{[
[[[1, 25]], 1/8806025134080],
[[[2, 25]], 1/8806025134080],
[[[1, 1], [2, 24]], 19/2935341711360],
[[[1, 2], [2, 23]], 13/81537269760],
[[[1, 3], [2, 22]], 1639/733835427840],
[[[1, 4], [2, 21]], 21733/1100753141760],
[[[1, 5], [2, 20]], 1771/15288238080],
[[[1, 5], [3, 10]], 1/2985984],
[[[1, 6], [2, 19]], 22691/48922361856],
[[[1, 7], [2, 18]], 105287/81537269760],
[[[1, 7], [3, 9]], 5/2985984],
[[[1, 8], [2, 17]], 22442167/8806025134080],
[[[1, 9], [2, 16]], 10897013/2935341711360],
[[[1, 9], [3, 8]], 107/39813120],
[[[1, 10], [2, 15]], 278039/61152952320],
[[[1, 11], [2, 14]], 357019/61152952320],
[[[1, 11], [3, 7]], 1009/268738560],
[[[1, 12], [2, 13]], 902993/122305904640],
[[[1, 13], [2, 12]], 902993/122305904640],
[[[1, 13], [3, 6]], 929/268738560],
[[[1, 14], [2, 11]], 357019/61152952320],
[[[1, 15], [2, 10]], 278039/61152952320],
[[[1, 15], [3, 5]], 911/716636160],
[[[1, 16], [2, 9]], 10897013/2935341711360],
[[[1, 17], [2, 8]], 22442167/8806025134080],
[[[1, 17], [3, 4]], 3583/17199267840],
[[[1, 17], [4, 4]], 1/61152952320],
[[[1, 18], [2, 7]], 105287/81537269760],
[[[1, 19], [2, 6]], 22691/48922361856],
[[[1, 19], [3, 3]], 2359/137594142720],
[[[1, 20], [2, 5]], 1771/15288238080],
[[[1, 21], [2, 4]], 21733/1100753141760],
[[[1, 21], [3, 2]], 263/366917713920],
[[[1, 21], [4, 2]], 1/366917713920],
[[[1, 21], [5, 1]], 1/61152952320],
[[[1, 22], [2, 3]], 1639/733835427840],
[[[1, 23], [2, 2]], 13/81537269760],
[[[1, 23], [3, 1]], 1/68797071360],
[[[1, 24], [2, 1]], 19/2935341711360],
[[[2, 5], [6, 10]], 1/2985984],
[[[2, 7], [6, 9]], 5/2985984],
[[[2, 9], [6, 8]], 107/39813120],
[[[2, 11], [6, 7]], 1009/268738560],
[[[2, 13], [6, 6]], 929/268738560],
[[[2, 15], [6, 5]], 911/716636160],
[[[2, 17], [4, 4]], 1/61152952320],
[[[2, 17], [6, 4]], 3583/17199267840],
[[[2, 19], [6, 3]], 2359/137594142720],
[[[2, 21], [4, 2]], 1/366917713920],
[[[2, 21], [6, 2]], 263/366917713920],
[[[2, 21], [10, 1]], 1/61152952320],
[[[2, 23], [6, 1]], 1/68797071360],
[[[1, 1], [2, 6], [6, 9]], 5/995328],
[[[1, 1], [2, 8], [6, 8]], 43/2654208],
[[[1, 1], [2, 10], [4, 7]], 1/212336640],
[[[1, 1], [2, 10], [6, 7]], 7/552960],
[[[1, 1], [2, 12], [6, 6]], 1343/89579520],
[[[1, 1], [2, 14], [4, 5]], 1/566231040],
[[[1, 1], [2, 14], [6, 5]], 1/73728],
[[[1, 1], [2, 16], [4, 4]], 11/20384317440],
[[[1, 1], [2, 16], [6, 4]], 3589/955514880],
[[[1, 1], [2, 18], [4, 3]], 1/2038431744],
[[[1, 1], [2, 18], [6, 3]], 5173/11466178560],
[[[1, 1], [2, 20], [4, 2]], 1/8153726976],
[[[1, 1], [2, 20], [6, 2]], 523/20384317440],
[[[1, 1], [2, 20], [10, 1]], 7/10192158720],
[[[1, 1], [2, 22], [4, 1]], 7/244611809280],
[[[1, 1], [2, 22], [6, 1]], 41/61152952320],
[[[1, 2], [2, 7], [4, 8]], 1/2359296],
[[[1, 2], [2, 7], [6, 8]], 65/2654208],
[[[1, 2], [2, 9], [4, 7]], 1/14155776],
[[[1, 2], [2, 9], [6, 7]], 13/331776],
[[[1, 2], [2, 11], [4, 6]], 41/424673280],
[[[1, 2], [2, 11], [6, 6]], 19/1866240],
[[[1, 2], [2, 13], [4, 5]], 61/1698693120],
[[[1, 2], [2, 13], [6, 5]], 475/11943936],
[[[1, 2], [2, 15], [4, 4]], 7/212336640],
[[[1, 2], [2, 15], [6, 4]], 45361/1911029760],
[[[1, 2], [2, 17], [4, 3]], 163/10192158720],
[[[1, 2], [2, 17], [6, 3]], 35093/7644119040],
[[[1, 2], [2, 19], [4, 2]], 11/2264924160],
[[[1, 2], [2, 19], [6, 2]], 45653/122305904640],
[[[1, 2], [2, 19], [10, 1]], 1/83886080],
[[[1, 2], [2, 21], [3, 1]], 1/137594142720],
[[[1, 2], [2, 21], [4, 1]], 313/244611809280],
[[[1, 2], [2, 21], [6, 1]], 199/15288238080],
[[[1, 3], [2, 6], [4, 8]], 1/2359296],
[[[1, 3], [2, 6], [6, 8]], 1/7962624],
[[[1, 3], [2, 8], [4, 7]], 103/15728640],
[[[1, 3], [2, 8], [6, 7]], 41/995328],
[[[1, 3], [2, 10], [4, 6]], 41/28311552],
[[[1, 3], [2, 10], [6, 6]], 71/4478976],
[[[1, 3], [2, 12], [4, 5]], 1247/1019215872],
[[[1, 3], [2, 12], [6, 5]], 583/17915904],
[[[1, 3], [2, 14], [4, 4]], 305/509607936],
[[[1, 3], [2, 14], [6, 4]], 45457/716636160],
[[[1, 3], [2, 16], [4, 3]], 6137/20384317440],
[[[1, 3], [2, 16], [6, 3]], 87889/3822059520],
[[[1, 3], [2, 18], [4, 2]], 731/6794772480],
[[[1, 3], [2, 18], [6, 2]], 52673/18345885696],
[[[1, 3], [2, 18], [10, 1]], 569/5096079360],
[[[1, 3], [2, 20], [3, 1]], 1/3057647616],
[[[1, 3], [2, 20], [4, 1]], 217/9059696640],
[[[1, 3], [2, 20], [6, 1]], 25577/183458856960],
[[[1, 3], [3, 8], [9, 1]], 1/373248],
[[[1, 4], [2, 5], [4, 8]], 3/524288],
[[[1, 4], [2, 7], [4, 7]], 329/28311552],
[[[1, 4], [2, 7], [6, 7]], 1/663552],
[[[1, 4], [2, 9], [4, 6]], 1763/53084160],
[[[1, 4], [2, 9], [6, 6]], 899/53747712],
[[[1, 4], [2, 11], [4, 5]], 72397/5096079360],
[[[1, 4], [2, 11], [6, 5]], 359/23887872],
[[[1, 4], [2, 13], [4, 4]], 55279/7644119040],
[[[1, 4], [2, 13], [6, 4]], 213989/2866544640],
[[[1, 4], [2, 13], [8, 2]], 19/637009920],
[[[1, 4], [2, 15], [4, 3]], 7819/2264924160],
[[[1, 4], [2, 15], [6, 3]], 8334857/137594142720],
[[[1, 4], [2, 17], [3, 2]], 1/8599633920],
[[[1, 4], [2, 17], [4, 2]], 91829/73383542784],
[[[1, 4], [2, 17], [6, 2]], 520151/40768634880],
[[[1, 4], [2, 17], [10, 1]], 38009/61152952320],
[[[1, 4], [2, 19], [3, 1]], 47/7644119040],
[[[1, 4], [2, 19], [4, 1]], 20047/81537269760],
[[[1, 4], [2, 19], [6, 1]], 20861/22932357120],
[[[1, 5], [2, 4], [4, 8]], 3/524288],
[[[1, 5], [2, 6], [4, 7]], 211/2359296],
[[[1, 5], [2, 8], [4, 6]], 1703/14155776],
[[[1, 5], [2, 8], [6, 6]], 1/221184],
[[[1, 5], [2, 10], [4, 5]], 22441/188743680],
[[[1, 5], [2, 10], [6, 5]], 23/5971968],
[[[1, 5], [2, 12], [4, 4]], 8773/159252480],
[[[1, 5], [2, 12], [6, 4]], 4823/95551488],
[[[1, 5], [2, 12], [8, 2]], 133/212336640],
[[[1, 5], [2, 14], [4, 3]], 120749/5096079360],
[[[1, 5], [2, 14], [6, 3]], 167551/1911029760],
[[[1, 5], [2, 16], [3, 2]], 11/2866544640],
[[[1, 5], [2, 16], [4, 2]], 996059/122305904640],
[[[1, 5], [2, 16], [6, 2]], 2080639/61152952320],
[[[1, 5], [2, 16], [10, 1]], 21961/10192158720],
[[[1, 5], [2, 18], [3, 1]], 161/2548039680],
[[[1, 5], [2, 18], [4, 1]], 74723/48922361856],
[[[1, 5], [2, 18], [6, 1]], 46289/12230590464],
[[[1, 5], [3, 6], [6, 4]], 73/2985984],
[[[1, 5], [3, 6], [12, 2]], 1/82944],
[[[1, 5], [3, 7], [9, 1]], 5/373248],
[[[1, 5], [3, 8], [5, 1]], 1/829440],
[[[1, 5], [3, 8], [6, 2]], 1/1492992],
[[[1, 5], [3, 8], [12, 1]], 1/248832],
[[[1, 6], [2, 1], [3, 9]], 5/995328],
[[[1, 6], [2, 3], [3, 8]], 1/7962624],
[[[1, 6], [2, 3], [4, 8]], 1/2359296],
[[[1, 6], [2, 5], [4, 7]], 211/2359296],
[[[1, 6], [2, 7], [4, 6]], 6065/14155776],
[[[1, 6], [2, 9], [4, 5]], 742559/1698693120],
[[[1, 6], [2, 9], [6, 5]], 7/11943936],
[[[1, 6], [2, 11], [4, 4]], 254027/955514880],
[[[1, 6], [2, 11], [6, 4]], 3889/191102976],
[[[1, 6], [2, 11], [8, 2]], 371/79626240],
[[[1, 6], [2, 13], [4, 3]], 512777/5096079360],
[[[1, 6], [2, 13], [6, 3]], 298691/3822059520],
[[[1, 6], [2, 15], [3, 2]], 1/19906560],
[[[1, 6], [2, 15], [4, 2]], 17773/566231040],
[[[1, 6], [2, 15], [6, 2]], 1379089/24461180928],
[[[1, 6], [2, 15], [10, 1]], 6557/1358954496],
[[[1, 6], [2, 17], [3, 1]], 53767/137594142720],
[[[1, 6], [2, 17], [4, 1]], 1469153/244611809280],
[[[1, 6], [2, 17], [6, 1]], 31511/3057647616],
[[[1, 7], [2, 2], [3, 8]], 65/2654208],
[[[1, 7], [2, 2], [4, 8]], 1/2359296],
[[[1, 7], [2, 4], [3, 7]], 1/663552],
[[[1, 7], [2, 4], [4, 7]], 329/28311552],
[[[1, 7], [2, 6], [4, 6]], 6065/14155776],
[[[1, 7], [2, 8], [3, 5]], 1/429981696],
[[[1, 7], [2, 8], [4, 5]], 631981/637009920],
[[[1, 7], [2, 8], [6, 5]], 1/17915904],
[[[1, 7], [2, 10], [3, 4]], 43/127401984],
[[[1, 7], [2, 10], [4, 4]], 16935467/22932357120],
[[[1, 7], [2, 10], [6, 4]], 721/143327232],
[[[1, 7], [2, 10], [8, 2]], 1901/119439360],
[[[1, 7], [2, 12], [3, 3]], 259/3057647616],
[[[1, 7], [2, 12], [4, 3]], 74617/251658240],
[[[1, 7], [2, 12], [6, 3]], 84781/1911029760],
[[[1, 7], [2, 14], [3, 2]], 14021/40768634880],
[[[1, 7], [2, 14], [4, 2]], 302977/3822059520],
[[[1, 7], [2, 14], [5, 1]], 457/20384317440],
[[[1, 7], [2, 14], [6, 2]], 2813699/45864714240],
[[[1, 7], [2, 14], [8, 1]], 1/17694720],
[[[1, 7], [2, 14], [10, 1]], 18559/2548039680],
[[[1, 7], [2, 16], [3, 1]], 69401/45864714240],
[[[1, 7], [2, 16], [4, 1]], 628567/40768634880],
[[[1, 7], [2, 16], [6, 1]], 691073/36691771392],
[[[1, 7], [3, 5], [4, 4]], 1/2985984],
[[[1, 7], [3, 5], [6, 4]], 1/2985984],
[[[1, 7], [3, 5], [12, 2]], 1/82944],
[[[1, 7], [3, 6], [9, 1]], 107/4976640],
[[[1, 7], [3, 7], [5, 1]], 1/207360],
[[[1, 7], [3, 7], [6, 2]], 1/497664],
[[[1, 7], [3, 7], [12, 1]], 1/82944],
[[[1, 8], [2, 1], [3, 8]], 43/2654208],
[[[1, 8], [2, 3], [3, 7]], 41/995328],
[[[1, 8], [2, 3], [4, 7]], 103/15728640],
[[[1, 8], [2, 5], [3, 6]], 1/221184],
[[[1, 8], [2, 5], [4, 6]], 1703/14155776],
[[[1, 8], [2, 7], [3, 5]], 1/17915904],
[[[1, 8], [2, 7], [4, 5]], 631981/637009920],
[[[1, 8], [2, 7], [6, 5]], 1/429981696],
[[[1, 8], [2, 9], [3, 4]], 1195/573308928],
[[[1, 8], [2, 9], [4, 4]], 1453913/1132462080],
[[[1, 8], [2, 9], [6, 4]], 6311/3439853568],
[[[1, 8], [2, 9], [8, 2]], 2897/106168320],
[[[1, 8], [2, 11], [3, 3]], 8117/3822059520],
[[[1, 8], [2, 11], [4, 3]], 39800209/61152952320],
[[[1, 8], [2, 11], [6, 3]], 2626073/137594142720],
[[[1, 8], [2, 13], [3, 2]], 109969/61152952320],
[[[1, 8], [2, 13], [4, 2]], 3342587/20384317440],
[[[1, 8], [2, 13], [5, 1]], 463/1132462080],
[[[1, 8], [2, 13], [6, 2]], 50937431/1100753141760],
[[[1, 8], [2, 13], [8, 1]], 49/53084160],
[[[1, 8], [2, 13], [10, 1]], 485947/61152952320],
[[[1, 8], [2, 15], [3, 1]], 46361/12230590464],
[[[1, 8], [2, 15], [4, 1]], 226661/8153726976],
[[[1, 8], [2, 15], [6, 1]], 3299419/137594142720],
[[[1, 9], [2, 2], [3, 7]], 13/331776],
[[[1, 9], [2, 2], [4, 7]], 1/14155776],
[[[1, 9], [2, 4], [3, 6]], 899/53747712],
[[[1, 9], [2, 4], [4, 6]], 1763/53084160],
[[[1, 9], [2, 6], [3, 5]], 7/11943936],
[[[1, 9], [2, 6], [4, 5]], 742559/1698693120],
[[[1, 9], [2, 8], [3, 4]], 6311/3439853568],
[[[1, 9], [2, 8], [4, 4]], 1453913/1132462080],
[[[1, 9], [2, 8], [6, 4]], 1195/573308928],
[[[1, 9], [2, 8], [8, 2]], 2897/106168320],
[[[1, 9], [2, 10], [3, 3]], 17425/1528823808],
[[[1, 9], [2, 10], [4, 3]], 164309/169869312],
[[[1, 9], [2, 10], [6, 3]], 32765/2293235712],
[[[1, 9], [2, 12], [3, 2]], 350501/40768634880],
[[[1, 9], [2, 12], [4, 2]], 6199873/20384317440],
[[[1, 9], [2, 12], [5, 1]], 17971/6794772480],
[[[1, 9], [2, 12], [6, 2]], 1955311/61152952320],
[[[1, 9], [2, 12], [8, 1]], 169/31850496],
[[[1, 9], [2, 12], [10, 1]], 27523/3397386240],
[[[1, 9], [2, 14], [3, 1]], 107117/15288238080],
[[[1, 9], [2, 14], [4, 1]], 1837/42467328],
[[[1, 9], [2, 14], [6, 1]], 4290061/183458856960],
[[[1, 9], [3, 4], [4, 4]], 11/23887872],
[[[1, 9], [3, 4], [6, 4]], 1/119439360],
[[[1, 9], [3, 4], [12, 2]], 1/3317760],
[[[1, 9], [3, 5], [9, 1]], 41/3732480],
[[[1, 9], [3, 6], [4, 2]], 1/559872],
[[[1, 9], [3, 6], [5, 1]], 1/207360],
[[[1, 9], [3, 6], [6, 2]], 1/737280],
[[[1, 9], [3, 6], [12, 1]], 1/122880],
[[[1, 10], [2, 1], [3, 7]], 7/552960],
[[[1, 10], [2, 1], [4, 7]], 1/212336640],
[[[1, 10], [2, 3], [3, 6]], 71/4478976],
[[[1, 10], [2, 3], [4, 6]], 41/28311552],
[[[1, 10], [2, 5], [3, 5]], 23/5971968],
[[[1, 10], [2, 5], [4, 5]], 22441/188743680],
[[[1, 10], [2, 7], [3, 4]], 721/143327232],
[[[1, 10], [2, 7], [4, 4]], 16935467/22932357120],
[[[1, 10], [2, 7], [6, 4]], 43/127401984],
[[[1, 10], [2, 7], [8, 2]], 1901/119439360],
[[[1, 10], [2, 9], [3, 3]], 32765/2293235712],
[[[1, 10], [2, 9], [4, 3]], 164309/169869312],
[[[1, 10], [2, 9], [6, 3]], 17425/1528823808],
[[[1, 10], [2, 11], [3, 2]], 252509/10192158720],
[[[1, 10], [2, 11], [4, 2]], 1038889/2548039680],
[[[1, 10], [2, 11], [5, 1]], 797/113246208],
[[[1, 10], [2, 11], [6, 2]], 1247789/40768634880],
[[[1, 10], [2, 11], [8, 1]], 2039/159252480],
[[[1, 10], [2, 11], [10, 1]], 17993/2264924160],
[[[1, 10], [2, 13], [3, 1]], 791347/61152952320],
[[[1, 10], [2, 13], [4, 1]], 1044287/15288238080],
[[[1, 10], [2, 13], [6, 1]], 118289/5096079360],
[[[1, 11], [2, 2], [3, 6]], 19/1866240],
[[[1, 11], [2, 2], [4, 6]], 41/424673280],
[[[1, 11], [2, 4], [3, 5]], 359/23887872],
[[[1, 11], [2, 4], [4, 5]], 72397/5096079360],
[[[1, 11], [2, 6], [3, 4]], 3889/191102976],
[[[1, 11], [2, 6], [4, 4]], 254027/955514880],
[[[1, 11], [2, 6], [8, 2]], 371/79626240],
[[[1, 11], [2, 8], [3, 3]], 2626073/137594142720],
[[[1, 11], [2, 8], [4, 3]], 39800209/61152952320],
[[[1, 11], [2, 8], [6, 3]], 8117/3822059520],
[[[1, 11], [2, 10], [3, 2]], 1247789/40768634880],
[[[1, 11], [2, 10], [4, 2]], 1038889/2548039680],
[[[1, 11], [2, 10], [5, 1]], 17993/2264924160],
[[[1, 11], [2, 10], [6, 2]], 252509/10192158720],
[[[1, 11], [2, 10], [8, 1]], 2039/159252480],
[[[1, 11], [2, 10], [10, 1]], 797/113246208],
[[[1, 11], [2, 12], [3, 1]], 115303/5096079360],
[[[1, 11], [2, 12], [4, 1]], 91435/1019215872],
[[[1, 11], [2, 12], [6, 1]], 527003/20384317440],
[[[1, 11], [3, 3], [4, 4]], 143/955514880],
[[[1, 11], [3, 4], [9, 1]], 1/3732480],
[[[1, 11], [3, 5], [4, 2]], 5/1990656],
[[[1, 11], [3, 5], [5, 1]], 1/116640],
[[[1, 11], [3, 5], [6, 2]], 1/29859840],
[[[1, 11], [3, 5], [12, 1]], 1/4976640],
[[[1, 12], [2, 1], [3, 6]], 1343/89579520],
[[[1, 12], [2, 3], [3, 5]], 583/17915904],
[[[1, 12], [2, 3], [4, 5]], 1247/1019215872],
[[[1, 12], [2, 5], [3, 4]], 4823/95551488],
[[[1, 12], [2, 5], [4, 4]], 8773/159252480],
[[[1, 12], [2, 5], [8, 2]], 133/212336640],
[[[1, 12], [2, 7], [3, 3]], 84781/1911029760],
[[[1, 12], [2, 7], [4, 3]], 74617/251658240],
[[[1, 12], [2, 7], [6, 3]], 259/3057647616],
[[[1, 12], [2, 9], [3, 2]], 1955311/61152952320],
[[[1, 12], [2, 9], [4, 2]], 6199873/20384317440],
[[[1, 12], [2, 9], [5, 1]], 27523/3397386240],
[[[1, 12], [2, 9], [6, 2]], 350501/40768634880],
[[[1, 12], [2, 9], [8, 1]], 169/31850496],
[[[1, 12], [2, 9], [10, 1]], 17971/6794772480],
[[[1, 12], [2, 11], [3, 1]], 527003/20384317440],
[[[1, 12], [2, 11], [4, 1]], 91435/1019215872],
[[[1, 12], [2, 11], [6, 1]], 115303/5096079360],
[[[1, 13], [2, 2], [3, 5]], 475/11943936],
[[[1, 13], [2, 2], [4, 5]], 61/1698693120],
[[[1, 13], [2, 4], [3, 4]], 213989/2866544640],
[[[1, 13], [2, 4], [4, 4]], 55279/7644119040],
[[[1, 13], [2, 4], [8, 2]], 19/637009920],
[[[1, 13], [2, 6], [3, 3]], 298691/3822059520],
[[[1, 13], [2, 6], [4, 3]], 512777/5096079360],
[[[1, 13], [2, 8], [3, 2]], 50937431/1100753141760],
[[[1, 13], [2, 8], [4, 2]], 3342587/20384317440],
[[[1, 13], [2, 8], [5, 1]], 485947/61152952320],
[[[1, 13], [2, 8], [6, 2]], 109969/61152952320],
[[[1, 13], [2, 8], [8, 1]], 49/53084160],
[[[1, 13], [2, 8], [10, 1]], 463/1132462080],
[[[1, 13], [2, 10], [3, 1]], 118289/5096079360],
[[[1, 13], [2, 10], [4, 1]], 1044287/15288238080],
[[[1, 13], [2, 10], [6, 1]], 791347/61152952320],
[[[1, 13], [3, 2], [4, 4]], 149/7644119040],
[[[1, 13], [3, 4], [4, 2]], 209/238878720],
[[[1, 13], [3, 4], [5, 1]], 7/1866240],
[[[1, 13], [4, 4], [5, 1]], 1/424673280],
[[[1, 14], [2, 1], [3, 5]], 1/73728],
[[[1, 14], [2, 1], [4, 5]], 1/566231040],
[[[1, 14], [2, 3], [3, 4]], 45457/716636160],
[[[1, 14], [2, 3], [4, 4]], 305/509607936],
[[[1, 14], [2, 5], [3, 3]], 167551/1911029760],
[[[1, 14], [2, 5], [4, 3]], 120749/5096079360],
[[[1, 14], [2, 7], [3, 2]], 2813699/45864714240],
[[[1, 14], [2, 7], [4, 2]], 302977/3822059520],
[[[1, 14], [2, 7], [5, 1]], 18559/2548039680],
[[[1, 14], [2, 7], [6, 2]], 14021/40768634880],
[[[1, 14], [2, 7], [8, 1]], 1/17694720],
[[[1, 14], [2, 7], [10, 1]], 457/20384317440],
[[[1, 14], [2, 9], [3, 1]], 4290061/183458856960],
[[[1, 14], [2, 9], [4, 1]], 1837/42467328],
[[[1, 14], [2, 9], [6, 1]], 107117/15288238080],
[[[1, 15], [2, 2], [3, 4]], 45361/1911029760],
[[[1, 15], [2, 2], [4, 4]], 7/212336640],
[[[1, 15], [2, 4], [3, 3]], 8334857/137594142720],
[[[1, 15], [2, 4], [4, 3]], 7819/2264924160],
[[[1, 15], [2, 6], [3, 2]], 1379089/24461180928],
[[[1, 15], [2, 6], [4, 2]], 17773/566231040],
[[[1, 15], [2, 6], [5, 1]], 6557/1358954496],
[[[1, 15], [2, 6], [6, 2]], 1/19906560],
[[[1, 15], [2, 8], [3, 1]], 3299419/137594142720],
[[[1, 15], [2, 8], [4, 1]], 226661/8153726976],
[[[1, 15], [2, 8], [6, 1]], 46361/12230590464],
[[[1, 15], [3, 1], [4, 4]], 1/955514880],
[[[1, 15], [3, 3], [4, 2]], 739/5733089280],
[[[1, 15], [3, 3], [5, 1]], 73/119439360],
[[[1, 16], [2, 1], [3, 4]], 3589/955514880],
[[[1, 16], [2, 1], [4, 4]], 11/20384317440],
[[[1, 16], [2, 3], [3, 3]], 87889/3822059520],
[[[1, 16], [2, 3], [4, 3]], 6137/20384317440],
[[[1, 16], [2, 5], [3, 2]], 2080639/61152952320],
[[[1, 16], [2, 5], [4, 2]], 996059/122305904640],
[[[1, 16], [2, 5], [5, 1]], 21961/10192158720],
[[[1, 16], [2, 5], [6, 2]], 11/2866544640],
[[[1, 16], [2, 7], [3, 1]], 691073/36691771392],
[[[1, 16], [2, 7], [4, 1]], 628567/40768634880],
[[[1, 16], [2, 7], [6, 1]], 69401/45864714240],
[[[1, 17], [2, 2], [3, 3]], 35093/7644119040],
[[[1, 17], [2, 2], [4, 3]], 163/10192158720],
[[[1, 17], [2, 4], [3, 2]], 520151/40768634880],
[[[1, 17], [2, 4], [4, 2]], 91829/73383542784],
[[[1, 17], [2, 4], [5, 1]], 38009/61152952320],
[[[1, 17], [2, 4], [6, 2]], 1/8599633920],
[[[1, 17], [2, 6], [3, 1]], 31511/3057647616],
[[[1, 17], [2, 6], [4, 1]], 1469153/244611809280],
[[[1, 17], [2, 6], [6, 1]], 53767/137594142720],
[[[1, 17], [3, 2], [4, 2]], 1/113246208],
[[[1, 17], [3, 2], [5, 1]], 43/955514880],
[[[1, 17], [4, 2], [5, 1]], 1/2548039680],
[[[1, 18], [2, 1], [3, 3]], 5173/11466178560],
[[[1, 18], [2, 1], [4, 3]], 1/2038431744],
[[[1, 18], [2, 3], [3, 2]], 52673/18345885696],
[[[1, 18], [2, 3], [4, 2]], 731/6794772480],
[[[1, 18], [2, 3], [5, 1]], 569/5096079360],
[[[1, 18], [2, 5], [3, 1]], 46289/12230590464],
[[[1, 18], [2, 5], [4, 1]], 74723/48922361856],
[[[1, 18], [2, 5], [6, 1]], 161/2548039680],
[[[1, 19], [2, 2], [3, 2]], 45653/122305904640],
[[[1, 19], [2, 2], [4, 2]], 11/2264924160],
[[[1, 19], [2, 2], [5, 1]], 1/83886080],
[[[1, 19], [2, 4], [3, 1]], 20861/22932357120],
[[[1, 19], [2, 4], [4, 1]], 20047/81537269760],
[[[1, 19], [2, 4], [6, 1]], 47/7644119040],
[[[1, 19], [3, 1], [4, 2]], 1/3822059520],
[[[1, 19], [3, 1], [5, 1]], 11/7644119040],
[[[1, 20], [2, 1], [3, 2]], 523/20384317440],
[[[1, 20], [2, 1], [4, 2]], 1/8153726976],
[[[1, 20], [2, 1], [5, 1]], 7/10192158720],
[[[1, 20], [2, 3], [3, 1]], 25577/183458856960],
[[[1, 20], [2, 3], [4, 1]], 217/9059696640],
[[[1, 20], [2, 3], [6, 1]], 1/3057647616],
[[[1, 21], [2, 2], [3, 1]], 199/15288238080],
[[[1, 21], [2, 2], [4, 1]], 313/244611809280],
[[[1, 21], [2, 2], [6, 1]], 1/137594142720],
[[[1, 22], [2, 1], [3, 1]], 41/61152952320],
[[[1, 22], [2, 1], [4, 1]], 7/244611809280],
[[[2, 3], [6, 8], [18, 1]], 1/373248],
[[[2, 5], [3, 2], [6, 8]], 1/1492992],
[[[2, 5], [3, 4], [6, 6]], 73/2985984],
[[[2, 5], [6, 6], [12, 2]], 1/82944],
[[[2, 5], [6, 7], [18, 1]], 5/373248],
[[[2, 5], [6, 8], [10, 1]], 1/829440],
[[[2, 5], [6, 8], [12, 1]], 1/248832],
[[[2, 7], [3, 2], [6, 7]], 1/497664],
[[[2, 7], [3, 4], [6, 5]], 1/2985984],
[[[2, 7], [4, 4], [6, 5]], 1/2985984],
[[[2, 7], [6, 5], [12, 2]], 1/82944],
[[[2, 7], [6, 6], [18, 1]], 107/4976640],
[[[2, 7], [6, 7], [10, 1]], 1/207360],
[[[2, 7], [6, 7], [12, 1]], 1/82944],
[[[2, 9], [3, 2], [6, 6]], 1/737280],
[[[2, 9], [3, 4], [6, 4]], 1/119439360],
[[[2, 9], [4, 2], [6, 6]], 1/559872],
[[[2, 9], [4, 4], [6, 4]], 11/23887872],
[[[2, 9], [6, 4], [12, 2]], 1/3317760],
[[[2, 9], [6, 5], [18, 1]], 41/3732480],
[[[2, 9], [6, 6], [10, 1]], 1/207360],
[[[2, 9], [6, 6], [12, 1]], 1/122880],
[[[2, 11], [3, 2], [6, 5]], 1/29859840],
[[[2, 11], [4, 2], [6, 5]], 5/1990656],
[[[2, 11], [4, 4], [6, 3]], 143/955514880],
[[[2, 11], [6, 4], [18, 1]], 1/3732480],
[[[2, 11], [6, 5], [10, 1]], 1/116640],
[[[2, 11], [6, 5], [12, 1]], 1/4976640],
[[[2, 13], [4, 2], [6, 4]], 209/238878720],
[[[2, 13], [4, 4], [6, 2]], 149/7644119040],
[[[2, 13], [4, 4], [10, 1]], 1/424673280],
[[[2, 13], [6, 4], [10, 1]], 7/1866240],
[[[2, 15], [4, 2], [6, 3]], 739/5733089280],
[[[2, 15], [4, 4], [6, 1]], 1/955514880],
[[[2, 15], [6, 3], [10, 1]], 73/119439360],
[[[2, 17], [4, 2], [6, 2]], 1/113246208],
[[[2, 17], [4, 2], [10, 1]], 1/2548039680],
[[[2, 17], [6, 2], [10, 1]], 43/955514880],
[[[2, 19], [4, 2], [6, 1]], 1/3822059520],
[[[2, 19], [6, 1], [10, 1]], 11/7644119040],
[[[1, 1], [2, 4], [3, 1], [6, 9]], 1/331776],
[[[1, 1], [2, 4], [3, 3], [6, 7]], 1/165888],
[[[1, 1], [2, 4], [3, 5], [6, 5]], 155/995328],
[[[1, 1], [2, 4], [6, 7], [18, 1]], 5/124416],
[[[1, 1], [2, 6], [3, 1], [6, 8]], 1/55296],
[[[1, 1], [2, 6], [3, 2], [6, 7]], 1/165888],
[[[1, 1], [2, 6], [3, 3], [6, 6]], 5/248832],
[[[1, 1], [2, 6], [3, 4], [6, 5]], 1/995328],
[[[1, 1], [2, 6], [3, 5], [6, 4]], 1/497664],
[[[1, 1], [2, 6], [4, 1], [6, 8]], 1/1327104],
[[[1, 1], [2, 6], [4, 5], [6, 4]], 1/1327104],
[[[1, 1], [2, 6], [4, 7], [6, 2]], 1/5308416],
[[[1, 1], [2, 6], [4, 7], [10, 1]], 1/1474560],
[[[1, 1], [2, 6], [6, 5], [12, 2]], 1/27648],
[[[1, 1], [2, 6], [6, 6], [18, 1]], 43/331776],
[[[1, 1], [2, 6], [6, 7], [10, 1]], 1/69120],
[[[1, 1], [2, 6], [6, 7], [12, 1]], 1/27648],
[[[1, 1], [2, 8], [3, 1], [6, 7]], 641/19906560],
[[[1, 1], [2, 8], [3, 2], [6, 6]], 11/1327104],
[[[1, 1], [2, 8], [3, 3], [6, 5]], 121/9953280],
[[[1, 1], [2, 8], [3, 4], [6, 4]], 1/7962624],
[[[1, 1], [2, 8], [3, 5], [6, 3]], 1/19906560],
[[[1, 1], [2, 8], [4, 1], [6, 7]], 1/331776],
[[[1, 1], [2, 8], [4, 3], [6, 5]], 1/124416],
[[[1, 1], [2, 8], [4, 4], [6, 4]], 7/3981312],
[[[1, 1], [2, 8], [4, 5], [6, 3]], 1/589824],
[[[1, 1], [2, 8], [4, 7], [6, 1]], 1/5308416],
[[[1, 1], [2, 8], [6, 4], [12, 2]], 1/221184],
[[[1, 1], [2, 8], [6, 5], [18, 1]], 7/69120],
[[[1, 1], [2, 8], [6, 6], [10, 1]], 1/34560],
[[[1, 1], [2, 8], [6, 6], [12, 1]], 11/221184],
[[[1, 1], [2, 10], [3, 1], [6, 6]], 2107/89579520],
[[[1, 1], [2, 10], [3, 2], [6, 5]], 1/1658880],
[[[1, 1], [2, 10], [3, 3], [6, 4]], 1/3317760],
[[[1, 1], [2, 10], [4, 1], [6, 6]], 19/995328],
[[[1, 1], [2, 10], [4, 1], [8, 3]], 1/8847360],
[[[1, 1], [2, 10], [4, 2], [6, 5]], 5/497664],
[[[1, 1], [2, 10], [4, 3], [6, 4]], 13/884736],
[[[1, 1], [2, 10], [4, 3], [8, 2]], 1/17694720],
[[[1, 1], [2, 10], [4, 4], [6, 3]], 23/15925248],
[[[1, 1], [2, 10], [4, 5], [6, 2]], 71/141557760],
[[[1, 1], [2, 10], [4, 5], [8, 1]], 1/106168320],
[[[1, 1], [2, 10], [4, 5], [10, 1]], 1/23592960],
[[[1, 1], [2, 10], [4, 5], [12, 1]], 1/6635520],
[[[1, 1], [2, 10], [6, 4], [18, 1]], 7/1244160],
[[[1, 1], [2, 10], [6, 5], [12, 1]], 1/276480],
[[[1, 1], [2, 12], [3, 1], [6, 5]], 79/22394880],
[[[1, 1], [2, 12], [4, 1], [6, 5]], 41/1492992],
[[[1, 1], [2, 12], [4, 2], [6, 4]], 71/7962624],
[[[1, 1], [2, 12], [4, 3], [6, 3]], 757/159252480],
[[[1, 1], [2, 12], [4, 4], [6, 2]], 133/424673280],
[[[1, 1], [2, 12], [4, 4], [10, 1]], 1/23592960],
[[[1, 1], [2, 12], [4, 5], [6, 1]], 11/212336640],
[[[1, 1], [2, 12], [6, 4], [10, 1]], 1/38880],
[[[1, 1], [2, 14], [3, 1], [6, 4]], 73/143327232],
[[[1, 1], [2, 14], [4, 1], [6, 4]], 9149/955514880],
[[[1, 1], [2, 14], [4, 2], [6, 3]], 11/4976640],
[[[1, 1], [2, 14], [4, 3], [6, 2]], 1513/2548039680],
[[[1, 1], [2, 14], [4, 3], [10, 1]], 1/28311552],
[[[1, 1], [2, 14], [4, 4], [6, 1]], 31/1274019840],
[[[1, 1], [2, 14], [6, 3], [10, 1]], 43/4976640],
[[[1, 1], [2, 16], [3, 1], [6, 3]], 43/1146617856],
[[[1, 1], [2, 16], [4, 1], [6, 3]], 5261/3822059520],
[[[1, 1], [2, 16], [4, 2], [6, 2]], 563/2548039680],
[[[1, 1], [2, 16], [4, 2], [10, 1]], 1/84934656],
[[[1, 1], [2, 16], [4, 3], [6, 1]], 13/424673280],
[[[1, 1], [2, 16], [6, 2], [10, 1]], 53/53084160],
[[[1, 1], [2, 18], [3, 1], [6, 2]], 11/9172942848],
[[[1, 1], [2, 18], [4, 1], [6, 2]], 5629/61152952320],
[[[1, 1], [2, 18], [4, 1], [10, 1]], 1/377487360],
[[[1, 1], [2, 18], [4, 2], [6, 1]], 23/2548039680],
[[[1, 1], [2, 18], [6, 1], [10, 1]], 29/637009920],
[[[1, 1], [2, 20], [3, 1], [6, 1]], 1/73383542784],
[[[1, 1], [2, 20], [4, 1], [6, 1]], 83/30576476160],
[[[1, 2], [2, 3], [3, 2], [6, 8]], 7/995328],
[[[1, 2], [2, 3], [3, 3], [6, 7]], 1/36864],
[[[1, 2], [2, 3], [3, 4], [6, 6]], 7/497664],
[[[1, 2], [2, 3], [3, 5], [6, 5]], 1/165888],
[[[1, 2], [2, 3], [3, 6], [6, 4]], 127/995328],
[[[1, 2], [2, 3], [3, 7], [6, 3]], 1/331776],
[[[1, 2], [2, 5], [3, 1], [6, 8]], 65/1492992],
[[[1, 2], [2, 5], [3, 2], [6, 7]], 65/995328],
[[[1, 2], [2, 5], [3, 3], [6, 6]], 1/11664],
[[[1, 2], [2, 5], [3, 4], [6, 5]], 5/55296],
[[[1, 2], [2, 5], [3, 5], [6, 4]], 1/55296],
[[[1, 2], [2, 5], [3, 6], [6, 3]], 1/995328],
[[[1, 2], [2, 5], [4, 1], [6, 8]], 1/1327104],
[[[1, 2], [2, 5], [4, 6], [6, 3]], 11/5308416],
[[[1, 2], [2, 5], [6, 6], [18, 1]], 65/331776],
[[[1, 2], [2, 7], [3, 1], [6, 7]], 643/3981312],
[[[1, 2], [2, 7], [3, 2], [6, 6]], 679/4423680],
[[[1, 2], [2, 7], [3, 3], [6, 5]], 3793/29859840],
[[[1, 2], [2, 7], [3, 4], [6, 4]], 379/13271040],
[[[1, 2], [2, 7], [3, 5], [6, 3]], 1/1327104],
[[[1, 2], [2, 7], [3, 6], [6, 2]], 1/39813120],
[[[1, 2], [2, 7], [4, 1], [6, 7]], 1/82944],
[[[1, 2], [2, 7], [4, 2], [8, 3]], 1/46080],
[[[1, 2], [2, 7], [4, 4], [6, 4]], 11/884736],
[[[1, 2], [2, 7], [4, 4], [8, 2]], 1/196608],
[[[1, 2], [2, 7], [4, 5], [6, 3]], 11/2654208],
[[[1, 2], [2, 7], [4, 6], [6, 2]], 31/4718592],
[[[1, 2], [2, 7], [4, 6], [8, 1]], 1/1105920],
[[[1, 2], [2, 7], [4, 6], [10, 1]], 119/11796480],
[[[1, 2], [2, 7], [4, 6], [12, 1]], 1/73728],
[[[1, 2], [2, 7], [4, 7], [6, 1]], 1/1769472],
[[[1, 2], [2, 7], [6, 4], [12, 2]], 1/73728],
[[[1, 2], [2, 7], [6, 5], [18, 1]], 13/41472],
[[[1, 2], [2, 7], [6, 6], [10, 1]], 1/23040],
[[[1, 2], [2, 7], [6, 6], [12, 1]], 17/221184],
[[[1, 2], [2, 9], [3, 1], [4, 6]], 1/53084160],
[[[1, 2], [2, 9], [3, 1], [6, 6]], 17893/134369280],
[[[1, 2], [2, 9], [3, 2], [6, 5]], 677/9953280],
[[[1, 2], [2, 9], [3, 3], [6, 4]], 77/14929920],
[[[1, 2], [2, 9], [3, 4], [6, 3]], 7/9953280],
[[[1, 2], [2, 9], [4, 1], [6, 6]], 7/331776],
[[[1, 2], [2, 9], [4, 1], [8, 3]], 7/2949120],
[[[1, 2], [2, 9], [4, 2], [6, 5]], 43/995328],
[[[1, 2], [2, 9], [4, 3], [6, 4]], 89/1990656],
[[[1, 2], [2, 9], [4, 3], [8, 2]], 37/5898240],
[[[1, 2], [2, 9], [4, 4], [6, 3]], 97/2654208],
[[[1, 2], [2, 9], [4, 5], [6, 2]], 29/7077888],
[[[1, 2], [2, 9], [4, 5], [8, 1]], 7/35389440],
[[[1, 2], [2, 9], [4, 5], [10, 1]], 1/1966080],
[[[1, 2], [2, 9], [4, 5], [12, 1]], 1/442368],
[[[1, 2], [2, 9], [4, 6], [6, 1]], 29/8847360],
[[[1, 2], [2, 9], [6, 4], [18, 1]], 1/25920],
[[[1, 2], [2, 9], [6, 5], [12, 1]], 1/55296],
[[[1, 2], [2, 11], [3, 1], [6, 5]], 269/7464960],
[[[1, 2], [2, 11], [3, 2], [6, 4]], 1/622080],
[[[1, 2], [2, 11], [4, 1], [6, 5]], 35/373248],
[[[1, 2], [2, 11], [4, 2], [6, 4]], 1799/15925248],
[[[1, 2], [2, 11], [4, 2], [8, 2]], 29/35389440],
[[[1, 2], [2, 11], [4, 3], [6, 3]], 689/15925248],
[[[1, 2], [2, 11], [4, 4], [6, 2]], 3073/283115520],
[[[1, 2], [2, 11], [4, 4], [8, 1]], 1/884736],
[[[1, 2], [2, 11], [4, 4], [10, 1]], 13/15728640],
[[[1, 2], [2, 11], [4, 4], [12, 1]], 1/2654208],
[[[1, 2], [2, 11], [4, 5], [6, 1]], 13/17694720],
[[[1, 2], [2, 11], [6, 4], [10, 1]], 1/51840],
[[[1, 2], [2, 13], [3, 1], [6, 4]], 427/44789760],
[[[1, 2], [2, 13], [4, 1], [6, 4]], 2237/23887872],
[[[1, 2], [2, 13], [4, 2], [6, 3]], 17407/424673280],
[[[1, 2], [2, 13], [4, 3], [6, 2]], 497/53084160],
[[[1, 2], [2, 13], [4, 3], [10, 1]], 1/1474560],
[[[1, 2], [2, 13], [4, 4], [6, 1]], 19/17694720],
[[[1, 2], [2, 13], [6, 3], [10, 1]], 41/1105920],
[[[1, 2], [2, 15], [3, 1], [6, 3]], 10111/8599633920],
[[[1, 2], [2, 15], [4, 1], [6, 3]], 8903/382205952],
[[[1, 2], [2, 15], [4, 2], [6, 2]], 55379/10192158720],
[[[1, 2], [2, 15], [4, 2], [10, 1]], 151/566231040],
[[[1, 2], [2, 15], [4, 3], [6, 1]], 113/159252480],
[[[1, 2], [2, 15], [6, 2], [10, 1]], 287/35389440],
[[[1, 2], [2, 17], [3, 1], [4, 2]], 1/11466178560],
[[[1, 2], [2, 17], [3, 1], [6, 2]], 47/764411904],
[[[1, 2], [2, 17], [3, 1], [10, 1]], 1/955514880],
[[[1, 2], [2, 17], [4, 1], [6, 2]], 35101/15288238080],
[[[1, 2], [2, 17], [4, 1], [10, 1]], 23/283115520],
[[[1, 2], [2, 17], [4, 2], [6, 1]], 733/2548039680],
[[[1, 2], [2, 17], [6, 1], [10, 1]], 241/424673280],
[[[1, 2], [2, 19], [3, 1], [6, 1]], 233/183458856960],
[[[1, 2], [2, 19], [4, 1], [6, 1]], 713/7644119040],
[[[1, 3], [2, 2], [3, 3], [6, 7]], 1/331776],
[[[1, 3], [2, 2], [3, 4], [6, 6]], 127/995328],
[[[1, 3], [2, 2], [3, 5], [6, 5]], 1/165888],
[[[1, 3], [2, 2], [3, 6], [6, 4]], 7/497664],
[[[1, 3], [2, 2], [3, 7], [6, 3]], 1/36864],
[[[1, 3], [2, 2], [3, 8], [6, 2]], 7/995328],
[[[1, 3], [2, 4], [3, 2], [6, 7]], 11/110592],
[[[1, 3], [2, 4], [3, 3], [6, 6]], 17/82944],
[[[1, 3], [2, 4], [3, 4], [6, 5]], 37/165888],
[[[1, 3], [2, 4], [3, 5], [6, 4]], 23/82944],
[[[1, 3], [2, 4], [3, 6], [6, 3]], 67/995328],
[[[1, 3], [2, 4], [4, 3], [8, 3]], 1/4096],
[[[1, 3], [2, 4], [4, 7], [6, 2]], 1/786432],
[[[1, 3], [2, 4], [4, 7], [8, 1]], 1/98304],
[[[1, 3], [2, 4], [4, 7], [10, 1]], 3/655360],
[[[1, 3], [2, 4], [6, 6], [18, 1]], 1/995328],
[[[1, 3], [2, 6], [3, 1], [4, 7]], 1/589824],
[[[1, 3], [2, 6], [3, 1], [6, 7]], 259/1327104],
[[[1, 3], [2, 6], [3, 2], [6, 6]], 4165/7962624],
[[[1, 3], [2, 6], [3, 3], [6, 5]], 941/1990656],
[[[1, 3], [2, 6], [3, 4], [6, 4]], 2347/4423680],
[[[1, 3], [2, 6], [3, 5], [6, 3]], 19/1327104],
[[[1, 3], [2, 6], [3, 6], [6, 2]], 1/2654208],
[[[1, 3], [2, 6], [4, 1], [6, 7]], 1/110592],
[[[1, 3], [2, 6], [4, 2], [8, 3]], 1/6144],
[[[1, 3], [2, 6], [4, 4], [8, 2]], 13/196608],
[[[1, 3], [2, 6], [4, 5], [6, 3]], 481/15925248],
[[[1, 3], [2, 6], [4, 6], [6, 2]], 71/7077888],
[[[1, 3], [2, 6], [4, 6], [8, 1]], 1/147456],
[[[1, 3], [2, 6], [4, 6], [10, 1]], 1/131072],
[[[1, 3], [2, 6], [4, 6], [12, 1]], 1/73728],
[[[1, 3], [2, 6], [4, 7], [6, 1]], 7/1179648],
[[[1, 3], [2, 6], [6, 4], [12, 2]], 1/221184],
[[[1, 3], [2, 6], [6, 5], [18, 1]], 41/124416],
[[[1, 3], [2, 6], [6, 6], [12, 1]], 1/663552],
[[[1, 3], [2, 8], [3, 1], [4, 6]], 1/3538944],
[[[1, 3], [2, 8], [3, 1], [6, 6]], 109/331776],
[[[1, 3], [2, 8], [3, 2], [4, 5]], 1/39813120],
[[[1, 3], [2, 8], [3, 2], [6, 5]], 233/559872],
[[[1, 3], [2, 8], [3, 3], [6, 4]], 1193/9953280],
[[[1, 3], [2, 8], [3, 4], [6, 3]], 11/995328],
[[[1, 3], [2, 8], [3, 5], [6, 2]], 1/3317760],
[[[1, 3], [2, 8], [4, 1], [6, 6]], 5/110592],
[[[1, 3], [2, 8], [4, 1], [8, 3]], 13/737280],
[[[1, 3], [2, 8], [4, 2], [6, 5]], 1/1492992],
[[[1, 3], [2, 8], [4, 3], [6, 4]], 223/3981312],
[[[1, 3], [2, 8], [4, 3], [8, 2]], 203/1474560],
[[[1, 3], [2, 8], [4, 4], [6, 3]], 1163/15925248],
[[[1, 3], [2, 8], [4, 5], [6, 2]], 799/10616832],
[[[1, 3], [2, 8], [4, 5], [8, 1]], 89/1769472],
[[[1, 3], [2, 8], [4, 5], [10, 1]], 25/589824],
[[[1, 3], [2, 8], [4, 5], [12, 1]], 23/552960],
[[[1, 3], [2, 8], [4, 6], [6, 1]], 101/7077888],
[[[1, 3], [2, 8], [6, 4], [18, 1]], 7/62208],
[[[1, 3], [2, 8], [6, 5], [12, 1]], 5/165888],
[[[1, 3], [2, 10], [3, 1], [4, 5]], 13/53084160],
[[[1, 3], [2, 10], [3, 1], [6, 5]], 17/186624],
[[[1, 3], [2, 10], [3, 2], [4, 4]], 163/1146617856],
[[[1, 3], [2, 10], [3, 2], [6, 4]], 389/11197440],
[[[1, 3], [2, 10], [3, 2], [8, 2]], 1/95551488],
[[[1, 3], [2, 10], [3, 3], [6, 3]], 1/414720],
[[[1, 3], [2, 10], [4, 1], [6, 5]], 7/248832],
[[[1, 3], [2, 10], [4, 2], [6, 4]], 3007/11943936],
[[[1, 3], [2, 10], [4, 2], [8, 2]], 697/35389440],
[[[1, 3], [2, 10], [4, 3], [6, 3]], 7825/31850496],
[[[1, 3], [2, 10], [4, 4], [5, 1]], 163/318504960],
[[[1, 3], [2, 10], [4, 4], [6, 2]], 1669/21233664],
[[[1, 3], [2, 10], [4, 4], [8, 1]], 53/2949120],
[[[1, 3], [2, 10], [4, 4], [10, 1]], 1/131072],
[[[1, 3], [2, 10], [4, 4], [12, 1]], 31/4423680],
[[[1, 3], [2, 10], [4, 5], [6, 1]], 257/10616832],
[[[1, 3], [2, 10], [5, 1], [8, 2]], 1/26542080],
[[[1, 3], [2, 10], [6, 4], [10, 1]], 1/155520],
[[[1, 3], [2, 12], [3, 1], [6, 4]], 653/11943936],
[[[1, 3], [2, 12], [3, 2], [6, 3]], 5/5971968],
[[[1, 3], [2, 12], [4, 1], [6, 4]], 3821/15925248],
[[[1, 3], [2, 12], [4, 1], [8, 2]], 19/106168320],
[[[1, 3], [2, 12], [4, 2], [6, 3]], 44821/159252480],
[[[1, 3], [2, 12], [4, 3], [6, 2]], 150847/1698693120],
[[[1, 3], [2, 12], [4, 3], [8, 1]], 113/70778880],
[[[1, 3], [2, 12], [4, 3], [10, 1]], 1849/283115520],
[[[1, 3], [2, 12], [4, 3], [12, 1]], 19/39813120],
[[[1, 3], [2, 12], [4, 4], [6, 1]], 5701/424673280],
[[[1, 3], [2, 12], [6, 3], [10, 1]], 247/4976640],
[[[1, 3], [2, 14], [3, 1], [4, 3]], 1/106168320],
[[[1, 3], [2, 14], [3, 1], [6, 3]], 24179/1911029760],
[[[1, 3], [2, 14], [3, 2], [6, 2]], 7/143327232],
[[[1, 3], [2, 14], [4, 1], [6, 3]], 57787/424673280],
[[[1, 3], [2, 14], [4, 2], [6, 2]], 954377/15288238080],
[[[1, 3], [2, 14], [4, 2], [10, 1]], 2893/849346560],
[[[1, 3], [2, 14], [4, 3], [6, 1]], 24569/2548039680],
[[[1, 3], [2, 14], [6, 2], [10, 1]], 79/2654208],
[[[1, 3], [2, 16], [3, 1], [4, 2]], 11/3822059520],
[[[1, 3], [2, 16], [3, 1], [6, 2]], 8119/7644119040],
[[[1, 3], [2, 16], [3, 1], [10, 1]], 1/31850496],
[[[1, 3], [2, 16], [3, 2], [6, 1]], 1/1146617856],
[[[1, 3], [2, 16], [4, 1], [6, 2]], 224117/10192158720],
[[[1, 3], [2, 16], [4, 1], [10, 1]], 553/566231040],
[[[1, 3], [2, 16], [4, 2], [6, 1]], 72283/15288238080],
[[[1, 3], [2, 16], [6, 1], [10, 1]], 2291/637009920],
[[[1, 3], [2, 18], [3, 1], [4, 1]], 1/764411904],
[[[1, 3], [2, 18], [3, 1], [6, 1]], 4159/122305904640],
[[[1, 3], [2, 18], [4, 1], [6, 1]], 6593/5096079360],
[[[1, 3], [3, 4], [6, 4], [9, 1]], 73/373248],
[[[1, 3], [3, 4], [9, 1], [12, 2]], 1/10368],
[[[1, 3], [3, 6], [5, 1], [9, 1]], 1/103680],
[[[1, 3], [3, 6], [6, 2], [9, 1]], 1/186624],
[[[1, 3], [3, 6], [9, 1], [12, 1]], 1/31104],
[[[1, 4], [2, 1], [3, 5], [6, 5]], 155/995328],
[[[1, 4], [2, 1], [3, 7], [6, 3]], 1/165888],
[[[1, 4], [2, 1], [3, 7], [9, 1]], 5/124416],
[[[1, 4], [2, 1], [3, 9], [6, 1]], 1/331776],
[[[1, 4], [2, 3], [3, 2], [4, 7]], 1/786432],
[[[1, 4], [2, 3], [3, 3], [6, 6]], 67/995328],
[[[1, 4], [2, 3], [3, 4], [6, 5]], 23/82944],
[[[1, 4], [2, 3], [3, 5], [6, 4]], 37/165888],
[[[1, 4], [2, 3], [3, 6], [6, 3]], 17/82944],
[[[1, 4], [2, 3], [3, 6], [9, 1]], 1/995328],
[[[1, 4], [2, 3], [3, 7], [6, 2]], 11/110592],
[[[1, 4], [2, 3], [4, 3], [8, 3]], 1/4096],
[[[1, 4], [2, 3], [4, 7], [5, 1]], 3/655360],
[[[1, 4], [2, 3], [4, 7], [8, 1]], 1/98304],
[[[1, 4], [2, 5], [3, 1], [4, 7]], 1/589824],
[[[1, 4], [2, 5], [3, 1], [6, 7]], 1/1327104],
[[[1, 4], [2, 5], [3, 2], [4, 6]], 1/442368],
[[[1, 4], [2, 5], [3, 2], [6, 6]], 2609/5971968],
[[[1, 4], [2, 5], [3, 3], [6, 5]], 199/221184],
[[[1, 4], [2, 5], [3, 4], [6, 4]], 289/331776],
[[[1, 4], [2, 5], [3, 5], [6, 3]], 437/737280],
[[[1, 4], [2, 5], [3, 6], [6, 2]], 1/663552],
[[[1, 4], [2, 5], [4, 2], [8, 3]], 1/3072],
[[[1, 4], [2, 5], [4, 4], [8, 2]], 17/16384],
[[[1, 4], [2, 5], [4, 5], [6, 3]], 1/995328],
[[[1, 4], [2, 5], [4, 6], [6, 2]], 877/42467328],
[[[1, 4], [2, 5], [4, 6], [8, 1]], 5/36864],
[[[1, 4], [2, 5], [4, 6], [10, 1]], 781/11796480],
[[[1, 4], [2, 5], [4, 6], [12, 1]], 1/6144],
[[[1, 4], [2, 5], [4, 7], [6, 1]], 5/589824],
[[[1, 4], [2, 5], [6, 5], [18, 1]], 1/82944],
[[[1, 4], [2, 7], [3, 1], [4, 6]], 3/131072],
[[[1, 4], [2, 7], [3, 1], [6, 6]], 91/331776],
[[[1, 4], [2, 7], [3, 2], [4, 5]], 161/127401984],
[[[1, 4], [2, 7], [3, 2], [6, 5]], 13343/13436928],
[[[1, 4], [2, 7], [3, 3], [4, 4]], 1/89579520],
[[[1, 4], [2, 7], [3, 3], [6, 4]], 401/622080],
[[[1, 4], [2, 7], [3, 3], [8, 2]], 1/7464960],
[[[1, 4], [2, 7], [3, 4], [6, 3]], 281/1990656],
[[[1, 4], [2, 7], [3, 5], [6, 2]], 23/4976640],
[[[1, 4], [2, 7], [4, 1], [6, 6]], 1/36864],
[[[1, 4], [2, 7], [4, 1], [8, 3]], 43/737280],
