from functools import lru_cache from random import randint from bisect import * @lru_cache def miller_rabin(p): if p == 2: return 1 if p == 3: return 1 if p % 2 == 0: return 0 d, s = p-1, 0 while d % 2 == 0: d //= 2; s += 1 for _ in range(10): x = pow(randint(2, p-2), d, p) for _ in range(s): y = x**2 % p if y == 1 and x != 1 and x != p-1: return 0 x = y if y != 1: return 0 return 1 def gcd(a, b): while b: a, b = b, a % b return a @lru_cache def pollard_rho(n): c = 1 while True: x, y, d = 2, 2, 1 while d == 1: x = (x*x+c)%n y = (y*y+c)%n; y = (y*y+c)%n d = gcd(abs(x-y), n) if d != n: return d else: c += 1 @lru_cache def pf(n): if n <= LIMIT: f = {} while n != 1: pp = spf[n] if n % pp == 0: k = 0 while n % pp == 0: n //= pp; k += 1 if k: f[pp] = k return f elif miller_rabin(n): return {n: 1} else: f = {} p = pollard_rho(n) for k, v in pf(p).items(): if k not in f: f[k] = 0 f[k] += v for k, v in pf(n//p).items(): if k not in f: f[k] = 0 f[k] += v return f precompute = False if precompute: LIMIT = 3*10**7 spf = list(range(LIMIT+1)) primes = [] p = 2 while p <= LIMIT: if spf[p] == p: primes.append(p) for i in range(p*p, LIMIT+1, p): if spf[i] == i: spf[i] = p if p == 2: p -= 1 p += 2 works = [] for i in range(1, 10**8, 2): ''' Suppose i = p1^k1 p2^k2 ... pn^kn Then ndiv(i^i) = (i*k1+1)(i*k2+1)...(i*kn+1) Suffices to find ndiv(ndiv(i^i)) ''' fact_d = {} for _, k in pf(i).items(): for p2, k2 in pf(i*k+1).items(): if p2 not in fact_d: fact_d[p2] = 0 fact_d[p2] += k2 # fact_d is the prime factorization if ndiv(i^i) f = 1 for _, k in fact_d.items(): f *= k+1 if i % f: break if i % f == 0: works.append(i) print(works) diff = [(works[i+1]-works[i])//2 for i in range(len(works)-1)] else: diff = 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57,5783,4300,10260,13520,2680,3570,210,2900,460,8670,2310,3510,5670,180,1248,3492,980,358,1395,1887,2180,4450,4710,5300,910,5460,735,2541,7644,6110,3120,3640,1040,12130,13500,6230,8620,1640,7420,380,220,300,4890,8630,1560,4680,2460,670,330,3080,10620,7060,1410,1410,4160,1560,1066,3614,2980,140,8140,14960,238,1122,12240,4250,3010,1800,2600,4210,470,4060,8940,7404,2696,6800,260,1770,690,300,2205,3105,1190,1480,13860,1400,1870,2316,8294,4810,4410,1700,660,2785,3315,1620,13460,3430,1380,798,2205,7727,4810,24890,7240,5240,6240,12480,300,120,1140,3250,11310,2895,882,5583,6450,830,10270,650,11440,6380,3160,2420,4090,1110,7280,2340,11653,12527,8980,30,870,360,1470,588,702,900,1800,3150,390,5540,6420,7510,3410,700,860,1560,2080,5720,4680,1660,2073,12387,4680,6060,3066,13754,3120,1480,420,7760,1260,3328,3432,5940,8160,2720,5020,1560,1040,1560,4680,10620,4980,6240,5746,1014,2420,14110,3230,5200,3495,1575,2700,6410,900,1560,1620,7090,1320,3830,700,1040,1560,6208,6090,3612,1190,5440,2