u16.rs

use lazy_static::lazy_static;

lazy_static! {
    /// A static lookup table of all odd numbers in the u16 range.
    pub static ref ODDS: [u16; 32768] = [
        1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,
        79,81,83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,135,137,139,
        141,143,145,147,149,151,153,155,157,159,161,163,165,167,169,171,173,175,177,179,181,183,185,187,189,191,193,195,
        197,199,201,203,205,207,209,211,213,215,217,219,221,223,225,227,229,231,233,235,237,239,241,243,245,247,249,251,
        253,255,257,259,261,263,265,267,269,271,273,275,277,279,281,283,285,287,289,291,293,295,297,299,301,303,305,307,
        309,311,313,315,317,319,321,323,325,327,329,331,333,335,337,339,341,343,345,347,349,351,353,355,357,359,361,363,
        365,367,369,371,373,375,377,379,381,383,385,387,389,391,393,395,397,399,401,403,405,407,409,411,413,415,417,419,
        421,423,425,427,429,431,433,435,437,439,441,443,445,447,449,451,453,455,457,459,461,463,465,467,469,471,473,475,
        477,479,481,483,485,487,489,491,493,495,497,499,501,503,505,507,509,511,513,515,517,519,521,523,525,527,529,531,
        533,535,537,539,541,543,545,547,549,551,553,555,557,559,561,563,565,567,569,571,573,575,577,579,581,583,585,587,
        589,591,593,595,597,599,601,603,605,607,609,611,613,615,617,619,621,623,625,627,629,631,633,635,637,639,641,643,
        645,647,649,651,653,655,657,659,661,663,665,667,669,671,673,675,677,679,681,683,685,687,689,691,693,695,697,699,
        701,703,705,707,709,711,713,715,717,719,721,723,725,727,729,731,733,735,737,739,741,743,745,747,749,751,753,755,
        757,759,761,763,765,767,769,771,773,775,777,779,781,783,785,787,789,791,793,795,797,799,801,803,805,807,809,811,
        813,815,817,819,821,823,825,827,829,831,833,835,837,839,841,843,845,847,849,851,853,855,857,859,861,863,865,867,
        869,871,873,875,877,879,881,883,885,887,889,891,893,895,897,899,901,903,905,907,909,911,913,915,917,919,921,923,
        925,927,929,931,933,935,937,939,941,943,945,947,949,951,953,955,957,959,961,963,965,967,969,971,973,975,977,979,
        981,983,985,987,989,991,993,995,997,999,1001,1003,1005,1007,1009,1011,1013,1015,1017,1019,1021,1023,1025,1027,
        1029,1031,1033,1035,1037,1039,1041,1043,1045,1047,1049,1051,1053,1055,1057,1059,1061,1063,1065,1067,1069,1071,
        1073,1075,1077,1079,1081,1083,1085,1087,1089,1091,1093,1095,1097,1099,1101,1103,1105,1107,1109,1111,1113,1115,
        1117,1119,1121,1123,1125,1127,1129,1131,1133,1135,1137,1139,1141,1143,1145,1147,1149,1151,1153,1155,1157,1159,
        1161,1163,1165,1167,1169,1171,1173,1175,1177,1179,1181,1183,1185,1187,1189,1191,1193,1195,1197,1199,1201,1203,
        1205,1207,1209,1211,1213,1215,1217,1219,1221,1223,1225,1227,1229,1231,1233,1235,1237,1239,1241,1243,1245,1247,
        1249,1251,1253,1255,1257,1259,1261,1263,1265,1267,1269,1271,1273,1275,1277,1279,1281,1283,1285,1287,1289,1291,
        1293,1295,1297,1299,1301,1303,1305,1307,1309,1311,1313,1315,1317,1319,1321,1323,1325,1327,1329,1331,1333,1335,
        1337,1339,1341,1343,1345,1347,1349,1351,1353,1355,1357,1359,1361,1363,1365,1367,1369,1371,1373,1375,1377,1379,
        1381,1383,1385,1387,1389,1391,1393,1395,1397,1399,1401,1403,1405,1407,1409,1411,1413,1415,1417,1419,1421,1423,
        1425,1427,1429,1431,1433,1435,1437,1439,1441,1443,1445,1447,1449,1451,1453,1455,1457,1459,1461,1463,1465,1467,
        1469,1471,1473,1475,1477,1479,1481,1483,1485,1487,1489,1491,1493,1495,1497,1499,1501,1503,1505,1507,1509,1511,
        1513,1515,1517,1519,1521,1523,1525,1527,1529,1531,1533,1535,1537,1539,1541,1543,1545,1547,1549,1551,1553,1555,
        1557,1559,1561,1563,1565,1567,1569,1571,1573,1575,1577,1579,1581,1583,1585,1587,1589,1591,1593,1595,1597,1599,
        1601,1603,1605,1607,1609,1611,1613,1615,1617,1619,1621,1623,1625,1627,1629,1631,1633,1635,1637,1639,1641,1643,
        1645,1647,1649,1651,1653,1655,1657,1659,1661,1663,1665,1667,1669,1671,1673,1675,1677,1679,1681,1683,1685,1687,
        1689,1691,1693,1695,1697,1699,1701,1703,1705,1707,1709,1711,1713,1715,1717,1719,1721,1723,1725,1727,1729,1731,
        1733,1735,1737,1739,1741,1743,1745,1747,1749,1751,1753,1755,1757,1759,1761,1763,1765,1767,1769,1771,1773,1775,
        1777,1779,1781,1783,1785,1787,1789,1791,1793,1795,1797,1799,1801,1803,1805,1807,1809,1811,1813,1815,1817,1819,
        1821,1823,1825,1827,1829,1831,1833,1835,1837,1839,1841,1843,1845,1847,1849,1851,1853,1855,1857,1859,1861,1863,
        1865,1867,1869,1871,1873,1875,1877,1879,1881,1883,1885,1887,1889,1891,1893,1895,1897,1899,1901,1903,1905,1907,
        1909,1911,1913,1915,1917,1919,1921,1923,1925,1927,1929,1931,1933,1935,1937,1939,1941,1943,1945,1947,1949,1951,
        1953,1955,1957,1959,1961,1963,1965,1967,1969,1971,1973,1975,1977,1979,1981,1983,1985,1987,1989,1991,1993,1995,
        1997,1999,2001,2003,2005,2007,2009,2011,2013,2015,2017,2019,2021,2023,2025,2027,2029,2031,2033,2035,2037,2039,
        2041,2043,2045,2047,2049,2051,2053,2055,2057,2059,2061,2063,2065,2067,2069,2071,2073,2075,2077,2079,2081,2083,
        2085,2087,2089,2091,2093,2095,2097,2099,2101,2103,2105,2107,2109,2111,2113,2115,2117,2119,2121,2123,2125,2127,
        2129,2131,2133,2135,2137,2139,2141,2143,2145,2147,2149,2151,2153,2155,2157,2159,2161,2163,2165,2167,2169,2171,
        2173,2175,2177,2179,2181,2183,2185,2187,2189,2191,2193,2195,2197,2199,2201,2203,2205,2207,2209,2211,2213,2215,
        2217,2219,2221,2223,2225,2227,2229,2231,2233,2235,2237,2239,2241,2243,2245,2247,2249,2251,2253,2255,2257,2259,
        2261,2263,2265,2267,2269,2271,2273,2275,2277,2279,2281,2283,2285,2287,2289,2291,2293,2295,2297,2299,2301,2303,
        2305,2307,2309,2311,2313,2315,2317,2319,2321,2323,2325,2327,2329,2331,2333,2335,2337,2339,2341,2343,2345,2347,
        2349,2351,2353,2355,2357,2359,2361,2363,2365,2367,2369,2371,2373,2375,2377,2379,2381,2383,2385,2387,2389,2391,
