4, 1], [5, 1]], 79/522547200],
[[[1, 16], [2, 1], [3, 1], [4, 1], [8, 1]], 1/149299200],
[[[1, 16], [2, 1], [3, 1], [5, 1], [6, 1]], 107/15676416000],
[[[1, 16], [2, 3], [3, 1], [4, 1], [6, 1]], 103/783820800],
[[[1, 17], [2, 2], [3, 1], [4, 1], [6, 1]], 59/15676416000],
[[[2, 1], [3, 2], [6, 1], [9, 2], [18, 1]], 1/162],
[[[2, 1], [6, 3], [10, 1], [18, 1], [30, 1]], 1/135],
[[[2, 3], [6, 2], [10, 1], [14, 1], [30, 1]], 1/210],
[[[1, 1], [2, 2], [3, 1], [6, 4], [9, 1], [18, 1]], 1/2916],
[[[1, 1], [2, 2], [3, 1], [6, 4], [10, 1], [30, 1]], 1/270],
[[[1, 1], [2, 2], [3, 3], [6, 2], [9, 1], [18, 1]], 1/324],
[[[1, 1], [2, 2], [4, 1], [6, 2], [8, 1], [18, 2]], 1/432],
[[[1, 1], [2, 2], [4, 1], [6, 2], [10, 1], [18, 2]], 1/1080],
[[[1, 1], [2, 2], [4, 1], [6, 2], [10, 2], [30, 1]], 1/300],
[[[1, 1], [2, 2], [6, 2], [10, 1], [14, 1], [30, 1]], 1/210],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 6], [12, 1]], 1/3888],
[[[1, 1], [2, 4], [3, 1], [6, 2], [10, 2], [18, 1]], 1/2700],
[[[1, 1], [2, 4], [3, 1], [6, 3], [9, 1], [18, 1]], 1/1944],
[[[1, 1], [2, 4], [3, 1], [6, 3], [10, 1], [30, 1]], 1/540],
[[[1, 1], [2, 4], [3, 1], [6, 3], [14, 1], [18, 1]], 1/252],
[[[1, 1], [2, 4], [3, 1], [6, 4], [10, 1], [18, 1]], 19/4860],
[[[1, 1], [2, 4], [4, 1], [6, 3], [10, 1], [30, 1]], 1/360],
[[[1, 1], [2, 4], [4, 1], [6, 4], [8, 1], [18, 1]], 1/432],
[[[1, 1], [2, 4], [4, 1], [6, 4], [10, 1], [18, 1]], 1/1080],
[[[1, 1], [2, 6], [3, 1], [4, 1], [6, 5], [12, 1]], 1/2592],
[[[1, 1], [2, 6], [3, 1], [6, 1], [10, 2], [14, 1]], 1/4200],
[[[1, 1], [2, 6], [3, 1], [6, 2], [9, 1], [18, 1]], 1/38880],
[[[1, 1], [2, 6], [3, 1], [6, 3], [10, 1], [14, 1]], 1/7560],
[[[1, 1], [2, 6], [3, 1], [6, 3], [10, 1], [18, 1]], 13/19440],
[[[1, 1], [2, 6], [4, 1], [6, 1], [10, 2], [18, 1]], 1/3600],
[[[1, 1], [2, 6], [4, 1], [6, 2], [8, 1], [10, 2]], 1/7200],
[[[1, 1], [2, 6], [4, 1], [6, 2], [10, 1], [30, 1]], 1/7200],
[[[1, 1], [2, 6], [4, 1], [6, 3], [10, 1], [18, 1]], 1/6480],
[[[1, 1], [2, 6], [4, 1], [6, 4], [8, 1], [10, 1]], 1/25920],
[[[1, 1], [2, 8], [3, 1], [4, 1], [6, 4], [12, 1]], 1/51840],
[[[1, 1], [2, 8], [3, 1], [6, 1], [9, 1], [18, 1]], 1/6531840],
[[[1, 1], [2, 8], [3, 1], [6, 2], [10, 1], [14, 1]], 1/7560],
[[[1, 1], [2, 8], [3, 1], [6, 2], [10, 1], [18, 1]], 1/194400],
[[[1, 1], [2, 8], [4, 1], [6, 1], [8, 1], [10, 2]], 1/7200],
[[[1, 1], [2, 8], [4, 1], [6, 2], [10, 1], [14, 1]], 1/10080],
[[[1, 1], [2, 8], [4, 1], [6, 2], [10, 1], [18, 1]], 1/6480],
[[[1, 1], [2, 8], [4, 1], [6, 3], [8, 1], [10, 1]], 1/12960],
[[[1, 1], [2, 10], [3, 1], [4, 1], [6, 3], [12, 1]], 1/8709120],
[[[1, 1], [2, 10], [3, 1], [6, 1], [10, 1], [14, 1]], 1/302400],
[[[1, 1], [2, 10], [4, 1], [6, 1], [10, 1], [14, 1]], 1/10080],
[[[1, 1], [2, 10], [4, 1], [6, 1], [10, 1], [18, 1]], 1/259200],
[[[1, 1], [2, 10], [4, 1], [6, 2], [8, 1], [10, 1]], 7/172800],
[[[1, 1], [2, 12], [4, 1], [6, 1], [8, 1], [10, 1]], 1/518400],
[[[1, 2], [2, 1], [3, 2], [4, 1], [5, 1], [9, 2]], 1/1080],
[[[1, 2], [2, 1], [3, 2], [4, 1], [5, 2], [15, 1]], 1/300],
[[[1, 2], [2, 1], [3, 2], [4, 1], [8, 1], [9, 2]], 1/432],
[[[1, 2], [2, 1], [3, 2], [5, 1], [7, 1], [15, 1]], 1/210],
[[[1, 2], [2, 1], [3, 2], [6, 3], [9, 1], [18, 1]], 1/324],
[[[1, 2], [2, 1], [3, 4], [5, 1], [6, 1], [15, 1]], 1/270],
[[[1, 2], [2, 1], [3, 4], [6, 1], [9, 1], [18, 1]], 1/2916],
[[[1, 2], [2, 3], [3, 1], [6, 3], [9, 1], [18, 1]], 1/648],
[[[1, 2], [2, 3], [3, 1], [6, 3], [10, 1], [30, 1]], 1/180],
[[[1, 2], [2, 3], [3, 1], [6, 3], [14, 1], [18, 1]], 1/252],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 5], [12, 1]], 5/1944],
[[[1, 2], [2, 3], [3, 2], [6, 2], [9, 1], [18, 1]], 1/162],
[[[1, 2], [2, 3], [3, 2], [6, 3], [10, 1], [18, 1]], 1/3240],
[[[1, 2], [2, 3], [3, 4], [4, 1], [6, 3], [12, 1]], 1/432],
[[[1, 2], [2, 3], [4, 1], [6, 3], [10, 1], [30, 1]], 1/360],
[[[1, 2], [2, 3], [4, 2], [6, 2], [10, 1], [30, 1]], 1/480],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 1], [10, 3]], 1/6000],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 3], [10, 2]], 1/10800],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 4], [18, 1]], 19/7776],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 5], [8, 1]], 7/7776],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 5], [10, 1]], 7/19440],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 5], [12, 1]], 1/864],
[[[1, 2], [2, 5], [3, 1], [4, 2], [6, 4], [12, 1]], 1/576],
[[[1, 2], [2, 5], [3, 1], [6, 1], [10, 2], [14, 1]], 1/4200],
[[[1, 2], [2, 5], [3, 1], [6, 2], [9, 1], [18, 1]], 1/2592],
[[[1, 2], [2, 5], [3, 1], [6, 3], [10, 1], [14, 1]], 1/7560],
[[[1, 2], [2, 5], [3, 1], [6, 3], [10, 1], [18, 1]], 11/3240],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 4], [12, 1]], 1/648],
[[[1, 2], [2, 5], [3, 2], [6, 2], [10, 1], [14, 1]], 1/5040],
[[[1, 2], [2, 5], [4, 1], [6, 1], [10, 2], [18, 1]], 1/3600],
[[[1, 2], [2, 5], [4, 1], [6, 2], [10, 1], [30, 1]], 1/720],