420,300,220,12060,3150,390,9390,1140,1245,7985,6730,3600,6480,210,1700,6900,14940,3640,3060,7760,4480,120,18210,830,5440,140,457,6303,10020,1940,5746,2394,1220,4597,1413,1130,1570,6300,4370,8590,3240,5190,936,2444,6040,980,5220,5700,910,1050,5320,620,690,10190,4620,520,8460,3500,835,2465,1837,1103,6970,540,1790,7000,2940,5720,6100,6380,1560,598,3042,6630,5175,2235,180,18540,11154,1626,4290,1130,4680,8590,770,3120,7800,3640,3570,5270,8230,5160,1170,1980,126,1239,435,3500,2470,4620,3830,13513,7427,1360,5780,2080,4710,234,2336,7800,16120,5720,700,5600,70,16254,813,4773,4890,2360,2200,300,15618,4242,1980,1170,3050,10860,73,11427,4074,966,3740,5605,1335,9900,320,6085,6395,5890,6678,42,5490,8490,1107,5583,8450,5070,2665,455,3540,1140,8380,980,100,3360,5964,4116,5180,5110,6470,6130,8810,4168,1092,8360,940,9930,1370,6900,1690,1820,6916,11234,13600,1605,575,9190,170,1560,1560,2800,20,400,7700,3120,520,3453,10587,3210,1860,1170,650,27370,2720,4620,3540,12060,10837,83,790,1290,2310,2910,2060,8320,13140,5580,2001,7359,4758,4082,4680,3420,220,1430,130,5720,7660,660,11580,900,2300,4300,1820,238,6552,3480,570,7920,380,3120,8320,7280,10920,4260,5440,237,983,4680,790,2330,6240,14830,1290,510,2310,1860,2600,5620,1140,3570,2690,5830,6210,1460,10980,9520,2720,180,3900,13600,180,2600,5070,25480,650,3430,1170,4578,362,2200,5810,4290,5200,2900,1360,7230,6710,2080,2600,420,2700,3670,1010,1753,1575,8112,3993,4077,7296,1274,1560,670,4530,330,1464,2886,2697,4973,4290,1240,5180,7000,30780,9750,8450,6838,2067,5835,2420,4680,9360,460,3180,5220,210,4830,1700,10920,4180,897,1163,7800,3640,870,3290,3180,2680,10080,9200,280,3960,2360,17140,2886,1274,4540,4680,140,580,1365,8325,2490,4400,2080,3140,14670,1650,5980,1470,4914,9576,420,8100,2180,130,2370,260,3445,2015,2626,1191,4283,18940,5370,5160,450,980,2728,392,2700,20050,3276,1154,1030,5280,7070,520,3780,5400,4340,4914,306,4140,2848,6612,6140,1560,1480,5280,3624,2226,2310,680,1180,8700,2544,7856,1090,1370,5860,213,1818,5909,2460,3640,1040,1315,7865,1740,4290,4780,4110,6720,5580,2600,4680,3640,1040,1620,4620,3120,12670,4070,940,7280,520,8790,30210,5850,1740,1790,10380,1860,7500,9070,2394,4136,8296,4158,636,7710,4160,900,2220,7800,12715,105,4620,240,4680,498,10122,3420,7800,5720,2170,3170,7036,1664,1024,4716,1880,1090,1890,15540,7890,9783,1427,1060,330,3030,4550,1950,9360,3300,8977,203,520,2130,8280,3780,14190,90,650,7420,2460,2600,3796,12324,9165,2795,6040,3500,2800,3480,6020,3120,6240,24960,9060,4237,3363,6090,6930,480,1580,15060,5200,9660,2300,420,9520,3660,3140,5100,4680,1560,7150,4305,4145,6460,924,6476,10450,6890,5500,2300,3420,4380,20800,30,7047,12683,9460,2720,3100,2400,15660,1890,2210,4720,6200,8700,6520,210,3780,1730,4540,900,5640,1160,14140,690,4380,5520,330,7280,300,2950,4830