[[[1, 4], [2, 7], [4, 2], [6, 5]], 1/17915904],
[[[1, 4], [2, 7], [4, 3], [6, 4]], 1/663552],
[[[1, 4], [2, 7], [4, 3], [8, 2]], 1153/1474560],
[[[1, 4], [2, 7], [4, 4], [6, 3]], 22007/191102976],
[[[1, 4], [2, 7], [4, 5], [5, 1]], 113/35389440],
[[[1, 4], [2, 7], [4, 5], [6, 2]], 3203/21233664],
[[[1, 4], [2, 7], [4, 5], [8, 1]], 325/1769472],
[[[1, 4], [2, 7], [4, 5], [10, 1]], 229/1966080],
[[[1, 4], [2, 7], [4, 5], [12, 1]], 19/110592],
[[[1, 4], [2, 7], [4, 6], [6, 1]], 259/2654208],
[[[1, 4], [2, 7], [6, 3], [8, 2]], 1/124416],
[[[1, 4], [2, 7], [6, 4], [18, 1]], 11/82944],
[[[1, 4], [2, 7], [6, 5], [12, 1]], 1/110592],
[[[1, 4], [2, 9], [3, 1], [4, 5]], 197/53084160],
[[[1, 4], [2, 9], [3, 1], [6, 5]], 25/186624],
[[[1, 4], [2, 9], [3, 2], [4, 4]], 37/21233664],
[[[1, 4], [2, 9], [3, 2], [6, 4]], 20489/53747712],
[[[1, 4], [2, 9], [3, 2], [8, 2]], 1/2949120],
[[[1, 4], [2, 9], [3, 3], [4, 3]], 1/1327104],
[[[1, 4], [2, 9], [3, 3], [6, 3]], 89/1244160],
[[[1, 4], [2, 9], [3, 4], [6, 2]], 89/9953280],
[[[1, 4], [2, 9], [4, 1], [6, 5]], 1/124416],
[[[1, 4], [2, 9], [4, 2], [6, 4]], 8129/143327232],
[[[1, 4], [2, 9], [4, 2], [8, 2]], 1519/8847360],
[[[1, 4], [2, 9], [4, 3], [6, 3]], 307/884736],
[[[1, 4], [2, 9], [4, 4], [5, 1]], 91/17694720],
[[[1, 4], [2, 9], [4, 4], [6, 2]], 195263/509607936],
[[[1, 4], [2, 9], [4, 4], [8, 1]], 563/2949120],
[[[1, 4], [2, 9], [4, 4], [10, 1]], 15119/141557760],
[[[1, 4], [2, 9], [4, 4], [12, 1]], 259/3317760],
[[[1, 4], [2, 9], [4, 5], [6, 1]], 745/5308416],
[[[1, 4], [2, 9], [5, 1], [8, 2]], 1/1474560],
[[[1, 4], [2, 9], [6, 2], [8, 2]], 83/10616832],
[[[1, 4], [2, 9], [6, 4], [10, 1]], 1/1866240],
[[[1, 4], [2, 9], [8, 2], [10, 1]], 11/2949120],
[[[1, 4], [2, 11], [3, 1], [4, 4]], 2851/955514880],
[[[1, 4], [2, 11], [3, 1], [6, 4]], 319/2985984],
[[[1, 4], [2, 11], [3, 1], [8, 2]], 7/79626240],
[[[1, 4], [2, 11], [3, 2], [4, 3]], 1187/3057647616],
[[[1, 4], [2, 11], [3, 2], [6, 3]], 979/26873856],
[[[1, 4], [2, 11], [3, 3], [6, 2]], 1/497664],
[[[1, 4], [2, 11], [4, 1], [6, 4]], 151/884736],
[[[1, 4], [2, 11], [4, 1], [8, 2]], 421/106168320],
[[[1, 4], [2, 11], [4, 2], [6, 3]], 828947/1433272320],
[[[1, 4], [2, 11], [4, 3], [5, 1]], 1187/849346560],
[[[1, 4], [2, 11], [4, 3], [6, 2]], 30161/70778880],
[[[1, 4], [2, 11], [4, 3], [8, 1]], 2477/70778880],
[[[1, 4], [2, 11], [4, 3], [10, 1]], 443/11796480],
[[[1, 4], [2, 11], [4, 3], [12, 1]], 77/7962624],
[[[1, 4], [2, 11], [4, 4], [6, 1]], 18917/159252480],
[[[1, 4], [2, 11], [6, 1], [8, 2]], 17/13271040],
[[[1, 4], [2, 11], [6, 3], [10, 1]], 2047/59719680],
[[[1, 4], [2, 13], [3, 1], [4, 3]], 61/318504960],
[[[1, 4], [2, 13], [3, 1], [6, 3]], 14333/238878720],
[[[1, 4], [2, 13], [3, 2], [6, 2]], 943/537477120],
[[[1, 4], [2, 13], [3, 2], [10, 1]], 1/59719680],
[[[1, 4], [2, 13], [4, 1], [6, 3]], 52327/159252480],
[[[1, 4], [2, 13], [4, 2], [6, 2]], 28085023/91729428480],
[[[1, 4], [2, 13], [4, 2], [8, 1]], 143/106168320],
[[[1, 4], [2, 13], [4, 2], [10, 1]], 22135/1019215872],
[[[1, 4], [2, 13], [4, 2], [12, 1]], 19/238878720],
[[[1, 4], [2, 13], [4, 3], [6, 1]], 32669/424673280],
[[[1, 4], [2, 13], [6, 2], [10, 1]], 8249/159252480],
[[[1, 4], [2, 15], [3, 1], [4, 2]], 17/159252480],
[[[1, 4], [2, 15], [3, 1], [6, 2]], 33157/3822059520],
[[[1, 4], [2, 15], [3, 1], [10, 1]], 13/35389440],
[[[1, 4], [2, 15], [3, 2], [6, 1]], 289/8599633920],
[[[1, 4], [2, 15], [4, 1], [6, 2]], 522857/5096079360],
[[[1, 4], [2, 15], [4, 1], [10, 1]], 1681/283115520],
[[[1, 4], [2, 15], [4, 2], [6, 1]], 871573/22932357120],
[[[1, 4], [2, 15], [6, 1], [10, 1]], 96053/7644119040],
[[[1, 4], [2, 17], [3, 1], [4, 1]], 163/3822059520],
[[[1, 4], [2, 17], [3, 1], [6, 1]], 2617/6115295232],
[[[1, 4], [2, 17], [4, 1], [6, 1]], 25/2654208],
[[[1, 5], [2, 2], [3, 3], [4, 6]], 11/5308416],
[[[1, 5], [2, 2], [3, 3], [6, 6]], 1/995328],
[[[1, 5], [2, 2], [3, 4], [6, 5]], 1/55296],
[[[1, 5], [2, 2], [3, 5], [6, 4]], 5/55296],
[[[1, 5], [2, 2], [3, 6], [6, 3]], 1/11664],
[[[1, 5], [2, 2], [3, 6], [9, 1]], 65/331776],
[[[1, 5], [2, 2], [3, 7], [6, 2]], 65/995328],
[[[1, 5], [2, 2], [3, 8], [4, 1]], 1/1327104],
[[[1, 5], [2, 2], [3, 8], [6, 1]], 65/1492992],
[[[1, 5], [2, 4], [3, 1], [4, 7]], 5/589824],
[[[1, 5], [2, 4], [3, 2], [4, 6]], 877/42467328],
[[[1, 5], [2, 4], [3, 2], [6, 6]], 1/663552],
[[[1, 5], [2, 4], [3, 3], [4, 5]], 1/995328],
[[[1, 5], [2, 4], [3, 3], [6, 5]], 437/737280],
[[[1, 5], [2, 4], [3, 4], [6, 4]], 289/331776],
[[[1, 5], [2, 4], [3, 5], [6, 3]], 199/221184],
[[[1, 5], [2, 4], [3, 5], [9, 1]], 1/82944],
[[[1, 5], [2, 4], [3, 6], [6, 2]], 2609/5971968],
[[[1, 5], [2, 4], [3, 7], [6, 1]], 1/1327104],
[[[1, 5], [2, 4], [4, 2], [8, 3]], 1/3072],
[[[1, 5], [2, 4], [4, 4], [8, 2]], 17/16384],
[[[1, 5], [2, 4], [4, 6], [5, 1]], 781/11796480],
[[[1, 5], [2, 4], [4, 6], [6, 2]], 1/442368],
[[[1, 5], [2, 4], [4, 6], [8, 1]], 5/36864],
[[[1, 5], [2, 4], [4, 6], [12, 1]], 1/6144],
[[[1, 5], [2, 4], [4, 7], [6, 1]], 1/589824],
[[[1, 5], [2, 6], [3, 1], [4, 6]], 91/3538944],
[[[1, 5], [2, 6], [3, 1], [6, 6]], 19/1990656],
[[[1, 5], [2, 6], [3, 2], [4, 5]], 353/10616832],
[[[1, 5], [2, 6], [3, 2], [6, 5]], 221/497664],
[[[1, 5], [2, 6], [3, 3], [4, 4]], 457/95551488],
[[[1, 5], [2, 6], [3, 3], [6, 4]], 797/746496],
[[[1, 5], [2, 6], [3, 3], [8, 2]], 1/497664],
[[[1, 5], [2, 6], [3, 4], [6, 3]], 901/1492992],
[[[1, 5], [2, 6], [3, 5], [6, 2]], 263/5971968],
[[[1, 5], [2, 6], [4, 1], [8, 3]], 413/4423680],
[[[1, 5], [2, 6], [4, 3], [6, 4]], 49/7962624],
[[[1, 5], [2, 6], [4, 3], [8, 2]], 15/8192],
[[[1, 5], [2, 6], [4, 4], [6, 3]], 181/7962624],
[[[1, 5], [2, 6], [4, 5], [5, 1]], 41/2949120],
[[[1, 5], [2, 6], [4, 5], [6, 2]], 2879/28311552],
[[[1, 5], [2, 6], [4, 5], [8, 1]], 347/393216],
[[[1, 5], [2, 6], [4, 5], [10, 1]], 6013/23592960],
[[[1, 5], [2, 6], [4, 5], [12, 1]], 11/18432],
[[[1, 5], [2, 6], [4, 6], [6, 1]], 901/7077888],
[[[1, 5], [2, 6], [6, 3], [8, 2]], 1/165888],
[[[1, 5], [2, 6], [6, 4], [18, 1]], 1/27648],
[[[1, 5], [2, 8], [3, 1], [4, 5]], 7127/79626240],
[[[1, 5], [2, 8], [3, 1], [6, 5]], 541/4478976],
[[[1, 5], [2, 8], [3, 2], [4, 4]], 5149/424673280],
[[[1, 5], [2, 8], [3, 2], [6, 4]], 19403/17915904],
[[[1, 5], [2, 8], [3, 2], [8, 2]], 241/53084160],
[[[1, 5], [2, 8], [3, 3], [4, 3]], 23/3732480],
[[[1, 5], [2, 8], [3, 3], [6, 3]], 193/414720],
[[[1, 5], [2, 8], [3, 4], [4, 2]], 1/995328],
[[[1, 5], [2, 8], [3, 4], [6, 2]], 2183/29859840],
[[[1, 5], [2, 8], [3, 5], [6, 1]], 1/373248],
[[[1, 5], [2, 8], [4, 1], [6, 5]], 1/1492992],
[[[1, 5], [2, 8], [4, 2], [6, 4]], 313/23887872],
[[[1, 5], [2, 8], [4, 2], [8, 2]], 201/327680],
[[[1, 5], [2, 8], [4, 3], [6, 3]], 5935/31850496],
[[[1, 5], [2, 8], [4, 4], [5, 1]], 1883/70778880],
[[[1, 5], [2, 8], [4, 4], [6, 2]], 53593/84934656],
[[[1, 5], [2, 8], [4, 4], [8, 1]], 817/983040],
[[[1, 5], [2, 8], [4, 4], [10, 1]], 8729/23592960],
[[[1, 5], [2, 8], [4, 4], [12, 1]], 79/221184],
[[[1, 5], [2, 8], [4, 5], [6, 1]], 7505/14155776],
[[[1, 5], [2, 8], [5, 1], [8, 2]], 7/983040],
[[[1, 5], [2, 8], [6, 2], [8, 2]], 55/1769472],
[[[1, 5], [2, 8], [8, 2], [10, 1]], 11/491520],
[[[1, 5], [2, 10], [3, 1], [4, 4]], 23791/716636160],
[[[1, 5], [2, 10], [3, 1], [6, 4]], 5231/71663616],
[[[1, 5], [2, 10], [3, 1], [8, 2]], 197/119439360],
[[[1, 5], [2, 10], [3, 2], [4, 3]], 2077/212336640],
[[[1, 5], [2, 10], [3, 2], [6, 3]], 5503/17915904],
[[[1, 5], [2, 10], [3, 3], [4, 2]], 449/254803968],
[[[1, 5], [2, 10], [3, 3], [6, 2]], 13/497664],
[[[1, 5], [2, 10], [3, 4], [6, 1]], 1/1492992],
[[[1, 5], [2, 10], [4, 1], [6, 4]], 2045/31850496],
[[[1, 5], [2, 10], [4, 1], [8, 2]], 125/3538944],
[[[1, 5], [2, 10], [4, 2], [6, 3]], 33359/95551488],
[[[1, 5], [2, 10], [4, 3], [5, 1]], 37/2359296],
[[[1, 5], [2, 10], [4, 3], [6, 2]], 29821/35389440],
[[[1, 5], [2, 10], [4, 3], [8, 1]], 61/184320],
[[[1, 5], [2, 10], [4, 3], [10, 1]], 3107/17694720],
[[[1, 5], [2, 10], [4, 3], [12, 1]], 17/245760],
[[[1, 5], [2, 10], [4, 4], [6, 1]], 230293/424673280],
[[[1, 5], [2, 10], [6, 1], [8, 2]], 23/1769472],
[[[1, 5], [2, 10], [6, 3], [10, 1]], 61/4976640],
[[[1, 5], [2, 12], [3, 1], [4, 3]], 3773/424673280],
[[[1, 5], [2, 12], [3, 1], [6, 3]], 124061/955514880],
[[[1, 5], [2, 12], [3, 2], [4, 2]], 547/2038431744],
[[[1, 5], [2, 12], [3, 2], [6, 2]], 41/1866240],
[[[1, 5], [2, 12], [3, 2], [10, 1]], 1/3317760],
[[[1, 5], [2, 12], [3, 3], [6, 1]], 1/11943936],
[[[1, 5], [2, 12], [4, 1], [6, 3]], 661597/1911029760],
[[[1, 5], [2, 12], [4, 2], [5, 1]], 547/566231040],
[[[1, 5], [2, 12], [4, 2], [6, 2]], 203573/318504960],
[[[1, 5], [2, 12], [4, 2], [8, 1]], 1099/35389440],
[[[1, 5], [2, 12], [4, 2], [10, 1]], 1193/17694720],
[[[1, 5], [2, 12], [4, 2], [12, 1]], 133/79626240],
[[[1, 5], [2, 12], [4, 3], [6, 1]], 108023/318504960],
[[[1, 5], [2, 12], [6, 2], [10, 1]], 1379/26542080],
[[[1, 5], [2, 14], [3, 1], [4, 2]], 823/477757440],
[[[1, 5], [2, 14], [3, 1], [6, 2]], 340405/9172942848],
[[[1, 5], [2, 14], [3, 1], [10, 1]], 43/19906560],
[[[1, 5], [2, 14], [3, 2], [4, 1]], 1/79626240],
[[[1, 5], [2, 14], [3, 2], [6, 1]], 2747/5733089280],
[[[1, 5], [2, 14], [4, 1], [6, 2]], 15198851/61152952320],
[[[1, 5], [2, 14], [4, 1], [8, 1]], 43/212336640],
[[[1, 5], [2, 14], [4, 1], [10, 1]], 13403/679477248],
[[[1, 5], [2, 14], [4, 2], [6, 1]], 2401001/15288238080],
[[[1, 5], [2, 14], [6, 1], [10, 1]], 539/21233664],
[[[1, 5], [2, 16], [3, 1], [4, 1]], 707/1274019840],
[[[1, 5], [2, 16], [3, 1], [6, 1]], 217081/73383542784],
[[[1, 5], [2, 16], [4, 1], [6, 1]], 400411/10192158720],
[[[1, 5], [3, 3], [6, 4], [9, 1]], 1/373248],
[[[1, 5], [3, 3], [9, 1], [12, 2]], 1/10368],
[[[1, 5], [3, 4], [5, 1], [6, 4]], 1/829440],
[[[1, 5], [3, 4], [5, 1], [12, 2]], 1/23040],
[[[1, 5], [3, 4], [6, 2], [12, 2]], 1/41472],
[[[1, 5], [3, 4], [6, 2], [24, 1]], 1/6912],
[[[1, 5], [3, 5], [5, 1], [9, 1]], 1/25920],
[[[1, 5], [3, 5], [6, 2], [9, 1]], 1/62208],
[[[1, 5], [3, 5], [9, 1], [12, 1]], 1/10368],
[[[1, 5], [3, 6], [5, 1], [6, 2]], 1/414720],
[[[1, 5], [3, 6], [5, 1], [12, 1]], 1/69120],
[[[1, 5], [3, 6], [6, 2], [12, 1]], 1/248832],
[[[1, 6], [2, 1], [3, 2], [4, 7]], 1/5308416],
[[[1, 6], [2, 1], [3, 4], [4, 5]], 1/1327104],
[[[1, 6], [2, 1], [3, 4], [6, 5]], 1/497664],
[[[1, 6], [2, 1], [3, 5], [6, 4]], 1/995328],
[[[1, 6], [2, 1], [3, 5], [12, 2]], 1/27648],
[[[1, 6], [2, 1], [3, 6], [6, 3]], 5/248832],
[[[1, 6], [2, 1], [3, 6], [9, 1]], 43/331776],
[[[1, 6], [2, 1], [3, 7], [5, 1]], 1/69120],
[[[1, 6], [2, 1], [3, 7], [6, 2]], 1/165888],
[[[1, 6], [2, 1], [3, 7], [12, 1]], 1/27648],
[[[1, 6], [2, 1], [3, 8], [4, 1]], 1/1327104],
[[[1, 6], [2, 1], [3, 8], [6, 1]], 1/55296],
[[[1, 6], [2, 1], [4, 7], [5, 1]], 1/1474560],
[[[1, 6], [2, 3], [3, 1], [4, 7]], 7/1179648],
[[[1, 6], [2, 3], [3, 2], [4, 6]], 71/7077888],
[[[1, 6], [2, 3], [3, 2], [6, 6]], 1/2654208],
[[[1, 6], [2, 3], [3, 3], [4, 5]], 481/15925248],
[[[1, 6], [2, 3], [3, 3], [6, 5]], 19/1327104],
[[[1, 6], [2, 3], [3, 4], [6, 4]], 2347/4423680],
[[[1, 6], [2, 3], [3, 4], [12, 2]], 1/221184],
[[[1, 6], [2, 3], [3, 5], [6, 3]], 941/1990656],
[[[1, 6], [2, 3], [3, 5], [9, 1]], 41/124416],
[[[1, 6], [2, 3], [3, 6], [6, 2]], 4165/7962624],
[[[1, 6], [2, 3], [3, 6], [12, 1]], 1/663552],
[[[1, 6], [2, 3], [3, 7], [4, 1]], 1/110592],
[[[1, 6], [2, 3], [3, 7], [6, 1]], 259/1327104],
[[[1, 6], [2, 3], [4, 2], [8, 3]], 1/6144],
[[[1, 6], [2, 3], [4, 4], [8, 2]], 13/196608],
[[[1, 6], [2, 3], [4, 6], [5, 1]], 1/131072],
[[[1, 6], [2, 3], [4, 6], [8, 1]], 1/147456],
[[[1, 6], [2, 3], [4, 6], [12, 1]], 1/73728],
[[[1, 6], [2, 3], [4, 7], [6, 1]], 1/589824],
[[[1, 6], [2, 5], [3, 1], [4, 6]], 901/7077888],
[[[1, 6], [2, 5], [3, 2], [4, 5]], 2879/28311552],
[[[1, 6], [2, 5], [3, 2], [6, 5]], 263/5971968],
[[[1, 6], [2, 5], [3, 3], [4, 4]], 181/7962624],
[[[1, 6], [2, 5], [3, 3], [6, 4]], 901/1492992],
[[[1, 6], [2, 5], [3, 3], [8, 2]], 1/165888],
[[[1, 6], [2, 5], [3, 4], [4, 3]], 49/7962624],
[[[1, 6], [2, 5], [3, 4], [6, 3]], 797/746496],
[[[1, 6], [2, 5], [3, 4], [9, 1]], 1/27648],
[[[1, 6], [2, 5], [3, 5], [6, 2]], 221/497664],
[[[1, 6], [2, 5], [3, 6], [6, 1]], 19/1990656],
[[[1, 6], [2, 5], [4, 1], [8, 3]], 413/4423680],
[[[1, 6], [2, 5], [4, 3], [8, 2]], 15/8192],
[[[1, 6], [2, 5], [4, 4], [6, 3]], 457/95551488],
[[[1, 6], [2, 5], [4, 5], [5, 1]], 6013/23592960],
[[[1, 6], [2, 5], [4, 5], [6, 2]], 353/10616832],
[[[1, 6], [2, 5], [4, 5], [8, 1]], 347/393216],
[[[1, 6], [2, 5], [4, 5], [10, 1]], 41/2949120],
[[[1, 6], [2, 5], [4, 5], [12, 1]], 11/18432],
[[[1, 6], [2, 5], [4, 6], [6, 1]], 91/3538944],
[[[1, 6], [2, 5], [6, 3], [8, 2]], 1/497664],
[[[1, 6], [2, 7], [3, 1], [4, 5]], 12379/63700992],
[[[1, 6], [2, 7], [3, 1], [6, 5]], 515/13436928],
[[[1, 6], [2, 7], [3, 2], [4, 4]], 280853/1911029760],
[[[1, 6], [2, 7], [3, 2], [6, 4]], 845/1492992],
[[[1, 6], [2, 7], [3, 2], [8, 2]], 767/39813120],
[[[1, 6], [2, 7], [3, 3], [4, 3]], 269/10616832],
[[[1, 6], [2, 7], [3, 3], [6, 3]], 305/248832],
[[[1, 6], [2, 7], [3, 4], [4, 2]], 1/165888],
[[[1, 6], [2, 7], [3, 4], [6, 2]], 1/3456],
[[[1, 6], [2, 7], [3, 5], [6, 1]], 1/62208],
[[[1, 6], [2, 7], [4, 2], [6, 4]], 257/15925248],
[[[1, 6], [2, 7], [4, 2], [8, 2]], 3413/3538944],
[[[1, 6], [2, 7], [4, 3], [6, 3]], 1685/15925248],
[[[1, 6], [2, 7], [4, 4], [5, 1]], 331/3932160],
[[[1, 6], [2, 7], [4, 4], [6, 2]], 164927/509607936],
[[[1, 6], [2, 7], [4, 4], [8, 1]], 7007/2949120],
[[[1, 6], [2, 7], [4, 4], [10, 1]], 22037/47185920],
[[[1, 6], [2, 7], [4, 4], [12, 1]], 305/442368],
[[[1, 6], [2, 7], [4, 5], [6, 1]], 3229/5308416],
[[[1, 6], [2, 7], [5, 1], [8, 2]], 7/245760],
[[[1, 6], [2, 7], [6, 2], [8, 2]], 263/10616832],
[[[1, 6], [2, 7], [8, 2], [10, 1]], 29/983040],
[[[1, 6], [2, 9], [3, 1], [4, 4]], 51329/212336640],
[[[1, 6], [2, 9], [3, 1], [6, 4]], 2089/26873856],
[[[1, 6], [2, 9], [3, 1], [8, 2]], 331/26542080],
[[[1, 6], [2, 9], [3, 2], [4, 3]], 57497/849346560],
[[[1, 6], [2, 9], [3, 2], [6, 3]], 1079/1244160],
[[[1, 6], [2, 9], [3, 3], [4, 2]], 2959/159252480],
[[[1, 6], [2, 9], [3, 3], [6, 2]], 1829/9953280],
[[[1, 6], [2, 9], [3, 3], [8, 1]], 1/995328],
[[[1, 6], [2, 9], [3, 4], [4, 1]], 385/191102976],
[[[1, 6], [2, 9], [3, 4], [6, 1]], 811/47775744],
[[[1, 6], [2, 9], [4, 1], [6, 4]], 323/23887872],
[[[1, 6], [2, 9], [4, 1], [8, 2]], 7669/53084160],
[[[1, 6], [2, 9], [4, 2], [6, 3]], 9605/42467328],
[[[1, 6], [2, 9], [4, 3], [5, 1]], 641/9437184],
[[[1, 6], [2, 9], [4, 3], [6, 2]], 13625/14155776],
[[[1, 6], [2, 9], [4, 3], [8, 1]], 2429/1769472],
[[[1, 6], [2, 9], [4, 3], [10, 1]], 5399/11796480],
[[[1, 6], [2, 9], [4, 3], [12, 1]], 1381/6635520],
[[[1, 6], [2, 9], [4, 4], [6, 1]], 25243/19906560],
[[[1, 6], [2, 9], [6, 1], [8, 2]], 115/2654208],
[[[1, 6], [2, 9], [6, 3], [10, 1]], 7/3317760],
[[[1, 6], [2, 11], [3, 1], [4, 3]], 696107/7644119040],
[[[1, 6], [2, 11], [3, 1], [6, 3]], 141269/859963392],
[[[1, 6], [2, 11], [3, 2], [4, 2]], 78299/5096079360],
[[[1, 6], [2, 11], [3, 2], [6, 2]], 33217/238878720],
[[[1, 6], [2, 11], [3, 2], [8, 1]], 1/7962624],
[[[1, 6], [2, 11], [3, 2], [10, 1]], 13/6635520],
[[[1, 6], [2, 11], [3, 3], [4, 1]], 193/254803968],
[[[1, 6], [2, 11], [3, 3], [6, 1]], 11983/1911029760],
[[[1, 6], [2, 11], [4, 1], [6, 3]], 38705/191102976],
[[[1, 6], [2, 11], [4, 2], [5, 1]], 1261/94371840],
[[[1, 6], [2, 11], [4, 2], [6, 2]], 1173337/1698693120],
[[[1, 6], [2, 11], [4, 2], [8, 1]], 4283/17694720],
[[[1, 6], [2, 11], [4, 2], [10, 1]], 37391/283115520],
[[[1, 6], [2, 11], [4, 2], [12, 1]], 43/3732480],
[[[1, 6], [2, 11], [4, 3], [6, 1]], 22223/26542080],
[[[1, 6], [2, 11], [5, 1], [8, 1]], 1/2211840],
[[[1, 6], [2, 11], [6, 2], [10, 1]], 37/1179648],
[[[1, 6], [2, 13], [3, 1], [4, 2]], 84643/5096079360],
[[[1, 6], [2, 13], [3, 1], [6, 2]], 193747/2149908480],
[[[1, 6], [2, 13], [3, 1], [10, 1]], 3281/477757440],
[[[1, 6], [2, 13], [3, 2], [4, 1]], 20141/61152952320],
[[[1, 6], [2, 13], [3, 2], [6, 1]], 65197/15288238080],
[[[1, 6], [2, 13], [4, 1], [5, 1]], 181/679477248],
[[[1, 6], [2, 13], [4, 1], [6, 2]], 834407/2548039680],
[[[1, 6], [2, 13], [4, 1], [8, 1]], 1079/212336640],
[[[1, 6], [2, 13], [4, 1], [10, 1]], 5279/141557760],
[[[1, 6], [2, 13], [4, 2], [6, 1]], 453533/1274019840],
[[[1, 6], [2, 13], [6, 1], [10, 1]], 457/14155776],
[[[1, 6], [2, 15], [3, 1], [4, 1]], 4769/1274019840],
[[[1, 6], [2, 15], [3, 1], [6, 1]], 13252607/1100753141760],
[[[1, 6], [2, 15], [4, 1], [6, 1]], 744563/7644119040],
[[[1, 7], [2, 2], [3, 1], [4, 7]], 1/1769472],
[[[1, 7], [2, 2], [3, 2], [4, 6]], 31/4718592],
[[[1, 7], [2, 2], [3, 2], [6, 6]], 1/39813120],
[[[1, 7], [2, 2], [3, 3], [4, 5]], 11/2654208],
[[[1, 7], [2, 2], [3, 3], [6, 5]], 1/1327104],
[[[1, 7], [2, 2], [3, 4], [4, 4]], 11/884736],
[[[1, 7], [2, 2], [3, 4], [6, 4]], 379/13271040],
[[[1, 7], [2, 2], [3, 4], [12, 2]], 1/73728],
[[[1, 7], [2, 2], [3, 5], [6, 3]], 3793/29859840],
[[[1, 7], [2, 2], [3, 5], [9, 1]], 13/41472],
[[[1, 7], [2, 2], [3, 6], [5, 1]], 1/23040],
[[[1, 7], [2, 2], [3, 6], [6, 2]], 679/4423680],
[[[1, 7], [2, 2], [3, 6], [12, 1]], 17/221184],
[[[1, 7], [2, 2], [3, 7], [4, 1]], 1/82944],
[[[1, 7], [2, 2], [3, 7], [6, 1]], 643/3981312],
[[[1, 7], [2, 2], [4, 2], [8, 3]], 1/46080],
[[[1, 7], [2, 2], [4, 4], [8, 2]], 1/196608],
[[[1, 7], [2, 2], [4, 6], [5, 1]], 119/11796480],
[[[1, 7], [2, 2], [4, 6], [8, 1]], 1/1105920],
[[[1, 7], [2, 2], [4, 6], [12, 1]], 1/73728],
[[[1, 7], [2, 4], [3, 1], [4, 6]], 259/2654208],
[[[1, 7], [2, 4], [3, 2], [4, 5]], 3203/21233664],
[[[1, 7], [2, 4], [3, 2], [6, 5]], 23/4976640],
[[[1, 7], [2, 4], [3, 3], [4, 4]], 22007/191102976],
[[[1, 7], [2, 4], [3, 3], [6, 4]], 281/1990656],
[[[1, 7], [2, 4], [3, 3], [8, 2]], 1/124416],
[[[1, 7], [2, 4], [3, 4], [4, 3]], 1/663552],
[[[1, 7], [2, 4], [3, 4], [6, 3]], 401/622080],
[[[1, 7], [2, 4], [3, 4], [9, 1]], 11/82944],
[[[1, 7], [2, 4], [3, 5], [4, 2]], 1/17915904],
[[[1, 7], [2, 4], [3, 5], [6, 2]], 13343/13436928],
[[[1, 7], [2, 4], [3, 5], [12, 1]], 1/110592],
[[[1, 7], [2, 4], [3, 6], [4, 1]], 1/36864],
[[[1, 7], [2, 4], [3, 6], [6, 1]], 91/331776],
[[[1, 7], [2, 4], [4, 1], [8, 3]], 43/737280],
[[[1, 7], [2, 4], [4, 3], [8, 2]], 1153/1474560],
[[[1, 7], [2, 4], [4, 4], [6, 3]], 1/89579520],
[[[1, 7], [2, 4], [4, 5], [5, 1]], 229/1966080],
[[[1, 7], [2, 4], [4, 5], [6, 2]], 161/127401984],
[[[1, 7], [2, 4], [4, 5], [8, 1]], 325/1769472],
[[[1, 7], [2, 4], [4, 5], [10, 1]], 113/35389440],
[[[1, 7], [2, 4], [4, 5], [12, 1]], 19/110592],
[[[1, 7], [2, 4], [4, 6], [6, 1]], 3/131072],
[[[1, 7], [2, 4], [6, 3], [8, 2]], 1/7464960],
[[[1, 7], [2, 6], [3, 1], [4, 5]], 3229/5308416],
[[[1, 7], [2, 6], [3, 1], [6, 5]], 1/62208],
[[[1, 7], [2, 6], [3, 2], [4, 4]], 164927/509607936],
[[[1, 7], [2, 6], [3, 2], [6, 4]], 1/3456],
[[[1, 7], [2, 6], [3, 2], [8, 2]], 263/10616832],
[[[1, 7], [2, 6], [3, 3], [4, 3]], 1685/15925248],
[[[1, 7], [2, 6], [3, 3], [6, 3]], 305/248832],
[[[1, 7], [2, 6], [3, 4], [4, 2]], 257/15925248],
[[[1, 7], [2, 6], [3, 4], [6, 2]], 845/1492992],
[[[1, 7], [2, 6], [3, 5], [6, 1]], 515/13436928],
[[[1, 7], [2, 6], [4, 2], [6, 4]], 1/165888],
[[[1, 7], [2, 6], [4, 2], [8, 2]], 3413/3538944],
[[[1, 7], [2, 6], [4, 3], [6, 3]], 269/10616832],
[[[1, 7], [2, 6], [4, 4], [5, 1]], 22037/47185920],
[[[1, 7], [2, 6], [4, 4], [6, 2]], 280853/1911029760],
[[[1, 7], [2, 6], [4, 4], [8, 1]], 7007/2949120],
[[[1, 7], [2, 6], [4, 4], [10, 1]], 331/3932160],
[[[1, 7], [2, 6], [4, 4], [12, 1]], 305/442368],
[[[1, 7], [2, 6], [4, 5], [6, 1]], 12379/63700992],
[[[1, 7], [2, 6], [5, 1], [8, 2]], 29/983040],
[[[1, 7], [2, 6], [6, 2], [8, 2]], 767/39813120],
[[[1, 7], [2, 6], [8, 2], [10, 1]], 7/245760],
[[[1, 7], [2, 8], [3, 1], [4, 4]], 67391/106168320],
[[[1, 7], [2, 8], [3, 1], [6, 4]], 3619/35831808],
[[[1, 7], [2, 8], [3, 1], [8, 2]], 571/13271040],
[[[1, 7], [2, 8], [3, 2], [4, 3]], 72133/212336640],
[[[1, 7], [2, 8], [3, 2], [6, 3]], 1853/1990656],
[[[1, 7], [2, 8], [3, 3], [4, 2]], 8305/127401984],
[[[1, 7], [2, 8], [3, 3], [5, 1]], 1/119439360],
[[[1, 7], [2, 8], [3, 3], [6, 2]], 1735/2985984],
[[[1, 7], [2, 8], [3, 3], [8, 1]], 1/165888],
[[[1, 7], [2, 8], [3, 4], [4, 1]], 97/7962624],
[[[1, 7], [2, 8], [3, 4], [6, 1]], 281/2985984],
[[[1, 7], [2, 8], [4, 1], [6, 4]], 17/1769472],
[[[1, 7], [2, 8], [4, 1], [8, 2]], 3587/13271040],
[[[1, 7], [2, 8], [4, 2], [6, 3]], 17093/95551488],
[[[1, 7], [2, 8], [4, 3], [5, 1]], 671/3932160],
[[[1, 7], [2, 8], [4, 3], [6, 2]], 113765/169869312],
[[[1, 7], [2, 8], [4, 3], [8, 1]], 93797/35389440],
[[[1, 7], [2, 8], [4, 3], [10, 1]], 70207/141557760],
[[[1, 7], [2, 8], [4, 3], [12, 1]], 2747/9953280],
[[[1, 7], [2, 8], [4, 4], [6, 1]], 994999/764411904],
[[[1, 7], [2, 8], [5, 1], [6, 3]], 7/622080],
[[[1, 7], [2, 8], [6, 1], [8, 2]], 4613/79626240],
[[[1, 7], [2, 8], [6, 3], [8, 1]], 1/331776],
[[[1, 7], [2, 8], [6, 3], [10, 1]], 1/4976640],
[[[1, 7], [2, 10], [3, 1], [4, 3]], 43379/106168320],
[[[1, 7], [2, 10], [3, 1], [6, 3]], 707917/2866544640],
[[[1, 7], [2, 10], [3, 2], [4, 2]], 421501/3397386240],
[[[1, 7], [2, 10], [3, 2], [5, 1]], 43/35389440],
[[[1, 7], [2, 10], [3, 2], [6, 2]], 2101/4423680],
[[[1, 7], [2, 10], [3, 2], [8, 1]], 47/9953280],
[[[1, 7], [2, 10], [3, 2], [10, 1]], 1/184320],
[[[1, 7], [2, 10], [3, 3], [4, 1]], 28139/1911029760],
[[[1, 7], [2, 10], [3, 3], [6, 1]], 12259/191102976],
[[[1, 7], [2, 10], [4, 1], [6, 3]], 13105/127401984],
[[[1, 7], [2, 10], [4, 2], [5, 1]], 37547/566231040],
[[[1, 7], [2, 10], [4, 2], [6, 2]], 1951109/2548039680],
[[[1, 7], [2, 10], [4, 2], [8, 1]], 42311/53084160],
[[[1, 7], [2, 10], [4, 2], [10, 1]], 13283/47185920],
[[[1, 7], [2, 10], [4, 2], [12, 1]], 593/17915904],
[[[1, 7], [2, 10], [4, 3], [6, 1]], 615281/424673280],
[[[1, 7], [2, 10], [5, 1], [6, 2]], 31/6635520],
[[[1, 7], [2, 10], [5, 1], [8, 1]], 1/184320],
[[[1, 7], [2, 10], [6, 2], [8, 1]], 17/2654208],
[[[1, 7], [2, 10], [6, 2], [10, 1]], 151/13271040],
[[[1, 7], [2, 10], [8, 1], [10, 1]], 1/737280],
[[[1, 7], [2, 12], [3, 1], [4, 2]], 250313/2548039680],
[[[1, 7], [2, 12], [3, 1], [5, 1]], 259/849346560],
[[[1, 7], [2, 12], [3, 1], [6, 2]], 123569/764411904],
[[[1, 7], [2, 12], [3, 1], [8, 1]], 17/19906560],
[[[1, 7], [2, 12], [3, 1], [10, 1]], 323/26542080],
[[[1, 7], [2, 12], [3, 2], [4, 1]], 38221/5096079360],
[[[1, 7], [2, 12], [3, 2], [6, 1]], 34871/1274019840],
[[[1, 7], [2, 12], [4, 1], [5, 1]], 1237/283115520],
[[[1, 7], [2, 12], [4, 1], [6, 2]], 478033/1698693120],
[[[1, 7], [2, 12], [4, 1], [8, 1]], 829/19906560],
[[[1, 7], [2, 12], [4, 1], [10, 1]], 4709/94371840],
[[[1, 7], [2, 12], [4, 2], [6, 1]], 1447981/2548039680],
[[[1, 7], [2, 12], [5, 1], [6, 1]], 59/106168320],
[[[1, 7], [2, 12], [6, 1], [8, 1]], 1/829440],
[[[1, 7], [2, 12], [6, 1], [10, 1]], 569/21233664],
[[[1, 7], [2, 14], [3, 1], [4, 1]], 38347/2548039680],
[[[1, 7], [2, 14], [3, 1], [6, 1]], 11438927/366917713920],
[[[1, 7], [2, 14], [4, 1], [6, 1]], 8585/56623104],
[[[1, 7], [3, 2], [6, 4], [9, 1]], 1/14929920],
[[[1, 7], [3, 2], [9, 1], [12, 2]], 1/414720],
[[[1, 7], [3, 3], [4, 4], [5, 1]], 1/829440],
[[[1, 7], [3, 4], [5, 1], [9, 1]], 1/25920],
[[[1, 7], [3, 4], [6, 2], [9, 1]], 1/92160],
[[[1, 7], [3, 4], [9, 1], [12, 1]], 1/15360],
[[[1, 7], [3, 5], [5, 1], [6, 2]], 1/207360],
[[[1, 7], [3, 5], [5, 1], [12, 1]], 1/34560],
[[[1, 7], [3, 5], [6, 2], [12, 1]], 1/248832],
[[[1, 8], [2, 1], [3, 1], [4, 7]], 1/5308416],
[[[1, 8], [2, 1], [3, 3], [4, 5]], 1/589824],
[[[1, 8], [2, 1], [3, 3], [6, 5]], 1/19906560],
[[[1, 8], [2, 1], [3, 4], [4, 4]], 7/3981312],
[[[1, 8], [2, 1], [3, 4], [6, 4]], 1/7962624],
[[[1, 8], [2, 1], [3, 4], [12, 2]], 1/221184],
[[[1, 8], [2, 1], [3, 5], [4, 3]], 1/124416],
[[[1, 8], [2, 1], [3, 5], [6, 3]], 121/9953280],
[[[1, 8], [2, 1], [3, 5], [9, 1]], 7/69120],
[[[1, 8], [2, 1], [3, 6], [5, 1]], 1/34560],
[[[1, 8], [2, 1], [3, 6], [6, 2]], 11/1327104],
[[[1, 8], [2, 1], [3, 6], [12, 1]], 11/221184],
[[[1, 8], [2, 1], [3, 7], [4, 1]], 1/331776],
[[[1, 8], [2, 1], [3, 7], [6, 1]], 641/19906560],
[[[1, 8], [2, 3], [3, 1], [4, 6]], 101/7077888],
[[[1, 8], [2, 3], [3, 2], [4, 5]], 799/10616832],
[[[1, 8], [2, 3], [3, 2], [6, 5]], 1/3317760],
[[[1, 8], [2, 3], [3, 3], [4, 4]], 1163/15925248],
[[[1, 8], [2, 3], [3, 3], [6, 4]], 11/995328],
[[[1, 8], [2, 3], [3, 4], [4, 3]], 223/3981312],
[[[1, 8], [2, 3], [3, 4], [6, 3]], 1193/9953280],
[[[1, 8], [2, 3], [3, 4], [9, 1]], 7/62208],
[[[1, 8], [2, 3], [3, 5], [4, 2]], 1/1492992],
[[[1, 8], [2, 3], [3, 5], [6, 2]], 233/559872],
[[[1, 8], [2, 3], [3, 5], [12, 1]], 5/165888],
[[[1, 8], [2, 3], [3, 6], [4, 1]], 5/110592],
[[[1, 8], [2, 3], [3, 6], [6, 1]], 109/331776],
[[[1, 8], [2, 3], [4, 1], [8, 3]], 13/737280],
[[[1, 8], [2, 3], [4, 3], [8, 2]], 203/1474560],
[[[1, 8], [2, 3], [4, 5], [5, 1]], 25/589824],
[[[1, 8], [2, 3], [4, 5], [6, 2]], 1/39813120],
[[[1, 8], [2, 3], [4, 5], [8, 1]], 89/1769472],
[[[1, 8], [2, 3], [4, 5], [12, 1]], 23/552960],
[[[1, 8], [2, 3], [4, 6], [6, 1]], 1/3538944],
[[[1, 8], [2, 5], [3, 1], [4, 5]], 7505/14155776],
[[[1, 8], [2, 5], [3, 1], [6, 5]], 1/373248],
[[[1, 8], [2, 5], [3, 2], [4, 4]], 53593/84934656],
[[[1, 8], [2, 5], [3, 2], [6, 4]], 2183/29859840],
[[[1, 8], [2, 5], [3, 2], [8, 2]], 55/1769472],
[[[1, 8], [2, 5], [3, 3], [4, 3]], 5935/31850496],
[[[1, 8], [2, 5], [3, 3], [6, 3]], 193/414720],
[[[1, 8], [2, 5], [3, 4], [4, 2]], 313/23887872],
[[[1, 8], [2, 5], [3, 4], [6, 2]], 19403/17915904],
[[[1, 8], [2, 5], [3, 5], [4, 1]], 1/1492992],
[[[1, 8], [2, 5], [3, 5], [6, 1]], 541/4478976],
[[[1, 8], [2, 5], [4, 2], [6, 4]], 1/995328],
[[[1, 8], [2, 5], [4, 2], [8, 2]], 201/327680],
[[[1, 8], [2, 5], [4, 3], [6, 3]], 23/3732480],
[[[1, 8], [2, 5], [4, 4], [5, 1]], 8729/23592960],
[[[1, 8], [2, 5], [4, 4], [6, 2]], 5149/424673280],
[[[1, 8], [2, 5], [4, 4], [8, 1]], 817/983040],
[[[1, 8], [2, 5], [4, 4], [10, 1]], 1883/70778880],
[[[1, 8], [2, 5], [4, 4], [12, 1]], 79/221184],
[[[1, 8], [2, 5], [4, 5], [6, 1]], 7127/79626240],
[[[1, 8], [2, 5], [5, 1], [8, 2]], 11/491520],
[[[1, 8], [2, 5], [6, 2], [8, 2]], 241/53084160],
[[[1, 8], [2, 5], [8, 2], [10, 1]], 7/983040],
[[[1, 8], [2, 7], [3, 1], [4, 4]], 994999/764411904],
[[[1, 8], [2, 7], [3, 1], [6, 4]], 281/2985984],
[[[1, 8], [2, 7], [3, 1], [8, 2]], 4613/79626240],
[[[1, 8], [2, 7], [3, 2], [4, 3]], 113765/169869312],
[[[1, 8], [2, 7], [3, 2], [6, 3]], 1735/2985984],
[[[1, 8], [2, 7], [3, 3], [4, 2]], 17093/95551488],
[[[1, 8], [2, 7], [3, 3], [5, 1]], 1/4976640],
[[[1, 8], [2, 7], [3, 3], [6, 2]], 1853/1990656],
[[[1, 8], [2, 7], [3, 3], [8, 1]], 1/331776],
[[[1, 8], [2, 7], [3, 3], [10, 1]], 7/622080],
[[[1, 8], [2, 7], [3, 4], [4, 1]], 17/1769472],
[[[1, 8], [2, 7], [3, 4], [6, 1]], 3619/35831808],
[[[1, 8], [2, 7], [4, 1], [6, 4]], 97/7962624],
[[[1, 8], [2, 7], [4, 1], [8, 2]], 3587/13271040],
[[[1, 8], [2, 7], [4, 2], [6, 3]], 8305/127401984],
[[[1, 8], [2, 7], [4, 3], [5, 1]], 70207/141557760],
[[[1, 8], [2, 7], [4, 3], [6, 2]], 72133/212336640],
[[[1, 8], [2, 7], [4, 3], [8, 1]], 93797/35389440],
[[[1, 8], [2, 7], [4, 3], [10, 1]], 671/3932160],
[[[1, 8], [2, 7], [4, 3], [12, 1]], 2747/9953280],
[[[1, 8], [2, 7], [4, 4], [6, 1]], 67391/106168320],
[[[1, 8], [2, 7], [6, 1], [8, 2]], 571/13271040],
[[[1, 8], [2, 7], [6, 3], [8, 1]], 1/165888],
[[[1, 8], [2, 7], [6, 3], [10, 1]], 1/119439360],
[[[1, 8], [2, 9], [3, 1], [4, 3]], 397447/424673280],
[[[1, 8], [2, 9], [3, 1], [6, 3]], 64541/238878720],
[[[1, 8], [2, 9], [3, 2], [4, 2]], 107377/283115520],
[[[1, 8], [2, 9], [3, 2], [5, 1]], 397/53084160],
[[[1, 8], [2, 9], [3, 2], [6, 2]], 18167/19906560],
[[[1, 8], [2, 9], [3, 2], [8, 1]], 1/36864],
[[[1, 8], [2, 9], [3, 2], [10, 1]], 91/6635520],
[[[1, 8], [2, 9], [3, 3], [4, 1]], 18455/254803968],
[[[1, 8], [2, 9], [3, 3], [6, 1]], 86005/382205952],
[[[1, 8], [2, 9], [4, 1], [6, 3]], 3127/31850496],
[[[1, 8], [2, 9], [4, 2], [5, 1]], 1451/9437184],
[[[1, 8], [2, 9], [4, 2], [6, 2]], 1677/2621440],
[[[1, 8], [2, 9], [4, 2], [8, 1]], 1609/1327104],
[[[1, 8], [2, 9], [4, 2], [10, 1]], 10253/35389440],
[[[1, 8], [2, 9], [4, 2], [12, 1]], 119/2654208],
[[[1, 8], [2, 9], [4, 3], [6, 1]], 957821/637009920],
[[[1, 8], [2, 9], [5, 1], [6, 2]], 31/1105920],
[[[1, 8], [2, 9], [5, 1], [8, 1]], 1/55296],
[[[1, 8], [2, 9], [6, 2], [8, 1]], 1/36864],
[[[1, 8], [2, 9], [6, 2], [10, 1]], 1909/318504960],
[[[1, 8], [2, 9], [8, 1], [10, 1]], 1/92160],
[[[1, 8], [2, 11], [3, 1], [4, 2]], 1709549/5096079360],
[[[1, 8], [2, 11], [3, 1], [5, 1]], 263/70778880],
[[[1, 8], [2, 11], [3, 1], [6, 2]], 132769/477757440],
[[[1, 8], [2, 11], [3, 1], [8, 1]], 49/4976640],
[[[1, 8], [2, 11], [3, 1], [10, 1]], 155/10616832],
[[[1, 8], [2, 11], [3, 2], [4, 1]], 124177/2038431744],
[[[1, 8], [2, 11], [3, 2], [6, 1]], 888679/7644119040],
[[[1, 8], [2, 11], [4, 1], [5, 1]], 14441/566231040],
[[[1, 8], [2, 11], [4, 1], [6, 2]], 212647/849346560],
[[[1, 8], [2, 11], [4, 1], [8, 1]], 3931/26542080],
[[[1, 8], [2, 11], [4, 1], [10, 1]], 2105/28311552],
[[[1, 8], [2, 11], [4, 2], [6, 1]], 219749/254803968],
[[[1, 8], [2, 11], [5, 1], [6, 1]], 121/17694720],
[[[1, 8], [2, 11], [6, 1], [8, 1]], 1/81920],
[[[1, 8], [2, 11], [6, 1], [10, 1]], 44119/2548039680],
[[[1, 8], [2, 13], [3, 1], [4, 1]], 1355623/30576476160],
[[[1, 8], [2, 13], [3, 1], [6, 1]], 7554901/122305904640],
[[[1, 8], [2, 13], [4, 1], [6, 1]], 46243/254803968],
[[[1, 9], [2, 2], [3, 1], [4, 6]], 29/8847360],
[[[1, 9], [2, 2], [3, 2], [4, 5]], 29/7077888],
[[[1, 9], [2, 2], [3, 3], [4, 4]], 97/2654208],
[[[1, 9], [2, 2], [3, 3], [6, 4]], 7/9953280],
[[[1, 9], [2, 2], [3, 4], [4, 3]], 89/1990656],
[[[1, 9], [2, 2], [3, 4], [6, 3]], 77/14929920],
[[[1, 9], [2, 2], [3, 4], [9, 1]], 1/25920],
[[[1, 9], [2, 2], [3, 5], [4, 2]], 43/995328],
[[[1, 9], [2, 2], [3, 5], [6, 2]], 677/9953280],
[[[1, 9], [2, 2], [3, 5], [12, 1]], 1/55296],
[[[1, 9], [2, 2], [3, 6], [4, 1]], 7/331776],
[[[1, 9], [2, 2], [3, 6], [6, 1]], 17893/134369280],
[[[1, 9], [2, 2], [4, 1], [8, 3]], 7/2949120],
[[[1, 9], [2, 2], [4, 3], [8, 2]], 37/5898240],
[[[1, 9], [2, 2], [4, 5], [5, 1]], 1/1966080],
[[[1, 9], [2, 2], [4, 5], [8, 1]], 7/35389440],
[[[1, 9], [2, 2], [4, 5], [12, 1]], 1/442368],
[[[1, 9], [2, 2], [4, 6], [6, 1]], 1/53084160],
[[[1, 9], [2, 4], [3, 1], [4, 5]], 745/5308416],
[[[1, 9], [2, 4], [3, 2], [4, 4]], 195263/509607936],
[[[1, 9], [2, 4], [3, 2], [6, 4]], 89/9953280],
[[[1, 9], [2, 4], [3, 2], [8, 2]], 83/10616832],
[[[1, 9], [2, 4], [3, 3], [4, 3]], 307/884736],
[[[1, 9], [2, 4], [3, 3], [6, 3]], 89/1244160],
[[[1, 9], [2, 4], [3, 4], [4, 2]], 8129/143327232],
[[[1, 9], [2, 4], [3, 4], [5, 1]], 1/1866240],
[[[1, 9], [2, 4], [3, 4], [6, 2]], 20489/53747712],
[[[1, 9], [2, 4], [3, 5], [4, 1]], 1/124416],
[[[1, 9], [2, 4], [3, 5], [6, 1]], 25/186624],
[[[1, 9], [2, 4], [4, 2], [8, 2]], 1519/8847360],
[[[1, 9], [2, 4], [4, 3], [6, 3]], 1/1327104],
[[[1, 9], [2, 4], [4, 4], [5, 1]], 15119/141557760],
[[[1, 9], [2, 4], [4, 4], [6, 2]], 37/21233664],
[[[1, 9], [2, 4], [4, 4], [8, 1]], 563/2949120],
[[[1, 9], [2, 4], [4, 4], [10, 1]], 91/17694720],
[[[1, 9], [2, 4], [4, 4], [12, 1]], 259/3317760],
[[[1, 9], [2, 4], [4, 5], [6, 1]], 197/53084160],
[[[1, 9], [2, 4], [5, 1], [8, 2]], 11/2949120],
[[[1, 9], [2, 4], [6, 2], [8, 2]], 1/2949120],
[[[1, 9], [2, 4], [8, 2], [10, 1]], 1/1474560],
[[[1, 9], [2, 6], [3, 1], [4, 4]], 25243/19906560],
[[[1, 9], [2, 6], [3, 1], [6, 4]], 811/47775744],
[[[1, 9], [2, 6], [3, 1], [8, 2]], 115/2654208],
[[[1, 9], [2, 6], [3, 2], [4, 3]], 13625/14155776],
[[[1, 9], [2, 6], [3, 2], [6, 3]], 1829/9953280],
[[[1, 9], [2, 6], [3, 3], [4, 2]], 9605/42467328],
[[[1, 9], [2, 6], [3, 3], [5, 1]], 7/3317760],
[[[1, 9], [2, 6], [3, 3], [6, 2]], 1079/1244160],
[[[1, 9], [2, 6], [3, 4], [4, 1]], 323/23887872],
[[[1, 9], [2, 6], [3, 4], [6, 1]], 2089/26873856],
[[[1, 9], [2, 6], [4, 1], [6, 4]], 385/191102976],
[[[1, 9], [2, 6], [4, 1], [8, 2]], 7669/53084160],
[[[1, 9], [2, 6], [4, 2], [6, 3]], 2959/159252480],
[[[1, 9], [2, 6], [4, 3], [5, 1]], 5399/11796480],
[[[1, 9], [2, 6], [4, 3], [6, 2]], 57497/849346560],
[[[1, 9], [2, 6], [4, 3], [8, 1]], 2429/1769472],
[[[1, 9], [2, 6], [4, 3], [10, 1]], 641/9437184],
[[[1, 9], [2, 6], [4, 3], [12, 1]], 1381/6635520],
[[[1, 9], [2, 6], [4, 4], [6, 1]], 51329/212336640],
[[[1, 9], [2, 6], [6, 1], [8, 2]], 331/26542080],
[[[1, 9], [2, 6], [6, 3], [8, 1]], 1/995328],
[[[1, 9], [2, 8], [3, 1], [4, 3]], 957821/637009920],
[[[1, 9], [2, 8], [3, 1], [6, 3]], 86005/382205952],
[[[1, 9], [2, 8], [3, 2], [4, 2]], 1677/2621440],
[[[1, 9], [2, 8], [3, 2], [5, 1]], 1909/318504960],
[[[1, 9], [2, 8], [3, 2], [6, 2]], 18167/19906560],
[[[1, 9], [2, 8], [3, 2], [8, 1]], 1/36864],
[[[1, 9], [2, 8], [3, 2], [10, 1]], 31/1105920],
[[[1, 9], [2, 8], [3, 3], [4, 1]], 3127/31850496],
[[[1, 9], [2, 8], [3, 3], [6, 1]], 64541/238878720],
[[[1, 9], [2, 8], [4, 1], [6, 3]], 18455/254803968],
[[[1, 9], [2, 8], [4, 2], [5, 1]], 10253/35389440],
[[[1, 9], [2, 8], [4, 2], [6, 2]], 107377/283115520],
[[[1, 9], [2, 8], [4, 2], [8, 1]], 1609/1327104],
[[[1, 9], [2, 8], [4, 2], [10, 1]], 1451/9437184],
[[[1, 9], [2, 8], [4, 2], [12, 1]], 119/2654208],
[[[1, 9], [2, 8], [4, 3], [6, 1]], 397447/424673280],
[[[1, 9], [2, 8], [5, 1], [6, 2]], 91/6635520],
[[[1, 9], [2, 8], [5, 1], [8, 1]], 1/92160],
[[[1, 9], [2, 8], [6, 2], [8, 1]], 1/36864],
[[[1, 9], [2, 8], [6, 2], [10, 1]], 397/53084160],
[[[1, 9], [2, 8], [8, 1], [10, 1]], 1/55296],
[[[1, 9], [2, 10], [3, 1], [4, 2]], 555011/849346560],
[[[1, 9], [2, 10], [3, 1], [5, 1]], 617/47185920],
[[[1, 9], [2, 10], [3, 1], [6, 2]], 1738129/5096079360],
[[[1, 9], [2, 10], [3, 1], [8, 1]], 169/4976640],
[[[1, 9], [2, 10], [3, 1], [10, 1]], 11/552960],
[[[1, 9], [2, 10], [3, 2], [4, 1]], 11971/62914560],
[[[1, 9], [2, 10], [3, 2], [6, 1]], 353233/1274019840],
[[[1, 9], [2, 10], [4, 1], [5, 1]], 17867/283115520],
[[[1, 9], [2, 10], [4, 1], [6, 2]], 1031389/4076863488],
[[[1, 9], [2, 10], [4, 1], [8, 1]], 81329/318504960],
[[[1, 9], [2, 10], [4, 1], [10, 1]], 54491/679477248],
[[[1, 9], [2, 10], [4, 2], [6, 1]], 191593/212336640],
[[[1, 9], [2, 10], [5, 1], [6, 1]], 2533/106168320],
[[[1, 9], [2, 10], [6, 1], [8, 1]], 59/1658880],
[[[1, 9], [2, 10], [6, 1], [10, 1]], 2611/212336640],
[[[1, 9], [2, 12], [3, 1], [4, 1]], 8051/70778880],
[[[1, 9], [2, 12], [3, 1], [6, 1]], 13800449/122305904640],
[[[1, 9], [2, 12], [4, 1], [6, 1]], 1405081/6115295232],
[[[1, 9], [3, 2], [4, 4], [5, 1]], 1/2211840],
[[[1, 9], [3, 3], [6, 2], [9, 1]], 1/3732480],
[[[1, 9], [3, 3], [9, 1], [12, 1]], 1/622080],
[[[1, 9], [3, 4], [4, 2], [5, 1]], 1/155520],
[[[1, 9], [3, 4], [6, 2], [12, 1]], 1/9953280],
[[[1, 10], [2, 1], [3, 2], [4, 5]], 71/141557760],
[[[1, 10], [2, 1], [3, 3], [4, 4]], 23/15925248],
[[[1, 10], [2, 1], [3, 4], [4, 3]], 13/884736],
[[[1, 10], [2, 1], [3, 4], [6, 3]], 1/3317760],
[[[1, 10], [2, 1], [3, 4], [9, 1]], 7/1244160],
[[[1, 10], [2, 1], [3, 5], [4, 2]], 5/497664],
[[[1, 10], [2, 1], [3, 5], [6, 2]], 1/1658880],
[[[1, 10], [2, 1], [3, 5], [12, 1]], 1/276480],
[[[1, 10], [2, 1], [3, 6], [4, 1]], 19/995328],
[[[1, 10], [2, 1], [3, 6], [6, 1]], 2107/89579520],
[[[1, 10], [2, 1], [4, 1], [8, 3]], 1/8847360],
[[[1, 10], [2, 1], [4, 3], [8, 2]], 1/17694720],
[[[1, 10], [2, 1], [4, 5], [5, 1]], 1/23592960],