        2393,2395,2397,2399,2401,2403,2405,2407,2409,2411,2413,2415,2417,2419,2421,2423,2425,2427,2429,2431,2433,2435,
        2437,2439,2441,2443,2445,2447,2449,2451,2453,2455,2457,2459,2461,2463,2465,2467,2469,2471,2473,2475,2477,2479,
        2481,2483,2485,2487,2489,2491,2493,2495,2497,2499,2501,2503,2505,2507,2509,2511,2513,2515,2517,2519,2521,2523,
        2525,2527,2529,2531,2533,2535,2537,2539,2541,2543,2545,2547,2549,2551,2553,2555,2557,2559,2561,2563,2565,2567,
        2569,2571,2573,2575,2577,2579,2581,2583,2585,2587,2589,2591,2593,2595,2597,2599,2601,2603,2605,2607,2609,2611,
        2613,2615,2617,2619,2621,2623,2625,2627,2629,2631,2633,2635,2637,2639,2641,2643,2645,2647,2649,2651,2653,2655,
        2657,2659,2661,2663,2665,2667,2669,2671,2673,2675,2677,2679,2681,2683,2685,2687,2689,2691,2693,2695,2697,2699,
        2701,2703,2705,2707,2709,2711,2713,2715,2717,2719,2721,2723,2725,2727,2729,2731,2733,2735,2737,2739,2741,2743,
        2745,2747,2749,2751,2753,2755,2757,2759,2761,2763,2765,2767,2769,2771,2773,2775,2777,2779,2781,2783,2785,2787,
        2789,2791,2793,2795,2797,2799,2801,2803,2805,2807,2809,2811,2813,2815,2817,2819,2821,2823,2825,2827,2829,2831,
        2833,2835,2837,2839,2841,2843,2845,2847,2849,2851,2853,2855,2857,2859,2861,2863,2865,2867,2869,2871,2873,2875,
        2877,2879,2881,2883,2885,2887,2889,2891,2893,2895,2897,2899,2901,2903,2905,2907,2909,2911,2913,2915,2917,2919,
        2921,2923,2925,2927,2929,2931,2933,2935,2937,2939,2941,2943,2945,2947,2949,2951,2953,2955,2957,2959,2961,2963,
        2965,2967,2969,2971,2973,2975,2977,2979,2981,2983,2985,2987,2989,2991,2993,2995,2997,2999,3001,3003,3005,3007,
        3009,3011,3013,3015,3017,3019,3021,3023,3025,3027,3029,3031,3033,3035,3037,3039,3041,3043,3045,3047,3049,3051,
        3053,3055,3057,3059,3061,3063,3065,3067,3069,3071,3073,3075,3077,3079,3081,3083,3085,3087,3089,3091,3093,3095,
        3097,3099,3101,3103,3105,3107,3109,3111,3113,3115,3117,3119,3121,3123,3125,3127,3129,3131,3133,3135,3137,3139,
        3141,3143,3145,3147,3149,3151,3153,3155,3157,3159,3161,3163,3165,3167,3169,3171,3173,3175,3177,3179,3181,3183,
        3185,3187,3189,3191,3193,3195,3197,3199,3201,3203,3205,3207,3209,3211,3213,3215,3217,3219,3221,3223,3225,3227,
        3229,3231,3233,3235,3237,3239,3241,3243,3245,3247,3249,3251,3253,3255,3257,3259,3261,3263,3265,3267,3269,3271,
        3273,3275,3277,3279,3281,3283,3285,3287,3289,3291,3293,3295,3297,3299,3301,3303,3305,3307,3309,3311,3313,3315,
        3317,3319,3321,3323,3325,3327,3329,3331,3333,3335,3337,3339,3341,3343,3345,3347,3349,3351,3353,3355,3357,3359,
        3361,3363,3365,3367,3369,3371,3373,3375,3377,3379,3381,3383,3385,3387,3389,3391,3393,3395,3397,3399,3401,3403,
        3405,3407,3409,3411,3413,3415,3417,3419,3421,3423,3425,3427,3429,3431,3433,3435,3437,3439,3441,3443,3445,3447,
        3449,3451,3453,3455,3457,3459,3461,3463,3465,3467,3469,3471,3473,3475,3477,3479,3481,3483,3485,3487,3489,3491,
        3493,3495,3497,3499,3501,3503,3505,3507,3509,3511,3513,3515,3517,3519,3521,3523,3525,3527,3529,3531,3533,3535,
        3537,3539,3541,3543,3545,3547,3549,3551,3553,3555,3557,3559,3561,3563,3565,3567,3569,3571,3573,3575,3577,3579,
        3581,3583,3585,3587,3589,3591,3593,3595,3597,3599,3601,3603,3605,3607,3609,3611,3613,3615,3617,3619,3621,3623,
        3625,3627,3629,3631,3633,3635,3637,3639,3641,3643,3645,3647,3649,3651,3653,3655,3657,3659,3661,3663,3665,3667,
        3669,3671,3673,3675,3677,3679,3681,3683,3685,3687,3689,3691,3693,3695,3697,3699,3701,3703,3705,3707,3709,3711,
        3713,3715,3717,3719,3721,3723,3725,3727,3729,3731,3733,3735,3737,3739,3741,3743,3745,3747,3749,3751,3753,3755,
        3757,3759,3761,3763,3765,3767,3769,3771,3773,3775,3777,3779,3781,3783,3785,3787,3789,3791,3793,3795,3797,3799,
        3801,3803,3805,3807,3809,3811,3813,3815,3817,3819,3821,3823,3825,3827,3829,3831,3833,3835,3837,3839,3841,3843,
        3845,3847,3849,3851,3853,3855,3857,3859,3861,3863,3865,3867,3869,3871,3873,3875,3877,3879,3881,3883,3885,3887,
        3889,3891,3893,3895,3897,3899,3901,3903,3905,3907,3909,3911,3913,3915,3917,3919,3921,3923,3925,3927,3929,3931,
        3933,3935,3937,3939,3941,3943,3945,3947,3949,3951,3953,3955,3957,3959,3961,3963,3965,3967,3969,3971,3973,3975,
        3977,3979,3981,3983,3985,3987,3989,3991,3993,3995,3997,3999,4001,4003,4005,4007,4009,4011,4013,4015,4017,4019,
        4021,4023,4025,4027,4029,4031,4033,4035,4037,4039,4041,4043,4045,4047,4049,4051,4053,4055,4057,4059,4061,4063,
        4065,4067,4069,4071,4073,4075,4077,4079,4081,4083,4085,4087,4089,4091,4093,4095,4097,4099,4101,4103,4105,4107,
        4109,4111,4113,4115,4117,4119,4121,4123,4125,4127,4129,4131,4133,4135,4137,4139,4141,4143,4145,4147,4149,4151,
        4153,4155,4157,4159,4161,4163,4165,4167,4169,4171,4173,4175,4177,4179,4181,4183,4185,4187,4189,4191,4193,4195,
        4197,4199,4201,4203,4205,4207,4209,4211,4213,4215,4217,4219,4221,4223,4225,4227,4229,4231,4233,4235,4237,4239,
        4241,4243,4245,4247,4249,4251,4253,4255,4257,4259,4261,4263,4265,4267,4269,4271,4273,4275,4277,4279,4281,4283,
        4285,4287,4289,4291,4293,4295,4297,4299,4301,4303,4305,4307,4309,4311,4313,4315,4317,4319,4321,4323,4325,4327,
        4329,4331,4333,4335,4337,4339,4341,4343,4345,4347,4349,4351,4353,4355,4357,4359,4361,4363,4365,4367,4369,4371,
        4373,4375,4377,4379,4381,4383,4385,4387,4389,4391,4393,4395,4397,4399,4401,4403,4405,4407,4409,4411,4413,4415,
        4417,4419,4421,4423,4425,4427,4429,4431,4433,4435,4437,4439,4441,4443,4445,4447,4449,4451,4453,4455,4457,4459,
        4461,4463,4465,4467,4469,4471,4473,4475,4477,4479,4481,4483,4485,4487,4489,4491,4493,4495,4497,4499,4501,4503,
        4505,4507,4509,4511,4513,4515,4517,4519,4521,4523,4525,4527,4529,4531,4533,4535,4537,4539,4541,4543,4545,4547,