,1800,10400,4285,915,2600,4680,130,1430,598,3042,150,5643,3567,2600,7500,7150,2730,11880,2720,780,4680,2230,1230,180,9813,2667,12420,918,3302,12100,380,2530,3890,2200,740,13330,2730,1995,2898,1947,11724,1596,1740,1040,220,2010,1410,11934,19026,3360,5780,1500,9360,1560,70,450,1040,5413,2387,3120,520,2600,19540,2300,2230,24867,12803,13140,7800,2520,2160,2080,1040,10920,2770,6530,918,8008,15927,987,2720,10,1230,3150,1950,9360,8808,729,2813,1170,3120,14470,1800,7130,16060,5628,5805,3707,1534,6266,3940,3360,10245,7415,6240,8700,595,3485,2820,1240,320,5200,7800,2600,420,1426,2834,4810,2307,4323,2820,3240,3270,3530,9700,2277,1623,1620,1100,3580,2600,2740,600,3420,2600,3460,12270,78,1352,12180,3420,3640,7254,714,1392,2010,6525,6545,13705,8295,900,1830,230,2626,2994,2760,4520,12280,2900,4680,520,20,10380,1660,1560,9260,1620,460,1170,660,14810,4144,3236,3540,10060,3240,1470,22490,3820,2013,27,3024,10536,5060,730,1490,4810,3120,14910,870,2630,180,1180,380,850,1980,3590,5020,6630,590,4080,5860,3666,6594,3780,1590,2990,10500,4030,650,6240,1560,6940,3980,17680,1170,2990,5460,1000,378,2522,180,4500,9360,11440,2600,1066,8294,2920,2250,1460,4950,2460,1390,1665,11505,3510,12090,11934,26,4680,1560,1018,5222,4060,7380,10704,216,6753,1047,3570,1110,11460,4200,3480,1140,2180,2266,5439,2751,1404,380,660,1560,12480,3120,13000,6890,100,11184,219,16067,2278,3162,6380,420,4260,1435,3705,10080,4020,2460,1700,520,1140,240,180,2600,6240,2100,4200,6700,4680,3540,1857,8223,1980,1170,6110,2626,21594,3585,3395,3120,1885,8715,2420,1150,3840,5390,3580,7800,4220,1510,570,1440,120,4380,300,520,4160,13530,21678,1712,1480,3780,13460,7800,6760,8840,1660,5685,1115,250,5850,7280,1360,200,5460,11518,722,670,918,2492,1750,24830,6240,7800,1660,9660,120,6240,5720,3250,2090,136,764,3730,15330,5900,4900,1340,5850,9100,5850,1560,7280,3120,853,11807,910,470,9360,7930,1430,300,3100,12200,6240,2170,1860,1170,2073,3827,2940,1140,420,3660,10600,5720,300,5200,1170,9230,4690,3110,715,7085,6580,180,8450,5070,4680,16120,8840,1690,1950,620,11340,1870,3110,1260,6760,16460,4080,730,3170,1560,670,5570,540,1020,7800,6040,6440,8580,10530,3115,525,10350,360,22050,5096,2314,4160,520,5720,1560,1740,8140,4160,1560,17620,1620,11960,6994,2886,2700,330,4640,6750,1258,442,2600,1040,1560,2620,2720,6100,180,210,5460,2990,6240,4680,2700,7210,8940,390,1500,2625,288,12227,9130,1790,780,4450,11870,520,60,1704,8696,390,4810,140,900,25480,14420,2220,1660,9780,8790,288,2882,1560,4168,2772,795,65,3120,8320,7280,580,3873,227,3250,9828,2522,700,5540,940,620,3640,3510,650,5020,11480,5440,9960,3486,8904,16550,3640,5060,3780,265,7665,1560,5070,5757,6203,520,546,3614,1560,3120,5335,315,8988,2382,6380,2080,140,1420,4160,10740,1740,5200,11960,3640,7488,2037,875,1560,6760,7800,2600,2740,1080,5