(*maximal facets from Dan Ciubotaru *)

max:=
{1/216,7/216,11/216,79/1080,109/1080,149/1080,209/1080,751/1080},
{1/216,7/216,11/216,79/1080,109/1080,209/1080,329/1080,931/1080},
{1/216,7/216,11/216,109/1080,149/1080,209/1080,329/1080,1001/1080},
{13/216,17/216,109/1080,139/1080,179/1080,239/1080,359/1080,221/216},
{1/216,11/216,79/1080,109/1080,149/1080,209/1080,329/1080,209/216},
{5/216,13/216,109/1080,139/1080,179/1080,239/1080,359/1080,233/216},
{5/216,13/216,17/216,109/1080,179/1080,239/1080,359/1080,1219/1080},
{0,1/18,1/12,67/540,17/90,11/45,16/45,311/270},
{5/216,13/216,17/216,109/1080,139/1080,179/1080,359/1080,1319/1080},
{0,1/18,1/12,67/540,41/270,17/90,16/45,56/45},
{-1/40,29/360,13/120,137/1080,161/1080,77/360,137/360,457/360},
{-1/90,7/180,31/540,17/180,59/270,17/60,9/20,241/180},
{1/360,19/360,107/1080,49/360,191/1080,29/120,49/120,467/360},
{1/108,1/27,8/135,31/270,107/540,41/135,127/270,367/270},
{1/216,1/24,11/120,53/360,83/360,293/1080,181/360,167/120},
{-5/216,5/72,43/360,7/40,31/120,323/1080,131/360,551/360},
{1/216,1/24,11/120,53/360,83/360,293/1080,73/120,539/360},
{-5/216,5/72,43/360,7/40,31/120,323/1080,169/360,589/360},
{17/1200,77/1200,49/400,251/1200,361/1200,29/80,109/240,2039/1200},
{1/108,1/27,8/135,31/270,107/540,41/135,173/270,413/270},
{-1/108,1/18,7/90,2/15,13/60,17/45,23/45,463/270},
{9/400,67/1200,97/1200,67/400,311/1200,97/240,119/240,2089/1200},
{-1/40,29/360,13/120,137/1080,161/1080,77/360,263/360,583/360},
{-13/180,41/360,97/720,119/720,73/360,211/720,449/720,167/90},
{-1/90,7/180,31/540,17/180,59/270,17/60,119/180,31/20},
{-47/1200,77/1200,97/1200,137/1200,301/1200,431/1200,649/1200,2099/1200},
{-47/1080,127/1080,167/1080,211/1080,241/1080,341/1080,619/1080,2113/1080},
{-1/108,1/18,7/90,2/15,77/270,17/45,23/45,107/60},
{1/360,19/360,107/1080,49/360,191/1080,29/120,253/360,191/120},
{-2/75,23/300,71/600,91/600,16/75,193/600,347/600,134/75},
{1/108,2/27,2/15,107/540,67/270,46/135,74/135,28/15},
{0,29/200,107/600,39/200,43/200,107/300,163/300,2},
{11/240,149/1200,209/1200,239/1200,283/1200,151/400,209/400,469/240},
{-11/240,149/1200,209/1200,239/1200,283/1200,151/400,209/400,491/240},
{0,19/220,28/165,71/330,63/220,137/330,163/330,2},
{0,1/18,1/12,67/540,41/270,17/90,34/45,74/45},
{-7/200,17/200,11/100,103/600,41/200,51/200,129/200,577/300},
{0,13/150,3/25,121/600,47/200,57/200,123/200,2},
{47/1080,127/1080,167/1080,211/1080,241/1080,341/1080,619/1080,2207/1080},
{1/108,1/18,7/90,2/15,77/270,17/45,23/45,133/60},
{-1/108,2/27,2/15,107/540,67/270,46/135,74/135,32/15},
{0,1/18,1/12,67/540,28/135,43/135,229/270,469/270},
{-7/200,17/200,11/100,103/600,51/200,71/200,159/200,577/300},
{0,13/150,3/25,121/600,57/200,77/200,153/200,2},
{77/1080,157/1080,197/1080,241/1080,311/1080,491/1080,809/1080,2237/1080},
{1/60,11/120,17/100,137/600,199/600,289/600,109/150,217/100},
{1/195,61/780,22/195,29/156,103/260,133/260,553/780,119/52},