[[[1, 2], [2, 5], [4, 1], [6, 3], [10, 1], [18, 1]], 1/6480],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 2], [10, 2]], 7/10800],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 3], [14, 1]], 1/12096],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 3], [18, 1]], 19/77760],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 4], [8, 1]], 1/15552],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 4], [10, 1]], 11/38880],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 4], [12, 1]], 1/3456],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 3], [12, 1]], 1/11520],
[[[1, 2], [2, 7], [3, 1], [6, 1], [9, 1], [18, 1]], 1/181440],
[[[1, 2], [2, 7], [3, 1], [6, 2], [10, 1], [14, 1]], 1/1890],
[[[1, 2], [2, 7], [3, 1], [6, 2], [10, 1], [18, 1]], 1/12960],
[[[1, 2], [2, 7], [3, 2], [4, 1], [6, 3], [12, 1]], 1/51840],
[[[1, 2], [2, 7], [4, 1], [6, 1], [8, 1], [10, 2]], 1/2400],
[[[1, 2], [2, 7], [4, 1], [6, 2], [10, 1], [14, 1]], 1/5040],
[[[1, 2], [2, 7], [4, 1], [6, 2], [10, 1], [18, 1]], 1/1620],
[[[1, 2], [2, 7], [4, 1], [6, 3], [8, 1], [10, 1]], 1/4320],
[[[1, 2], [2, 7], [4, 2], [6, 1], [10, 1], [18, 1]], 1/5760],
[[[1, 2], [2, 7], [4, 2], [6, 2], [8, 1], [10, 1]], 1/5760],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 1], [10, 2]], 49/432000],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 2], [14, 1]], 1/12096],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 2], [18, 1]], 1/311040],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 3], [8, 1]], 7/207360],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 3], [10, 1]], 29/86400],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 3], [12, 1]], 1/241920],
[[[1, 2], [2, 9], [3, 1], [6, 1], [10, 1], [14, 1]], 1/18900],
[[[1, 2], [2, 9], [3, 2], [4, 1], [6, 2], [12, 1]], 1/8709120],
[[[1, 2], [2, 9], [4, 1], [6, 1], [10, 1], [14, 1]], 1/2016],
[[[1, 2], [2, 9], [4, 1], [6, 1], [10, 1], [18, 1]], 1/16200],
[[[1, 2], [2, 9], [4, 1], [6, 2], [8, 1], [10, 1]], 1/3840],
[[[1, 2], [2, 9], [4, 2], [6, 1], [8, 1], [10, 1]], 1/5760],
[[[1, 2], [2, 11], [3, 1], [4, 1], [6, 1], [14, 1]], 1/483840],
[[[1, 2], [2, 11], [3, 1], [4, 1], [6, 2], [8, 1]], 1/622080],
[[[1, 2], [2, 11], [3, 1], [4, 1], [6, 2], [10, 1]], 47/777600],
[[[1, 2], [2, 11], [4, 1], [6, 1], [8, 1], [10, 1]], 1/28800],
[[[1, 2], [2, 13], [3, 1], [4, 1], [6, 1], [8, 1]], 1/49766400],
[[[1, 2], [2, 13], [3, 1], [4, 1], [6, 1], [10, 1]], 1151/870912000],
[[[1, 3], [2, 2], [3, 2], [4, 2], [5, 1], [15, 1]], 1/480],
[[[1, 3], [2, 2], [3, 2], [6, 2], [9, 1], [18, 1]], 1/162],
[[[1, 3], [2, 2], [3, 3], [4, 1], [5, 1], [15, 1]], 1/360],
[[[1, 3], [2, 2], [3, 3], [4, 1], [6, 4], [12, 1]], 1/432],
[[[1, 3], [2, 2], [3, 3], [5, 1], [6, 1], [15, 1]], 1/180],
[[[1, 3], [2, 2], [3, 3], [5, 1], [6, 2], [9, 1]], 1/3240],
[[[1, 3], [2, 2], [3, 3], [6, 1], [7, 1], [9, 1]], 1/252],
[[[1, 3], [2, 2], [3, 3], [6, 1], [9, 1], [18, 1]], 1/648],
[[[1, 3], [2, 2], [3, 5], [4, 1], [6, 2], [12, 1]], 5/1944],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 4], [18, 1]], 19/7776],
[[[1, 3], [2, 4], [3, 1], [4, 2], [6, 3], [18, 1]], 1/576],
[[[1, 3], [2, 4], [3, 1], [4, 2], [6, 4], [12, 1]], 1/576],
[[[1, 3], [2, 4], [3, 1], [4, 3], [6, 3], [12, 1]], 1/768],
[[[1, 3], [2, 4], [3, 1], [6, 2], [9, 1], [18, 1]], 1/864],
[[[1, 3], [2, 4], [3, 1], [6, 3], [10, 1], [18, 1]], 1/720],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 2], [10, 2]], 1/7200],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 3], [18, 1]], 1/5184],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 4], [8, 1]], 7/2592],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 4], [10, 1]], 7/6480],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 4], [12, 1]], 1/216],
[[[1, 3], [2, 4], [3, 2], [4, 2], [6, 3], [12, 1]], 1/576],
[[[1, 3], [2, 4], [3, 2], [4, 3], [6, 2], [12, 1]], 1/768],
[[[1, 3], [2, 4], [3, 2], [6, 1], [9, 1], [18, 1]], 1/2592],
[[[1, 3], [2, 4], [3, 2], [6, 2], [10, 1], [14, 1]], 1/5040],
[[[1, 3], [2, 4], [3, 3], [4, 1], [5, 1], [6, 3]], 1/2592],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 2], [9, 1]], 1/5184],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 3], [8, 1]], 5/5184],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 3], [12, 1]], 1/216],
[[[1, 3], [2, 4], [3, 3], [4, 2], [6, 2], [12, 1]], 1/576],
[[[1, 3], [2, 4], [4, 1], [6, 2], [10, 1], [30, 1]], 1/480],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 2], [10, 2]], 1/1200],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 3], [14, 1]], 1/6048],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 3], [18, 1]], 13/7776],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 4], [8, 1]], 1/5184],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 4], [10, 1]], 13/38880],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 4], [12, 1]], 1/1152],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 1], [10, 2]], 1/3200],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 2], [18, 1]], 1/6912],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 3], [8, 1]], 1/6912],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 3], [10, 1]], 1/8640],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 3], [12, 1]], 1/1152],
[[[1, 3], [2, 6], [3, 1], [6, 1], [9, 1], [18, 1]], 1/17280],
[[[1, 3], [2, 6], [3, 1], [6, 2], [10, 1], [14, 1]], 1/2520],