[[[1, 10], [2, 1], [4, 5], [8, 1]], 1/106168320],
[[[1, 10], [2, 1], [4, 5], [12, 1]], 1/6635520],
[[[1, 10], [2, 3], [3, 1], [4, 5]], 257/10616832],
[[[1, 10], [2, 3], [3, 2], [4, 4]], 1669/21233664],
[[[1, 10], [2, 3], [3, 3], [4, 3]], 7825/31850496],
[[[1, 10], [2, 3], [3, 3], [6, 3]], 1/414720],
[[[1, 10], [2, 3], [3, 4], [4, 2]], 3007/11943936],
[[[1, 10], [2, 3], [3, 4], [5, 1]], 1/155520],
[[[1, 10], [2, 3], [3, 4], [6, 2]], 389/11197440],
[[[1, 10], [2, 3], [3, 5], [4, 1]], 7/248832],
[[[1, 10], [2, 3], [3, 5], [6, 1]], 17/186624],
[[[1, 10], [2, 3], [4, 2], [8, 2]], 697/35389440],
[[[1, 10], [2, 3], [4, 4], [5, 1]], 1/131072],
[[[1, 10], [2, 3], [4, 4], [6, 2]], 163/1146617856],
[[[1, 10], [2, 3], [4, 4], [8, 1]], 53/2949120],
[[[1, 10], [2, 3], [4, 4], [10, 1]], 163/318504960],
[[[1, 10], [2, 3], [4, 4], [12, 1]], 31/4423680],
[[[1, 10], [2, 3], [4, 5], [6, 1]], 13/53084160],
[[[1, 10], [2, 3], [6, 2], [8, 2]], 1/95551488],
[[[1, 10], [2, 3], [8, 2], [10, 1]], 1/26542080],
[[[1, 10], [2, 5], [3, 1], [4, 4]], 230293/424673280],
[[[1, 10], [2, 5], [3, 1], [6, 4]], 1/1492992],
[[[1, 10], [2, 5], [3, 1], [8, 2]], 23/1769472],
[[[1, 10], [2, 5], [3, 2], [4, 3]], 29821/35389440],
[[[1, 10], [2, 5], [3, 2], [6, 3]], 13/497664],
[[[1, 10], [2, 5], [3, 3], [4, 2]], 33359/95551488],
[[[1, 10], [2, 5], [3, 3], [5, 1]], 61/4976640],
[[[1, 10], [2, 5], [3, 3], [6, 2]], 5503/17915904],
[[[1, 10], [2, 5], [3, 4], [4, 1]], 2045/31850496],
[[[1, 10], [2, 5], [3, 4], [6, 1]], 5231/71663616],
[[[1, 10], [2, 5], [4, 1], [8, 2]], 125/3538944],
[[[1, 10], [2, 5], [4, 2], [6, 3]], 449/254803968],
[[[1, 10], [2, 5], [4, 3], [5, 1]], 3107/17694720],
[[[1, 10], [2, 5], [4, 3], [6, 2]], 2077/212336640],
[[[1, 10], [2, 5], [4, 3], [8, 1]], 61/184320],
[[[1, 10], [2, 5], [4, 3], [10, 1]], 37/2359296],
[[[1, 10], [2, 5], [4, 3], [12, 1]], 17/245760],
[[[1, 10], [2, 5], [4, 4], [6, 1]], 23791/716636160],
[[[1, 10], [2, 5], [6, 1], [8, 2]], 197/119439360],
[[[1, 10], [2, 7], [3, 1], [4, 3]], 615281/424673280],
[[[1, 10], [2, 7], [3, 1], [6, 3]], 12259/191102976],
[[[1, 10], [2, 7], [3, 2], [4, 2]], 1951109/2548039680],
[[[1, 10], [2, 7], [3, 2], [5, 1]], 151/13271040],
[[[1, 10], [2, 7], [3, 2], [6, 2]], 2101/4423680],
[[[1, 10], [2, 7], [3, 2], [8, 1]], 17/2654208],
[[[1, 10], [2, 7], [3, 2], [10, 1]], 31/6635520],
[[[1, 10], [2, 7], [3, 3], [4, 1]], 13105/127401984],
[[[1, 10], [2, 7], [3, 3], [6, 1]], 707917/2866544640],
[[[1, 10], [2, 7], [4, 1], [6, 3]], 28139/1911029760],
[[[1, 10], [2, 7], [4, 2], [5, 1]], 13283/47185920],
[[[1, 10], [2, 7], [4, 2], [6, 2]], 421501/3397386240],
[[[1, 10], [2, 7], [4, 2], [8, 1]], 42311/53084160],
[[[1, 10], [2, 7], [4, 2], [10, 1]], 37547/566231040],
[[[1, 10], [2, 7], [4, 2], [12, 1]], 593/17915904],
[[[1, 10], [2, 7], [4, 3], [6, 1]], 43379/106168320],
[[[1, 10], [2, 7], [5, 1], [6, 2]], 1/184320],
[[[1, 10], [2, 7], [5, 1], [8, 1]], 1/737280],
[[[1, 10], [2, 7], [6, 2], [8, 1]], 47/9953280],
[[[1, 10], [2, 7], [6, 2], [10, 1]], 43/35389440],
[[[1, 10], [2, 7], [8, 1], [10, 1]], 1/184320],
[[[1, 10], [2, 9], [3, 1], [4, 2]], 191593/212336640],
[[[1, 10], [2, 9], [3, 1], [5, 1]], 2611/212336640],
[[[1, 10], [2, 9], [3, 1], [6, 2]], 353233/1274019840],
[[[1, 10], [2, 9], [3, 1], [8, 1]], 59/1658880],
[[[1, 10], [2, 9], [3, 1], [10, 1]], 2533/106168320],
[[[1, 10], [2, 9], [3, 2], [4, 1]], 1031389/4076863488],
[[[1, 10], [2, 9], [3, 2], [6, 1]], 1738129/5096079360],
[[[1, 10], [2, 9], [4, 1], [5, 1]], 54491/679477248],
[[[1, 10], [2, 9], [4, 1], [6, 2]], 11971/62914560],
[[[1, 10], [2, 9], [4, 1], [8, 1]], 81329/318504960],
[[[1, 10], [2, 9], [4, 1], [10, 1]], 17867/283115520],
[[[1, 10], [2, 9], [4, 2], [6, 1]], 555011/849346560],
[[[1, 10], [2, 9], [5, 1], [6, 1]], 11/552960],
[[[1, 10], [2, 9], [6, 1], [8, 1]], 169/4976640],
[[[1, 10], [2, 9], [6, 1], [10, 1]], 617/47185920],
[[[1, 10], [2, 11], [3, 1], [4, 1]], 1096513/5096079360],
[[[1, 10], [2, 11], [3, 1], [6, 1]], 20461231/122305904640],
[[[1, 10], [2, 11], [4, 1], [6, 1]], 133031/509607936],
[[[1, 11], [2, 2], [3, 1], [4, 5]], 13/17694720],
[[[1, 11], [2, 2], [3, 2], [4, 4]], 3073/283115520],
[[[1, 11], [2, 2], [3, 3], [4, 3]], 689/15925248],
[[[1, 11], [2, 2], [3, 4], [4, 2]], 1799/15925248],
[[[1, 11], [2, 2], [3, 4], [5, 1]], 1/51840],
[[[1, 11], [2, 2], [3, 4], [6, 2]], 1/622080],
[[[1, 11], [2, 2], [3, 5], [4, 1]], 35/373248],
[[[1, 11], [2, 2], [3, 5], [6, 1]], 269/7464960],
[[[1, 11], [2, 2], [4, 2], [8, 2]], 29/35389440],
[[[1, 11], [2, 2], [4, 4], [5, 1]], 13/15728640],
[[[1, 11], [2, 2], [4, 4], [8, 1]], 1/884736],
[[[1, 11], [2, 2], [4, 4], [12, 1]], 1/2654208],
[[[1, 11], [2, 4], [3, 1], [4, 4]], 18917/159252480],
[[[1, 11], [2, 4], [3, 1], [8, 2]], 17/13271040],
[[[1, 11], [2, 4], [3, 2], [4, 3]], 30161/70778880],
[[[1, 11], [2, 4], [3, 2], [6, 3]], 1/497664],
[[[1, 11], [2, 4], [3, 3], [4, 2]], 828947/1433272320],
[[[1, 11], [2, 4], [3, 3], [5, 1]], 2047/59719680],
[[[1, 11], [2, 4], [3, 3], [6, 2]], 979/26873856],
[[[1, 11], [2, 4], [3, 4], [4, 1]], 151/884736],
[[[1, 11], [2, 4], [3, 4], [6, 1]], 319/2985984],
[[[1, 11], [2, 4], [4, 1], [8, 2]], 421/106168320],
[[[1, 11], [2, 4], [4, 3], [5, 1]], 443/11796480],
[[[1, 11], [2, 4], [4, 3], [6, 2]], 1187/3057647616],
[[[1, 11], [2, 4], [4, 3], [8, 1]], 2477/70778880],
[[[1, 11], [2, 4], [4, 3], [10, 1]], 1187/849346560],
[[[1, 11], [2, 4], [4, 3], [12, 1]], 77/7962624],
[[[1, 11], [2, 4], [4, 4], [6, 1]], 2851/955514880],
[[[1, 11], [2, 4], [6, 1], [8, 2]], 7/79626240],
[[[1, 11], [2, 6], [3, 1], [4, 3]], 22223/26542080],
[[[1, 11], [2, 6], [3, 1], [6, 3]], 11983/1911029760],
[[[1, 11], [2, 6], [3, 2], [4, 2]], 1173337/1698693120],
[[[1, 11], [2, 6], [3, 2], [5, 1]], 37/1179648],
[[[1, 11], [2, 6], [3, 2], [6, 2]], 33217/238878720],
[[[1, 11], [2, 6], [3, 3], [4, 1]], 38705/191102976],
[[[1, 11], [2, 6], [3, 3], [6, 1]], 141269/859963392],
[[[1, 11], [2, 6], [4, 1], [6, 3]], 193/254803968],
[[[1, 11], [2, 6], [4, 2], [5, 1]], 37391/283115520],
[[[1, 11], [2, 6], [4, 2], [6, 2]], 78299/5096079360],
[[[1, 11], [2, 6], [4, 2], [8, 1]], 4283/17694720],
[[[1, 11], [2, 6], [4, 2], [10, 1]], 1261/94371840],
[[[1, 11], [2, 6], [4, 2], [12, 1]], 43/3732480],
[[[1, 11], [2, 6], [4, 3], [6, 1]], 696107/7644119040],
[[[1, 11], [2, 6], [5, 1], [6, 2]], 13/6635520],
[[[1, 11], [2, 6], [6, 2], [8, 1]], 1/7962624],
[[[1, 11], [2, 6], [8, 1], [10, 1]], 1/2211840],
[[[1, 11], [2, 8], [3, 1], [4, 2]], 219749/254803968],
[[[1, 11], [2, 8], [3, 1], [5, 1]], 44119/2548039680],
[[[1, 11], [2, 8], [3, 1], [6, 2]], 888679/7644119040],
[[[1, 11], [2, 8], [3, 1], [8, 1]], 1/81920],
[[[1, 11], [2, 8], [3, 1], [10, 1]], 121/17694720],
[[[1, 11], [2, 8], [3, 2], [4, 1]], 212647/849346560],
[[[1, 11], [2, 8], [3, 2], [6, 1]], 132769/477757440],
[[[1, 11], [2, 8], [4, 1], [5, 1]], 2105/28311552],
[[[1, 11], [2, 8], [4, 1], [6, 2]], 124177/2038431744],
[[[1, 11], [2, 8], [4, 1], [8, 1]], 3931/26542080],
[[[1, 11], [2, 8], [4, 1], [10, 1]], 14441/566231040],
[[[1, 11], [2, 8], [4, 2], [6, 1]], 1709549/5096079360],
[[[1, 11], [2, 8], [5, 1], [6, 1]], 155/10616832],
[[[1, 11], [2, 8], [6, 1], [8, 1]], 49/4976640],
[[[1, 11], [2, 8], [6, 1], [10, 1]], 263/70778880],
[[[1, 11], [2, 10], [3, 1], [4, 1]], 133031/509607936],
[[[1, 11], [2, 10], [3, 1], [6, 1]], 20461231/122305904640],
[[[1, 11], [2, 10], [4, 1], [6, 1]], 1096513/5096079360],
[[[1, 11], [3, 1], [4, 4], [5, 1]], 1/17694720],
[[[1, 11], [3, 3], [4, 2], [5, 1]], 13/4976640],
[[[1, 12], [2, 1], [3, 1], [4, 5]], 11/212336640],
[[[1, 12], [2, 1], [3, 2], [4, 4]], 133/424673280],
[[[1, 12], [2, 1], [3, 3], [4, 3]], 757/159252480],
[[[1, 12], [2, 1], [3, 4], [4, 2]], 71/7962624],
[[[1, 12], [2, 1], [3, 4], [5, 1]], 1/38880],
[[[1, 12], [2, 1], [3, 5], [4, 1]], 41/1492992],
[[[1, 12], [2, 1], [3, 5], [6, 1]], 79/22394880],
[[[1, 12], [2, 1], [4, 4], [5, 1]], 1/23592960],
[[[1, 12], [2, 3], [3, 1], [4, 4]], 5701/424673280],
[[[1, 12], [2, 3], [3, 2], [4, 3]], 150847/1698693120],
[[[1, 12], [2, 3], [3, 3], [4, 2]], 44821/159252480],
[[[1, 12], [2, 3], [3, 3], [5, 1]], 247/4976640],
[[[1, 12], [2, 3], [3, 3], [6, 2]], 5/5971968],
[[[1, 12], [2, 3], [3, 4], [4, 1]], 3821/15925248],
[[[1, 12], [2, 3], [3, 4], [6, 1]], 653/11943936],
[[[1, 12], [2, 3], [4, 1], [8, 2]], 19/106168320],
[[[1, 12], [2, 3], [4, 3], [5, 1]], 1849/283115520],
[[[1, 12], [2, 3], [4, 3], [8, 1]], 113/70778880],
[[[1, 12], [2, 3], [4, 3], [12, 1]], 19/39813120],
[[[1, 12], [2, 5], [3, 1], [4, 3]], 108023/318504960],
[[[1, 12], [2, 5], [3, 1], [6, 3]], 1/11943936],
[[[1, 12], [2, 5], [3, 2], [4, 2]], 203573/318504960],
[[[1, 12], [2, 5], [3, 2], [5, 1]], 1379/26542080],
[[[1, 12], [2, 5], [3, 2], [6, 2]], 41/1866240],
[[[1, 12], [2, 5], [3, 3], [4, 1]], 661597/1911029760],
[[[1, 12], [2, 5], [3, 3], [6, 1]], 124061/955514880],
[[[1, 12], [2, 5], [4, 2], [5, 1]], 1193/17694720],
[[[1, 12], [2, 5], [4, 2], [6, 2]], 547/2038431744],
[[[1, 12], [2, 5], [4, 2], [8, 1]], 1099/35389440],
[[[1, 12], [2, 5], [4, 2], [10, 1]], 547/566231040],
[[[1, 12], [2, 5], [4, 2], [12, 1]], 133/79626240],
[[[1, 12], [2, 5], [4, 3], [6, 1]], 3773/424673280],
[[[1, 12], [2, 5], [5, 1], [6, 2]], 1/3317760],
[[[1, 12], [2, 7], [3, 1], [4, 2]], 1447981/2548039680],
[[[1, 12], [2, 7], [3, 1], [5, 1]], 569/21233664],
[[[1, 12], [2, 7], [3, 1], [6, 2]], 34871/1274019840],
[[[1, 12], [2, 7], [3, 1], [8, 1]], 1/829440],
[[[1, 12], [2, 7], [3, 1], [10, 1]], 59/106168320],
[[[1, 12], [2, 7], [3, 2], [4, 1]], 478033/1698693120],
[[[1, 12], [2, 7], [3, 2], [6, 1]], 123569/764411904],
[[[1, 12], [2, 7], [4, 1], [5, 1]], 4709/94371840],
[[[1, 12], [2, 7], [4, 1], [6, 2]], 38221/5096079360],
[[[1, 12], [2, 7], [4, 1], [8, 1]], 829/19906560],
[[[1, 12], [2, 7], [4, 1], [10, 1]], 1237/283115520],
[[[1, 12], [2, 7], [4, 2], [6, 1]], 250313/2548039680],
[[[1, 12], [2, 7], [5, 1], [6, 1]], 323/26542080],
[[[1, 12], [2, 7], [6, 1], [8, 1]], 17/19906560],
[[[1, 12], [2, 7], [6, 1], [10, 1]], 259/849346560],
[[[1, 12], [2, 9], [3, 1], [4, 1]], 1405081/6115295232],
[[[1, 12], [2, 9], [3, 1], [6, 1]], 13800449/122305904640],
[[[1, 12], [2, 9], [4, 1], [6, 1]], 8051/70778880],
[[[1, 13], [2, 2], [3, 1], [4, 4]], 19/17694720],
[[[1, 13], [2, 2], [3, 2], [4, 3]], 497/53084160],
[[[1, 13], [2, 2], [3, 3], [4, 2]], 17407/424673280],
[[[1, 13], [2, 2], [3, 3], [5, 1]], 41/1105920],
[[[1, 13], [2, 2], [3, 4], [4, 1]], 2237/23887872],
[[[1, 13], [2, 2], [3, 4], [6, 1]], 427/44789760],
[[[1, 13], [2, 2], [4, 3], [5, 1]], 1/1474560],
[[[1, 13], [2, 4], [3, 1], [4, 3]], 32669/424673280],
[[[1, 13], [2, 4], [3, 2], [4, 2]], 28085023/91729428480],
[[[1, 13], [2, 4], [3, 2], [5, 1]], 8249/159252480],
[[[1, 13], [2, 4], [3, 2], [6, 2]], 943/537477120],
[[[1, 13], [2, 4], [3, 3], [4, 1]], 52327/159252480],
[[[1, 13], [2, 4], [3, 3], [6, 1]], 14333/238878720],
[[[1, 13], [2, 4], [4, 2], [5, 1]], 22135/1019215872],
[[[1, 13], [2, 4], [4, 2], [8, 1]], 143/106168320],
[[[1, 13], [2, 4], [4, 2], [12, 1]], 19/238878720],
[[[1, 13], [2, 4], [4, 3], [6, 1]], 61/318504960],
[[[1, 13], [2, 4], [5, 1], [6, 2]], 1/59719680],
[[[1, 13], [2, 6], [3, 1], [4, 2]], 453533/1274019840],
[[[1, 13], [2, 6], [3, 1], [5, 1]], 457/14155776],
[[[1, 13], [2, 6], [3, 1], [6, 2]], 65197/15288238080],
[[[1, 13], [2, 6], [3, 2], [4, 1]], 834407/2548039680],
[[[1, 13], [2, 6], [3, 2], [6, 1]], 193747/2149908480],
[[[1, 13], [2, 6], [4, 1], [5, 1]], 5279/141557760],
[[[1, 13], [2, 6], [4, 1], [6, 2]], 20141/61152952320],
[[[1, 13], [2, 6], [4, 1], [8, 1]], 1079/212336640],
[[[1, 13], [2, 6], [4, 1], [10, 1]], 181/679477248],
[[[1, 13], [2, 6], [4, 2], [6, 1]], 84643/5096079360],
[[[1, 13], [2, 6], [5, 1], [6, 1]], 3281/477757440],
[[[1, 13], [2, 8], [3, 1], [4, 1]], 46243/254803968],
[[[1, 13], [2, 8], [3, 1], [6, 1]], 7554901/122305904640],
[[[1, 13], [2, 8], [4, 1], [6, 1]], 1355623/30576476160],
[[[1, 13], [3, 2], [4, 2], [5, 1]], 1/2654208],
[[[1, 14], [2, 1], [3, 1], [4, 4]], 31/1274019840],
[[[1, 14], [2, 1], [3, 2], [4, 3]], 1513/2548039680],
[[[1, 14], [2, 1], [3, 3], [4, 2]], 11/4976640],
[[[1, 14], [2, 1], [3, 3], [5, 1]], 43/4976640],
[[[1, 14], [2, 1], [3, 4], [4, 1]], 9149/955514880],
[[[1, 14], [2, 1], [3, 4], [6, 1]], 73/143327232],
[[[1, 14], [2, 1], [4, 3], [5, 1]], 1/28311552],
[[[1, 14], [2, 3], [3, 1], [4, 3]], 24569/2548039680],
[[[1, 14], [2, 3], [3, 2], [4, 2]], 954377/15288238080],
[[[1, 14], [2, 3], [3, 2], [5, 1]], 79/2654208],
[[[1, 14], [2, 3], [3, 2], [6, 2]], 7/143327232],
[[[1, 14], [2, 3], [3, 3], [4, 1]], 57787/424673280],
[[[1, 14], [2, 3], [3, 3], [6, 1]], 24179/1911029760],
[[[1, 14], [2, 3], [4, 2], [5, 1]], 2893/849346560],
[[[1, 14], [2, 3], [4, 3], [6, 1]], 1/106168320],
[[[1, 14], [2, 5], [3, 1], [4, 2]], 2401001/15288238080],
[[[1, 14], [2, 5], [3, 1], [5, 1]], 539/21233664],
[[[1, 14], [2, 5], [3, 1], [6, 2]], 2747/5733089280],
[[[1, 14], [2, 5], [3, 2], [4, 1]], 15198851/61152952320],
[[[1, 14], [2, 5], [3, 2], [6, 1]], 340405/9172942848],
[[[1, 14], [2, 5], [4, 1], [5, 1]], 13403/679477248],
[[[1, 14], [2, 5], [4, 1], [6, 2]], 1/79626240],
[[[1, 14], [2, 5], [4, 1], [8, 1]], 43/212336640],
[[[1, 14], [2, 5], [4, 2], [6, 1]], 823/477757440],
[[[1, 14], [2, 5], [5, 1], [6, 1]], 43/19906560],
[[[1, 14], [2, 7], [3, 1], [4, 1]], 8585/56623104],
[[[1, 14], [2, 7], [3, 1], [6, 1]], 11438927/366917713920],
[[[1, 14], [2, 7], [4, 1], [6, 1]], 38347/2548039680],
[[[1, 15], [2, 2], [3, 1], [4, 3]], 113/159252480],
[[[1, 15], [2, 2], [3, 2], [4, 2]], 55379/10192158720],
[[[1, 15], [2, 2], [3, 2], [5, 1]], 287/35389440],
[[[1, 15], [2, 2], [3, 3], [4, 1]], 8903/382205952],
[[[1, 15], [2, 2], [3, 3], [6, 1]], 10111/8599633920],
[[[1, 15], [2, 2], [4, 2], [5, 1]], 151/566231040],
[[[1, 15], [2, 4], [3, 1], [4, 2]], 871573/22932357120],
[[[1, 15], [2, 4], [3, 1], [5, 1]], 96053/7644119040],
[[[1, 15], [2, 4], [3, 1], [6, 2]], 289/8599633920],
[[[1, 15], [2, 4], [3, 2], [4, 1]], 522857/5096079360],
[[[1, 15], [2, 4], [3, 2], [6, 1]], 33157/3822059520],
[[[1, 15], [2, 4], [4, 1], [5, 1]], 1681/283115520],
[[[1, 15], [2, 4], [4, 2], [6, 1]], 17/159252480],
[[[1, 15], [2, 4], [5, 1], [6, 1]], 13/35389440],
[[[1, 15], [2, 6], [3, 1], [4, 1]], 744563/7644119040],
[[[1, 15], [2, 6], [3, 1], [6, 1]], 13252607/1100753141760],
[[[1, 15], [2, 6], [4, 1], [6, 1]], 4769/1274019840],
[[[1, 15], [3, 1], [4, 2], [5, 1]], 7/318504960],
[[[1, 16], [2, 1], [3, 1], [4, 3]], 13/424673280],
[[[1, 16], [2, 1], [3, 2], [4, 2]], 563/2548039680],
[[[1, 16], [2, 1], [3, 2], [5, 1]], 53/53084160],
[[[1, 16], [2, 1], [3, 3], [4, 1]], 5261/3822059520],
[[[1, 16], [2, 1], [3, 3], [6, 1]], 43/1146617856],
[[[1, 16], [2, 1], [4, 2], [5, 1]], 1/84934656],
[[[1, 16], [2, 3], [3, 1], [4, 2]], 72283/15288238080],
[[[1, 16], [2, 3], [3, 1], [5, 1]], 2291/637009920],
[[[1, 16], [2, 3], [3, 1], [6, 2]], 1/1146617856],
[[[1, 16], [2, 3], [3, 2], [4, 1]], 224117/10192158720],
[[[1, 16], [2, 3], [3, 2], [6, 1]], 8119/7644119040],
[[[1, 16], [2, 3], [4, 1], [5, 1]], 553/566231040],
[[[1, 16], [2, 3], [4, 2], [6, 1]], 11/3822059520],
[[[1, 16], [2, 3], [5, 1], [6, 1]], 1/31850496],
[[[1, 16], [2, 5], [3, 1], [4, 1]], 400411/10192158720],
[[[1, 16], [2, 5], [3, 1], [6, 1]], 217081/73383542784],
[[[1, 16], [2, 5], [4, 1], [6, 1]], 707/1274019840],
[[[1, 17], [2, 2], [3, 1], [4, 2]], 733/2548039680],
[[[1, 17], [2, 2], [3, 1], [5, 1]], 241/424673280],
[[[1, 17], [2, 2], [3, 2], [4, 1]], 35101/15288238080],
[[[1, 17], [2, 2], [3, 2], [6, 1]], 47/764411904],
[[[1, 17], [2, 2], [4, 1], [5, 1]], 23/283115520],
[[[1, 17], [2, 2], [4, 2], [6, 1]], 1/11466178560],
[[[1, 17], [2, 2], [5, 1], [6, 1]], 1/955514880],
[[[1, 17], [2, 4], [3, 1], [4, 1]], 25/2654208],
[[[1, 17], [2, 4], [3, 1], [6, 1]], 2617/6115295232],
[[[1, 17], [2, 4], [4, 1], [6, 1]], 163/3822059520],
[[[1, 18], [2, 1], [3, 1], [4, 2]], 23/2548039680],
[[[1, 18], [2, 1], [3, 1], [5, 1]], 29/637009920],
[[[1, 18], [2, 1], [3, 2], [4, 1]], 5629/61152952320],
[[[1, 18], [2, 1], [3, 2], [6, 1]], 11/9172942848],
[[[1, 18], [2, 1], [4, 1], [5, 1]], 1/377487360],
[[[1, 18], [2, 3], [3, 1], [4, 1]], 6593/5096079360],
[[[1, 18], [2, 3], [3, 1], [6, 1]], 4159/122305904640],
[[[1, 18], [2, 3], [4, 1], [6, 1]], 1/764411904],
[[[1, 19], [2, 2], [3, 1], [4, 1]], 713/7644119040],
[[[1, 19], [2, 2], [3, 1], [6, 1]], 233/183458856960],
[[[1, 20], [2, 1], [3, 1], [4, 1]], 83/30576476160],
[[[1, 20], [2, 1], [3, 1], [6, 1]], 1/73383542784],
[[[2, 3], [3, 2], [6, 6], [18, 1]], 1/186624],
[[[2, 3], [3, 4], [6, 4], [18, 1]], 73/373248],
[[[2, 3], [6, 4], [12, 2], [18, 1]], 1/10368],
[[[2, 3], [6, 6], [10, 1], [18, 1]], 1/103680],
[[[2, 3], [6, 6], [12, 1], [18, 1]], 1/31104],
[[[2, 5], [3, 2], [6, 4], [12, 2]], 1/41472],
[[[2, 5], [3, 2], [6, 4], [24, 1]], 1/6912],
[[[2, 5], [3, 2], [6, 5], [18, 1]], 1/62208],
[[[2, 5], [3, 2], [6, 6], [10, 1]], 1/414720],
[[[2, 5], [3, 2], [6, 6], [12, 1]], 1/248832],
[[[2, 5], [3, 4], [6, 3], [18, 1]], 1/373248],
[[[2, 5], [3, 4], [6, 4], [10, 1]], 1/829440],
[[[2, 5], [6, 3], [12, 2], [18, 1]], 1/10368],
[[[2, 5], [6, 4], [10, 1], [12, 2]], 1/23040],
[[[2, 5], [6, 5], [10, 1], [18, 1]], 1/25920],
[[[2, 5], [6, 5], [12, 1], [18, 1]], 1/10368],
[[[2, 5], [6, 6], [10, 1], [12, 1]], 1/69120],
[[[2, 7], [3, 2], [6, 4], [18, 1]], 1/92160],
[[[2, 7], [3, 2], [6, 5], [10, 1]], 1/207360],
[[[2, 7], [3, 2], [6, 5], [12, 1]], 1/248832],
[[[2, 7], [3, 4], [6, 2], [18, 1]], 1/14929920],
[[[2, 7], [4, 4], [6, 3], [10, 1]], 1/829440],
[[[2, 7], [6, 2], [12, 2], [18, 1]], 1/414720],
[[[2, 7], [6, 4], [10, 1], [18, 1]], 1/25920],
[[[2, 7], [6, 4], [12, 1], [18, 1]], 1/15360],
[[[2, 7], [6, 5], [10, 1], [12, 1]], 1/34560],
[[[2, 9], [3, 2], [6, 3], [18, 1]], 1/3732480],
[[[2, 9], [3, 2], [6, 4], [12, 1]], 1/9953280],
[[[2, 9], [4, 2], [6, 4], [10, 1]], 1/155520],
[[[2, 9], [4, 4], [6, 2], [10, 1]], 1/2211840],
[[[2, 9], [6, 3], [12, 1], [18, 1]], 1/622080],
[[[2, 11], [4, 2], [6, 3], [10, 1]], 13/4976640],
[[[2, 11], [4, 4], [6, 1], [10, 1]], 1/17694720],
[[[2, 13], [4, 2], [6, 2], [10, 1]], 1/2654208],
[[[2, 15], [4, 2], [6, 1], [10, 1]], 7/318504960],
[[[1, 1], [2, 2], [3, 1], [6, 7], [18, 1]], 1/124416],
[[[1, 1], [2, 2], [3, 3], [6, 5], [18, 1]], 1/62208],
[[[1, 1], [2, 2], [3, 5], [6, 3], [18, 1]], 1/13824],
[[[1, 1], [2, 2], [4, 1], [6, 4], [12, 3]], 1/20736],
[[[1, 1], [2, 2], [4, 3], [6, 4], [12, 2]], 1/10368],
[[[1, 1], [2, 4], [3, 1], [6, 5], [12, 2]], 1/9216],
[[[1, 1], [2, 4], [3, 1], [6, 6], [18, 1]], 1/15552],
[[[1, 1], [2, 4], [3, 1], [6, 7], [10, 1]], 1/138240],
[[[1, 1], [2, 4], [3, 1], [6, 7], [12, 1]], 1/27648],
[[[1, 1], [2, 4], [3, 2], [6, 5], [18, 1]], 1/20736],
[[[1, 1], [2, 4], [3, 3], [5, 1], [6, 5]], 1/34560],
[[[1, 1], [2, 4], [3, 3], [6, 3], [12, 2]], 19/124416],
[[[1, 1], [2, 4], [3, 3], [6, 3], [24, 1]], 19/20736],
[[[1, 1], [2, 4], [3, 3], [6, 4], [18, 1]], 1/15552],
[[[1, 1], [2, 4], [3, 3], [6, 5], [10, 1]], 1/69120],
[[[1, 1], [2, 4], [3, 3], [6, 5], [12, 1]], 1/27648],
[[[1, 1], [2, 4], [3, 4], [6, 3], [18, 1]], 1/124416],
[[[1, 1], [2, 4], [3, 5], [6, 3], [10, 1]], 1/138240],
[[[1, 1], [2, 4], [4, 1], [6, 3], [8, 3]], 1/27648],
[[[1, 1], [2, 4], [4, 1], [6, 3], [12, 3]], 1/20736],
[[[1, 1], [2, 4], [4, 1], [6, 6], [18, 1]], 1/165888],
[[[1, 1], [2, 4], [4, 3], [6, 3], [12, 2]], 1/10368],
[[[1, 1], [2, 4], [4, 5], [6, 3], [8, 1]], 1/331776],
[[[1, 1], [2, 4], [6, 3], [12, 2], [18, 1]], 1/3456],
[[[1, 1], [2, 4], [6, 5], [10, 1], [18, 1]], 1/8640],
[[[1, 1], [2, 4], [6, 5], [12, 1], [18, 1]], 1/3456],
[[[1, 1], [2, 6], [3, 1], [4, 4], [6, 4]], 1/995328],
[[[1, 1], [2, 6], [3, 1], [6, 4], [12, 2]], 1/13824],
[[[1, 1], [2, 6], [3, 1], [6, 5], [18, 1]], 1/7776],
[[[1, 1], [2, 6], [3, 1], [6, 6], [10, 1]], 1/23040],
[[[1, 1], [2, 6], [3, 1], [6, 6], [12, 1]], 5/41472],
[[[1, 1], [2, 6], [3, 2], [4, 1], [6, 6]], 1/663552],
[[[1, 1], [2, 6], [3, 2], [6, 4], [18, 1]], 11/165888],
[[[1, 1], [2, 6], [3, 2], [6, 5], [10, 1]], 1/69120],
[[[1, 1], [2, 6], [3, 2], [6, 5], [12, 1]], 1/82944],
[[[1, 1], [2, 6], [3, 3], [4, 1], [6, 5]], 1/6144],
[[[1, 1], [2, 6], [3, 3], [6, 3], [18, 1]], 1/31104],
[[[1, 1], [2, 6], [3, 3], [6, 4], [10, 1]], 1/23040],
[[[1, 1], [2, 6], [3, 3], [6, 4], [12, 1]], 1/41472],
[[[1, 1], [2, 6], [3, 4], [4, 1], [6, 4]], 1/1327104],
[[[1, 1], [2, 6], [3, 4], [6, 2], [18, 1]], 1/995328],
[[[1, 1], [2, 6], [4, 1], [6, 2], [8, 3]], 1/24576],
[[[1, 1], [2, 6], [4, 1], [6, 2], [12, 3]], 1/829440],
[[[1, 1], [2, 6], [4, 1], [6, 4], [12, 2]], 1/36864],
[[[1, 1], [2, 6], [4, 1], [6, 5], [18, 1]], 1/41472],
[[[1, 1], [2, 6], [4, 1], [6, 6], [12, 1]], 1/110592],
[[[1, 1], [2, 6], [4, 1], [8, 3], [10, 1]], 1/61440],
[[[1, 1], [2, 6], [4, 3], [6, 2], [8, 2]], 1/442368],
[[[1, 1], [2, 6], [4, 3], [6, 2], [12, 2]], 1/414720],
[[[1, 1], [2, 6], [4, 3], [8, 2], [10, 1]], 1/122880],
[[[1, 1], [2, 6], [4, 5], [6, 2], [8, 1]], 1/294912],
[[[1, 1], [2, 6], [4, 5], [6, 2], [10, 1]], 1/368640],
[[[1, 1], [2, 6], [4, 5], [6, 2], [12, 1]], 1/165888],
[[[1, 1], [2, 6], [4, 5], [8, 1], [10, 1]], 1/737280],
[[[1, 1], [2, 6], [4, 5], [10, 1], [12, 1]], 1/46080],
[[[1, 1], [2, 6], [6, 2], [12, 2], [18, 1]], 1/27648],
[[[1, 1], [2, 6], [6, 4], [10, 1], [18, 1]], 1/4320],
[[[1, 1], [2, 6], [6, 4], [12, 1], [18, 1]], 11/27648],
[[[1, 1], [2, 6], [6, 5], [10, 1], [12, 1]], 1/11520],
[[[1, 1], [2, 8], [3, 1], [4, 2], [6, 5]], 1/186624],
[[[1, 1], [2, 8], [3, 1], [4, 4], [6, 3]], 1/2654208],
[[[1, 1], [2, 8], [3, 1], [6, 3], [12, 2]], 1/552960],
[[[1, 1], [2, 8], [3, 1], [6, 4], [18, 1]], 1/15360],
[[[1, 1], [2, 8], [3, 1], [6, 5], [10, 1]], 1/17280],
[[[1, 1], [2, 8], [3, 1], [6, 5], [12, 1]], 121/1658880],
[[[1, 1], [2, 8], [3, 2], [4, 1], [6, 5]], 1/331776],
[[[1, 1], [2, 8], [3, 2], [6, 3], [18, 1]], 1/207360],
[[[1, 1], [2, 8], [3, 2], [6, 4], [12, 1]], 1/663552],
[[[1, 1], [2, 8], [3, 3], [6, 2], [18, 1]], 1/1244160],
[[[1, 1], [2, 8], [3, 3], [6, 3], [12, 1]], 1/1658880],
[[[1, 1], [2, 8], [4, 1], [6, 1], [8, 3]], 1/184320],
[[[1, 1], [2, 8], [4, 1], [6, 4], [18, 1]], 1/41472],
[[[1, 1], [2, 8], [4, 1], [6, 5], [12, 1]], 1/55296],
[[[1, 1], [2, 8], [4, 3], [6, 1], [8, 2]], 1/442368],
[[[1, 1], [2, 8], [4, 3], [6, 3], [10, 1]], 1/34560],
[[[1, 1], [2, 8], [4, 4], [6, 2], [10, 1]], 1/368640],
[[[1, 1], [2, 8], [4, 5], [6, 1], [8, 1]], 1/2211840],
[[[1, 1], [2, 8], [4, 5], [6, 1], [10, 1]], 1/1474560],
[[[1, 1], [2, 8], [4, 5], [6, 1], [12, 1]], 1/165888],
[[[1, 1], [2, 8], [6, 3], [12, 1], [18, 1]], 1/34560],
[[[1, 1], [2, 10], [3, 1], [4, 2], [6, 4]], 13/5971968],
[[[1, 1], [2, 10], [3, 1], [4, 4], [6, 2]], 1/21233664],
[[[1, 1], [2, 10], [3, 1], [6, 3], [18, 1]], 1/622080],
[[[1, 1], [2, 10], [3, 1], [6, 4], [12, 1]], 1/552960],
[[[1, 1], [2, 10], [4, 1], [6, 4], [10, 1]], 1/17280],
[[[1, 1], [2, 10], [4, 2], [6, 3], [10, 1]], 7/414720],
[[[1, 1], [2, 10], [4, 3], [6, 2], [10, 1]], 7/737280],
[[[1, 1], [2, 10], [4, 3], [8, 1], [12, 1]], 1/3317760],
[[[1, 1], [2, 10], [4, 4], [6, 1], [10, 1]], 1/1474560],
[[[1, 1], [2, 12], [3, 1], [4, 2], [6, 3]], 5/15925248],
[[[1, 1], [2, 12], [3, 1], [4, 4], [6, 1]], 1/509607936],
[[[1, 1], [2, 12], [4, 1], [6, 3], [10, 1]], 1/46080],
[[[1, 1], [2, 12], [4, 2], [6, 2], [10, 1]], 11/2211840],
[[[1, 1], [2, 12], [4, 3], [6, 1], [10, 1]], 1/983040],
[[[1, 1], [2, 14], [3, 1], [4, 2], [6, 2]], 7/382205952],
[[[1, 1], [2, 14], [4, 1], [6, 2], [10, 1]], 17/5898240],
[[[1, 1], [2, 14], [4, 2], [6, 1], [10, 1]], 1/2211840],
[[[1, 1], [2, 16], [3, 1], [4, 2], [6, 1]], 1/3057647616],
[[[1, 1], [2, 16], [4, 1], [6, 1], [10, 1]], 11/70778880],
[[[1, 2], [2, 1], [3, 3], [6, 5], [9, 1]], 1/13824],
[[[1, 2], [2, 1], [3, 4], [4, 1], [12, 3]], 1/20736],
[[[1, 2], [2, 1], [3, 4], [4, 3], [12, 2]], 1/10368],
[[[1, 2], [2, 1], [3, 5], [6, 3], [9, 1]], 1/62208],
[[[1, 2], [2, 1], [3, 7], [6, 1], [9, 1]], 1/124416],
[[[1, 2], [2, 3], [3, 1], [6, 5], [12, 2]], 1/41472],
[[[1, 2], [2, 3], [3, 1], [6, 5], [24, 1]], 1/6912],
[[[1, 2], [2, 3], [3, 1], [6, 6], [18, 1]], 5/46656],
[[[1, 2], [2, 3], [3, 2], [4, 2], [12, 3]], 1/9216],
[[[1, 2], [2, 3], [3, 2], [4, 4], [12, 2]], 1/4608],
[[[1, 2], [2, 3], [3, 2], [6, 4], [12, 2]], 7/27648],
[[[1, 2], [2, 3], [3, 2], [6, 5], [18, 1]], 1/10368],
[[[1, 2], [2, 3], [3, 2], [6, 6], [10, 1]], 1/276480],
[[[1, 2], [2, 3], [3, 2], [6, 6], [12, 1]], 7/82944],
[[[1, 2], [2, 3], [3, 3], [6, 3], [12, 2]], 1/9216],
[[[1, 2], [2, 3], [3, 3], [6, 4], [9, 1]], 1/10368],
[[[1, 2], [2, 3], [3, 3], [6, 4], [18, 1]], 5/46656],
[[[1, 2], [2, 3], [3, 3], [6, 5], [10, 1]], 1/11520],
[[[1, 2], [2, 3], [3, 3], [6, 5], [12, 1]], 1/27648],
[[[1, 2], [2, 3], [3, 4], [5, 1], [6, 4]], 1/5760],
[[[1, 2], [2, 3], [3, 4], [6, 2], [12, 2]], 5/41472],
[[[1, 2], [2, 3], [3, 4], [6, 2], [24, 1]], 5/6912],
[[[1, 2], [2, 3], [3, 4], [6, 3], [18, 1]], 1/3456],
[[[1, 2], [2, 3], [3, 4], [6, 4], [10, 1]], 1/138240],
[[[1, 2], [2, 3], [3, 4], [6, 4], [12, 1]], 7/82944],
[[[1, 2], [2, 3], [3, 5], [6, 2], [9, 1]], 1/31104],
[[[1, 2], [2, 3], [3, 5], [6, 3], [12, 1]], 1/27648],
[[[1, 2], [2, 3], [3, 6], [6, 2], [10, 1]], 1/276480],
[[[1, 2], [2, 3], [4, 1], [6, 3], [12, 3]], 1/6912],
[[[1, 2], [2, 3], [4, 1], [6, 6], [18, 1]], 1/165888],
[[[1, 2], [2, 3], [4, 2], [6, 2], [8, 3]], 1/18432],
[[[1, 2], [2, 3], [4, 2], [6, 2], [12, 3]], 1/9216],
[[[1, 2], [2, 3], [4, 2], [6, 4], [12, 2]], 1/3456],
[[[1, 2], [2, 3], [4, 2], [8, 3], [10, 1]], 1/5120],
[[[1, 2], [2, 3], [4, 3], [6, 3], [12, 2]], 1/3456],
[[[1, 2], [2, 3], [4, 4], [6, 2], [12, 2]], 1/4608],
[[[1, 2], [2, 3], [4, 6], [6, 2], [8, 1]], 1/442368],
[[[1, 2], [2, 3], [4, 6], [8, 1], [10, 1]], 1/122880],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 7]], 1/221184],
[[[1, 2], [2, 5], [3, 1], [4, 4], [6, 4]], 1/186624],
[[[1, 2], [2, 5], [3, 1], [4, 5], [6, 3]], 1/442368],
[[[1, 2], [2, 5], [3, 1], [4, 6], [6, 2]], 1/1327104],
[[[1, 2], [2, 5], [3, 1], [4, 6], [10, 1]], 1/368640],
[[[1, 2], [2, 5], [3, 1], [4, 7], [6, 1]], 1/1769472],
[[[1, 2], [2, 5], [3, 1], [6, 4], [8, 2]], 1/15552],
[[[1, 2], [2, 5], [3, 1], [6, 4], [12, 2]], 5/20736],
[[[1, 2], [2, 5], [3, 1], [6, 4], [24, 1]], 1/6912],
[[[1, 2], [2, 5], [3, 1], [6, 5], [18, 1]], 1/1944],
[[[1, 2], [2, 5], [3, 1], [6, 6], [10, 1]], 19/207360],
[[[1, 2], [2, 5], [3, 1], [6, 6], [12, 1]], 37/124416],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 6]], 1/663552],
[[[1, 2], [2, 5], [3, 2], [4, 1], [8, 3]], 1/221184],
[[[1, 2], [2, 5], [3, 2], [6, 3], [8, 2]], 1/6912],
[[[1, 2], [2, 5], [3, 2], [6, 3], [12, 2]], 5/82944],
[[[1, 2], [2, 5], [3, 2], [6, 3], [24, 1]], 1/6912],
[[[1, 2], [2, 5], [3, 2], [6, 4], [18, 1]], 65/165888],
[[[1, 2], [2, 5], [3, 2], [6, 5], [10, 1]], 7/69120],
[[[1, 2], [2, 5], [3, 2], [6, 5], [12, 1]], 11/27648],
[[[1, 2], [2, 5], [3, 3], [4, 1], [6, 5]], 1/36864],
[[[1, 2], [2, 5], [3, 3], [6, 3], [9, 1]], 7/207360],
[[[1, 2], [2, 5], [3, 3], [6, 3], [18, 1]], 193/373248],
[[[1, 2], [2, 5], [3, 3], [6, 4], [10, 1]], 19/207360],
[[[1, 2], [2, 5], [3, 3], [6, 4], [12, 1]], 1/6912],
[[[1, 2], [2, 5], [3, 4], [4, 1], [6, 4]], 1361/1327104],
[[[1, 2], [2, 5], [3, 4], [6, 2], [18, 1]], 1/331776],
[[[1, 2], [2, 5], [3, 4], [6, 3], [10, 1]], 7/69120],
[[[1, 2], [2, 5], [3, 4], [6, 3], [12, 1]], 1/82944],
[[[1, 2], [2, 5], [3, 5], [4, 1], [6, 3]], 1/221184],
[[[1, 2], [2, 5], [4, 1], [5, 1], [8, 3]], 1/61440],
[[[1, 2], [2, 5], [4, 1], [6, 2], [8, 3]], 5/36864],
[[[1, 2], [2, 5], [4, 1], [6, 2], [12, 3]], 1/55296],
[[[1, 2], [2, 5], [4, 1], [6, 4], [12, 2]], 1/36864],
[[[1, 2], [2, 5], [4, 1], [6, 5], [18, 1]], 1/10368],
[[[1, 2], [2, 5], [4, 1], [6, 6], [12, 1]], 1/110592],
[[[1, 2], [2, 5], [4, 1], [8, 3], [10, 1]], 1/10240],
[[[1, 2], [2, 5], [4, 2], [6, 1], [8, 3]], 1/4608],
[[[1, 2], [2, 5], [4, 2], [6, 3], [8, 2]], 13/55296],
[[[1, 2], [2, 5], [4, 2], [6, 3], [12, 2]], 1/3456],
[[[1, 2], [2, 5], [4, 3], [6, 2], [8, 2]], 1/73728],
[[[1, 2], [2, 5], [4, 3], [6, 2], [12, 2]], 1/27648],
[[[1, 2], [2, 5], [4, 3], [8, 2], [10, 1]], 1/20480],
[[[1, 2], [2, 5], [4, 4], [6, 3], [8, 1]], 1/27648],
[[[1, 2], [2, 5], [4, 4], [6, 3], [12, 1]], 1/20736],
[[[1, 2], [2, 5], [4, 5], [6, 2], [8, 1]], 5/442368],
[[[1, 2], [2, 5], [4, 5], [8, 1], [10, 1]], 1/122880],
[[[1, 2], [2, 5], [4, 6], [6, 1], [8, 1]], 1/110592],
[[[1, 2], [2, 5], [4, 6], [6, 1], [10, 1]], 11/1474560],
[[[1, 2], [2, 5], [6, 2], [12, 2], [18, 1]], 1/9216],
[[[1, 2], [2, 5], [6, 4], [10, 1], [18, 1]], 1/2880],
[[[1, 2], [2, 5], [6, 4], [12, 1], [18, 1]], 17/27648],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 6]], 1/36864],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 5]], 1/559872],
[[[1, 2], [2, 7], [3, 1], [4, 3], [6, 4]], 1/41472],
[[[1, 2], [2, 7], [3, 1], [4, 4], [6, 3]], 29/3981312],
[[[1, 2], [2, 7], [3, 1], [4, 5], [6, 2]], 1/1769472],
[[[1, 2], [2, 7], [3, 1], [4, 6], [6, 1]], 1/1327104],
[[[1, 2], [2, 7], [3, 1], [6, 3], [8, 2]], 5/82944],
[[[1, 2], [2, 7], [3, 1], [6, 3], [12, 2]], 17/552960],
[[[1, 2], [2, 7], [3, 1], [6, 3], [24, 1]], 1/46080],
[[[1, 2], [2, 7], [3, 1], [6, 4], [18, 1]], 29/69120],
[[[1, 2], [2, 7], [3, 1], [6, 5], [10, 1]], 7/25920],
[[[1, 2], [2, 7], [3, 1], [6, 5], [12, 1]], 377/995328],
[[[1, 2], [2, 7], [3, 2], [4, 1], [6, 5]], 1/82944],
[[[1, 2], [2, 7], [3, 2], [4, 2], [6, 4]], 1/9216],
[[[1, 2], [2, 7], [3, 2], [4, 2], [8, 2]], 1/442368],
[[[1, 2], [2, 7], [3, 2], [6, 2], [8, 2]], 1/55296],
[[[1, 2], [2, 7], [3, 2], [6, 2], [12, 2]], 1/1105920],
[[[1, 2], [2, 7], [3, 2], [6, 3], [18, 1]], 5/41472],
[[[1, 2], [2, 7], [3, 2], [6, 4], [10, 1]], 1/4320],
[[[1, 2], [2, 7], [3, 2], [6, 4], [12, 1]], 1/5760],
[[[1, 2], [2, 7], [3, 3], [4, 1], [6, 4]], 1/36864],
[[[1, 2], [2, 7], [3, 3], [6, 2], [18, 1]], 23/1866240],
[[[1, 2], [2, 7], [3, 3], [6, 3], [12, 1]], 1/110592],
[[[1, 2], [2, 7], [3, 4], [6, 2], [12, 1]], 1/3317760],
[[[1, 2], [2, 7], [4, 1], [6, 1], [8, 3]], 1/18432],
[[[1, 2], [2, 7], [4, 1], [6, 4], [18, 1]], 7/41472],
[[[1, 2], [2, 7], [4, 1], [6, 5], [12, 1]], 1/13824],
[[[1, 2], [2, 7], [4, 2], [5, 1], [8, 2]], 1/122880],
[[[1, 2], [2, 7], [4, 2], [6, 2], [8, 2]], 79/294912],
[[[1, 2], [2, 7], [4, 2], [6, 2], [12, 2]], 1/138240],
[[[1, 2], [2, 7], [4, 2], [8, 2], [10, 1]], 29/245760],
[[[1, 2], [2, 7], [4, 3], [6, 1], [8, 2]], 1/16384],
[[[1, 2], [2, 7], [4, 4], [6, 2], [8, 1]], 11/196608],
[[[1, 2], [2, 7], [4, 4], [6, 2], [10, 1]], 11/245760],
[[[1, 2], [2, 7], [4, 4], [6, 2], [12, 1]], 7/110592],
[[[1, 2], [2, 7], [4, 4], [8, 1], [10, 1]], 7/98304],
[[[1, 2], [2, 7], [4, 4], [8, 1], [12, 1]], 1/34560],
[[[1, 2], [2, 7], [4, 4], [10, 1], [12, 1]], 1/18432],
[[[1, 2], [2, 7], [4, 5], [6, 1], [8, 1]], 1/221184],
[[[1, 2], [2, 7], [4, 5], [6, 1], [10, 1]], 1/245760],
[[[1, 2], [2, 7], [4, 5], [6, 1], [12, 1]], 1/55296],
[[[1, 2], [2, 7], [6, 3], [12, 1], [18, 1]], 1/6912],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 5]], 7/82944],
[[[1, 2], [2, 9], [3, 1], [4, 2], [6, 4]], 37/2239488],
[[[1, 2], [2, 9], [3, 1], [4, 2], [8, 2]], 1/4423680],
[[[1, 2], [2, 9], [3, 1], [4, 3], [6, 3]], 7/884736],
[[[1, 2], [2, 9], [3, 1], [4, 4], [6, 2]], 23/4976640],
[[[1, 2], [2, 9], [3, 1], [4, 4], [12, 1]], 1/1658880],
[[[1, 2], [2, 9], [3, 1], [4, 5], [6, 1]], 1/28311552],
[[[1, 2], [2, 9], [3, 1], [6, 2], [8, 2]], 53/6635520],
[[[1, 2], [2, 9], [3, 1], [6, 3], [18, 1]], 11/373248],
[[[1, 2], [2, 9], [3, 1], [6, 4], [10, 1]], 1/58320],
[[[1, 2], [2, 9], [3, 1], [6, 4], [12, 1]], 77/2488320],
[[[1, 2], [2, 9], [3, 2], [4, 2], [6, 3]], 1/110592],
[[[1, 2], [2, 9], [3, 2], [4, 3], [8, 1]], 1/3538944],
[[[1, 2], [2, 9], [3, 2], [6, 2], [18, 1]], 1/414720],
[[[1, 2], [2, 9], [3, 2], [6, 3], [12, 1]], 7/1658880],
[[[1, 2], [2, 9], [4, 2], [6, 1], [8, 2]], 19/491520],
[[[1, 2], [2, 9], [4, 2], [6, 3], [10, 1]], 43/276480],
[[[1, 2], [2, 9], [4, 3], [5, 1], [8, 1]], 1/983040],
[[[1, 2], [2, 9], [4, 3], [6, 2], [10, 1]], 11/184320],
[[[1, 2], [2, 9], [4, 3], [8, 1], [12, 1]], 7/1105920],
[[[1, 2], [2, 9], [4, 4], [6, 1], [8, 1]], 19/737280],
[[[1, 2], [2, 9], [4, 4], [6, 1], [10, 1]], 1/81920],
[[[1, 2], [2, 9], [4, 4], [6, 1], [12, 1]], 1/61440],
[[[1, 2], [2, 11], [3, 1], [4, 1], [6, 4]], 1/55296],
[[[1, 2], [2, 11], [3, 1], [4, 2], [6, 3]], 1771/358318080],
[[[1, 2], [2, 11], [3, 1], [4, 3], [6, 2]], 1/1179648],
[[[1, 2], [2, 11], [3, 1], [4, 4], [6, 1]], 1813/3822059520],
[[[1, 2], [2, 11], [3, 1], [6, 1], [8, 2]], 29/159252480],
[[[1, 2], [2, 11], [3, 1], [6, 3], [10, 1]], 13/1866240],
[[[1, 2], [2, 11], [3, 2], [4, 2], [6, 2]], 1/884736],
[[[1, 2], [2, 11], [4, 1], [6, 3], [10, 1]], 1/6912],
[[[1, 2], [2, 11], [4, 2], [6, 2], [10, 1]], 31/491520],
[[[1, 2], [2, 11], [4, 3], [6, 1], [10, 1]], 19/1474560],
[[[1, 2], [2, 13], [3, 1], [4, 1], [6, 3]], 17/7077888],
[[[1, 2], [2, 13], [3, 1], [4, 2], [6, 2]], 689/1433272320],
[[[1, 2], [2, 13], [3, 1], [4, 2], [10, 1]], 1/79626240],
[[[1, 2], [2, 13], [3, 1], [4, 3], [6, 1]], 5/169869312],
[[[1, 2], [2, 13], [3, 1], [6, 2], [10, 1]], 1/995328],
[[[1, 2], [2, 13], [4, 1], [6, 2], [10, 1]], 29/737280],
[[[1, 2], [2, 13], [4, 2], [6, 1], [10, 1]], 179/23592960],
[[[1, 2], [2, 15], [3, 1], [4, 1], [6, 2]], 11/84934656],
[[[1, 2], [2, 15], [3, 1], [4, 2], [6, 1]], 353/22932357120],
[[[1, 2], [2, 15], [3, 1], [6, 1], [10, 1]], 7/119439360],
[[[1, 2], [2, 15], [4, 1], [6, 1], [10, 1]], 13/3932160],
[[[1, 2], [2, 17], [3, 1], [4, 1], [6, 1]], 1/452984832],
[[[1, 3], [2, 2], [3, 2], [4, 2], [8, 3]], 1/18432],
[[[1, 3], [2, 2], [3, 2], [4, 2], [12, 3]], 1/9216],
[[[1, 3], [2, 2], [3, 2], [4, 4], [12, 2]], 1/4608],
[[[1, 3], [2, 2], [3, 2], [4, 6], [8, 1]], 1/442368],
[[[1, 3], [2, 2], [3, 2], [5, 1], [6, 6]], 1/276480],
[[[1, 3], [2, 2], [3, 2], [6, 4], [12, 2]], 5/41472],
[[[1, 3], [2, 2], [3, 2], [6, 4], [24, 1]], 5/6912],
[[[1, 3], [2, 2], [3, 2], [6, 5], [18, 1]], 1/31104],
[[[1, 3], [2, 2], [3, 3], [4, 1], [12, 3]], 1/6912],
[[[1, 3], [2, 2], [3, 3], [4, 3], [12, 2]], 1/3456],
[[[1, 3], [2, 2], [3, 3], [6, 3], [12, 2]], 1/9216],
[[[1, 3], [2, 2], [3, 3], [6, 4], [9, 1]], 1/3456],
[[[1, 3], [2, 2], [3, 3], [6, 5], [12, 1]], 1/27648],
[[[1, 3], [2, 2], [3, 4], [4, 2], [12, 2]], 1/3456],
[[[1, 3], [2, 2], [3, 4], [5, 1], [6, 4]], 1/138240],
[[[1, 3], [2, 2], [3, 4], [6, 2], [12, 2]], 7/27648],
[[[1, 3], [2, 2], [3, 4], [6, 3], [9, 1]], 5/46656],
[[[1, 3], [2, 2], [3, 4], [6, 3], [18, 1]], 1/10368],
[[[1, 3], [2, 2], [3, 4], [6, 4], [10, 1]], 1/5760],
[[[1, 3], [2, 2], [3, 4], [6, 4], [12, 1]], 7/82944],
[[[1, 3], [2, 2], [3, 5], [5, 1], [6, 3]], 1/11520],
[[[1, 3], [2, 2], [3, 5], [6, 1], [12, 2]], 1/41472],
[[[1, 3], [2, 2], [3, 5], [6, 1], [24, 1]], 1/6912],
[[[1, 3], [2, 2], [3, 5], [6, 2], [9, 1]], 1/10368],
[[[1, 3], [2, 2], [3, 5], [6, 3], [12, 1]], 1/27648],
[[[1, 3], [2, 2], [3, 6], [4, 1], [9, 1]], 1/165888],
[[[1, 3], [2, 2], [3, 6], [5, 1], [6, 2]], 1/276480],
[[[1, 3], [2, 2], [3, 6], [6, 1], [9, 1]], 5/46656],
[[[1, 3], [2, 2], [3, 6], [6, 2], [12, 1]], 7/82944],
[[[1, 3], [2, 2], [4, 2], [5, 1], [8, 3]], 1/5120],
[[[1, 3], [2, 2], [4, 2], [6, 2], [12, 3]], 1/9216],
[[[1, 3], [2, 2], [4, 4], [6, 2], [12, 2]], 1/4608],
[[[1, 3], [2, 2], [4, 6], [5, 1], [8, 1]], 1/122880],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 7]], 1/221184],
[[[1, 3], [2, 4], [3, 1], [4, 5], [6, 3]], 1/165888],
[[[1, 3], [2, 4], [3, 1], [4, 6], [6, 2]], 11/1769472],