{-9/400,67/1200,97/1200,67/400,311/1200,97/240,119/240,2711/1200},
{-8/195,31/390,41/390,44/195,24/65,29/52,183/260,154/65},
{13/1200,107/1200,197/1200,301/1200,137/400,97/240,119/240,937/400},
{-17/780,77/780,127/780,17/60,111/260,1/2,42/65,631/260},
{5/72,11/120,43/360,169/1080,229/1080,349/1080,71/72,15/8},
{2/27,67/540,41/270,17/90,11/45,16/45,53/54,221/108},
{61/720,43/360,53/360,89/360,13/45,67/180,44/45,1553/720},
{5/216,13/216,17/216,109/1080,139/1080,179/1080,841/1080,1801/1080},
{0,5/54,31/270,77/540,97/540,127/540,353/540,2},
{7/200,17/200,11/100,103/600,41/200,51/200,129/200,623/300},
{257/2160,361/2160,401/2160,101/432,71/240,949/2160,2093/2160,551/240},
{13/180,41/360,97/720,119/720,73/360,211/720,449/720,193/90},
{47/1200,77/1200,97/1200,137/1200,301/1200,431/1200,649/1200,2701/1200},
{3/32,21/160,259/1440,319/1440,161/480,793/1440,281/288,1151/480},
{2/75,23/300,71/600,91/600,16/75,193/600,347/600,166/75},
{5/216,13/216,17/216,109/1080,199/1080,319/1080,941/1080,1901/1080},
{0,5/54,31/270,77/540,127/540,187/540,443/540,2},
{7/200,17/200,11/100,103/600,51/200,71/200,159/200,623/300},
{77/780,107/780,61/390,12/65,103/390,79/195,203/260,1709/780},
{41/720,71/720,3/20,8/45,53/180,161/360,37/48,1637/720},
{27/260,103/780,59/390,37/195,289/780,38/65,749/780,953/390},
{13/255,29/340,7/60,77/510,377/1020,251/510,196/255,2417/1020},
{1/108,1/18,7/90,2/15,13/60,17/45,23/45,617/270},
{19/216,139/1080,179/1080,259/1080,313/1080,727/1080,209/216,2707/1080},
{1/195,61/780,22/195,29/156,131/390,109/195,59/78,953/390},
{13/216,23/216,179/1080,239/1080,329/1080,373/1080,587/1080,2633/1080},
{17/108,28/135,3/10,17/45,239/540,271/540,103/108,253/90},
{53/1680,167/1680,97/560,27/112,97/240,37/80,79/112,4307/1680},
{5/216,13/216,23/216,31/216,43/216,67/216,199/216,391/216},
{0,5/54,77/540,97/540,127/540,187/540,239/270,2},
{47/1200,107/1200,59/400,271/1200,331/1200,451/1200,1063/1200,847/400},
{11/120,2/15,131/720,79/360,193/720,101/240,203/240,397/180},
{1/24,23/264,239/1320,299/1320,141/440,643/1320,1151/1320,1021/440},
{23/360,11/120,103/720,133/720,137/360,133/240,79/90,1729/720},
{1/40,1/12,97/600,71/300,63/200,47/75,523/600,743/300},
{5/96,29/288,41/160,51/160,593/1440,239/480,1171/1440,3827/1440},
{29/540,61/540,8/45,23/90,47/135,43/108,53/108,79/30},
{227/1080,271/1080,361/1080,421/1080,97/216,107/216,973/1080,3247/1080},
{7/160,187/1440,107/480,137/480,127/288,47/96,929/1440,4033/1440},
{41/560,221/1680,33/112,29/80,733/1680,121/240,85/112,4873/1680},
{59/400,89/400,127/400,33/80,131/240,253/400,381/400,3751/1200},
{47/1560,191/1560,85/312,211/520,271/520,1021/1560,1249/1560,1587/520},
{1/108,37/540,13/135,2/15,17/90,3/10,113/108,209/108},
{-1/60,67/600,41/300,17/100,11/50,8/25,16/15,269/120},
{1/80,5/48,11/80,17/80,21/80,29/80,17/16,559/240},
{13/288,229/1440,269/1440,319/1440,383/1440,593/1440,313/288,3533/1440},
{1/60,67/600,17/100,11/50,179/600,71/150,16/15,757/300},