        4549,4551,4553,4555,4557,4559,4561,4563,4565,4567,4569,4571,4573,4575,4577,4579,4581,4583,4585,4587,4589,4591,
        4593,4595,4597,4599,4601,4603,4605,4607,4609,4611,4613,4615,4617,4619,4621,4623,4625,4627,4629,4631,4633,4635,
        4637,4639,4641,4643,4645,4647,4649,4651,4653,4655,4657,4659,4661,4663,4665,4667,4669,4671,4673,4675,4677,4679,
        4681,4683,4685,4687,4689,4691,4693,4695,4697,4699,4701,4703,4705,4707,4709,4711,4713,4715,4717,4719,4721,4723,
        4725,4727,4729,4731,4733,4735,4737,4739,4741,4743,4745,4747,4749,4751,4753,4755,4757,4759,4761,4763,4765,4767,
        4769,4771,4773,4775,4777,4779,4781,4783,4785,4787,4789,4791,4793,4795,4797,4799,4801,4803,4805,4807,4809,4811,
        4813,4815,4817,4819,4821,4823,4825,4827,4829,4831,4833,4835,4837,4839,4841,4843,4845,4847,4849,4851,4853,4855,
        4857,4859,4861,4863,4865,4867,4869,4871,4873,4875,4877,4879,4881,4883,4885,4887,4889,4891,4893,4895,4897,4899,
        4901,4903,4905,4907,4909,4911,4913,4915,4917,4919,4921,4923,4925,4927,4929,4931,4933,4935,4937,4939,4941,4943,
        4945,4947,4949,4951,4953,4955,4957,4959,4961,4963,4965,4967,4969,4971,4973,4975,4977,4979,4981,4983,4985,4987,
        4989,4991,4993,4995,4997,4999,5001,5003,5005,5007,5009,5011,5013,5015,5017,5019,5021,5023,5025,5027,5029,5031,
        5033,5035,5037,5039,5041,5043,5045,5047,5049,5051,5053,5055,5057,5059,5061,5063,5065,5067,5069,5071,5073,5075,
        5077,5079,5081,5083,5085,5087,5089,5091,5093,5095,5097,5099,5101,5103,5105,5107,5109,5111,5113,5115,5117,5119,
        5121,5123,5125,5127,5129,5131,5133,5135,5137,5139,5141,5143,5145,5147,5149,5151,5153,5155,5157,5159,5161,5163,
        5165,5167,5169,5171,5173,5175,5177,5179,5181,5183,5185,5187,5189,5191,5193,5195,5197,5199,5201,5203,5205,5207,
        5209,5211,5213,5215,5217,5219,5221,5223,5225,5227,5229,5231,5233,5235,5237,5239,5241,5243,5245,5247,5249,5251,
        5253,5255,5257,5259,5261,5263,5265,5267,5269,5271,5273,5275,5277,5279,5281,5283,5285,5287,5289,5291,5293,5295,
        5297,5299,5301,5303,5305,5307,5309,5311,5313,5315,5317,5319,5321,5323,5325,5327,5329,5331,5333,5335,5337,5339,
        5341,5343,5345,5347,5349,5351,5353,5355,5357,5359,5361,5363,5365,5367,5369,5371,5373,5375,5377,5379,5381,5383,
        5385,5387,5389,5391,5393,5395,5397,5399,5401,5403,5405,5407,5409,5411,5413,5415,5417,5419,5421,5423,5425,5427,
        5429,5431,5433,5435,5437,5439,5441,5443,5445,5447,5449,5451,5453,5455,5457,5459,5461,5463,5465,5467,5469,5471,
        5473,5475,5477,5479,5481,5483,5485,5487,5489,5491,5493,5495,5497,5499,5501,5503,5505,5507,5509,5511,5513,5515,
        5517,5519,5521,5523,5525,5527,5529,5531,5533,5535,5537,5539,5541,5543,5545,5547,5549,5551,5553,5555,5557,5559,
        5561,5563,5565,5567,5569,5571,5573,5575,5577,5579,5581,5583,5585,5587,5589,5591,5593,5595,5597,5599,5601,5603,
        5605,5607,5609,5611,5613,5615,5617,5619,5621,5623,5625,5627,5629,5631,5633,5635,5637,5639,5641,5643,5645,5647,
        5649,5651,5653,5655,5657,5659,5661,5663,5665,5667,5669,5671,5673,5675,5677,5679,5681,5683,5685,5687,5689,5691,
        5693,5695,5697,5699,5701,5703,5705,5707,5709,5711,5713,5715,5717,5719,5721,5723,5725,5727,5729,5731,5733,5735,
        5737,5739,5741,5743,5745,5747,5749,5751,5753,5755,5757,5759,5761,5763,5765,5767,5769,5771,5773,5775,5777,5779,
        5781,5783,5785,5787,5789,5791,5793,5795,5797,5799,5801,5803,5805,5807,5809,5811,5813,5815,5817,5819,5821,5823,
        5825,5827,5829,5831,5833,5835,5837,5839,5841,5843,5845,5847,5849,5851,5853,5855,5857,5859,5861,5863,5865,5867,
        5869,5871,5873,5875,5877,5879,5881,5883,5885,5887,5889,5891,5893,5895,5897,5899,5901,5903,5905,5907,5909,5911,
        5913,5915,5917,5919,5921,5923,5925,5927,5929,5931,5933,5935,5937,5939,5941,5943,5945,5947,5949,5951,5953,5955,
        5957,5959,5961,5963,5965,5967,5969,5971,5973,5975,5977,5979,5981,5983,5985,5987,5989,5991,5993,5995,5997,5999,
        6001,6003,6005,6007,6009,6011,6013,6015,6017,6019,6021,6023,6025,6027,6029,6031,6033,6035,6037,6039,6041,6043,
        6045,6047,6049,6051,6053,6055,6057,6059,6061,6063,6065,6067,6069,6071,6073,6075,6077,6079,6081,6083,6085,6087,
        6089,6091,6093,6095,6097,6099,6101,6103,6105,6107,6109,6111,6113,6115,6117,6119,6121,6123,6125,6127,6129,6131,
        6133,6135,6137,6139,6141,6143,6145,6147,6149,6151,6153,6155,6157,6159,6161,6163,6165,6167,6169,6171,6173,6175,
        6177,6179,6181,6183,6185,6187,6189,6191,6193,6195,6197,6199,6201,6203,6205,6207,6209,6211,6213,6215,6217,6219,
        6221,6223,6225,6227,6229,6231,6233,6235,6237,6239,6241,6243,6245,6247,6249,6251,6253,6255,6257,6259,6261,6263,
        6265,6267,6269,6271,6273,6275,6277,6279,6281,6283,6285,6287,6289,6291,6293,6295,6297,6299,6301,6303,6305,6307,
        6309,6311,6313,6315,6317,6319,6321,6323,6325,6327,6329,6331,6333,6335,6337,6339,6341,6343,6345,6347,6349,6351,
        6353,6355,6357,6359,6361,6363,6365,6367,6369,6371,6373,6375,6377,6379,6381,6383,6385,6387,6389,6391,6393,6395,
        6397,6399,6401,6403,6405,6407,6409,6411,6413,6415,6417,6419,6421,6423,6425,6427,6429,6431,6433,6435,6437,6439,
        6441,6443,6445,6447,6449,6451,6453,6455,6457,6459,6461,6463,6465,6467,6469,6471,6473,6475,6477,6479,6481,6483,
        6485,6487,6489,6491,6493,6495,6497,6499,6501,6503,6505,6507,6509,6511,6513,6515,6517,6519,6521,6523,6525,6527,
        6529,6531,6533,6535,6537,6539,6541,6543,6545,6547,6549,6551,6553,6555,6557,6559,6561,6563,6565,6567,6569,6571,
        6573,6575,6577,6579,6581,6583,6585,6587,6589,6591,6593,6595,6597,6599,6601,6603,6605,6607,6609,6611,6613,6615,
        6617,6619,6621,6623,6625,6627,6629,6631,6633,6635,6637,6639,6641,6643,6645,6647,6649,6651,6653,6655,6657,6659,
        6661,6663,6665,6667,6669,6671,6673,6675,6677,6679,6681,6683,6685,6687,6689,6691,6693,6695,6697,6699,6701,6703,
        6705,6707,6709,6711,6713,6715,6717,6719,6721,6723,6725,6727,6729,6731,6733,6735,6737,6739,6741,6743,6745,6747,