[[[1, 3], [2, 4], [3, 1], [4, 7], [6, 1]], 1/262144],
[[[1, 3], [2, 4], [3, 1], [6, 4], [12, 2]], 1/13824],
[[[1, 3], [2, 4], [3, 1], [6, 4], [24, 1]], 1/2304],
[[[1, 3], [2, 4], [3, 1], [6, 5], [18, 1]], 1/2592],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 6]], 11/73728],
[[[1, 3], [2, 4], [3, 2], [4, 1], [8, 3]], 1/36864],
[[[1, 3], [2, 4], [3, 2], [4, 1], [12, 3]], 1/55296],
[[[1, 3], [2, 4], [3, 2], [4, 3], [8, 2]], 1/73728],
[[[1, 3], [2, 4], [3, 2], [4, 3], [12, 2]], 19/27648],
[[[1, 3], [2, 4], [3, 2], [4, 4], [6, 3]], 7/559872],
[[[1, 3], [2, 4], [3, 2], [4, 5], [6, 2]], 5/497664],
[[[1, 3], [2, 4], [3, 2], [4, 5], [10, 1]], 1/276480],
[[[1, 3], [2, 4], [3, 2], [4, 6], [6, 1]], 1/442368],
[[[1, 3], [2, 4], [3, 2], [5, 1], [6, 5]], 1/69120],
[[[1, 3], [2, 4], [3, 2], [6, 3], [8, 2]], 7/46656],
[[[1, 3], [2, 4], [3, 2], [6, 3], [12, 2]], 41/248832],
[[[1, 3], [2, 4], [3, 2], [6, 3], [24, 1]], 7/20736],
[[[1, 3], [2, 4], [3, 2], [6, 4], [18, 1]], 353/497664],
[[[1, 3], [2, 4], [3, 2], [6, 5], [10, 1]], 1/13824],
[[[1, 3], [2, 4], [3, 2], [6, 5], [12, 1]], 17/27648],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 5]], 7/110592],
[[[1, 3], [2, 4], [3, 3], [6, 2], [8, 2]], 1/20736],
[[[1, 3], [2, 4], [3, 3], [6, 2], [12, 2]], 1/6912],
[[[1, 3], [2, 4], [3, 3], [6, 2], [24, 1]], 1/1152],
[[[1, 3], [2, 4], [3, 3], [6, 3], [9, 1]], 1/4608],
[[[1, 3], [2, 4], [3, 3], [6, 3], [18, 1]], 49/124416],
[[[1, 3], [2, 4], [3, 3], [6, 4], [10, 1]], 1/23040],
[[[1, 3], [2, 4], [3, 3], [6, 4], [12, 1]], 11/13824],
[[[1, 3], [2, 4], [3, 4], [4, 1], [6, 4]], 13/110592],
[[[1, 3], [2, 4], [3, 4], [5, 1], [6, 3]], 1/69120],
[[[1, 3], [2, 4], [3, 4], [6, 2], [9, 1]], 19/93312],
[[[1, 3], [2, 4], [3, 4], [6, 2], [18, 1]], 43/331776],
[[[1, 3], [2, 4], [3, 4], [6, 3], [10, 1]], 1/13824],
[[[1, 3], [2, 4], [3, 4], [6, 3], [12, 1]], 35/82944],
[[[1, 3], [2, 4], [3, 5], [4, 1], [6, 3]], 173/221184],
[[[1, 3], [2, 4], [3, 5], [6, 2], [10, 1]], 1/23040],
[[[1, 3], [2, 4], [3, 6], [4, 1], [6, 2]], 1/221184],
[[[1, 3], [2, 4], [4, 1], [5, 1], [8, 3]], 1/10240],
[[[1, 3], [2, 4], [4, 1], [6, 2], [8, 3]], 1/36864],
[[[1, 3], [2, 4], [4, 1], [6, 2], [12, 3]], 1/18432],
[[[1, 3], [2, 4], [4, 1], [6, 5], [18, 1]], 1/13824],
[[[1, 3], [2, 4], [4, 1], [8, 3], [10, 1]], 1/10240],
[[[1, 3], [2, 4], [4, 2], [6, 1], [8, 3]], 1/3072],
[[[1, 3], [2, 4], [4, 2], [6, 3], [8, 2]], 1/27648],
[[[1, 3], [2, 4], [4, 2], [6, 3], [12, 2]], 1/1152],
[[[1, 3], [2, 4], [4, 3], [5, 1], [8, 2]], 1/20480],
[[[1, 3], [2, 4], [4, 3], [6, 2], [8, 2]], 1/4608],
[[[1, 3], [2, 4], [4, 3], [6, 2], [12, 2]], 7/9216],
[[[1, 3], [2, 4], [4, 3], [8, 2], [10, 1]], 1/1280],
[[[1, 3], [2, 4], [4, 4], [5, 1], [6, 3]], 1/622080],
[[[1, 3], [2, 4], [4, 5], [6, 2], [8, 1]], 25/884736],
[[[1, 3], [2, 4], [4, 5], [6, 2], [12, 1]], 1/27648],
[[[1, 3], [2, 4], [4, 5], [8, 1], [10, 1]], 5/49152],
[[[1, 3], [2, 4], [4, 5], [8, 1], [12, 1]], 1/3072],
[[[1, 3], [2, 4], [4, 5], [10, 1], [12, 1]], 1/7680],
[[[1, 3], [2, 4], [4, 6], [6, 1], [8, 1]], 1/73728],
[[[1, 3], [2, 4], [5, 1], [6, 3], [8, 2]], 1/51840],
[[[1, 3], [2, 4], [6, 2], [12, 2], [18, 1]], 1/27648],
[[[1, 3], [2, 4], [6, 4], [12, 1], [18, 1]], 1/82944],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 6]], 7/82944],
[[[1, 3], [2, 6], [3, 1], [4, 1], [8, 3]], 1/69120],
[[[1, 3], [2, 6], [3, 1], [4, 3], [6, 4]], 17/248832],
[[[1, 3], [2, 6], [3, 1], [4, 3], [8, 2]], 1/49152],
[[[1, 3], [2, 6], [3, 1], [4, 4], [6, 3]], 49/884736],
[[[1, 3], [2, 6], [3, 1], [4, 5], [6, 2]], 25/884736],
[[[1, 3], [2, 6], [3, 1], [4, 5], [10, 1]], 13/368640],
[[[1, 3], [2, 6], [3, 1], [4, 5], [12, 1]], 1/18432],
[[[1, 3], [2, 6], [3, 1], [4, 6], [6, 1]], 151/14155776],
[[[1, 3], [2, 6], [3, 1], [6, 3], [8, 2]], 1/4608],
[[[1, 3], [2, 6], [3, 1], [6, 3], [12, 2]], 11/110592],
[[[1, 3], [2, 6], [3, 1], [6, 3], [24, 1]], 1/9216],
[[[1, 3], [2, 6], [3, 1], [6, 4], [18, 1]], 31/41472],
[[[1, 3], [2, 6], [3, 1], [6, 5], [10, 1]], 1/3456],
[[[1, 3], [2, 6], [3, 1], [6, 5], [12, 1]], 161/331776],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 5]], 25/110592],
[[[1, 3], [2, 6], [3, 2], [4, 2], [6, 4]], 85/746496],
[[[1, 3], [2, 6], [3, 2], [4, 2], [8, 2]], 1/49152],
[[[1, 3], [2, 6], [3, 2], [4, 4], [6, 2]], 5/2985984],
[[[1, 3], [2, 6], [3, 2], [4, 4], [8, 1]], 1/589824],
[[[1, 3], [2, 6], [3, 2], [4, 5], [6, 1]], 1/995328],
[[[1, 3], [2, 6], [3, 2], [5, 1], [6, 4]], 1/13824],
[[[1, 3], [2, 6], [3, 2], [6, 2], [8, 2]], 1/7776],
[[[1, 3], [2, 6], [3, 2], [6, 2], [12, 2]], 109/3317760],
[[[1, 3], [2, 6], [3, 2], [6, 2], [24, 1]], 1/8640],
[[[1, 3], [2, 6], [3, 2], [6, 3], [18, 1]], 49/124416],
[[[1, 3], [2, 6], [3, 2], [6, 4], [8, 1]], 1/5184],
[[[1, 3], [2, 6], [3, 2], [6, 4], [10, 1]], 1/1440],
[[[1, 3], [2, 6], [3, 2], [6, 4], [12, 1]], 35/55296],
[[[1, 3], [2, 6], [3, 3], [4, 1], [6, 4]], 19/82944],
[[[1, 3], [2, 6], [3, 3], [4, 1], [8, 2]], 1/165888],
[[[1, 3], [2, 6], [3, 3], [4, 2], [6, 3]], 1/1536],
[[[1, 3], [2, 6], [3, 3], [6, 1], [8, 2]], 1/165888],
[[[1, 3], [2, 6], [3, 3], [6, 2], [18, 1]], 5/124416],
[[[1, 3], [2, 6], [3, 3], [6, 3], [8, 1]], 1/5184],
[[[1, 3], [2, 6], [3, 3], [6, 3], [10, 1]], 1/2880],
[[[1, 3], [2, 6], [3, 3], [6, 3], [12, 1]], 11/110592],
[[[1, 3], [2, 6], [3, 4], [4, 1], [6, 3]], 1/13824],
[[[1, 3], [2, 6], [3, 4], [6, 2], [12, 1]], 1/221184],
[[[1, 3], [2, 6], [4, 1], [6, 1], [8, 3]], 1/6144],
[[[1, 3], [2, 6], [4, 1], [6, 3], [8, 2]], 1/20736],
[[[1, 3], [2, 6], [4, 1], [6, 4], [18, 1]], 5/13824],
[[[1, 3], [2, 6], [4, 1], [6, 5], [12, 1]], 1/18432],
[[[1, 3], [2, 6], [4, 2], [5, 1], [8, 2]], 3/40960],
[[[1, 3], [2, 6], [4, 2], [6, 2], [8, 2]], 77/73728],
[[[1, 3], [2, 6], [4, 2], [6, 2], [12, 2]], 1/9216],
[[[1, 3], [2, 6], [4, 2], [8, 2], [10, 1]], 43/61440],
[[[1, 3], [2, 6], [4, 3], [6, 1], [8, 2]], 35/36864],
[[[1, 3], [2, 6], [4, 3], [6, 3], [8, 1]], 19/110592],
[[[1, 3], [2, 6], [4, 3], [6, 3], [12, 1]], 1/7776],
[[[1, 3], [2, 6], [4, 4], [5, 1], [6, 2]], 1/1658880],
[[[1, 3], [2, 6], [4, 4], [5, 1], [8, 1]], 1/163840],
[[[1, 3], [2, 6], [4, 4], [6, 2], [8, 1]], 11/73728],
[[[1, 3], [2, 6], [4, 4], [6, 2], [12, 1]], 11/55296],
[[[1, 3], [2, 6], [4, 4], [8, 1], [10, 1]], 3/20480],
[[[1, 3], [2, 6], [4, 4], [8, 1], [12, 1]], 1/4608],
[[[1, 3], [2, 6], [4, 4], [10, 1], [12, 1]], 1/5120],
[[[1, 3], [2, 6], [4, 5], [6, 1], [8, 1]], 53/442368],
[[[1, 3], [2, 6], [4, 5], [6, 1], [10, 1]], 31/294912],
[[[1, 3], [2, 6], [4, 5], [6, 1], [12, 1]], 1/6912],
[[[1, 3], [2, 6], [5, 1], [6, 2], [8, 2]], 1/138240],
[[[1, 3], [2, 6], [6, 3], [12, 1], [18, 1]], 5/20736],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 5]], 169/746496],
[[[1, 3], [2, 8], [3, 1], [4, 2], [6, 4]], 415/2985984],
[[[1, 3], [2, 8], [3, 1], [4, 2], [8, 2]], 37/1474560],
[[[1, 3], [2, 8], [3, 1], [4, 3], [6, 3]], 197/1327104],
[[[1, 3], [2, 8], [3, 1], [4, 4], [6, 2]], 1/32768],
[[[1, 3], [2, 8], [3, 1], [4, 4], [12, 1]], 1/110592],
[[[1, 3], [2, 8], [3, 1], [4, 5], [6, 1]], 997/70778880],
[[[1, 3], [2, 8], [3, 1], [6, 2], [8, 2]], 1/12288],
[[[1, 3], [2, 8], [3, 1], [6, 3], [18, 1]], 1/6480],
[[[1, 3], [2, 8], [3, 1], [6, 4], [12, 1]], 23/165888],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 4]], 431/1658880],
[[[1, 3], [2, 8], [3, 2], [4, 1], [8, 2]], 7/6635520],
[[[1, 3], [2, 8], [3, 2], [4, 2], [6, 3]], 19/497664],
[[[1, 3], [2, 8], [3, 2], [4, 3], [6, 2]], 11/442368],
[[[1, 3], [2, 8], [3, 2], [4, 3], [8, 1]], 7/1769472],
[[[1, 3], [2, 8], [3, 2], [4, 3], [12, 1]], 1/1244160],
[[[1, 3], [2, 8], [3, 2], [4, 4], [6, 1]], 55/47775744],
[[[1, 3], [2, 8], [3, 2], [6, 1], [8, 2]], 1/3981312],
[[[1, 3], [2, 8], [3, 2], [6, 2], [18, 1]], 47/1244160],
[[[1, 3], [2, 8], [3, 2], [6, 3], [8, 1]], 1/20736],
[[[1, 3], [2, 8], [3, 2], [6, 3], [12, 1]], 11/165888],
[[[1, 3], [2, 8], [3, 3], [4, 1], [6, 3]], 1/20736],
[[[1, 3], [2, 8], [3, 3], [4, 2], [6, 2]], 1/331776],
[[[1, 3], [2, 8], [3, 3], [4, 2], [8, 1]], 1/663552],
[[[1, 3], [2, 8], [3, 3], [6, 2], [8, 1]], 1/41472],
[[[1, 3], [2, 8], [3, 3], [6, 2], [12, 1]], 1/552960],
[[[1, 3], [2, 8], [4, 1], [5, 1], [8, 2]], 1/368640],
[[[1, 3], [2, 8], [4, 1], [6, 2], [8, 2]], 83/1769472],
[[[1, 3], [2, 8], [4, 1], [8, 2], [10, 1]], 11/491520],
[[[1, 3], [2, 8], [4, 2], [6, 1], [8, 2]], 613/1474560],
[[[1, 3], [2, 8], [4, 2], [6, 3], [10, 1]], 1/414720],
[[[1, 3], [2, 8], [4, 3], [5, 1], [8, 1]], 7/491520],
[[[1, 3], [2, 8], [4, 3], [6, 2], [8, 1]], 95/393216],
[[[1, 3], [2, 8], [4, 3], [6, 2], [10, 1]], 223/1105920],
[[[1, 3], [2, 8], [4, 3], [6, 2], [12, 1]], 83/663552],
[[[1, 3], [2, 8], [4, 3], [8, 1], [10, 1]], 151/983040],
[[[1, 3], [2, 8], [4, 3], [8, 1], [12, 1]], 23/552960],
[[[1, 3], [2, 8], [4, 3], [10, 1], [12, 1]], 11/184320],
[[[1, 3], [2, 8], [4, 4], [5, 1], [6, 1]], 11/2654208],
[[[1, 3], [2, 8], [4, 4], [6, 1], [8, 1]], 47/294912],
[[[1, 3], [2, 8], [4, 4], [6, 1], [10, 1]], 31/491520],
[[[1, 3], [2, 8], [4, 4], [6, 1], [12, 1]], 13/110592],
[[[1, 3], [2, 8], [5, 1], [6, 1], [8, 2]], 1/1105920],
[[[1, 3], [2, 10], [3, 1], [4, 1], [6, 4]], 53/331776],
[[[1, 3], [2, 10], [3, 1], [4, 1], [8, 2]], 1/4423680],
[[[1, 3], [2, 10], [3, 1], [4, 2], [6, 3]], 2879/47775744],
[[[1, 3], [2, 10], [3, 1], [4, 3], [6, 2]], 1273/26542080],
[[[1, 3], [2, 10], [3, 1], [4, 3], [8, 1]], 13/2211840],
[[[1, 3], [2, 10], [3, 1], [4, 3], [10, 1]], 1/4423680],
[[[1, 3], [2, 10], [3, 1], [4, 3], [12, 1]], 1/1658880],
[[[1, 3], [2, 10], [3, 1], [4, 4], [6, 1]], 1483/283115520],
[[[1, 3], [2, 10], [3, 1], [6, 1], [8, 2]], 11/2949120],
[[[1, 3], [2, 10], [3, 1], [6, 3], [10, 1]], 7/155520],
[[[1, 3], [2, 10], [3, 2], [4, 1], [6, 3]], 1/82944],
[[[1, 3], [2, 10], [3, 2], [4, 2], [6, 2]], 23/1990656],
[[[1, 3], [2, 10], [3, 2], [4, 2], [8, 1]], 1/5308416],
[[[1, 3], [2, 10], [3, 2], [4, 2], [12, 1]], 1/35831808],
[[[1, 3], [2, 10], [3, 2], [4, 3], [6, 1]], 1/442368],
[[[1, 3], [2, 10], [3, 2], [6, 2], [8, 1]], 1/331776],
[[[1, 3], [2, 10], [3, 3], [4, 1], [6, 2]], 1/165888],
[[[1, 3], [2, 10], [3, 3], [4, 2], [6, 1]], 1/2654208],
[[[1, 3], [2, 10], [4, 1], [6, 1], [8, 2]], 17/2211840],
[[[1, 3], [2, 10], [4, 1], [6, 3], [10, 1]], 7/69120],
[[[1, 3], [2, 10], [4, 2], [5, 1], [8, 1]], 1/1474560],
[[[1, 3], [2, 10], [4, 2], [5, 1], [12, 1]], 1/9953280],
[[[1, 3], [2, 10], [4, 2], [6, 2], [10, 1]], 337/1105920],
[[[1, 3], [2, 10], [4, 3], [6, 1], [8, 1]], 161/2949120],
[[[1, 3], [2, 10], [4, 3], [6, 1], [10, 1]], 737/8847360],
[[[1, 3], [2, 10], [4, 3], [6, 1], [12, 1]], 17/829440],
[[[1, 3], [2, 12], [3, 1], [4, 1], [6, 3]], 5429/119439360],
[[[1, 3], [2, 12], [3, 1], [4, 2], [6, 2]], 10183/1274019840],
[[[1, 3], [2, 12], [3, 1], [4, 2], [10, 1]], 1/4423680],
[[[1, 3], [2, 12], [3, 1], [4, 3], [6, 1]], 16367/5096079360],
[[[1, 3], [2, 12], [3, 1], [6, 2], [10, 1]], 11/829440],
[[[1, 3], [2, 12], [3, 2], [4, 1], [6, 2]], 1/1327104],
[[[1, 3], [2, 12], [3, 2], [4, 2], [6, 1]], 1/95551488],
[[[1, 3], [2, 12], [4, 1], [6, 2], [10, 1]], 239/1474560],
[[[1, 3], [2, 12], [4, 2], [6, 1], [10, 1]], 589/8847360],
[[[1, 3], [2, 14], [3, 1], [4, 1], [6, 2]], 8291/1911029760],
[[[1, 3], [2, 14], [3, 1], [4, 1], [10, 1]], 1/10616832],
[[[1, 3], [2, 14], [3, 1], [4, 2], [6, 1]], 10763/30576476160],
[[[1, 3], [2, 14], [3, 1], [6, 1], [10, 1]], 1/829440],
[[[1, 3], [2, 14], [4, 1], [6, 1], [10, 1]], 607/23592960],
[[[1, 3], [2, 16], [3, 1], [4, 1], [6, 1]], 761/5096079360],
[[[1, 3], [3, 2], [5, 1], [6, 4], [9, 1]], 1/103680],
[[[1, 3], [3, 2], [5, 1], [9, 1], [12, 2]], 1/2880],
[[[1, 3], [3, 2], [6, 2], [9, 1], [12, 2]], 1/5184],
[[[1, 3], [3, 2], [6, 2], [9, 1], [24, 1]], 1/864],
[[[1, 3], [3, 4], [5, 1], [6, 2], [9, 1]], 1/51840],
[[[1, 3], [3, 4], [5, 1], [9, 1], [12, 1]], 1/8640],
[[[1, 3], [3, 4], [6, 2], [9, 1], [12, 1]], 1/31104],
[[[1, 4], [2, 1], [3, 3], [4, 1], [8, 3]], 1/27648],
[[[1, 4], [2, 1], [3, 3], [4, 1], [12, 3]], 1/20736],
[[[1, 4], [2, 1], [3, 3], [4, 3], [12, 2]], 1/10368],
[[[1, 4], [2, 1], [3, 3], [4, 5], [8, 1]], 1/331776],
[[[1, 4], [2, 1], [3, 3], [5, 1], [6, 5]], 1/138240],
[[[1, 4], [2, 1], [3, 3], [6, 3], [12, 2]], 19/124416],
[[[1, 4], [2, 1], [3, 3], [6, 3], [24, 1]], 19/20736],
[[[1, 4], [2, 1], [3, 3], [6, 4], [9, 1]], 1/124416],
[[[1, 4], [2, 1], [3, 3], [9, 1], [12, 2]], 1/3456],
[[[1, 4], [2, 1], [3, 4], [6, 3], [9, 1]], 1/15552],
[[[1, 4], [2, 1], [3, 5], [5, 1], [6, 3]], 1/69120],
[[[1, 4], [2, 1], [3, 5], [5, 1], [9, 1]], 1/8640],
[[[1, 4], [2, 1], [3, 5], [6, 1], [12, 2]], 1/9216],
[[[1, 4], [2, 1], [3, 5], [6, 2], [9, 1]], 1/20736],
[[[1, 4], [2, 1], [3, 5], [6, 3], [10, 1]], 1/34560],
[[[1, 4], [2, 1], [3, 5], [6, 3], [12, 1]], 1/27648],
[[[1, 4], [2, 1], [3, 5], [9, 1], [12, 1]], 1/3456],
[[[1, 4], [2, 1], [3, 6], [4, 1], [9, 1]], 1/165888],
[[[1, 4], [2, 1], [3, 6], [6, 1], [9, 1]], 1/15552],
[[[1, 4], [2, 1], [3, 7], [5, 1], [6, 1]], 1/138240],
[[[1, 4], [2, 1], [3, 7], [6, 1], [12, 1]], 1/27648],
[[[1, 4], [2, 3], [3, 1], [4, 2], [8, 3]], 1/3072],
[[[1, 4], [2, 3], [3, 1], [4, 6], [6, 2]], 1/442368],
[[[1, 4], [2, 3], [3, 1], [4, 6], [8, 1]], 1/73728],
[[[1, 4], [2, 3], [3, 1], [4, 7], [6, 1]], 1/262144],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 6]], 1/221184],
[[[1, 4], [2, 3], [3, 2], [4, 1], [8, 3]], 1/36864],
[[[1, 4], [2, 3], [3, 2], [4, 1], [12, 3]], 1/18432],
[[[1, 4], [2, 3], [3, 2], [4, 3], [8, 2]], 1/4608],
[[[1, 4], [2, 3], [3, 2], [4, 3], [12, 2]], 7/9216],
[[[1, 4], [2, 3], [3, 2], [4, 5], [6, 2]], 5/497664],
[[[1, 4], [2, 3], [3, 2], [4, 5], [8, 1]], 25/884736],
[[[1, 4], [2, 3], [3, 2], [4, 5], [12, 1]], 1/27648],
[[[1, 4], [2, 3], [3, 2], [4, 6], [6, 1]], 11/1769472],
[[[1, 4], [2, 3], [3, 2], [5, 1], [6, 5]], 1/23040],
[[[1, 4], [2, 3], [3, 2], [6, 3], [8, 2]], 1/20736],
[[[1, 4], [2, 3], [3, 2], [6, 3], [12, 2]], 1/6912],
[[[1, 4], [2, 3], [3, 2], [6, 3], [24, 1]], 1/1152],
[[[1, 4], [2, 3], [3, 2], [6, 4], [9, 1]], 43/331776],
[[[1, 4], [2, 3], [3, 2], [6, 4], [18, 1]], 19/93312],
[[[1, 4], [2, 3], [3, 2], [9, 1], [12, 2]], 1/27648],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 5]], 173/221184],
[[[1, 4], [2, 3], [3, 3], [4, 2], [8, 2]], 1/27648],
[[[1, 4], [2, 3], [3, 3], [4, 2], [12, 2]], 1/1152],
[[[1, 4], [2, 3], [3, 3], [4, 4], [6, 2]], 7/559872],
[[[1, 4], [2, 3], [3, 3], [4, 4], [10, 1]], 1/622080],
[[[1, 4], [2, 3], [3, 3], [4, 5], [6, 1]], 1/165888],
[[[1, 4], [2, 3], [3, 3], [5, 1], [6, 4]], 1/13824],
[[[1, 4], [2, 3], [3, 3], [6, 2], [8, 2]], 7/46656],
[[[1, 4], [2, 3], [3, 3], [6, 2], [12, 2]], 41/248832],
[[[1, 4], [2, 3], [3, 3], [6, 2], [24, 1]], 7/20736],
[[[1, 4], [2, 3], [3, 3], [6, 3], [9, 1]], 49/124416],
[[[1, 4], [2, 3], [3, 3], [6, 3], [18, 1]], 1/4608],
[[[1, 4], [2, 3], [3, 3], [6, 4], [10, 1]], 1/69120],
[[[1, 4], [2, 3], [3, 3], [6, 4], [12, 1]], 35/82944],
[[[1, 4], [2, 3], [3, 3], [8, 2], [10, 1]], 1/51840],
[[[1, 4], [2, 3], [3, 4], [4, 1], [6, 4]], 13/110592],
[[[1, 4], [2, 3], [3, 4], [5, 1], [6, 3]], 1/23040],
[[[1, 4], [2, 3], [3, 4], [6, 1], [12, 2]], 1/13824],
[[[1, 4], [2, 3], [3, 4], [6, 1], [24, 1]], 1/2304],
[[[1, 4], [2, 3], [3, 4], [6, 2], [9, 1]], 353/497664],
[[[1, 4], [2, 3], [3, 4], [6, 3], [12, 1]], 11/13824],
[[[1, 4], [2, 3], [3, 4], [9, 1], [12, 1]], 1/82944],
[[[1, 4], [2, 3], [3, 5], [4, 1], [6, 3]], 7/110592],
[[[1, 4], [2, 3], [3, 5], [4, 1], [9, 1]], 1/13824],
[[[1, 4], [2, 3], [3, 5], [5, 1], [6, 2]], 1/13824],
[[[1, 4], [2, 3], [3, 5], [6, 1], [9, 1]], 1/2592],
[[[1, 4], [2, 3], [3, 5], [6, 2], [10, 1]], 1/69120],
[[[1, 4], [2, 3], [3, 5], [6, 2], [12, 1]], 17/27648],
[[[1, 4], [2, 3], [3, 6], [4, 1], [6, 2]], 11/73728],
[[[1, 4], [2, 3], [3, 7], [4, 1], [6, 1]], 1/221184],
[[[1, 4], [2, 3], [4, 1], [5, 1], [8, 3]], 1/10240],
[[[1, 4], [2, 3], [4, 1], [6, 2], [8, 3]], 1/36864],
[[[1, 4], [2, 3], [4, 1], [6, 2], [12, 3]], 1/55296],
[[[1, 4], [2, 3], [4, 1], [8, 3], [10, 1]], 1/10240],
[[[1, 4], [2, 3], [4, 3], [5, 1], [8, 2]], 1/1280],
[[[1, 4], [2, 3], [4, 3], [6, 2], [8, 2]], 1/73728],
[[[1, 4], [2, 3], [4, 3], [6, 2], [12, 2]], 19/27648],
[[[1, 4], [2, 3], [4, 3], [8, 2], [10, 1]], 1/20480],
[[[1, 4], [2, 3], [4, 5], [5, 1], [6, 2]], 1/276480],
[[[1, 4], [2, 3], [4, 5], [5, 1], [8, 1]], 5/49152],
[[[1, 4], [2, 3], [4, 5], [5, 1], [12, 1]], 1/7680],
[[[1, 4], [2, 3], [4, 5], [8, 1], [12, 1]], 1/3072],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 6]], 19/331776],
[[[1, 4], [2, 5], [3, 1], [4, 1], [8, 3]], 11/110592],
[[[1, 4], [2, 5], [3, 1], [4, 3], [8, 2]], 13/49152],
[[[1, 4], [2, 5], [3, 1], [4, 4], [6, 3]], 119/1492992],
[[[1, 4], [2, 5], [3, 1], [4, 5], [6, 2]], 593/5308416],
[[[1, 4], [2, 5], [3, 1], [4, 5], [10, 1]], 1/184320],
[[[1, 4], [2, 5], [3, 1], [4, 5], [12, 1]], 1/18432],
[[[1, 4], [2, 5], [3, 1], [4, 6], [6, 1]], 1063/14155776],
[[[1, 4], [2, 5], [3, 1], [6, 3], [8, 2]], 35/497664],
[[[1, 4], [2, 5], [3, 1], [6, 3], [12, 2]], 19/331776],
[[[1, 4], [2, 5], [3, 1], [6, 3], [24, 1]], 5/27648],
[[[1, 4], [2, 5], [3, 1], [6, 4], [18, 1]], 1/4608],
[[[1, 4], [2, 5], [3, 1], [6, 5], [12, 1]], 1/110592],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 5]], 1/1728],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 4]], 1/3072],
[[[1, 4], [2, 5], [3, 2], [4, 2], [8, 2]], 1/12288],
[[[1, 4], [2, 5], [3, 2], [4, 2], [12, 2]], 1/9216],
[[[1, 4], [2, 5], [3, 2], [4, 3], [6, 3]], 121/746496],
[[[1, 4], [2, 5], [3, 2], [4, 4], [6, 2]], 1/6912],
[[[1, 4], [2, 5], [3, 2], [4, 4], [8, 1]], 1/73728],
[[[1, 4], [2, 5], [3, 2], [4, 4], [10, 1]], 5/110592],
[[[1, 4], [2, 5], [3, 2], [4, 4], [12, 1]], 1/13824],
[[[1, 4], [2, 5], [3, 2], [4, 5], [6, 1]], 133/3981312],
[[[1, 4], [2, 5], [3, 2], [5, 1], [6, 4]], 1/11520],
[[[1, 4], [2, 5], [3, 2], [6, 2], [8, 2]], 71/165888],
[[[1, 4], [2, 5], [3, 2], [6, 2], [12, 2]], 7/55296],
[[[1, 4], [2, 5], [3, 2], [6, 2], [24, 1]], 1/2304],
[[[1, 4], [2, 5], [3, 2], [6, 3], [9, 1]], 11/82944],
[[[1, 4], [2, 5], [3, 2], [6, 3], [18, 1]], 161/746496],
[[[1, 4], [2, 5], [3, 2], [6, 4], [10, 1]], 5/10368],
[[[1, 4], [2, 5], [3, 2], [6, 4], [12, 1]], 7/18432],
[[[1, 4], [2, 5], [3, 2], [8, 2], [10, 1]], 1/46080],
[[[1, 4], [2, 5], [3, 3], [4, 1], [6, 4]], 155/331776],
[[[1, 4], [2, 5], [3, 3], [4, 1], [8, 2]], 1/27648],
[[[1, 4], [2, 5], [3, 3], [4, 2], [6, 3]], 1/1536],
[[[1, 4], [2, 5], [3, 3], [4, 3], [8, 1]], 1/110592],
[[[1, 4], [2, 5], [3, 3], [4, 4], [6, 1]], 1/2239488],
[[[1, 4], [2, 5], [3, 3], [5, 1], [6, 3]], 1/2160],
[[[1, 4], [2, 5], [3, 3], [6, 1], [8, 2]], 31/746496],
[[[1, 4], [2, 5], [3, 3], [6, 1], [12, 2]], 23/2488320],
[[[1, 4], [2, 5], [3, 3], [6, 1], [24, 1]], 23/414720],
[[[1, 4], [2, 5], [3, 3], [6, 2], [9, 1]], 1/31104],
[[[1, 4], [2, 5], [3, 3], [6, 2], [18, 1]], 17/41472],
[[[1, 4], [2, 5], [3, 3], [6, 3], [8, 1]], 1/15552],
[[[1, 4], [2, 5], [3, 3], [6, 3], [10, 1]], 1/2160],
[[[1, 4], [2, 5], [3, 3], [6, 3], [12, 1]], 107/331776],
[[[1, 4], [2, 5], [3, 4], [4, 1], [6, 3]], 7/6912],
[[[1, 4], [2, 5], [3, 4], [4, 2], [6, 2]], 1/3072],
[[[1, 4], [2, 5], [3, 4], [6, 1], [9, 1]], 1/248832],
[[[1, 4], [2, 5], [3, 4], [6, 2], [8, 1]], 1/15552],
[[[1, 4], [2, 5], [3, 4], [6, 2], [10, 1]], 1/7680],
[[[1, 4], [2, 5], [3, 4], [6, 2], [12, 1]], 1/55296],
[[[1, 4], [2, 5], [3, 5], [4, 1], [6, 2]], 1/13824],
[[[1, 4], [2, 5], [4, 1], [6, 1], [8, 3]], 1/6144],
[[[1, 4], [2, 5], [4, 1], [6, 3], [8, 2]], 5/165888],
[[[1, 4], [2, 5], [4, 1], [6, 4], [18, 1]], 1/4608],
[[[1, 4], [2, 5], [4, 2], [5, 1], [8, 2]], 1/5120],
[[[1, 4], [2, 5], [4, 2], [6, 2], [8, 2]], 397/884736],
[[[1, 4], [2, 5], [4, 2], [6, 2], [12, 2]], 1/3072],
[[[1, 4], [2, 5], [4, 2], [6, 4], [8, 1]], 1/82944],
[[[1, 4], [2, 5], [4, 2], [8, 2], [10, 1]], 181/245760],
[[[1, 4], [2, 5], [4, 3], [5, 1], [6, 3]], 1/51840],
[[[1, 4], [2, 5], [4, 3], [6, 1], [8, 2]], 7/4608],
[[[1, 4], [2, 5], [4, 3], [6, 3], [8, 1]], 1/27648],
[[[1, 4], [2, 5], [4, 3], [6, 3], [12, 1]], 1/31104],
[[[1, 4], [2, 5], [4, 4], [5, 1], [6, 2]], 1/276480],
[[[1, 4], [2, 5], [4, 4], [5, 1], [8, 1]], 1/20480],
[[[1, 4], [2, 5], [4, 4], [6, 2], [8, 1]], 47/294912],
[[[1, 4], [2, 5], [4, 4], [6, 2], [12, 1]], 55/331776],
[[[1, 4], [2, 5], [4, 4], [8, 1], [10, 1]], 47/81920],
[[[1, 4], [2, 5], [4, 4], [8, 1], [12, 1]], 1/2304],
[[[1, 4], [2, 5], [4, 4], [10, 1], [12, 1]], 31/92160],
[[[1, 4], [2, 5], [4, 5], [5, 1], [6, 1]], 1/276480],
[[[1, 4], [2, 5], [4, 5], [6, 1], [8, 1]], 37/221184],
[[[1, 4], [2, 5], [4, 5], [6, 1], [12, 1]], 1/4608],
[[[1, 4], [2, 5], [5, 1], [6, 2], [8, 2]], 1/23040],
[[[1, 4], [2, 5], [6, 3], [12, 1], [18, 1]], 1/13824],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 5]], 29/82944],
[[[1, 4], [2, 7], [3, 1], [4, 2], [6, 4]], 1/4608],
[[[1, 4], [2, 7], [3, 1], [4, 2], [8, 2]], 931/4423680],
[[[1, 4], [2, 7], [3, 1], [4, 3], [6, 3]], 1801/3981312],
[[[1, 4], [2, 7], [3, 1], [4, 4], [6, 2]], 1259/3981312],
[[[1, 4], [2, 7], [3, 1], [4, 4], [8, 1]], 17/98304],
[[[1, 4], [2, 7], [3, 1], [4, 4], [10, 1]], 17/163840],
[[[1, 4], [2, 7], [3, 1], [4, 4], [12, 1]], 1/12288],
[[[1, 4], [2, 7], [3, 1], [4, 5], [6, 1]], 461/5308416],
[[[1, 4], [2, 7], [3, 1], [6, 2], [8, 2]], 365/1327104],
[[[1, 4], [2, 7], [3, 1], [6, 3], [18, 1]], 1/3456],
[[[1, 4], [2, 7], [3, 1], [6, 4], [12, 1]], 11/55296],
[[[1, 4], [2, 7], [3, 1], [8, 2], [10, 1]], 1/122880],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 4]], 943/995328],
[[[1, 4], [2, 7], [3, 2], [4, 1], [8, 2]], 997/26542080],
[[[1, 4], [2, 7], [3, 2], [4, 2], [6, 3]], 67/331776],
[[[1, 4], [2, 7], [3, 2], [4, 3], [6, 2]], 157/1327104],
[[[1, 4], [2, 7], [3, 2], [4, 3], [8, 1]], 23/1179648],
[[[1, 4], [2, 7], [3, 2], [4, 3], [12, 1]], 25/1990656],
[[[1, 4], [2, 7], [3, 2], [4, 4], [6, 1]], 331/10616832],
[[[1, 4], [2, 7], [3, 2], [6, 1], [8, 2]], 47/1658880],
[[[1, 4], [2, 7], [3, 2], [6, 2], [9, 1]], 1/138240],
[[[1, 4], [2, 7], [3, 2], [6, 2], [18, 1]], 169/933120],
[[[1, 4], [2, 7], [3, 2], [6, 3], [8, 1]], 1/3456],
[[[1, 4], [2, 7], [3, 2], [6, 3], [10, 1]], 11/23328],
[[[1, 4], [2, 7], [3, 2], [6, 3], [12, 1]], 1/4096],
[[[1, 4], [2, 7], [3, 3], [4, 1], [6, 3]], 457/622080],
[[[1, 4], [2, 7], [3, 3], [4, 2], [6, 2]], 1/13824],
[[[1, 4], [2, 7], [3, 3], [4, 2], [8, 1]], 5/331776],
[[[1, 4], [2, 7], [3, 3], [4, 2], [12, 1]], 1/2799360],
[[[1, 4], [2, 7], [3, 3], [4, 3], [6, 1]], 11/1327104],
[[[1, 4], [2, 7], [3, 3], [6, 2], [8, 1]], 5/31104],
[[[1, 4], [2, 7], [3, 3], [6, 2], [12, 1]], 23/829440],
[[[1, 4], [2, 7], [3, 4], [4, 1], [6, 2]], 1/62208],
[[[1, 4], [2, 7], [3, 4], [4, 1], [8, 1]], 1/497664],
[[[1, 4], [2, 7], [3, 4], [6, 1], [8, 1]], 1/124416],
[[[1, 4], [2, 7], [4, 1], [5, 1], [8, 2]], 73/1474560],
[[[1, 4], [2, 7], [4, 1], [6, 2], [8, 2]], 47/221184],
[[[1, 4], [2, 7], [4, 1], [8, 2], [10, 1]], 1/7680],
[[[1, 4], [2, 7], [4, 2], [6, 1], [8, 2]], 1297/884736],
[[[1, 4], [2, 7], [4, 2], [6, 3], [8, 1]], 253/663552],
[[[1, 4], [2, 7], [4, 2], [6, 3], [10, 1]], 1/4976640],
[[[1, 4], [2, 7], [4, 2], [6, 3], [12, 1]], 1/46656],
[[[1, 4], [2, 7], [4, 3], [5, 1], [6, 2]], 1/30720],
[[[1, 4], [2, 7], [4, 3], [5, 1], [8, 1]], 23/327680],
[[[1, 4], [2, 7], [4, 3], [5, 1], [12, 1]], 1/552960],
[[[1, 4], [2, 7], [4, 3], [6, 2], [8, 1]], 521/589824],
[[[1, 4], [2, 7], [4, 3], [6, 2], [10, 1]], 1/184320],
[[[1, 4], [2, 7], [4, 3], [6, 2], [12, 1]], 77/165888],
[[[1, 4], [2, 7], [4, 3], [8, 1], [10, 1]], 347/491520],
[[[1, 4], [2, 7], [4, 3], [8, 1], [12, 1]], 11/110592],
[[[1, 4], [2, 7], [4, 3], [10, 1], [12, 1]], 1/3072],
[[[1, 4], [2, 7], [4, 4], [5, 1], [6, 1]], 19/1105920],
[[[1, 4], [2, 7], [4, 4], [6, 1], [8, 1]], 31/36864],
[[[1, 4], [2, 7], [4, 4], [6, 1], [10, 1]], 6557/17694720],
[[[1, 4], [2, 7], [4, 4], [6, 1], [12, 1]], 181/331776],
[[[1, 4], [2, 7], [5, 1], [6, 1], [8, 2]], 1/92160],
[[[1, 4], [2, 7], [6, 1], [8, 2], [10, 1]], 1/46080],
[[[1, 4], [2, 9], [3, 1], [4, 1], [6, 4]], 19/93312],
[[[1, 4], [2, 9], [3, 1], [4, 1], [8, 2]], 119/13271040],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 3]], 4901/7962624],
[[[1, 4], [2, 9], [3, 1], [4, 3], [5, 1]], 1/368640],
[[[1, 4], [2, 9], [3, 1], [4, 3], [6, 2]], 361/1179648],
[[[1, 4], [2, 9], [3, 1], [4, 3], [8, 1]], 667/8847360],
[[[1, 4], [2, 9], [3, 1], [4, 3], [10, 1]], 1/368640],
[[[1, 4], [2, 9], [3, 1], [4, 3], [12, 1]], 17/1658880],
[[[1, 4], [2, 9], [3, 1], [4, 4], [6, 1]], 148601/1274019840],
[[[1, 4], [2, 9], [3, 1], [6, 1], [8, 2]], 1723/53084160],
[[[1, 4], [2, 9], [3, 1], [6, 3], [10, 1]], 1/34560],
[[[1, 4], [2, 9], [3, 2], [4, 1], [6, 3]], 13/110592],
[[[1, 4], [2, 9], [3, 2], [4, 2], [6, 2]], 473/2654208],
[[[1, 4], [2, 9], [3, 2], [4, 2], [8, 1]], 37/2211840],
[[[1, 4], [2, 9], [3, 2], [4, 2], [12, 1]], 1/1105920],
[[[1, 4], [2, 9], [3, 2], [4, 3], [6, 1]], 89/3981312],
[[[1, 4], [2, 9], [3, 2], [6, 2], [8, 1]], 1/27648],
[[[1, 4], [2, 9], [3, 2], [6, 2], [10, 1]], 19/311040],
[[[1, 4], [2, 9], [3, 3], [4, 1], [6, 2]], 13/248832],
[[[1, 4], [2, 9], [3, 3], [4, 1], [8, 1]], 1/1990656],
[[[1, 4], [2, 9], [3, 3], [4, 2], [6, 1]], 1/147456],
[[[1, 4], [2, 9], [3, 3], [6, 1], [8, 1]], 1/995328],
[[[1, 4], [2, 9], [3, 4], [4, 1], [6, 1]], 1/497664],
[[[1, 4], [2, 9], [4, 1], [6, 1], [8, 2]], 119/1474560],
[[[1, 4], [2, 9], [4, 1], [6, 3], [10, 1]], 1/34560],
[[[1, 4], [2, 9], [4, 2], [5, 1], [8, 1]], 7/368640],
[[[1, 4], [2, 9], [4, 2], [5, 1], [12, 1]], 1/552960],
[[[1, 4], [2, 9], [4, 2], [6, 2], [8, 1]], 1543/4423680],
[[[1, 4], [2, 9], [4, 2], [6, 2], [10, 1]], 2611/13271040],
[[[1, 4], [2, 9], [4, 2], [6, 2], [12, 1]], 83/3981312],
[[[1, 4], [2, 9], [4, 2], [8, 1], [10, 1]], 113/737280],
[[[1, 4], [2, 9], [4, 2], [10, 1], [12, 1]], 11/1105920],
[[[1, 4], [2, 9], [4, 3], [5, 1], [6, 1]], 13/884736],
[[[1, 4], [2, 9], [4, 3], [6, 1], [8, 1]], 379/737280],
[[[1, 4], [2, 9], [4, 3], [6, 1], [10, 1]], 67/245760],
[[[1, 4], [2, 9], [4, 3], [6, 1], [12, 1]], 65/331776],
[[[1, 4], [2, 11], [3, 1], [4, 1], [6, 3]], 11965/47775744],
[[[1, 4], [2, 11], [3, 1], [4, 2], [6, 2]], 3769/26542080],
[[[1, 4], [2, 11], [3, 1], [4, 2], [8, 1]], 17/4423680],
[[[1, 4], [2, 11], [3, 1], [4, 2], [10, 1]], 13/4423680],
[[[1, 4], [2, 11], [3, 1], [4, 2], [12, 1]], 7/29859840],
[[[1, 4], [2, 11], [3, 1], [4, 3], [6, 1]], 64981/1698693120],
[[[1, 4], [2, 11], [3, 1], [6, 2], [10, 1]], 29/552960],
[[[1, 4], [2, 11], [3, 2], [4, 1], [6, 2]], 17/1327104],
[[[1, 4], [2, 11], [3, 2], [4, 1], [8, 1]], 1/10616832],
[[[1, 4], [2, 11], [3, 2], [4, 2], [6, 1]], 5141/424673280],
[[[1, 4], [2, 11], [3, 2], [6, 1], [10, 1]], 1/2488320],
[[[1, 4], [2, 11], [3, 3], [4, 1], [6, 1]], 1/3981312],
[[[1, 4], [2, 11], [4, 1], [5, 1], [8, 1]], 1/2949120],
[[[1, 4], [2, 11], [4, 1], [6, 2], [10, 1]], 149/737280],
[[[1, 4], [2, 11], [4, 2], [6, 1], [8, 1]], 367/6635520],
[[[1, 4], [2, 11], [4, 2], [6, 1], [10, 1]], 6253/26542080],
[[[1, 4], [2, 11], [4, 2], [6, 1], [12, 1]], 17/4976640],
[[[1, 4], [2, 13], [3, 1], [4, 1], [6, 2]], 59123/1274019840],
[[[1, 4], [2, 13], [3, 1], [4, 1], [10, 1]], 1/552960],
[[[1, 4], [2, 13], [3, 1], [4, 2], [6, 1]], 28741/3397386240],
[[[1, 4], [2, 13], [3, 1], [6, 1], [10, 1]], 1/110592],
[[[1, 4], [2, 13], [3, 2], [4, 1], [6, 1]], 5/63700992],
[[[1, 4], [2, 13], [4, 1], [6, 1], [10, 1]], 53/589824],
[[[1, 4], [2, 15], [3, 1], [4, 1], [6, 1]], 82741/30576476160],
[[[1, 5], [2, 2], [3, 1], [4, 2], [8, 3]], 1/4608],
[[[1, 5], [2, 2], [3, 1], [4, 6], [5, 1]], 11/1474560],
[[[1, 5], [2, 2], [3, 1], [4, 6], [8, 1]], 1/110592],
[[[1, 5], [2, 2], [3, 1], [4, 7], [6, 1]], 1/1769472],
[[[1, 5], [2, 2], [3, 2], [4, 1], [8, 3]], 5/36864],
[[[1, 5], [2, 2], [3, 2], [4, 1], [12, 3]], 1/55296],
[[[1, 5], [2, 2], [3, 2], [4, 3], [8, 2]], 1/73728],
[[[1, 5], [2, 2], [3, 2], [4, 3], [12, 2]], 1/27648],
[[[1, 5], [2, 2], [3, 2], [4, 5], [8, 1]], 5/442368],
[[[1, 5], [2, 2], [3, 2], [4, 6], [6, 1]], 1/1327104],
[[[1, 5], [2, 2], [3, 2], [6, 4], [9, 1]], 1/331776],
[[[1, 5], [2, 2], [3, 2], [9, 1], [12, 2]], 1/9216],
[[[1, 5], [2, 2], [3, 3], [4, 1], [6, 5]], 1/221184],
[[[1, 5], [2, 2], [3, 3], [4, 2], [8, 2]], 13/55296],
[[[1, 5], [2, 2], [3, 3], [4, 2], [12, 2]], 1/3456],
[[[1, 5], [2, 2], [3, 3], [4, 4], [8, 1]], 1/27648],
[[[1, 5], [2, 2], [3, 3], [4, 4], [12, 1]], 1/20736],
[[[1, 5], [2, 2], [3, 3], [4, 5], [6, 1]], 1/442368],
[[[1, 5], [2, 2], [3, 3], [5, 1], [6, 4]], 7/69120],
[[[1, 5], [2, 2], [3, 3], [6, 2], [8, 2]], 1/6912],
[[[1, 5], [2, 2], [3, 3], [6, 2], [12, 2]], 5/82944],
[[[1, 5], [2, 2], [3, 3], [6, 2], [24, 1]], 1/6912],
[[[1, 5], [2, 2], [3, 3], [6, 3], [9, 1]], 193/373248],
[[[1, 5], [2, 2], [3, 3], [6, 3], [18, 1]], 7/207360],
[[[1, 5], [2, 2], [3, 3], [6, 4], [12, 1]], 1/82944],
[[[1, 5], [2, 2], [3, 4], [4, 1], [6, 4]], 1361/1327104],
[[[1, 5], [2, 2], [3, 4], [4, 1], [12, 2]], 1/36864],
[[[1, 5], [2, 2], [3, 4], [4, 4], [6, 1]], 1/186624],
[[[1, 5], [2, 2], [3, 4], [5, 1], [6, 3]], 19/207360],
[[[1, 5], [2, 2], [3, 4], [5, 1], [9, 1]], 1/2880],
[[[1, 5], [2, 2], [3, 4], [6, 1], [8, 2]], 1/15552],
[[[1, 5], [2, 2], [3, 4], [6, 1], [12, 2]], 5/20736],
[[[1, 5], [2, 2], [3, 4], [6, 1], [24, 1]], 1/6912],
[[[1, 5], [2, 2], [3, 4], [6, 2], [9, 1]], 65/165888],
[[[1, 5], [2, 2], [3, 4], [6, 3], [12, 1]], 1/6912],
[[[1, 5], [2, 2], [3, 4], [9, 1], [12, 1]], 17/27648],
[[[1, 5], [2, 2], [3, 5], [4, 1], [6, 3]], 1/36864],
[[[1, 5], [2, 2], [3, 5], [4, 1], [9, 1]], 1/10368],
[[[1, 5], [2, 2], [3, 5], [5, 1], [6, 2]], 7/69120],
[[[1, 5], [2, 2], [3, 5], [6, 1], [9, 1]], 1/1944],
[[[1, 5], [2, 2], [3, 5], [6, 2], [12, 1]], 11/27648],
[[[1, 5], [2, 2], [3, 6], [4, 1], [6, 2]], 1/663552],
[[[1, 5], [2, 2], [3, 6], [4, 1], [12, 1]], 1/110592],
[[[1, 5], [2, 2], [3, 6], [5, 1], [6, 1]], 19/207360],
[[[1, 5], [2, 2], [3, 6], [6, 1], [12, 1]], 37/124416],
[[[1, 5], [2, 2], [3, 7], [4, 1], [6, 1]], 1/221184],
[[[1, 5], [2, 2], [4, 1], [5, 1], [8, 3]], 1/10240],
[[[1, 5], [2, 2], [4, 1], [6, 2], [8, 3]], 1/221184],
[[[1, 5], [2, 2], [4, 1], [8, 3], [10, 1]], 1/61440],
[[[1, 5], [2, 2], [4, 3], [5, 1], [8, 2]], 1/20480],
[[[1, 5], [2, 2], [4, 5], [5, 1], [8, 1]], 1/122880],
[[[1, 5], [2, 2], [4, 6], [5, 1], [6, 1]], 1/368640],
[[[1, 5], [2, 4], [3, 1], [4, 1], [8, 3]], 1/6144],
[[[1, 5], [2, 4], [3, 1], [4, 3], [8, 2]], 7/4608],
[[[1, 5], [2, 4], [3, 1], [4, 4], [6, 3]], 1/2239488],
[[[1, 5], [2, 4], [3, 1], [4, 5], [6, 2]], 133/3981312],
[[[1, 5], [2, 4], [3, 1], [4, 5], [8, 1]], 37/221184],
[[[1, 5], [2, 4], [3, 1], [4, 5], [10, 1]], 1/276480],
[[[1, 5], [2, 4], [3, 1], [4, 5], [12, 1]], 1/4608],
[[[1, 5], [2, 4], [3, 1], [4, 6], [6, 1]], 1063/14155776],
[[[1, 5], [2, 4], [3, 1], [6, 3], [8, 2]], 31/746496],
[[[1, 5], [2, 4], [3, 1], [6, 3], [12, 2]], 23/2488320],
[[[1, 5], [2, 4], [3, 1], [6, 3], [24, 1]], 23/414720],
[[[1, 5], [2, 4], [3, 1], [6, 4], [18, 1]], 1/248832],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 5]], 1/13824],
[[[1, 5], [2, 4], [3, 2], [4, 2], [6, 4]], 1/3072],
[[[1, 5], [2, 4], [3, 2], [4, 2], [8, 2]], 397/884736],
[[[1, 5], [2, 4], [3, 2], [4, 2], [12, 2]], 1/3072],
[[[1, 5], [2, 4], [3, 2], [4, 4], [6, 2]], 1/6912],
[[[1, 5], [2, 4], [3, 2], [4, 4], [8, 1]], 47/294912],
[[[1, 5], [2, 4], [3, 2], [4, 4], [10, 1]], 1/276480],
[[[1, 5], [2, 4], [3, 2], [4, 4], [12, 1]], 55/331776],
[[[1, 5], [2, 4], [3, 2], [4, 5], [6, 1]], 593/5308416],
[[[1, 5], [2, 4], [3, 2], [5, 1], [6, 4]], 1/7680],
[[[1, 5], [2, 4], [3, 2], [6, 2], [8, 2]], 71/165888],
[[[1, 5], [2, 4], [3, 2], [6, 2], [12, 2]], 7/55296],
[[[1, 5], [2, 4], [3, 2], [6, 2], [24, 1]], 1/2304],
[[[1, 5], [2, 4], [3, 2], [6, 3], [9, 1]], 17/41472],
[[[1, 5], [2, 4], [3, 2], [6, 3], [18, 1]], 1/31104],
[[[1, 5], [2, 4], [3, 2], [6, 4], [8, 1]], 1/15552],
[[[1, 5], [2, 4], [3, 2], [6, 4], [12, 1]], 1/55296],
[[[1, 5], [2, 4], [3, 2], [8, 2], [10, 1]], 1/23040],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 4]], 7/6912],
[[[1, 5], [2, 4], [3, 3], [4, 1], [8, 2]], 5/165888],
[[[1, 5], [2, 4], [3, 3], [4, 2], [6, 3]], 1/1536],
[[[1, 5], [2, 4], [3, 3], [4, 3], [6, 2]], 121/746496],
[[[1, 5], [2, 4], [3, 3], [4, 3], [8, 1]], 1/27648],
[[[1, 5], [2, 4], [3, 3], [4, 3], [10, 1]], 1/51840],
[[[1, 5], [2, 4], [3, 3], [4, 3], [12, 1]], 1/31104],
[[[1, 5], [2, 4], [3, 3], [4, 4], [6, 1]], 119/1492992],
[[[1, 5], [2, 4], [3, 3], [5, 1], [6, 3]], 1/2160],
[[[1, 5], [2, 4], [3, 3], [6, 1], [8, 2]], 35/497664],
[[[1, 5], [2, 4], [3, 3], [6, 1], [12, 2]], 19/331776],
[[[1, 5], [2, 4], [3, 3], [6, 1], [24, 1]], 5/27648],
[[[1, 5], [2, 4], [3, 3], [6, 2], [9, 1]], 161/746496],
[[[1, 5], [2, 4], [3, 3], [6, 2], [18, 1]], 11/82944],
[[[1, 5], [2, 4], [3, 3], [6, 3], [8, 1]], 1/15552],
[[[1, 5], [2, 4], [3, 3], [6, 3], [10, 1]], 1/2160],
[[[1, 5], [2, 4], [3, 3], [6, 3], [12, 1]], 107/331776],
[[[1, 5], [2, 4], [3, 3], [9, 1], [12, 1]], 1/13824],
[[[1, 5], [2, 4], [3, 4], [4, 1], [6, 3]], 155/331776],
[[[1, 5], [2, 4], [3, 4], [4, 1], [9, 1]], 1/4608],
[[[1, 5], [2, 4], [3, 4], [4, 2], [6, 2]], 1/3072],
[[[1, 5], [2, 4], [3, 4], [4, 2], [8, 1]], 1/82944],
[[[1, 5], [2, 4], [3, 4], [5, 1], [6, 2]], 5/10368],
[[[1, 5], [2, 4], [3, 4], [6, 1], [9, 1]], 1/4608],
[[[1, 5], [2, 4], [3, 4], [6, 2], [10, 1]], 1/11520],
[[[1, 5], [2, 4], [3, 4], [6, 2], [12, 1]], 7/18432],
[[[1, 5], [2, 4], [3, 5], [4, 1], [6, 2]], 1/1728],
[[[1, 5], [2, 4], [3, 5], [6, 1], [12, 1]], 1/110592],
[[[1, 5], [2, 4], [3, 6], [4, 1], [6, 1]], 19/331776],
[[[1, 5], [2, 4], [4, 1], [6, 1], [8, 3]], 11/110592],
[[[1, 5], [2, 4], [4, 1], [6, 3], [8, 2]], 1/27648],
[[[1, 5], [2, 4], [4, 2], [5, 1], [8, 2]], 181/245760],
[[[1, 5], [2, 4], [4, 2], [6, 2], [8, 2]], 1/12288],
[[[1, 5], [2, 4], [4, 2], [6, 2], [12, 2]], 1/9216],
[[[1, 5], [2, 4], [4, 2], [8, 2], [10, 1]], 1/5120],
[[[1, 5], [2, 4], [4, 3], [6, 1], [8, 2]], 13/49152],
[[[1, 5], [2, 4], [4, 3], [6, 3], [8, 1]], 1/110592],
[[[1, 5], [2, 4], [4, 4], [5, 1], [6, 2]], 5/110592],
[[[1, 5], [2, 4], [4, 4], [5, 1], [8, 1]], 47/81920],
[[[1, 5], [2, 4], [4, 4], [5, 1], [12, 1]], 31/92160],
[[[1, 5], [2, 4], [4, 4], [6, 2], [8, 1]], 1/73728],
[[[1, 5], [2, 4], [4, 4], [6, 2], [12, 1]], 1/13824],
[[[1, 5], [2, 4], [4, 4], [8, 1], [10, 1]], 1/20480],
[[[1, 5], [2, 4], [4, 4], [8, 1], [12, 1]], 1/2304],
[[[1, 5], [2, 4], [4, 5], [5, 1], [6, 1]], 1/184320],
[[[1, 5], [2, 4], [4, 5], [6, 1], [12, 1]], 1/18432],
[[[1, 5], [2, 4], [5, 1], [6, 2], [8, 2]], 1/46080],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 5]], 49/248832],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 4]], 145/5971968],
[[[1, 5], [2, 6], [3, 1], [4, 2], [8, 2]], 2297/4423680],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 3]], 97/331776],
[[[1, 5], [2, 6], [3, 1], [4, 4], [5, 1]], 49/2949120],
[[[1, 5], [2, 6], [3, 1], [4, 4], [6, 2]], 132197/191102976],
[[[1, 5], [2, 6], [3, 1], [4, 4], [8, 1]], 61/147456],
[[[1, 5], [2, 6], [3, 1], [4, 4], [10, 1]], 23/184320],
[[[1, 5], [2, 6], [3, 1], [4, 4], [12, 1]], 19/110592],
[[[1, 5], [2, 6], [3, 1], [4, 5], [6, 1]], 130561/254803968],
[[[1, 5], [2, 6], [3, 1], [5, 1], [6, 4]], 1/7776],
[[[1, 5], [2, 6], [3, 1], [6, 2], [8, 2]], 77/248832],
[[[1, 5], [2, 6], [3, 1], [6, 3], [18, 1]], 19/124416],
[[[1, 5], [2, 6], [3, 1], [6, 4], [8, 1]], 1/41472],
[[[1, 5], [2, 6], [3, 1], [6, 4], [12, 1]], 19/331776],
[[[1, 5], [2, 6], [3, 1], [8, 2], [10, 1]], 1/30720],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 4]], 4165/2985984],
