lib_rapid 0.7.0

//! Here you'll find common used constants from several mathematical fields.
/// π² / 6.
pub const PISQRDIV6: f64 = 1.6449340668482264364724151666460251892189499012067984377355582293;
/// 180 / π.
pub const RADDEGRATE: f64 = 57.295779513082320876798154814105170332405472466564321549160243861;
/// π / 180.
pub const DEGRADRATE: f64 = 0.0174532925199432957692369076848861271344287188854172545609719144;
/// π.
pub const PI: f64 = 3.1415926535897932384626433832795028841971693993751058209749445923;
/// √π.
pub const SQRTPI: f64 = 1.7724538509055160272981674833411451827975494561223871282138077898;
/// τ.
pub const TAU: f64 = 6.2831853071795864769252867665590057683943387987502116419498891846;
/// π / 2.
pub const HALFPI: f64 = 1.5707963267948966192313216916397514420985846996875529104874722961;
/// Eulers number.
pub const E: f64 = 2.7182818284590452353602874713526624977572470936999595749669676277;
/// The square root of Eulers number.
pub const SQRTE: f64 = 1.6487212707001281468486507878141635716537761007101480115750793116;
/// √2.
pub const SQRT2: f64 = 1.4142135623730950488016887242096980785696718753769480731766797379;
/// √3.
pub const SQRT3: f64 = 1.7320508075688772935274463415058723669428052538103806280558069794;
/// √5.
pub const SQRT5: f64 = 2.2360679774997896964091736687312762354406183596115257242708972454;
/// The golden ratio φ.
pub const GOLDENRATIO: f64 = 1.6180339887498948482045868343656381177203091798057628621354486227;
/// The Euler-Mascheroni constant, γ.
pub const EULERMASCHERONI: f64 = 0.5772156649015328606065120900824024310421593359399235988057672348;
/// The Twin Primes Constant.
pub const TWINPRIMES: f64 = 0.6601618158468695739278121100145557784326233602847334133194484233;
/// ln(2).
pub const LN2: f64 = 0.6931471805599453094172321214581765680755001343602552541206800094;
/// ln(3).
pub const LN3: f64 = 1.0986122886681096913952452369225257046474905578227494517346943336;
/// ln(5).
pub const LN5: f64 = 1.6094379124341003746007593332261876395256013542685177219126478914;
/// ζ(3).
pub const ZETA3: f64 = 1.2020569031595942853997381615114499907649862923404988817922715553;
/// ∛2.
pub const CUBEROOT2: f64 = 1.2599210498948731647672106072782283505702514647015079800819751121;
/// ∛3.
pub const CUBEROOT3: f64 = 1.4422495703074083823216383107801095883918692534993505775464161945;
/// the speed of light, c.
pub const LIGHTSPEED: f64 = 299_792_458.0;
/// Gravity of Earth, denoted as g
pub const EARTHGRAVITY: f64 = 9.80665;
/// Wallis Constant.
pub const WALLISCONSTANT: f64 = 2.0945514815423265914823865405793029638573061056282391803041285290;
/// The Laplace limit, λ.
pub const LAPLACELIMIT: f64 = 0.6627434193491815809747420971092529070562335491150224175203925349;
/// Gauss's constant.
pub const GAUSSCONSTANT: f64 = 0.8346268416740731862814297327990468089939930134903470024498273701;
/// Cahen's constant, C.
pub const CAHENSCONSTANT: f64 = 0.6434105462883380261822543077575647632865878602682395059870309203;
/// The parabolic constant, P₂.
pub const P2: f64 = 2.2955871493926380740342980491894903875978322036385834839299753466;
/// The Dottie number.
pub const DOTTIENUMBER: f64 = 0.7390851332151606416553120876738734040134117589007574649656806357;
/// The Meissel-Mertens constant.
pub const MEISSELMERTENS: f64 = 0.2614972128476427837554268386086958590515666482611992061920642139;
/// Gelfond's constant e^π.
pub const ETOPI: f64 = 23.140692632779269005729086367948547380266106242600211993445046409;
/// The golden angle.
pub const GOLDENANGLE: f64 = 2.3999632297286533222315555066336138531249990110581150429351127507;
/// The area of the Mandelbrot fractal.
pub const MANDELBROTAREA: f64 = 1.5065918849;
/// The Gieseking constant.
pub const GIESEKINGCONSTANT: f64 =
    1.0149416064096536250212025542745202859416893075302997920174891067;
/// The Bloch-Landau constant.
pub const BLOCHLANDAU: f64 = 0.5432589653429767069527282953006132311388632937583569889557325691;
/// The Golomb-Dickman constant.
pub const GOLOMBDICKMAN: f64 = 0.6243299885435508709929363831008372441796426201805292869735519024;
/// The Feller-Tornier constant.
pub const FELLERTORNIER: f64 = 0.6613170494696223352897658462741185332854752898329;
/// The 2^(√2).
pub const TWOTOSQRT2: f64 = 2.6651441426902251886502972498731398482742113137146594928359795933;
/// The Khinchin's constant.
pub const KHINCHINSCONSTANT: f64 =
    2.6854520010653064453097148354817956938203822939944629530511523455;
/// Mill's constant.
pub const MILLSCONSTANT: f64 = 1.3063778838630806904686144926026057129167845851567136443680537599;
/// π / ln(2).
pub const PIOVERLN2: f64 = 4.5323601418271938096276829457166668101718614677237955841860165479;
/// Loch's constant.
pub const LOCHSCONSTANT: f64 = 0.9702701143920339257402560192100108337812847047851612866103505299;
/// Niven's constant.
pub const NIVENSCONSTANT: f64 = 1.7052111401053677642885514534345081607620276516534690999942849065;
/// Reciprocal Fibonacci constant.
pub const RECIPFIBCONST: f64 = 3.3598856662431775531720113029189271796889051337319684864955538153;
/// Backhouse's constant.
pub const BACKHOUSECONST: f64 = 1.4560749485826896713995953511165435576531783748471315402707024374;
/// The MRB constant.
pub const MRBCONSTANT: f64 = 0.1878596424620671202485179340542732300559030949001387861720046840;
/// Somos' quadratic recurrence constant.
pub const QUADRECURR: f64 = 1.6616879496335941212958189227499507499644186350250682081897111680;
/// The plastic number.
pub const PLASTICNUMBER: f64 = 1.3247179572447460259609088544780973407344040569017333645340150503;

