#include <bits/stdc++.h> static int primes[] = {2,3,5,7, 11, 13, 17, 19, 23, 29 ,31, 37, 41, 43, 47, 53, 59, 61, 67, 71 ,73, 79, 83, 89, 97,101,103,107,109,113 , 127,131,137,139,149,151,157,163,167,173 , 179,181,191,193,197,199,211,223,227,229 , 233,239,241,251,257,263,269,271,277,281 , 283,293,307,311,313,317,331,337,347,349 , 353,359,367,373,379,383,389,397,401,409 , 419,421,431,433,439,443,449,457,461,463 , 467,479,487,491,499,503,509,521,523,541 , 547,557,563,569,571,577,587,593,599,601 , 607,613,617,619,631,641,643,647,653,659 , 661,673,677,683,691,701,709,719,727,733 , 739,743,751,757,761,769,773,787,797,809 , 811,821,823,827,829,839,853,857,859,863 , 877,881,883,887,907,911,919,929,937,941 , 947,953,967,971,977,983,991,997, 1009, 1013 ,1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069 ,1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151 ,1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223 ,1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291 ,1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373 ,1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451 ,1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511 ,1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583 ,1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657 ,1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733 ,1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811 ,1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889 ,1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987 ,1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053 ,2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129 ,2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213 ,2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287 ,2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357 ,2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423 ,2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531 ,2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617 ,2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687 ,2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741 ,2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819 ,2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903 ,2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999 ,3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079 ,3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181 ,3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257 ,3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331 ,3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413 ,3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511 ,3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571 ,3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643 ,3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727 ,3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821 ,3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907 ,3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989 ,4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057 ,4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139 ,4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231 ,4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297 ,4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409 ,4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493 ,4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583 ,4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657 ,4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751 ,4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831 ,4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937 ,4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003 ,5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087 ,5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179 ,5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279 ,5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387 ,5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443 ,5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521 ,5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639 ,5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693 ,5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791 ,5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857 ,5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939 ,5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053 ,6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133 ,6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221 ,6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301 ,6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367 ,6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473 ,6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571 ,6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673 ,6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761 ,6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833 ,6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917 ,6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997 ,7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103 ,7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207 ,7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297 ,7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411 ,7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499 ,7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561 ,7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643 ,7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723 ,7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829 ,7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919 ,7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017 ,8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111 ,8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219 ,8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291 ,8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387 ,8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501 ,8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597 ,8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677 ,8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741 ,8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831 ,8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929 ,8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011 ,9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109 ,9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199 ,9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283 ,9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377 ,9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439 ,9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533 ,9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631 ,9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733 ,9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811 ,9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887 ,9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973,10007 , 10009,10037,10039,10061,10067,10069,10079,10091,10093,10099 , 10103,10111,10133,10139,10141,10151,10159,10163,10169,10177 , 10181,10193,10211,10223,10243,10247,10253,10259,10267,10271 , 10273,10289,10301,10303,10313,10321,10331,10333,10337,10343 , 10357,10369,10391,10399,10427,10429,10433,10453,10457,10459 , 10463,10477,10487,10499,10501,10513,10529,10531,10559,10567 , 10589,10597,10601,10607,10613,10627,10631,10639,10651,10657 , 10663,10667,10687,10691,10709,10711,10723,10729,10733,10739 , 10753,10771,10781,10789,10799,10831,10837,10847,10853,10859 , 10861,10867,10883,10889,10891,10903,10909,10937,10939,10949 , 10957,10973,10979,10987,10993,11003,11027,11047,11057,11059 , 11069,11071,11083,11087,11093,11113,11117,11119,11131,11149 , 11159,11161,11171,11173,11177,11197,11213,11239,11243,11251 , 11257,11261,11273,11279,11287,11299,11311,11317,11321,11329 , 11351,11353,11369,11383,11393,11399,11411,11423,11437,11443 , 11447,11467,11471,11483,11489,11491,11497,11503,11519,11527 , 11549,11551,11579,11587,11593,11597,11617,11621,11633,11657 , 11677,11681,11689,11699,11701,11717,11719,11731,11743,11777 , 11779,11783,11789,11801,11807,11813,11821,11827,11831,11833 , 11839,11863,11867,11887,11897,11903,11909,11923,11927,11933 , 11939,11941,11953,11959,11969,11971,11981,11987,12007,12011 , 12037,12041,12043,12049,12071,12073,12097,12101,12107,12109 , 12113,12119,12143,12149,12157,12161,12163,12197,12203,12211 , 12227,12239,12241,12251,12253,12263,12269,12277,12281,12289 , 12301,12323,12329,12343,12347,12373,12377,12379,12391,12401 , 12409,12413,12421,12433,12437,12451,12457,12473,12479,12487 , 12491,12497,12503,12511,12517,12527,12539,12541,12547,12553 , 12569,12577,12583,12589,12601,12611,12613,12619,12637,12641 , 12647,12653,12659,12671,12689,12697,12703,12713,12721,12739 , 12743,12757,12763,12781,12791,12799,12809,12821,12823,12829 , 12841,12853,12889,12893,12899,12907,12911,12917,12919,12923 , 12941,12953,12959,12967,12973,12979,12983,13001,13003,13007 , 13009,13033,13037,13043,13049,13063,13093,13099,13103,13109 , 13121,13127,13147,13151,13159,13163,13171,13177,13183,13187 , 13217,13219,13229,13241,13249,13259,13267,13291,13297,13309 , 13313,13327,13331,13337,13339,13367,13381,13397,13399,13411 , 13417,13421,13441,13451,13457,13463,13469,13477,13487,13499 , 13513,13523,13537,13553,13567,13577,13591,13597,13613,13619 , 13627,13633,13649,13669,13679,13681,13687,13691,13693,13697 , 13709,13711,13721,13723,13729,13751,13757,13759,13763,13781 , 13789,13799,13807,13829,13831,13841,13859,13873,13877,13879 , 13883,13901,13903,13907,13913,13921,13931,13933,13963,13967 , 13997,13999,14009,14011,14029,14033,14051,14057,14071,14081 , 14083,14087,14107,14143,14149,14153,14159,14173,14177,14197 , 14207,14221,14243,14249,14251,14281,14293,14303,14321,14323 , 14327,14341,14347,14369,14387,14389,14401,14407,14411,14419 , 14423,14431,14437,14447,14449,14461,14479,14489,14503,14519 , 14533,14537,14543,14549,14551,14557,14561,14563,14591,14593 , 14621,14627,14629,14633,14639,14653,14657,14669,14683,14699 , 14713,14717,14723,14731,14737,14741,14747,14753,14759,14767 , 14771,14779,14783,14797,14813,14821,14827,14831,14843,14851 , 14867,14869,14879,14887,14891,14897,14923,14929,14939,14947 , 14951,14957,14969,14983,15013,15017,15031,15053,15061,15073 , 15077,15083,15091,15101,15107,15121,15131,15137,15139,15149 , 15161,15173,15187,15193,15199,15217,15227,15233,15241,15259 , 15263,15269,15271,15277,15287,15289,15299,15307,15313,15319 , 15329,15331,15349,15359,15361,15373,15377,15383,15391,15401 , 15413,15427,15439,15443,15451,15461,15467,15473,15493,15497 , 15511,15527,15541,15551,15559,15569,15581,15583,15601,15607 , 15619,15629,15641,15643,15647,15649,15661,15667,15671,15679 , 15683,15727,15731,15733,15737,15739,15749,15761,15767,15773 , 