#include <stdio.h>
#include <math.h>
int prime[79000] = {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
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,253741,253751,253763,253769,253777,253787,253789,253801
,253811,253819,253823,253853,253867,253871,253879,253901
,253907,253909,253919,253937,253949,253951,253969,253987
,253993,253999,254003,254021,254027,254039,254041,254047
,254053,254071,254083,254119,254141,254147,254161,254179
,254197,254207,254209,254213,254249,254257,254279,254281
,254291,254299,254329,254369,254377,254383,254389,254407
,254413,254437,254447,254461,254489,254491,254519,254537
,254557,254593,254623,254627,254647,254659,254663,254699
,254713,254729,254731,254741,254747,254753,254773,254777
,254783,254791,254803,254827,254831,254833,254857,254869
,254873,254879,254887,254899,254911,254927,254929,254941
,254959,254963,254971,254977,254987,254993,255007,255019
,255023,255043,255049,255053,255071,255077,255083,255097
,255107,255121,255127,255133,255137,255149,255173,255179
,255181,255191,255193,255197,255209,255217,255239,255247
,255251,255253,255259,255313,255329,255349,255361,255371
,255383,255413,255419,255443,255457,255467,255469,255473
,255487,255499,255503,255511,255517,255523,255551,255571
,255587,255589,255613,255617,255637,255641,255649,255653
,255659,255667,255679,255709,255713,255733,255743,255757
,255763,255767,255803,255839,255841,255847,255851,255859
,255869,255877,255887,255907,255917,255919,255923,255947
,255961,255971,255973,255977,255989,256019,256021,256031
,256033,256049,256057,256079,256093,256117,256121,256129
,256133,256147,256163,256169,256181,256187,256189,256199
,256211,256219,256279,256301,256307,256313,256337,256349
,256363,256369,256391,256393,256423,256441,256469,256471
,256483,256489,256493,256499,256517,256541,256561,256567
,256577,256579,256589,256603,256609,256639,256643,256651
,256661,256687,256699,256721,256723,256757,256771,256799
,256801,256813,256831,256873,256877,256889,256901,256903
,256931,256939,256957,256967,256981,257003,257017,257053
,257069,257077,257093,257099,257107,257123,257141,257161
,257171,257177,257189,257219,257221,257239,257249,257263
,257273,257281,257287,257293,257297,257311,257321,257339
,257351,257353,257371,257381,257399,257401,257407,257437
,257443,257447,257459,257473,257489,257497,257501,257503
,257519,257539,257561,257591,257611,257627,257639,257657
,257671,257687,257689,257707,257711,257713,257717,257731
,257783,257791,257797,257837,257857,257861,257863,257867
,257869,257879,257893,257903,257921,257947,257953,257981
,257987,257989,257993,258019,258023,258031,258061,258067
,258101,258107,258109,258113,258119,258127,258131,258143
,258157,258161,258173,258197,258211,258233,258241,258253
,258277,258283,258299,258317,258319,258329,258331,258337
,258353,258373,258389,258403,258407,258413,258421,258437
,258443,258449,258469,258487,258491,258499,258521,258527
,258539,258551,258563,258569,258581,258607,258611,258613
,258617,258623,258631,258637,258659,258673,258677,258691
,258697,258703,258707,258721,258733,258737,258743,258763
,258779,258787,258803,258809,258827,258847,258871,258887
,258917,258919,258949,258959,258967,258971,258977,258983
,258991,259001,259009,259019,259033,259099,259121,259123
,259151,259157,259159,259163,259169,259177,259183,259201
,259211,259213,259219,259229,259271,259277,259309,259321
,259339,259379,259381,259387,259397,259411,259421,259429
,259451,259453,259459,259499,259507,259517,259531,259537
,259547,259577,259583,259603,259619,259621,259627,259631
,259639,259643,259657,259667,259681,259691,259697,259717
,259723,259733,259751,259771,259781,259783,259801,259813
,259823,259829,259837,259841,259867,259907,259933,259937
,259943,259949,259967,259991,259993,260003,260009,260011
,260017,260023,260047,260081,260089,260111,260137,260171
,260179,260189,260191,260201,260207,260209,260213,260231