        6749,6751,6753,6755,6757,6759,6761,6763,6765,6767,6769,6771,6773,6775,6777,6779,6781,6783,6785,6787,6789,6791,
        6793,6795,6797,6799,6801,6803,6805,6807,6809,6811,6813,6815,6817,6819,6821,6823,6825,6827,6829,6831,6833,6835,
        6837,6839,6841,6843,6845,6847,6849,6851,6853,6855,6857,6859,6861,6863,6865,6867,6869,6871,6873,6875,6877,6879,
        6881,6883,6885,6887,6889,6891,6893,6895,6897,6899,6901,6903,6905,6907,6909,6911,6913,6915,6917,6919,6921,6923,
        6925,6927,6929,6931,6933,6935,6937,6939,6941,6943,6945,6947,6949,6951,6953,6955,6957,6959,6961,6963,6965,6967,
        6969,6971,6973,6975,6977,6979,6981,6983,6985,6987,6989,6991,6993,6995,6997,6999,7001,7003,7005,7007,7009,7011,
        7013,7015,7017,7019,7021,7023,7025,7027,7029,7031,7033,7035,7037,7039,7041,7043,7045,7047,7049,7051,7053,7055,
        7057,7059,7061,7063,7065,7067,7069,7071,7073,7075,7077,7079,7081,7083,7085,7087,7089,7091,7093,7095,7097,7099,
        7101,7103,7105,7107,7109,7111,7113,7115,7117,7119,7121,7123,7125,7127,7129,7131,7133,7135,7137,7139,7141,7143,
        7145,7147,7149,7151,7153,7155,7157,7159,7161,7163,7165,7167,7169,7171,7173,7175,7177,7179,7181,7183,7185,7187,
        7189,7191,7193,7195,7197,7199,7201,7203,7205,7207,7209,7211,7213,7215,7217,7219,7221,7223,7225,7227,7229,7231,
        7233,7235,7237,7239,7241,7243,7245,7247,7249,7251,7253,7255,7257,7259,7261,7263,7265,7267,7269,7271,7273,7275,
        7277,7279,7281,7283,7285,7287,7289,7291,7293,7295,7297,7299,7301,7303,7305,7307,7309,7311,7313,7315,7317,7319,
        7321,7323,7325,7327,7329,7331,7333,7335,7337,7339,7341,7343,7345,7347,7349,7351,7353,7355,7357,7359,7361,7363,
        7365,7367,7369,7371,7373,7375,7377,7379,7381,7383,7385,7387,7389,7391,7393,7395,7397,7399,7401,7403,7405,7407,
        7409,7411,7413,7415,7417,7419,7421,7423,7425,7427,7429,7431,7433,7435,7437,7439,7441,7443,7445,7447,7449,7451,
        7453,7455,7457,7459,7461,7463,7465,7467,7469,7471,7473,7475,7477,7479,7481,7483,7485,7487,7489,7491,7493,7495,
        7497,7499,7501,7503,7505,7507,7509,7511,7513,7515,7517,7519,7521,7523,7525,7527,7529,7531,7533,7535,7537,7539,
        7541,7543,7545,7547,7549,7551,7553,7555,7557,7559,7561,7563,7565,7567,7569,7571,7573,7575,7577,7579,7581,7583,
        7585,7587,7589,7591,7593,7595,7597,7599,7601,7603,7605,7607,7609,7611,7613,7615,7617,7619,7621,7623,7625,7627,
        7629,7631,7633,7635,7637,7639,7641,7643,7645,7647,7649,7651,7653,7655,7657,7659,7661,7663,7665,7667,7669,7671,
        7673,7675,7677,7679,7681,7683,7685,7687,7689,7691,7693,7695,7697,7699,7701,7703,7705,7707,7709,7711,7713,7715,
        7717,7719,7721,7723,7725,7727,7729,7731,7733,7735,7737,7739,7741,7743,7745,7747,7749,7751,7753,7755,7757,7759,
        7761,7763,7765,7767,7769,7771,7773,7775,7777,7779,7781,7783,7785,7787,7789,7791,7793,7795,7797,7799,7801,7803,
        7805,7807,7809,7811,7813,7815,7817,7819,7821,7823,7825,7827,7829,7831,7833,7835,7837,7839,7841,7843,7845,7847,
        7849,7851,7853,7855,7857,7859,7861,7863,7865,7867,7869,7871,7873,7875,7877,7879,7881,7883,7885,7887,7889,7891,
        7893,7895,7897,7899,7901,7903,7905,7907,7909,7911,7913,7915,7917,7919,7921,7923,7925,7927,7929,7931,7933,7935,
        7937,7939,7941,7943,7945,7947,7949,7951,7953,7955,7957,7959,7961,7963,7965,7967,7969,7971,7973,7975,7977,7979,
        7981,7983,7985,7987,7989,7991,7993,7995,7997,7999,8001,8003,8005,8007,8009,8011,8013,8015,8017,8019,8021,8023,
        8025,8027,8029,8031,8033,8035,8037,8039,8041,8043,8045,8047,8049,8051,8053,8055,8057,8059,8061,8063,8065,8067,
        8069,8071,8073,8075,8077,8079,8081,8083,8085,8087,8089,8091,8093,8095,8097,8099,8101,8103,8105,8107,8109,8111,
        8113,8115,8117,8119,8121,8123,8125,8127,8129,8131,8133,8135,8137,8139,8141,8143,8145,8147,8149,8151,8153,8155,
        8157,8159,8161,8163,8165,8167,8169,8171,8173,8175,8177,8179,8181,8183,8185,8187,8189,8191,8193,8195,8197,8199,
        8201,8203,8205,8207,8209,8211,8213,8215,8217,8219,8221,8223,8225,8227,8229,8231,8233,8235,8237,8239,8241,8243,
        8245,8247,8249,8251,8253,8255,8257,8259,8261,8263,8265,8267,8269,8271,8273,8275,8277,8279,8281,8283,8285,8287,
        8289,8291,8293,8295,8297,8299,8301,8303,8305,8307,8309,8311,8313,8315,8317,8319,8321,8323,8325,8327,8329,8331,
        8333,8335,8337,8339,8341,8343,8345,8347,8349,8351,8353,8355,8357,8359,8361,8363,8365,8367,8369,8371,8373,8375,
        8377,8379,8381,8383,8385,8387,8389,8391,8393,8395,8397,8399,8401,8403,8405,8407,8409,8411,8413,8415,8417,8419,
        8421,8423,8425,8427,8429,8431,8433,8435,8437,8439,8441,8443,8445,8447,8449,8451,8453,8455,8457,8459,8461,8463,
        8465,8467,8469,8471,8473,8475,8477,8479,8481,8483,8485,8487,8489,8491,8493,8495,8497,8499,8501,8503,8505,8507,
        8509,8511,8513,8515,8517,8519,8521,8523,8525,8527,8529,8531,8533,8535,8537,8539,8541,8543,8545,8547,8549,8551,
        8553,8555,8557,8559,8561,8563,8565,8567,8569,8571,8573,8575,8577,8579,8581,8583,8585,8587,8589,8591,8593,8595,
        8597,8599,8601,8603,8605,8607,8609,8611,8613,8615,8617,8619,8621,8623,8625,8627,8629,8631,8633,8635,8637,8639,
        8641,8643,8645,8647,8649,8651,8653,8655,8657,8659,8661,8663,8665,8667,8669,8671,8673,8675,8677,8679,8681,8683,
        8685,8687,8689,8691,8693,8695,8697,8699,8701,8703,8705,8707,8709,8711,8713,8715,8717,8719,8721,8723,8725,8727,
        8729,8731,8733,8735,8737,8739,8741,8743,8745,8747,8749,8751,8753,8755,8757,8759,8761,8763,8765,8767,8769,8771,
        8773,8775,8777,8779,8781,8783,8785,8787,8789,8791,8793,8795,8797,8799,8801,8803,8805,8807,8809,8811,8813,8815,
        8817,8819,8821,8823,8825,8827,8829,8831,8833,8835,8837,8839,8841,8843,8845,8847,8849,8851,8853,8855,8857,8859,
        8861,8863,8865,8867,8869,8871,8873,8875,8877,8879,8881,8883,8885,8887,8889,8891,8893,8895,8897,8899,8901,8903,
        8905,8907,8909,8911,8913,8915,8917,8919,8921,8923,8925,8927,8929,8931,8933,8935,8937,8939,8941,8943,8945,8947,