[[[1, 3], [2, 6], [3, 1], [6, 2], [10, 1], [18, 1]], 1/4320],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 2], [14, 1]], 1/8064],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 3], [8, 1]], 1/10368],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 3], [10, 1]], 13/25920],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 3], [12, 1]], 1/3456],
[[[1, 3], [2, 6], [3, 2], [4, 2], [6, 2], [12, 1]], 1/11520],
[[[1, 3], [2, 6], [4, 1], [6, 2], [10, 1], [14, 1]], 1/10080],
[[[1, 3], [2, 6], [4, 1], [6, 2], [10, 1], [18, 1]], 1/2160],
[[[1, 3], [2, 6], [4, 2], [6, 1], [10, 1], [18, 1]], 1/2880],
[[[1, 3], [2, 6], [4, 2], [6, 2], [8, 1], [10, 1]], 1/5760],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 1], [10, 2]], 1/1600],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 2], [14, 1]], 5/12096],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 2], [18, 1]], 1/19440],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 3], [8, 1]], 1/4608],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 3], [10, 1]], 37/25920],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 3], [12, 1]], 1/23040],
[[[1, 3], [2, 8], [3, 1], [4, 2], [6, 1], [14, 1]], 1/10752],
[[[1, 3], [2, 8], [3, 1], [4, 2], [6, 2], [8, 1]], 1/6912],
[[[1, 3], [2, 8], [3, 1], [4, 2], [6, 2], [10, 1]], 1/2160],
[[[1, 3], [2, 8], [3, 1], [6, 1], [10, 1], [14, 1]], 1/5040],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 2], [8, 1]], 1/414720],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 2], [10, 1]], 71/518400],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 2], [12, 1]], 1/241920],
[[[1, 3], [2, 8], [4, 1], [6, 1], [10, 1], [14, 1]], 1/1440],
[[[1, 3], [2, 8], [4, 1], [6, 1], [10, 1], [18, 1]], 1/4320],
[[[1, 3], [2, 8], [4, 1], [6, 2], [8, 1], [10, 1]], 1/2304],
[[[1, 3], [2, 8], [4, 2], [6, 1], [8, 1], [10, 1]], 1/1440],
[[[1, 3], [2, 10], [3, 1], [4, 1], [6, 1], [14, 1]], 17/483840],
[[[1, 3], [2, 10], [3, 1], [4, 1], [6, 2], [8, 1]], 1/34560],
[[[1, 3], [2, 10], [3, 1], [4, 1], [6, 2], [10, 1]], 143/259200],
[[[1, 3], [2, 10], [3, 1], [4, 2], [6, 1], [8, 1]], 1/276480],
[[[1, 3], [2, 10], [3, 1], [4, 2], [6, 1], [10, 1]], 91/1382400],
[[[1, 3], [2, 10], [4, 1], [6, 1], [8, 1], [10, 1]], 1/5760],
[[[1, 3], [2, 12], [3, 1], [4, 1], [6, 1], [8, 1]], 1/1658880],
[[[1, 3], [2, 12], [3, 1], [4, 1], [6, 1], [10, 1]], 1163/43545600],
[[[1, 4], [2, 1], [3, 2], [5, 2], [6, 1], [9, 1]], 1/2700],
[[[1, 4], [2, 1], [3, 3], [4, 1], [5, 1], [15, 1]], 1/360],
[[[1, 4], [2, 1], [3, 3], [5, 1], [6, 1], [15, 1]], 1/540],
[[[1, 4], [2, 1], [3, 3], [6, 1], [7, 1], [9, 1]], 1/252],
[[[1, 4], [2, 1], [3, 3], [6, 1], [9, 1], [18, 1]], 1/1944],
[[[1, 4], [2, 1], [3, 4], [4, 1], [5, 1], [9, 1]], 1/1080],
[[[1, 4], [2, 1], [3, 4], [4, 1], [8, 1], [9, 1]], 1/432],
[[[1, 4], [2, 1], [3, 4], [5, 1], [6, 1], [9, 1]], 19/4860],
[[[1, 4], [2, 1], [3, 6], [4, 1], [6, 1], [12, 1]], 1/3888],
[[[1, 4], [2, 3], [3, 1], [6, 2], [9, 1], [18, 1]], 1/2592],
[[[1, 4], [2, 3], [3, 2], [4, 1], [5, 1], [15, 1]], 1/480],
[[[1, 4], [2, 3], [3, 2], [4, 1], [5, 2], [6, 2]], 1/7200],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 3], [18, 1]], 1/5184],
[[[1, 4], [2, 3], [3, 2], [4, 2], [6, 3], [12, 1]], 1/576],
[[[1, 4], [2, 3], [3, 2], [4, 3], [6, 2], [12, 1]], 1/768],
[[[1, 4], [2, 3], [3, 2], [5, 1], [6, 2], [7, 1]], 1/5040],
[[[1, 4], [2, 3], [3, 2], [6, 1], [9, 1], [18, 1]], 1/864],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 2], [9, 1]], 1/5184],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 3], [8, 1]], 5/5184],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 3], [10, 1]], 1/2592],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 3], [12, 1]], 1/216],
[[[1, 4], [2, 3], [3, 3], [4, 2], [6, 1], [9, 1]], 1/576],
[[[1, 4], [2, 3], [3, 3], [4, 2], [6, 2], [12, 1]], 1/576],
[[[1, 4], [2, 3], [3, 3], [4, 3], [6, 1], [12, 1]], 1/768],
[[[1, 4], [2, 3], [3, 3], [5, 1], [6, 1], [9, 1]], 1/720],
[[[1, 4], [2, 3], [3, 4], [4, 1], [5, 1], [6, 2]], 7/6480],
[[[1, 4], [2, 3], [3, 4], [4, 1], [6, 1], [9, 1]], 19/7776],
[[[1, 4], [2, 3], [3, 4], [4, 1], [6, 2], [8, 1]], 7/2592],
[[[1, 4], [2, 3], [3, 4], [4, 1], [6, 2], [12, 1]], 1/216],
[[[1, 4], [2, 3], [3, 4], [4, 2], [6, 1], [12, 1]], 1/576],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 3], [14, 1]], 1/12096],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 3], [18, 1]], 11/5184],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 4], [12, 1]], 1/3456],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 1], [10, 2]], 1/4800],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 2], [18, 1]], 1/3456],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 3], [8, 1]], 1/6912],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 3], [10, 1]], 1/17280],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 3], [12, 1]], 1/768],
[[[1, 4], [2, 5], [3, 1], [6, 1], [9, 1], [18, 1]], 7/20736],
[[[1, 4], [2, 5], [3, 1], [6, 2], [10, 1], [18, 1]], 1/12960],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 2], [7, 1]], 1/8064],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 2], [14, 1]], 1/4032],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 3], [8, 1]], 1/3456],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 3], [10, 1]], 1/1728],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 3], [12, 1]], 1/1152],