,260263,260269,260317,260329,260339,260363,260387,260399
,260411,260413,260417,260419,260441,260453,260461,260467
,260483,260489,260527,260539,260543,260549,260551,260569
,260573,260581,260587,260609,260629,260647,260651,260671
,260677,260713,260717,260723,260747,260753,260761,260773
,260791,260807,260809,260849,260857,260861,260863,260873
,260879,260893,260921,260941,260951,260959,260969,260983
,260987,260999,261011,261013,261017,261031,261043,261059
,261061,261071,261077,261089,261101,261127,261167,261169
,261223,261229,261241,261251,261271,261281,261301,261323
,261329,261337,261347,261353,261379,261389,261407,261427
,261431,261433,261439,261451,261463,261467,261509,261523
,261529,261557,261563,261577,261581,261587,261593,261601
,261619,261631,261637,261641,261643,261673,261697,261707
,261713,261721,261739,261757,261761,261773,261787,261791
,261799,261823,261847,261881,261887,261917,261959,261971
,261973,261977,261983,262007,262027,262049,262051,262069
,262079,262103,262109,262111,262121,262127,262133,262139
,262147,262151,262153,262187,262193,262217,262231,262237
,262253,262261,262271,262303,262313,262321,262331,262337
,262349,262351,262369,262387,262391,262399,262411,262433
,262459,262469,262489,262501,262511,262513,262519,262541
,262543,262553,262567,262583,262597,262621,262627,262643
,262649,262651,262657,262681,262693,262697,262709,262723
,262733,262739,262741,262747,262781,262783,262807,262819
,262853,262877,262883,262897,262901,262909,262937,262949
,262957,262981,263009,263023,263047,263063,263071,263077
,263083,263089,263101,263111,263119,263129,263167,263171
,263183,263191,263201,263209,263213,263227,263239,263257
,263267,263269,263273,263287,263293,263303,263323,263369
,263383,263387,263399,263401,263411,263423,263429,263437
,263443,263489,263491,263503,263513,263519,263521,263533
,263537,263561,263567,263573,263591,263597,263609,263611
,263621,263647,263651,263657,263677,263723,263729,263737
,263759,263761,263803,263819,263821,263827,263843,263849
,263863,263867,263869,263881,263899,263909,263911,263927
,263933,263941,263951,263953,263957,263983,264007,264013
,264029,264031,264053,264059,264071,264083,264091,264101
,264113,264127,264133,264137,264139,264167,264169,264179
,264211,264221,264263,264269,264283,264289,264301,264323
,264331,264343,264349,264353,264359,264371,264391,264403
,264437,264443,264463,264487,264527,264529,264553,264559
,264577,264581,264599,264601,264619,264631,264637,264643
,264659,264697,264731,264739,264743,264749,264757,264763
,264769,264779,264787,264791,264793,264811,264827,264829
,264839,264871,264881,264889,264893,264899,264919,264931
,264949,264959,264961,264977,264991,264997,265003,265007
,265021,265037,265079,265091,265093,265117,265123,265129
,265141,265151,265157,265163,265169,265193,265207,265231
,265241,265247,265249,265261,265271,265273,265277,265313
,265333,265337,265339,265381,265399,265403,265417,265423
,265427,265451,265459,265471,265483,265493,265511,265513
,265541,265543,265547,265561,265567,265571,265579,265607
,265613,265619,265621,265703,265709,265711,265717,265729
,265739,265747,265757,265781,265787,265807,265813,265819
,265831,265841,265847,265861,265871,265873,265883,265891
,265921,265957,265961,265987,266003,266009,266023,266027
,266029,266047,266051,266053,266059,266081,266083,266089
,266093,266099,266111,266117,266129,266137,266153,266159
,266177,266183,266221,266239,266261,266269,266281,266291
,266293,266297,266333,266351,266353,266359,266369,266381
,266401,266411,266417,266447,266449,266477,266479,266489
,266491,266521,266549,266587,266599,266603,266633,266641
,266647,266663,266671,266677,266681,266683,266687,266689
,266701,266711,266719,266759,266767,266797,266801,266821
,266837,266839,266863,266867,266891,266897,266899,266909
,266921,266927,266933,266947,266953,266957,266971,266977
,266983,266993,266999,267017,267037,267049,267097,267131
