#include <bits/stdc++.h>
using namespace std;
int a[] = {
    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};
int main() {
  int t, n;
  cin >> t;
  while (t--) {
    cin >> n;
    int arr[n];
    int sum = 0;
    int j = 0, k = 0;
    for (int i = 0; i < n; i++) {
      cin >> arr[i];
      sum = sum + arr[i];
      if (arr[i] % 2 != 0) {
        j = arr[i], k = i;
      }
    }
    int m = sizeof(a) / sizeof(int);
    if (binary_search(a, a + m, sum)) {
      cout << n - 1 << endl;
      for (int i = 0; i < n; i++) {
        if (i == k)
          continue;
        else
          cout << i + 1 << " ";
      }
      cout << endl;
    } else {
      cout << n << endl;
      for (int i = 0; i < n; i++) {
        cout << i + 1 << " ";
      }
      cout << endl;
    }
  }
  return 0;
}

### Prompt

Please create a solution in cpp to the following problem:

A bow adorned with nameless flowers that bears the earnest hopes of an equally nameless person.

You have obtained the elegant bow known as the Windblume Ode. Inscribed in the weapon is an array of n (n ≥ 3) positive distinct integers (i.e. different, no duplicates are allowed).

Find the largest subset (i.e. having the maximum number of elements) of this array such that its sum is a composite number. A positive integer x is called composite if there exists a positive integer y such that 1 < y < x and x is divisible by y.

If there are multiple subsets with this largest size with the composite sum, you can output any of them. It can be proven that under the constraints of the problem such a non-empty subset always exists.

Input

Each test consists of multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The first line of each test case contains an integer n (3 ≤ n ≤ 100) — the length of the array.

The second line of each test case contains n distinct integers a_{1},a_{2},...,a_{n} (1 ≤ a_{i} ≤ 200) — the elements of the array.

Output

Each test case should have two lines of output.

The first line should contain a single integer x: the size of the largest subset with composite sum. The next line should contain x space separated integers representing the indices of the subset of the initial array.

Example

Input


4
3
8 1 2
4
6 9 4 2
9
1 2 3 4 5 6 7 8 9
3
200 199 198


Output


2
2 1
4
2 1 4 3
9
6 9 1 2 3 4 5 7 8
3
1 2 3 

Note

In the first test case, the subset \\{a_2, a_1\} has a sum of 9, which is a composite number. The only subset of size 3 has a prime sum equal to 11. Note that you could also have selected the subset \\{a_1, a_3\} with sum 8 + 2 = 10, which is composite as it's divisible by 2.

In the second test case, the sum of all elements equals to 21, which is a composite number. Here we simply take the whole array as our subset.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int a[] = {
    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};
int main() {
  int t, n;
  cin >> t;
  while (t--) {
    cin >> n;
    int arr[n];
    int sum = 0;
    int j = 0, k = 0;
    for (int i = 0; i < n; i++) {
      cin >> arr[i];
      sum = sum + arr[i];
      if (arr[i] % 2 != 0) {
        j = arr[i], k = i;
      }
    }
    int m = sizeof(a) / sizeof(int);
    if (binary_search(a, a + m, sum)) {
      cout << n - 1 << endl;
      for (int i = 0; i < n; i++) {
        if (i == k)
          continue;
        else
          cout << i + 1 << " ";
      }
      cout << endl;
    } else {
      cout << n << endl;
      for (int i = 0; i < n; i++) {
        cout << i + 1 << " ";
      }
      cout << endl;
    }
  }
  return 0;
}

```