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static const unsigned long primes[]={2,3,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49,53,59,61,

67,71,73,79,83,89,97,101,103,107,109,113,121,127,131,137,139,149,151,157,

163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,

269,271,277,281,283,289,293,307,311,313,317,331,337,347,349,353,359,361,367,373,

379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,

499,503,509,521,523,529,541,547,557,563,569,571,577,587,593,599,601,607,613,617,

619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,

757,761,769,773,787,797,809,811,821,823,827,829,839,841,853,857,859,863,877,881,

883,887,907,911,919,929,937,941,947,953,961,967,971,977,983,991,997,1009,1013,1019,

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,

1301,1303,1307,1319,1321,1327,1361,1367,1369,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,

1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,

1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1681,1693,1697,1699,1709,1721,1723,

1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1849,1861,1867,1871,1873,1877,

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,

2207,2209,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,

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,

2801,2803,2809,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,

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,

3469,3481,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,

3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3721,3727,3733,3739,3761,3767,

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,

4451,4457,4463,4481,4483,4489,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,