670,1430,5200,2106,494,10920,9376,10904,1560,3013,315,6132,18573,1607,3120,3640,540,13560,2540,660,8050,1170,1040,8340,4140,5380,678,6552,15470,364,2756,916,464,778,3302,5460,4297,15273,710,520,2600,11245,7995,6630,5330,2704,966,390,6810,12530,6760,900,6380,7800,2530,7506,1482,1502,1900,7410,30,180,13290,510,5780,4720,10880,8320,3090,4710,5720,6240,4426,5004,1490,6240,580,3360,15300,4755,8465,12780,820,740,7800,9360,985,155,4060,20,2515,5850,455,8770,6890,1000,6510,2310,3120,1040,520,5694,4286,420,940,6860,3160,480,4680,2600,3120,5640,2160,3160,420,915,1575,170,4500,8968,4032,6420,1560,4113,3167,4680,1144,12516,2360,1630,13550,2290,7590,2106,3614,2665,7355,900,2770,1910,3718,1092,1950,13520,5200,1580,4660,4160,6240,910,12090,7280,1378,2,840,2460,3250,22050,4340,3780,8050,1170,1040,13330,6330,4260,1170,1430,2140,3360,4380,8840,520,2670,6170,1560,2740,6320,4980,520,1040,15900,1480,6930,5850,7377,1463,1380,4080,3900,2620,23900,10465,2015,3940,4380,1248,4472,1560,3640,576,14804,4080,20400,180,1255,1995,8610,200,11340,10420,3620,11065,225,3270,1437,12393,11510,1258,5457,2475,594,4916,3820,2541,1439,6060,1360,3500,598,9842,4900,8190,7670,1560,11340,1660,2940,840,1940,3670,4130,5220,1240,2840,5910,10410,10780,6264,2394,1742,580,2720,4080,2680,11340,5964,716,2140,7350,3810,2300,3120,520,570,2030,4680,18720,1560,3120,8590,3890,3874,4446,3090,690,1940,3640,1040,5620,12240,8580,7854,26,2470,2210,880,680,8320,1040,5200,57,6053,7930,78,4382,3960,160,8970,2210,9360,7800,9700,8877,1703,1560,4780,560,2590,3315,5915,20254,29631,2925,2210,3160,60,3510,60,1370,11230,8270,900,660,1560,5940,300,2170,2120,8190,1560,568,1932,6860,11830,13430,4140,3880,2600,3900,780,5100,2700,1900,4110,4910,193,8028,6209,70,8310,5270,9646,2834,220,2720,180,520,1170,1950,16236,8724,1140,1560,16410,6300,8390,6240,2470,4290,1940,4080,4380,3985,6615,2100,6810,2330,4680,3250,7670,40,8820,3360,3380,2140,1200,2900,520,3300,3240,1260,2600,5850,17490,60,160,2310,2058,2877,3312,1463,820,6510,14810,4090,1110,4160,1140,7588,2192,3120,3120,7800,13870,4470,3500,1930,9510,1980,5300,2080,93,2481,7826,910,2210,3640,26910,60,3710,1180,2840,660,3120,520,7566,2004,1647,13113,3690,6300,5720,540,4080,253,2427,14540,9610,1310,670,5570,520,78,1092,3570,5660,3120,520,3510,4670,2680,1400,4060,1380,300,813,2457,804,1896,2030,1560,13000,11418,639,563,1420,2600,3670,810,6750,2310,600,3030,3170,2230,830,1560,5200,1662,9468,7070,10210,10730,1360,6300,10020,2720,4030,3315,2025,7010,9190,16680,2630,3880,1940,3700,10770,2690,1500,1620,4297,383,520,2600,598,3582,2720,1990,3678,3192,1260,3260,4680,1560,2106,8194,6270,530,580,288,2312,3420,2430,12730,210,5430,1260,8840,4486,194,9880,9140,15300,4680,3871,7049,2260,1380,7820,1210,2700,1790,220,300,12620,900,3180,1500,4810,6110,6760