# Copyright 2019 Google LLC
#
# This source code is licensed under the BSD-style license found in the
# LICENSE file in the root directory of this source tree.

import bisect


FIRST_1000_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,
]


def next_prime(n):
  assert n < 7919
  return FIRST_1000_PRIMES[bisect.bisect_right(FIRST_1000_PRIMES, n)]