15787,15791,15797,15803,15809,15817,15823,15859,15877,15881 , 15887,15889,15901,15907,15913,15919,15923,15937,15959,15971 , 15973,15991,16001,16007,16033,16057,16061,16063,16067,16069 , 16073,16087,16091,16097,16103,16111,16127,16139,16141,16183 , 16187,16189,16193,16217,16223,16229,16231,16249,16253,16267 , 16273,16301,16319,16333,16339,16349,16361,16363,16369,16381 , 16411,16417,16421,16427,16433,16447,16451,16453,16477,16481 , 16487,16493,16519,16529,16547,16553,16561,16567,16573,16603 , 16607,16619,16631,16633,16649,16651,16657,16661,16673,16691 , 16693,16699,16703,16729,16741,16747,16759,16763,16787,16811 , 16823,16829,16831,16843,16871,16879,16883,16889,16901,16903 , 16921,16927,16931,16937,16943,16963,16979,16981,16987,16993 , 17011,17021,17027,17029,17033,17041,17047,17053,17077,17093 , 17099,17107,17117,17123,17137,17159,17167,17183,17189,17191 , 17203,17207,17209,17231,17239,17257,17291,17293,17299,17317 , 17321,17327,17333,17341,17351,17359,17377,17383,17387,17389 , 17393,17401,17417,17419,17431,17443,17449,17467,17471,17477 , 17483,17489,17491,17497,17509,17519,17539,17551,17569,17573 , 17579,17581,17597,17599,17609,17623,17627,17657,17659,17669 , 17681,17683,17707,17713,17729,17737,17747,17749,17761,17783 , 17789,17791,17807,17827,17837,17839,17851,17863,17881,17891 , 17903,17909,17911,17921,17923,17929,17939,17957,17959,17971 , 17977,17981,17987,17989,18013,18041,18043,18047,18049,18059 , 18061,18077,18089,18097,18119,18121,18127,18131,18133,18143 , 18149,18169,18181,18191,18199,18211,18217,18223,18229,18233 , 18251,18253,18257,18269,18287,18289,18301,18307,18311,18313 , 18329,18341,18353,18367,18371,18379,18397,18401,18413,18427 , 18433,18439,18443,18451,18457,18461,18481,18493,18503,18517 , 18521,18523,18539,18541,18553,18583,18587,18593,18617,18637 , 18661,18671,18679,18691,18701,18713,18719,18731,18743,18749 , 18757,18773,18787,18793,18797,18803,18839,18859,18869,18899 , 18911,18913,18917,18919,18947,18959,18973,18979,19001,19009 , 19013,19031,19037,19051,19069,19073,19079,19081,19087,19121 , 19139,19141,19157,19163,19181,19183,19207,19211,19213,19219 , 19231,19237,19249,19259,19267,19273,19289,19301,19309,19319 , 19333,19373,19379,19381,19387,19391,19403,19417,19421,19423 , 19427,19429,19433,19441,19447,19457,19463,19469,19471,19477 , 19483,19489,19501,19507,19531,19541,19543,19553,19559,19571 , 19577,19583,19597,19603,19609,19661,19681,19687,19697,19699 , 19709,19717,19727,19739,19751,19753,19759,19763,19777,19793 , 19801,19813,19819,19841,19843,19853,19861,19867,19889,19891 , 19913,19919,19927,19937,19949,19961,19963,19973,19979,19991 , 19993,19997,20011,20021,20023,20029,20047,20051,20063,20071 , 20089,20101,20107,20113,20117,20123,20129,20143,20147,20149 , 20161,20173,20177,20183,20201,20219,20231,20233,20249,20261 , 20269,20287,20297,20323,20327,20333,20341,20347,20353,20357 , 20359,20369,20389,20393,20399,20407,20411,20431,20441,20443 , 20477,20479,20483,20507,20509,20521,20533,20543,20549,20551 , 20563,20593,20599,20611,20627,20639,20641,20663,20681,20693 , 20707,20717,20719,20731,20743,20747,20749,20753,20759,20771 , 20773,20789,20807,20809,20849,20857,20873,20879,20887,20897 , 20899,20903,20921,20929,20939,20947,20959,20963,20981,20983 , 21001,21011,21013,21017,21019,21023,21031,21059,21061,21067 , 21089,21101,21107,21121,21139,21143,21149,21157,21163,21169 , 21179,21187,21191,21193,21211,21221,21227,21247,21269,21277 , 21283,21313,21317,21319,21323,21341,21347,21377,21379,21383 , 21391,21397,21401,21407,21419,21433,21467,21481,21487,21491 , 21493,21499,21503,21517,21521,21523,21529,21557,21559,21563 , 21569,21577,21587,21589,21599,21601,21611,21613,21617,21647 , 21649,21661,21673,21683,21701,21713,21727,21737,21739,21751 , 21757,21767,21773,21787,21799,21803,21817,21821,21839,21841 , 21851,21859,21863,21871,21881,21893,21911,21929,21937,21943 , 21961,21977,21991,21997,22003,22013,22027,22031,22037,22039 , 22051,22063,22067,22073,22079,22091,22093,22109,22111,22123 , 22129,22133,22147,22153,22157,22159,22171,22189,22193,22229 , 22247,22259,22271,22273,22277,22279,22283,22291,22303,22307 , 22343,22349,22367,22369,22381,22391,22397,22409,22433,22441 , 22447,22453,22469,22481,22483,22501,22511,22531,22541,22543 , 22549,22567,22571,22573,22613,22619,22621,22637,22639,22643 , 22651,22669,22679,22691,22697,22699,22709,22717,22721,22727 , 22739,22741,22751,22769,22777,22783,22787,22807,22811,22817 , 22853,22859,22861,22871,22877,22901,22907,22921,22937,22943 , 22961,22963,22973,22993,23003,23011,23017,23021,23027,23029 , 23039,23041,23053,23057,23059,23063,23071,23081,23087,23099 , 23117,23131,23143,23159,23167,23173,23189,23197,23201,23203 , 23209,23227,23251,23269,23279,23291,23293,23297,23311,23321 , 23327,23333,23339,23357,23369,23371,23399,23417,23431,23447 , 23459,23473,23497,23509,23531,23537,23539,23549,23557,23561 , 23563,23567,23581,23593,23599,23603,23609,23623,23627,23629 , 23633,23663,23669,23671,23677,23687,23689,23719,23741,23743 , 23747,23753,23761,23767,23773,23789,23801,23813,23819,23827 , 23831,23833,23857,23869,23873,23879,23887,23893,23899,23909 , 23911,23917,23929,23957,23971,23977,23981,23993,24001,24007 , 24019,24023,24029,24043,24049,24061,24071,24077,24083,24091 , 24097,24103,24107,24109,24113,24121,24133,24137,24151,24169 , 24179,24181,24197,24203,24223,24229,24239,24247,24251,24281 , 24317,24329,24337,24359,24371,24373,24379,24391,24407,24413 , 