,234,986,9700,7800,5720,1260,1834,1806,440,5020,2835,2475,6430,6500,1040,3640,7380,9780,8840,9360,100,7230,4170,7038,3075,3477,6110,7800,1504,1616,10920,1560,6240,3120,4810,6174,336,9240,9080,14460,1140,1560,7150,1740,5103,7787,60,17620,1620,2600,9334,26,3250,6290,1380,18685,35,4680,13300,1880,1798,6762,12660,234,5226,2720,9484,536,4680,286,9074,2140,924,966,1170,7460,1900,2600,6240,9660,685,5775,1040,14430,1170,1380,700,2730,3120,20150,1900,4040,14860,8840,4810,4550,520,8580,1260,3680,9880,4680,5720,10920,877,683,10920,10920,1560,7800,2893,8547,2600,940,1140,30,8820,2690,628,312,3140,4080,3700,3300,15420,1170,1950,16530,1670,7800,7800,160,4520,3460,12140,2665,13455,1040,388,342,10290,8220,936,2724,12240,1260,1040,4030,650,2500,8420,4810,13755,155,3340,1340,1560,14040,4300,2040,9260,7800,1260,820,5850,1530,3990,16710,5720,13020,1450,9870,5970,6090,6540,7500,2600,1560,12820,6800,4080,5134,876,5130,2520,5180,1140,400,4410,795,635,520,2600,2080,9360,20,24480,8650,870,1340,2760,490,2990,2848,452,5440,6800,7314,3666,6700,9420,234,8946,336,3774,540,4860,330,23760,380,5200,1140,7700,6820,980,520,5400,5390,8110,1380,13580,25840,2180,6100,8460,2300,820,390,840,3390,1230,5070,11960,6240,30784,936,1770,13830,20660,2788,2552,8158,2822,490,258,1052,2820,4680,5200,3510,1890,840,3120,11960,900,6900,2080,2600,9180,9457,14553,110,2590,2490,15414,5486,7800,2080,6110,4290,6240,754,2226,720,330,1170,4680,5910,1370,6500,2860,6700,1386,9464,5430,2500,5720,1288,4452,2060,5740,500,3853,22847,4760,260,8658,1092,650,4380,1960,6140,1560,13324,5916,1620,4100,20968,2132,7093,4127,1560,730,6890,180,5220,1750,13440,16130,1360,255,845,2158,3042,2730,3210,3420,2600,780,7150,1050,5060,3060,3180,12480,5377,4503,11960,3016,5724,5300,11230,13110,2700,3020,1660,7280,2533,6207,6210,1170,21840,2670,13500,3590,5200,3120,6620,6900,15600,4870,2280,10530,1560,4290,15170,1860,3580,7340,397,9903,8420,6838,10262,10980,190,330,2600,460,5124,266,390,2530,2670,1040,3700,6765,455,9360,3120,910,3770,6940,210,1170,2568,7785,467,10500,23584,1974,987,1535,40,4640,2980,4820,664,1416,1560,1040,1066,494,9670,10610,4020,1360,180,3800,3640,8790,14610,8220,2310,3330,1220,1500,3180,4330,14390,904,5336,460,10941,39,2418,182,10920,5740,3906,2364,1800,3480,4620,3990,510,110,12610,9770,14020,2600,3120,3250,5145,5865,2094,1716,7070,5020,3140,2710,1890,9030,1050,6620,4540,2805,8255,5245,7235,328,2142,10095,4595,5638,1122,5850,6734,2716,10206,9854,6817,983,11440,2660,460,5720,265,3465,9660,3770,9334,8346,4160,3510,4060,8030,1780,1340,5608,6872,2158,3042,360,5360,5070,5850,1465,7791,1764,1980,180,3980,220,10700,2470,650,6784,15576,8840,1560,38746,3894,2600,7996,1364,14560,3795,2865,8160,840,3240,1926,6594,2360,19620,1560,85,2925,290,10740,1690,5590,5330,1950,7340,5440,2