[[[1, 5], [2, 6], [3, 2], [4, 1], [8, 2]], 97/442368],
[[[1, 5], [2, 6], [3, 2], [4, 2], [6, 3]], 329/497664],
[[[1, 5], [2, 6], [3, 2], [4, 3], [6, 2]], 467/663552],
[[[1, 5], [2, 6], [3, 2], [4, 3], [8, 1]], 97/294912],
[[[1, 5], [2, 6], [3, 2], [4, 3], [10, 1]], 1/7680],
[[[1, 5], [2, 6], [3, 2], [4, 3], [12, 1]], 13/165888],
[[[1, 5], [2, 6], [3, 2], [4, 4], [6, 1]], 937/5308416],
[[[1, 5], [2, 6], [3, 2], [5, 1], [6, 3]], 1/6480],
[[[1, 5], [2, 6], [3, 2], [6, 1], [8, 2]], 247/1327104],
[[[1, 5], [2, 6], [3, 2], [6, 2], [9, 1]], 7/82944],
[[[1, 5], [2, 6], [3, 2], [6, 2], [18, 1]], 1/3888],
[[[1, 5], [2, 6], [3, 2], [6, 3], [8, 1]], 1/2592],
[[[1, 5], [2, 6], [3, 2], [6, 3], [12, 1]], 7/27648],
[[[1, 5], [2, 6], [3, 3], [4, 1], [6, 3]], 257/124416],
[[[1, 5], [2, 6], [3, 3], [4, 2], [6, 2]], 239/995328],
[[[1, 5], [2, 6], [3, 3], [4, 2], [8, 1]], 5/110592],
[[[1, 5], [2, 6], [3, 3], [4, 2], [12, 1]], 1/186624],
[[[1, 5], [2, 6], [3, 3], [4, 3], [6, 1]], 1073/23887872],
[[[1, 5], [2, 6], [3, 3], [5, 1], [6, 2]], 1/12960],
[[[1, 5], [2, 6], [3, 3], [6, 1], [9, 1]], 1/41472],
[[[1, 5], [2, 6], [3, 3], [6, 2], [8, 1]], 53/124416],
[[[1, 5], [2, 6], [3, 3], [6, 2], [12, 1]], 5/36864],
[[[1, 5], [2, 6], [3, 4], [4, 1], [6, 2]], 2581/4976640],
[[[1, 5], [2, 6], [3, 4], [4, 1], [8, 1]], 1/82944],
[[[1, 5], [2, 6], [3, 4], [4, 2], [6, 1]], 5/248832],
[[[1, 5], [2, 6], [3, 4], [6, 1], [8, 1]], 1/20736],
[[[1, 5], [2, 6], [4, 1], [5, 1], [8, 2]], 79/368640],
[[[1, 5], [2, 6], [4, 1], [6, 2], [8, 2]], 223/884736],
[[[1, 5], [2, 6], [4, 1], [6, 4], [8, 1]], 1/165888],
[[[1, 5], [2, 6], [4, 1], [8, 2], [10, 1]], 11/49152],
[[[1, 5], [2, 6], [4, 2], [5, 1], [6, 3]], 1/17280],
[[[1, 5], [2, 6], [4, 2], [6, 1], [8, 2]], 133/98304],
[[[1, 5], [2, 6], [4, 2], [6, 3], [8, 1]], 25/110592],
[[[1, 5], [2, 6], [4, 2], [6, 3], [12, 1]], 1/62208],
[[[1, 5], [2, 6], [4, 3], [5, 1], [6, 2]], 1/11520],
[[[1, 5], [2, 6], [4, 3], [5, 1], [8, 1]], 17/81920],
[[[1, 5], [2, 6], [4, 3], [5, 1], [12, 1]], 1/46080],
[[[1, 5], [2, 6], [4, 3], [6, 2], [8, 1]], 2867/3538944],
[[[1, 5], [2, 6], [4, 3], [6, 2], [10, 1]], 49/2211840],
[[[1, 5], [2, 6], [4, 3], [6, 2], [12, 1]], 7/36864],
[[[1, 5], [2, 6], [4, 3], [8, 1], [10, 1]], 401/327680],
[[[1, 5], [2, 6], [4, 3], [8, 1], [12, 1]], 1/12288],
[[[1, 5], [2, 6], [4, 3], [10, 1], [12, 1]], 23/92160],
[[[1, 5], [2, 6], [4, 4], [5, 1], [6, 1]], 83/1105920],
[[[1, 5], [2, 6], [4, 4], [6, 1], [8, 1]], 175/147456],
[[[1, 5], [2, 6], [4, 4], [6, 1], [10, 1]], 3/81920],
[[[1, 5], [2, 6], [4, 4], [6, 1], [12, 1]], 71/110592],
[[[1, 5], [2, 6], [5, 1], [6, 1], [8, 2]], 11/184320],
[[[1, 5], [2, 8], [3, 1], [4, 1], [6, 4]], 91/248832],
[[[1, 5], [2, 8], [3, 1], [4, 1], [8, 2]], 1277/13271040],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 3]], 57869/47775744],
[[[1, 5], [2, 8], [3, 1], [4, 3], [5, 1]], 1/46080],
[[[1, 5], [2, 8], [3, 1], [4, 3], [6, 2]], 3745/2654208],
[[[1, 5], [2, 8], [3, 1], [4, 3], [8, 1]], 971/2211840],
[[[1, 5], [2, 8], [3, 1], [4, 3], [10, 1]], 727/4423680],
[[[1, 5], [2, 8], [3, 1], [4, 3], [12, 1]], 301/4976640],
[[[1, 5], [2, 8], [3, 1], [4, 4], [6, 1]], 810995/1528823808],
[[[1, 5], [2, 8], [3, 1], [5, 1], [6, 3]], 1/20736],
[[[1, 5], [2, 8], [3, 1], [6, 1], [8, 2]], 20659/159252480],
[[[1, 5], [2, 8], [3, 1], [6, 3], [8, 1]], 25/331776],
[[[1, 5], [2, 8], [3, 1], [6, 3], [10, 1]], 1/155520],
[[[1, 5], [2, 8], [3, 2], [4, 1], [6, 3]], 5/4608],
[[[1, 5], [2, 8], [3, 2], [4, 2], [5, 1]], 1/276480],
[[[1, 5], [2, 8], [3, 2], [4, 2], [6, 2]], 1811/2654208],
[[[1, 5], [2, 8], [3, 2], [4, 2], [8, 1]], 7/46080],
[[[1, 5], [2, 8], [3, 2], [4, 2], [12, 1]], 67/6635520],
[[[1, 5], [2, 8], [3, 2], [4, 3], [6, 1]], 3095/10616832],
[[[1, 5], [2, 8], [3, 2], [5, 1], [6, 2]], 1/25920],
[[[1, 5], [2, 8], [3, 2], [6, 2], [8, 1]], 13/51840],
[[[1, 5], [2, 8], [3, 2], [6, 2], [10, 1]], 19/51840],
[[[1, 5], [2, 8], [3, 3], [4, 1], [6, 2]], 349/995328],
[[[1, 5], [2, 8], [3, 3], [4, 1], [8, 1]], 1/51840],
[[[1, 5], [2, 8], [3, 3], [4, 2], [6, 1]], 385/7962624],
[[[1, 5], [2, 8], [3, 3], [5, 1], [6, 1]], 1/103680],
[[[1, 5], [2, 8], [3, 3], [6, 1], [8, 1]], 47/1244160],
[[[1, 5], [2, 8], [3, 4], [4, 1], [6, 1]], 1/62208],
[[[1, 5], [2, 8], [4, 1], [6, 1], [8, 2]], 1469/4423680],
[[[1, 5], [2, 8], [4, 1], [6, 3], [8, 1]], 43/663552],
[[[1, 5], [2, 8], [4, 1], [6, 3], [10, 1]], 1/414720],
[[[1, 5], [2, 8], [4, 2], [5, 1], [6, 2]], 13/184320],
[[[1, 5], [2, 8], [4, 2], [5, 1], [8, 1]], 1/7680],
[[[1, 5], [2, 8], [4, 2], [5, 1], [12, 1]], 13/1105920],
[[[1, 5], [2, 8], [4, 2], [6, 2], [8, 1]], 19/12288],
[[[1, 5], [2, 8], [4, 2], [6, 2], [10, 1]], 103/2211840],
[[[1, 5], [2, 8], [4, 2], [6, 2], [12, 1]], 55/663552],
[[[1, 5], [2, 8], [4, 2], [8, 1], [10, 1]], 7/7680],
[[[1, 5], [2, 8], [4, 2], [10, 1], [12, 1]], 11/184320],
[[[1, 5], [2, 8], [4, 3], [5, 1], [6, 1]], 11/122880],
[[[1, 5], [2, 8], [4, 3], [6, 1], [8, 1]], 19277/8847360],
[[[1, 5], [2, 8], [4, 3], [6, 1], [10, 1]], 4327/8847360],
[[[1, 5], [2, 8], [4, 3], [6, 1], [12, 1]], 7/12288],
[[[1, 5], [2, 10], [3, 1], [4, 1], [6, 3]], 27101/39813120],
[[[1, 5], [2, 10], [3, 1], [4, 2], [5, 1]], 449/70778880],
[[[1, 5], [2, 10], [3, 1], [4, 2], [6, 2]], 46247/53084160],
[[[1, 5], [2, 10], [3, 1], [4, 2], [8, 1]], 179/2211840],
[[[1, 5], [2, 10], [3, 1], [4, 2], [10, 1]], 11/491520],
[[[1, 5], [2, 10], [3, 1], [4, 2], [12, 1]], 197/44789760],
[[[1, 5], [2, 10], [3, 1], [4, 3], [6, 1]], 60307/169869312],
[[[1, 5], [2, 10], [3, 1], [5, 1], [6, 2]], 1/165888],
[[[1, 5], [2, 10], [3, 1], [6, 2], [8, 1]], 13/829440],
[[[1, 5], [2, 10], [3, 1], [6, 2], [10, 1]], 5/82944],
[[[1, 5], [2, 10], [3, 2], [4, 1], [6, 2]], 1157/4976640],
[[[1, 5], [2, 10], [3, 2], [4, 1], [8, 1]], 497/79626240],
[[[1, 5], [2, 10], [3, 2], [4, 1], [10, 1]], 1/3317760],
[[[1, 5], [2, 10], [3, 2], [4, 2], [6, 1]], 1063/8847360],
[[[1, 5], [2, 10], [3, 2], [5, 1], [6, 1]], 1/414720],
[[[1, 5], [2, 10], [3, 2], [6, 1], [8, 1]], 49/4976640],
[[[1, 5], [2, 10], [3, 2], [6, 1], [10, 1]], 1/207360],
[[[1, 5], [2, 10], [3, 3], [4, 1], [6, 1]], 7397/318504960],
[[[1, 5], [2, 10], [4, 1], [5, 1], [8, 1]], 1/98304],
[[[1, 5], [2, 10], [4, 1], [6, 2], [8, 1]], 961/17694720],
[[[1, 5], [2, 10], [4, 1], [6, 2], [10, 1]], 1117/8847360],
[[[1, 5], [2, 10], [4, 1], [8, 1], [10, 1]], 71/2949120],
[[[1, 5], [2, 10], [4, 2], [5, 1], [6, 1]], 1/65536],
[[[1, 5], [2, 10], [4, 2], [6, 1], [8, 1]], 37/61440],
[[[1, 5], [2, 10], [4, 2], [6, 1], [10, 1]], 2353/8847360],
[[[1, 5], [2, 10], [4, 2], [6, 1], [12, 1]], 23/663552],
[[[1, 5], [2, 12], [3, 1], [4, 1], [6, 2]], 15707/63700992],
[[[1, 5], [2, 12], [3, 1], [4, 1], [8, 1]], 17/19906560],
[[[1, 5], [2, 12], [3, 1], [4, 1], [10, 1]], 7/552960],
[[[1, 5], [2, 12], [3, 1], [4, 2], [6, 1]], 2782933/30576476160],
[[[1, 5], [2, 12], [3, 1], [5, 1], [6, 1]], 1/3981312],
[[[1, 5], [2, 12], [3, 1], [6, 1], [8, 1]], 11/13271040],
[[[1, 5], [2, 12], [3, 1], [6, 1], [10, 1]], 5/165888],
[[[1, 5], [2, 12], [3, 2], [4, 1], [6, 1]], 30829/3822059520],
[[[1, 5], [2, 12], [4, 1], [6, 1], [8, 1]], 227/26542080],
[[[1, 5], [2, 12], [4, 1], [6, 1], [10, 1]], 1721/11796480],
[[[1, 5], [2, 14], [3, 1], [4, 1], [6, 1]], 464041/20384317440],
[[[1, 5], [3, 3], [5, 1], [6, 2], [9, 1]], 1/25920],
[[[1, 5], [3, 3], [5, 1], [9, 1], [12, 1]], 1/4320],
[[[1, 5], [3, 3], [6, 2], [9, 1], [12, 1]], 1/31104],
[[[1, 5], [3, 4], [4, 2], [6, 2], [12, 1]], 1/20736],
[[[1, 5], [3, 4], [5, 1], [6, 2], [12, 1]], 1/69120],
[[[1, 6], [2, 1], [3, 2], [4, 1], [8, 3]], 1/24576],
[[[1, 6], [2, 1], [3, 2], [4, 1], [12, 3]], 1/829440],
[[[1, 6], [2, 1], [3, 2], [4, 3], [8, 2]], 1/442368],
[[[1, 6], [2, 1], [3, 2], [4, 3], [12, 2]], 1/414720],
[[[1, 6], [2, 1], [3, 2], [4, 5], [5, 1]], 1/368640],
[[[1, 6], [2, 1], [3, 2], [4, 5], [8, 1]], 1/294912],
[[[1, 6], [2, 1], [3, 2], [4, 5], [12, 1]], 1/165888],
[[[1, 6], [2, 1], [3, 2], [6, 4], [9, 1]], 1/995328],
[[[1, 6], [2, 1], [3, 2], [9, 1], [12, 2]], 1/27648],
[[[1, 6], [2, 1], [3, 3], [6, 3], [9, 1]], 1/31104],
[[[1, 6], [2, 1], [3, 4], [4, 1], [6, 4]], 1/1327104],
[[[1, 6], [2, 1], [3, 4], [4, 1], [12, 2]], 1/36864],
[[[1, 6], [2, 1], [3, 4], [4, 4], [6, 1]], 1/995328],
[[[1, 6], [2, 1], [3, 4], [5, 1], [6, 3]], 1/23040],
[[[1, 6], [2, 1], [3, 4], [5, 1], [9, 1]], 1/4320],
[[[1, 6], [2, 1], [3, 4], [6, 1], [12, 2]], 1/13824],
[[[1, 6], [2, 1], [3, 4], [6, 2], [9, 1]], 11/165888],
[[[1, 6], [2, 1], [3, 4], [6, 3], [12, 1]], 1/41472],
[[[1, 6], [2, 1], [3, 4], [9, 1], [12, 1]], 11/27648],
[[[1, 6], [2, 1], [3, 5], [4, 1], [6, 3]], 1/6144],
[[[1, 6], [2, 1], [3, 5], [4, 1], [9, 1]], 1/41472],
[[[1, 6], [2, 1], [3, 5], [5, 1], [6, 2]], 1/69120],
[[[1, 6], [2, 1], [3, 5], [5, 1], [12, 1]], 1/11520],
[[[1, 6], [2, 1], [3, 5], [6, 1], [9, 1]], 1/7776],
[[[1, 6], [2, 1], [3, 5], [6, 2], [12, 1]], 1/82944],
[[[1, 6], [2, 1], [3, 6], [4, 1], [6, 2]], 1/663552],
[[[1, 6], [2, 1], [3, 6], [4, 1], [12, 1]], 1/110592],
[[[1, 6], [2, 1], [3, 6], [5, 1], [6, 1]], 1/23040],
[[[1, 6], [2, 1], [3, 6], [6, 1], [12, 1]], 5/41472],
[[[1, 6], [2, 1], [4, 1], [5, 1], [8, 3]], 1/61440],
[[[1, 6], [2, 1], [4, 3], [5, 1], [8, 2]], 1/122880],
[[[1, 6], [2, 1], [4, 5], [5, 1], [8, 1]], 1/737280],
[[[1, 6], [2, 1], [4, 5], [5, 1], [12, 1]], 1/46080],
[[[1, 6], [2, 3], [3, 1], [4, 1], [8, 3]], 1/6144],
[[[1, 6], [2, 3], [3, 1], [4, 3], [8, 2]], 35/36864],
[[[1, 6], [2, 3], [3, 1], [4, 5], [5, 1]], 31/294912],
[[[1, 6], [2, 3], [3, 1], [4, 5], [6, 2]], 1/995328],
[[[1, 6], [2, 3], [3, 1], [4, 5], [8, 1]], 53/442368],
[[[1, 6], [2, 3], [3, 1], [4, 5], [12, 1]], 1/6912],
[[[1, 6], [2, 3], [3, 1], [4, 6], [6, 1]], 151/14155776],
[[[1, 6], [2, 3], [3, 1], [6, 3], [8, 2]], 1/165888],
[[[1, 6], [2, 3], [3, 2], [4, 2], [8, 2]], 77/73728],
[[[1, 6], [2, 3], [3, 2], [4, 2], [12, 2]], 1/9216],
[[[1, 6], [2, 3], [3, 2], [4, 4], [6, 2]], 5/2985984],
[[[1, 6], [2, 3], [3, 2], [4, 4], [8, 1]], 11/73728],
[[[1, 6], [2, 3], [3, 2], [4, 4], [10, 1]], 1/1658880],
[[[1, 6], [2, 3], [3, 2], [4, 4], [12, 1]], 11/55296],
[[[1, 6], [2, 3], [3, 2], [4, 5], [6, 1]], 25/884736],
[[[1, 6], [2, 3], [3, 2], [6, 2], [8, 2]], 1/7776],
[[[1, 6], [2, 3], [3, 2], [6, 2], [12, 2]], 109/3317760],
[[[1, 6], [2, 3], [3, 2], [6, 2], [24, 1]], 1/8640],
[[[1, 6], [2, 3], [3, 2], [6, 3], [9, 1]], 5/124416],
[[[1, 6], [2, 3], [3, 2], [6, 4], [12, 1]], 1/221184],
[[[1, 6], [2, 3], [3, 2], [8, 2], [10, 1]], 1/138240],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 4]], 1/13824],
[[[1, 6], [2, 3], [3, 3], [4, 1], [8, 2]], 1/20736],
[[[1, 6], [2, 3], [3, 3], [4, 2], [6, 3]], 1/1536],
[[[1, 6], [2, 3], [3, 3], [4, 3], [8, 1]], 19/110592],
[[[1, 6], [2, 3], [3, 3], [4, 3], [12, 1]], 1/7776],
[[[1, 6], [2, 3], [3, 3], [4, 4], [6, 1]], 49/884736],
[[[1, 6], [2, 3], [3, 3], [5, 1], [6, 3]], 1/2880],
[[[1, 6], [2, 3], [3, 3], [6, 1], [8, 2]], 1/4608],
[[[1, 6], [2, 3], [3, 3], [6, 1], [12, 2]], 11/110592],
[[[1, 6], [2, 3], [3, 3], [6, 1], [24, 1]], 1/9216],
[[[1, 6], [2, 3], [3, 3], [6, 2], [9, 1]], 49/124416],
[[[1, 6], [2, 3], [3, 3], [6, 3], [8, 1]], 1/5184],
[[[1, 6], [2, 3], [3, 3], [6, 3], [12, 1]], 11/110592],
[[[1, 6], [2, 3], [3, 3], [9, 1], [12, 1]], 5/20736],
[[[1, 6], [2, 3], [3, 4], [4, 1], [6, 3]], 19/82944],
[[[1, 6], [2, 3], [3, 4], [4, 1], [9, 1]], 5/13824],
[[[1, 6], [2, 3], [3, 4], [4, 2], [6, 2]], 85/746496],
[[[1, 6], [2, 3], [3, 4], [4, 3], [6, 1]], 17/248832],
[[[1, 6], [2, 3], [3, 4], [5, 1], [6, 2]], 1/1440],
[[[1, 6], [2, 3], [3, 4], [6, 1], [9, 1]], 31/41472],
[[[1, 6], [2, 3], [3, 4], [6, 2], [8, 1]], 1/5184],
[[[1, 6], [2, 3], [3, 4], [6, 2], [10, 1]], 1/13824],
[[[1, 6], [2, 3], [3, 4], [6, 2], [12, 1]], 35/55296],
[[[1, 6], [2, 3], [3, 5], [4, 1], [6, 2]], 25/110592],
[[[1, 6], [2, 3], [3, 5], [4, 1], [12, 1]], 1/18432],
[[[1, 6], [2, 3], [3, 5], [5, 1], [6, 1]], 1/3456],
[[[1, 6], [2, 3], [3, 5], [6, 1], [12, 1]], 161/331776],
[[[1, 6], [2, 3], [3, 6], [4, 1], [6, 1]], 7/82944],
[[[1, 6], [2, 3], [4, 1], [6, 1], [8, 3]], 1/69120],
[[[1, 6], [2, 3], [4, 1], [6, 3], [8, 2]], 1/165888],
[[[1, 6], [2, 3], [4, 2], [5, 1], [8, 2]], 43/61440],
[[[1, 6], [2, 3], [4, 2], [6, 2], [8, 2]], 1/49152],
[[[1, 6], [2, 3], [4, 2], [8, 2], [10, 1]], 3/40960],
[[[1, 6], [2, 3], [4, 3], [6, 1], [8, 2]], 1/49152],
[[[1, 6], [2, 3], [4, 4], [5, 1], [8, 1]], 3/20480],
[[[1, 6], [2, 3], [4, 4], [5, 1], [12, 1]], 1/5120],
[[[1, 6], [2, 3], [4, 4], [6, 2], [8, 1]], 1/589824],
[[[1, 6], [2, 3], [4, 4], [8, 1], [10, 1]], 1/163840],
[[[1, 6], [2, 3], [4, 4], [8, 1], [12, 1]], 1/4608],
[[[1, 6], [2, 3], [4, 5], [5, 1], [6, 1]], 13/368640],
[[[1, 6], [2, 3], [4, 5], [6, 1], [12, 1]], 1/18432],
[[[1, 6], [2, 5], [3, 1], [4, 2], [6, 4]], 5/248832],
[[[1, 6], [2, 5], [3, 1], [4, 2], [8, 2]], 133/98304],
[[[1, 6], [2, 5], [3, 1], [4, 3], [6, 3]], 1073/23887872],
[[[1, 6], [2, 5], [3, 1], [4, 4], [5, 1]], 3/81920],
[[[1, 6], [2, 5], [3, 1], [4, 4], [6, 2]], 937/5308416],
[[[1, 6], [2, 5], [3, 1], [4, 4], [8, 1]], 175/147456],
[[[1, 6], [2, 5], [3, 1], [4, 4], [10, 1]], 83/1105920],
[[[1, 6], [2, 5], [3, 1], [4, 4], [12, 1]], 71/110592],
[[[1, 6], [2, 5], [3, 1], [4, 5], [6, 1]], 130561/254803968],
[[[1, 6], [2, 5], [3, 1], [6, 2], [8, 2]], 247/1327104],
[[[1, 6], [2, 5], [3, 1], [6, 3], [18, 1]], 1/41472],
[[[1, 6], [2, 5], [3, 1], [6, 4], [8, 1]], 1/20736],
[[[1, 6], [2, 5], [3, 1], [8, 2], [10, 1]], 11/184320],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 4]], 2581/4976640],
[[[1, 6], [2, 5], [3, 2], [4, 1], [8, 2]], 223/884736],
[[[1, 6], [2, 5], [3, 2], [4, 2], [6, 3]], 239/995328],
[[[1, 6], [2, 5], [3, 2], [4, 3], [5, 1]], 49/2211840],
[[[1, 6], [2, 5], [3, 2], [4, 3], [6, 2]], 467/663552],
[[[1, 6], [2, 5], [3, 2], [4, 3], [8, 1]], 2867/3538944],
[[[1, 6], [2, 5], [3, 2], [4, 3], [10, 1]], 1/11520],
[[[1, 6], [2, 5], [3, 2], [4, 3], [12, 1]], 7/36864],
[[[1, 6], [2, 5], [3, 2], [4, 4], [6, 1]], 132197/191102976],
[[[1, 6], [2, 5], [3, 2], [6, 1], [8, 2]], 77/248832],
[[[1, 6], [2, 5], [3, 2], [6, 2], [9, 1]], 1/3888],
[[[1, 6], [2, 5], [3, 2], [6, 2], [18, 1]], 7/82944],
[[[1, 6], [2, 5], [3, 2], [6, 3], [8, 1]], 53/124416],
[[[1, 6], [2, 5], [3, 2], [6, 3], [10, 1]], 1/12960],
[[[1, 6], [2, 5], [3, 2], [6, 3], [12, 1]], 5/36864],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 3]], 257/124416],
[[[1, 6], [2, 5], [3, 3], [4, 2], [6, 2]], 329/497664],
[[[1, 6], [2, 5], [3, 3], [4, 2], [8, 1]], 25/110592],
[[[1, 6], [2, 5], [3, 3], [4, 2], [10, 1]], 1/17280],
[[[1, 6], [2, 5], [3, 3], [4, 2], [12, 1]], 1/62208],
[[[1, 6], [2, 5], [3, 3], [4, 3], [6, 1]], 97/331776],
[[[1, 6], [2, 5], [3, 3], [6, 1], [9, 1]], 19/124416],
[[[1, 6], [2, 5], [3, 3], [6, 2], [8, 1]], 1/2592],
[[[1, 6], [2, 5], [3, 3], [6, 2], [10, 1]], 1/6480],
[[[1, 6], [2, 5], [3, 3], [6, 2], [12, 1]], 7/27648],
[[[1, 6], [2, 5], [3, 4], [4, 1], [6, 2]], 4165/2985984],
[[[1, 6], [2, 5], [3, 4], [4, 1], [8, 1]], 1/165888],
[[[1, 6], [2, 5], [3, 4], [4, 2], [6, 1]], 145/5971968],
[[[1, 6], [2, 5], [3, 4], [6, 1], [8, 1]], 1/41472],
[[[1, 6], [2, 5], [3, 4], [6, 1], [10, 1]], 1/7776],
[[[1, 6], [2, 5], [3, 4], [6, 1], [12, 1]], 19/331776],
[[[1, 6], [2, 5], [3, 5], [4, 1], [6, 1]], 49/248832],
[[[1, 6], [2, 5], [4, 1], [5, 1], [8, 2]], 11/49152],
[[[1, 6], [2, 5], [4, 1], [6, 2], [8, 2]], 97/442368],
[[[1, 6], [2, 5], [4, 1], [6, 4], [8, 1]], 1/82944],
[[[1, 6], [2, 5], [4, 1], [8, 2], [10, 1]], 79/368640],
[[[1, 6], [2, 5], [4, 2], [6, 1], [8, 2]], 2297/4423680],
[[[1, 6], [2, 5], [4, 2], [6, 3], [8, 1]], 5/110592],
[[[1, 6], [2, 5], [4, 2], [6, 3], [12, 1]], 1/186624],
[[[1, 6], [2, 5], [4, 3], [5, 1], [6, 2]], 1/7680],
[[[1, 6], [2, 5], [4, 3], [5, 1], [8, 1]], 401/327680],
[[[1, 6], [2, 5], [4, 3], [5, 1], [12, 1]], 23/92160],
[[[1, 6], [2, 5], [4, 3], [6, 2], [8, 1]], 97/294912],
[[[1, 6], [2, 5], [4, 3], [6, 2], [12, 1]], 13/165888],
[[[1, 6], [2, 5], [4, 3], [8, 1], [10, 1]], 17/81920],
[[[1, 6], [2, 5], [4, 3], [8, 1], [12, 1]], 1/12288],
[[[1, 6], [2, 5], [4, 3], [10, 1], [12, 1]], 1/46080],
[[[1, 6], [2, 5], [4, 4], [5, 1], [6, 1]], 23/184320],
[[[1, 6], [2, 5], [4, 4], [6, 1], [8, 1]], 61/147456],
[[[1, 6], [2, 5], [4, 4], [6, 1], [10, 1]], 49/2949120],
[[[1, 6], [2, 5], [4, 4], [6, 1], [12, 1]], 19/110592],
[[[1, 6], [2, 5], [5, 1], [6, 1], [8, 2]], 1/30720],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 4]], 91/497664],
[[[1, 6], [2, 7], [3, 1], [4, 1], [8, 2]], 299/829440],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 3]], 1691/1990656],
[[[1, 6], [2, 7], [3, 1], [4, 3], [5, 1]], 743/8847360],
[[[1, 6], [2, 7], [3, 1], [4, 3], [6, 2]], 21863/10616832],
[[[1, 6], [2, 7], [3, 1], [4, 3], [8, 1]], 11029/8847360],
[[[1, 6], [2, 7], [3, 1], [4, 3], [10, 1]], 23/61440],
[[[1, 6], [2, 7], [3, 1], [4, 3], [12, 1]], 19/124416],
[[[1, 6], [2, 7], [3, 1], [4, 4], [6, 1]], 104711/56623104],
[[[1, 6], [2, 7], [3, 1], [5, 1], [6, 3]], 1/3456],
[[[1, 6], [2, 7], [3, 1], [6, 1], [8, 2]], 14023/53084160],
[[[1, 6], [2, 7], [3, 1], [6, 3], [8, 1]], 1/4608],
[[[1, 6], [2, 7], [3, 1], [6, 3], [10, 1]], 11/373248],
[[[1, 6], [2, 7], [3, 2], [4, 1], [6, 3]], 1517/746496],
[[[1, 6], [2, 7], [3, 2], [4, 2], [5, 1]], 1/46080],
[[[1, 6], [2, 7], [3, 2], [4, 2], [6, 2]], 2215/884736],
[[[1, 6], [2, 7], [3, 2], [4, 2], [8, 1]], 3467/6635520],
[[[1, 6], [2, 7], [3, 2], [4, 2], [10, 1]], 101/552960],
[[[1, 6], [2, 7], [3, 2], [4, 2], [12, 1]], 587/14929920],
[[[1, 6], [2, 7], [3, 2], [4, 3], [6, 1]], 481/589824],
[[[1, 6], [2, 7], [3, 2], [5, 1], [6, 2]], 1/4320],
[[[1, 6], [2, 7], [3, 2], [6, 2], [8, 1]], 227/331776],
[[[1, 6], [2, 7], [3, 2], [6, 2], [10, 1]], 1/3840],
[[[1, 6], [2, 7], [3, 3], [4, 1], [6, 2]], 95/124416],
[[[1, 6], [2, 7], [3, 3], [4, 1], [8, 1]], 7/62208],
[[[1, 6], [2, 7], [3, 3], [4, 2], [6, 1]], 6187/15925248],
[[[1, 6], [2, 7], [3, 3], [5, 1], [6, 1]], 1/17280],
[[[1, 6], [2, 7], [3, 3], [6, 1], [8, 1]], 7/31104],
[[[1, 6], [2, 7], [3, 3], [6, 1], [10, 1]], 11/103680],
[[[1, 6], [2, 7], [3, 4], [4, 1], [6, 1]], 157/2985984],
[[[1, 6], [2, 7], [4, 1], [5, 1], [6, 3]], 1/12960],
[[[1, 6], [2, 7], [4, 1], [6, 1], [8, 2]], 251/491520],
[[[1, 6], [2, 7], [4, 1], [6, 3], [8, 1]], 5/41472],
[[[1, 6], [2, 7], [4, 2], [5, 1], [6, 2]], 7/30720],
[[[1, 6], [2, 7], [4, 2], [5, 1], [8, 1]], 127/368640],
[[[1, 6], [2, 7], [4, 2], [5, 1], [12, 1]], 1/30720],
[[[1, 6], [2, 7], [4, 2], [6, 2], [8, 1]], 2003/1769472],
[[[1, 6], [2, 7], [4, 2], [6, 2], [10, 1]], 257/4423680],
[[[1, 6], [2, 7], [4, 2], [6, 2], [12, 1]], 239/3981312],
[[[1, 6], [2, 7], [4, 2], [8, 1], [10, 1]], 467/491520],
[[[1, 6], [2, 7], [4, 2], [10, 1], [12, 1]], 7/122880],
[[[1, 6], [2, 7], [4, 3], [5, 1], [6, 1]], 373/1474560],
[[[1, 6], [2, 7], [4, 3], [6, 1], [8, 1]], 6287/2211840],
[[[1, 6], [2, 7], [4, 3], [6, 1], [10, 1]], 239/1474560],
[[[1, 6], [2, 7], [4, 3], [6, 1], [12, 1]], 143/331776],
[[[1, 6], [2, 7], [5, 1], [6, 2], [8, 1]], 1/34560],
[[[1, 6], [2, 9], [3, 1], [4, 1], [6, 3]], 41959/31850496],
[[[1, 6], [2, 9], [3, 1], [4, 2], [5, 1]], 161/2949120],
[[[1, 6], [2, 9], [3, 1], [4, 2], [6, 2]], 26023/10616832],
[[[1, 6], [2, 9], [3, 1], [4, 2], [8, 1]], 3283/6635520],
[[[1, 6], [2, 9], [3, 1], [4, 2], [10, 1]], 179/1105920],
[[[1, 6], [2, 9], [3, 1], [4, 2], [12, 1]], 89/3317760],
[[[1, 6], [2, 9], [3, 1], [4, 3], [6, 1]], 945731/637009920],
[[[1, 6], [2, 9], [3, 1], [5, 1], [6, 2]], 1/13824],
[[[1, 6], [2, 9], [3, 1], [5, 1], [8, 1]], 1/276480],
[[[1, 6], [2, 9], [3, 1], [6, 2], [8, 1]], 37/276480],
[[[1, 6], [2, 9], [3, 1], [6, 2], [10, 1]], 559/4976640],
[[[1, 6], [2, 9], [3, 2], [4, 1], [5, 1]], 77/10616832],
[[[1, 6], [2, 9], [3, 2], [4, 1], [6, 2]], 3307/2488320],
[[[1, 6], [2, 9], [3, 2], [4, 1], [8, 1]], 517/5898240],
[[[1, 6], [2, 9], [3, 2], [4, 1], [10, 1]], 1/276480],
[[[1, 6], [2, 9], [3, 2], [4, 2], [6, 1]], 26561/42467328],
[[[1, 6], [2, 9], [3, 2], [5, 1], [6, 1]], 1/34560],
[[[1, 6], [2, 9], [3, 2], [6, 1], [8, 1]], 41/414720],
[[[1, 6], [2, 9], [3, 2], [6, 1], [10, 1]], 13/276480],
[[[1, 6], [2, 9], [3, 3], [4, 1], [6, 1]], 803/4423680],
[[[1, 6], [2, 9], [4, 1], [5, 1], [6, 2]], 43/1105920],
[[[1, 6], [2, 9], [4, 1], [5, 1], [8, 1]], 731/8847360],
[[[1, 6], [2, 9], [4, 1], [6, 2], [8, 1]], 2681/8847360],
[[[1, 6], [2, 9], [4, 1], [6, 2], [10, 1]], 89/2211840],
[[[1, 6], [2, 9], [4, 1], [8, 1], [10, 1]], 239/1474560],
[[[1, 6], [2, 9], [4, 2], [5, 1], [6, 1]], 191/1474560],
[[[1, 6], [2, 9], [4, 2], [6, 1], [8, 1]], 299/147456],
[[[1, 6], [2, 9], [4, 2], [6, 1], [10, 1]], 12367/35389440],
[[[1, 6], [2, 9], [4, 2], [6, 1], [12, 1]], 103/995328],
[[[1, 6], [2, 9], [5, 1], [6, 1], [8, 1]], 1/138240],
[[[1, 6], [2, 11], [3, 1], [4, 1], [5, 1]], 193/70778880],
[[[1, 6], [2, 11], [3, 1], [4, 1], [6, 2]], 168439/212336640],
[[[1, 6], [2, 11], [3, 1], [4, 1], [8, 1]], 643/26542080],
[[[1, 6], [2, 11], [3, 1], [4, 1], [10, 1]], 43/1105920],
[[[1, 6], [2, 11], [3, 1], [4, 2], [6, 1]], 5539429/10192158720],
[[[1, 6], [2, 11], [3, 1], [5, 1], [6, 1]], 1/221184],
[[[1, 6], [2, 11], [3, 1], [6, 1], [8, 1]], 79/6635520],
[[[1, 6], [2, 11], [3, 1], [6, 1], [10, 1]], 287/4976640],
[[[1, 6], [2, 11], [3, 2], [4, 1], [6, 1]], 4111/42467328],
[[[1, 6], [2, 11], [4, 1], [5, 1], [6, 1]], 11/1966080],
[[[1, 6], [2, 11], [4, 1], [6, 1], [8, 1]], 691/6635520],
[[[1, 6], [2, 11], [4, 1], [6, 1], [10, 1]], 2371/17694720],
[[[1, 6], [2, 13], [3, 1], [4, 1], [6, 1]], 2205647/20384317440],
[[[1, 7], [2, 2], [3, 1], [4, 1], [8, 3]], 1/18432],
[[[1, 7], [2, 2], [3, 1], [4, 3], [8, 2]], 1/16384],
[[[1, 7], [2, 2], [3, 1], [4, 5], [5, 1]], 1/245760],
[[[1, 7], [2, 2], [3, 1], [4, 5], [8, 1]], 1/221184],
[[[1, 7], [2, 2], [3, 1], [4, 5], [12, 1]], 1/55296],
[[[1, 7], [2, 2], [3, 1], [4, 6], [6, 1]], 1/1327104],
[[[1, 7], [2, 2], [3, 2], [4, 2], [8, 2]], 79/294912],
[[[1, 7], [2, 2], [3, 2], [4, 2], [12, 2]], 1/138240],
[[[1, 7], [2, 2], [3, 2], [4, 4], [5, 1]], 11/245760],
[[[1, 7], [2, 2], [3, 2], [4, 4], [8, 1]], 11/196608],
[[[1, 7], [2, 2], [3, 2], [4, 4], [12, 1]], 7/110592],
[[[1, 7], [2, 2], [3, 2], [4, 5], [6, 1]], 1/1769472],
[[[1, 7], [2, 2], [3, 2], [6, 2], [8, 2]], 1/55296],
[[[1, 7], [2, 2], [3, 2], [6, 2], [12, 2]], 1/1105920],
[[[1, 7], [2, 2], [3, 2], [6, 3], [9, 1]], 23/1866240],
[[[1, 7], [2, 2], [3, 2], [6, 4], [12, 1]], 1/3317760],
[[[1, 7], [2, 2], [3, 3], [4, 4], [6, 1]], 29/3981312],
[[[1, 7], [2, 2], [3, 3], [6, 1], [8, 2]], 5/82944],
[[[1, 7], [2, 2], [3, 3], [6, 1], [12, 2]], 17/552960],
[[[1, 7], [2, 2], [3, 3], [6, 1], [24, 1]], 1/46080],
[[[1, 7], [2, 2], [3, 3], [6, 2], [9, 1]], 5/41472],
[[[1, 7], [2, 2], [3, 3], [6, 3], [12, 1]], 1/110592],
[[[1, 7], [2, 2], [3, 3], [9, 1], [12, 1]], 1/6912],
[[[1, 7], [2, 2], [3, 4], [4, 1], [6, 3]], 1/36864],
[[[1, 7], [2, 2], [3, 4], [4, 1], [9, 1]], 7/41472],
[[[1, 7], [2, 2], [3, 4], [4, 2], [6, 2]], 1/9216],
[[[1, 7], [2, 2], [3, 4], [4, 3], [6, 1]], 1/41472],
[[[1, 7], [2, 2], [3, 4], [5, 1], [6, 2]], 1/4320],
[[[1, 7], [2, 2], [3, 4], [6, 1], [9, 1]], 29/69120],
[[[1, 7], [2, 2], [3, 4], [6, 2], [12, 1]], 1/5760],
[[[1, 7], [2, 2], [3, 5], [4, 1], [6, 2]], 1/82944],
[[[1, 7], [2, 2], [3, 5], [4, 1], [12, 1]], 1/13824],
[[[1, 7], [2, 2], [3, 5], [4, 2], [6, 1]], 1/559872],
[[[1, 7], [2, 2], [3, 5], [5, 1], [6, 1]], 7/25920],
[[[1, 7], [2, 2], [3, 5], [6, 1], [12, 1]], 377/995328],
[[[1, 7], [2, 2], [3, 6], [4, 1], [6, 1]], 1/36864],
[[[1, 7], [2, 2], [4, 2], [5, 1], [8, 2]], 29/245760],
[[[1, 7], [2, 2], [4, 2], [6, 2], [8, 2]], 1/442368],
[[[1, 7], [2, 2], [4, 2], [8, 2], [10, 1]], 1/122880],
[[[1, 7], [2, 2], [4, 4], [5, 1], [8, 1]], 7/98304],
[[[1, 7], [2, 2], [4, 4], [5, 1], [12, 1]], 1/18432],
[[[1, 7], [2, 2], [4, 4], [8, 1], [12, 1]], 1/34560],
[[[1, 7], [2, 4], [3, 1], [4, 2], [8, 2]], 1297/884736],
[[[1, 7], [2, 4], [3, 1], [4, 3], [6, 3]], 11/1327104],
[[[1, 7], [2, 4], [3, 1], [4, 4], [5, 1]], 6557/17694720],
[[[1, 7], [2, 4], [3, 1], [4, 4], [6, 2]], 331/10616832],
[[[1, 7], [2, 4], [3, 1], [4, 4], [8, 1]], 31/36864],
[[[1, 7], [2, 4], [3, 1], [4, 4], [10, 1]], 19/1105920],
[[[1, 7], [2, 4], [3, 1], [4, 4], [12, 1]], 181/331776],
[[[1, 7], [2, 4], [3, 1], [4, 5], [6, 1]], 461/5308416],
[[[1, 7], [2, 4], [3, 1], [5, 1], [8, 2]], 1/46080],
[[[1, 7], [2, 4], [3, 1], [6, 2], [8, 2]], 47/1658880],
[[[1, 7], [2, 4], [3, 1], [6, 4], [8, 1]], 1/124416],
[[[1, 7], [2, 4], [3, 1], [8, 2], [10, 1]], 1/92160],
[[[1, 7], [2, 4], [3, 2], [4, 1], [6, 4]], 1/62208],
[[[1, 7], [2, 4], [3, 2], [4, 1], [8, 2]], 47/221184],
[[[1, 7], [2, 4], [3, 2], [4, 2], [6, 3]], 1/13824],
[[[1, 7], [2, 4], [3, 2], [4, 3], [5, 1]], 1/184320],
[[[1, 7], [2, 4], [3, 2], [4, 3], [6, 2]], 157/1327104],
[[[1, 7], [2, 4], [3, 2], [4, 3], [8, 1]], 521/589824],
[[[1, 7], [2, 4], [3, 2], [4, 3], [10, 1]], 1/30720],
[[[1, 7], [2, 4], [3, 2], [4, 3], [12, 1]], 77/165888],
[[[1, 7], [2, 4], [3, 2], [4, 4], [6, 1]], 1259/3981312],
[[[1, 7], [2, 4], [3, 2], [6, 1], [8, 2]], 365/1327104],
[[[1, 7], [2, 4], [3, 2], [6, 2], [9, 1]], 169/933120],
[[[1, 7], [2, 4], [3, 2], [6, 2], [18, 1]], 1/138240],
[[[1, 7], [2, 4], [3, 2], [6, 3], [8, 1]], 5/31104],
[[[1, 7], [2, 4], [3, 2], [6, 3], [12, 1]], 23/829440],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 3]], 457/622080],
[[[1, 7], [2, 4], [3, 3], [4, 2], [5, 1]], 1/4976640],
[[[1, 7], [2, 4], [3, 3], [4, 2], [6, 2]], 67/331776],
[[[1, 7], [2, 4], [3, 3], [4, 2], [8, 1]], 253/663552],
[[[1, 7], [2, 4], [3, 3], [4, 2], [12, 1]], 1/46656],
[[[1, 7], [2, 4], [3, 3], [4, 3], [6, 1]], 1801/3981312],
[[[1, 7], [2, 4], [3, 3], [5, 1], [6, 2]], 11/23328],
[[[1, 7], [2, 4], [3, 3], [6, 1], [9, 1]], 1/3456],
[[[1, 7], [2, 4], [3, 3], [6, 2], [8, 1]], 1/3456],
[[[1, 7], [2, 4], [3, 3], [6, 2], [12, 1]], 1/4096],
[[[1, 7], [2, 4], [3, 4], [4, 1], [6, 2]], 943/995328],
[[[1, 7], [2, 4], [3, 4], [4, 2], [6, 1]], 1/4608],
[[[1, 7], [2, 4], [3, 4], [6, 1], [12, 1]], 11/55296],
[[[1, 7], [2, 4], [3, 5], [4, 1], [6, 1]], 29/82944],
[[[1, 7], [2, 4], [4, 1], [5, 1], [8, 2]], 1/7680],
[[[1, 7], [2, 4], [4, 1], [6, 2], [8, 2]], 997/26542080],
[[[1, 7], [2, 4], [4, 1], [6, 4], [8, 1]], 1/497664],
[[[1, 7], [2, 4], [4, 1], [8, 2], [10, 1]], 73/1474560],
[[[1, 7], [2, 4], [4, 2], [6, 1], [8, 2]], 931/4423680],
[[[1, 7], [2, 4], [4, 2], [6, 3], [8, 1]], 5/331776],
[[[1, 7], [2, 4], [4, 2], [6, 3], [12, 1]], 1/2799360],
[[[1, 7], [2, 4], [4, 3], [5, 1], [8, 1]], 347/491520],
[[[1, 7], [2, 4], [4, 3], [5, 1], [12, 1]], 1/3072],
[[[1, 7], [2, 4], [4, 3], [6, 2], [8, 1]], 23/1179648],
[[[1, 7], [2, 4], [4, 3], [6, 2], [12, 1]], 25/1990656],
[[[1, 7], [2, 4], [4, 3], [8, 1], [10, 1]], 23/327680],
[[[1, 7], [2, 4], [4, 3], [8, 1], [12, 1]], 11/110592],
[[[1, 7], [2, 4], [4, 3], [10, 1], [12, 1]], 1/552960],
[[[1, 7], [2, 4], [4, 4], [5, 1], [6, 1]], 17/163840],
[[[1, 7], [2, 4], [4, 4], [6, 1], [8, 1]], 17/98304],
[[[1, 7], [2, 4], [4, 4], [6, 1], [12, 1]], 1/12288],
[[[1, 7], [2, 4], [5, 1], [6, 1], [8, 2]], 1/122880],
[[[1, 7], [2, 6], [3, 1], [4, 1], [6, 4]], 157/2985984],
[[[1, 7], [2, 6], [3, 1], [4, 1], [8, 2]], 251/491520],
[[[1, 7], [2, 6], [3, 1], [4, 2], [6, 3]], 6187/15925248],
[[[1, 7], [2, 6], [3, 1], [4, 3], [5, 1]], 239/1474560],
[[[1, 7], [2, 6], [3, 1], [4, 3], [6, 2]], 481/589824],
[[[1, 7], [2, 6], [3, 1], [4, 3], [8, 1]], 6287/2211840],
[[[1, 7], [2, 6], [3, 1], [4, 3], [10, 1]], 373/1474560],
[[[1, 7], [2, 6], [3, 1], [4, 3], [12, 1]], 143/331776],
[[[1, 7], [2, 6], [3, 1], [4, 4], [6, 1]], 104711/56623104],
[[[1, 7], [2, 6], [3, 1], [5, 1], [6, 3]], 11/103680],
[[[1, 7], [2, 6], [3, 1], [6, 1], [8, 2]], 14023/53084160],
[[[1, 7], [2, 6], [3, 1], [6, 3], [8, 1]], 7/31104],
[[[1, 7], [2, 6], [3, 1], [6, 3], [10, 1]], 1/17280],
[[[1, 7], [2, 6], [3, 2], [4, 1], [6, 3]], 95/124416],
[[[1, 7], [2, 6], [3, 2], [4, 2], [5, 1]], 257/4423680],
[[[1, 7], [2, 6], [3, 2], [4, 2], [6, 2]], 2215/884736],
[[[1, 7], [2, 6], [3, 2], [4, 2], [8, 1]], 2003/1769472],
[[[1, 7], [2, 6], [3, 2], [4, 2], [10, 1]], 7/30720],
[[[1, 7], [2, 6], [3, 2], [4, 2], [12, 1]], 239/3981312],
[[[1, 7], [2, 6], [3, 2], [4, 3], [6, 1]], 21863/10616832],
[[[1, 7], [2, 6], [3, 2], [5, 1], [6, 2]], 1/3840],
[[[1, 7], [2, 6], [3, 2], [6, 2], [8, 1]], 227/331776],
[[[1, 7], [2, 6], [3, 2], [6, 2], [10, 1]], 1/4320],
[[[1, 7], [2, 6], [3, 2], [8, 1], [10, 1]], 1/34560],
[[[1, 7], [2, 6], [3, 3], [4, 1], [6, 2]], 1517/746496],
[[[1, 7], [2, 6], [3, 3], [4, 1], [8, 1]], 5/41472],
[[[1, 7], [2, 6], [3, 3], [4, 1], [10, 1]], 1/12960],
[[[1, 7], [2, 6], [3, 3], [4, 2], [6, 1]], 1691/1990656],
[[[1, 7], [2, 6], [3, 3], [5, 1], [6, 1]], 11/373248],
[[[1, 7], [2, 6], [3, 3], [6, 1], [8, 1]], 1/4608],
[[[1, 7], [2, 6], [3, 3], [6, 1], [10, 1]], 1/3456],
[[[1, 7], [2, 6], [3, 4], [4, 1], [6, 1]], 91/497664],
[[[1, 7], [2, 6], [4, 1], [6, 1], [8, 2]], 299/829440],
[[[1, 7], [2, 6], [4, 1], [6, 3], [8, 1]], 7/62208],
[[[1, 7], [2, 6], [4, 2], [5, 1], [6, 2]], 101/552960],
[[[1, 7], [2, 6], [4, 2], [5, 1], [8, 1]], 467/491520],
[[[1, 7], [2, 6], [4, 2], [5, 1], [12, 1]], 7/122880],
[[[1, 7], [2, 6], [4, 2], [6, 2], [8, 1]], 3467/6635520],
[[[1, 7], [2, 6], [4, 2], [6, 2], [10, 1]], 1/46080],
[[[1, 7], [2, 6], [4, 2], [6, 2], [12, 1]], 587/14929920],
[[[1, 7], [2, 6], [4, 2], [8, 1], [10, 1]], 127/368640],
[[[1, 7], [2, 6], [4, 2], [10, 1], [12, 1]], 1/30720],
[[[1, 7], [2, 6], [4, 3], [5, 1], [6, 1]], 23/61440],
[[[1, 7], [2, 6], [4, 3], [6, 1], [8, 1]], 11029/8847360],
[[[1, 7], [2, 6], [4, 3], [6, 1], [10, 1]], 743/8847360],
[[[1, 7], [2, 6], [4, 3], [6, 1], [12, 1]], 19/124416],
[[[1, 7], [2, 8], [3, 1], [4, 1], [6, 3]], 7139/7962624],
[[[1, 7], [2, 8], [3, 1], [4, 2], [5, 1]], 1021/7077888],
[[[1, 7], [2, 8], [3, 1], [4, 2], [6, 2]], 644011/212336640],
[[[1, 7], [2, 8], [3, 1], [4, 2], [8, 1]], 893/737280],
[[[1, 7], [2, 8], [3, 1], [4, 2], [10, 1]], 589/1474560],
[[[1, 7], [2, 8], [3, 1], [4, 2], [12, 1]], 13/184320],
[[[1, 7], [2, 8], [3, 1], [4, 3], [6, 1]], 986357/283115520],
[[[1, 7], [2, 8], [3, 1], [5, 1], [6, 2]], 221/829440],
[[[1, 7], [2, 8], [3, 1], [5, 1], [8, 1]], 1/46080],
[[[1, 7], [2, 8], [3, 1], [6, 2], [8, 1]], 23/69120],
[[[1, 7], [2, 8], [3, 1], [6, 2], [10, 1]], 11/165888],
[[[1, 7], [2, 8], [3, 1], [8, 1], [10, 1]], 1/69120],
[[[1, 7], [2, 8], [3, 2], [4, 1], [5, 1]], 97/2211840],
[[[1, 7], [2, 8], [3, 2], [4, 1], [6, 2]], 1067/368640],
[[[1, 7], [2, 8], [3, 2], [4, 1], [8, 1]], 1657/4423680],
[[[1, 7], [2, 8], [3, 2], [4, 1], [10, 1]], 49/552960],
[[[1, 7], [2, 8], [3, 2], [4, 2], [6, 1]], 84401/53084160],
[[[1, 7], [2, 8], [3, 2], [5, 1], [6, 1]], 59/552960],
[[[1, 7], [2, 8], [3, 2], [6, 1], [8, 1]], 539/1658880],
[[[1, 7], [2, 8], [3, 2], [6, 1], [10, 1]], 1/5760],
[[[1, 7], [2, 8], [3, 3], [4, 1], [6, 1]], 127261/238878720],
[[[1, 7], [2, 8], [4, 1], [5, 1], [6, 2]], 11/55296],
[[[1, 7], [2, 8], [4, 1], [5, 1], [8, 1]], 35/147456],
[[[1, 7], [2, 8], [4, 1], [6, 2], [8, 1]], 913/1966080],
[[[1, 7], [2, 8], [4, 1], [6, 2], [10, 1]], 17/491520],
[[[1, 7], [2, 8], [4, 1], [8, 1], [10, 1]], 2221/8847360],
[[[1, 7], [2, 8], [4, 2], [5, 1], [6, 1]], 1483/4423680],
[[[1, 7], [2, 8], [4, 2], [6, 1], [8, 1]], 28411/13271040],
[[[1, 7], [2, 8], [4, 2], [6, 1], [10, 1]], 601/2949120],
[[[1, 7], [2, 8], [4, 2], [6, 1], [12, 1]], 3173/29859840],
[[[1, 7], [2, 8], [5, 1], [6, 1], [8, 1]], 1/23040],
[[[1, 7], [2, 8], [6, 1], [8, 1], [10, 1]], 1/92160],
[[[1, 7], [2, 10], [3, 1], [4, 1], [5, 1]], 1037/35389440],
[[[1, 7], [2, 10], [3, 1], [4, 1], [6, 2]], 524027/318504960],
[[[1, 7], [2, 10], [3, 1], [4, 1], [8, 1]], 3629/19906560],
[[[1, 7], [2, 10], [3, 1], [4, 1], [10, 1]], 1973/26542080],
[[[1, 7], [2, 10], [3, 1], [4, 2], [6, 1]], 1004927/566231040],
[[[1, 7], [2, 10], [3, 1], [5, 1], [6, 1]], 449/13271040],
[[[1, 7], [2, 10], [3, 1], [6, 1], [8, 1]], 1409/19906560],
[[[1, 7], [2, 10], [3, 1], [6, 1], [10, 1]], 379/3317760],
[[[1, 7], [2, 10], [3, 2], [4, 1], [6, 1]], 618481/1274019840],
[[[1, 7], [2, 10], [4, 1], [5, 1], [6, 1]], 67/1105920],
[[[1, 7], [2, 10], [4, 1], [6, 1], [8, 1]], 32627/79626240],
[[[1, 7], [2, 10], [4, 1], [6, 1], [10, 1]], 271/2359296],
[[[1, 7], [2, 12], [3, 1], [4, 1], [6, 1]], 2098573/6115295232],
[[[1, 7], [3, 2], [6, 2], [9, 1], [12, 1]], 1/1244160],
[[[1, 8], [2, 1], [3, 1], [4, 1], [8, 3]], 1/184320],
[[[1, 8], [2, 1], [3, 1], [4, 3], [8, 2]], 1/442368],
[[[1, 8], [2, 1], [3, 1], [4, 5], [5, 1]], 1/1474560],
[[[1, 8], [2, 1], [3, 1], [4, 5], [8, 1]], 1/2211840],
[[[1, 8], [2, 1], [3, 1], [4, 5], [12, 1]], 1/165888],
[[[1, 8], [2, 1], [3, 2], [4, 4], [5, 1]], 1/368640],
[[[1, 8], [2, 1], [3, 2], [6, 3], [9, 1]], 1/1244160],
[[[1, 8], [2, 1], [3, 3], [4, 3], [5, 1]], 1/34560],
[[[1, 8], [2, 1], [3, 3], [4, 4], [6, 1]], 1/2654208],
[[[1, 8], [2, 1], [3, 3], [6, 1], [12, 2]], 1/552960],
[[[1, 8], [2, 1], [3, 3], [6, 2], [9, 1]], 1/207360],
[[[1, 8], [2, 1], [3, 3], [6, 3], [12, 1]], 1/1658880],
[[[1, 8], [2, 1], [3, 3], [9, 1], [12, 1]], 1/34560],
[[[1, 8], [2, 1], [3, 4], [4, 1], [9, 1]], 1/41472],
[[[1, 8], [2, 1], [3, 4], [6, 1], [9, 1]], 1/15360],
[[[1, 8], [2, 1], [3, 4], [6, 2], [12, 1]], 1/663552],
[[[1, 8], [2, 1], [3, 5], [4, 1], [6, 2]], 1/331776],
[[[1, 8], [2, 1], [3, 5], [4, 1], [12, 1]], 1/55296],
[[[1, 8], [2, 1], [3, 5], [4, 2], [6, 1]], 1/186624],
[[[1, 8], [2, 1], [3, 5], [5, 1], [6, 1]], 1/17280],
[[[1, 8], [2, 1], [3, 5], [6, 1], [12, 1]], 121/1658880],
[[[1, 8], [2, 3], [3, 1], [4, 2], [8, 2]], 613/1474560],
[[[1, 8], [2, 3], [3, 1], [4, 4], [5, 1]], 31/491520],
[[[1, 8], [2, 3], [3, 1], [4, 4], [6, 2]], 55/47775744],
[[[1, 8], [2, 3], [3, 1], [4, 4], [8, 1]], 47/294912],
[[[1, 8], [2, 3], [3, 1], [4, 4], [10, 1]], 11/2654208],
[[[1, 8], [2, 3], [3, 1], [4, 4], [12, 1]], 13/110592],
[[[1, 8], [2, 3], [3, 1], [4, 5], [6, 1]], 997/70778880],
[[[1, 8], [2, 3], [3, 1], [6, 2], [8, 2]], 1/3981312],
[[[1, 8], [2, 3], [3, 1], [8, 2], [10, 1]], 1/1105920],
[[[1, 8], [2, 3], [3, 2], [4, 1], [8, 2]], 83/1769472],
[[[1, 8], [2, 3], [3, 2], [4, 2], [6, 3]], 1/331776],
[[[1, 8], [2, 3], [3, 2], [4, 3], [5, 1]], 223/1105920],
[[[1, 8], [2, 3], [3, 2], [4, 3], [6, 2]], 11/442368],
[[[1, 8], [2, 3], [3, 2], [4, 3], [8, 1]], 95/393216],
[[[1, 8], [2, 3], [3, 2], [4, 3], [12, 1]], 83/663552],
[[[1, 8], [2, 3], [3, 2], [4, 4], [6, 1]], 1/32768],
[[[1, 8], [2, 3], [3, 2], [6, 1], [8, 2]], 1/12288],
[[[1, 8], [2, 3], [3, 2], [6, 2], [9, 1]], 47/1244160],
[[[1, 8], [2, 3], [3, 2], [6, 3], [8, 1]], 1/41472],
[[[1, 8], [2, 3], [3, 2], [6, 3], [12, 1]], 1/552960],
[[[1, 8], [2, 3], [3, 3], [4, 1], [6, 3]], 1/20736],
[[[1, 8], [2, 3], [3, 3], [4, 2], [5, 1]], 1/414720],
[[[1, 8], [2, 3], [3, 3], [4, 2], [6, 2]], 19/497664],
[[[1, 8], [2, 3], [3, 3], [4, 3], [6, 1]], 197/1327104],
[[[1, 8], [2, 3], [3, 3], [6, 1], [9, 1]], 1/6480],
[[[1, 8], [2, 3], [3, 3], [6, 2], [8, 1]], 1/20736],
[[[1, 8], [2, 3], [3, 3], [6, 2], [12, 1]], 11/165888],
[[[1, 8], [2, 3], [3, 4], [4, 1], [6, 2]], 431/1658880],
[[[1, 8], [2, 3], [3, 4], [4, 2], [6, 1]], 415/2985984],
[[[1, 8], [2, 3], [3, 4], [6, 1], [12, 1]], 23/165888],
[[[1, 8], [2, 3], [3, 5], [4, 1], [6, 1]], 169/746496],
[[[1, 8], [2, 3], [4, 1], [5, 1], [8, 2]], 11/491520],
[[[1, 8], [2, 3], [4, 1], [6, 2], [8, 2]], 7/6635520],
[[[1, 8], [2, 3], [4, 1], [8, 2], [10, 1]], 1/368640],
[[[1, 8], [2, 3], [4, 2], [6, 1], [8, 2]], 37/1474560],