{1/40,19/200,3/25,17/100,73/200,107/200,127/120,1571/600},
{-1/240,109/1200,149/1200,259/1200,383/1200,697/1200,253/240,3227/1200},
{1/48,149/1200,83/400,121/400,493/1200,587/1200,259/240,1157/400},
{-1/240,109/1200,149/1200,259/1200,383/1200,697/1200,253/240,4103/1200},
{-1/128,233/1920,101/640,671/1920,181/384,1507/1920,407/384,455/128},
{1/48,149/1200,83/400,121/400,493/1200,587/1200,259/240,3919/1200},
{-1/288,73/480,349/1440,563/1440,87/160,977/1440,313/288,4829/1440},
{0,169/960,199/960,343/960,25/48,287/320,209/192,233/64},
{7/144,35/144,41/144,1/3,55/144,77/144,163/144,73/18},
{13/180,49/180,11/36,37/90,7/15,59/90,41/36,38/9},
{1/40,19/200,3/25,17/100,73/200,107/200,127/120,2099/600},
{5/144,97/720,13/80,209/720,203/360,191/240,155/144,223/60},
{13/276,29/92,25/69,59/138,34/69,227/276,80/69,1213/276},
{13/408,123/680,9/40,583/2040,1247/2040,1811/2040,149/136,7787/2040},
{1/104,53/312,83/312,107/312,241/312,287/312,341/312,1205/312},
{5/132,1/3,19/44,1/2,163/264,37/44,103/88,601/132},
{-1/120,3/20,9/40,11/40,43/120,13/24,131/120,15/4},
{1/72,25/144,35/144,3/8,17/36,103/144,79/72,563/144},
{11/456,539/2280,763/2280,47/120,389/760,647/760,511/456,9311/2280},
{5/456,529/2280,943/2280,1063/2280,509/760,2011/2280,511/456,509/120},
{1/108,5/108,2/27,4/27,11/54,17/54,10/9,2},
{-1/54,2/27,11/108,19/108,25/108,37/108,41/36,83/36},
{1/40,3/40,13/120,9/40,11/40,3/8,7/6,12/5},
{2/27,7/54,1/6,2/9,7/27,23/54,43/36,275/108},
{1/54,2/27,5/36,1/4,17/54,13/27,43/36,287/108},
{1/36,7/108,5/54,11/54,13/36,19/36,31/27,73/27},
{-1/60,1/15,1/10,1/4,1/3,17/30,47/40,337/120},
{1/120,11/120,7/40,13/40,49/120,59/120,5/4,91/30},
{-1/60,1/15,1/10,1/4,1/3,17/30,47/40,85/24},
{-1/68,1/12,9/68,79/204,97/204,53/68,257/204,257/68},
{1/120,11/120,7/40,13/40,49/120,59/120,5/4,52/15},
{-1/39,4/39,8/39,16/39,41/78,53/78,17/13,47/13},
{0,1/7,5/28,8/21,43/84,11/12,215/168,649/168},
{1/12,7/36,1/4,35/108,13/36,19/36,139/108,151/36},
{5/36,2/9,19/72,5/12,11/24,49/72,193/144,71/16},
{1/36,7/108,5/54,11/54,13/36,19/36,31/27,97/27},
{7/144,13/144,17/144,49/144,77/144,115/144,59/48,187/48},
{3/32,13/48,31/96,41/96,23/48,27/32,11/8,37/8},
{17/312,43/312,19/104,97/312,179/312,283/312,389/312,1247/312},
{1/80,29/240,11/48,103/240,197/240,15/16,319/240,989/240},
{13/168,13/42,23/56,89/168,53/84,143/168,247/168,823/168},
{-1/108,11/108,5/27,8/27,13/36,19/36,67/54,209/54},
{1/36,1/9,13/72,29/72,17/36,53/72,31/24,49/12},
{5/112,59/336,31/112,19/48,167/336,99/112,449/336,481/112},
{5/312,55/312,115/312,163/312,223/312,283/312,451/312,1421/312},
{1/60,23/120,29/120,7/20,2/5,1/2,67/60,253/60},
{1/36,7/36,17/72,5/12,1/2,97/144,10/9,647/144},
{1/78,41/156,47/156,11/26,1/2,133/156,179/156,123/26},
{1/52,15/52,19/52,29/52,35/52,131/156,181/156,257/52},
{1/30,2/15,11/60,7/20,2/5,1/2,19/15,131/30},
{2/39,5/39,1/6,11/26,1/2,55/78,101/78,123/26},
{1/36,7/36,17/72,5/12,1/2,8/9,191/144,709/144},
{1/24,2/9,11/36,11/18,53/72,7/8,35/24,193/36},