120,180,1560,184,4496,3700,22170,6390,500,7800,1564,6236,1560,7296,504,10570,168,12012,8450,6760,33,8807,10570,1490,6478,2457,845,14170,12350,3120,1560,3640,1352,12168,2140,3030,30,4680,2600,2470,8918,1792,6897,11123,190,5010,2600,6760,7740,10080,6510,4790,7800,520,2600,208,1352,1560,4900,1764,4776,1740,1290,900,8030,4810,6630,1392,1208,18720,2410,5390,9736,11649,16055,1045,4155,3510,4290,5300,3540,2830,4500,9830,1560,520,1260,2900,6058,42,2517,15303,5070,7350,1100,2260,6360,33,12017,2730,5200,9654,746,8515,1905,840,1089,3251,10920,4654,2106,11433,1047,20,4840,13461,6179,9820,1040,3640,5655,4745,3640,4160,5230,1010,1186,8174,2020,12240,1340,8230,7890,650,930,3060,6370,10970,3430,2010,7446,3822,672,10560,9360,1040,11800,680,4680,3730,4070,9360,3940,2300,4060,2700,7320,860,1360,360,2580,357,8943,1100,5580,4300,7280,14950,546,1664,940,2310,2990,11500,1890,10010,19240,1380,4314,1092,8169,6755,3250,1040,10920,1570,2148,2352,2250,1040,3120,13078,2522,1560,8320,26000,1960,5840,520,10400,6214,651,7632,4223,70,1830,4830,50,1800,4990,1575,1595,3150,1950,340,180,3120,690,2700,120,650,3120,1033,1047,2300,2770,3770,6790,1010,1560,4500,8200,4460,2080,5850,3003,24297,1170,22100,1510,1638,13232,7800,520,9780,6990,780,2210,12480,1060,8300,1260,4300,2940,7170,2700,210,9500,5473,10127,1690,2700,6434,12466,9470,430,3600,5330,15370,2544,3626,300,1060,2060,1900,180,1830,6270,4250,14790,4705,4515,3680,9360,9304,5156,1660,1430,16770,5200,3120,10590,1370,4810,4550,520,3540,3740,24670,8610,234,9126,6140,2890,6630,4100,14040,6240,3250,1050,5730,2160,7440,6384,5366,2940,9370,5190,5610,3627,13929,3354,5720,3300,730,650,9880,993,3687,16458,1602,204,2016,3717,443,42250,1430,8398,4082,24960,9640,240,3120,2730,4550,11830,9450,2640,6180,3390,6690,380,1260,11800,8780,2896,1494,8090,13390,8450,1560,3120,2620,2580,4560,11040,1980,1110,3570,12240,2420,8632,3458,11284,4706,16315,8985,180,4710,3090,2600,2149,971,4300,3500,8380,4710,63,2967,2600,14740,5670,530,4540,264,2336,9360,6994,2366,7800,4680,1690,2130,2940,7080,860,1360,1620,2460,4080,3860,1510,4704,806,21160,3150,3276,974,2380,17680,2080,300,1780,1040,3300,12300,2140,3240,2420,4680,3120,1534,3206,5350,4548,5502,1050,3950,8140,3120,897,7623,8780,12240,2206,3614,5500,740,9880,2064,2616,5720,20890,1470,2288,132,6420,7180,2720,3750,1950,7150,1170,717,6563,460,7860,15260,4440,6118,1742,3640,8840,5200,23166,10634,3120,11980,3750,5055,2615,4300,1940,12480,6370,11090,1260,11695,645,8160,300,4680,11190,7010,7800,4380,300,700,2420,1660,30,3120,5460,7410,5720,9900,6220,1940,5440,4080,7100,5140,8540,6240,5620,4260,1140,420,3120,2600,10800,1030,2730,7280,1560,3120,1380,27805,16055,2380,1494,3276,2436,13944,7854,1376,4966,2534,5500,6980,3550,1850,5820,9880,3540,11670,2751,239,6240,7150,2210,3640,7280