        8949,8951,8953,8955,8957,8959,8961,8963,8965,8967,8969,8971,8973,8975,8977,8979,8981,8983,8985,8987,8989,8991,
        8993,8995,8997,8999,9001,9003,9005,9007,9009,9011,9013,9015,9017,9019,9021,9023,9025,9027,9029,9031,9033,9035,
        9037,9039,9041,9043,9045,9047,9049,9051,9053,9055,9057,9059,9061,9063,9065,9067,9069,9071,9073,9075,9077,9079,
        9081,9083,9085,9087,9089,9091,9093,9095,9097,9099,9101,9103,9105,9107,9109,9111,9113,9115,9117,9119,9121,9123,
        9125,9127,9129,9131,9133,9135,9137,9139,9141,9143,9145,9147,9149,9151,9153,9155,9157,9159,9161,9163,9165,9167,
        9169,9171,9173,9175,9177,9179,9181,9183,9185,9187,9189,9191,9193,9195,9197,9199,9201,9203,9205,9207,9209,9211,
        9213,9215,9217,9219,9221,9223,9225,9227,9229,9231,9233,9235,9237,9239,9241,9243,9245,9247,9249,9251,9253,9255,
        9257,9259,9261,9263,9265,9267,9269,9271,9273,9275,9277,9279,9281,9283,9285,9287,9289,9291,9293,9295,9297,9299,
        9301,9303,9305,9307,9309,9311,9313,9315,9317,9319,9321,9323,9325,9327,9329,9331,9333,9335,9337,9339,9341,9343,
        9345,9347,9349,9351,9353,9355,9357,9359,9361,9363,9365,9367,9369,9371,9373,9375,9377,9379,9381,9383,9385,9387,
        9389,9391,9393,9395,9397,9399,9401,9403,9405,9407,9409,9411,9413,9415,9417,9419,9421,9423,9425,9427,9429,9431,
        9433,9435,9437,9439,9441,9443,9445,9447,9449,9451,9453,9455,9457,9459,9461,9463,9465,9467,9469,9471,9473,9475,
        9477,9479,9481,9483,9485,9487,9489,9491,9493,9495,9497,9499,9501,9503,9505,9507,9509,9511,9513,9515,9517,9519,
        9521,9523,9525,9527,9529,9531,9533,9535,9537,9539,9541,9543,9545,9547,9549,9551,9553,9555,9557,9559,9561,9563,
        9565,9567,9569,9571,9573,9575,9577,9579,9581,9583,9585,9587,9589,9591,9593,9595,9597,9599,9601,9603,9605,9607,
        9609,9611,9613,9615,9617,9619,9621,9623,9625,9627,9629,9631,9633,9635,9637,9639,9641,9643,9645,9647,9649,9651,
        9653,9655,9657,9659,9661,9663,9665,9667,9669,9671,9673,9675,9677,9679,9681,9683,9685,9687,9689,9691,9693,9695,
        9697,9699,9701,9703,9705,9707,9709,9711,9713,9715,9717,9719,9721,9723,9725,9727,9729,9731,9733,9735,9737,9739,
        9741,9743,9745,9747,9749,9751,9753,9755,9757,9759,9761,9763,9765,9767,9769,9771,9773,9775,9777,9779,9781,9783,
        9785,9787,9789,9791,9793,9795,9797,9799,9801,9803,9805,9807,9809,9811,9813,9815,9817,9819,9821,9823,9825,9827,
        9829,9831,9833,9835,9837,9839,9841,9843,9845,9847,9849,9851,9853,9855,9857,9859,9861,9863,9865,9867,9869,9871,
        9873,9875,9877,9879,9881,9883,9885,9887,9889,9891,9893,9895,9897,9899,9901,9903,9905,9907,9909,9911,9913,9915,
        9917,9919,9921,9923,9925,9927,9929,9931,9933,9935,9937,9939,9941,9943,9945,9947,9949,9951,9953,9955,9957,9959,
        9961,9963,9965,9967,9969,9971,9973,9975,9977,9979,9981,9983,9985,9987,9989,9991,9993,9995,9997,9999,10001,10003,
        10005,10007,10009,10011,10013,10015,10017,10019,10021,10023,10025,10027,10029,10031,10033,10035,10037,10039,10041,
        10043,10045,10047,10049,10051,10053,10055,10057,10059,10061,10063,10065,10067,10069,10071,10073,10075,10077,10079,
        10081,10083,10085,10087,10089,10091,10093,10095,10097,10099,10101,10103,10105,10107,10109,10111,10113,10115,10117,
        10119,10121,10123,10125,10127,10129,10131,10133,10135,10137,10139,10141,10143,10145,10147,10149,10151,10153,10155,
        10157,10159,10161,10163,10165,10167,10169,10171,10173,10175,10177,10179,10181,10183,10185,10187,10189,10191,10193,
        10195,10197,10199,10201,10203,10205,10207,10209,10211,10213,10215,10217,10219,10221,10223,10225,10227,10229,10231,
        10233,10235,10237,10239,10241,10243,10245,10247,10249,10251,10253,10255,10257,10259,10261,10263,10265,10267,10269,
        10271,10273,10275,10277,10279,10281,10283,10285,10287,10289,10291,10293,10295,10297,10299,10301,10303,10305,10307,
        10309,10311,10313,10315,10317,10319,10321,10323,10325,10327,10329,10331,10333,10335,10337,10339,10341,10343,10345,
        10347,10349,10351,10353,10355,10357,10359,10361,10363,10365,10367,10369,10371,10373,10375,10377,10379,10381,10383,
        10385,10387,10389,10391,10393,10395,10397,10399,10401,10403,10405,10407,10409,10411,10413,10415,10417,10419,10421,
        10423,10425,10427,10429,10431,10433,10435,10437,10439,10441,10443,10445,10447,10449,10451,10453,10455,10457,10459,
        10461,10463,10465,10467,10469,10471,10473,10475,10477,10479,10481,10483,10485,10487,10489,10491,10493,10495,10497,
        10499,10501,10503,10505,10507,10509,10511,10513,10515,10517,10519,10521,10523,10525,10527,10529,10531,10533,10535,
        10537,10539,10541,10543,10545,10547,10549,10551,10553,10555,10557,10559,10561,10563,10565,10567,10569,10571,10573,
        10575,10577,10579,10581,10583,10585,10587,10589,10591,10593,10595,10597,10599,10601,10603,10605,10607,10609,10611,
        10613,10615,10617,10619,10621,10623,10625,10627,10629,10631,10633,10635,10637,10639,10641,10643,10645,10647,10649,
        10651,10653,10655,10657,10659,10661,10663,10665,10667,10669,10671,10673,10675,10677,10679,10681,10683,10685,10687,
        10689,10691,10693,10695,10697,10699,10701,10703,10705,10707,10709,10711,10713,10715,10717,10719,10721,10723,10725,
        10727,10729,10731,10733,10735,10737,10739,10741,10743,10745,10747,10749,10751,10753,10755,10757,10759,10761,10763,
        10765,10767,10769,10771,10773,10775,10777,10779,10781,10783,10785,10787,10789,10791,10793,10795,10797,10799,10801,
        10803,10805,10807,10809,10811,10813,10815,10817,10819,10821,10823,10825,10827,10829,10831,10833,10835,10837,10839,
        10841,10843,10845,10847,10849,10851,10853,10855,10857,10859,10861,10863,10865,10867,10869,10871,10873,10875,10877,
        10879,10881,10883,10885,10887,10889,10891,10893,10895,10897,10899,10901,10903,10905,10907,10909,10911,10913,10915,
        10917,10919,10921,10923,10925,10927,10929,10931,10933,10935,10937,10939,10941,10943,10945,10947,10949,10951,10953,