[[[1, 4], [2, 5], [3, 2], [4, 2], [5, 1], [6, 2]], 1/11520],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 1], [9, 1]], 1/6912],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 2], [8, 1]], 1/2304],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 2], [10, 1]], 1/5760],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 2], [12, 1]], 5/2304],
[[[1, 4], [2, 5], [3, 3], [4, 1], [6, 2], [12, 1]], 1/3456],
[[[1, 4], [2, 5], [4, 2], [6, 1], [10, 1], [18, 1]], 1/5760],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 1], [10, 2]], 7/9600],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 2], [14, 1]], 1/1728],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 2], [18, 1]], 1/5184],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 3], [8, 1]], 5/13824],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 3], [10, 1]], 7/5760],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 3], [12, 1]], 1/6912],
[[[1, 4], [2, 7], [3, 1], [4, 2], [6, 1], [14, 1]], 1/3584],
[[[1, 4], [2, 7], [3, 1], [4, 2], [6, 2], [8, 1]], 1/1728],
[[[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]], 1/6144],
[[[1, 4], [2, 7], [3, 1], [4, 3], [6, 1], [10, 1]], 1/5120],
[[[1, 4], [2, 7], [3, 1], [6, 1], [10, 1], [14, 1]], 1/5040],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 2], [8, 1]], 1/27648],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 2], [10, 1]], 11/17280],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 2], [12, 1]], 1/23040],
[[[1, 4], [2, 7], [4, 1], [6, 1], [10, 1], [14, 1]], 1/3360],
[[[1, 4], [2, 7], [4, 1], [6, 1], [10, 1], [18, 1]], 1/4320],
[[[1, 4], [2, 7], [4, 1], [6, 2], [8, 1], [10, 1]], 1/34560],
[[[1, 4], [2, 7], [4, 2], [6, 1], [8, 1], [10, 1]], 1/1920],
[[[1, 4], [2, 9], [3, 1], [4, 1], [6, 1], [14, 1]], 19/120960],
[[[1, 4], [2, 9], [3, 1], [4, 1], [6, 2], [8, 1]], 1/6912],
[[[1, 4], [2, 9], [3, 1], [4, 1], [6, 2], [10, 1]], 1/640],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 1], [8, 1]], 1/17280],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 1], [10, 1]], 307/691200],
[[[1, 4], [2, 9], [4, 1], [6, 1], [8, 1], [10, 1]], 1/3456],
[[[1, 4], [2, 11], [3, 1], [4, 1], [6, 1], [8, 1]], 7/1105920],
[[[1, 4], [2, 11], [3, 1], [4, 1], [6, 1], [10, 1]], 1097/6451200],
[[[1, 5], [2, 2], [3, 1], [4, 1], [5, 2], [9, 1]], 1/3600],
[[[1, 5], [2, 2], [3, 1], [4, 1], [5, 3], [6, 1]], 1/6000],
[[[1, 5], [2, 2], [3, 1], [5, 2], [6, 1], [7, 1]], 1/4200],
[[[1, 5], [2, 2], [3, 2], [4, 1], [5, 1], [15, 1]], 1/720],
[[[1, 5], [2, 2], [3, 2], [5, 1], [6, 2], [7, 1]], 1/5040],
[[[1, 5], [2, 2], [3, 2], [6, 1], [9, 1], [18, 1]], 1/2592],
[[[1, 5], [2, 2], [3, 3], [4, 1], [5, 1], [9, 1]], 1/6480],
[[[1, 5], [2, 2], [3, 3], [4, 1], [5, 2], [6, 1]], 1/10800],
[[[1, 5], [2, 2], [3, 3], [5, 1], [6, 1], [7, 1]], 1/7560],
[[[1, 5], [2, 2], [3, 3], [5, 1], [6, 1], [9, 1]], 11/3240],
[[[1, 5], [2, 2], [3, 4], [4, 1], [6, 1], [9, 1]], 19/7776],
[[[1, 5], [2, 2], [3, 4], [4, 1], [6, 2], [12, 1]], 1/648],
[[[1, 5], [2, 2], [3, 4], [4, 2], [6, 1], [12, 1]], 1/576],
[[[1, 5], [2, 2], [3, 5], [4, 1], [5, 1], [6, 1]], 7/19440],
[[[1, 5], [2, 2], [3, 5], [4, 1], [6, 1], [8, 1]], 7/7776],
[[[1, 5], [2, 2], [3, 5], [4, 1], [6, 1], [12, 1]], 1/864],
[[[1, 5], [2, 4], [3, 1], [4, 2], [5, 1], [9, 1]], 1/5760],
[[[1, 5], [2, 4], [3, 1], [4, 2], [5, 2], [6, 1]], 1/4800],
[[[1, 5], [2, 4], [3, 1], [4, 2], [6, 2], [18, 1]], 1/6912],
[[[1, 5], [2, 4], [3, 1], [6, 1], [9, 1], [18, 1]], 7/20736],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 2], [7, 1]], 1/4032],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 2], [14, 1]], 1/8064],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 3], [12, 1]], 1/3456],
[[[1, 5], [2, 4], [3, 2], [4, 2], [5, 1], [6, 2]], 1/5760],
[[[1, 5], [2, 4], [3, 2], [4, 2], [6, 1], [9, 1]], 1/3456],
[[[1, 5], [2, 4], [3, 2], [4, 2], [6, 2], [8, 1]], 1/2304],
[[[1, 5], [2, 4], [3, 2], [4, 2], [6, 2], [10, 1]], 1/11520],
[[[1, 5], [2, 4], [3, 2], [4, 2], [6, 2], [12, 1]], 5/2304],
[[[1, 5], [2, 4], [3, 2], [5, 1], [6, 1], [9, 1]], 1/12960],
[[[1, 5], [2, 4], [3, 3], [4, 1], [5, 1], [6, 2]], 1/1728],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 1], [7, 1]], 1/12096],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 1], [9, 1]], 11/5184],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 2], [8, 1]], 1/3456],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 2], [12, 1]], 1/1152],
[[[1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [6, 1]], 1/17280],
[[[1, 5], [2, 4], [3, 3], [4, 2], [6, 1], [8, 1]], 1/6912],
[[[1, 5], [2, 4], [3, 3], [4, 2], [6, 1], [12, 1]], 1/768],
[[[1, 5], [2, 4], [3, 4], [4, 1], [6, 1], [12, 1]], 1/3456],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 1], [10, 2]], 1/7200],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 2], [14, 1]], 1/4032],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 2], [18, 1]], 1/5184],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 3], [8, 1]], 1/41472],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 3], [10, 1]], 1/25920],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 3], [12, 1]], 1/9216],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 1], [7, 1]], 1/10752],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 1], [14, 1]], 1/3584],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 2], [8, 1]], 1/2304],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 2], [10, 1]], 1/1920],