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,267217,267227,267229,267233,267259,267271,267277,267299
,267301,267307,267317,267341,267353,267373,267389,267391
,267401,267403,267413,267419,267431,267433,267439,267451
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,267523,267541,267551,267557,267569,267581,267587,267593
,267601,267611,267613,267629,267637,267643,267647,267649
,267661,267667,267671,267677,267679,267713,267719,267721
,267727,267737,267739,267749,267763,267781,267791,267797
,267803,267811,267829,267833,267857,267863,267877,267887
,267893,267899,267901,267907,267913,267929,267941,267959
,267961,268003,268013,268043,268049,268063,268069,268091
,268123,268133,268153,268171,268189,268199,268207,268211
,268237,268253,268267,268271,268283,268291,268297,268343
,268403,268439,268459,268487,268493,268501,268507,268517
,268519,268529,268531,268537,268547,268573,268607,268613
,268637,268643,268661,268693,268721,268729,268733,268747
,268757,268759,268771,268777,268781,268783,268789,268811
,268813,268817,268819,268823,268841,268843,268861,268883
,268897,268909,268913,268921,268927,268937,268969,268973
,268979,268993,268997,268999,269023,269029,269039,269041
,269057,269063,269069,269089,269117,269131,269141,269167
,269177,269179,269183,269189,269201,269209,269219,269221
,269231,269237,269251,269257,269281,269317,269327,269333
,269341,269351,269377,269383,269387,269389,269393,269413
,269419,269429,269431,269441,269461,269473,269513,269519
,269527,269539,269543,269561,269573,269579,269597,269617
,269623,269641,269651,269663,269683,269701,269713,269719
,269723,269741,269749,269761,269779,269783,269791,269851
,269879,269887,269891,269897,269923,269939,269947,269953
,269981,269987,270001,270029,270031,270037,270059,270071
,270073,270097,270121,270131,270133,270143,270157,270163
,270167,270191,270209,270217,270223,270229,270239,270241
,270269,270271,270287,270299,270307,270311,270323,270329
,270337,270343,270371,270379,270407,270421,270437,270443
,270451,270461,270463,270493,270509,270527,270539,270547
,270551,270553,270563,270577,270583,270587,270593,270601
,270619,270631,270653,270659,270667,270679,270689,270701
,270709,270719,270737,270749,270761,270763,270791,270797
,270799,270821,270833,270841,270859,270899,270913,270923
,270931,270937,270953,270961,270967,270973,271003,271013
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,271127,271129,271163,271169,271177,271181,271211,271217
,271231,271241,271253,271261,271273,271277,271279,271289
,271333,271351,271357,271363,271367,271393,271409,271429
,271451,271463,271471,271483,271489,271499,271501,271517
,271549,271553,271571,271573,271597,271603,271619,271637
,271639,271651,271657,271693,271703,271723,271729,271753
,271769,271771,271787,271807,271811,271829,271841,271849
,271853,271861,271867,271879,271897,271903,271919,271927
,271939,271967,271969,271981,272003,272009,272011,272029
,272039,272053,272059,272093,272131,272141,272171,272179
,272183,272189,272191,272201,272203,272227,272231,272249
,272257,272263,272267,272269,272287,272299,272317,272329
,272333,272341,272347,272351,272353,272359,272369,272381
,272383,272399,272407,272411,272417,272423,272449,272453
,272477,272507,272533,272537,272539,272549,272563,272567
,272581,272603,272621,272651,272659,272683,272693,272717
,272719,272737,272759,272761,272771,272777,272807,272809
,272813,272863,272879,272887,272903,272911,272917,272927
,272933,272959,272971,272981,272983,272989,272999,273001
,273029,273043,273047,273059,273061,273067,273073,273083
,273107,273113,273127,273131,273149,273157,273181,273187
,273193,273233,273253,273269,273271,273281,273283,273289
,273311,273313,273323,273349,273359,273367,273433,273457
,273473,273503,273517,273521,273527,273551,273569,273601
,273613,273617,273629,273641,273643,273653,273697,273709
,273719,273727,273739,273773,273787,273797,273803,273821