        10955,10957,10959,10961,10963,10965,10967,10969,10971,10973,10975,10977,10979,10981,10983,10985,10987,10989,10991,
        10993,10995,10997,10999,11001,11003,11005,11007,11009,11011,11013,11015,11017,11019,11021,11023,11025,11027,11029,
        11031,11033,11035,11037,11039,11041,11043,11045,11047,11049,11051,11053,11055,11057,11059,11061,11063,11065,11067,
        11069,11071,11073,11075,11077,11079,11081,11083,11085,11087,11089,11091,11093,11095,11097,11099,11101,11103,11105,
        11107,11109,11111,11113,11115,11117,11119,11121,11123,11125,11127,11129,11131,11133,11135,11137,11139,11141,11143,
        11145,11147,11149,11151,11153,11155,11157,11159,11161,11163,11165,11167,11169,11171,11173,11175,11177,11179,11181,
        11183,11185,11187,11189,11191,11193,11195,11197,11199,11201,11203,11205,11207,11209,11211,11213,11215,11217,11219,
        11221,11223,11225,11227,11229,11231,11233,11235,11237,11239,11241,11243,11245,11247,11249,11251,11253,11255,11257,
        11259,11261,11263,11265,11267,11269,11271,11273,11275,11277,11279,11281,11283,11285,11287,11289,11291,11293,11295,
        11297,11299,11301,11303,11305,11307,11309,11311,11313,11315,11317,11319,11321,11323,11325,11327,11329,11331,11333,
        11335,11337,11339,11341,11343,11345,11347,11349,11351,11353,11355,11357,11359,11361,11363,11365,11367,11369,11371,
        11373,11375,11377,11379,11381,11383,11385,11387,11389,11391,11393,11395,11397,11399,11401,11403,11405,11407,11409,
        11411,11413,11415,11417,11419,11421,11423,11425,11427,11429,11431,11433,11435,11437,11439,11441,11443,11445,11447,
        11449,11451,11453,11455,11457,11459,11461,11463,11465,11467,11469,11471,11473,11475,11477,11479,11481,11483,11485,
        11487,11489,11491,11493,11495,11497,11499,11501,11503,11505,11507,11509,11511,11513,11515,11517,11519,11521,11523,
        11525,11527,11529,11531,11533,11535,11537,11539,11541,11543,11545,11547,11549,11551,11553,11555,11557,11559,11561,
        11563,11565,11567,11569,11571,11573,11575,11577,11579,11581,11583,11585,11587,11589,11591,11593,11595,11597,11599,
        11601,11603,11605,11607,11609,11611,11613,11615,11617,11619,11621,11623,11625,11627,11629,11631,11633,11635,11637,
        11639,11641,11643,11645,11647,11649,11651,11653,11655,11657,11659,11661,11663,11665,11667,11669,11671,11673,11675,
        11677,11679,11681,11683,11685,11687,11689,11691,11693,11695,11697,11699,11701,11703,11705,11707,11709,11711,11713,
        11715,11717,11719,11721,11723,11725,11727,11729,11731,11733,11735,11737,11739,11741,11743,11745,11747,11749,11751,
        11753,11755,11757,11759,11761,11763,11765,11767,11769,11771,11773,11775,11777,11779,11781,11783,11785,11787,11789,
        11791,11793,11795,11797,11799,11801,11803,11805,11807,11809,11811,11813,11815,11817,11819,11821,11823,11825,11827,
        11829,11831,11833,11835,11837,11839,11841,11843,11845,11847,11849,11851,11853,11855,11857,11859,11861,11863,11865,
        11867,11869,11871,11873,11875,11877,11879,11881,11883,11885,11887,11889,11891,11893,11895,11897,11899,11901,11903,
        11905,11907,11909,11911,11913,11915,11917,11919,11921,11923,11925,11927,11929,11931,11933,11935,11937,11939,11941,
        11943,11945,11947,11949,11951,11953,11955,11957,11959,11961,11963,11965,11967,11969,11971,11973,11975,11977,11979,
        11981,11983,11985,11987,11989,11991,11993,11995,11997,11999,12001,12003,12005,12007,12009,12011,12013,12015,12017,
        12019,12021,12023,12025,12027,12029,12031,12033,12035,12037,12039,12041,12043,12045,12047,12049,12051,12053,12055,
        12057,12059,12061,12063,12065,12067,12069,12071,12073,12075,12077,12079,12081,12083,12085,12087,12089,12091,12093,
        12095,12097,12099,12101,12103,12105,12107,12109,12111,12113,12115,12117,12119,12121,12123,12125,12127,12129,12131,
        12133,12135,12137,12139,12141,12143,12145,12147,12149,12151,12153,12155,12157,12159,12161,12163,12165,12167,12169,
        12171,12173,12175,12177,12179,12181,12183,12185,12187,12189,12191,12193,12195,12197,12199,12201,12203,12205,12207,
        12209,12211,12213,12215,12217,12219,12221,12223,12225,12227,12229,12231,12233,12235,12237,12239,12241,12243,12245,
        12247,12249,12251,12253,12255,12257,12259,12261,12263,12265,12267,12269,12271,12273,12275,12277,12279,12281,12283,
        12285,12287,12289,12291,12293,12295,12297,12299,12301,12303,12305,12307,12309,12311,12313,12315,12317,12319,12321,
        12323,12325,12327,12329,12331,12333,12335,12337,12339,12341,12343,12345,12347,12349,12351,12353,12355,12357,12359,
        12361,12363,12365,12367,12369,12371,12373,12375,12377,12379,12381,12383,12385,12387,12389,12391,12393,12395,12397,
        12399,12401,12403,12405,12407,12409,12411,12413,12415,12417,12419,12421,12423,12425,12427,12429,12431,12433,12435,
        12437,12439,12441,12443,12445,12447,12449,12451,12453,12455,12457,12459,12461,12463,12465,12467,12469,12471,12473,
        12475,12477,12479,12481,12483,12485,12487,12489,12491,12493,12495,12497,12499,12501,12503,12505,12507,12509,12511,
        12513,12515,12517,12519,12521,12523,12525,12527,12529,12531,12533,12535,12537,12539,12541,12543,12545,12547,12549,
        12551,12553,12555,12557,12559,12561,12563,12565,12567,12569,12571,12573,12575,12577,12579,12581,12583,12585,12587,
        12589,12591,12593,12595,12597,12599,12601,12603,12605,12607,12609,12611,12613,12615,12617,12619,12621,12623,12625,
        12627,12629,12631,12633,12635,12637,12639,12641,12643,12645,12647,12649,12651,12653,12655,12657,12659,12661,12663,
        12665,12667,12669,12671,12673,12675,12677,12679,12681,12683,12685,12687,12689,12691,12693,12695,12697,12699,12701,
        12703,12705,12707,12709,12711,12713,12715,12717,12719,12721,12723,12725,12727,12729,12731,12733,12735,12737,12739,
        12741,12743,12745,12747,12749,12751,12753,12755,12757,12759,12761,12763,12765,12767,12769,12771,12773,12775,12777,