[[[1, 5], [2, 6], [3, 1], [4, 3], [5, 1], [6, 1]], 1/15360],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 1], [8, 1]], 1/2048],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 1], [10, 1]], 1/3840],
[[[1, 5], [2, 6], [3, 1], [6, 1], [10, 1], [14, 1]], 1/20160],
[[[1, 5], [2, 6], [3, 2], [4, 1], [5, 1], [6, 2]], 1/17280],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 1], [9, 1]], 1/20736],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 2], [8, 1]], 1/6912],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 2], [10, 1]], 7/11520],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 2], [12, 1]], 7/27648],
[[[1, 5], [2, 6], [4, 1], [6, 1], [10, 1], [18, 1]], 1/17280],
[[[1, 5], [2, 8], [3, 1], [4, 1], [6, 1], [14, 1]], 1/4032],
[[[1, 5], [2, 8], [3, 1], [4, 1], [6, 2], [8, 1]], 5/20736],
[[[1, 5], [2, 8], [3, 1], [4, 1], [6, 2], [10, 1]], 71/51840],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 1], [8, 1]], 1/4608],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 1], [10, 1]], 13/15360],
[[[1, 5], [2, 8], [4, 1], [6, 1], [8, 1], [10, 1]], 1/11520],
[[[1, 5], [2, 10], [3, 1], [4, 1], [6, 1], [8, 1]], 23/829440],
[[[1, 5], [2, 10], [3, 1], [4, 1], [6, 1], [10, 1]], 457/1036800],
[[[1, 6], [2, 1], [3, 1], [4, 1], [5, 2], [9, 1]], 1/3600],
[[[1, 6], [2, 1], [3, 1], [5, 2], [6, 1], [7, 1]], 1/4200],
[[[1, 6], [2, 1], [3, 2], [4, 1], [5, 1], [15, 1]], 1/7200],
[[[1, 6], [2, 1], [3, 2], [4, 1], [5, 2], [8, 1]], 1/7200],
[[[1, 6], [2, 1], [3, 2], [6, 1], [9, 1], [18, 1]], 1/38880],
[[[1, 6], [2, 1], [3, 3], [4, 1], [5, 1], [9, 1]], 1/6480],
[[[1, 6], [2, 1], [3, 3], [5, 1], [6, 1], [7, 1]], 1/7560],
[[[1, 6], [2, 1], [3, 3], [5, 1], [6, 1], [9, 1]], 13/19440],
[[[1, 6], [2, 1], [3, 4], [4, 1], [5, 1], [8, 1]], 1/25920],
[[[1, 6], [2, 1], [3, 5], [4, 1], [6, 1], [12, 1]], 1/2592],
[[[1, 6], [2, 3], [3, 1], [4, 2], [5, 1], [9, 1]], 1/2880],
[[[1, 6], [2, 3], [3, 1], [4, 2], [5, 2], [6, 1]], 1/3200],
[[[1, 6], [2, 3], [3, 1], [6, 1], [9, 1], [18, 1]], 1/17280],
[[[1, 6], [2, 3], [3, 2], [4, 1], [5, 1], [7, 1]], 1/10080],
[[[1, 6], [2, 3], [3, 2], [4, 1], [5, 1], [9, 1]], 1/2160],
[[[1, 6], [2, 3], [3, 2], [4, 1], [5, 2], [6, 1]], 1/1200],
[[[1, 6], [2, 3], [3, 2], [4, 1], [6, 2], [7, 1]], 1/8064],
[[[1, 6], [2, 3], [3, 2], [4, 2], [5, 1], [8, 1]], 1/5760],
[[[1, 6], [2, 3], [3, 2], [4, 2], [6, 1], [9, 1]], 1/6912],
[[[1, 6], [2, 3], [3, 2], [4, 2], [6, 2], [12, 1]], 1/11520],
[[[1, 6], [2, 3], [3, 2], [5, 1], [6, 1], [7, 1]], 1/2520],
[[[1, 6], [2, 3], [3, 2], [5, 1], [6, 1], [9, 1]], 1/4320],
[[[1, 6], [2, 3], [3, 3], [4, 1], [5, 1], [6, 2]], 13/25920],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 1], [7, 1]], 1/6048],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 1], [9, 1]], 13/7776],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 2], [8, 1]], 1/10368],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 2], [12, 1]], 1/3456],
[[[1, 6], [2, 3], [3, 3], [4, 2], [5, 1], [6, 1]], 1/8640],
[[[1, 6], [2, 3], [3, 3], [4, 2], [6, 1], [8, 1]], 1/6912],
[[[1, 6], [2, 3], [3, 3], [4, 2], [6, 1], [12, 1]], 1/1152],
[[[1, 6], [2, 3], [3, 4], [4, 1], [5, 1], [6, 1]], 13/38880],
[[[1, 6], [2, 3], [3, 4], [4, 1], [6, 1], [8, 1]], 1/5184],
[[[1, 6], [2, 3], [3, 4], [4, 1], [6, 1], [12, 1]], 1/1152],
[[[1, 6], [2, 5], [3, 1], [4, 1], [5, 1], [9, 1]], 1/17280],
[[[1, 6], [2, 5], [3, 1], [4, 1], [5, 2], [6, 1]], 1/7200],
[[[1, 6], [2, 5], [3, 1], [4, 1], [6, 2], [18, 1]], 1/20736],
[[[1, 6], [2, 5], [3, 1], [4, 2], [6, 1], [7, 1]], 1/3584],
[[[1, 6], [2, 5], [3, 1], [4, 2], [6, 1], [14, 1]], 1/10752],
[[[1, 6], [2, 5], [3, 1], [4, 3], [5, 1], [6, 1]], 1/3840],
[[[1, 6], [2, 5], [3, 1], [4, 3], [6, 1], [8, 1]], 1/2048],
[[[1, 6], [2, 5], [3, 1], [4, 3], [6, 1], [10, 1]], 1/15360],
[[[1, 6], [2, 5], [3, 1], [5, 1], [6, 1], [7, 1]], 1/20160],
[[[1, 6], [2, 5], [3, 2], [4, 1], [5, 1], [6, 2]], 7/11520],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 1], [7, 1]], 1/4032],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 1], [9, 1]], 1/5184],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 2], [8, 1]], 1/6912],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 2], [10, 1]], 1/17280],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 2], [12, 1]], 7/27648],
[[[1, 6], [2, 5], [3, 2], [4, 2], [5, 1], [6, 1]], 1/1920],
[[[1, 6], [2, 5], [3, 2], [4, 2], [6, 1], [8, 1]], 1/2304],
[[[1, 6], [2, 5], [3, 3], [4, 1], [5, 1], [6, 1]], 1/25920],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 1], [8, 1]], 1/41472],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 1], [12, 1]], 1/9216],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 1], [7, 1]], 1/32256],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 1], [14, 1]], 5/32256],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 2], [8, 1]], 1/13824],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 2], [10, 1]], 1/4320],