[[[1, 8], [2, 3], [4, 2], [6, 3], [8, 1]], 1/663552],
[[[1, 8], [2, 3], [4, 3], [5, 1], [8, 1]], 151/983040],
[[[1, 8], [2, 3], [4, 3], [5, 1], [12, 1]], 11/184320],
[[[1, 8], [2, 3], [4, 3], [6, 2], [8, 1]], 7/1769472],
[[[1, 8], [2, 3], [4, 3], [6, 2], [12, 1]], 1/1244160],
[[[1, 8], [2, 3], [4, 3], [8, 1], [10, 1]], 7/491520],
[[[1, 8], [2, 3], [4, 3], [8, 1], [12, 1]], 23/552960],
[[[1, 8], [2, 3], [4, 4], [6, 1], [12, 1]], 1/110592],
[[[1, 8], [2, 5], [3, 1], [4, 1], [6, 4]], 1/62208],
[[[1, 8], [2, 5], [3, 1], [4, 1], [8, 2]], 1469/4423680],
[[[1, 8], [2, 5], [3, 1], [4, 2], [6, 3]], 385/7962624],
[[[1, 8], [2, 5], [3, 1], [4, 3], [5, 1]], 4327/8847360],
[[[1, 8], [2, 5], [3, 1], [4, 3], [6, 2]], 3095/10616832],
[[[1, 8], [2, 5], [3, 1], [4, 3], [8, 1]], 19277/8847360],
[[[1, 8], [2, 5], [3, 1], [4, 3], [10, 1]], 11/122880],
[[[1, 8], [2, 5], [3, 1], [4, 3], [12, 1]], 7/12288],
[[[1, 8], [2, 5], [3, 1], [4, 4], [6, 1]], 810995/1528823808],
[[[1, 8], [2, 5], [3, 1], [6, 1], [8, 2]], 20659/159252480],
[[[1, 8], [2, 5], [3, 1], [6, 3], [8, 1]], 47/1244160],
[[[1, 8], [2, 5], [3, 1], [6, 3], [10, 1]], 1/103680],
[[[1, 8], [2, 5], [3, 2], [4, 1], [6, 3]], 349/995328],
[[[1, 8], [2, 5], [3, 2], [4, 2], [5, 1]], 103/2211840],
[[[1, 8], [2, 5], [3, 2], [4, 2], [6, 2]], 1811/2654208],
[[[1, 8], [2, 5], [3, 2], [4, 2], [8, 1]], 19/12288],
[[[1, 8], [2, 5], [3, 2], [4, 2], [10, 1]], 13/184320],
[[[1, 8], [2, 5], [3, 2], [4, 2], [12, 1]], 55/663552],
[[[1, 8], [2, 5], [3, 2], [4, 3], [6, 1]], 3745/2654208],
[[[1, 8], [2, 5], [3, 2], [5, 1], [6, 2]], 19/51840],
[[[1, 8], [2, 5], [3, 2], [6, 2], [8, 1]], 13/51840],
[[[1, 8], [2, 5], [3, 2], [6, 2], [10, 1]], 1/25920],
[[[1, 8], [2, 5], [3, 3], [4, 1], [5, 1]], 1/414720],
[[[1, 8], [2, 5], [3, 3], [4, 1], [6, 2]], 5/4608],
[[[1, 8], [2, 5], [3, 3], [4, 1], [8, 1]], 43/663552],
[[[1, 8], [2, 5], [3, 3], [4, 2], [6, 1]], 57869/47775744],
[[[1, 8], [2, 5], [3, 3], [5, 1], [6, 1]], 1/155520],
[[[1, 8], [2, 5], [3, 3], [6, 1], [8, 1]], 25/331776],
[[[1, 8], [2, 5], [3, 3], [6, 1], [10, 1]], 1/20736],
[[[1, 8], [2, 5], [3, 4], [4, 1], [6, 1]], 91/248832],
[[[1, 8], [2, 5], [4, 1], [6, 1], [8, 2]], 1277/13271040],
[[[1, 8], [2, 5], [4, 1], [6, 3], [8, 1]], 1/51840],
[[[1, 8], [2, 5], [4, 2], [5, 1], [8, 1]], 7/7680],
[[[1, 8], [2, 5], [4, 2], [5, 1], [12, 1]], 11/184320],
[[[1, 8], [2, 5], [4, 2], [6, 2], [8, 1]], 7/46080],
[[[1, 8], [2, 5], [4, 2], [6, 2], [10, 1]], 1/276480],
[[[1, 8], [2, 5], [4, 2], [6, 2], [12, 1]], 67/6635520],
[[[1, 8], [2, 5], [4, 2], [8, 1], [10, 1]], 1/7680],
[[[1, 8], [2, 5], [4, 2], [10, 1], [12, 1]], 13/1105920],
[[[1, 8], [2, 5], [4, 3], [5, 1], [6, 1]], 727/4423680],
[[[1, 8], [2, 5], [4, 3], [6, 1], [8, 1]], 971/2211840],
[[[1, 8], [2, 5], [4, 3], [6, 1], [10, 1]], 1/46080],
[[[1, 8], [2, 5], [4, 3], [6, 1], [12, 1]], 301/4976640],
[[[1, 8], [2, 7], [3, 1], [4, 1], [6, 3]], 127261/238878720],
[[[1, 8], [2, 7], [3, 1], [4, 2], [5, 1]], 601/2949120],
[[[1, 8], [2, 7], [3, 1], [4, 2], [6, 2]], 84401/53084160],
[[[1, 8], [2, 7], [3, 1], [4, 2], [8, 1]], 28411/13271040],
[[[1, 8], [2, 7], [3, 1], [4, 2], [10, 1]], 1483/4423680],
[[[1, 8], [2, 7], [3, 1], [4, 2], [12, 1]], 3173/29859840],
[[[1, 8], [2, 7], [3, 1], [4, 3], [6, 1]], 986357/283115520],
[[[1, 8], [2, 7], [3, 1], [5, 1], [6, 2]], 1/5760],
[[[1, 8], [2, 7], [3, 1], [5, 1], [8, 1]], 1/92160],
[[[1, 8], [2, 7], [3, 1], [6, 2], [8, 1]], 539/1658880],
[[[1, 8], [2, 7], [3, 1], [6, 2], [10, 1]], 59/552960],
[[[1, 8], [2, 7], [3, 1], [8, 1], [10, 1]], 1/23040],
[[[1, 8], [2, 7], [3, 2], [4, 1], [5, 1]], 17/491520],
[[[1, 8], [2, 7], [3, 2], [4, 1], [6, 2]], 1067/368640],
[[[1, 8], [2, 7], [3, 2], [4, 1], [8, 1]], 913/1966080],
[[[1, 8], [2, 7], [3, 2], [4, 1], [10, 1]], 11/55296],
[[[1, 8], [2, 7], [3, 2], [4, 2], [6, 1]], 644011/212336640],
[[[1, 8], [2, 7], [3, 2], [5, 1], [6, 1]], 11/165888],
[[[1, 8], [2, 7], [3, 2], [6, 1], [8, 1]], 23/69120],
[[[1, 8], [2, 7], [3, 2], [6, 1], [10, 1]], 221/829440],
[[[1, 8], [2, 7], [3, 3], [4, 1], [6, 1]], 7139/7962624],
[[[1, 8], [2, 7], [4, 1], [5, 1], [6, 2]], 49/552960],
[[[1, 8], [2, 7], [4, 1], [5, 1], [8, 1]], 2221/8847360],
[[[1, 8], [2, 7], [4, 1], [6, 2], [8, 1]], 1657/4423680],
[[[1, 8], [2, 7], [4, 1], [6, 2], [10, 1]], 97/2211840],
[[[1, 8], [2, 7], [4, 1], [8, 1], [10, 1]], 35/147456],
[[[1, 8], [2, 7], [4, 2], [5, 1], [6, 1]], 589/1474560],
[[[1, 8], [2, 7], [4, 2], [6, 1], [8, 1]], 893/737280],
[[[1, 8], [2, 7], [4, 2], [6, 1], [10, 1]], 1021/7077888],
[[[1, 8], [2, 7], [4, 2], [6, 1], [12, 1]], 13/184320],
[[[1, 8], [2, 7], [5, 1], [6, 1], [8, 1]], 1/69120],
[[[1, 8], [2, 7], [6, 1], [8, 1], [10, 1]], 1/46080],
[[[1, 8], [2, 9], [3, 1], [4, 1], [5, 1]], 3929/42467328],
[[[1, 8], [2, 9], [3, 1], [4, 1], [6, 2]], 221507/127401984],
[[[1, 8], [2, 9], [3, 1], [4, 1], [8, 1]], 2749/5308416],
[[[1, 8], [2, 9], [3, 1], [4, 1], [10, 1]], 29/184320],
[[[1, 8], [2, 9], [3, 1], [4, 2], [6, 1]], 891067/283115520],
[[[1, 8], [2, 9], [3, 1], [5, 1], [6, 1]], 59/552960],
[[[1, 8], [2, 9], [3, 1], [6, 1], [8, 1]], 827/4423680],
[[[1, 8], [2, 9], [3, 1], [6, 1], [10, 1]], 259/2211840],
[[[1, 8], [2, 9], [3, 2], [4, 1], [6, 1]], 30461/26542080],
[[[1, 8], [2, 9], [4, 1], [5, 1], [6, 1]], 139/737280],
[[[1, 8], [2, 9], [4, 1], [6, 1], [8, 1]], 1421/2211840],
[[[1, 8], [2, 9], [4, 1], [6, 1], [10, 1]], 155/1769472],
[[[1, 8], [2, 11], [3, 1], [4, 1], [6, 1]], 405575/509607936],
[[[1, 9], [2, 2], [3, 1], [4, 2], [8, 2]], 19/491520],
[[[1, 9], [2, 2], [3, 1], [4, 4], [5, 1]], 1/81920],
[[[1, 9], [2, 2], [3, 1], [4, 4], [8, 1]], 19/737280],
[[[1, 9], [2, 2], [3, 1], [4, 4], [12, 1]], 1/61440],
[[[1, 9], [2, 2], [3, 1], [4, 5], [6, 1]], 1/28311552],
[[[1, 9], [2, 2], [3, 2], [4, 3], [5, 1]], 11/184320],
[[[1, 9], [2, 2], [3, 2], [4, 4], [6, 1]], 23/4976640],
[[[1, 9], [2, 2], [3, 2], [6, 1], [8, 2]], 53/6635520],
[[[1, 9], [2, 2], [3, 2], [6, 2], [9, 1]], 1/414720],
[[[1, 9], [2, 2], [3, 3], [4, 2], [5, 1]], 43/276480],
[[[1, 9], [2, 2], [3, 3], [4, 2], [6, 2]], 1/110592],
[[[1, 9], [2, 2], [3, 3], [4, 3], [6, 1]], 7/884736],
[[[1, 9], [2, 2], [3, 3], [6, 1], [9, 1]], 11/373248],
[[[1, 9], [2, 2], [3, 3], [6, 2], [12, 1]], 7/1658880],
[[[1, 9], [2, 2], [3, 4], [4, 2], [6, 1]], 37/2239488],
[[[1, 9], [2, 2], [3, 4], [5, 1], [6, 1]], 1/58320],
[[[1, 9], [2, 2], [3, 4], [6, 1], [12, 1]], 77/2488320],
[[[1, 9], [2, 2], [3, 5], [4, 1], [6, 1]], 7/82944],
[[[1, 9], [2, 2], [4, 2], [6, 1], [8, 2]], 1/4423680],
[[[1, 9], [2, 2], [4, 3], [6, 2], [8, 1]], 1/3538944],
[[[1, 9], [2, 2], [4, 3], [8, 1], [10, 1]], 1/983040],
[[[1, 9], [2, 2], [4, 3], [8, 1], [12, 1]], 7/1105920],
[[[1, 9], [2, 2], [4, 4], [6, 1], [12, 1]], 1/1658880],
[[[1, 9], [2, 4], [3, 1], [4, 1], [6, 4]], 1/497664],
[[[1, 9], [2, 4], [3, 1], [4, 1], [8, 2]], 119/1474560],
[[[1, 9], [2, 4], [3, 1], [4, 2], [6, 3]], 1/147456],
[[[1, 9], [2, 4], [3, 1], [4, 3], [5, 1]], 67/245760],
[[[1, 9], [2, 4], [3, 1], [4, 3], [6, 2]], 89/3981312],
[[[1, 9], [2, 4], [3, 1], [4, 3], [8, 1]], 379/737280],
[[[1, 9], [2, 4], [3, 1], [4, 3], [10, 1]], 13/884736],
[[[1, 9], [2, 4], [3, 1], [4, 3], [12, 1]], 65/331776],
[[[1, 9], [2, 4], [3, 1], [4, 4], [6, 1]], 148601/1274019840],
[[[1, 9], [2, 4], [3, 1], [6, 1], [8, 2]], 1723/53084160],
[[[1, 9], [2, 4], [3, 1], [6, 3], [8, 1]], 1/995328],
[[[1, 9], [2, 4], [3, 2], [4, 1], [6, 3]], 13/248832],
[[[1, 9], [2, 4], [3, 2], [4, 2], [5, 1]], 2611/13271040],
[[[1, 9], [2, 4], [3, 2], [4, 2], [6, 2]], 473/2654208],
[[[1, 9], [2, 4], [3, 2], [4, 2], [8, 1]], 1543/4423680],
[[[1, 9], [2, 4], [3, 2], [4, 2], [12, 1]], 83/3981312],
[[[1, 9], [2, 4], [3, 2], [4, 3], [6, 1]], 361/1179648],
[[[1, 9], [2, 4], [3, 2], [5, 1], [6, 2]], 19/311040],
[[[1, 9], [2, 4], [3, 2], [6, 2], [8, 1]], 1/27648],
[[[1, 9], [2, 4], [3, 3], [4, 1], [5, 1]], 1/34560],
[[[1, 9], [2, 4], [3, 3], [4, 1], [6, 2]], 13/110592],
[[[1, 9], [2, 4], [3, 3], [4, 2], [6, 1]], 4901/7962624],
[[[1, 9], [2, 4], [3, 3], [5, 1], [6, 1]], 1/34560],
[[[1, 9], [2, 4], [3, 4], [4, 1], [6, 1]], 19/93312],
[[[1, 9], [2, 4], [4, 1], [6, 1], [8, 2]], 119/13271040],
[[[1, 9], [2, 4], [4, 1], [6, 3], [8, 1]], 1/1990656],
[[[1, 9], [2, 4], [4, 2], [5, 1], [8, 1]], 113/737280],
[[[1, 9], [2, 4], [4, 2], [5, 1], [12, 1]], 11/1105920],
[[[1, 9], [2, 4], [4, 2], [6, 2], [8, 1]], 37/2211840],
[[[1, 9], [2, 4], [4, 2], [6, 2], [12, 1]], 1/1105920],
[[[1, 9], [2, 4], [4, 2], [8, 1], [10, 1]], 7/368640],
[[[1, 9], [2, 4], [4, 2], [10, 1], [12, 1]], 1/552960],
[[[1, 9], [2, 4], [4, 3], [5, 1], [6, 1]], 1/368640],
[[[1, 9], [2, 4], [4, 3], [6, 1], [8, 1]], 667/8847360],
[[[1, 9], [2, 4], [4, 3], [6, 1], [10, 1]], 1/368640],
[[[1, 9], [2, 4], [4, 3], [6, 1], [12, 1]], 17/1658880],
[[[1, 9], [2, 6], [3, 1], [4, 1], [6, 3]], 803/4423680],
[[[1, 9], [2, 6], [3, 1], [4, 2], [5, 1]], 12367/35389440],
[[[1, 9], [2, 6], [3, 1], [4, 2], [6, 2]], 26561/42467328],
[[[1, 9], [2, 6], [3, 1], [4, 2], [8, 1]], 299/147456],
[[[1, 9], [2, 6], [3, 1], [4, 2], [10, 1]], 191/1474560],
[[[1, 9], [2, 6], [3, 1], [4, 2], [12, 1]], 103/995328],
[[[1, 9], [2, 6], [3, 1], [4, 3], [6, 1]], 945731/637009920],
[[[1, 9], [2, 6], [3, 1], [5, 1], [6, 2]], 13/276480],
[[[1, 9], [2, 6], [3, 1], [6, 2], [8, 1]], 41/414720],
[[[1, 9], [2, 6], [3, 1], [6, 2], [10, 1]], 1/34560],
[[[1, 9], [2, 6], [3, 1], [8, 1], [10, 1]], 1/138240],
[[[1, 9], [2, 6], [3, 2], [4, 1], [5, 1]], 89/2211840],
[[[1, 9], [2, 6], [3, 2], [4, 1], [6, 2]], 3307/2488320],
[[[1, 9], [2, 6], [3, 2], [4, 1], [8, 1]], 2681/8847360],
[[[1, 9], [2, 6], [3, 2], [4, 1], [10, 1]], 43/1105920],
[[[1, 9], [2, 6], [3, 2], [4, 2], [6, 1]], 26023/10616832],
[[[1, 9], [2, 6], [3, 2], [5, 1], [6, 1]], 559/4976640],
[[[1, 9], [2, 6], [3, 2], [6, 1], [8, 1]], 37/276480],
[[[1, 9], [2, 6], [3, 2], [6, 1], [10, 1]], 1/13824],
[[[1, 9], [2, 6], [3, 3], [4, 1], [6, 1]], 41959/31850496],
[[[1, 9], [2, 6], [4, 1], [5, 1], [6, 2]], 1/276480],
[[[1, 9], [2, 6], [4, 1], [5, 1], [8, 1]], 239/1474560],
[[[1, 9], [2, 6], [4, 1], [6, 2], [8, 1]], 517/5898240],
[[[1, 9], [2, 6], [4, 1], [6, 2], [10, 1]], 77/10616832],
[[[1, 9], [2, 6], [4, 1], [8, 1], [10, 1]], 731/8847360],
[[[1, 9], [2, 6], [4, 2], [5, 1], [6, 1]], 179/1105920],
[[[1, 9], [2, 6], [4, 2], [6, 1], [8, 1]], 3283/6635520],
[[[1, 9], [2, 6], [4, 2], [6, 1], [10, 1]], 161/2949120],
[[[1, 9], [2, 6], [4, 2], [6, 1], [12, 1]], 89/3317760],
[[[1, 9], [2, 6], [6, 1], [8, 1], [10, 1]], 1/276480],
[[[1, 9], [2, 8], [3, 1], [4, 1], [5, 1]], 155/1769472],
[[[1, 9], [2, 8], [3, 1], [4, 1], [6, 2]], 30461/26542080],
[[[1, 9], [2, 8], [3, 1], [4, 1], [8, 1]], 1421/2211840],
[[[1, 9], [2, 8], [3, 1], [4, 1], [10, 1]], 139/737280],
[[[1, 9], [2, 8], [3, 1], [4, 2], [6, 1]], 891067/283115520],
[[[1, 9], [2, 8], [3, 1], [5, 1], [6, 1]], 259/2211840],
[[[1, 9], [2, 8], [3, 1], [6, 1], [8, 1]], 827/4423680],
[[[1, 9], [2, 8], [3, 1], [6, 1], [10, 1]], 59/552960],
[[[1, 9], [2, 8], [3, 2], [4, 1], [6, 1]], 221507/127401984],
[[[1, 9], [2, 8], [4, 1], [5, 1], [6, 1]], 29/184320],
[[[1, 9], [2, 8], [4, 1], [6, 1], [8, 1]], 2749/5308416],
[[[1, 9], [2, 8], [4, 1], [6, 1], [10, 1]], 3929/42467328],
[[[1, 9], [2, 10], [3, 1], [4, 1], [6, 1]], 25080059/20384317440],
[[[1, 10], [2, 1], [3, 1], [4, 4], [5, 1]], 1/1474560],
[[[1, 10], [2, 1], [3, 2], [4, 3], [5, 1]], 7/737280],
[[[1, 10], [2, 1], [3, 2], [4, 4], [6, 1]], 1/21233664],
[[[1, 10], [2, 1], [3, 3], [4, 2], [5, 1]], 7/414720],
[[[1, 10], [2, 1], [3, 3], [6, 1], [9, 1]], 1/622080],
[[[1, 10], [2, 1], [3, 4], [4, 1], [5, 1]], 1/17280],
[[[1, 10], [2, 1], [3, 4], [4, 2], [6, 1]], 13/5971968],
[[[1, 10], [2, 1], [3, 4], [6, 1], [12, 1]], 1/552960],
[[[1, 10], [2, 1], [4, 3], [8, 1], [12, 1]], 1/3317760],
[[[1, 10], [2, 3], [3, 1], [4, 1], [8, 2]], 17/2211840],
[[[1, 10], [2, 3], [3, 1], [4, 2], [6, 3]], 1/2654208],
[[[1, 10], [2, 3], [3, 1], [4, 3], [5, 1]], 737/8847360],
[[[1, 10], [2, 3], [3, 1], [4, 3], [6, 2]], 1/442368],
[[[1, 10], [2, 3], [3, 1], [4, 3], [8, 1]], 161/2949120],
[[[1, 10], [2, 3], [3, 1], [4, 3], [12, 1]], 17/829440],
[[[1, 10], [2, 3], [3, 1], [4, 4], [6, 1]], 1483/283115520],
[[[1, 10], [2, 3], [3, 1], [6, 1], [8, 2]], 11/2949120],
[[[1, 10], [2, 3], [3, 2], [4, 1], [6, 3]], 1/165888],
[[[1, 10], [2, 3], [3, 2], [4, 2], [5, 1]], 337/1105920],
[[[1, 10], [2, 3], [3, 2], [4, 2], [6, 2]], 23/1990656],
[[[1, 10], [2, 3], [3, 2], [4, 3], [6, 1]], 1273/26542080],
[[[1, 10], [2, 3], [3, 2], [6, 2], [8, 1]], 1/331776],
[[[1, 10], [2, 3], [3, 3], [4, 1], [5, 1]], 7/69120],
[[[1, 10], [2, 3], [3, 3], [4, 1], [6, 2]], 1/82944],
[[[1, 10], [2, 3], [3, 3], [4, 2], [6, 1]], 2879/47775744],
[[[1, 10], [2, 3], [3, 3], [5, 1], [6, 1]], 7/155520],
[[[1, 10], [2, 3], [3, 4], [4, 1], [6, 1]], 53/331776],
[[[1, 10], [2, 3], [4, 1], [6, 1], [8, 2]], 1/4423680],
[[[1, 10], [2, 3], [4, 2], [6, 2], [8, 1]], 1/5308416],
[[[1, 10], [2, 3], [4, 2], [6, 2], [12, 1]], 1/35831808],
[[[1, 10], [2, 3], [4, 2], [8, 1], [10, 1]], 1/1474560],
[[[1, 10], [2, 3], [4, 2], [10, 1], [12, 1]], 1/9953280],
[[[1, 10], [2, 3], [4, 3], [5, 1], [6, 1]], 1/4423680],
[[[1, 10], [2, 3], [4, 3], [6, 1], [8, 1]], 13/2211840],
[[[1, 10], [2, 3], [4, 3], [6, 1], [12, 1]], 1/1658880],
[[[1, 10], [2, 5], [3, 1], [4, 1], [6, 3]], 7397/318504960],
[[[1, 10], [2, 5], [3, 1], [4, 2], [5, 1]], 2353/8847360],
[[[1, 10], [2, 5], [3, 1], [4, 2], [6, 2]], 1063/8847360],
[[[1, 10], [2, 5], [3, 1], [4, 2], [8, 1]], 37/61440],
[[[1, 10], [2, 5], [3, 1], [4, 2], [10, 1]], 1/65536],
[[[1, 10], [2, 5], [3, 1], [4, 2], [12, 1]], 23/663552],
[[[1, 10], [2, 5], [3, 1], [4, 3], [6, 1]], 60307/169869312],
[[[1, 10], [2, 5], [3, 1], [5, 1], [6, 2]], 1/207360],
[[[1, 10], [2, 5], [3, 1], [6, 2], [8, 1]], 49/4976640],
[[[1, 10], [2, 5], [3, 1], [6, 2], [10, 1]], 1/414720],
[[[1, 10], [2, 5], [3, 2], [4, 1], [5, 1]], 1117/8847360],
[[[1, 10], [2, 5], [3, 2], [4, 1], [6, 2]], 1157/4976640],
[[[1, 10], [2, 5], [3, 2], [4, 1], [8, 1]], 961/17694720],
[[[1, 10], [2, 5], [3, 2], [4, 2], [6, 1]], 46247/53084160],
[[[1, 10], [2, 5], [3, 2], [5, 1], [6, 1]], 5/82944],
[[[1, 10], [2, 5], [3, 2], [6, 1], [8, 1]], 13/829440],
[[[1, 10], [2, 5], [3, 2], [6, 1], [10, 1]], 1/165888],
[[[1, 10], [2, 5], [3, 3], [4, 1], [6, 1]], 27101/39813120],
[[[1, 10], [2, 5], [4, 1], [5, 1], [6, 2]], 1/3317760],
[[[1, 10], [2, 5], [4, 1], [5, 1], [8, 1]], 71/2949120],
[[[1, 10], [2, 5], [4, 1], [6, 2], [8, 1]], 497/79626240],
[[[1, 10], [2, 5], [4, 1], [8, 1], [10, 1]], 1/98304],
[[[1, 10], [2, 5], [4, 2], [5, 1], [6, 1]], 11/491520],
[[[1, 10], [2, 5], [4, 2], [6, 1], [8, 1]], 179/2211840],
[[[1, 10], [2, 5], [4, 2], [6, 1], [10, 1]], 449/70778880],
[[[1, 10], [2, 5], [4, 2], [6, 1], [12, 1]], 197/44789760],
[[[1, 10], [2, 7], [3, 1], [4, 1], [5, 1]], 271/2359296],
[[[1, 10], [2, 7], [3, 1], [4, 1], [6, 2]], 618481/1274019840],
[[[1, 10], [2, 7], [3, 1], [4, 1], [8, 1]], 32627/79626240],
[[[1, 10], [2, 7], [3, 1], [4, 1], [10, 1]], 67/1105920],
[[[1, 10], [2, 7], [3, 1], [4, 2], [6, 1]], 1004927/566231040],
[[[1, 10], [2, 7], [3, 1], [5, 1], [6, 1]], 379/3317760],
[[[1, 10], [2, 7], [3, 1], [6, 1], [8, 1]], 1409/19906560],
[[[1, 10], [2, 7], [3, 1], [6, 1], [10, 1]], 449/13271040],
[[[1, 10], [2, 7], [3, 2], [4, 1], [6, 1]], 524027/318504960],
[[[1, 10], [2, 7], [4, 1], [5, 1], [6, 1]], 1973/26542080],
[[[1, 10], [2, 7], [4, 1], [6, 1], [8, 1]], 3629/19906560],
[[[1, 10], [2, 7], [4, 1], [6, 1], [10, 1]], 1037/35389440],
[[[1, 10], [2, 9], [3, 1], [4, 1], [6, 1]], 25080059/20384317440],
[[[1, 11], [2, 2], [3, 1], [4, 3], [5, 1]], 19/1474560],
[[[1, 11], [2, 2], [3, 1], [4, 4], [6, 1]], 1813/3822059520],
[[[1, 11], [2, 2], [3, 1], [6, 1], [8, 2]], 29/159252480],
[[[1, 11], [2, 2], [3, 2], [4, 2], [5, 1]], 31/491520],
[[[1, 11], [2, 2], [3, 2], [4, 2], [6, 2]], 1/884736],
[[[1, 11], [2, 2], [3, 2], [4, 3], [6, 1]], 1/1179648],
[[[1, 11], [2, 2], [3, 3], [4, 1], [5, 1]], 1/6912],
[[[1, 11], [2, 2], [3, 3], [4, 2], [6, 1]], 1771/358318080],
[[[1, 11], [2, 2], [3, 3], [5, 1], [6, 1]], 13/1866240],
[[[1, 11], [2, 2], [3, 4], [4, 1], [6, 1]], 1/55296],
[[[1, 11], [2, 4], [3, 1], [4, 1], [6, 3]], 1/3981312],
[[[1, 11], [2, 4], [3, 1], [4, 2], [5, 1]], 6253/26542080],
[[[1, 11], [2, 4], [3, 1], [4, 2], [6, 2]], 5141/424673280],
[[[1, 11], [2, 4], [3, 1], [4, 2], [8, 1]], 367/6635520],
[[[1, 11], [2, 4], [3, 1], [4, 2], [12, 1]], 17/4976640],
[[[1, 11], [2, 4], [3, 1], [4, 3], [6, 1]], 64981/1698693120],
[[[1, 11], [2, 4], [3, 1], [5, 1], [6, 2]], 1/2488320],
[[[1, 11], [2, 4], [3, 2], [4, 1], [5, 1]], 149/737280],
[[[1, 11], [2, 4], [3, 2], [4, 1], [6, 2]], 17/1327104],
[[[1, 11], [2, 4], [3, 2], [4, 2], [6, 1]], 3769/26542080],
[[[1, 11], [2, 4], [3, 2], [5, 1], [6, 1]], 29/552960],
[[[1, 11], [2, 4], [3, 3], [4, 1], [6, 1]], 11965/47775744],
[[[1, 11], [2, 4], [4, 1], [6, 2], [8, 1]], 1/10616832],
[[[1, 11], [2, 4], [4, 1], [8, 1], [10, 1]], 1/2949120],
[[[1, 11], [2, 4], [4, 2], [5, 1], [6, 1]], 13/4423680],
[[[1, 11], [2, 4], [4, 2], [6, 1], [8, 1]], 17/4423680],
[[[1, 11], [2, 4], [4, 2], [6, 1], [12, 1]], 7/29859840],
[[[1, 11], [2, 6], [3, 1], [4, 1], [5, 1]], 2371/17694720],
[[[1, 11], [2, 6], [3, 1], [4, 1], [6, 2]], 4111/42467328],
[[[1, 11], [2, 6], [3, 1], [4, 1], [8, 1]], 691/6635520],
[[[1, 11], [2, 6], [3, 1], [4, 1], [10, 1]], 11/1966080],
[[[1, 11], [2, 6], [3, 1], [4, 2], [6, 1]], 5539429/10192158720],
[[[1, 11], [2, 6], [3, 1], [5, 1], [6, 1]], 287/4976640],
[[[1, 11], [2, 6], [3, 1], [6, 1], [8, 1]], 79/6635520],
[[[1, 11], [2, 6], [3, 1], [6, 1], [10, 1]], 1/221184],
[[[1, 11], [2, 6], [3, 2], [4, 1], [6, 1]], 168439/212336640],
[[[1, 11], [2, 6], [4, 1], [5, 1], [6, 1]], 43/1105920],
[[[1, 11], [2, 6], [4, 1], [6, 1], [8, 1]], 643/26542080],
[[[1, 11], [2, 6], [4, 1], [6, 1], [10, 1]], 193/70778880],
[[[1, 11], [2, 8], [3, 1], [4, 1], [6, 1]], 405575/509607936],
[[[1, 12], [2, 1], [3, 1], [4, 3], [5, 1]], 1/983040],
[[[1, 12], [2, 1], [3, 1], [4, 4], [6, 1]], 1/509607936],
[[[1, 12], [2, 1], [3, 2], [4, 2], [5, 1]], 11/2211840],
[[[1, 12], [2, 1], [3, 3], [4, 1], [5, 1]], 1/46080],
[[[1, 12], [2, 1], [3, 3], [4, 2], [6, 1]], 5/15925248],
[[[1, 12], [2, 3], [3, 1], [4, 2], [5, 1]], 589/8847360],
[[[1, 12], [2, 3], [3, 1], [4, 2], [6, 2]], 1/95551488],
[[[1, 12], [2, 3], [3, 1], [4, 3], [6, 1]], 16367/5096079360],
[[[1, 12], [2, 3], [3, 2], [4, 1], [5, 1]], 239/1474560],
[[[1, 12], [2, 3], [3, 2], [4, 1], [6, 2]], 1/1327104],
[[[1, 12], [2, 3], [3, 2], [4, 2], [6, 1]], 10183/1274019840],
[[[1, 12], [2, 3], [3, 2], [5, 1], [6, 1]], 11/829440],
[[[1, 12], [2, 3], [3, 3], [4, 1], [6, 1]], 5429/119439360],
[[[1, 12], [2, 3], [4, 2], [5, 1], [6, 1]], 1/4423680],
[[[1, 12], [2, 5], [3, 1], [4, 1], [5, 1]], 1721/11796480],
[[[1, 12], [2, 5], [3, 1], [4, 1], [6, 2]], 30829/3822059520],
[[[1, 12], [2, 5], [3, 1], [4, 1], [8, 1]], 227/26542080],
[[[1, 12], [2, 5], [3, 1], [4, 2], [6, 1]], 2782933/30576476160],
[[[1, 12], [2, 5], [3, 1], [5, 1], [6, 1]], 5/165888],
[[[1, 12], [2, 5], [3, 1], [6, 1], [8, 1]], 11/13271040],
[[[1, 12], [2, 5], [3, 1], [6, 1], [10, 1]], 1/3981312],
[[[1, 12], [2, 5], [3, 2], [4, 1], [6, 1]], 15707/63700992],
[[[1, 12], [2, 5], [4, 1], [5, 1], [6, 1]], 7/552960],
[[[1, 12], [2, 5], [4, 1], [6, 1], [8, 1]], 17/19906560],
[[[1, 12], [2, 7], [3, 1], [4, 1], [6, 1]], 2098573/6115295232],
[[[1, 13], [2, 2], [3, 1], [4, 2], [5, 1]], 179/23592960],
[[[1, 13], [2, 2], [3, 1], [4, 3], [6, 1]], 5/169869312],
[[[1, 13], [2, 2], [3, 2], [4, 1], [5, 1]], 29/737280],
[[[1, 13], [2, 2], [3, 2], [4, 2], [6, 1]], 689/1433272320],
[[[1, 13], [2, 2], [3, 2], [5, 1], [6, 1]], 1/995328],
[[[1, 13], [2, 2], [3, 3], [4, 1], [6, 1]], 17/7077888],
[[[1, 13], [2, 2], [4, 2], [5, 1], [6, 1]], 1/79626240],
[[[1, 13], [2, 4], [3, 1], [4, 1], [5, 1]], 53/589824],
[[[1, 13], [2, 4], [3, 1], [4, 1], [6, 2]], 5/63700992],
[[[1, 13], [2, 4], [3, 1], [4, 2], [6, 1]], 28741/3397386240],
[[[1, 13], [2, 4], [3, 1], [5, 1], [6, 1]], 1/110592],
[[[1, 13], [2, 4], [3, 2], [4, 1], [6, 1]], 59123/1274019840],
[[[1, 13], [2, 4], [4, 1], [5, 1], [6, 1]], 1/552960],
[[[1, 13], [2, 6], [3, 1], [4, 1], [6, 1]], 2205647/20384317440],
[[[1, 14], [2, 1], [3, 1], [4, 2], [5, 1]], 1/2211840],
[[[1, 14], [2, 1], [3, 2], [4, 1], [5, 1]], 17/5898240],
[[[1, 14], [2, 1], [3, 2], [4, 2], [6, 1]], 7/382205952],
[[[1, 14], [2, 3], [3, 1], [4, 1], [5, 1]], 607/23592960],
[[[1, 14], [2, 3], [3, 1], [4, 2], [6, 1]], 10763/30576476160],
[[[1, 14], [2, 3], [3, 1], [5, 1], [6, 1]], 1/829440],
[[[1, 14], [2, 3], [3, 2], [4, 1], [6, 1]], 8291/1911029760],
[[[1, 14], [2, 3], [4, 1], [5, 1], [6, 1]], 1/10616832],
[[[1, 14], [2, 5], [3, 1], [4, 1], [6, 1]], 464041/20384317440],
[[[1, 15], [2, 2], [3, 1], [4, 1], [5, 1]], 13/3932160],
[[[1, 15], [2, 2], [3, 1], [4, 2], [6, 1]], 353/22932357120],
[[[1, 15], [2, 2], [3, 1], [5, 1], [6, 1]], 7/119439360],
[[[1, 15], [2, 2], [3, 2], [4, 1], [6, 1]], 11/84934656],
[[[1, 15], [2, 4], [3, 1], [4, 1], [6, 1]], 82741/30576476160],
[[[1, 16], [2, 1], [3, 1], [4, 1], [5, 1]], 11/70778880],
[[[1, 16], [2, 1], [3, 1], [4, 2], [6, 1]], 1/3057647616],
[[[1, 16], [2, 3], [3, 1], [4, 1], [6, 1]], 761/5096079360],
[[[1, 17], [2, 2], [3, 1], [4, 1], [6, 1]], 1/452984832],
[[[2, 3], [3, 2], [6, 2], [12, 2], [18, 1]], 1/5184],
[[[2, 3], [3, 2], [6, 2], [18, 1], [24, 1]], 1/864],
[[[2, 3], [3, 2], [6, 4], [10, 1], [18, 1]], 1/51840],
[[[2, 3], [3, 2], [6, 4], [12, 1], [18, 1]], 1/31104],
[[[2, 3], [3, 4], [6, 2], [10, 1], [18, 1]], 1/103680],
[[[2, 3], [6, 2], [10, 1], [12, 2], [18, 1]], 1/2880],
[[[2, 3], [6, 4], [10, 1], [12, 1], [18, 1]], 1/8640],
[[[2, 5], [3, 2], [4, 2], [6, 4], [12, 1]], 1/20736],
[[[2, 5], [3, 2], [6, 3], [10, 1], [18, 1]], 1/25920],
[[[2, 5], [3, 2], [6, 3], [12, 1], [18, 1]], 1/31104],
[[[2, 5], [3, 2], [6, 4], [10, 1], [12, 1]], 1/69120],
[[[2, 5], [6, 3], [10, 1], [12, 1], [18, 1]], 1/4320],
[[[2, 7], [3, 2], [6, 2], [12, 1], [18, 1]], 1/1244160],
[[[1, 1], [2, 2], [3, 1], [4, 1], [6, 3], [12, 3]], 1/13824],
[[[1, 1], [2, 2], [3, 1], [4, 1], [6, 5], [12, 2]], 1/41472],
[[[1, 1], [2, 2], [3, 1], [4, 1], [6, 7], [12, 1]], 1/497664],
[[[1, 1], [2, 2], [3, 1], [6, 3], [12, 2], [18, 1]], 1/3456],
[[[1, 1], [2, 2], [3, 1], [6, 5], [12, 1], [18, 1]], 1/10368],
[[[1, 1], [2, 2], [3, 2], [4, 1], [6, 2], [12, 3]], 1/4608],
[[[1, 1], [2, 2], [3, 2], [4, 1], [6, 4], [12, 2]], 1/13824],
[[[1, 1], [2, 2], [3, 2], [4, 1], [6, 6], [12, 1]], 1/18432],
[[[1, 1], [2, 2], [3, 3], [4, 1], [6, 1], [12, 3]], 1/6912],
[[[1, 1], [2, 2], [3, 3], [4, 1], [6, 3], [12, 2]], 1/41472],
[[[1, 1], [2, 2], [3, 3], [4, 1], [6, 5], [12, 1]], 1/248832],
[[[1, 1], [2, 2], [3, 3], [4, 3], [6, 1], [12, 2]], 1/3456],
[[[1, 1], [2, 2], [3, 3], [5, 1], [6, 3], [18, 1]], 1/4320],
[[[1, 1], [2, 2], [3, 3], [6, 1], [12, 2], [18, 1]], 1/15552],
[[[1, 1], [2, 2], [3, 3], [6, 1], [18, 1], [24, 1]], 1/2592],
[[[1, 1], [2, 2], [3, 3], [6, 3], [12, 1], [18, 1]], 1/10368],
[[[1, 1], [2, 2], [3, 4], [4, 1], [6, 2], [12, 2]], 1/13824],
[[[1, 1], [2, 2], [3, 4], [4, 1], [6, 4], [12, 1]], 1/82944],
[[[1, 1], [2, 2], [3, 5], [4, 1], [6, 3], [12, 1]], 73/497664],
[[[1, 1], [2, 2], [3, 6], [4, 1], [6, 2], [12, 1]], 1/165888],
[[[1, 1], [2, 2], [4, 1], [6, 2], [10, 1], [12, 3]], 1/5760],
[[[1, 1], [2, 2], [4, 1], [6, 4], [12, 1], [24, 1]], 1/3456],
[[[1, 1], [2, 2], [4, 3], [6, 2], [10, 1], [12, 2]], 1/2880],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 2], [8, 3]], 1/9216],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 2], [12, 3]], 1/13824],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 4], [12, 2]], 1/13824],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 6], [12, 1]], 5/497664],
[[[1, 1], [2, 4], [3, 1], [5, 1], [6, 3], [12, 2]], 1/34560],
[[[1, 1], [2, 4], [3, 1], [5, 1], [6, 3], [24, 1]], 1/5760],
[[[1, 1], [2, 4], [3, 1], [6, 3], [10, 1], [12, 2]], 1/3840],
[[[1, 1], [2, 4], [3, 1], [6, 4], [10, 1], [18, 1]], 1/8640],
[[[1, 1], [2, 4], [3, 1], [6, 4], [12, 1], [18, 1]], 1/2592],
[[[1, 1], [2, 4], [3, 1], [6, 5], [10, 1], [12, 1]], 1/11520],
[[[1, 1], [2, 4], [3, 2], [4, 1], [6, 3], [12, 2]], 1/6912],
[[[1, 1], [2, 4], [3, 2], [4, 1], [6, 4], [18, 1]], 1/82944],
[[[1, 1], [2, 4], [3, 2], [4, 1], [6, 5], [12, 1]], 1/13824],
[[[1, 1], [2, 4], [3, 2], [6, 3], [10, 1], [18, 1]], 1/8640],
[[[1, 1], [2, 4], [3, 2], [6, 3], [12, 1], [18, 1]], 1/10368],
[[[1, 1], [2, 4], [3, 3], [4, 1], [6, 2], [12, 2]], 1/41472],
[[[1, 1], [2, 4], [3, 3], [4, 1], [6, 3], [18, 1]], 1/768],
[[[1, 1], [2, 4], [3, 3], [4, 1], [6, 4], [12, 1]], 1/82944],
[[[1, 1], [2, 4], [3, 3], [4, 2], [6, 3], [12, 1]], 19/62208],
[[[1, 1], [2, 4], [3, 3], [6, 2], [10, 1], [18, 1]], 1/8640],
[[[1, 1], [2, 4], [3, 3], [6, 3], [10, 1], [12, 1]], 1/11520],
[[[1, 1], [2, 4], [3, 4], [4, 1], [6, 2], [18, 1]], 1/165888],
[[[1, 1], [2, 4], [3, 4], [4, 1], [6, 3], [12, 1]], 1/41472],
[[[1, 1], [2, 4], [3, 5], [4, 1], [6, 2], [12, 1]], 1/497664],
[[[1, 1], [2, 4], [4, 1], [6, 1], [8, 3], [10, 1]], 1/7680],
[[[1, 1], [2, 4], [4, 1], [6, 2], [12, 2], [18, 1]], 1/4608],
[[[1, 1], [2, 4], [4, 1], [6, 3], [12, 1], [24, 1]], 1/3456],
[[[1, 1], [2, 4], [4, 1], [6, 4], [12, 1], [18, 1]], 1/13824],
[[[1, 1], [2, 4], [4, 3], [6, 3], [8, 1], [12, 1]], 1/10368],
[[[1, 1], [2, 4], [4, 5], [6, 1], [8, 1], [10, 1]], 1/92160],
[[[1, 1], [2, 4], [6, 3], [10, 1], [12, 1], [18, 1]], 1/1440],
[[[1, 1], [2, 6], [3, 1], [4, 1], [6, 1], [8, 3]], 1/73728],
[[[1, 1], [2, 6], [3, 1], [4, 1], [6, 1], [12, 3]], 1/552960],
[[[1, 1], [2, 6], [3, 1], [4, 1], [6, 3], [12, 2]], 37/552960],
[[[1, 1], [2, 6], [3, 1], [4, 1], [6, 3], [24, 1]], 1/9216],
[[[1, 1], [2, 6], [3, 1], [4, 1], [6, 5], [12, 1]], 107/6635520],
[[[1, 1], [2, 6], [3, 1], [4, 2], [6, 2], [8, 2]], 1/18432],
[[[1, 1], [2, 6], [3, 1], [4, 3], [6, 3], [12, 1]], 1/27648],
[[[1, 1], [2, 6], [3, 1], [6, 3], [10, 1], [18, 1]], 1/4320],
[[[1, 1], [2, 6], [3, 1], [6, 3], [12, 1], [18, 1]], 1/5184],
[[[1, 1], [2, 6], [3, 1], [6, 4], [10, 1], [12, 1]], 1/3840],
[[[1, 1], [2, 6], [3, 2], [4, 1], [6, 3], [18, 1]], 1/41472],
[[[1, 1], [2, 6], [3, 2], [4, 1], [6, 4], [12, 1]], 11/61440],
[[[1, 1], [2, 6], [3, 2], [6, 2], [12, 1], [18, 1]], 1/82944],
[[[1, 1], [2, 6], [3, 3], [4, 1], [6, 1], [12, 2]], 1/1658880],
[[[1, 1], [2, 6], [3, 3], [4, 1], [6, 3], [12, 1]], 1/122880],
[[[1, 1], [2, 6], [3, 5], [4, 1], [6, 1], [12, 1]], 1/19906560],
[[[1, 1], [2, 6], [4, 1], [6, 2], [12, 1], [24, 1]], 1/138240],
[[[1, 1], [2, 6], [4, 1], [6, 3], [12, 1], [18, 1]], 1/6912],
[[[1, 1], [2, 6], [4, 3], [6, 2], [8, 1], [12, 1]], 1/9216],
[[[1, 1], [2, 6], [4, 3], [8, 1], [10, 1], [12, 1]], 1/23040],
[[[1, 1], [2, 8], [3, 1], [4, 1], [6, 2], [12, 2]], 1/829440],
[[[1, 1], [2, 8], [3, 1], [4, 1], [6, 4], [12, 1]], 41/4976640],
[[[1, 1], [2, 8], [3, 1], [4, 2], [6, 1], [8, 2]], 1/147456],
[[[1, 1], [2, 8], [3, 1], [4, 3], [6, 2], [8, 1]], 1/147456],
[[[1, 1], [2, 8], [3, 1], [6, 2], [12, 1], [18, 1]], 1/207360],
[[[1, 1], [2, 8], [3, 3], [4, 1], [6, 2], [12, 1]], 1/4976640],
[[[1, 1], [2, 8], [4, 3], [6, 1], [8, 1], [12, 1]], 1/69120],
[[[1, 1], [2, 10], [3, 1], [4, 1], [6, 3], [12, 1]], 1/4976640],
[[[1, 1], [2, 10], [3, 1], [4, 3], [6, 1], [8, 1]], 1/1179648],
[[[1, 2], [2, 1], [3, 1], [4, 1], [6, 3], [12, 3]], 1/6912],
[[[1, 2], [2, 1], [3, 1], [4, 3], [6, 3], [12, 2]], 1/3456],
[[[1, 2], [2, 1], [3, 1], [6, 3], [9, 1], [12, 2]], 1/15552],
[[[1, 2], [2, 1], [3, 1], [6, 3], [9, 1], [24, 1]], 1/2592],
[[[1, 2], [2, 1], [3, 2], [4, 1], [5, 1], [12, 3]], 1/5760],
[[[1, 2], [2, 1], [3, 2], [4, 1], [6, 2], [12, 3]], 1/4608],
[[[1, 2], [2, 1], [3, 2], [4, 1], [6, 4], [12, 2]], 1/13824],
[[[1, 2], [2, 1], [3, 2], [4, 1], [6, 6], [12, 1]], 1/165888],
[[[1, 2], [2, 1], [3, 2], [4, 3], [5, 1], [12, 2]], 1/2880],
[[[1, 2], [2, 1], [3, 3], [4, 1], [6, 1], [12, 3]], 1/13824],
[[[1, 2], [2, 1], [3, 3], [4, 1], [6, 3], [12, 2]], 1/41472],
[[[1, 2], [2, 1], [3, 3], [4, 1], [6, 5], [12, 1]], 73/497664],
[[[1, 2], [2, 1], [3, 3], [6, 1], [9, 1], [12, 2]], 1/3456],
[[[1, 2], [2, 1], [3, 3], [6, 3], [9, 1], [10, 1]], 1/4320],
[[[1, 2], [2, 1], [3, 3], [6, 3], [9, 1], [12, 1]], 1/10368],
[[[1, 2], [2, 1], [3, 4], [4, 1], [6, 2], [12, 2]], 1/13824],
[[[1, 2], [2, 1], [3, 4], [4, 1], [6, 4], [12, 1]], 1/82944],
[[[1, 2], [2, 1], [3, 4], [4, 1], [12, 1], [24, 1]], 1/3456],
[[[1, 2], [2, 1], [3, 5], [4, 1], [6, 1], [12, 2]], 1/41472],
[[[1, 2], [2, 1], [3, 5], [4, 1], [6, 3], [12, 1]], 1/248832],
[[[1, 2], [2, 1], [3, 5], [6, 1], [9, 1], [12, 1]], 1/10368],
[[[1, 2], [2, 1], [3, 6], [4, 1], [6, 2], [12, 1]], 1/18432],
[[[1, 2], [2, 1], [3, 7], [4, 1], [6, 1], [12, 1]], 1/497664],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 2], [8, 3]], 1/9216],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 2], [12, 3]], 1/4608],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 4], [12, 2]], 1/4608],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 6], [12, 1]], 5/165888],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 1], [8, 3]], 1/6144],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 1], [12, 3]], 1/3072],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 3], [12, 2]], 1/9216],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 5], [12, 1]], 115/331776],
[[[1, 2], [2, 3], [3, 1], [4, 5], [6, 2], [8, 1]], 1/110592],
[[[1, 2], [2, 3], [3, 1], [4, 6], [6, 1], [8, 1]], 1/147456],
[[[1, 2], [2, 3], [3, 1], [6, 2], [9, 1], [12, 2]], 1/15552],
[[[1, 2], [2, 3], [3, 1], [6, 2], [9, 1], [24, 1]], 1/2592],
[[[1, 2], [2, 3], [3, 1], [6, 3], [10, 1], [12, 2]], 1/11520],
[[[1, 2], [2, 3], [3, 1], [6, 3], [10, 1], [24, 1]], 1/1920],
[[[1, 2], [2, 3], [3, 1], [6, 4], [10, 1], [18, 1]], 1/25920],
[[[1, 2], [2, 3], [3, 1], [6, 4], [12, 1], [18, 1]], 5/7776],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 1], [8, 3]], 1/27648],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 3], [12, 2]], 5/6912],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 4], [18, 1]], 1/82944],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 5], [12, 1]], 11/41472],
[[[1, 2], [2, 3], [3, 2], [4, 2], [6, 4], [12, 1]], 1/9216],
[[[1, 2], [2, 3], [3, 2], [4, 2], [12, 1], [24, 1]], 1/1536],
[[[1, 2], [2, 3], [3, 2], [5, 1], [6, 2], [12, 2]], 1/5760],
[[[1, 2], [2, 3], [3, 2], [5, 1], [6, 2], [24, 1]], 1/960],
[[[1, 2], [2, 3], [3, 2], [6, 1], [12, 2], [18, 1]], 1/5184],
[[[1, 2], [2, 3], [3, 2], [6, 1], [18, 1], [24, 1]], 1/864],
[[[1, 2], [2, 3], [3, 2], [6, 2], [10, 1], [12, 2]], 1/7680],
[[[1, 2], [2, 3], [3, 2], [6, 3], [12, 1], [18, 1]], 1/1728],
[[[1, 2], [2, 3], [3, 2], [6, 4], [10, 1], [12, 1]], 1/23040],
[[[1, 2], [2, 3], [3, 3], [4, 1], [6, 2], [12, 2]], 23/41472],
[[[1, 2], [2, 3], [3, 3], [4, 1], [6, 3], [18, 1]], 1/6912],
[[[1, 2], [2, 3], [3, 3], [4, 1], [6, 4], [12, 1]], 29/248832],
[[[1, 2], [2, 3], [3, 3], [4, 2], [6, 1], [12, 2]], 1/1024],
[[[1, 2], [2, 3], [3, 3], [4, 2], [6, 3], [12, 1]], 1/55296],
[[[1, 2], [2, 3], [3, 3], [6, 2], [9, 1], [12, 1]], 1/5184],
[[[1, 2], [2, 3], [3, 3], [6, 2], [10, 1], [18, 1]], 1/25920],
[[[1, 2], [2, 3], [3, 4], [4, 1], [6, 2], [18, 1]], 65/165888],
[[[1, 2], [2, 3], [3, 4], [4, 1], [6, 3], [12, 1]], 5/41472],
[[[1, 2], [2, 3], [3, 4], [4, 2], [6, 2], [12, 1]], 101/82944],
[[[1, 2], [2, 3], [3, 4], [6, 2], [10, 1], [12, 1]], 1/23040],
[[[1, 2], [2, 3], [3, 5], [4, 1], [6, 2], [12, 1]], 43/497664],
[[[1, 2], [2, 3], [3, 5], [4, 2], [6, 1], [12, 1]], 1/110592],
[[[1, 2], [2, 3], [4, 1], [5, 1], [6, 1], [8, 3]], 1/7680],
[[[1, 2], [2, 3], [4, 1], [6, 2], [12, 2], [18, 1]], 1/4608],
[[[1, 2], [2, 3], [4, 1], [6, 3], [12, 1], [24, 1]], 1/1152],
[[[1, 2], [2, 3], [4, 1], [6, 4], [12, 1], [18, 1]], 1/13824],
[[[1, 2], [2, 3], [4, 2], [6, 2], [10, 1], [12, 2]], 1/960],
[[[1, 2], [2, 3], [4, 2], [6, 2], [12, 1], [24, 1]], 1/1536],
[[[1, 2], [2, 3], [4, 4], [6, 2], [8, 1], [12, 1]], 1/13824],
[[[1, 2], [2, 3], [4, 4], [8, 1], [10, 1], [12, 1]], 1/3840],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 1], [8, 3]], 7/73728],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 1], [12, 3]], 1/36864],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 3], [8, 2]], 1/6912],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 3], [12, 2]], 53/110592],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 3], [24, 1]], 1/9216],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 4], [18, 1]], 1/13824],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 5], [12, 1]], 67/442368],
[[[1, 2], [2, 5], [3, 1], [4, 2], [6, 2], [8, 2]], 19/110592],
[[[1, 2], [2, 5], [3, 1], [4, 2], [6, 2], [12, 2]], 1/4608],
[[[1, 2], [2, 5], [3, 1], [4, 2], [6, 4], [12, 1]], 407/746496],
[[[1, 2], [2, 5], [3, 1], [4, 2], [8, 2], [10, 1]], 1/30720],
[[[1, 2], [2, 5], [3, 1], [4, 3], [6, 1], [8, 2]], 7/147456],
[[[1, 2], [2, 5], [3, 1], [4, 3], [6, 3], [12, 1]], 1/27648],
[[[1, 2], [2, 5], [3, 1], [4, 4], [6, 2], [10, 1]], 1/69120],
[[[1, 2], [2, 5], [3, 1], [4, 4], [6, 2], [12, 1]], 1/41472],
[[[1, 2], [2, 5], [3, 1], [4, 4], [10, 1], [12, 1]], 1/11520],
[[[1, 2], [2, 5], [3, 1], [4, 5], [6, 1], [8, 1]], 1/884736],
[[[1, 2], [2, 5], [3, 1], [4, 5], [6, 1], [12, 1]], 1/55296],
[[[1, 2], [2, 5], [3, 1], [6, 1], [9, 1], [12, 2]], 1/622080],
[[[1, 2], [2, 5], [3, 1], [6, 1], [9, 1], [24, 1]], 1/103680],
[[[1, 2], [2, 5], [3, 1], [6, 1], [12, 2], [18, 1]], 1/41472],
[[[1, 2], [2, 5], [3, 1], [6, 1], [18, 1], [24, 1]], 1/6912],
[[[1, 2], [2, 5], [3, 1], [6, 2], [8, 2], [10, 1]], 1/5760],
[[[1, 2], [2, 5], [3, 1], [6, 3], [10, 1], [18, 1]], 1/1296],
[[[1, 2], [2, 5], [3, 1], [6, 3], [12, 1], [18, 1]], 5/7776],
[[[1, 2], [2, 5], [3, 1], [6, 4], [10, 1], [12, 1]], 19/34560],
[[[1, 2], [2, 5], [3, 2], [4, 1], [5, 1], [6, 4]], 1/5760],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 2], [8, 2]], 1/6912],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 2], [12, 2]], 7/27648],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 2], [24, 1]], 1/1536],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 3], [18, 1]], 1/10368],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 4], [12, 1]], 89/331776],
[[[1, 2], [2, 5], [3, 2], [4, 2], [6, 1], [8, 2]], 1/55296],
[[[1, 2], [2, 5], [3, 2], [4, 2], [6, 2], [18, 1]], 1/1152],
[[[1, 2], [2, 5], [3, 2], [4, 2], [6, 3], [12, 1]], 1/20736],
[[[1, 2], [2, 5], [3, 2], [4, 3], [6, 2], [12, 1]], 1/4608],
[[[1, 2], [2, 5], [3, 2], [6, 2], [10, 1], [18, 1]], 1/2880],
[[[1, 2], [2, 5], [3, 2], [6, 2], [12, 1], [18, 1]], 1/27648],
[[[1, 2], [2, 5], [3, 2], [6, 3], [10, 1], [12, 1]], 7/11520],
[[[1, 2], [2, 5], [3, 3], [4, 1], [6, 1], [12, 2]], 1/110592],
[[[1, 2], [2, 5], [3, 3], [4, 1], [6, 2], [18, 1]], 1/13824],
[[[1, 2], [2, 5], [3, 3], [4, 1], [6, 3], [12, 1]], 2335/1990656],
[[[1, 2], [2, 5], [3, 3], [4, 2], [6, 2], [12, 1]], 1/27648],
[[[1, 2], [2, 5], [3, 4], [4, 1], [6, 2], [12, 1]], 1/41472],
[[[1, 2], [2, 5], [3, 5], [4, 1], [6, 1], [12, 1]], 1/1327104],
[[[1, 2], [2, 5], [4, 1], [6, 2], [12, 1], [24, 1]], 1/9216],
[[[1, 2], [2, 5], [4, 1], [6, 3], [12, 1], [18, 1]], 1/1728],
[[[1, 2], [2, 5], [4, 2], [5, 1], [6, 1], [8, 2]], 1/15360],
[[[1, 2], [2, 5], [4, 2], [6, 1], [8, 2], [10, 1]], 13/15360],
[[[1, 2], [2, 5], [4, 3], [6, 2], [8, 1], [12, 1]], 5/13824],
[[[1, 2], [2, 5], [4, 3], [8, 1], [10, 1], [12, 1]], 1/3840],
[[[1, 2], [2, 5], [4, 4], [6, 1], [8, 1], [10, 1]], 1/7680],