        12779,12781,12783,12785,12787,12789,12791,12793,12795,12797,12799,12801,12803,12805,12807,12809,12811,12813,12815,
        12817,12819,12821,12823,12825,12827,12829,12831,12833,12835,12837,12839,12841,12843,12845,12847,12849,12851,12853,
        12855,12857,12859,12861,12863,12865,12867,12869,12871,12873,12875,12877,12879,12881,12883,12885,12887,12889,12891,
        12893,12895,12897,12899,12901,12903,12905,12907,12909,12911,12913,12915,12917,12919,12921,12923,12925,12927,12929,
        12931,12933,12935,12937,12939,12941,12943,12945,12947,12949,12951,12953,12955,12957,12959,12961,12963,12965,12967,
        12969,12971,12973,12975,12977,12979,12981,12983,12985,12987,12989,12991,12993,12995,12997,12999,13001,13003,13005,
        13007,13009,13011,13013,13015,13017,13019,13021,13023,13025,13027,13029,13031,13033,13035,13037,13039,13041,13043,
        13045,13047,13049,13051,13053,13055,13057,13059,13061,13063,13065,13067,13069,13071,13073,13075,13077,13079,13081,
        13083,13085,13087,13089,13091,13093,13095,13097,13099,13101,13103,13105,13107,13109,13111,13113,13115,13117,13119,
        13121,13123,13125,13127,13129,13131,13133,13135,13137,13139,13141,13143,13145,13147,13149,13151,13153,13155,13157,
        13159,13161,13163,13165,13167,13169,13171,13173,13175,13177,13179,13181,13183,13185,13187,13189,13191,13193,13195,
        13197,13199,13201,13203,13205,13207,13209,13211,13213,13215,13217,13219,13221,13223,13225,13227,13229,13231,13233,
        13235,13237,13239,13241,13243,13245,13247,13249,13251,13253,13255,13257,13259,13261,13263,13265,13267,13269,13271,
        13273,13275,13277,13279,13281,13283,13285,13287,13289,13291,13293,13295,13297,13299,13301,13303,13305,13307,13309,
        13311,13313,13315,13317,13319,13321,13323,13325,13327,13329,13331,13333,13335,13337,13339,13341,13343,13345,13347,
        13349,13351,13353,13355,13357,13359,13361,13363,13365,13367,13369,13371,13373,13375,13377,13379,13381,13383,13385,
        13387,13389,13391,13393,13395,13397,13399,13401,13403,13405,13407,13409,13411,13413,13415,13417,13419,13421,13423,
        13425,13427,13429,13431,13433,13435,13437,13439,13441,13443,13445,13447,13449,13451,13453,13455,13457,13459,13461,
        13463,13465,13467,13469,13471,13473,13475,13477,13479,13481,13483,13485,13487,13489,13491,13493,13495,13497,13499,
        13501,13503,13505,13507,13509,13511,13513,13515,13517,13519,13521,13523,13525,13527,13529,13531,13533,13535,13537,
        13539,13541,13543,13545,13547,13549,13551,13553,13555,13557,13559,13561,13563,13565,13567,13569,13571,13573,13575,
        13577,13579,13581,13583,13585,13587,13589,13591,13593,13595,13597,13599,13601,13603,13605,13607,13609,13611,13613,
        13615,13617,13619,13621,13623,13625,13627,13629,13631,13633,13635,13637,13639,13641,13643,13645,13647,13649,13651,
        13653,13655,13657,13659,13661,13663,13665,13667,13669,13671,13673,13675,13677,13679,13681,13683,13685,13687,13689,
        13691,13693,13695,13697,13699,13701,13703,13705,13707,13709,13711,13713,13715,13717,13719,13721,13723,13725,13727,
        13729,13731,13733,13735,13737,13739,13741,13743,13745,13747,13749,13751,13753,13755,13757,13759,13761,13763,13765,
        13767,13769,13771,13773,13775,13777,13779,13781,13783,13785,13787,13789,13791,13793,13795,13797,13799,13801,13803,
        13805,13807,13809,13811,13813,13815,13817,13819,13821,13823,13825,13827,13829,13831,13833,13835,13837,13839,13841,
        13843,13845,13847,13849,13851,13853,13855,13857,13859,13861,13863,13865,13867,13869,13871,13873,13875,13877,13879,
        13881,13883,13885,13887,13889,13891,13893,13895,13897,13899,13901,13903,13905,13907,13909,13911,13913,13915,13917,
        13919,13921,13923,13925,13927,13929,13931,13933,13935,13937,13939,13941,13943,13945,13947,13949,13951,13953,13955,
        13957,13959,13961,13963,13965,13967,13969,13971,13973,13975,13977,13979,13981,13983,13985,13987,13989,13991,13993,
        13995,13997,13999,14001,14003,14005,14007,14009,14011,14013,14015,14017,14019,14021,14023,14025,14027,14029,14031,
        14033,14035,14037,14039,14041,14043,14045,14047,14049,14051,14053,14055,14057,14059,14061,14063,14065,14067,14069,
        14071,14073,14075,14077,14079,14081,14083,14085,14087,14089,14091,14093,14095,14097,14099,14101,14103,14105,14107,
        14109,14111,14113,14115,14117,14119,14121,14123,14125,14127,14129,14131,14133,14135,14137,14139,14141,14143,14145,
        14147,14149,14151,14153,14155,14157,14159,14161,14163,14165,14167,14169,14171,14173,14175,14177,14179,14181,14183,
        14185,14187,14189,14191,14193,14195,14197,14199,14201,14203,14205,14207,14209,14211,14213,14215,14217,14219,14221,
        14223,14225,14227,14229,14231,14233,14235,14237,14239,14241,14243,14245,14247,14249,14251,14253,14255,14257,14259,
        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64261,64263,64265,64267,64269,64271,64273,64275,64277,64279,64281,64283,64285,64287,64289,64291,64293,64295,64297,64299,64301,64303,64305,64307,64309,64311,64313,64315,64317,64319,64321,64323,64325,64327,64329,64331,64333,64335,64337,64339,64341,64343,64345,64347,64349,64351,64353,64355,64357,64359,64361,64363,64365,64367,64369,64371,64373,64375,64377,64379,64381,64383,64385,64387,64389,64391,64393,64395,64397,64399,64401,64403,64405,64407,64409,64411,64413,64415,64417,64419,64421,64423,64425,64427,64429,64431,64433,64435,64437,64439,64441,64443,64445,64447,64449,64451,64453,64455,64457,64459,64461,64463,64465,64467,64469,64471,64473,64475,64477,64479,64481,64483,64485,64487,64489,64491,64493,64495,64497,64499,64501,64503,64505,64507,64509,64511,64513,64515,64517,64519,64521,64523,64525,64527,64529,64531,64533,64535,64537,64539,64541,64543,64545,64547,64549,64551,64553,64555,64557,64559,64561,64563,64565,64567,64569,64571,64573,64575,64577,64579,64581,64583,64585,64587,64589,64591,64593,64595,64597,64599