Problem:
Score: 400 points

Problem Statement

Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:

a_i (1 \leq i \leq N) is a prime number at most 55 555.

The values of a_1, a_2, ..., a_N are all different.

In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.

If there are multiple such sequences, printing any of them is accepted.

Notes

An integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.

Constraints

N is an integer between 5 and 55 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.

Sample Input 1

5

Sample Output 1

3 5 7 11 31

Let us see if this output actually satisfies the conditions.

First, 3, 5, 7, 11 and 31 are all different, and all of them are prime numbers.

The only way to choose five among them is to choose all of them, whose sum is a_1+a_2+a_3+a_4+a_5=57, which is a composite number.

There are also other possible outputs, such as 2 3 5 7 13, 11 13 17 19 31 and 7 11 5 31 3.

Sample Input 2

6

Sample Output 2

2 3 5 7 11 13

2, 3, 5, 7, 11, 13 are all different prime numbers.

2+3+5+7+11=28 is a composite number.

2+3+5+7+13=30 is a composite number.

2+3+5+11+13=34 is a composite number.

2+3+7+11+13=36 is a composite number.

2+5+7+11+13=38 is a composite number.

3+5+7+11+13=39 is a composite number.

Thus, the sequence 2 3 5 7 11 13 satisfies the conditions.