,273827,273857,273881,273899,273901,273913,273919,273929
,273941,273943,273967,273971,273979,273997,274007,274019
,274033,274061,274069,274081,274093,274103,274117,274121
,274123,274139,274147,274163,274171,274177,274187,274199
,274201,274213,274223,274237,274243,274259,274271,274277
,274283,274301,274333,274349,274357,274361,274403,274423
,274441,274451,274453,274457,274471,274489,274517,274529
,274579,274583,274591,274609,274627,274661,274667,274679
,274693,274697,274709,274711,274723,274739,274751,274777
,274783,274787,274811,274817,274829,274831,274837,274843
,274847,274853,274861,274867,274871,274889,274909,274931
,274943,274951,274957,274961,274973,274993,275003,275027
,275039,275047,275053,275059,275083,275087,275129,275131
,275147,275153,275159,275161,275167,275183,275201,275207
,275227,275251,275263,275269,275299,275309,275321,275323
,275339,275357,275371,275389,275393,275399,275419,275423
,275447,275449,275453,275459,275461,275489,275491,275503
,275521,275531,275543,275549,275573,275579,275581,275591
,275593,275599,275623,275641,275651,275657,275669,275677
,275699,275711,275719,275729,275741,275767,275773,275783
,275813,275827,275837,275881,275897,275911,275917,275921
,275923,275929,275939,275941,275963,275969,275981,275987
,275999,276007,276011,276019,276037,276041,276043,276047
,276049,276079,276083,276091,276113,276137,276151,276173
,276181,276187,276191,276209,276229,276239,276247,276251
,276257,276277,276293,276319,276323,276337,276343,276347
,276359,276371,276373,276389,276401,276439,276443,276449
,276461,276467,276487,276499,276503,276517,276527,276553
,276557,276581,276587,276589,276593,276599,276623,276629
,276637,276671,276673,276707,276721,276739,276763,276767
,276779,276781,276817,276821,276823,276827,276833,276839
,276847,276869,276883,276901,276907,276917,276919,276929
,276949,276953,276961,276977,277003,277007,277021,277051
,277063,277073,277087,277097,277099,277157,277163,277169
,277177,277183,277213,277217,277223,277231,277247,277259
,277261,277273,277279,277297,277301,277309,277331,277363
,277373,277411,277421,277427,277429,277483,277493,277499
,277513,277531,277547,277549,277567,277577,277579,277597
,277601,277603,277637,277639,277643,277657,277663,277687
,277691,277703,277741,277747,277751,277757,277787,277789
,277793,277813,277829,277847,277859,277883,277889,277891
,277897,277903,277919,277961,277993,277999,278017,278029
,278041,278051,278063,278071,278087,278111,278119,278123
,278143,278147,278149,278177,278191,278207,278209,278219
,278227,278233,278237,278261,278269,278279,278321,278329};
void bkt(int pas, int k, int* div, int* usedprime, int nrused, int semn, int* track, int n, int prim){
if(pas==k+1){
int total = 1;
//printf("track: ");
for(int i=1; i<k+2; i++) {
total *= track[i];
//printf("%d ", track[i]);
}
//printf("\n");
total = total * prim;
//printf("Se elimina %d div falsi\n", semn*(n/total-1));
*div = *div + semn*(n/total-1);
} else {
for(int i=0; i<nrused; i++)
if(usedprime[i] > track[pas]){
track[pas+1] = usedprime[i];
bkt(pas+1, k, div, usedprime, nrused, semn, track, n, prim);
}
}
}
int main() {
FILE *in = fopen("fractii.in", "r");
FILE *out = fopen("fractii.out", "w");
int N;
fscanf(in, "%d", &N);
long long int count = 1;
for (int i = 2; i <= N; i++) {
int usedprime[169];
int nrused=0;
int div = 0;
//printf("%d:\n", i);
for (int j = 0; prime[j] <= i/2; j++) {
if (i % prime[j] == 0) {
div+=i/prime[j]-1;
//printf(" %d\n",prime[j]);
//printf("Se adauga %d divizori\n", i/prime[j]-1);
for(int k=0; k<nrused; k++){
int semn, track[k+2];
track[0] = 0;
if(k%2==0) semn = -1;
else semn = 1;
//printf(" %d\n", k);
bkt(0, k, &div,usedprime,nrused,semn,track,i,prime[j]);
//printf("In total sunt %d div", div);
}
//printf("\n");
usedprime[nrused] = prime[j];
nrused++;
}
}
//printf("\n\n");
count += 2 * (i - 1 - div);
}
fprintf(out, "%llu", count);
}
Florin Sausage Gust