24419,24421,24439,24443,24469,24473,24481,24499,24509,24517 , 24527,24533,24547,24551,24571,24593,24611,24623,24631,24659 , 24671,24677,24683,24691,24697,24709,24733,24749,24763,24767 , 24781,24793,24799,24809,24821,24841,24847,24851,24859,24877 , 24889,24907,24917,24919,24923,24943,24953,24967,24971,24977 , 24979,24989,25013,25031,25033,25037,25057,25073,25087,25097 , 25111,25117,25121,25127,25147,25153,25163,25169,25171,25183 , 25189,25219,25229,25237,25243,25247,25253,25261,25301,25303 , 25307,25309,25321,25339,25343,25349,25357,25367,25373,25391 , 25409,25411,25423,25439,25447,25453,25457,25463,25469,25471 , 25523,25537,25541,25561,25577,25579,25583,25589,25601,25603 , 25609,25621,25633,25639,25643,25657,25667,25673,25679,25693 , 25703,25717,25733,25741,25747,25759,25763,25771,25793,25799 , 25801,25819,25841,25847,25849,25867,25873,25889,25903,25913 , 25919,25931,25933,25939,25943,25951,25969,25981,25997,25999 , 26003,26017,26021,26029,26041,26053,26083,26099,26107,26111 , 26113,26119,26141,26153,26161,26171,26177,26183,26189,26203 , 26209,26227,26237,26249,26251,26261,26263,26267,26293,26297 , 26309,26317,26321,26339,26347,26357,26371,26387,26393,26399 , 26407,26417,26423,26431,26437,26449,26459,26479,26489,26497 , 26501,26513,26539,26557,26561,26573,26591,26597,26627,26633 , 26641,26647,26669,26681,26683,26687,26693,26699,26701,26711 , 26713,26717,26723,26729,26731,26737,26759,26777,26783,26801 , 26813,26821,26833,26839,26849,26861,26863,26879,26881,26891 , 26893,26903,26921,26927,26947,26951,26953,26959,26981,26987 , 26993,27011,27017,27031,27043,27059,27061,27067,27073,27077 , 27091,27103,27107,27109,27127,27143,27179,27191,27197,27211 , 27239,27241,27253,27259,27271,27277,27281,27283,27299,27329 , 27337,27361,27367,27397,27407,27409,27427,27431,27437,27449 , 27457,27479,27481,27487,27509,27527,27529,27539,27541,27551 , 27581,27583,27611,27617,27631,27647,27653,27673,27689,27691 , 27697,27701,27733,27737,27739,27743,27749,27751,27763,27767 , 27773,27779,27791,27793,27799,27803,27809,27817,27823,27827 , 27847,27851,27883,27893,27901,27917,27919,27941,27943,27947 , 27953,27961,27967,27983,27997,28001,28019,28027,28031,28051 , 28057,28069,28081,28087,28097,28099,28109,28111,28123,28151 , 28163,28181,28183,28201,28211,28219,28229,28277,28279,28283 , 28289,28297,28307,28309,28319,28349,28351,28387,28393,28403 , 28409,28411,28429,28433,28439,28447,28463,28477,28493,28499 , 28513,28517,28537,28541,28547,28549,28559,28571,28573,28579 , 28591,28597,28603,28607,28619,28621,28627,28631,28643,28649 , 28657,28661,28663,28669,28687,28697,28703,28711,28723,28729 , 28751,28753,28759,28771,28789,28793,28807,28813,28817,28837 , 28843,28859,28867,28871,28879,28901,28909,28921,28927,28933 , 28949,28961,28979,29009,29017,29021,29023,29027,29033,29059 , 29063,29077,29101,29123,29129,29131,29137,29147,29153,29167 , 29173,29179,29191,29201,29207,29209,29221,29231,29243,29251 , 29269,29287,29297,29303,29311,29327,29333,29339,29347,29363 , 29383,29387,29389,29399,29401,29411,29423,29429,29437,29443 , 29453,29473,29483,29501,29527,29531,29537,29567,29569,29573 , 29581,29587,29599,29611,29629,29633,29641,29663,29669,29671 , 29683,29717,29723,29741,29753,29759,29761,29789,29803,29819 , 29833,29837,29851,29863,29867,29873,29879,29881,29917,29921 , 29927,29947,29959,29983,29989,30011,30013,30029,30047,30059 , 30071,30089,30091,30097,30103,30109,30113,30119,30133,30137 , 30139,30161,30169,30181,30187,30197,30203,30211,30223,30241 , 30253,30259,30269,30271,30293,30307,30313,30319,30323,30341 , 30347,30367,30389,30391,30403,30427,30431,30449,30467,30469 , 30491,30493,30497,30509,30517,30529,30539,30553,30557,30559 , 30577,30593,30631,30637,30643,30649,30661,30671,30677,30689 , 30697,30703,30707,30713,30727,30757,30763,30773,30781,30803 , 30809,30817,30829,30839,30841,30851,30853,30859,30869,30871 , 30881,30893,30911,30931,30937,30941,30949,30971,30977,30983 , 31013,31019,31033,31039,31051,31063,31069,31079,31081,31091 , 31121,31123,31139,31147,31151,31153,31159,31177,31181,31183 , 31189,31193,31219,31223,31231,31237,31247,31249,31253,31259 , 31267,31271,31277,31307,31319,31321,31327,31333,31337,31357 , 31379,31387,31391,31393,31397,31469,31477,31481,31489,31511 , 31513,31517,31531,31541,31543,31547,31567,31573,31583,31601 , 31607}; int ret = 0; typedef std::vector<int> VI; typedef std::map<int, int> MII; VI getFractals(int n){ MII ret; int i = 0; while(n > 1){ if(primes[i] * primes[i] > n){ ret[n]++; break; } if(n % primes[i]){ i++; continue; } ret[primes[i]]++; n/=primes[i]; } VI fractals; for(auto it : ret){ int count = it.second; int el = it.first; int p = 1; while(count){ fractals.push_back(el); el *= el; count >>=1; } } return fractals; } void checkFractal(int product){ product--; int n = product; VI fractals = getFractals(product); int ii = (1 << fractals.size()); for(int i = 1; i <= ii-1; i++){ int index = 0; int el = i; int product = 1; while(el){ if(el & 1) product *= fractals[index]; index++; el >>= 1; } if(n % product == 0 && product >= 2 && n/product >= 3) ret++; } } int main() { int n; std::cin >> n; auto fractals = getFractals(n); int ii = (1 << fractals.size()); for(int i = 1; i <= ii; i++){ int index = 0; int el = i; int product = 1; while(el){ if(el & 1) product *= fractals[index]; index++; el >>= 1; } if(product > 6 && n % product == 0) checkFractal(product); } std::cout << ret << std::endl; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 | #include <bits/stdc++.h> static int primes[] = {2,3,5,7, 11, 13, 17, 19, 23, 29 ,31, 37, 41, 43, 47, 53, 59, 61, 67, 71 ,73, 79, 83, 89, 97,101,103,107,109,113 , 127,131,137,139,149,151,157,163,167,173 , 179,181,191,193,197,199,211,223,227,229 , 233,239,241,251,257,263,269,271,277,281 , 283,293,307,311,313,317,331,337,347,349 , 353,359,367,373,379,383,389,397,401,409 , 419,421,431,433,439,443,449,457,461,463 , 467,479,487,491,499,503,509,521,523,541 , 547,557,563,569,571,577,587,593,599,601 , 607,613,617,619,631,641,643,647,653,659 , 661,673,677,683,691,701,709,719,727,733 , 739,743,751,757,761,769,773,787,797,809 , 811,821,823,827,829,839,853,857,859,863 , 877,881,883,887,907,911,919,929,937,941 , 947,953,967,971,977,983,991,997, 1009, 1013 ,1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069 ,1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151 ,1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223 ,1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291 ,1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373 ,1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451 ,1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511 ,1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583 ,1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657 ,1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733 ,1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811 ,1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889 ,1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987 ,1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053 ,2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129 ,2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213 ,2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287 ,2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357 ,2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423 ,2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531 ,2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617 ,2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687 ,2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741 ,2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819 ,2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903 ,2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999 ,3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079 ,3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181 ,3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257 ,3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331 ,3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413 ,3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511 ,3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571 ,3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643 ,3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727 ,3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821 ,3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907 ,3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989 ,4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057 ,4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139 ,4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231 ,4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297 ,4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409 ,4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493 ,4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583 ,4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657 ,4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751 ,4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831 ,4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937 ,4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003 ,5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087 ,5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179 ,5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279 ,5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387 ,5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443 ,5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521 ,5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639 ,5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693 ,5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791 ,5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857 ,5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939 ,5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053 ,6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133 ,6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221 ,6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301 ,6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367 ,6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473 ,6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571 ,6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673 ,6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761 ,6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833 ,6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917 ,6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997 ,7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103 ,7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207 ,7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297 ,7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411 ,7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499 ,7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561 ,7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643 ,7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723 ,7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829 ,7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919 ,7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017 ,8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111 ,8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219 ,8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291 ,8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387 ,8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501 ,8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597 ,8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677 ,8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741 ,8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831 ,8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929 ,8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011 ,9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109 ,9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199 ,9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283 ,9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377 ,9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439 ,9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533 ,9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631 ,9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733 ,9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811 ,9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887 ,9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973,10007 , 10009,10037,10039,10061,10067,10069,10079,10091,10093,10099 , 10103,10111,10133,10139,10141,10151,10159,10163,10169,10177 , 10181,10193,10211,10223,10243,10247,10253,10259,10267,10271 , 10273,10289,10301,10303,10313,10321,10331,10333,10337,10343 , 10357,10369,10391,10399,10427,10429,10433,10453,10457,10459 , 10463,10477,10487,10499,10501,10513,10529,10531,10559,10567 , 10589,10597,10601,10607,10613,10627,10631,10639,10651,10657 , 10663,10667,10687,10691,10709,10711,10723,10729,10733,10739 , 10753,10771,10781,10789,10799,10831,10837,10847,10853,10859 , 10861,10867,10883,10889,10891,10903,10909,10937,10939,10949 , 10957,10973,10979,10987,10993,11003,11027,11047,11057,11059 , 11069,11071,11083,11087,11093,11113,11117,11119,11131,11149 , 11159,11161,11171,11173,11177,11197,11213,11239,11243,11251 , 11257,11261,11273,11279,11287,11299,11311,11317,11321,11329 , 11351,11353,11369,11383,11393,11399,11411,11423,11437,11443 , 11447,11467,11471,11483,11489,11491,11497,11503,11519,11527 , 11549,11551,11579,11587,11593,11597,11617,11621,11633,11657 , 11677,11681,11689,11699,11701,11717,11719,11731,11743,11777 , 11779,11783,11789,11801,11807,11813,11821,11827,11831,11833 , 11839,11863,11867,11887,11897,11903,11909,11923,11927,11933 , 11939,11941,11953,11959,11969,11971,11981,11987,12007,12011 , 12037,12041,12043,12049,12071,12073,12097,12101,12107,12109 , 12113,12119,12143,12149,12157,12161,12163,12197,12203,12211 , 12227,12239,12241,12251,12253,12263,12269,12277,12281,12289 , 12301,12323,12329,12343,12347,12373,12377,12379,12391,12401 , 12409,12413,12421,12433,12437,12451,12457,12473,12479,12487 , 12491,12497,12503,12511,12517,12527,12539,12541,12547,12553 , 12569,12577,12583,12589,12601,12611,12613,12619,12637,12641 , 12647,12653,12659,12671,12689,12697,12703,12713,12721,12739 , 12743,12757,12763,12781,12791,12799,12809,12821,12823,12829 , 12841,12853,12889,12893,12899,12907,12911,12917,12919,12923 , 12941,12953,12959,12967,12973,12979,12983,13001,13003,13007 , 13009,13033,13037,13043,13049,13063,13093,13099,13103,13109 , 13121,13127,13147,13151,13159,13163,13171,13177,13183,13187 , 13217,13219,13229,13241,13249,13259,13267,13291,13297,13309 , 13313,13327,13331,13337,13339,13367,13381,13397,13399,13411 , 13417,13421,13441,13451,13457,13463,13469,13477,13487,13499 , 13513,13523,13537,13553,13567,13577,13591,13597,13613,13619 , 13627,13633,13649,13669,13679,13681,13687,13691,13693,13697 , 13709,13711,13721,13723,13729,13751,13757,13759,13763,13781 , 13789,13799,13807,13829,13831,13841,13859,13873,13877,13879 , 13883,13901,13903,13907,13913,13921,13931,13933,13963,13967 , 13997,13999,14009,14011,14029,14033,14051,14057,14071,14081 , 14083,14087,14107,14143,14149,14153,14159,14173,14177,14197 , 14207,14221,14243,14249,14251,14281,14293,14303,14321,14323 , 14327,14341,14347,14369,14387,14389,14401,14407,14411,14419 , 14423,14431,14437,14447,14449,14461,14479,14489,14503,14519 , 14533,14537,14543,14549,14551,14557,14561,14563,14591,14593 , 14621,14627,14629,14633,14639,14653,14657,14669,14683,14699 , 14713,14717,14723,14731,14737,14741,14747,14753,14759,14767 , 14771,14779,14783,14797,14813,14821,14827,14831,14843,14851 , 14867,14869,14879,14887,14891,14897,14923,14929,14939,14947 , 14951,14957,14969,14983,15013,15017,15031,15053,15061,15073 , 15077,15083,15091,15101,15107,15121,15131,15137,15139,15149 , 15161,15173,15187,15193,15199,15217,15227,15233,15241,15259 , 15263,15269,15271,15277,15287,15289,15299,15307,15313,15319 , 15329,15331,15349,15359,15361,15373,15377,15383,15391,15401 , 15413,15427,15439,15443,15451,15461,15467,15473,15493,15497 , 15511,15527,15541,15551,15559,15569,15581,15583,15601,15607 , 15619,15629,15641,15643,15647,15649,15661,15667,15671,15679 , 15683,15727,15731,15733,15737,15739,15749,15761,15767,15773 , 15787,15791,15797,15803,15809,15817,15823,15859,15877,15881 , 15887,15889,15901,15907,15913,15919,15923,15937,15959,15971 , 15973,15991,16001,16007,16033,16057,16061,16063,16067,16069 , 16073,16087,16091,16097,16103,16111,16127,16139,16141,16183 , 16187,16189,16193,16217,16223,16229,16231,16249,16253,16267 , 16273,16301,16319,16333,16339,16349,16361,16363,16369,16381 , 16411,16417,16421,16427,16433,16447,16451,16453,16477,16481 , 16487,16493,16519,16529,16547,16553,16561,16567,16573,16603 , 16607,16619,16631,16633,16649,16651,16657,16661,16673,16691 , 16693,16699,16703,16729,16741,16747,16759,16763,16787,16811 , 16823,16829,16831,16843,16871,16879,16883,16889,16901,16903 , 16921,16927,16931,16937,16943,16963,16979,16981,16987,16993 , 17011,17021,17027,17029,17033,17041,17047,17053,17077,17093 , 17099,17107,17117,17123,17137,17159,17167,17183,17189,17191 , 17203,17207,17209,17231,17239,17257,17291,17293,17299,17317 , 17321,17327,17333,17341,17351,17359,17377,17383,17387,17389 , 17393,17401,17417,17419,17431,17443,17449,17467,17471,17477 , 17483,17489,17491,17497,17509,17519,17539,17551,17569,17573 , 17579,17581,17597,17599,17609,17623,17627,17657,17659,17669 , 17681,17683,17707,17713,17729,17737,17747,17749,17761,17783 , 17789,17791,17807,17827,17837,17839,17851,17863,17881,17891 , 17903,17909,17911,17921,17923,17929,17939,17957,17959,17971 , 17977,17981,17987,17989,18013,18041,18043,18047,18049,18059 , 18061,18077,18089,18097,18119,18121,18127,18131,18133,18143 , 18149,18169,18181,18191,18199,18211,18217,18223,18229,18233 , 18251,18253,18257,18269,18287,18289,18301,18307,18311,18313 , 18329,18341,18353,18367,18371,18379,18397,18401,18413,18427 , 18433,18439,18443,18451,18457,18461,18481,18493,18503,18517 , 18521,18523,18539,18541,18553,18583,18587,18593,18617,18637 , 18661,18671,18679,18691,18701,18713,18719,18731,18743,18749 , 18757,18773,18787,18793,18797,18803,18839,18859,18869,18899 , 18911,18913,18917,18919,18947,18959,18973,18979,19001,19009 , 19013,19031,19037,19051,19069,19073,19079,19081,19087,19121 , 19139,19141,19157,19163,19181,19183,19207,19211,19213,19219 , 19231,19237,19249,19259,19267,19273,19289,19301,19309,19319 , 19333,19373,19379,19381,19387,19391,19403,19417,19421,19423 , 19427,19429,19433,19441,19447,19457,19463,19469,19471,19477 , 19483,19489,19501,19507,19531,19541,19543,19553,19559,19571 , 19577,19583,19597,19603,19609,19661,19681,19687,19697,19699 , 19709,19717,19727,19739,19751,19753,19759,19763,19777,19793 , 19801,19813,19819,19841,19843,19853,19861,19867,19889,19891 , 19913,19919,19927,19937,19949,19961,19963,19973,19979,19991 , 19993,19997,20011,20021,20023,20029,20047,20051,20063,20071 , 20089,20101,20107,20113,20117,20123,20129,20143,20147,20149 , 20161,20173,20177,20183,20201,20219,20231,20233,20249,20261 , 20269,20287,20297,20323,20327,20333,20341,20347,20353,20357 , 20359,20369,20389,20393,20399,20407,20411,20431,20441,20443 , 20477,20479,20483,20507,20509,20521,20533,20543,20549,20551 , 20563,20593,20599,20611,20627,20639,20641,20663,20681,20693 , 20707,20717,20719,20731,20743,20747,20749,20753,20759,20771 , 20773,20789,20807,20809,20849,20857,20873,20879,20887,20897 , 20899,20903,20921,20929,20939,20947,20959,20963,20981,20983 , 21001,21011,21013,21017,21019,21023,21031,21059,21061,21067 , 21089,21101,21107,21121,21139,21143,21149,21157,21163,21169 , 21179,21187,21191,21193,21211,21221,21227,21247,21269,21277 , 21283,21313,21317,21319,21323,21341,21347,21377,21379,21383 , 21391,21397,21401,21407,21419,21433,21467,21481,21487,21491 , 21493,21499,21503,21517,21521,21523,21529,21557,21559,21563 , 21569,21577,21587,21589,21599,21601,21611,21613,21617,21647 , 21649,21661,21673,21683,21701,21713,21727,21737,21739,21751 , 21757,21767,21773,21787,21799,21803,21817,21821,21839,21841 , 21851,21859,21863,21871,21881,21893,21911,21929,21937,21943 , 21961,21977,21991,21997,22003,22013,22027,22031,22037,22039 , 22051,22063,22067,22073,22079,22091,22093,22109,22111,22123 , 22129,22133,22147,22153,22157,22159,22171,22189,22193,22229 , 22247,22259,22271,22273,22277,22279,22283,22291,22303,22307 , 22343,22349,22367,22369,22381,22391,22397,22409,22433,22441 , 22447,22453,22469,22481,22483,22501,22511,22531,22541,22543 , 22549,22567,22571,22573,22613,22619,22621,22637,22639,22643 , 22651,22669,22679,22691,22697,22699,22709,22717,22721,22727 , 22739,22741,22751,22769,22777,22783,22787,22807,22811,22817 , 22853,22859,22861,22871,22877,22901,22907,22921,22937,22943 , 22961,22963,22973,22993,23003,23011,23017,23021,23027,23029 , 23039,23041,23053,23057,23059,23063,23071,23081,23087,23099 , 23117,23131,23143,23159,23167,23173,23189,23197,23201,23203 , 23209,23227,23251,23269,23279,23291,23293,23297,23311,23321 , 23327,23333,23339,23357,23369,23371,23399,23417,23431,23447 , 23459,23473,23497,23509,23531,23537,23539,23549,23557,23561 , 23563,23567,23581,23593,23599,23603,23609,23623,23627,23629 , 23633,23663,23669,23671,23677,23687,23689,23719,23741,23743 , 23747,23753,23761,23767,23773,23789,23801,23813,23819,23827 , 23831,23833,23857,23869,23873,23879,23887,23893,23899,23909 , 23911,23917,23929,23957,23971,23977,23981,23993,24001,24007 , 24019,24023,24029,24043,24049,24061,24071,24077,24083,24091 , 24097,24103,24107,24109,24113,24121,24133,24137,24151,24169 , 24179,24181,24197,24203,24223,24229,24239,24247,24251,24281 , 24317,24329,24337,24359,24371,24373,24379,24391,24407,24413 , 24419,24421,24439,24443,24469,24473,24481,24499,24509,24517 , 24527,24533,24547,24551,24571,24593,24611,24623,24631,24659 , 24671,24677,24683,24691,24697,24709,24733,24749,24763,24767 , 24781,24793,24799,24809,24821,24841,24847,24851,24859,24877 , 24889,24907,24917,24919,24923,24943,24953,24967,24971,24977 , 24979,24989,25013,25031,25033,25037,25057,25073,25087,25097 , 25111,25117,25121,25127,25147,25153,25163,25169,25171,25183 , 25189,25219,25229,25237,25243,25247,25253,25261,25301,25303 , 25307,25309,25321,25339,25343,25349,25357,25367,25373,25391 , 25409,25411,25423,25439,25447,25453,25457,25463,25469,25471 , 25523,25537,25541,25561,25577,25579,25583,25589,25601,25603 , 25609,25621,25633,25639,25643,25657,25667,25673,25679,25693 , 25703,25717,25733,25741,25747,25759,25763,25771,25793,25799 , 25801,25819,25841,25847,25849,25867,25873,25889,25903,25913 , 25919,25931,25933,25939,25943,25951,25969,25981,25997,25999 , 26003,26017,26021,26029,26041,26053,26083,26099,26107,26111 , 26113,26119,26141,26153,26161,26171,26177,26183,26189,26203 , 26209,26227,26237,26249,26251,26261,26263,26267,26293,26297 , 26309,26317,26321,26339,26347,26357,26371,26387,26393,26399 , 26407,26417,26423,26431,26437,26449,26459,26479,26489,26497 , 26501,26513,26539,26557,26561,26573,26591,26597,26627,26633 , 26641,26647,26669,26681,26683,26687,26693,26699,26701,26711 , 26713,26717,26723,26729,26731,26737,26759,26777,26783,26801 , 26813,26821,26833,26839,26849,26861,26863,26879,26881,26891 , 26893,26903,26921,26927,26947,26951,26953,26959,26981,26987 , 26993,27011,27017,27031,27043,27059,27061,27067,27073,27077 , 27091,27103,27107,27109,27127,27143,27179,27191,27197,27211 , 27239,27241,27253,27259,27271,27277,27281,27283,27299,27329 , 27337,27361,27367,27397,27407,27409,27427,27431,27437,27449 , 27457,27479,27481,27487,27509,27527,27529,27539,27541,27551 , 27581,27583,27611,27617,27631,27647,27653,27673,27689,27691 , 27697,27701,27733,27737,27739,27743,27749,27751,27763,27767 , 27773,27779,27791,27793,27799,27803,27809,27817,27823,27827 , 27847,27851,27883,27893,27901,27917,27919,27941,27943,27947 , 27953,27961,27967,27983,27997,28001,28019,28027,28031,28051 , 28057,28069,28081,28087,28097,28099,28109,28111,28123,28151 , 28163,28181,28183,28201,28211,28219,28229,28277,28279,28283 , 28289,28297,28307,28309,28319,28349,28351,28387,28393,28403 , 28409,28411,28429,28433,28439,28447,28463,28477,28493,28499 , 28513,28517,28537,28541,28547,28549,28559,28571,28573,28579 , 28591,28597,28603,28607,28619,28621,28627,28631,28643,28649 , 28657,28661,28663,28669,28687,28697,28703,28711,28723,28729 , 28751,28753,28759,28771,28789,28793,28807,28813,28817,28837 , 28843,28859,28867,28871,28879,28901,28909,28921,28927,28933 , 28949,28961,28979,29009,29017,29021,29023,29027,29033,29059 , 29063,29077,29101,29123,29129,29131,29137,29147,29153,29167 , 29173,29179,29191,29201,29207,29209,29221,29231,29243,29251 , 29269,29287,29297,29303,29311,29327,29333,29339,29347,29363 , 29383,29387,29389,29399,29401,29411,29423,29429,29437,29443 , 29453,29473,29483,29501,29527,29531,29537,29567,29569,29573 , 29581,29587,29599,29611,29629,29633,29641,29663,29669,29671 , 29683,29717,29723,29741,29753,29759,29761,29789,29803,29819 , 29833,29837,29851,29863,29867,29873,29879,29881,29917,29921 , 29927,29947,29959,29983,29989,30011,30013,30029,30047,30059 , 30071,30089,30091,30097,30103,30109,30113,30119,30133,30137 , 30139,30161,30169,30181,30187,30197,30203,30211,30223,30241 , 30253,30259,30269,30271,30293,30307,30313,30319,30323,30341 , 30347,30367,30389,30391,30403,30427,30431,30449,30467,30469 , 30491,30493,30497,30509,30517,30529,30539,30553,30557,30559 , 30577,30593,30631,30637,30643,30649,30661,30671,30677,30689 , 30697,30703,30707,30713,30727,30757,30763,30773,30781,30803 , 30809,30817,30829,30839,30841,30851,30853,30859,30869,30871 , 30881,30893,30911,30931,30937,30941,30949,30971,30977,30983 , 31013,31019,31033,31039,31051,31063,31069,31079,31081,31091 , 31121,31123,31139,31147,31151,31153,31159,31177,31181,31183 , 31189,31193,31219,31223,31231,31237,31247,31249,31253,31259 , 31267,31271,31277,31307,31319,31321,31327,31333,31337,31357 , 31379,31387,31391,31393,31397,31469,31477,31481,31489,31511 , 31513,31517,31531,31541,31543,31547,31567,31573,31583,31601 , 31607}; int ret = 0; typedef std::vector<int> VI; typedef std::map<int, int> MII; VI getFractals(int n){ MII ret; int i = 0; while(n > 1){ if(primes[i] * primes[i] > n){ ret[n]++; break; } if(n % primes[i]){ i++; continue; } ret[primes[i]]++; n/=primes[i]; } VI fractals; for(auto it : ret){ int count = it.second; int el = it.first; int p = 1; while(count){ fractals.push_back(el); el *= el; count >>=1; } } return fractals; } void checkFractal(int product){ product--; int n = product; VI fractals = getFractals(product); int ii = (1 << fractals.size()); for(int i = 1; i <= ii-1; i++){ int index = 0; int el = i; int product = 1; while(el){ if(el & 1) product *= fractals[index]; index++; el >>= 1; } if(n % product == 0 && product >= 2 && n/product >= 3) ret++; } } int main() { int n; std::cin >> n; auto fractals = getFractals(n); int ii = (1 << fractals.size()); for(int i = 1; i <= ii; i++){ int index = 0; int el = i; int product = 1; while(el){ if(el & 1) product *= fractals[index]; index++; el >>= 1; } if(product > 6 && n % product == 0) checkFractal(product); } std::cout << ret << std::endl; } |