[[[1, 6], [2, 7], [3, 1], [4, 2], [5, 1], [6, 1]], 1/18432],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 1], [8, 1]], 5/18432],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 1], [10, 1]], 23/46080],
[[[1, 6], [2, 9], [3, 1], [4, 1], [6, 1], [8, 1]], 11/221184],
[[[1, 6], [2, 9], [3, 1], [4, 1], [6, 1], [10, 1]], 247/552960],
[[[1, 7], [2, 2], [3, 1], [4, 1], [5, 2], [8, 1]], 1/2400],
[[[1, 7], [2, 2], [3, 1], [4, 2], [5, 1], [9, 1]], 1/5760],
[[[1, 7], [2, 2], [3, 1], [6, 1], [9, 1], [18, 1]], 1/181440],
[[[1, 7], [2, 2], [3, 2], [4, 1], [5, 1], [7, 1]], 1/5040],
[[[1, 7], [2, 2], [3, 2], [4, 1], [5, 1], [9, 1]], 1/1620],
[[[1, 7], [2, 2], [3, 2], [4, 1], [5, 2], [6, 1]], 7/10800],
[[[1, 7], [2, 2], [3, 2], [4, 2], [5, 1], [8, 1]], 1/5760],
[[[1, 7], [2, 2], [3, 2], [5, 1], [6, 1], [7, 1]], 1/1890],
[[[1, 7], [2, 2], [3, 2], [5, 1], [6, 1], [9, 1]], 1/12960],
[[[1, 7], [2, 2], [3, 3], [4, 1], [5, 1], [8, 1]], 1/4320],
[[[1, 7], [2, 2], [3, 3], [4, 1], [6, 1], [7, 1]], 1/12096],
[[[1, 7], [2, 2], [3, 3], [4, 1], [6, 1], [9, 1]], 19/77760],
[[[1, 7], [2, 2], [3, 3], [4, 1], [6, 2], [12, 1]], 1/51840],
[[[1, 7], [2, 2], [3, 3], [4, 2], [6, 1], [12, 1]], 1/11520],
[[[1, 7], [2, 2], [3, 4], [4, 1], [5, 1], [6, 1]], 11/38880],
[[[1, 7], [2, 2], [3, 4], [4, 1], [6, 1], [8, 1]], 1/15552],
[[[1, 7], [2, 2], [3, 4], [4, 1], [6, 1], [12, 1]], 1/3456],
[[[1, 7], [2, 4], [3, 1], [4, 1], [5, 1], [7, 1]], 1/3360],
[[[1, 7], [2, 4], [3, 1], [4, 1], [5, 1], [9, 1]], 1/4320],
[[[1, 7], [2, 4], [3, 1], [4, 1], [5, 2], [6, 1]], 7/9600],
[[[1, 7], [2, 4], [3, 1], [4, 2], [5, 1], [8, 1]], 1/1920],
[[[1, 7], [2, 4], [3, 1], [4, 2], [6, 1], [7, 1]], 1/3584],
[[[1, 7], [2, 4], [3, 1], [4, 3], [5, 1], [6, 1]], 1/5120],
[[[1, 7], [2, 4], [3, 1], [4, 3], [6, 1], [8, 1]], 1/6144],
[[[1, 7], [2, 4], [3, 1], [5, 1], [6, 1], [7, 1]], 1/5040],
[[[1, 7], [2, 4], [3, 2], [4, 1], [5, 1], [6, 2]], 11/17280],
[[[1, 7], [2, 4], [3, 2], [4, 1], [5, 1], [8, 1]], 1/34560],
[[[1, 7], [2, 4], [3, 2], [4, 1], [6, 1], [7, 1]], 1/1728],
[[[1, 7], [2, 4], [3, 2], [4, 1], [6, 1], [9, 1]], 1/5184],
[[[1, 7], [2, 4], [3, 2], [4, 1], [6, 2], [8, 1]], 1/27648],
[[[1, 7], [2, 4], [3, 2], [4, 1], [6, 2], [12, 1]], 1/23040],
[[[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]], 1/1728],
[[[1, 7], [2, 4], [3, 3], [4, 1], [5, 1], [6, 1]], 7/5760],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 1], [8, 1]], 5/13824],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 1], [12, 1]], 1/6912],
[[[1, 7], [2, 6], [3, 1], [4, 1], [6, 1], [7, 1]], 5/32256],
[[[1, 7], [2, 6], [3, 1], [4, 1], [6, 1], [14, 1]], 1/32256],
[[[1, 7], [2, 6], [3, 1], [4, 2], [5, 1], [6, 1]], 23/46080],
[[[1, 7], [2, 6], [3, 1], [4, 2], [6, 1], [8, 1]], 5/18432],
[[[1, 7], [2, 6], [3, 1], [4, 2], [6, 1], [10, 1]], 1/18432],
[[[1, 7], [2, 6], [3, 2], [4, 1], [5, 1], [6, 1]], 1/4320],
[[[1, 7], [2, 6], [3, 2], [4, 1], [6, 1], [8, 1]], 1/13824],
[[[1, 7], [2, 8], [3, 1], [4, 1], [5, 1], [6, 1]], 7/552960],
[[[1, 7], [2, 8], [3, 1], [4, 1], [6, 1], [8, 1]], 7/221184],
[[[1, 7], [2, 8], [3, 1], [4, 1], [6, 1], [10, 1]], 7/46080],
[[[1, 8], [2, 1], [3, 1], [4, 1], [5, 2], [8, 1]], 1/7200],
[[[1, 8], [2, 1], [3, 1], [6, 1], [9, 1], [18, 1]], 1/6531840],
[[[1, 8], [2, 1], [3, 2], [4, 1], [5, 1], [7, 1]], 1/10080],
[[[1, 8], [2, 1], [3, 2], [4, 1], [5, 1], [9, 1]], 1/6480],
[[[1, 8], [2, 1], [3, 2], [5, 1], [6, 1], [7, 1]], 1/7560],
[[[1, 8], [2, 1], [3, 2], [5, 1], [6, 1], [9, 1]], 1/194400],
[[[1, 8], [2, 1], [3, 3], [4, 1], [5, 1], [8, 1]], 1/12960],
[[[1, 8], [2, 1], [3, 4], [4, 1], [6, 1], [12, 1]], 1/51840],
[[[1, 8], [2, 3], [3, 1], [4, 1], [5, 1], [7, 1]], 1/1440],
[[[1, 8], [2, 3], [3, 1], [4, 1], [5, 1], [9, 1]], 1/4320],
[[[1, 8], [2, 3], [3, 1], [4, 1], [5, 2], [6, 1]], 1/1600],
[[[1, 8], [2, 3], [3, 1], [4, 2], [5, 1], [8, 1]], 1/1440],
[[[1, 8], [2, 3], [3, 1], [4, 2], [6, 1], [7, 1]], 1/10752],
[[[1, 8], [2, 3], [3, 1], [5, 1], [6, 1], [7, 1]], 1/5040],
[[[1, 8], [2, 3], [3, 2], [4, 1], [5, 1], [6, 2]], 71/518400],
[[[1, 8], [2, 3], [3, 2], [4, 1], [5, 1], [8, 1]], 1/2304],
[[[1, 8], [2, 3], [3, 2], [4, 1], [6, 1], [7, 1]], 5/12096],
[[[1, 8], [2, 3], [3, 2], [4, 1], [6, 1], [9, 1]], 1/19440],
[[[1, 8], [2, 3], [3, 2], [4, 1], [6, 2], [8, 1]], 1/414720],
[[[1, 8], [2, 3], [3, 2], [4, 1], [6, 2], [12, 1]], 1/241920],
[[[1, 8], [2, 3], [3, 2], [4, 2], [5, 1], [6, 1]], 1/2160],
[[[1, 8], [2, 3], [3, 2], [4, 2], [6, 1], [8, 1]], 1/6912],
[[[1, 8], [2, 3], [3, 3], [4, 1], [5, 1], [6, 1]], 37/25920],
[[[1, 8], [2, 3], [3, 3], [4, 1], [6, 1], [8, 1]], 1/4608],
[[[1, 8], [2, 3], [3, 3], [4, 1], [6, 1], [12, 1]], 1/23040],
[[[1, 8], [2, 5], [3, 1], [4, 1], [5, 1], [8, 1]], 1/11520],
[[[1, 8], [2, 5], [3, 1], [4, 1], [6, 1], [7, 1]], 1/4032],
[[[1, 8], [2, 5], [3, 1], [4, 2], [5, 1], [6, 1]], 13/15360],
[[[1, 8], [2, 5], [3, 1], [4, 2], [6, 1], [8, 1]], 1/4608],
[[[1, 8], [2, 5], [3, 2], [4, 1], [5, 1], [6, 1]], 71/51840],
[[[1, 8], [2, 5], [3, 2], [4, 1], [6, 1], [8, 1]], 5/20736],
[[[1, 8], [2, 7], [3, 1], [4, 1], [5, 1], [6, 1]], 7/46080],