,64601,64603,64605,64607,64609,64611,64613,64615,64617,64619,64621,64623,64625,64627,64629,64631,64633,64635,64637,64639,64641,64643,64645,64647,64649,64651,64653,64655,64657,64659,64661,64663,64665,64667,64669,64671,64673,64675,64677,64679,64681,64683,64685,64687,64689,64691,64693,64695,64697,64699,64701,64703,64705,64707,64709,64711,64713,64715,64717,64719,64721,64723,64725,64727,64729,64731,64733,64735,64737,64739,64741,64743,64745,64747,64749,64751,64753,64755,64757,64759,64761,64763,64765,64767,64769,64771,64773,64775,64777,64779,64781,64783,64785,64787,64789,64791,64793,64795,64797,64799,64801,64803,64805,64807,64809,64811,64813,64815,64817,64819,64821,64823,64825,64827,64829,64831,64833,64835,64837,64839,64841,64843,64845,64847,64849,64851,64853,64855,64857,64859,64861,64863,64865,64867,64869,64871,64873,64875,64877,64879,64881,64883,64885,64887,64889,64891,64893,64895,64897,64899,64901,64903,64905,64907,64909,64911,64913,64915,64917,64919,64921,64923,64925,64927,64929,64931,64933,64935,64937,64939,64941,64943,64945,64947,64949,64951,64953,64955,64957,64959,64961,64963,64965,64967,64969,64971,64973,64975,64977,64979,64981,64983,64985,64987,64989,64991,64993,64995,64997,64999,65001,65003,65005,65007,65009,65011,65013,65015,65017,65019,65021,65023,65025,65027,65029,65031,65033,65035,65037,65039,65041,65043,65045,65047,65049,65051,65053,65055,65057,65059,65061,65063,65065,65067,65069,65071,65073,65075,65077,65079,65081,65083,65085,65087,65089,65091,65093,65095,65097,65099,65101,65103,65105,65107,65109,65111,65113,65115,65117,65119,65121,65123,65125,65127,65129,65131,65133,65135,65137,65139,65141,65143,65145,65147,65149,65151,65153,65155,65157,65159,65161,65163,65165,65167,65169,65171,65173,65175,65177,65179,65181,65183,65185,65187,65189,65191,65193,65195,65197,65199,65201,65203,65205,65207,65209,65211,65213,65215,65217,65219,65221,65223,65225,65227,65229,65231,65233,65235,65237,65239,65241,65243,65245,65247,65249,65251,65253,65255,65257,65259,65261,65263,65265,65267,65269,65271,65273,65275,65277,65279,65281,65283,65285,65287,65289,65291,65293,65295,65297,65299,65301,65303,65305,65307,65309,65311,65313,65315,65317,65319,65321,65323,65325,65327,65329,65331,65333,65335,65337,65339,65341,65343,65345,65347,65349,65351,65353,65355,65357,65359,65361,65363,65365,65367,65369,65371,65373,65375,65377,65379,65381,65383,65385,65387,65389,65391,65393,65395,65397,65399,65401,65403,65405,65407,65409,65411,65413,65415,65417,65419,65421,65423,65425,65427,65429,65431,65433,65435,65437,65439,65441,65443,65445,65447,65449,65451,65453,65455,65457,65459,65461,65463,65465,65467,65469,65471,65473,65475,65477,65479,65481,65483,65485,65487,65489,65491,65493,65495,65497,65499,65501,65503,65505,65507,65509,65511,65513,65515,65517,65519,65521,65523,65525,65527,65529,65531,65533,65535
    ];
}

/// Returns true if the given number is odd.
pub fn is_odd(num: u16) -> bool {
    if num == 0u16 {
        false
    } else if num == 1u16 {
        true
    } else if num == 2u16 {
        false
    } else if num == 3u16 {
        true
    } else if num == 4u16 {
        false
    } else if num == 5u16 {
        true
    } else if num == 6u16 {
        false
    } else if num == 7u16 {
        true
    } else if num == 8u16 {
        false
    } else if num == 9u16 {
        true
    } else if num == 10u16 {
        false
    } else if num == 11u16 {
        true
    } else if num == 12u16 {
        false
    } else if num == 13u16 {
        true
    } else if num == 14u16 {
        false
    } else if num == 15u16 {
        true
    } else if num == 16u16 {
        false
    } else if num == 17u16 {
        true
    } else if num == 18u16 {
        false
    } else if num == 19u16 {
        true
    } else if num == 20u16 {
        false
    } else if num == 21u16 {
        true
    } else if num == 22u16 {
        false
    } else if num == 23u16 {
        true
    } else if num == 24u16 {
        false
    } else if num == 25u16 {
        true
    } else if num == 26u16 {
        false
    } else if num == 27u16 {
        true
    } else if num == 28u16 {
        false
    } else if num == 29u16 {
        true
    } else if num == 30u16 {
        false
    } else if num == 31u16 {
        true
    } else if num == 32u16 {
        false
    } else if num == 33u16 {
        true
    } else if num == 34u16 {
        false
    } else if num == 35u16 {
        true
    } else if num == 36u16 {
        false
    } else if num == 37u16 {
        true
    } else if num == 38u16 {
        false
    } else if num == 39u16 {
        true
    } else if num == 40u16 {
        false
    } else if num == 41u16 {
        true
    } else if num == 42u16 {
        false
    } else if num == 43u16 {
        true
    } else if num == 44u16 {
        false
    } else if num == 45u16 {
        true
    } else if num == 46u16 {
        false
    } else if num == 47u16 {
        true
    } else if num == 48u16 {
        false
    } else if num == 49u16 {
        true
    } else if num == 50u16 {
        false
    } else if num == 51u16 {
        true
    } else if num == 52u16 {
        false
    } else if num == 53u16 {
        true
    } else if num == 54u16 {
        false
    } else if num == 55u16 {
        true
    } else if num == 56u16 {
        false
    } else if num == 57u16 {
        true
    } else if num == 58u16 {
        false
    } else if num == 59u16 {
        true
    } else if num == 60u16 {
        false
    } else if num == 61u16 {
        true
    } else if num == 62u16 {
        false
    } else if num == 63u16 {
        true
    } else if num == 64u16 {
        false
    } else if num == 65u16 {
        true
    } else if num == 66u16 {
        false
    } else if num == 67u16 {
        true
    } else if num == 68u16 {
        false
    } else if num == 69u16 {
        true
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