Sample Input 3

8

Sample Output 3

2 5 7 13 19 37 67 79

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

n = int(input())
d=[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, 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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, 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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, 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47711, 47713, 47717, 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807, 47809, 47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, 47947, 47951, 47963, 47969, 47977, 47981, 48017, 48023, 48029, 48049, 48073, 48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163, 48179, 48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383, 48397, 48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487, 48491, 48497, 48523, 48527, 48533, 48539, 48541, 48563, 48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649, 48661, 48673, 48677, 48679, 48731, 48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, 48799, 48809, 48817, 48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883, 48889, 48907, 48947, 48953, 48973, 48989, 48991, 49003, 49009, 49019, 49031, 49033, 49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 49123, 49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201, 49207, 49211, 49223, 49253, 49261, 49277, 49279, 49297, 49307, 49331, 49333, 49339, 49363, 49367, 49369, 49391, 49393, 49409, 49411, 49417, 49429, 49433, 49451, 49459, 49463, 49477, 49481, 49499, 49523, 49529, 49531, 49537, 49547, 49549, 49559, 49597, 49603, 49613, 49627, 49633, 49639, 49663, 49667, 49669, 49681, 49697, 49711, 49727, 49739, 49741, 49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853, 49871, 49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 49957, 49991, 49993, 49999, 50021, 50023, 50033, 50047, 50051, 50053, 50069, 50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129, 50131, 50147, 50153, 50159, 50177, 50207, 50221, 50227, 50231, 50261, 50263, 50273, 50287, 50291, 50311, 50321, 50329, 50333, 50341, 50359, 50363, 50377, 50383, 50387, 50411, 50417, 50423, 50441, 50459, 50461, 50497, 50503, 50513, 50527, 50539, 50543, 50549, 50551, 50581, 50587, 50591, 50593, 50599, 50627, 50647, 50651, 50671, 50683, 50707, 50723, 50741, 50753, 50767, 50773, 50777, 50789, 50821, 50833, 50839, 50849, 50857, 50867, 50873, 50891, 50893, 50909, 50923, 50929, 50951, 50957, 50969, 50971, 50989, 50993, 51001, 51031, 51043, 51047, 51059, 51061, 51071, 51109, 51131, 51133, 51137, 51151, 51157, 51169, 51193, 51197, 51199, 51203, 51217, 51229, 51239, 51241, 51257, 51263, 51283, 51287, 51307, 51329, 51341, 51343, 51347, 51349, 51361, 51383, 51407, 51413, 51419, 51421, 51427, 51431, 51437, 51439, 51449, 51461, 51473, 51479, 51481, 51487, 51503, 51511, 51517, 51521, 51539, 51551, 51563, 51577, 51581, 51593, 51599, 51607, 51613, 51631, 51637, 51647, 51659, 51673, 51679, 51683, 51691, 51713, 51719, 51721, 51749, 51767, 51769, 51787, 51797, 51803, 51817, 51827, 51829, 51839, 51853, 51859, 51869, 51871, 51893, 51899, 51907, 51913, 51929, 51941, 51949, 51971, 51973, 51977, 51991, 52009, 52021, 52027, 52051, 52057, 52067, 52069, 52081, 52103, 52121, 52127, 52147, 52153, 52163, 52177, 52181, 52183, 52189, 52201, 52223, 52237, 52249, 52253, 52259, 52267, 52289, 52291, 52301, 52313, 52321, 52361, 52363, 52369, 52379, 52387, 52391, 52433, 52453, 52457, 52489, 52501, 52511, 52517, 52529, 52541, 52543, 52553, 52561, 52567, 52571, 52579, 52583, 52609, 52627, 52631, 52639, 52667, 52673, 52691, 52697, 52709, 52711, 52721, 52727, 52733, 52747, 52757, 52769, 52783, 52807, 52813, 52817, 52837, 52859, 52861, 52879, 52883, 52889, 52901, 52903, 52919, 52937, 52951, 52957, 52963, 52967, 52973, 52981, 52999, 53003, 53017, 53047, 53051, 53069, 53077, 53087, 53089, 53093, 53101, 53113, 53117, 53129, 53147, 53149, 53161, 53171, 53173, 53189, 53197, 53201, 53231, 53233, 53239, 53267, 53269, 53279, 53281, 53299, 53309, 53323, 53327, 53353, 53359, 53377, 53381, 53401, 53407, 53411, 53419, 53437, 53441, 53453, 53479, 53503, 53507, 53527, 53549, 53551, 53569, 53591, 53593, 53597, 53609, 53611, 53617, 53623, 53629, 53633, 53639, 53653, 53657, 53681, 53693, 53699, 53717, 53719, 53731, 53759, 53773, 53777, 53783, 53791, 53813, 53819, 53831, 53849, 53857, 53861, 53881, 53887, 53891, 53897, 53899, 53917, 53923, 53927, 53939, 53951, 53959, 53987, 53993, 54001, 54011, 54013, 54037, 54049, 54059, 54083, 54091, 54101, 54121, 54133, 54139, 54151, 54163, 54167, 54181, 54193, 54217, 54251, 54269, 54277, 54287, 54293, 54311, 54319, 54323, 54331, 54347, 54361, 54367, 54371, 54377, 54401, 54403, 54409, 54413, 54419, 54421, 54437, 54443, 54449, 54469, 54493, 54497, 54499, 54503, 54517, 54521, 54539, 54541, 54547, 54559, 54563, 54577, 54581, 54583, 54601, 54617, 54623, 54629, 54631, 54647, 54667, 54673, 54679, 54709, 54713, 54721, 54727, 54751, 54767, 54773, 54779, 54787, 54799, 54829, 54833, 54851, 54869, 54877, 54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973, 54979, 54983, 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073, 55079, 55103, 55109, 55117, 55127, 55147, 55163, 55171, 55201, 55207, 55213, 55217, 55219, 55229, 55243, 55249, 55259, 55291, 55313, 55331, 55333, 55337, 55339, 55343, 55351, 55373, 55381, 55399, 55411, 55439, 55441, 55457, 55469, 55487, 55501, 55511, 55529, 55541, 55547]


e=d[:5]
i=5
while(len(e)<n):
    x=e[-5:]
    t=sum(e[-5:])
    k = [t+d[i]-e[0],t+d[i]-e[1],t+d[i]-e[2],t+d[i]-e[3],t+d[i]-e[4],]
    j=0
    for z in k:
        if z in d:
            j+=1
    if j==0:
        e.append(d[i])
    i+=1
c=[]
for i in range(n):
    c.append(str(e[i]))
print(' '.join(c))