[[[1, 8], [2, 7], [3, 1], [4, 1], [6, 1], [8, 1]], 7/221184],
[[[1, 8], [2, 7], [3, 1], [4, 1], [6, 1], [10, 1]], 7/552960],
[[[1, 9], [2, 2], [3, 1], [4, 1], [5, 1], [7, 1]], 1/2016],
[[[1, 9], [2, 2], [3, 1], [4, 1], [5, 1], [9, 1]], 1/16200],
[[[1, 9], [2, 2], [3, 1], [4, 1], [5, 2], [6, 1]], 49/432000],
[[[1, 9], [2, 2], [3, 1], [4, 2], [5, 1], [8, 1]], 1/5760],
[[[1, 9], [2, 2], [3, 1], [5, 1], [6, 1], [7, 1]], 1/18900],
[[[1, 9], [2, 2], [3, 2], [4, 1], [5, 1], [8, 1]], 1/3840],
[[[1, 9], [2, 2], [3, 2], [4, 1], [6, 1], [7, 1]], 1/12096],
[[[1, 9], [2, 2], [3, 2], [4, 1], [6, 1], [9, 1]], 1/311040],
[[[1, 9], [2, 2], [3, 2], [4, 1], [6, 2], [12, 1]], 1/8709120],
[[[1, 9], [2, 2], [3, 3], [4, 1], [5, 1], [6, 1]], 29/86400],
[[[1, 9], [2, 2], [3, 3], [4, 1], [6, 1], [8, 1]], 7/207360],
[[[1, 9], [2, 2], [3, 3], [4, 1], [6, 1], [12, 1]], 1/241920],
[[[1, 9], [2, 4], [3, 1], [4, 1], [5, 1], [8, 1]], 1/3456],
[[[1, 9], [2, 4], [3, 1], [4, 1], [6, 1], [7, 1]], 19/120960],
[[[1, 9], [2, 4], [3, 1], [4, 2], [5, 1], [6, 1]], 307/691200],
[[[1, 9], [2, 4], [3, 1], [4, 2], [6, 1], [8, 1]], 1/17280],
[[[1, 9], [2, 4], [3, 2], [4, 1], [5, 1], [6, 1]], 1/640],
[[[1, 9], [2, 4], [3, 2], [4, 1], [6, 1], [8, 1]], 1/6912],
[[[1, 9], [2, 6], [3, 1], [4, 1], [5, 1], [6, 1]], 247/552960],
[[[1, 9], [2, 6], [3, 1], [4, 1], [6, 1], [8, 1]], 11/221184],
[[[1, 10], [2, 1], [3, 1], [4, 1], [5, 1], [7, 1]], 1/10080],
[[[1, 10], [2, 1], [3, 1], [4, 1], [5, 1], [9, 1]], 1/259200],
[[[1, 10], [2, 1], [3, 1], [5, 1], [6, 1], [7, 1]], 1/302400],
[[[1, 10], [2, 1], [3, 2], [4, 1], [5, 1], [8, 1]], 7/172800],
[[[1, 10], [2, 1], [3, 3], [4, 1], [6, 1], [12, 1]], 1/8709120],
[[[1, 10], [2, 3], [3, 1], [4, 1], [5, 1], [8, 1]], 1/5760],
[[[1, 10], [2, 3], [3, 1], [4, 1], [6, 1], [7, 1]], 17/483840],
[[[1, 10], [2, 3], [3, 1], [4, 2], [5, 1], [6, 1]], 91/1382400],
[[[1, 10], [2, 3], [3, 1], [4, 2], [6, 1], [8, 1]], 1/276480],
[[[1, 10], [2, 3], [3, 2], [4, 1], [5, 1], [6, 1]], 143/259200],
[[[1, 10], [2, 3], [3, 2], [4, 1], [6, 1], [8, 1]], 1/34560],
[[[1, 10], [2, 5], [3, 1], [4, 1], [5, 1], [6, 1]], 457/1036800],
[[[1, 10], [2, 5], [3, 1], [4, 1], [6, 1], [8, 1]], 23/829440],
[[[1, 11], [2, 2], [3, 1], [4, 1], [5, 1], [8, 1]], 1/28800],
[[[1, 11], [2, 2], [3, 1], [4, 1], [6, 1], [7, 1]], 1/483840],
[[[1, 11], [2, 2], [3, 2], [4, 1], [5, 1], [6, 1]], 47/777600],
[[[1, 11], [2, 2], [3, 2], [4, 1], [6, 1], [8, 1]], 1/622080],
[[[1, 11], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1]], 1097/6451200],
[[[1, 11], [2, 4], [3, 1], [4, 1], [6, 1], [8, 1]], 7/1105920],
[[[1, 12], [2, 1], [3, 1], [4, 1], [5, 1], [8, 1]], 1/518400],
[[[1, 12], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1]], 1163/43545600],
[[[1, 12], [2, 3], [3, 1], [4, 1], [6, 1], [8, 1]], 1/1658880],
[[[1, 13], [2, 2], [3, 1], [4, 1], [5, 1], [6, 1]], 1151/870912000],
[[[1, 13], [2, 2], [3, 1], [4, 1], [6, 1], [8, 1]], 1/49766400],
[[[1, 1], [2, 2], [3, 1], [4, 1], [6, 4], [12, 1], [18, 1]], 1/216],
[[[1, 1], [2, 2], [3, 1], [6, 1], [7, 1], [9, 1], [18, 1]], 1/252],
[[[1, 1], [2, 2], [3, 1], [6, 1], [9, 1], [14, 1], [18, 1]], 1/252],
[[[1, 1], [2, 2], [3, 1], [6, 2], [9, 1], [10, 1], [18, 1]], 1/270],
[[[1, 1], [2, 2], [3, 3], [4, 1], [6, 2], [9, 1], [12, 1]], 1/216],
[[[1, 1], [2, 2], [4, 1], [6, 2], [8, 1], [10, 1], [30, 1]], 1/120],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 3], [12, 1], [14, 1]], 1/336],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 4], [10, 1], [12, 1]], 1/360],
[[[1, 1], [2, 4], [3, 1], [6, 1], [9, 1], [10, 1], [18, 1]], 1/2160],
[[[1, 1], [2, 6], [3, 1], [4, 1], [6, 3], [10, 1], [12, 1]], 1/2880],
[[[1, 2], [2, 1], [3, 1], [6, 1], [7, 1], [9, 1], [18, 1]], 1/252],
[[[1, 2], [2, 1], [3, 1], [6, 1], [9, 1], [14, 1], [18, 1]], 1/252],
[[[1, 2], [2, 1], [3, 2], [4, 1], [5, 1], [8, 1], [15, 1]], 1/120],
[[[1, 2], [2, 1], [3, 2], [4, 1], [6, 3], [12, 1], [18, 1]], 1/216],
[[[1, 2], [2, 1], [3, 2], [5, 1], [6, 1], [9, 1], [18, 1]], 1/270],
[[[1, 2], [2, 1], [3, 4], [4, 1], [6, 1], [9, 1], [12, 1]], 1/216],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 2], [9, 1], [18, 1]], 1/432],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 3], [8, 1], [18, 1]], 1/144],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 3], [10, 1], [18, 1]], 1/360],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 3], [12, 1], [14, 1]], 1/336],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 1], [9, 1], [18, 1]], 1/576],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 3], [8, 1], [12, 1]], 1/192],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 3], [10, 1], [12, 1]], 1/480],
[[[1, 2], [2, 3], [3, 1], [5, 1], [6, 1], [9, 1], [18, 1]], 1/720],
[[[1, 2], [2, 3], [3, 1], [6, 1], [9, 1], [10, 1], [18, 1]], 1/360],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 1], [9, 1], [18, 1]], 1/432],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 2], [7, 1], [12, 1]], 1/336],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 2], [12, 1], [14, 1]], 1/336],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 3], [10, 1], [12, 1]], 1/360],
[[[1, 2], [2, 3], [3, 2], [4, 2], [5, 1], [6, 2], [12, 1]], 1/480],