[[[1, 2], [2, 5], [4, 4], [6, 1], [8, 1], [12, 1]], 1/3456],
[[[1, 2], [2, 5], [4, 4], [6, 1], [10, 1], [12, 1]], 1/5760],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 2], [8, 2]], 1/27648],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 2], [12, 2]], 1/46080],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 3], [18, 1]], 1/6912],
[[[1, 2], [2, 7], [3, 1], [4, 1], [6, 4], [12, 1]], 11/46080],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 1], [8, 2]], 31/442368],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 3], [8, 1]], 1/27648],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 3], [10, 1]], 1/155520],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 3], [12, 1]], 199/622080],
[[[1, 2], [2, 7], [3, 1], [4, 3], [6, 2], [8, 1]], 1/18432],
[[[1, 2], [2, 7], [3, 1], [4, 4], [6, 1], [8, 1]], 1/196608],
[[[1, 2], [2, 7], [3, 1], [4, 4], [6, 1], [10, 1]], 1/552960],
[[[1, 2], [2, 7], [3, 1], [4, 4], [6, 1], [12, 1]], 1/41472],
[[[1, 2], [2, 7], [3, 1], [6, 1], [8, 2], [10, 1]], 1/46080],
[[[1, 2], [2, 7], [3, 1], [6, 2], [12, 1], [18, 1]], 23/311040],
[[[1, 2], [2, 7], [3, 2], [4, 1], [6, 1], [8, 2]], 1/55296],
[[[1, 2], [2, 7], [3, 2], [4, 1], [6, 1], [12, 2]], 1/276480],
[[[1, 2], [2, 7], [3, 2], [4, 1], [6, 3], [8, 1]], 1/13824],
[[[1, 2], [2, 7], [3, 2], [4, 1], [6, 3], [12, 1]], 1/20480],
[[[1, 2], [2, 7], [3, 2], [4, 2], [6, 2], [8, 1]], 1/27648],
[[[1, 2], [2, 7], [3, 2], [4, 3], [6, 1], [8, 1]], 1/442368],
[[[1, 2], [2, 7], [3, 3], [4, 1], [6, 2], [12, 1]], 1/276480],
[[[1, 2], [2, 7], [3, 4], [4, 1], [6, 1], [12, 1]], 1/1658880],
[[[1, 2], [2, 7], [4, 3], [5, 1], [6, 1], [8, 1]], 1/122880],
[[[1, 2], [2, 7], [4, 3], [6, 1], [8, 1], [12, 1]], 1/6912],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 1], [8, 2]], 1/442368],
[[[1, 2], [2, 9], [3, 1], [4, 1], [6, 3], [12, 1]], 7/1658880],
[[[1, 2], [2, 9], [3, 1], [4, 2], [6, 2], [8, 1]], 1/110592],
[[[1, 2], [2, 9], [3, 1], [4, 2], [6, 2], [10, 1]], 1/414720],
[[[1, 2], [2, 9], [3, 1], [4, 2], [6, 2], [12, 1]], 53/2488320],
[[[1, 2], [2, 9], [3, 1], [4, 3], [6, 1], [8, 1]], 7/589824],
[[[1, 2], [2, 9], [3, 2], [4, 1], [6, 2], [8, 1]], 1/110592],
[[[1, 2], [2, 9], [3, 2], [4, 1], [6, 2], [12, 1]], 1/829440],
[[[1, 2], [2, 9], [3, 2], [4, 2], [6, 1], [8, 1]], 1/221184],
[[[1, 2], [2, 11], [3, 1], [4, 2], [6, 1], [8, 1]], 1/1769472],
[[[1, 2], [2, 11], [3, 1], [4, 2], [6, 1], [10, 1]], 1/3317760],
[[[1, 2], [2, 11], [3, 1], [4, 2], [6, 1], [12, 1]], 29/59719680],
[[[1, 3], [2, 2], [3, 1], [4, 1], [6, 2], [8, 3]], 1/27648],
[[[1, 3], [2, 2], [3, 1], [4, 1], [8, 3], [10, 1]], 1/7680],
[[[1, 3], [2, 2], [3, 1], [4, 2], [6, 1], [8, 3]], 1/6144],
[[[1, 3], [2, 2], [3, 1], [4, 2], [6, 1], [12, 3]], 1/3072],
[[[1, 3], [2, 2], [3, 1], [4, 2], [6, 3], [12, 2]], 1/1024],
[[[1, 3], [2, 2], [3, 1], [4, 2], [6, 5], [12, 1]], 1/110592],
[[[1, 3], [2, 2], [3, 1], [4, 6], [6, 1], [8, 1]], 1/147456],
[[[1, 3], [2, 2], [3, 1], [6, 2], [9, 1], [12, 2]], 1/5184],
[[[1, 3], [2, 2], [3, 1], [6, 2], [9, 1], [24, 1]], 1/864],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 1], [8, 3]], 1/9216],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 1], [12, 3]], 1/4608],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 3], [12, 2]], 23/41472],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 4], [9, 1]], 65/165888],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 5], [12, 1]], 43/497664],
[[[1, 3], [2, 2], [3, 2], [4, 1], [9, 1], [12, 2]], 1/4608],
[[[1, 3], [2, 2], [3, 2], [4, 2], [5, 1], [12, 2]], 1/960],
[[[1, 3], [2, 2], [3, 2], [4, 2], [6, 4], [12, 1]], 101/82944],
[[[1, 3], [2, 2], [3, 2], [4, 2], [12, 1], [24, 1]], 1/1536],
[[[1, 3], [2, 2], [3, 2], [4, 4], [8, 1], [12, 1]], 1/13824],
[[[1, 3], [2, 2], [3, 2], [4, 5], [6, 1], [8, 1]], 1/110592],
[[[1, 3], [2, 2], [3, 2], [5, 1], [6, 2], [12, 2]], 1/7680],
[[[1, 3], [2, 2], [3, 2], [5, 1], [6, 3], [9, 1]], 1/25920],
[[[1, 3], [2, 2], [3, 2], [5, 1], [6, 4], [12, 1]], 1/23040],
[[[1, 3], [2, 2], [3, 2], [6, 1], [12, 2], [18, 1]], 1/15552],
[[[1, 3], [2, 2], [3, 2], [6, 1], [18, 1], [24, 1]], 1/2592],
[[[1, 3], [2, 2], [3, 2], [6, 2], [10, 1], [12, 2]], 1/5760],
[[[1, 3], [2, 2], [3, 2], [6, 2], [10, 1], [24, 1]], 1/960],
[[[1, 3], [2, 2], [3, 2], [6, 3], [12, 1], [18, 1]], 1/5184],
[[[1, 3], [2, 2], [3, 3], [4, 1], [6, 2], [12, 2]], 5/6912],
[[[1, 3], [2, 2], [3, 3], [4, 1], [6, 3], [9, 1]], 1/6912],
[[[1, 3], [2, 2], [3, 3], [4, 1], [6, 4], [12, 1]], 5/41472],
[[[1, 3], [2, 2], [3, 3], [4, 1], [12, 1], [24, 1]], 1/1152],
[[[1, 3], [2, 2], [3, 3], [4, 2], [6, 1], [12, 2]], 1/9216],
[[[1, 3], [2, 2], [3, 3], [4, 2], [6, 3], [12, 1]], 1/55296],
[[[1, 3], [2, 2], [3, 3], [5, 1], [6, 1], [12, 2]], 1/11520],
[[[1, 3], [2, 2], [3, 3], [5, 1], [6, 1], [24, 1]], 1/1920],
[[[1, 3], [2, 2], [3, 3], [6, 2], [9, 1], [12, 1]], 1/1728],
[[[1, 3], [2, 2], [3, 4], [4, 1], [6, 1], [12, 2]], 1/4608],
[[[1, 3], [2, 2], [3, 4], [4, 1], [6, 2], [9, 1]], 1/82944],
[[[1, 3], [2, 2], [3, 4], [4, 1], [6, 3], [12, 1]], 29/248832],
[[[1, 3], [2, 2], [3, 4], [4, 1], [9, 1], [12, 1]], 1/13824],
[[[1, 3], [2, 2], [3, 4], [4, 2], [6, 2], [12, 1]], 1/9216],
[[[1, 3], [2, 2], [3, 4], [5, 1], [6, 1], [9, 1]], 1/25920],
[[[1, 3], [2, 2], [3, 4], [5, 1], [6, 2], [12, 1]], 1/23040],
[[[1, 3], [2, 2], [3, 4], [6, 1], [9, 1], [12, 1]], 5/7776],
[[[1, 3], [2, 2], [3, 5], [4, 1], [6, 2], [12, 1]], 11/41472],
[[[1, 3], [2, 2], [3, 5], [4, 2], [6, 1], [12, 1]], 115/331776],
[[[1, 3], [2, 2], [3, 6], [4, 1], [6, 1], [12, 1]], 5/165888],
[[[1, 3], [2, 2], [4, 2], [6, 2], [12, 1], [24, 1]], 1/1536],
[[[1, 3], [2, 2], [4, 4], [5, 1], [8, 1], [12, 1]], 1/3840],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 1], [8, 3]], 17/55296],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 1], [12, 3]], 1/9216],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 3], [8, 2]], 1/9216],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 3], [12, 2]], 19/27648],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 3], [24, 1]], 1/3072],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 4], [18, 1]], 1/10368],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 5], [12, 1]], 49/110592],
[[[1, 3], [2, 4], [3, 1], [4, 2], [6, 2], [8, 2]], 17/18432],
[[[1, 3], [2, 4], [3, 1], [4, 2], [6, 2], [12, 2]], 1/1152],
[[[1, 3], [2, 4], [3, 1], [4, 2], [6, 4], [12, 1]], 1/864],
[[[1, 3], [2, 4], [3, 1], [4, 2], [8, 2], [10, 1]], 1/5120],
[[[1, 3], [2, 4], [3, 1], [4, 3], [6, 1], [8, 2]], 17/24576],
[[[1, 3], [2, 4], [3, 1], [4, 3], [6, 3], [12, 1]], 79/82944],
[[[1, 3], [2, 4], [3, 1], [4, 4], [6, 2], [8, 1]], 1/9216],
[[[1, 3], [2, 4], [3, 1], [4, 4], [6, 2], [12, 1]], 1/6912],
[[[1, 3], [2, 4], [3, 1], [4, 5], [6, 1], [8, 1]], 3/32768],
[[[1, 3], [2, 4], [3, 1], [4, 5], [6, 1], [10, 1]], 1/92160],
[[[1, 3], [2, 4], [3, 1], [4, 5], [6, 1], [12, 1]], 1/9216],
[[[1, 3], [2, 4], [3, 1], [5, 1], [6, 2], [8, 2]], 1/5760],
[[[1, 3], [2, 4], [3, 1], [6, 1], [9, 1], [12, 2]], 1/41472],
[[[1, 3], [2, 4], [3, 1], [6, 1], [9, 1], [24, 1]], 1/6912],
[[[1, 3], [2, 4], [3, 1], [6, 1], [12, 2], [18, 1]], 1/13824],
[[[1, 3], [2, 4], [3, 1], [6, 1], [18, 1], [24, 1]], 1/2304],
[[[1, 3], [2, 4], [3, 1], [6, 3], [10, 1], [18, 1]], 1/4320],
[[[1, 3], [2, 4], [3, 1], [6, 3], [12, 1], [18, 1]], 1/5184],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 2], [8, 2]], 23/82944],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 2], [12, 2]], 149/165888],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 2], [24, 1]], 1/1536],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 3], [9, 1]], 17/41472],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 3], [18, 1]], 1/13824],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 4], [10, 1]], 1/1920],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 4], [12, 1]], 61/82944],
[[[1, 3], [2, 4], [3, 2], [4, 1], [8, 2], [10, 1]], 1/23040],
[[[1, 3], [2, 4], [3, 2], [4, 1], [12, 1], [24, 1]], 1/9216],
[[[1, 3], [2, 4], [3, 2], [4, 2], [6, 1], [8, 2]], 7/36864],
[[[1, 3], [2, 4], [3, 2], [4, 2], [6, 1], [12, 2]], 1/1536],
[[[1, 3], [2, 4], [3, 2], [4, 2], [6, 2], [18, 1]], 1/1152],
[[[1, 3], [2, 4], [3, 2], [4, 2], [6, 3], [12, 1]], 1391/2239488],
[[[1, 3], [2, 4], [3, 2], [4, 3], [6, 2], [12, 1]], 67/124416],
[[[1, 3], [2, 4], [3, 2], [4, 3], [10, 1], [12, 1]], 1/8640],
[[[1, 3], [2, 4], [3, 2], [4, 4], [6, 1], [12, 1]], 1/13824],
[[[1, 3], [2, 4], [3, 2], [5, 1], [6, 2], [9, 1]], 1/25920],
[[[1, 3], [2, 4], [3, 2], [5, 1], [6, 2], [18, 1]], 1/2160],
[[[1, 3], [2, 4], [3, 2], [5, 1], [6, 3], [12, 1]], 1/11520],
[[[1, 3], [2, 4], [3, 2], [6, 2], [10, 1], [18, 1]], 1/4320],
[[[1, 3], [2, 4], [3, 2], [6, 2], [12, 1], [18, 1]], 1/82944],
[[[1, 3], [2, 4], [3, 2], [6, 3], [10, 1], [12, 1]], 1/2304],
[[[1, 3], [2, 4], [3, 3], [4, 1], [5, 1], [6, 3]], 1/960],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 1], [8, 2]], 1/20736],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 1], [12, 2]], 5/55296],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 1], [24, 1]], 1/3072],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 2], [18, 1]], 13/10368],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 3], [12, 1]], 73/82944],
[[[1, 3], [2, 4], [3, 3], [4, 2], [6, 2], [12, 1]], 1/2304],
[[[1, 3], [2, 4], [3, 3], [4, 3], [6, 1], [12, 1]], 7/9216],
[[[1, 3], [2, 4], [3, 3], [6, 2], [10, 1], [12, 1]], 1/3840],
[[[1, 3], [2, 4], [3, 4], [4, 1], [6, 1], [9, 1]], 1/41472],
[[[1, 3], [2, 4], [3, 4], [4, 1], [6, 2], [12, 1]], 181/124416],
[[[1, 3], [2, 4], [3, 4], [4, 2], [6, 1], [12, 1]], 1/9216],
[[[1, 3], [2, 4], [3, 5], [4, 1], [6, 1], [12, 1]], 1/331776],
[[[1, 3], [2, 4], [4, 1], [5, 1], [6, 2], [8, 2]], 1/5760],
[[[1, 3], [2, 4], [4, 1], [6, 2], [12, 1], [24, 1]], 1/3072],
[[[1, 3], [2, 4], [4, 1], [6, 3], [12, 1], [18, 1]], 1/2304],
[[[1, 3], [2, 4], [4, 2], [5, 1], [6, 1], [8, 2]], 1/5120],
[[[1, 3], [2, 4], [4, 2], [5, 1], [6, 3], [12, 1]], 1/19440],
[[[1, 3], [2, 4], [4, 2], [6, 1], [8, 2], [10, 1]], 1/7680],
[[[1, 3], [2, 4], [4, 3], [6, 2], [8, 1], [12, 1]], 1/27648],
[[[1, 3], [2, 4], [4, 3], [8, 1], [10, 1], [12, 1]], 1/7680],
[[[1, 3], [2, 4], [4, 4], [6, 1], [8, 1], [12, 1]], 1/2304],
[[[1, 3], [2, 6], [3, 1], [4, 1], [5, 1], [8, 2]], 1/46080],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 2], [8, 2]], 35/55296],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 2], [12, 2]], 7/55296],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 3], [18, 1]], 13/20736],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 4], [8, 1]], 11/20736],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 4], [12, 1]], 109/110592],
[[[1, 3], [2, 6], [3, 1], [4, 1], [8, 2], [10, 1]], 1/30720],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 1], [8, 2]], 149/294912],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 3], [8, 1]], 1/6144],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 3], [12, 1]], 5/4608],
[[[1, 3], [2, 6], [3, 1], [4, 3], [6, 2], [8, 1]], 83/442368],
[[[1, 3], [2, 6], [3, 1], [4, 3], [6, 2], [10, 1]], 13/69120],
[[[1, 3], [2, 6], [3, 1], [4, 3], [6, 2], [12, 1]], 1/2304],
[[[1, 3], [2, 6], [3, 1], [4, 3], [8, 1], [10, 1]], 29/122880],
[[[1, 3], [2, 6], [3, 1], [4, 3], [10, 1], [12, 1]], 1/11520],
[[[1, 3], [2, 6], [3, 1], [4, 4], [6, 1], [8, 1]], 59/589824],
[[[1, 3], [2, 6], [3, 1], [4, 4], [6, 1], [10, 1]], 1/92160],
[[[1, 3], [2, 6], [3, 1], [4, 4], [6, 1], [12, 1]], 13/110592],
[[[1, 3], [2, 6], [3, 1], [5, 1], [6, 1], [8, 2]], 1/46080],
[[[1, 3], [2, 6], [3, 1], [6, 1], [8, 2], [10, 1]], 1/7680],
[[[1, 3], [2, 6], [3, 1], [6, 2], [12, 1], [18, 1]], 5/20736],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 1], [8, 2]], 11/82944],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 1], [12, 2]], 23/414720],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 2], [9, 1]], 7/207360],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 2], [18, 1]], 1/1536],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 3], [8, 1]], 5/20736],
[[[1, 3], [2, 6], [3, 2], [4, 1], [6, 3], [12, 1]], 761/829440],
[[[1, 3], [2, 6], [3, 2], [4, 2], [6, 2], [8, 1]], 35/165888],
[[[1, 3], [2, 6], [3, 2], [4, 2], [6, 2], [12, 1]], 7/7290],
[[[1, 3], [2, 6], [3, 2], [4, 3], [6, 1], [8, 1]], 5/110592],
[[[1, 3], [2, 6], [3, 2], [4, 3], [6, 1], [12, 1]], 1/31104],
[[[1, 3], [2, 6], [3, 3], [4, 1], [6, 2], [8, 1]], 1/13824],
[[[1, 3], [2, 6], [3, 3], [4, 1], [6, 2], [12, 1]], 31/331776],
[[[1, 3], [2, 6], [3, 3], [4, 2], [6, 1], [8, 1]], 1/82944],
[[[1, 3], [2, 6], [3, 4], [4, 1], [6, 1], [12, 1]], 23/2488320],
[[[1, 3], [2, 6], [4, 1], [5, 1], [6, 1], [8, 2]], 1/23040],
[[[1, 3], [2, 6], [4, 1], [6, 1], [8, 2], [10, 1]], 1/7680],
[[[1, 3], [2, 6], [4, 2], [5, 1], [6, 2], [8, 1]], 1/23040],
[[[1, 3], [2, 6], [4, 2], [5, 1], [6, 2], [12, 1]], 1/51840],
[[[1, 3], [2, 6], [4, 3], [5, 1], [6, 1], [8, 1]], 1/15360],
[[[1, 3], [2, 6], [4, 3], [6, 1], [8, 1], [10, 1]], 19/30720],
[[[1, 3], [2, 6], [4, 3], [6, 1], [8, 1], [12, 1]], 5/13824],
[[[1, 3], [2, 6], [4, 3], [6, 1], [10, 1], [12, 1]], 1/2880],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 1], [8, 2]], 701/8847360],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 3], [8, 1]], 1/2048],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 3], [10, 1]], 1/12960],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 3], [12, 1]], 31/552960],
[[[1, 3], [2, 8], [3, 1], [4, 2], [5, 1], [6, 2]], 1/92160],
[[[1, 3], [2, 8], [3, 1], [4, 2], [5, 1], [8, 1]], 1/184320],
[[[1, 3], [2, 8], [3, 1], [4, 2], [6, 2], [8, 1]], 1/4608],
[[[1, 3], [2, 8], [3, 1], [4, 2], [6, 2], [10, 1]], 1/69120],
[[[1, 3], [2, 8], [3, 1], [4, 2], [6, 2], [12, 1]], 1/4608],
[[[1, 3], [2, 8], [3, 1], [4, 3], [6, 1], [8, 1]], 559/3538944],
[[[1, 3], [2, 8], [3, 1], [4, 3], [6, 1], [10, 1]], 61/1105920],
[[[1, 3], [2, 8], [3, 1], [4, 3], [6, 1], [12, 1]], 71/1105920],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 2], [8, 1]], 1/10368],
[[[1, 3], [2, 8], [3, 2], [4, 1], [6, 2], [12, 1]], 11/497664],
[[[1, 3], [2, 8], [3, 2], [4, 2], [6, 1], [8, 1]], 1/20736],
[[[1, 3], [2, 8], [3, 2], [4, 2], [6, 1], [12, 1]], 1/1492992],
[[[1, 3], [2, 8], [3, 3], [4, 1], [6, 1], [8, 1]], 1/110592],
[[[1, 3], [2, 8], [3, 3], [4, 1], [6, 1], [12, 1]], 1/552960],
[[[1, 3], [2, 8], [4, 2], [5, 1], [6, 1], [8, 1]], 1/92160],
[[[1, 3], [2, 8], [4, 2], [5, 1], [6, 1], [12, 1]], 1/414720],
[[[1, 3], [2, 10], [3, 1], [4, 1], [6, 2], [8, 1]], 143/2211840],
[[[1, 3], [2, 10], [3, 1], [4, 1], [6, 2], [10, 1]], 7/276480],
[[[1, 3], [2, 10], [3, 1], [4, 2], [5, 1], [6, 1]], 1/737280],
[[[1, 3], [2, 10], [3, 1], [4, 2], [6, 1], [8, 1]], 17/737280],
[[[1, 3], [2, 10], [3, 1], [4, 2], [6, 1], [10, 1]], 1/276480],
[[[1, 3], [2, 10], [3, 1], [4, 2], [6, 1], [12, 1]], 11/1105920],
[[[1, 3], [2, 10], [3, 2], [4, 1], [6, 1], [8, 1]], 1/663552],
[[[1, 3], [2, 12], [3, 1], [4, 1], [6, 1], [8, 1]], 79/53084160],
[[[1, 3], [2, 12], [3, 1], [4, 1], [6, 1], [10, 1]], 1/368640],
[[[1, 3], [3, 2], [4, 2], [6, 2], [9, 1], [12, 1]], 1/2592],
[[[1, 3], [3, 2], [5, 1], [6, 2], [9, 1], [12, 1]], 1/8640],
[[[1, 4], [2, 1], [3, 1], [4, 1], [5, 1], [8, 3]], 1/7680],
[[[1, 4], [2, 1], [3, 1], [4, 5], [5, 1], [8, 1]], 1/92160],
[[[1, 4], [2, 1], [3, 2], [4, 1], [6, 1], [8, 3]], 1/9216],
[[[1, 4], [2, 1], [3, 2], [4, 1], [6, 1], [12, 3]], 1/13824],
[[[1, 4], [2, 1], [3, 2], [4, 1], [6, 3], [12, 2]], 1/41472],
[[[1, 4], [2, 1], [3, 2], [4, 1], [6, 4], [9, 1]], 1/165888],
[[[1, 4], [2, 1], [3, 2], [4, 1], [6, 5], [12, 1]], 1/497664],
[[[1, 4], [2, 1], [3, 2], [4, 1], [9, 1], [12, 2]], 1/4608],
[[[1, 4], [2, 1], [3, 2], [5, 1], [6, 3], [9, 1]], 1/8640],
[[[1, 4], [2, 1], [3, 3], [4, 1], [6, 2], [12, 2]], 1/6912],
[[[1, 4], [2, 1], [3, 3], [4, 1], [6, 3], [9, 1]], 1/768],
[[[1, 4], [2, 1], [3, 3], [4, 1], [6, 4], [12, 1]], 1/41472],
[[[1, 4], [2, 1], [3, 3], [4, 1], [12, 1], [24, 1]], 1/3456],
[[[1, 4], [2, 1], [3, 3], [4, 2], [6, 3], [12, 1]], 19/62208],
[[[1, 4], [2, 1], [3, 3], [4, 3], [8, 1], [12, 1]], 1/10368],
[[[1, 4], [2, 1], [3, 3], [5, 1], [6, 1], [12, 2]], 1/3840],
[[[1, 4], [2, 1], [3, 3], [5, 1], [6, 2], [9, 1]], 1/8640],
[[[1, 4], [2, 1], [3, 3], [5, 1], [6, 3], [12, 1]], 1/11520],
[[[1, 4], [2, 1], [3, 3], [5, 1], [9, 1], [12, 1]], 1/1440],
[[[1, 4], [2, 1], [3, 3], [6, 1], [10, 1], [12, 2]], 1/34560],
[[[1, 4], [2, 1], [3, 3], [6, 1], [10, 1], [24, 1]], 1/5760],
[[[1, 4], [2, 1], [3, 3], [6, 2], [9, 1], [12, 1]], 1/10368],
[[[1, 4], [2, 1], [3, 4], [4, 1], [6, 1], [12, 2]], 1/13824],
[[[1, 4], [2, 1], [3, 4], [4, 1], [6, 2], [9, 1]], 1/82944],
[[[1, 4], [2, 1], [3, 4], [4, 1], [6, 3], [12, 1]], 1/82944],
[[[1, 4], [2, 1], [3, 4], [4, 1], [9, 1], [12, 1]], 1/13824],
[[[1, 4], [2, 1], [3, 4], [5, 1], [6, 1], [9, 1]], 1/8640],
[[[1, 4], [2, 1], [3, 4], [6, 1], [9, 1], [12, 1]], 1/2592],
[[[1, 4], [2, 1], [3, 5], [4, 1], [6, 2], [12, 1]], 1/13824],
[[[1, 4], [2, 1], [3, 5], [5, 1], [6, 1], [12, 1]], 1/11520],
[[[1, 4], [2, 1], [3, 6], [4, 1], [6, 1], [12, 1]], 5/497664],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 1], [8, 3]], 17/55296],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 1], [12, 3]], 1/9216],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 3], [8, 2]], 1/20736],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 3], [12, 2]], 5/55296],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 3], [24, 1]], 1/3072],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 4], [18, 1]], 1/41472],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 5], [12, 1]], 1/331776],
[[[1, 4], [2, 3], [3, 1], [4, 2], [5, 1], [8, 2]], 1/7680],
[[[1, 4], [2, 3], [3, 1], [4, 2], [6, 2], [8, 2]], 7/36864],
[[[1, 4], [2, 3], [3, 1], [4, 2], [6, 2], [12, 2]], 1/1536],
[[[1, 4], [2, 3], [3, 1], [4, 2], [6, 4], [12, 1]], 1/9216],
[[[1, 4], [2, 3], [3, 1], [4, 2], [8, 2], [10, 1]], 1/5120],
[[[1, 4], [2, 3], [3, 1], [4, 3], [6, 1], [8, 2]], 17/24576],
[[[1, 4], [2, 3], [3, 1], [4, 3], [6, 3], [12, 1]], 7/9216],
[[[1, 4], [2, 3], [3, 1], [4, 4], [6, 2], [12, 1]], 1/13824],
[[[1, 4], [2, 3], [3, 1], [4, 4], [8, 1], [12, 1]], 1/2304],
[[[1, 4], [2, 3], [3, 1], [4, 5], [5, 1], [6, 1]], 1/92160],
[[[1, 4], [2, 3], [3, 1], [4, 5], [6, 1], [8, 1]], 3/32768],
[[[1, 4], [2, 3], [3, 1], [4, 5], [6, 1], [12, 1]], 1/9216],
[[[1, 4], [2, 3], [3, 1], [6, 1], [9, 1], [12, 2]], 1/13824],
[[[1, 4], [2, 3], [3, 1], [6, 1], [9, 1], [24, 1]], 1/2304],
[[[1, 4], [2, 3], [3, 1], [6, 1], [12, 2], [18, 1]], 1/41472],
[[[1, 4], [2, 3], [3, 1], [6, 1], [18, 1], [24, 1]], 1/6912],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 2], [8, 2]], 23/82944],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 2], [12, 2]], 149/165888],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 2], [24, 1]], 1/1536],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 3], [9, 1]], 13/10368],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 4], [12, 1]], 181/124416],
[[[1, 4], [2, 3], [3, 2], [4, 1], [8, 2], [10, 1]], 1/5760],
[[[1, 4], [2, 3], [3, 2], [4, 1], [12, 1], [24, 1]], 1/3072],
[[[1, 4], [2, 3], [3, 2], [4, 2], [6, 1], [8, 2]], 17/18432],
[[[1, 4], [2, 3], [3, 2], [4, 2], [6, 1], [12, 2]], 1/1152],
[[[1, 4], [2, 3], [3, 2], [4, 2], [6, 2], [9, 1]], 1/1152],
[[[1, 4], [2, 3], [3, 2], [4, 2], [6, 3], [12, 1]], 1/2304],
[[[1, 4], [2, 3], [3, 2], [4, 3], [6, 2], [12, 1]], 67/124416],
[[[1, 4], [2, 3], [3, 2], [4, 3], [8, 1], [12, 1]], 1/27648],
[[[1, 4], [2, 3], [3, 2], [4, 4], [6, 1], [8, 1]], 1/9216],
[[[1, 4], [2, 3], [3, 2], [4, 4], [6, 1], [12, 1]], 1/6912],
[[[1, 4], [2, 3], [3, 2], [5, 1], [6, 2], [9, 1]], 1/4320],
[[[1, 4], [2, 3], [3, 2], [5, 1], [6, 3], [12, 1]], 1/3840],
[[[1, 4], [2, 3], [3, 2], [6, 1], [8, 2], [10, 1]], 1/5760],
[[[1, 4], [2, 3], [3, 2], [6, 2], [9, 1], [10, 1]], 1/2160],
[[[1, 4], [2, 3], [3, 2], [6, 2], [9, 1], [12, 1]], 1/82944],
[[[1, 4], [2, 3], [3, 2], [6, 2], [10, 1], [18, 1]], 1/25920],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 1], [8, 2]], 1/9216],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 1], [12, 2]], 19/27648],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 1], [24, 1]], 1/3072],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 2], [9, 1]], 1/13824],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 2], [18, 1]], 17/41472],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 3], [10, 1]], 1/960],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 3], [12, 1]], 73/82944],
[[[1, 4], [2, 3], [3, 3], [4, 1], [9, 1], [12, 1]], 1/2304],
[[[1, 4], [2, 3], [3, 3], [4, 2], [6, 2], [12, 1]], 1391/2239488],
[[[1, 4], [2, 3], [3, 3], [4, 2], [10, 1], [12, 1]], 1/19440],
[[[1, 4], [2, 3], [3, 3], [4, 3], [6, 1], [12, 1]], 79/82944],
[[[1, 4], [2, 3], [3, 3], [5, 1], [6, 1], [9, 1]], 1/4320],
[[[1, 4], [2, 3], [3, 3], [5, 1], [6, 2], [12, 1]], 1/2304],
[[[1, 4], [2, 3], [3, 3], [6, 1], [9, 1], [12, 1]], 1/5184],
[[[1, 4], [2, 3], [3, 3], [6, 2], [10, 1], [12, 1]], 1/11520],
[[[1, 4], [2, 3], [3, 4], [4, 1], [5, 1], [6, 2]], 1/1920],
[[[1, 4], [2, 3], [3, 4], [4, 1], [6, 1], [9, 1]], 1/10368],
[[[1, 4], [2, 3], [3, 4], [4, 1], [6, 2], [12, 1]], 61/82944],
[[[1, 4], [2, 3], [3, 4], [4, 2], [6, 1], [12, 1]], 1/864],
[[[1, 4], [2, 3], [3, 5], [4, 1], [6, 1], [12, 1]], 49/110592],
[[[1, 4], [2, 3], [4, 1], [5, 1], [6, 2], [8, 2]], 1/23040],
[[[1, 4], [2, 3], [4, 1], [6, 2], [12, 1], [24, 1]], 1/9216],
[[[1, 4], [2, 3], [4, 2], [5, 1], [6, 1], [8, 2]], 1/5120],
[[[1, 4], [2, 3], [4, 3], [5, 1], [6, 2], [12, 1]], 1/8640],
[[[1, 4], [2, 3], [4, 3], [5, 1], [8, 1], [12, 1]], 1/7680],
[[[1, 4], [2, 5], [3, 1], [4, 1], [5, 1], [8, 2]], 1/7680],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 2], [8, 2]], 25/27648],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 2], [12, 2]], 1/3456],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 3], [18, 1]], 13/20736],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 4], [8, 1]], 1/20736],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 4], [12, 1]], 221/165888],
[[[1, 4], [2, 5], [3, 1], [4, 1], [8, 2], [10, 1]], 7/46080],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 1], [8, 2]], 1795/884736],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 3], [8, 1]], 1/1536],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 3], [12, 1]], 601/373248],
[[[1, 4], [2, 5], [3, 1], [4, 3], [5, 1], [8, 1]], 1/30720],
[[[1, 4], [2, 5], [3, 1], [4, 3], [6, 2], [8, 1]], 3/4096],
[[[1, 4], [2, 5], [3, 1], [4, 3], [6, 2], [12, 1]], 11/10368],
[[[1, 4], [2, 5], [3, 1], [4, 3], [8, 1], [10, 1]], 1/5120],
[[[1, 4], [2, 5], [3, 1], [4, 3], [10, 1], [12, 1]], 1/5760],
[[[1, 4], [2, 5], [3, 1], [4, 4], [6, 1], [8, 1]], 59/98304],
[[[1, 4], [2, 5], [3, 1], [4, 4], [6, 1], [10, 1]], 3/20480],
[[[1, 4], [2, 5], [3, 1], [4, 4], [6, 1], [12, 1]], 97/110592],
[[[1, 4], [2, 5], [3, 1], [5, 1], [6, 1], [8, 2]], 1/7680],
[[[1, 4], [2, 5], [3, 1], [5, 1], [6, 3], [8, 1]], 1/4320],
[[[1, 4], [2, 5], [3, 1], [6, 1], [8, 2], [10, 1]], 1/7680],
[[[1, 4], [2, 5], [3, 1], [6, 2], [12, 1], [18, 1]], 1/6912],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 1], [8, 2]], 35/82944],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 1], [12, 2]], 13/55296],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 2], [9, 1]], 13/41472],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 2], [18, 1]], 5/4608],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 3], [8, 1]], 31/20736],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 3], [12, 1]], 1919/995328],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 2], [8, 1]], 71/55296],
[[[1, 4], [2, 5], [3, 2], [4, 2], [6, 2], [12, 1]], 23/10368],
[[[1, 4], [2, 5], [3, 2], [4, 2], [8, 1], [10, 1]], 1/2880],
[[[1, 4], [2, 5], [3, 2], [4, 2], [10, 1], [12, 1]], 1/17280],
[[[1, 4], [2, 5], [3, 2], [4, 3], [6, 1], [8, 1]], 17/49152],
[[[1, 4], [2, 5], [3, 2], [4, 3], [6, 1], [12, 1]], 11/62208],
[[[1, 4], [2, 5], [3, 2], [5, 1], [6, 2], [8, 1]], 1/4320],
[[[1, 4], [2, 5], [3, 2], [6, 1], [9, 1], [12, 1]], 1/41472],
[[[1, 4], [2, 5], [3, 3], [4, 1], [6, 1], [9, 1]], 1/6912],
[[[1, 4], [2, 5], [3, 3], [4, 1], [6, 2], [8, 1]], 7/31104],
[[[1, 4], [2, 5], [3, 3], [4, 1], [6, 2], [12, 1]], 73/41472],
[[[1, 4], [2, 5], [3, 3], [4, 2], [6, 1], [8, 1]], 17/165888],
[[[1, 4], [2, 5], [3, 3], [4, 2], [6, 1], [12, 1]], 5651/5598720],
[[[1, 4], [2, 5], [3, 4], [4, 1], [6, 1], [8, 1]], 1/62208],
[[[1, 4], [2, 5], [3, 4], [4, 1], [6, 1], [12, 1]], 13/331776],
[[[1, 4], [2, 5], [4, 1], [5, 1], [6, 1], [8, 2]], 37/92160],
[[[1, 4], [2, 5], [4, 1], [5, 1], [6, 3], [8, 1]], 1/5760],
[[[1, 4], [2, 5], [4, 1], [6, 1], [8, 2], [10, 1]], 1/15360],
[[[1, 4], [2, 5], [4, 2], [5, 1], [6, 2], [8, 1]], 1/5760],
[[[1, 4], [2, 5], [4, 2], [5, 1], [6, 2], [12, 1]], 1/8640],
[[[1, 4], [2, 5], [4, 2], [6, 2], [8, 1], [10, 1]], 1/23040],
[[[1, 4], [2, 5], [4, 3], [5, 1], [6, 1], [8, 1]], 3/20480],
[[[1, 4], [2, 5], [4, 3], [5, 1], [6, 1], [12, 1]], 1/34560],
[[[1, 4], [2, 5], [4, 3], [6, 1], [8, 1], [10, 1]], 1/7680],
[[[1, 4], [2, 5], [4, 3], [6, 1], [8, 1], [12, 1]], 1/6912],
[[[1, 4], [2, 7], [3, 1], [4, 1], [5, 1], [6, 3]], 1/17280],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 1], [8, 2]], 4769/8847360],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 3], [8, 1]], 235/110592],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 3], [12, 1]], 85/331776],
[[[1, 4], [2, 7], [3, 1], [4, 2], [5, 1], [6, 2]], 1/23040],
[[[1, 4], [2, 7], [3, 1], [4, 2], [5, 1], [8, 1]], 1/18432],
[[[1, 4], [2, 7], [3, 1], [4, 2], [6, 2], [8, 1]], 25/12288],
[[[1, 4], [2, 7], [3, 1], [4, 2], [6, 2], [10, 1]], 83/138240],
[[[1, 4], [2, 7], [3, 1], [4, 2], [6, 2], [12, 1]], 293/497664],
[[[1, 4], [2, 7], [3, 1], [4, 2], [8, 1], [10, 1]], 7/30720],
[[[1, 4], [2, 7], [3, 1], [4, 2], [10, 1], [12, 1]], 1/46080],
[[[1, 4], [2, 7], [3, 1], [4, 3], [5, 1], [6, 1]], 11/368640],
[[[1, 4], [2, 7], [3, 1], [4, 3], [6, 1], [8, 1]], 2921/3538944],
[[[1, 4], [2, 7], [3, 1], [4, 3], [6, 1], [10, 1]], 17/92160],
[[[1, 4], [2, 7], [3, 1], [4, 3], [6, 1], [12, 1]], 317/663552],
[[[1, 4], [2, 7], [3, 1], [5, 1], [6, 2], [8, 1]], 1/17280],
[[[1, 4], [2, 7], [3, 2], [4, 1], [5, 1], [6, 2]], 1/17280],
[[[1, 4], [2, 7], [3, 2], [4, 1], [5, 1], [8, 1]], 1/138240],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 2], [8, 1]], 25/27648],
[[[1, 4], [2, 7], [3, 2], [4, 1], [6, 2], [12, 1]], 23/92160],
[[[1, 4], [2, 7], [3, 2], [4, 2], [6, 1], [8, 1]], 13/36864],
[[[1, 4], [2, 7], [3, 2], [4, 2], [6, 1], [10, 1]], 13/92160],
[[[1, 4], [2, 7], [3, 2], [4, 2], [6, 1], [12, 1]], 1/41472],
[[[1, 4], [2, 7], [3, 2], [5, 1], [6, 1], [8, 1]], 1/34560],
[[[1, 4], [2, 7], [3, 3], [4, 1], [6, 1], [8, 1]], 17/248832],
[[[1, 4], [2, 7], [3, 3], [4, 1], [6, 1], [12, 1]], 47/1658880],
[[[1, 4], [2, 7], [4, 1], [5, 1], [6, 2], [8, 1]], 1/15360],
[[[1, 4], [2, 7], [4, 2], [5, 1], [6, 1], [8, 1]], 1/5760],
[[[1, 4], [2, 7], [4, 2], [5, 1], [6, 1], [12, 1]], 1/34560],
[[[1, 4], [2, 7], [4, 2], [6, 1], [8, 1], [10, 1]], 173/184320],
[[[1, 4], [2, 7], [4, 2], [6, 1], [10, 1], [12, 1]], 1/17280],
[[[1, 4], [2, 9], [3, 1], [4, 1], [5, 1], [6, 2]], 1/69120],
[[[1, 4], [2, 9], [3, 1], [4, 1], [5, 1], [8, 1]], 1/552960],
[[[1, 4], [2, 9], [3, 1], [4, 1], [6, 2], [8, 1]], 53/69120],
[[[1, 4], [2, 9], [3, 1], [4, 1], [6, 2], [10, 1]], 11/69120],
[[[1, 4], [2, 9], [3, 1], [4, 2], [5, 1], [6, 1]], 1/73728],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 1], [8, 1]], 43/110592],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 1], [10, 1]], 299/2211840],
[[[1, 4], [2, 9], [3, 1], [4, 2], [6, 1], [12, 1]], 1459/19906560],
[[[1, 4], [2, 9], [3, 1], [5, 1], [6, 1], [8, 1]], 1/276480],
[[[1, 4], [2, 9], [3, 2], [4, 1], [5, 1], [6, 1]], 1/138240],
[[[1, 4], [2, 9], [3, 2], [4, 1], [6, 1], [8, 1]], 149/2211840],
[[[1, 4], [2, 9], [4, 1], [5, 1], [6, 1], [8, 1]], 1/122880],
[[[1, 4], [2, 11], [3, 1], [4, 1], [5, 1], [6, 1]], 1/1105920],
[[[1, 4], [2, 11], [3, 1], [4, 1], [6, 1], [8, 1]], 997/26542080],
[[[1, 4], [2, 11], [3, 1], [4, 1], [6, 1], [10, 1]], 19/552960],
[[[1, 5], [2, 2], [3, 1], [4, 1], [6, 1], [8, 3]], 7/73728],
[[[1, 5], [2, 2], [3, 1], [4, 1], [6, 1], [12, 3]], 1/36864],
[[[1, 5], [2, 2], [3, 1], [4, 1], [6, 3], [12, 2]], 1/110592],
[[[1, 5], [2, 2], [3, 1], [4, 1], [6, 5], [12, 1]], 1/1327104],
[[[1, 5], [2, 2], [3, 1], [4, 2], [5, 1], [8, 2]], 13/15360],
[[[1, 5], [2, 2], [3, 1], [4, 2], [6, 2], [8, 2]], 1/55296],
[[[1, 5], [2, 2], [3, 1], [4, 2], [8, 2], [10, 1]], 1/15360],
[[[1, 5], [2, 2], [3, 1], [4, 3], [6, 1], [8, 2]], 7/147456],
[[[1, 5], [2, 2], [3, 1], [4, 4], [5, 1], [8, 1]], 1/7680],
[[[1, 5], [2, 2], [3, 1], [4, 4], [5, 1], [12, 1]], 1/5760],
[[[1, 5], [2, 2], [3, 1], [4, 4], [8, 1], [12, 1]], 1/3456],
[[[1, 5], [2, 2], [3, 1], [4, 5], [6, 1], [8, 1]], 1/884736],
[[[1, 5], [2, 2], [3, 1], [4, 5], [6, 1], [12, 1]], 1/55296],
[[[1, 5], [2, 2], [3, 1], [6, 1], [9, 1], [12, 2]], 1/41472],
[[[1, 5], [2, 2], [3, 1], [6, 1], [9, 1], [24, 1]], 1/6912],
[[[1, 5], [2, 2], [3, 1], [6, 1], [12, 2], [18, 1]], 1/622080],
[[[1, 5], [2, 2], [3, 1], [6, 1], [18, 1], [24, 1]], 1/103680],
[[[1, 5], [2, 2], [3, 2], [4, 1], [6, 2], [8, 2]], 1/6912],
[[[1, 5], [2, 2], [3, 2], [4, 1], [6, 2], [12, 2]], 7/27648],
[[[1, 5], [2, 2], [3, 2], [4, 1], [6, 2], [24, 1]], 1/1536],
[[[1, 5], [2, 2], [3, 2], [4, 1], [6, 3], [9, 1]], 1/13824],
[[[1, 5], [2, 2], [3, 2], [4, 1], [6, 4], [12, 1]], 1/41472],
[[[1, 5], [2, 2], [3, 2], [4, 1], [12, 1], [24, 1]], 1/9216],
[[[1, 5], [2, 2], [3, 2], [4, 2], [6, 1], [8, 2]], 19/110592],
[[[1, 5], [2, 2], [3, 2], [4, 2], [6, 1], [12, 2]], 1/4608],
[[[1, 5], [2, 2], [3, 2], [4, 2], [6, 2], [9, 1]], 1/1152],
[[[1, 5], [2, 2], [3, 2], [4, 2], [6, 3], [12, 1]], 1/27648],
[[[1, 5], [2, 2], [3, 2], [4, 3], [6, 2], [12, 1]], 1/4608],
[[[1, 5], [2, 2], [3, 2], [4, 3], [8, 1], [12, 1]], 5/13824],
[[[1, 5], [2, 2], [3, 2], [4, 4], [5, 1], [6, 1]], 1/69120],
[[[1, 5], [2, 2], [3, 2], [4, 4], [6, 1], [12, 1]], 1/41472],
[[[1, 5], [2, 2], [3, 2], [5, 1], [6, 1], [8, 2]], 1/5760],
[[[1, 5], [2, 2], [3, 2], [5, 1], [6, 2], [9, 1]], 1/2880],
[[[1, 5], [2, 2], [3, 2], [6, 2], [9, 1], [12, 1]], 1/27648],
[[[1, 5], [2, 2], [3, 3], [4, 1], [6, 1], [8, 2]], 1/6912],
[[[1, 5], [2, 2], [3, 3], [4, 1], [6, 1], [12, 2]], 53/110592],
[[[1, 5], [2, 2], [3, 3], [4, 1], [6, 1], [24, 1]], 1/9216],
[[[1, 5], [2, 2], [3, 3], [4, 1], [6, 2], [9, 1]], 1/10368],
[[[1, 5], [2, 2], [3, 3], [4, 1], [6, 3], [12, 1]], 2335/1990656],
[[[1, 5], [2, 2], [3, 3], [4, 1], [9, 1], [12, 1]], 1/1728],
[[[1, 5], [2, 2], [3, 3], [4, 2], [6, 2], [12, 1]], 1/20736],
[[[1, 5], [2, 2], [3, 3], [4, 3], [6, 1], [12, 1]], 1/27648],
[[[1, 5], [2, 2], [3, 3], [5, 1], [6, 1], [9, 1]], 1/1296],
[[[1, 5], [2, 2], [3, 3], [5, 1], [6, 2], [12, 1]], 7/11520],
[[[1, 5], [2, 2], [3, 3], [6, 1], [9, 1], [12, 1]], 5/7776],
[[[1, 5], [2, 2], [3, 4], [4, 1], [6, 1], [9, 1]], 1/13824],
[[[1, 5], [2, 2], [3, 4], [4, 1], [6, 2], [10, 1]], 1/5760],
[[[1, 5], [2, 2], [3, 4], [4, 1], [6, 2], [12, 1]], 89/331776],
[[[1, 5], [2, 2], [3, 4], [4, 2], [6, 1], [12, 1]], 407/746496],
[[[1, 5], [2, 2], [3, 4], [5, 1], [6, 1], [12, 1]], 19/34560],
[[[1, 5], [2, 2], [3, 5], [4, 1], [6, 1], [12, 1]], 67/442368],
[[[1, 5], [2, 2], [4, 2], [5, 1], [6, 1], [8, 2]], 1/30720],
[[[1, 5], [2, 2], [4, 3], [5, 1], [8, 1], [12, 1]], 1/3840],
[[[1, 5], [2, 2], [4, 4], [5, 1], [6, 1], [12, 1]], 1/11520],
[[[1, 5], [2, 4], [3, 1], [4, 1], [5, 1], [8, 2]], 1/15360],
[[[1, 5], [2, 4], [3, 1], [4, 1], [6, 2], [8, 2]], 35/82944],
[[[1, 5], [2, 4], [3, 1], [4, 1], [6, 2], [12, 2]], 13/55296],
[[[1, 5], [2, 4], [3, 1], [4, 1], [6, 3], [18, 1]], 1/6912],
[[[1, 5], [2, 4], [3, 1], [4, 1], [6, 4], [8, 1]], 1/62208],
[[[1, 5], [2, 4], [3, 1], [4, 1], [6, 4], [12, 1]], 13/331776],
[[[1, 5], [2, 4], [3, 1], [4, 1], [8, 2], [10, 1]], 37/92160],
[[[1, 5], [2, 4], [3, 1], [4, 2], [6, 1], [8, 2]], 1795/884736],
[[[1, 5], [2, 4], [3, 1], [4, 2], [6, 3], [8, 1]], 17/165888],
[[[1, 5], [2, 4], [3, 1], [4, 2], [6, 3], [12, 1]], 5651/5598720],
[[[1, 5], [2, 4], [3, 1], [4, 3], [5, 1], [8, 1]], 1/7680],
[[[1, 5], [2, 4], [3, 1], [4, 3], [6, 2], [8, 1]], 17/49152],
[[[1, 5], [2, 4], [3, 1], [4, 3], [6, 2], [12, 1]], 11/62208],
[[[1, 5], [2, 4], [3, 1], [4, 3], [8, 1], [10, 1]], 3/20480],
[[[1, 5], [2, 4], [3, 1], [4, 3], [8, 1], [12, 1]], 1/6912],
[[[1, 5], [2, 4], [3, 1], [4, 3], [10, 1], [12, 1]], 1/34560],
[[[1, 5], [2, 4], [3, 1], [4, 4], [5, 1], [6, 1]], 3/20480],
[[[1, 5], [2, 4], [3, 1], [4, 4], [6, 1], [8, 1]], 59/98304],
[[[1, 5], [2, 4], [3, 1], [4, 4], [6, 1], [12, 1]], 97/110592],
[[[1, 5], [2, 4], [3, 1], [5, 1], [6, 1], [8, 2]], 1/7680],
[[[1, 5], [2, 4], [3, 1], [6, 1], [8, 2], [10, 1]], 1/7680],
[[[1, 5], [2, 4], [3, 1], [6, 2], [12, 1], [18, 1]], 1/41472],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 1], [8, 2]], 25/27648],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 1], [12, 2]], 1/3456],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 2], [9, 1]], 5/4608],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 2], [18, 1]], 13/41472],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 3], [8, 1]], 7/31104],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 3], [12, 1]], 73/41472],
[[[1, 5], [2, 4], [3, 2], [4, 2], [5, 1], [8, 1]], 1/23040],
[[[1, 5], [2, 4], [3, 2], [4, 2], [6, 2], [8, 1]], 71/55296],
[[[1, 5], [2, 4], [3, 2], [4, 2], [6, 2], [12, 1]], 23/10368],
[[[1, 5], [2, 4], [3, 2], [4, 2], [8, 1], [10, 1]], 1/5760],
[[[1, 5], [2, 4], [3, 2], [4, 2], [10, 1], [12, 1]], 1/8640],
[[[1, 5], [2, 4], [3, 2], [4, 3], [6, 1], [8, 1]], 3/4096],
[[[1, 5], [2, 4], [3, 2], [4, 3], [6, 1], [12, 1]], 11/10368],
[[[1, 5], [2, 4], [3, 2], [6, 1], [9, 1], [12, 1]], 1/6912],
[[[1, 5], [2, 4], [3, 2], [6, 2], [8, 1], [10, 1]], 1/4320],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 1], [9, 1]], 13/20736],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 2], [8, 1]], 31/20736],
[[[1, 5], [2, 4], [3, 3], [4, 1], [6, 2], [12, 1]], 1919/995328],
[[[1, 5], [2, 4], [3, 3], [4, 1], [8, 1], [10, 1]], 1/5760],
[[[1, 5], [2, 4], [3, 3], [4, 2], [6, 1], [8, 1]], 1/1536],
[[[1, 5], [2, 4], [3, 3], [4, 2], [6, 1], [12, 1]], 601/373248],
[[[1, 5], [2, 4], [3, 3], [6, 1], [8, 1], [10, 1]], 1/4320],
[[[1, 5], [2, 4], [3, 4], [4, 1], [6, 1], [8, 1]], 1/20736],
[[[1, 5], [2, 4], [3, 4], [4, 1], [6, 1], [12, 1]], 221/165888],
[[[1, 5], [2, 4], [4, 1], [5, 1], [6, 1], [8, 2]], 7/46080],
[[[1, 5], [2, 4], [4, 1], [6, 1], [8, 2], [10, 1]], 1/7680],
[[[1, 5], [2, 4], [4, 2], [5, 1], [6, 2], [8, 1]], 1/2880],
[[[1, 5], [2, 4], [4, 2], [5, 1], [6, 2], [12, 1]], 1/17280],
[[[1, 5], [2, 4], [4, 3], [5, 1], [6, 1], [8, 1]], 1/5120],
[[[1, 5], [2, 4], [4, 3], [5, 1], [6, 1], [12, 1]], 1/5760],
[[[1, 5], [2, 4], [4, 3], [6, 1], [8, 1], [10, 1]], 1/30720],
[[[1, 5], [2, 6], [3, 1], [4, 1], [5, 1], [6, 3]], 1/8640],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 1], [8, 2]], 3679/2654208],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 3], [8, 1]], 409/497664],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 3], [10, 1]], 1/17280],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 3], [12, 1]], 157/331776],