,1885,2795,1846,6474,1500,1620,3390,2990,380,14620,11320,60,1040,73,1487,430,4680,2310,3810,4370,340,1560,1220,3085,5313,2522,3120,1560,12480,12805,9035,7615,3605,670,10575,2415,1640,2980,3260,10740,790,3030,1040,853,10587,4160,1030,2898,3872,4740,23560,36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0,20280,3120,11617,4503,5580,3560,955,1995,2184,1386,2540,3718,3042,4580,2605,3150,3885,2436,6384,10695,2145,4160,1690,10920,2478,5192,11020,3360,4680,2720,2140,1470,1830,5540,1630,5070,12636,3684,2720,3900,2080,10340,4080,2610,13510,1700,8770,1110,860,1630,3810,12360,60,234,806,3120,520,3198,4872,3990,7518,8502,2310,4190,4080,7000,1140,380,2110,110,3120,4680,11380,8900,14220,6580,1040,540,6805,455,4144,536,7800,400,10520,1980,4080,14740,5660,1750,6660,4884,3926,2917,3713,4290,1660,4580,1560,17100,4080,1660,4956,3924,15080,4810,9230,2500,1668,162,3990,1980,7160,1260,6900,24480,6205,3315,6420,2600,3180,10678,2832,15363,1227,10041,5039,520,2010,2670,11960,4680,2500,4130,130,2420,1090,5460,7644,2646,1428,8142,8090,9880,4160,28080,9433,1347,3585,4215,1700,5100,19378,6342,3500,3120,300,11880,9880,1340,7800,3640,5973,267,4100,1750,1820,2210,905,8505,19320,1380,4910,9700,5304,15561,7515,13220,5200,10400,4680,3220,3960,620,2080,30,9408,10626,13736,460,2478,4004,6538,4725,515,7800,520,3990,2310,390,876,8778,4746,15960,1140,3375,555,10400,6760,3020,1660,9555,1125,3380,8160,1180,2600,1660,5490,14690,7800,3300,3460,1620,2540,1560,8320,7280,3120,910,13350,390,7008,3302,3055,321,5984,1560,10,8490,2420,2820,6540,1330,4910,4680,14040,6580,948,1772,3310,1638,312,180,2700,2121,1979,300,3120,10920,1776,5644,900,4845,2435,22660,350,4170,3910,1670,10270,650,6240,18100,2700,23400,4160,1408,3612,5900,400,4410,4368,4002,7100,6500,5980,16030,6525,6075,2388,182,4060,2700,6380,900,1560,1690,12170,5440,19700,3120,2158,10842,8840,1560,4680,4024,4916,2590,5630,1690,210,180,390,2210,8590,936,882,9912,6720,4160,8320,4700,1636,4064,6540,7890,70,1040,346,1974,4578,7202,2290,830,4680,430,6330,3120,1040,11220,1080,3300,4510,1730,7060,8540,8710,10530,4830,30,1380,4890,5640,6630,9750,1155,4487,1428,1380,2260,7854,7476,4830,210,1290,180,4440,5598,7917,14105,7800,5584,6896,8320,2013,12927,3260,6358,1722,9080,7720,210,2990,5890,870,2220,8778,4262,3460,1040,520,8840,6700,1785,12315,2310,2084,306,1150,390,1040,7620,3300,8020,6930,3276,3614,4780,1590,1130,1864,126,1950,3510,8450,1870,1770,11570,1530,817,4113,510,2780,85,9795,15630,10370,7150,4305,8085,714,4706,1570,3110,8800,1260,4500,960,3200,6040,3320,5200,6810,4578,8922,1088,1482,3250,11310,2600,1378,3302,3300,4690,4830,1350,10890,6140,397,263,2460,2080,900,5220,1160,23400,4966,9744,3110,1720,2370,3804,3276,2430,1860,4160,2140,4620,2180,3540,6760,3390,6710,820,7340,3190,1890,1100,190,1370