[[[1, 2], [2, 3], [3, 2], [4, 2], [6, 2], [8, 1], [12, 1]], 1/192],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 1], [8, 1], [10, 2]], 1/2400],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 1], [9, 1], [18, 1]], 1/8640],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 2], [10, 1], [18, 1]], 1/2160],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 3], [8, 1], [10, 1]], 1/4320],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 3], [10, 1], [12, 1]], 1/480],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 2], [10, 1], [12, 1]], 1/2880],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 1], [10, 1], [14, 1]], 1/3360],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 2], [8, 1], [10, 1]], 1/4320],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/172800],
[[[1, 3], [2, 2], [3, 1], [4, 1], [6, 2], [9, 1], [18, 1]], 1/432],
[[[1, 3], [2, 2], [3, 1], [4, 2], [6, 1], [9, 1], [18, 1]], 1/576],
[[[1, 3], [2, 2], [3, 1], [5, 1], [6, 1], [9, 1], [18, 1]], 1/360],
[[[1, 3], [2, 2], [3, 1], [6, 1], [9, 1], [10, 1], [18, 1]], 1/720],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 1], [9, 1], [18, 1]], 1/432],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 2], [7, 1], [12, 1]], 1/336],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 2], [12, 1], [14, 1]], 1/336],
[[[1, 3], [2, 2], [3, 2], [4, 2], [6, 2], [8, 1], [12, 1]], 1/192],
[[[1, 3], [2, 2], [3, 2], [4, 2], [6, 2], [10, 1], [12, 1]], 1/480],
[[[1, 3], [2, 2], [3, 3], [4, 1], [5, 1], [6, 1], [9, 1]], 1/360],
[[[1, 3], [2, 2], [3, 3], [4, 1], [5, 1], [6, 2], [12, 1]], 1/360],
[[[1, 3], [2, 2], [3, 3], [4, 1], [6, 1], [7, 1], [12, 1]], 1/336],
[[[1, 3], [2, 2], [3, 3], [4, 1], [6, 1], [8, 1], [9, 1]], 1/144],
[[[1, 3], [2, 2], [3, 3], [4, 2], [5, 1], [6, 1], [12, 1]], 1/480],
[[[1, 3], [2, 2], [3, 3], [4, 2], [6, 1], [8, 1], [12, 1]], 1/192],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 1], [9, 1], [18, 1]], 5/1728],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 2], [10, 1], [18, 1]], 1/2160],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 3], [10, 1], [12, 1]], 1/960],
[[[1, 3], [2, 4], [3, 2], [4, 1], [5, 1], [6, 2], [12, 1]], 1/960],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 2], [8, 1], [10, 1]], 1/2880],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 2], [10, 1], [12, 1]], 1/480],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 1], [10, 1], [14, 1]], 1/1680],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 2], [8, 1], [10, 1]], 1/1440],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 1/1920],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/11520],
[[[1, 4], [2, 1], [3, 1], [5, 1], [6, 1], [9, 1], [18, 1]], 1/2160],
[[[1, 4], [2, 1], [3, 3], [4, 1], [6, 1], [7, 1], [12, 1]], 1/336],
[[[1, 4], [2, 1], [3, 4], [4, 1], [5, 1], [6, 1], [12, 1]], 1/360],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 1], [9, 1], [18, 1]], 5/1728],
[[[1, 4], [2, 3], [3, 2], [4, 1], [5, 1], [6, 1], [9, 1]], 1/2160],
[[[1, 4], [2, 3], [3, 2], [4, 1], [5, 1], [6, 2], [8, 1]], 1/2880],
[[[1, 4], [2, 3], [3, 2], [4, 1], [5, 1], [6, 2], [12, 1]], 1/480],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 2], [10, 1], [12, 1]], 1/960],
[[[1, 4], [2, 3], [3, 3], [4, 1], [5, 1], [6, 1], [12, 1]], 1/960],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 1], [10, 1], [14, 1]], 1/3360],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 1/1920],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/3840],
[[[1, 5], [2, 2], [3, 1], [4, 1], [5, 2], [6, 1], [8, 1]], 1/2400],
[[[1, 5], [2, 2], [3, 1], [4, 1], [6, 1], [9, 1], [18, 1]], 1/8640],
[[[1, 5], [2, 2], [3, 2], [4, 1], [5, 1], [6, 1], [9, 1]], 1/2160],
[[[1, 5], [2, 2], [3, 2], [4, 1], [5, 1], [6, 2], [12, 1]], 1/2880],
[[[1, 5], [2, 2], [3, 3], [4, 1], [5, 1], [6, 1], [8, 1]], 1/4320],
[[[1, 5], [2, 2], [3, 3], [4, 1], [5, 1], [6, 1], [12, 1]], 1/480],
[[[1, 5], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1]], 1/3360],
[[[1, 5], [2, 4], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 1/1920],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/11520],
[[[1, 6], [2, 1], [3, 3], [4, 1], [5, 1], [6, 1], [12, 1]], 1/2880],
[[[1, 6], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1]], 1/1680],
[[[1, 6], [2, 3], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 1/1920],
[[[1, 6], [2, 3], [3, 2], [4, 1], [5, 1], [6, 1], [8, 1]], 1/1440],
[[[1, 6], [2, 5], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/11520],
[[[1, 7], [2, 2], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1]], 1/3360],
[[[1, 7], [2, 2], [3, 2], [4, 1], [5, 1], [6, 1], [8, 1]], 1/4320],
[[[1, 7], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/3840],
[[[1, 8], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/11520],
[[[1, 9], [2, 2], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/172800],
[[[1, 1], [2, 2], [3, 1], [4, 1], [5, 1], [6, 1], [9, 1], [18, 1]], 1/360],
[[[1, 1], [2, 2], [3, 1], [4, 1], [6, 1], [8, 1], [9, 1], [18, 1]], 1/144],
[[[1, 2], [2, 1], [3, 1], [4, 1], [6, 1], [8, 1], [9, 1], [18, 1]], 1/144],
[[[1, 2], [2, 1], [3, 1], [4, 1], [6, 1], [9, 1], [10, 1], [18, 1]], 1/360]
]}