{1/24,2/9,11/36,11/18,9/8,91/72,35/24,221/36},
{1/38,20/57,26/57,49/57,45/38,80/57,63/38,757/114},
{1/108,5/108,2/27,1/9,1/6,7/18,23/18,13/6},
{-1/54,2/27,11/108,5/36,7/36,5/12,47/36,89/36},
{1/72,5/72,23/216,37/216,49/216,97/216,289/216,185/72},
{19/240,31/240,13/80,3/16,53/240,25/48,329/240,217/80},
{1/24,11/120,3/20,1/5,31/120,67/120,169/120,113/40},
{1/20,1/12,13/120,19/120,3/10,3/5,29/20,59/20},
{1/144,11/144,19/144,31/144,41/144,91/144,35/24,73/24},
{1/120,11/120,5/24,37/120,47/120,61/120,29/20,13/4},
{1/144,11/144,19/144,31/144,41/144,91/144,35/24,31/8},
{0,5/57,17/114,20/57,49/114,91/114,92/57,473/114},
{1/120,11/120,5/24,37/120,47/120,61/120,29/20,73/20},
{-1/39,4/39,3/13,31/78,20/39,9/13,125/78,152/39},
{1/72,31/216,43/216,77/216,103/216,199/216,367/216,929/216},
{1/12,11/60,7/30,4/15,3/10,3/5,29/20,259/60},
{7/52,11/52,1/4,19/52,21/52,113/156,61/39,60/13},
{1/20,1/12,13/120,19/120,3/10,3/5,29/20,79/20},
{5/78,4/39,5/39,23/78,37/78,5/6,43/26,113/26},
{1/12,73/276,31/92,113/276,127/276,241/276,5/3,338/69},
{13/228,11/76,47/228,67/228,125/228,11/12,395/228,1027/228},
{1/52,23/156,43/156,55/156,119/156,49/52,289/156,725/156},
{1/19,35/114,25/57,1/2,23/38,17/19,7/4,1177/228},
{1/60,7/60,23/120,29/120,3/10,3/5,29/20,247/60},
{7/156,19/156,29/156,55/156,5/12,121/156,83/52,229/52},
{7/132,23/132,10/33,25/66,16/33,119/132,149/88,411/88},
{1/38,11/57,47/114,53/114,25/38,35/38,34/19,187/38},
{1/54,7/54,5/27,5/18,1/3,5/9,13/9,9/2},
{1/24,1/8,1/6,3/8,11/24,55/72,29/18,121/24},
{1/45,17/90,23/90,2/5,7/15,41/45,76/45,79/15},
{1/48,35/144,53/144,79/144,97/144,43/48,257/144,269/48},
{1/48,35/144,53/144,79/144,53/48,191/144,319/144,331/48},
{1/68,71/204,107/204,169/204,77/68,299/204,469/204,29/4},
{1/27,22/81,28/81,44/81,31/27,154/81,409/162,47/6},
{1/34,20/51,23/51,40/51,21/17,104/51,269/102,141/17},
{7/96,19/96,25/96,59/96,139/96,69/32,269/96,839/96},
{1/20,47/140,59/140,121/140,229/140,47/20,419/140,1317/140},
{-1/20,1/4,3/10,7/20,2/5,1/2,23/20,47/10},
{-1/20,1/4,3/10,2/5,1/2,13/20,23/20,5},
{-1/26,9/26,5/13,11/26,1/2,21/26,31/26,69/13},
{-1/26,9/26,11/26,1/2,8/13,21/26,31/26,72/13},
{-1/18,1/6,2/9,1/3,7/18,1/2,23/18,85/18},
{-1/20,3/20,1/5,2/5,1/2,7/10,13/10,51/10},
{-1/20,1/4,3/10,2/5,1/2,17/20,27/20,27/5},
{-1/20,1/4,7/20,11/20,7/10,17/20,29/20,59/10},
{-1/20,1/4,7/20,11/20,23/20,13/10,29/20,34/5},
{-1/34,13/34,1/2,29/34,41/34,49/34,57/34,261/34},
{-1/18,1/6,2/9,5/18,1/3,5/9,13/9,29/6},
{-1/20,3/20,1/5,7/20,9/20,3/4,8/5,107/20},
{-1/28,1/4,9/28,11/28,13/28,25/28,47/28,23/4},
{-1/24,7/24,5/12,1/2,5/8,7/8,7/4,37/6},
{-1/24,7/24,5/12,1/2,9/8,11/8,9/4,23/3},
{-1/34,13/34,19/34,27/34,39/34,3/2,79/34,283/34},
{-3/52,17/52,21/52,25/52,61/52,99/52,33/13,17/2},
{-1/22,29/66,1/2,49/66,83/66,45/22,175/66,607/66},
{-3/40,9/40,3/10,11/20,29/20,43/20,14/5,37/4},
{-3/62,23/62,29/62,53/62,103/62,147/62,187/62,643/62},
{-2/29,19/29,43/29,63/29,84/29,106/29,124/29,478/29}}