,1560,6070,6300,110,4060,2130,16910,190,8430,5100,6680,1360,900,3200,10320,8700,6900,9940,980,3640,7317,13343,3780,1210,2820,650,1560,1560,3120,8460,1240,8157,123,5420,1380,4660,2280,9480,5460,9500,286,5954,4680,2470,650,4915,9450,5625,3020,2443,1007,4740,3640,1040,1690,1995,7455,3654,126,5360,6240,1180,4110,5210,3436,18018,6666,440,5440,1260,24440,17160,10920,2950,690,2600,1180,390,1212,5018,18250,7230,3390,1490,658,14222,7800,4260,5100,16645,2735,190,4740,4290,19760,4680,2140,980,6160,210,15470,4060,620,2020,7770,3210,2600,286,1794,1040,940,13100,3120,520,2300,12780,3120,7800,3760,330,3710,4680,1900,1350,1370,1620,2080,9900,6690,7824,6266,4680,6240,3120,1900,6645,1335,2900,9880,3990,2990,3640,150,3048,4746,18081,9335,598,1632,7190,1500,7800,3718,5502,1260,440,14890,9198,1392,3120,3510,455,3025,1670,700,15260,11650,2210,18780,1500,6364,1266,20910,1100,6838,12222,2840,520,980,4680,3540,6600,4290,280,7670,2200,9093,947,220,7545,1155,1200,6740,520,5235,1005,17180,12538,7862,2460,13860,4270,5610,6420,10400,6240,4940,9100,910,5150,10600,6740,520,9540,5670,7730,1360,4245,900,7425,8883,4107,510,2670,8850,1410,30,110,1560,15100,980,1015,3185,3120,3250,1430,13468,11322,1730,4180,2060,6240,4680,420,6760,3740,2560,420,1700,1140,4080,6220,14180,2850,13650,2080,8658,182,1560,3835,675,690,5720,9060,1210,5850,1100,460,5720,7420,18060,1040,13900,140,3220,4580,4240,2000,11356,84,1040,1690,2990,6240,520,2600,2460,5340,1900,1610,2730,4186,9854,3250,6110,1560,3640,620,940,3888,792,2600,3190,320,9580,4530,1100,2980,360,480,860,3190,19827,903,234,1346,4080,610,1010,4680,4290,3640,1680,210,2660,14455,4265,4030,1710,5180,4620,60,4020,10198,3492,5790,10794,10946,4680,1560,1996,474,1560,2210,520,1560,4020,17820,1040,220,2718,1362,6555,8463,18122,4180,2120,1990,63,1527,2574,546,1460,5530,2630,11700,100,2640,2540,7200,520,10400,70,2910,465,5915,940,4130,5950,5720,14980,3765,72,31029,13794,2300,3120,15730,4970,100,7410,2010,12810,5850,4160,12970,1070,520,2010,3710,420,2700,9360,10780,7940,520,7280,2080,1140,1460,1620,4620,5694,3666,2935,7985,3660,8820,4510,456,2184,650,3340,1800,4038,1932,17178,8132,6190,1070,4810,1530,360,3930,290,6300,5335,3438,111,3236,300,1560,2340,490,8610,22880,7885,7215,1880,570,6328,7140,7982,14040,21840,700,2576,15964,3510,336,614,4510,1430,1560,1560,1560,3340,4460,3198,5782,1160,2860,4680,4830,1410,2600,4680,520,4160,520,7944,14841,6525,2930,11440,1040,7990,2930,1060,16100,580,7800,4968,15162,2690,4680,2080,2940,1220,1620,12240,796,10137,1307,4080,4080,7990,1430,4680,820,3780,7770,3450,2900,2080,6900,12054,3266,547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works = [1] for i in diff: works.append(works[-1]+2*i) a, b = map(int, input().split()) print(bisect_right(works, b)-bisect_left(works, a))