[[[1, 5], [2, 6], [3, 1], [4, 2], [5, 1], [6, 2]], 5/27648],
[[[1, 5], [2, 6], [3, 1], [4, 2], [5, 1], [8, 1]], 1/6144],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 2], [8, 1]], 2855/663552],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 2], [10, 1]], 1/11520],
[[[1, 5], [2, 6], [3, 1], [4, 2], [6, 2], [12, 1]], 41/93312],
[[[1, 5], [2, 6], [3, 1], [4, 2], [8, 1], [10, 1]], 37/46080],
[[[1, 5], [2, 6], [3, 1], [4, 2], [10, 1], [12, 1]], 1/11520],
[[[1, 5], [2, 6], [3, 1], [4, 3], [5, 1], [6, 1]], 7/92160],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 1], [8, 1]], 13339/3538944],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 1], [10, 1]], 65/110592],
[[[1, 5], [2, 6], [3, 1], [4, 3], [6, 1], [12, 1]], 1229/995328],
[[[1, 5], [2, 6], [3, 1], [5, 1], [6, 2], [8, 1]], 1/2880],
[[[1, 5], [2, 6], [3, 1], [6, 2], [8, 1], [10, 1]], 1/11520],
[[[1, 5], [2, 6], [3, 2], [4, 1], [5, 1], [6, 2]], 1/8640],
[[[1, 5], [2, 6], [3, 2], [4, 1], [5, 1], [8, 1]], 1/23040],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 2], [8, 1]], 31/12288],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 2], [10, 1]], 7/12960],
[[[1, 5], [2, 6], [3, 2], [4, 1], [6, 2], [12, 1]], 127/165888],
[[[1, 5], [2, 6], [3, 2], [4, 1], [8, 1], [10, 1]], 23/138240],
[[[1, 5], [2, 6], [3, 2], [4, 2], [5, 1], [6, 1]], 1/13824],
[[[1, 5], [2, 6], [3, 2], [4, 2], [6, 1], [8, 1]], 79/55296],
[[[1, 5], [2, 6], [3, 2], [4, 2], [6, 1], [10, 1]], 1/7680],
[[[1, 5], [2, 6], [3, 2], [4, 2], [6, 1], [12, 1]], 7/55296],
[[[1, 5], [2, 6], [3, 2], [5, 1], [6, 1], [8, 1]], 1/5760],
[[[1, 5], [2, 6], [3, 2], [6, 1], [8, 1], [10, 1]], 1/8640],
[[[1, 5], [2, 6], [3, 3], [4, 1], [6, 1], [8, 1]], 11/41472],
[[[1, 5], [2, 6], [3, 3], [4, 1], [6, 1], [10, 1]], 1/4320],
[[[1, 5], [2, 6], [3, 3], [4, 1], [6, 1], [12, 1]], 1087/4976640],
[[[1, 5], [2, 6], [4, 1], [5, 1], [6, 2], [8, 1]], 13/23040],
[[[1, 5], [2, 6], [4, 1], [6, 2], [8, 1], [10, 1]], 1/46080],
[[[1, 5], [2, 6], [4, 2], [5, 1], [6, 1], [8, 1]], 23/46080],
[[[1, 5], [2, 6], [4, 2], [5, 1], [6, 1], [12, 1]], 7/69120],
[[[1, 5], [2, 6], [4, 2], [6, 1], [8, 1], [10, 1]], 3/10240],
[[[1, 5], [2, 8], [3, 1], [4, 1], [5, 1], [6, 2]], 1/8640],
[[[1, 5], [2, 8], [3, 1], [4, 1], [5, 1], [8, 1]], 1/23040],
[[[1, 5], [2, 8], [3, 1], [4, 1], [6, 2], [8, 1]], 16541/6635520],
[[[1, 5], [2, 8], [3, 1], [4, 1], [6, 2], [10, 1]], 1/1536],
[[[1, 5], [2, 8], [3, 1], [4, 1], [8, 1], [10, 1]], 61/1105920],
[[[1, 5], [2, 8], [3, 1], [4, 2], [5, 1], [6, 1]], 241/2211840],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 1], [8, 1]], 31537/13271040],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 1], [10, 1]], 233/368640],
[[[1, 5], [2, 8], [3, 1], [4, 2], [6, 1], [12, 1]], 2807/11943936],
[[[1, 5], [2, 8], [3, 1], [5, 1], [6, 1], [8, 1]], 1/23040],
[[[1, 5], [2, 8], [3, 1], [6, 1], [8, 1], [10, 1]], 1/92160],
[[[1, 5], [2, 8], [3, 2], [4, 1], [5, 1], [6, 1]], 1/17280],
[[[1, 5], [2, 8], [3, 2], [4, 1], [6, 1], [8, 1]], 43/82944],
[[[1, 5], [2, 8], [3, 2], [4, 1], [6, 1], [10, 1]], 7/51840],
[[[1, 5], [2, 8], [4, 1], [5, 1], [6, 1], [8, 1]], 7/46080],
[[[1, 5], [2, 8], [4, 1], [6, 1], [8, 1], [10, 1]], 3/20480],
[[[1, 5], [2, 10], [3, 1], [4, 1], [5, 1], [6, 1]], 7/552960],
[[[1, 5], [2, 10], [3, 1], [4, 1], [6, 1], [8, 1]], 49373/159252480],
[[[1, 5], [2, 10], [3, 1], [4, 1], [6, 1], [10, 1]], 79/368640],
[[[1, 6], [2, 1], [3, 1], [4, 1], [6, 1], [8, 3]], 1/73728],
[[[1, 6], [2, 1], [3, 1], [4, 1], [6, 1], [12, 3]], 1/552960],
[[[1, 6], [2, 1], [3, 1], [4, 1], [6, 3], [12, 2]], 1/1658880],
[[[1, 6], [2, 1], [3, 1], [4, 1], [6, 5], [12, 1]], 1/19906560],
[[[1, 6], [2, 1], [3, 2], [4, 1], [12, 1], [24, 1]], 1/138240],
[[[1, 6], [2, 1], [3, 2], [4, 2], [6, 1], [8, 2]], 1/18432],
[[[1, 6], [2, 1], [3, 2], [4, 3], [8, 1], [12, 1]], 1/9216],
[[[1, 6], [2, 1], [3, 2], [6, 2], [9, 1], [12, 1]], 1/82944],
[[[1, 6], [2, 1], [3, 3], [4, 1], [6, 1], [12, 2]], 37/552960],
[[[1, 6], [2, 1], [3, 3], [4, 1], [6, 1], [24, 1]], 1/9216],
[[[1, 6], [2, 1], [3, 3], [4, 1], [6, 2], [9, 1]], 1/41472],
[[[1, 6], [2, 1], [3, 3], [4, 1], [6, 3], [12, 1]], 1/122880],
[[[1, 6], [2, 1], [3, 3], [4, 1], [9, 1], [12, 1]], 1/6912],
[[[1, 6], [2, 1], [3, 3], [4, 3], [6, 1], [12, 1]], 1/27648],
[[[1, 6], [2, 1], [3, 3], [5, 1], [6, 1], [9, 1]], 1/4320],
[[[1, 6], [2, 1], [3, 3], [6, 1], [9, 1], [12, 1]], 1/5184],
[[[1, 6], [2, 1], [3, 4], [4, 1], [6, 2], [12, 1]], 11/61440],
[[[1, 6], [2, 1], [3, 4], [5, 1], [6, 1], [12, 1]], 1/3840],
[[[1, 6], [2, 1], [3, 5], [4, 1], [6, 1], [12, 1]], 107/6635520],
[[[1, 6], [2, 1], [4, 3], [5, 1], [8, 1], [12, 1]], 1/23040],
[[[1, 6], [2, 3], [3, 1], [4, 1], [5, 1], [8, 2]], 1/7680],
[[[1, 6], [2, 3], [3, 1], [4, 1], [6, 2], [8, 2]], 11/82944],
[[[1, 6], [2, 3], [3, 1], [4, 1], [6, 2], [12, 2]], 23/414720],
[[[1, 6], [2, 3], [3, 1], [4, 1], [6, 4], [12, 1]], 23/2488320],
[[[1, 6], [2, 3], [3, 1], [4, 1], [8, 2], [10, 1]], 1/23040],
[[[1, 6], [2, 3], [3, 1], [4, 2], [6, 1], [8, 2]], 149/294912],
[[[1, 6], [2, 3], [3, 1], [4, 2], [6, 3], [8, 1]], 1/82944],
[[[1, 6], [2, 3], [3, 1], [4, 3], [5, 1], [8, 1]], 19/30720],
[[[1, 6], [2, 3], [3, 1], [4, 3], [5, 1], [12, 1]], 1/2880],
[[[1, 6], [2, 3], [3, 1], [4, 3], [6, 2], [8, 1]], 5/110592],
[[[1, 6], [2, 3], [3, 1], [4, 3], [6, 2], [12, 1]], 1/31104],
[[[1, 6], [2, 3], [3, 1], [4, 3], [8, 1], [10, 1]], 1/15360],
[[[1, 6], [2, 3], [3, 1], [4, 3], [8, 1], [12, 1]], 5/13824],
[[[1, 6], [2, 3], [3, 1], [4, 4], [5, 1], [6, 1]], 1/92160],
[[[1, 6], [2, 3], [3, 1], [4, 4], [6, 1], [8, 1]], 59/589824],
[[[1, 6], [2, 3], [3, 1], [4, 4], [6, 1], [12, 1]], 13/110592],
[[[1, 6], [2, 3], [3, 1], [5, 1], [6, 1], [8, 2]], 1/7680],
[[[1, 6], [2, 3], [3, 1], [6, 1], [8, 2], [10, 1]], 1/46080],
[[[1, 6], [2, 3], [3, 2], [4, 1], [6, 1], [8, 2]], 35/55296],
[[[1, 6], [2, 3], [3, 2], [4, 1], [6, 1], [12, 2]], 7/55296],
[[[1, 6], [2, 3], [3, 2], [4, 1], [6, 2], [9, 1]], 1/1536],
[[[1, 6], [2, 3], [3, 2], [4, 1], [6, 2], [18, 1]], 7/207360],
[[[1, 6], [2, 3], [3, 2], [4, 1], [6, 3], [8, 1]], 1/13824],
[[[1, 6], [2, 3], [3, 2], [4, 1], [6, 3], [12, 1]], 31/331776],
[[[1, 6], [2, 3], [3, 2], [4, 2], [6, 2], [8, 1]], 35/165888],
[[[1, 6], [2, 3], [3, 2], [4, 2], [6, 2], [12, 1]], 7/7290],
[[[1, 6], [2, 3], [3, 2], [4, 2], [8, 1], [10, 1]], 1/23040],
[[[1, 6], [2, 3], [3, 2], [4, 2], [10, 1], [12, 1]], 1/51840],
[[[1, 6], [2, 3], [3, 2], [4, 3], [5, 1], [6, 1]], 13/69120],
[[[1, 6], [2, 3], [3, 2], [4, 3], [6, 1], [8, 1]], 83/442368],
[[[1, 6], [2, 3], [3, 2], [4, 3], [6, 1], [12, 1]], 1/2304],
[[[1, 6], [2, 3], [3, 2], [6, 1], [9, 1], [12, 1]], 5/20736],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 1], [9, 1]], 13/20736],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 2], [8, 1]], 5/20736],
[[[1, 6], [2, 3], [3, 3], [4, 1], [6, 2], [12, 1]], 761/829440],
[[[1, 6], [2, 3], [3, 3], [4, 2], [6, 1], [8, 1]], 1/6144],
[[[1, 6], [2, 3], [3, 3], [4, 2], [6, 1], [12, 1]], 5/4608],
[[[1, 6], [2, 3], [3, 4], [4, 1], [6, 1], [8, 1]], 11/20736],
[[[1, 6], [2, 3], [3, 4], [4, 1], [6, 1], [12, 1]], 109/110592],
[[[1, 6], [2, 3], [4, 1], [5, 1], [6, 1], [8, 2]], 1/30720],
[[[1, 6], [2, 3], [4, 1], [6, 1], [8, 2], [10, 1]], 1/46080],
[[[1, 6], [2, 3], [4, 3], [5, 1], [6, 1], [8, 1]], 29/122880],
[[[1, 6], [2, 3], [4, 3], [5, 1], [6, 1], [12, 1]], 1/11520],
[[[1, 6], [2, 5], [3, 1], [4, 1], [5, 1], [6, 3]], 1/4320],
[[[1, 6], [2, 5], [3, 1], [4, 1], [6, 1], [8, 2]], 3679/2654208],
[[[1, 6], [2, 5], [3, 1], [4, 1], [6, 3], [8, 1]], 11/41472],
[[[1, 6], [2, 5], [3, 1], [4, 1], [6, 3], [12, 1]], 1087/4976640],
[[[1, 6], [2, 5], [3, 1], [4, 2], [5, 1], [6, 2]], 1/7680],
[[[1, 6], [2, 5], [3, 1], [4, 2], [5, 1], [8, 1]], 3/10240],
[[[1, 6], [2, 5], [3, 1], [4, 2], [6, 2], [8, 1]], 79/55296],
[[[1, 6], [2, 5], [3, 1], [4, 2], [6, 2], [10, 1]], 1/13824],
[[[1, 6], [2, 5], [3, 1], [4, 2], [6, 2], [12, 1]], 7/55296],
[[[1, 6], [2, 5], [3, 1], [4, 2], [8, 1], [10, 1]], 23/46080],
[[[1, 6], [2, 5], [3, 1], [4, 2], [10, 1], [12, 1]], 7/69120],
[[[1, 6], [2, 5], [3, 1], [4, 3], [5, 1], [6, 1]], 65/110592],
[[[1, 6], [2, 5], [3, 1], [4, 3], [6, 1], [8, 1]], 13339/3538944],
[[[1, 6], [2, 5], [3, 1], [4, 3], [6, 1], [10, 1]], 7/92160],
[[[1, 6], [2, 5], [3, 1], [4, 3], [6, 1], [12, 1]], 1229/995328],
[[[1, 6], [2, 5], [3, 1], [5, 1], [6, 2], [8, 1]], 1/8640],
[[[1, 6], [2, 5], [3, 1], [6, 2], [8, 1], [10, 1]], 1/5760],
[[[1, 6], [2, 5], [3, 2], [4, 1], [5, 1], [6, 2]], 7/12960],
[[[1, 6], [2, 5], [3, 2], [4, 1], [5, 1], [8, 1]], 1/46080],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 2], [8, 1]], 31/12288],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 2], [10, 1]], 1/8640],
[[[1, 6], [2, 5], [3, 2], [4, 1], [6, 2], [12, 1]], 127/165888],
[[[1, 6], [2, 5], [3, 2], [4, 1], [8, 1], [10, 1]], 13/23040],
[[[1, 6], [2, 5], [3, 2], [4, 2], [5, 1], [6, 1]], 1/11520],
[[[1, 6], [2, 5], [3, 2], [4, 2], [6, 1], [8, 1]], 2855/663552],
[[[1, 6], [2, 5], [3, 2], [4, 2], [6, 1], [10, 1]], 5/27648],
[[[1, 6], [2, 5], [3, 2], [4, 2], [6, 1], [12, 1]], 41/93312],
[[[1, 6], [2, 5], [3, 2], [5, 1], [6, 1], [8, 1]], 1/11520],
[[[1, 6], [2, 5], [3, 2], [6, 1], [8, 1], [10, 1]], 1/2880],
[[[1, 6], [2, 5], [3, 3], [4, 1], [5, 1], [6, 1]], 1/17280],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 1], [8, 1]], 409/497664],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 1], [10, 1]], 1/8640],
[[[1, 6], [2, 5], [3, 3], [4, 1], [6, 1], [12, 1]], 157/331776],
[[[1, 6], [2, 5], [4, 1], [5, 1], [6, 2], [8, 1]], 23/138240],
[[[1, 6], [2, 5], [4, 1], [6, 2], [8, 1], [10, 1]], 1/23040],
[[[1, 6], [2, 5], [4, 2], [5, 1], [6, 1], [8, 1]], 37/46080],
[[[1, 6], [2, 5], [4, 2], [5, 1], [6, 1], [12, 1]], 1/11520],
[[[1, 6], [2, 5], [4, 2], [6, 1], [8, 1], [10, 1]], 1/6144],
[[[1, 6], [2, 7], [3, 1], [4, 1], [5, 1], [6, 2]], 1/2560],
[[[1, 6], [2, 7], [3, 1], [4, 1], [5, 1], [8, 1]], 7/34560],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 2], [8, 1]], 563/221184],
[[[1, 6], [2, 7], [3, 1], [4, 1], [6, 2], [10, 1]], 13/69120],
[[[1, 6], [2, 7], [3, 1], [4, 1], [8, 1], [10, 1]], 17/46080],
[[[1, 6], [2, 7], [3, 1], [4, 2], [5, 1], [6, 1]], 11/36864],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 1], [8, 1]], 16367/2949120],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 1], [10, 1]], 2107/2211840],
[[[1, 6], [2, 7], [3, 1], [4, 2], [6, 1], [12, 1]], 529/1327104],
[[[1, 6], [2, 7], [3, 1], [5, 1], [6, 1], [8, 1]], 1/5760],
[[[1, 6], [2, 7], [3, 1], [6, 1], [8, 1], [10, 1]], 1/11520],
[[[1, 6], [2, 7], [3, 2], [4, 1], [5, 1], [6, 1]], 157/829440],
[[[1, 6], [2, 7], [3, 2], [4, 1], [6, 1], [8, 1]], 3293/2211840],
[[[1, 6], [2, 7], [3, 2], [4, 1], [6, 1], [10, 1]], 1/2304],
[[[1, 6], [2, 7], [4, 1], [5, 1], [6, 1], [8, 1]], 341/552960],
[[[1, 6], [2, 7], [4, 1], [6, 1], [8, 1], [10, 1]], 1/7680],
[[[1, 6], [2, 9], [3, 1], [4, 1], [5, 1], [6, 1]], 109/1105920],
[[[1, 6], [2, 9], [3, 1], [4, 1], [6, 1], [8, 1]], 4187/3538944],
[[[1, 6], [2, 9], [3, 1], [4, 1], [6, 1], [10, 1]], 347/552960],
[[[1, 7], [2, 2], [3, 1], [4, 1], [6, 2], [8, 2]], 1/55296],
[[[1, 7], [2, 2], [3, 1], [4, 1], [6, 2], [12, 2]], 1/276480],
[[[1, 7], [2, 2], [3, 1], [4, 1], [6, 4], [12, 1]], 1/1658880],
[[[1, 7], [2, 2], [3, 1], [4, 2], [6, 1], [8, 2]], 31/442368],
[[[1, 7], [2, 2], [3, 1], [4, 3], [6, 2], [8, 1]], 1/442368],
[[[1, 7], [2, 2], [3, 1], [4, 3], [8, 1], [10, 1]], 1/122880],
[[[1, 7], [2, 2], [3, 1], [4, 3], [8, 1], [12, 1]], 1/6912],
[[[1, 7], [2, 2], [3, 1], [4, 4], [5, 1], [6, 1]], 1/552960],
[[[1, 7], [2, 2], [3, 1], [4, 4], [6, 1], [8, 1]], 1/196608],
[[[1, 7], [2, 2], [3, 1], [4, 4], [6, 1], [12, 1]], 1/41472],
[[[1, 7], [2, 2], [3, 1], [5, 1], [6, 1], [8, 2]], 1/46080],
[[[1, 7], [2, 2], [3, 2], [4, 1], [6, 1], [8, 2]], 1/27648],
[[[1, 7], [2, 2], [3, 2], [4, 1], [6, 1], [12, 2]], 1/46080],
[[[1, 7], [2, 2], [3, 2], [4, 1], [6, 3], [12, 1]], 1/276480],
[[[1, 7], [2, 2], [3, 2], [4, 2], [6, 2], [8, 1]], 1/27648],
[[[1, 7], [2, 2], [3, 2], [4, 3], [6, 1], [8, 1]], 1/18432],
[[[1, 7], [2, 2], [3, 2], [6, 1], [9, 1], [12, 1]], 23/311040],
[[[1, 7], [2, 2], [3, 3], [4, 1], [6, 1], [9, 1]], 1/6912],
[[[1, 7], [2, 2], [3, 3], [4, 1], [6, 2], [8, 1]], 1/13824],
[[[1, 7], [2, 2], [3, 3], [4, 1], [6, 2], [12, 1]], 1/20480],
[[[1, 7], [2, 2], [3, 3], [4, 2], [5, 1], [6, 1]], 1/155520],
[[[1, 7], [2, 2], [3, 3], [4, 2], [6, 1], [8, 1]], 1/27648],
[[[1, 7], [2, 2], [3, 3], [4, 2], [6, 1], [12, 1]], 199/622080],
[[[1, 7], [2, 2], [3, 4], [4, 1], [6, 1], [12, 1]], 11/46080],
[[[1, 7], [2, 4], [3, 1], [4, 1], [6, 1], [8, 2]], 4769/8847360],
[[[1, 7], [2, 4], [3, 1], [4, 1], [6, 3], [8, 1]], 17/248832],
[[[1, 7], [2, 4], [3, 1], [4, 1], [6, 3], [12, 1]], 47/1658880],
[[[1, 7], [2, 4], [3, 1], [4, 2], [5, 1], [6, 2]], 13/92160],
[[[1, 7], [2, 4], [3, 1], [4, 2], [5, 1], [8, 1]], 173/184320],
[[[1, 7], [2, 4], [3, 1], [4, 2], [5, 1], [12, 1]], 1/17280],
[[[1, 7], [2, 4], [3, 1], [4, 2], [6, 2], [8, 1]], 13/36864],
[[[1, 7], [2, 4], [3, 1], [4, 2], [6, 2], [12, 1]], 1/41472],
[[[1, 7], [2, 4], [3, 1], [4, 2], [8, 1], [10, 1]], 1/5760],
[[[1, 7], [2, 4], [3, 1], [4, 2], [10, 1], [12, 1]], 1/34560],
[[[1, 7], [2, 4], [3, 1], [4, 3], [5, 1], [6, 1]], 17/92160],
[[[1, 7], [2, 4], [3, 1], [4, 3], [6, 1], [8, 1]], 2921/3538944],
[[[1, 7], [2, 4], [3, 1], [4, 3], [6, 1], [10, 1]], 11/368640],
[[[1, 7], [2, 4], [3, 1], [4, 3], [6, 1], [12, 1]], 317/663552],
[[[1, 7], [2, 4], [3, 1], [6, 2], [8, 1], [10, 1]], 1/34560],
[[[1, 7], [2, 4], [3, 2], [4, 1], [6, 2], [8, 1]], 25/27648],
[[[1, 7], [2, 4], [3, 2], [4, 1], [6, 2], [10, 1]], 1/17280],
[[[1, 7], [2, 4], [3, 2], [4, 1], [6, 2], [12, 1]], 23/92160],
[[[1, 7], [2, 4], [3, 2], [4, 1], [8, 1], [10, 1]], 1/15360],
[[[1, 7], [2, 4], [3, 2], [4, 2], [5, 1], [6, 1]], 83/138240],
[[[1, 7], [2, 4], [3, 2], [4, 2], [6, 1], [8, 1]], 25/12288],
[[[1, 7], [2, 4], [3, 2], [4, 2], [6, 1], [10, 1]], 1/23040],
[[[1, 7], [2, 4], [3, 2], [4, 2], [6, 1], [12, 1]], 293/497664],
[[[1, 7], [2, 4], [3, 2], [6, 1], [8, 1], [10, 1]], 1/17280],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 1], [8, 1]], 235/110592],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 1], [10, 1]], 1/17280],
[[[1, 7], [2, 4], [3, 3], [4, 1], [6, 1], [12, 1]], 85/331776],
[[[1, 7], [2, 4], [4, 1], [6, 2], [8, 1], [10, 1]], 1/138240],
[[[1, 7], [2, 4], [4, 2], [5, 1], [6, 1], [8, 1]], 7/30720],
[[[1, 7], [2, 4], [4, 2], [5, 1], [6, 1], [12, 1]], 1/46080],
[[[1, 7], [2, 4], [4, 2], [6, 1], [8, 1], [10, 1]], 1/18432],
[[[1, 7], [2, 6], [3, 1], [4, 1], [5, 1], [6, 2]], 1/2304],
[[[1, 7], [2, 6], [3, 1], [4, 1], [5, 1], [8, 1]], 1/7680],
[[[1, 7], [2, 6], [3, 1], [4, 1], [6, 2], [8, 1]], 3293/2211840],
[[[1, 7], [2, 6], [3, 1], [4, 1], [6, 2], [10, 1]], 157/829440],
[[[1, 7], [2, 6], [3, 1], [4, 1], [8, 1], [10, 1]], 341/552960],
[[[1, 7], [2, 6], [3, 1], [4, 2], [5, 1], [6, 1]], 2107/2211840],
[[[1, 7], [2, 6], [3, 1], [4, 2], [6, 1], [8, 1]], 16367/2949120],
[[[1, 7], [2, 6], [3, 1], [4, 2], [6, 1], [10, 1]], 11/36864],
[[[1, 7], [2, 6], [3, 1], [4, 2], [6, 1], [12, 1]], 529/1327104],
[[[1, 7], [2, 6], [3, 1], [5, 1], [6, 1], [8, 1]], 1/11520],
[[[1, 7], [2, 6], [3, 1], [6, 1], [8, 1], [10, 1]], 1/5760],
[[[1, 7], [2, 6], [3, 2], [4, 1], [5, 1], [6, 1]], 13/69120],
[[[1, 7], [2, 6], [3, 2], [4, 1], [6, 1], [8, 1]], 563/221184],
[[[1, 7], [2, 6], [3, 2], [4, 1], [6, 1], [10, 1]], 1/2560],
[[[1, 7], [2, 6], [4, 1], [5, 1], [6, 1], [8, 1]], 17/46080],
[[[1, 7], [2, 6], [4, 1], [6, 1], [8, 1], [10, 1]], 7/34560],
[[[1, 7], [2, 8], [3, 1], [4, 1], [5, 1], [6, 1]], 187/552960],
[[[1, 7], [2, 8], [3, 1], [4, 1], [6, 1], [8, 1]], 24479/10616832],
[[[1, 7], [2, 8], [3, 1], [4, 1], [6, 1], [10, 1]], 193/331776],
[[[1, 8], [2, 1], [3, 1], [4, 2], [6, 1], [8, 2]], 1/147456],
[[[1, 8], [2, 1], [3, 1], [4, 3], [8, 1], [12, 1]], 1/69120],
[[[1, 8], [2, 1], [3, 2], [4, 1], [6, 1], [12, 2]], 1/829440],
[[[1, 8], [2, 1], [3, 2], [4, 1], [6, 3], [12, 1]], 1/4976640],
[[[1, 8], [2, 1], [3, 2], [4, 3], [6, 1], [8, 1]], 1/147456],
[[[1, 8], [2, 1], [3, 2], [6, 1], [9, 1], [12, 1]], 1/207360],
[[[1, 8], [2, 1], [3, 4], [4, 1], [6, 1], [12, 1]], 41/4976640],
[[[1, 8], [2, 3], [3, 1], [4, 1], [6, 1], [8, 2]], 701/8847360],
[[[1, 8], [2, 3], [3, 1], [4, 1], [6, 3], [8, 1]], 1/110592],
[[[1, 8], [2, 3], [3, 1], [4, 1], [6, 3], [12, 1]], 1/552960],
[[[1, 8], [2, 3], [3, 1], [4, 2], [6, 2], [8, 1]], 1/20736],
[[[1, 8], [2, 3], [3, 1], [4, 2], [6, 2], [12, 1]], 1/1492992],
[[[1, 8], [2, 3], [3, 1], [4, 2], [8, 1], [10, 1]], 1/92160],
[[[1, 8], [2, 3], [3, 1], [4, 2], [10, 1], [12, 1]], 1/414720],
[[[1, 8], [2, 3], [3, 1], [4, 3], [5, 1], [6, 1]], 61/1105920],
[[[1, 8], [2, 3], [3, 1], [4, 3], [6, 1], [8, 1]], 559/3538944],
[[[1, 8], [2, 3], [3, 1], [4, 3], [6, 1], [12, 1]], 71/1105920],
[[[1, 8], [2, 3], [3, 2], [4, 1], [6, 2], [8, 1]], 1/10368],
[[[1, 8], [2, 3], [3, 2], [4, 1], [6, 2], [12, 1]], 11/497664],
[[[1, 8], [2, 3], [3, 2], [4, 2], [5, 1], [6, 1]], 1/69120],
[[[1, 8], [2, 3], [3, 2], [4, 2], [6, 1], [8, 1]], 1/4608],
[[[1, 8], [2, 3], [3, 2], [4, 2], [6, 1], [10, 1]], 1/92160],
[[[1, 8], [2, 3], [3, 2], [4, 2], [6, 1], [12, 1]], 1/4608],
[[[1, 8], [2, 3], [3, 3], [4, 1], [5, 1], [6, 1]], 1/12960],
[[[1, 8], [2, 3], [3, 3], [4, 1], [6, 1], [8, 1]], 1/2048],
[[[1, 8], [2, 3], [3, 3], [4, 1], [6, 1], [12, 1]], 31/552960],
[[[1, 8], [2, 3], [4, 2], [6, 1], [8, 1], [10, 1]], 1/184320],
[[[1, 8], [2, 5], [3, 1], [4, 1], [5, 1], [6, 2]], 7/51840],
[[[1, 8], [2, 5], [3, 1], [4, 1], [5, 1], [8, 1]], 3/20480],
[[[1, 8], [2, 5], [3, 1], [4, 1], [6, 2], [8, 1]], 43/82944],
[[[1, 8], [2, 5], [3, 1], [4, 1], [6, 2], [10, 1]], 1/17280],
[[[1, 8], [2, 5], [3, 1], [4, 1], [8, 1], [10, 1]], 7/46080],
[[[1, 8], [2, 5], [3, 1], [4, 2], [5, 1], [6, 1]], 233/368640],
[[[1, 8], [2, 5], [3, 1], [4, 2], [6, 1], [8, 1]], 31537/13271040],
[[[1, 8], [2, 5], [3, 1], [4, 2], [6, 1], [10, 1]], 241/2211840],
[[[1, 8], [2, 5], [3, 1], [4, 2], [6, 1], [12, 1]], 2807/11943936],
[[[1, 8], [2, 5], [3, 1], [5, 1], [6, 1], [8, 1]], 1/92160],
[[[1, 8], [2, 5], [3, 1], [6, 1], [8, 1], [10, 1]], 1/23040],
[[[1, 8], [2, 5], [3, 2], [4, 1], [5, 1], [6, 1]], 1/1536],
[[[1, 8], [2, 5], [3, 2], [4, 1], [6, 1], [8, 1]], 16541/6635520],
[[[1, 8], [2, 5], [3, 2], [4, 1], [6, 1], [10, 1]], 1/8640],
[[[1, 8], [2, 5], [4, 1], [5, 1], [6, 1], [8, 1]], 61/1105920],
[[[1, 8], [2, 5], [4, 1], [6, 1], [8, 1], [10, 1]], 1/23040],
[[[1, 8], [2, 7], [3, 1], [4, 1], [5, 1], [6, 1]], 193/331776],
[[[1, 8], [2, 7], [3, 1], [4, 1], [6, 1], [8, 1]], 24479/10616832],
[[[1, 8], [2, 7], [3, 1], [4, 1], [6, 1], [10, 1]], 187/552960],
[[[1, 9], [2, 2], [3, 1], [4, 1], [6, 1], [8, 2]], 1/442368],
[[[1, 9], [2, 2], [3, 1], [4, 2], [6, 2], [8, 1]], 1/221184],
[[[1, 9], [2, 2], [3, 1], [4, 3], [6, 1], [8, 1]], 7/589824],
[[[1, 9], [2, 2], [3, 2], [4, 1], [6, 2], [8, 1]], 1/110592],
[[[1, 9], [2, 2], [3, 2], [4, 1], [6, 2], [12, 1]], 1/829440],
[[[1, 9], [2, 2], [3, 2], [4, 2], [5, 1], [6, 1]], 1/414720],
[[[1, 9], [2, 2], [3, 2], [4, 2], [6, 1], [8, 1]], 1/110592],
[[[1, 9], [2, 2], [3, 2], [4, 2], [6, 1], [12, 1]], 53/2488320],
[[[1, 9], [2, 2], [3, 3], [4, 1], [6, 1], [12, 1]], 7/1658880],
[[[1, 9], [2, 4], [3, 1], [4, 1], [6, 2], [8, 1]], 149/2211840],
[[[1, 9], [2, 4], [3, 1], [4, 1], [6, 2], [10, 1]], 1/138240],
[[[1, 9], [2, 4], [3, 1], [4, 1], [8, 1], [10, 1]], 1/122880],
[[[1, 9], [2, 4], [3, 1], [4, 2], [5, 1], [6, 1]], 299/2211840],
[[[1, 9], [2, 4], [3, 1], [4, 2], [6, 1], [8, 1]], 43/110592],
[[[1, 9], [2, 4], [3, 1], [4, 2], [6, 1], [10, 1]], 1/73728],
[[[1, 9], [2, 4], [3, 1], [4, 2], [6, 1], [12, 1]], 1459/19906560],
[[[1, 9], [2, 4], [3, 1], [6, 1], [8, 1], [10, 1]], 1/276480],
[[[1, 9], [2, 4], [3, 2], [4, 1], [5, 1], [6, 1]], 11/69120],
[[[1, 9], [2, 4], [3, 2], [4, 1], [6, 1], [8, 1]], 53/69120],
[[[1, 9], [2, 4], [3, 2], [4, 1], [6, 1], [10, 1]], 1/69120],
[[[1, 9], [2, 4], [4, 1], [6, 1], [8, 1], [10, 1]], 1/552960],
[[[1, 9], [2, 6], [3, 1], [4, 1], [5, 1], [6, 1]], 347/552960],
[[[1, 9], [2, 6], [3, 1], [4, 1], [6, 1], [8, 1]], 4187/3538944],
[[[1, 9], [2, 6], [3, 1], [4, 1], [6, 1], [10, 1]], 109/1105920],
[[[1, 10], [2, 1], [3, 1], [4, 3], [6, 1], [8, 1]], 1/1179648],
[[[1, 10], [2, 1], [3, 3], [4, 1], [6, 1], [12, 1]], 1/4976640],
[[[1, 10], [2, 3], [3, 1], [4, 1], [6, 2], [8, 1]], 1/663552],
[[[1, 10], [2, 3], [3, 1], [4, 2], [5, 1], [6, 1]], 1/276480],
[[[1, 10], [2, 3], [3, 1], [4, 2], [6, 1], [8, 1]], 17/737280],
[[[1, 10], [2, 3], [3, 1], [4, 2], [6, 1], [10, 1]], 1/737280],
[[[1, 10], [2, 3], [3, 1], [4, 2], [6, 1], [12, 1]], 11/1105920],
[[[1, 10], [2, 3], [3, 2], [4, 1], [5, 1], [6, 1]], 7/276480],
[[[1, 10], [2, 3], [3, 2], [4, 1], [6, 1], [8, 1]], 143/2211840],
[[[1, 10], [2, 5], [3, 1], [4, 1], [5, 1], [6, 1]], 79/368640],
[[[1, 10], [2, 5], [3, 1], [4, 1], [6, 1], [8, 1]], 49373/159252480],
[[[1, 10], [2, 5], [3, 1], [4, 1], [6, 1], [10, 1]], 7/552960],
[[[1, 11], [2, 2], [3, 1], [4, 2], [5, 1], [6, 1]], 1/3317760],
[[[1, 11], [2, 2], [3, 1], [4, 2], [6, 1], [8, 1]], 1/1769472],
[[[1, 11], [2, 2], [3, 1], [4, 2], [6, 1], [12, 1]], 29/59719680],
[[[1, 11], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1]], 19/552960],
[[[1, 11], [2, 4], [3, 1], [4, 1], [6, 1], [8, 1]], 997/26542080],
[[[1, 11], [2, 4], [3, 1], [4, 1], [6, 1], [10, 1]], 1/1105920],
[[[1, 12], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1]], 1/368640],
[[[1, 12], [2, 3], [3, 1], [4, 1], [6, 1], [8, 1]], 79/53084160],
[[[2, 3], [3, 2], [4, 2], [6, 2], [12, 1], [18, 1]], 1/2592],
[[[2, 3], [3, 2], [6, 2], [10, 1], [12, 1], [18, 1]], 1/8640],
[[[1, 1], [2, 2], [3, 1], [4, 1], [6, 1], [10, 1], [12, 3]], 1/3840],
[[[1, 1], [2, 2], [3, 1], [4, 1], [6, 3], [10, 1], [12, 2]], 1/11520],
[[[1, 1], [2, 2], [3, 1], [4, 1], [6, 5], [10, 1], [12, 1]], 1/138240],
[[[1, 1], [2, 2], [3, 1], [5, 1], [6, 1], [12, 2], [18, 1]], 1/4320],
[[[1, 1], [2, 2], [3, 1], [5, 1], [6, 1], [18, 1], [24, 1]], 1/720],
[[[1, 1], [2, 2], [3, 2], [4, 1], [6, 4], [10, 1], [12, 1]], 1/5760],
[[[1, 1], [2, 2], [3, 3], [4, 1], [6, 1], [10, 1], [12, 2]], 1/11520],
[[[1, 1], [2, 2], [3, 3], [4, 1], [6, 1], [12, 1], [24, 1]], 1/1152],
[[[1, 1], [2, 2], [3, 3], [4, 1], [6, 3], [10, 1], [12, 1]], 1/69120],
[[[1, 1], [2, 2], [3, 3], [4, 2], [6, 1], [12, 1], [18, 1]], 1/7776],
[[[1, 1], [2, 2], [3, 5], [4, 1], [6, 1], [10, 1], [12, 1]], 1/138240],
[[[1, 1], [2, 2], [4, 1], [6, 2], [10, 1], [12, 1], [24, 1]], 1/960],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 1], [12, 2], [18, 1]], 1/6912],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 1], [18, 1], [24, 1]], 1/1152],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 2], [10, 1], [12, 2]], 1/5760],
[[[1, 1], [2, 4], [3, 1], [4, 1], [6, 4], [10, 1], [12, 1]], 1/34560],
[[[1, 1], [2, 4], [3, 1], [4, 2], [5, 1], [6, 3], [12, 1]], 1/17280],
[[[1, 1], [2, 4], [3, 1], [4, 3], [6, 1], [12, 1], [18, 1]], 1/3456],
[[[1, 1], [2, 4], [3, 1], [6, 2], [10, 1], [12, 1], [18, 1]], 1/1440],
[[[1, 1], [2, 4], [3, 2], [4, 1], [6, 2], [12, 1], [18, 1]], 17/13824],
[[[1, 1], [2, 4], [3, 3], [4, 1], [6, 2], [10, 1], [12, 1]], 1/34560],
[[[1, 1], [2, 4], [4, 3], [6, 1], [8, 1], [10, 1], [12, 1]], 1/2880],
[[[1, 1], [2, 6], [3, 1], [4, 1], [6, 3], [10, 1], [12, 1]], 1/34560],
[[[1, 2], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [12, 3]], 1/3840],
[[[1, 2], [2, 1], [3, 1], [4, 1], [5, 1], [6, 3], [12, 2]], 1/11520],
[[[1, 2], [2, 1], [3, 1], [4, 1], [5, 1], [6, 5], [12, 1]], 1/138240],
[[[1, 2], [2, 1], [3, 1], [4, 1], [6, 3], [12, 1], [24, 1]], 1/1152],
[[[1, 2], [2, 1], [3, 1], [4, 2], [6, 3], [9, 1], [12, 1]], 1/7776],
[[[1, 2], [2, 1], [3, 1], [6, 1], [9, 1], [10, 1], [12, 2]], 1/4320],
[[[1, 2], [2, 1], [3, 1], [6, 1], [9, 1], [10, 1], [24, 1]], 1/720],
[[[1, 2], [2, 1], [3, 2], [4, 1], [5, 1], [12, 1], [24, 1]], 1/960],
[[[1, 2], [2, 1], [3, 3], [4, 1], [5, 1], [6, 1], [12, 2]], 1/11520],
[[[1, 2], [2, 1], [3, 3], [4, 1], [5, 1], [6, 3], [12, 1]], 1/69120],
[[[1, 2], [2, 1], [3, 4], [4, 1], [5, 1], [6, 2], [12, 1]], 1/5760],
[[[1, 2], [2, 1], [3, 5], [4, 1], [5, 1], [6, 1], [12, 1]], 1/138240],
[[[1, 2], [2, 3], [3, 1], [4, 1], [5, 1], [6, 2], [12, 2]], 1/5760],
[[[1, 2], [2, 3], [3, 1], [4, 1], [5, 1], [6, 4], [12, 1]], 1/34560],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 1], [12, 2], [18, 1]], 1/6912],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 1], [18, 1], [24, 1]], 1/1152],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 2], [10, 1], [12, 2]], 1/1920],
[[[1, 2], [2, 3], [3, 1], [4, 1], [6, 4], [10, 1], [12, 1]], 1/11520],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 2], [9, 1], [12, 1]], 1/7776],
[[[1, 2], [2, 3], [3, 1], [4, 2], [6, 3], [10, 1], [12, 1]], 7/5760],
[[[1, 2], [2, 3], [3, 1], [4, 3], [6, 1], [12, 1], [18, 1]], 1/3456],
[[[1, 2], [2, 3], [3, 1], [4, 3], [6, 2], [8, 1], [12, 1]], 1/3456],
[[[1, 2], [2, 3], [3, 1], [4, 4], [6, 1], [8, 1], [12, 1]], 1/4608],
[[[1, 2], [2, 3], [3, 1], [6, 2], [10, 1], [12, 1], [18, 1]], 1/4320],
[[[1, 2], [2, 3], [3, 2], [4, 1], [5, 1], [6, 2], [18, 1]], 1/720],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 1], [10, 1], [12, 2]], 1/1920],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 2], [12, 1], [18, 1]], 1/13824],
[[[1, 2], [2, 3], [3, 2], [4, 1], [6, 3], [10, 1], [12, 1]], 1/11520],
[[[1, 2], [2, 3], [3, 2], [4, 2], [5, 1], [6, 2], [12, 1]], 1/2880],
[[[1, 2], [2, 3], [3, 2], [4, 2], [6, 1], [12, 1], [18, 1]], 1/2592],
[[[1, 2], [2, 3], [3, 3], [4, 1], [5, 1], [6, 2], [12, 1]], 1/34560],
[[[1, 2], [2, 3], [3, 3], [4, 1], [6, 1], [12, 1], [18, 1]], 1/2592],
[[[1, 2], [2, 3], [3, 3], [4, 1], [6, 2], [10, 1], [12, 1]], 1/11520],
[[[1, 2], [2, 3], [3, 4], [4, 1], [6, 1], [10, 1], [12, 1]], 1/11520],
[[[1, 2], [2, 5], [3, 1], [4, 1], [5, 1], [6, 3], [12, 1]], 7/34560],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 2], [12, 1], [18, 1]], 1/2304],
[[[1, 2], [2, 5], [3, 1], [4, 1], [6, 3], [10, 1], [12, 1]], 1/5760],
[[[1, 2], [2, 5], [3, 1], [4, 2], [6, 1], [9, 1], [12, 1]], 1/311040],
[[[1, 2], [2, 5], [3, 1], [4, 2], [6, 1], [12, 1], [18, 1]], 19/20736],
[[[1, 2], [2, 5], [3, 1], [4, 2], [6, 2], [10, 1], [12, 1]], 1/2160],
[[[1, 2], [2, 5], [3, 1], [4, 3], [6, 1], [8, 1], [12, 1]], 1/27648],
[[[1, 2], [2, 5], [3, 2], [4, 1], [6, 2], [10, 1], [12, 1]], 1/5760],
[[[1, 2], [2, 7], [3, 1], [4, 2], [6, 1], [10, 1], [12, 1]], 1/17280],
[[[1, 3], [2, 2], [3, 1], [4, 1], [5, 1], [6, 2], [12, 2]], 1/1920],
[[[1, 3], [2, 2], [3, 1], [4, 1], [5, 1], [6, 4], [12, 1]], 1/11520],
[[[1, 3], [2, 2], [3, 1], [4, 1], [6, 1], [9, 1], [12, 2]], 1/6912],
[[[1, 3], [2, 2], [3, 1], [4, 1], [6, 1], [9, 1], [24, 1]], 1/1152],
[[[1, 3], [2, 2], [3, 1], [4, 1], [6, 3], [9, 1], [12, 1]], 1/2592],
[[[1, 3], [2, 2], [3, 1], [4, 2], [6, 2], [9, 1], [12, 1]], 1/2592],
[[[1, 3], [2, 2], [3, 1], [4, 3], [6, 1], [9, 1], [12, 1]], 1/3456],
[[[1, 3], [2, 2], [3, 1], [4, 4], [6, 1], [8, 1], [12, 1]], 1/4608],
[[[1, 3], [2, 2], [3, 2], [4, 1], [5, 1], [6, 1], [12, 2]], 1/1920],
[[[1, 3], [2, 2], [3, 2], [4, 1], [5, 1], [6, 3], [12, 1]], 1/11520],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 1], [10, 1], [12, 2]], 1/5760],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 2], [9, 1], [10, 1]], 1/720],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 2], [9, 1], [12, 1]], 1/13824],
[[[1, 3], [2, 2], [3, 2], [4, 1], [6, 3], [10, 1], [12, 1]], 1/34560],
[[[1, 3], [2, 2], [3, 2], [4, 2], [6, 1], [12, 1], [18, 1]], 1/7776],
[[[1, 3], [2, 2], [3, 2], [4, 2], [6, 2], [10, 1], [12, 1]], 1/2880],
[[[1, 3], [2, 2], [3, 2], [4, 3], [6, 1], [8, 1], [12, 1]], 1/3456],
[[[1, 3], [2, 2], [3, 2], [5, 1], [6, 1], [9, 1], [12, 1]], 1/4320],
[[[1, 3], [2, 2], [3, 3], [4, 1], [5, 1], [6, 2], [12, 1]], 1/11520],
[[[1, 3], [2, 2], [3, 3], [4, 2], [5, 1], [6, 1], [12, 1]], 7/5760],
[[[1, 3], [2, 2], [3, 4], [4, 1], [5, 1], [6, 1], [12, 1]], 1/11520],
[[[1, 3], [2, 2], [3, 4], [4, 1], [6, 1], [10, 1], [12, 1]], 1/34560],
[[[1, 3], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1], [8, 2]], 1/5760],
[[[1, 3], [2, 4], [3, 1], [4, 1], [5, 1], [6, 3], [12, 1]], 1/5760],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 1], [8, 2], [10, 1]], 1/3840],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 2], [9, 1], [12, 1]], 1/2592],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 2], [12, 1], [18, 1]], 1/1728],
[[[1, 3], [2, 4], [3, 1], [4, 1], [6, 3], [10, 1], [12, 1]], 13/11520],
[[[1, 3], [2, 4], [3, 1], [4, 2], [6, 1], [9, 1], [12, 1]], 1/20736],
[[[1, 3], [2, 4], [3, 1], [4, 2], [6, 1], [12, 1], [18, 1]], 7/6912],
[[[1, 3], [2, 4], [3, 1], [4, 3], [6, 1], [8, 1], [12, 1]], 1/3072],
[[[1, 3], [2, 4], [3, 1], [4, 3], [6, 1], [10, 1], [12, 1]], 1/2880],
[[[1, 3], [2, 4], [3, 2], [4, 1], [5, 1], [6, 2], [12, 1]], 7/5760],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 1], [9, 1], [12, 1]], 1/6912],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 1], [12, 1], [18, 1]], 1/864],
[[[1, 3], [2, 4], [3, 2], [4, 1], [6, 2], [10, 1], [12, 1]], 1/1728],
[[[1, 3], [2, 4], [3, 3], [4, 1], [6, 1], [10, 1], [12, 1]], 1/3840],
[[[1, 3], [2, 6], [3, 1], [4, 1], [5, 1], [6, 2], [8, 1]], 1/11520],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 1], [9, 1], [12, 1]], 1/103680],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 1], [12, 1], [18, 1]], 1/6912],
[[[1, 3], [2, 6], [3, 1], [4, 1], [6, 2], [8, 1], [10, 1]], 1/720],
[[[1, 3], [2, 6], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 1/23040],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 1/15360],
[[[1, 3], [2, 6], [3, 1], [4, 2], [6, 1], [10, 1], [12, 1]], 1/2880],
[[[1, 3], [2, 8], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/92160],
[[[1, 3], [2, 8], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/5760],
[[[1, 4], [2, 1], [3, 1], [4, 1], [6, 1], [9, 1], [12, 2]], 1/6912],
[[[1, 4], [2, 1], [3, 1], [4, 1], [6, 1], [9, 1], [24, 1]], 1/1152],
[[[1, 4], [2, 1], [3, 1], [4, 3], [5, 1], [8, 1], [12, 1]], 1/2880],
[[[1, 4], [2, 1], [3, 1], [4, 3], [6, 1], [9, 1], [12, 1]], 1/3456],
[[[1, 4], [2, 1], [3, 2], [4, 1], [5, 1], [6, 1], [12, 2]], 1/5760],
[[[1, 4], [2, 1], [3, 2], [4, 1], [5, 1], [6, 3], [12, 1]], 1/34560],
[[[1, 4], [2, 1], [3, 2], [4, 1], [6, 2], [9, 1], [12, 1]], 17/13824],
[[[1, 4], [2, 1], [3, 2], [5, 1], [6, 1], [9, 1], [12, 1]], 1/1440],
[[[1, 4], [2, 1], [3, 3], [4, 2], [6, 1], [10, 1], [12, 1]], 1/17280],
[[[1, 4], [2, 1], [3, 4], [4, 1], [5, 1], [6, 1], [12, 1]], 1/34560],
[[[1, 4], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1], [8, 2]], 1/3840],
[[[1, 4], [2, 3], [3, 1], [4, 1], [5, 1], [6, 3], [12, 1]], 1/3840],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 1], [8, 2], [10, 1]], 1/5760],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 2], [9, 1], [12, 1]], 1/864],
[[[1, 4], [2, 3], [3, 1], [4, 1], [6, 2], [12, 1], [18, 1]], 1/6912],
[[[1, 4], [2, 3], [3, 1], [4, 2], [6, 1], [9, 1], [12, 1]], 7/6912],
[[[1, 4], [2, 3], [3, 1], [4, 2], [6, 1], [12, 1], [18, 1]], 1/20736],
[[[1, 4], [2, 3], [3, 1], [4, 3], [5, 1], [6, 1], [12, 1]], 1/2880],
[[[1, 4], [2, 3], [3, 1], [4, 3], [6, 1], [8, 1], [12, 1]], 1/3072],
[[[1, 4], [2, 3], [3, 2], [4, 1], [5, 1], [6, 2], [12, 1]], 1/1728],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 1], [9, 1], [12, 1]], 1/1728],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 1], [12, 1], [18, 1]], 1/2592],
[[[1, 4], [2, 3], [3, 2], [4, 1], [6, 2], [10, 1], [12, 1]], 7/5760],
[[[1, 4], [2, 3], [3, 3], [4, 1], [5, 1], [6, 1], [12, 1]], 13/11520],
[[[1, 4], [2, 3], [3, 3], [4, 1], [6, 1], [10, 1], [12, 1]], 1/5760],
[[[1, 4], [2, 5], [3, 1], [4, 1], [5, 1], [6, 2], [8, 1]], 1/3456],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 1], [9, 1], [12, 1]], 1/6912],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 1], [12, 1], [18, 1]], 1/2304],
[[[1, 4], [2, 5], [3, 1], [4, 1], [6, 2], [8, 1], [10, 1]], 1/5760],
[[[1, 4], [2, 5], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 11/46080],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 1/768],
[[[1, 4], [2, 5], [3, 1], [4, 2], [6, 1], [10, 1], [12, 1]], 1/5760],
[[[1, 4], [2, 5], [3, 2], [4, 1], [5, 1], [6, 1], [8, 1]], 1/17280],
[[[1, 4], [2, 5], [3, 2], [4, 1], [6, 1], [8, 1], [10, 1]], 1/3840],
[[[1, 4], [2, 7], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/8640],
[[[1, 4], [2, 7], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 101/92160],
[[[1, 5], [2, 2], [3, 1], [4, 2], [6, 1], [9, 1], [12, 1]], 19/20736],
[[[1, 5], [2, 2], [3, 1], [4, 2], [6, 1], [12, 1], [18, 1]], 1/311040],
[[[1, 5], [2, 2], [3, 1], [4, 3], [6, 1], [8, 1], [12, 1]], 1/27648],
[[[1, 5], [2, 2], [3, 2], [4, 1], [5, 1], [6, 2], [12, 1]], 1/5760],
[[[1, 5], [2, 2], [3, 2], [4, 1], [6, 1], [9, 1], [12, 1]], 1/2304],
[[[1, 5], [2, 2], [3, 2], [4, 2], [5, 1], [6, 1], [12, 1]], 1/2160],
[[[1, 5], [2, 2], [3, 3], [4, 1], [5, 1], [6, 1], [12, 1]], 1/5760],
[[[1, 5], [2, 2], [3, 3], [4, 1], [6, 1], [10, 1], [12, 1]], 7/34560],
[[[1, 5], [2, 4], [3, 1], [4, 1], [5, 1], [6, 2], [8, 1]], 1/3840],
[[[1, 5], [2, 4], [3, 1], [4, 1], [6, 1], [9, 1], [12, 1]], 1/2304],
[[[1, 5], [2, 4], [3, 1], [4, 1], [6, 1], [12, 1], [18, 1]], 1/6912],
[[[1, 5], [2, 4], [3, 1], [4, 1], [6, 2], [8, 1], [10, 1]], 1/17280],
[[[1, 5], [2, 4], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 1/768],
[[[1, 5], [2, 4], [3, 1], [4, 2], [5, 1], [6, 1], [12, 1]], 1/5760],
[[[1, 5], [2, 4], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 11/46080],
[[[1, 5], [2, 4], [3, 2], [4, 1], [5, 1], [6, 1], [8, 1]], 1/5760],
[[[1, 5], [2, 4], [3, 2], [4, 1], [6, 1], [8, 1], [10, 1]], 1/3456],
[[[1, 5], [2, 6], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 5/9216],
[[[1, 5], [2, 6], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 29/34560],
[[[1, 6], [2, 1], [3, 3], [4, 1], [5, 1], [6, 1], [12, 1]], 1/34560],
[[[1, 6], [2, 3], [3, 1], [4, 1], [6, 1], [9, 1], [12, 1]], 1/6912],
[[[1, 6], [2, 3], [3, 1], [4, 1], [6, 1], [12, 1], [18, 1]], 1/103680],
[[[1, 6], [2, 3], [3, 1], [4, 2], [5, 1], [6, 1], [8, 1]], 1/15360],
[[[1, 6], [2, 3], [3, 1], [4, 2], [5, 1], [6, 1], [12, 1]], 1/2880],
[[[1, 6], [2, 3], [3, 1], [4, 2], [6, 1], [8, 1], [10, 1]], 1/23040],
[[[1, 6], [2, 3], [3, 2], [4, 1], [5, 1], [6, 1], [8, 1]], 1/720],
[[[1, 6], [2, 3], [3, 2], [4, 1], [6, 1], [8, 1], [10, 1]], 1/11520],
[[[1, 6], [2, 5], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 29/34560],
[[[1, 6], [2, 5], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 5/9216],
[[[1, 7], [2, 2], [3, 1], [4, 2], [5, 1], [6, 1], [12, 1]], 1/17280],
[[[1, 7], [2, 4], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 101/92160],
[[[1, 7], [2, 4], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/8640],
[[[1, 8], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1], [8, 1]], 1/5760],
[[[1, 8], [2, 3], [3, 1], [4, 1], [6, 1], [8, 1], [10, 1]], 1/92160],
[[[1, 1], [2, 2], [3, 1], [4, 2], [5, 1], [6, 1], [12, 1], [18, 1]], 1/2160],
[[[1, 2], [2, 1], [3, 1], [4, 2], [6, 1], [9, 1], [10, 1], [12, 1]], 1/2160],
[[[1, 2], [2, 3], [3, 1], [4, 1], [5, 1], [6, 1], [12, 1], [18, 1]], 1/720],
[[[1, 3], [2, 2], [3, 1], [4, 1], [6, 1], [9, 1], [10, 1], [12, 1]], 1/720]
]}