pub(crate) const BASES_32: [u16; 256] = [
    15591, 2018, 166, 7429, 8064, 16045, 10503, 4399, 1949, 1295, 2776, 3620, 560, 3128, 5212,
    2657, 2300, 2021, 4652, 1471, 9336, 4018, 2398, 20462, 10277, 8028, 2213, 6219, 620, 3763,
    4852, 5012, 3185, 1333, 6227, 5298, 1074, 2391, 5113, 7061, 803, 1269, 3875, 422, 751, 580,
    4729, 10239, 746, 2951, 556, 2206, 3778, 481, 1522, 3476, 481, 2487, 3266, 5633, 488, 3373,
    6441, 3344, 17, 15105, 1490, 4154, 2036, 1882, 1813, 467, 3307, 14042, 6371, 658, 1005, 903,
    737, 1887, 7447, 1888, 2848, 1784, 7559, 3400, 951, 13969, 4304, 177, 41, 19875, 3110, 13221,
    8726, 571, 7043, 6943, 1199, 352, 6435, 165, 1169, 3315, 978, 233, 3003, 2562, 2994, 10587,
    10030, 2377, 1902, 5354, 4447, 1555, 263, 27027, 2283, 305, 669, 1912, 601, 6186, 429, 1930,
    14873, 1784, 1661, 524, 3577, 236, 2360, 6146, 2850, 55637, 1753, 4178, 8466, 222, 2579, 2743,
    2031, 2226, 2276, 374, 2132, 813, 23788, 1610, 4422, 5159, 1725, 3597, 3366, 14336, 579, 165,
    1375, 10018, 12616, 9816, 1371, 536, 1867, 10864, 857, 2206, 5788, 434, 8085, 17618, 727, 3639,
    1595, 4944, 2129, 2029, 8195, 8344, 6232, 9183, 8126, 1870, 3296, 7455, 8947, 25017, 541,
    19115, 368, 566, 5674, 411, 522, 1027, 8215, 2050, 6544, 10049, 614, 774, 2333, 3007, 35201,
    4706, 1152, 1785, 1028, 1540, 3743, 493, 4474, 2521, 26845, 8354, 864, 18915, 5465, 2447, 42,
    4511, 1660, 166, 1249, 6259, 2553, 304, 272, 7286, 73, 6554, 899, 2816, 5197, 13330, 7054,
    2818, 3199, 811, 922, 350, 7514, 4452, 3449, 2663, 4708, 418, 1621, 1171, 3471, 88, 11345, 412,
    1559, 194,
];

pub(crate) const PRIMELIST: [u16; 2048] = [
    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,
];

pub(crate) const BASES_64: [u32; 16384] = [
    2404423, 3027617, 3715179, 3264583, 1593555, 5853461, 1552463, 1896881, 2904107, 5600043,
    1356087, 2044251, 290821, 1150981, 1642719, 3076389, 667689, 2650251, 1200327, 1724421,
    4133355, 4494151, 1151005, 2674735, 2404773, 667731, 249897, 2904087, 1257551, 1298703, 815165,
    241669, 987333, 1839543, 1101997, 151581, 2216193, 3314043, 3387621, 1503569, 1569019, 2674851,
    2429437, 2798241, 1380357, 421955, 2330647, 1716501, 1101973, 2757207, 1200199, 3395643,
    987153, 1257519, 2945595, 1994825, 1642879, 1716607, 1470537, 274473, 5034585, 2707899, 741477,
    2871903, 323643, 1052677, 1503513, 1110213, 3371237, 864345, 5157741, 2830397, 4723085,
    1896521, 3518631, 913487, 2674725, 1274089, 1445893, 397317, 2650461, 462937, 2535471, 815171,
    1150993, 299037, 1675281, 2011285, 1273861, 2281743, 290821, 4305755, 1552533, 2945205,
    1282185, 2625573, 339999, 1028275, 1429797, 217093, 4133591, 1110033, 3150567, 1913109, 274445,
    3322029, 1995003, 1527957, 954595, 979071, 446495, 1896509, 987327, 1642501, 3617519, 733323,
    979101, 3314187, 1298503, 2535857, 1642555, 1052715, 3371339, 4084005, 1445941, 782425, 979047,
    1200307, 1527851, 1888713, 2084869, 618609, 1552551, 520199, 1052865, 987141, 1527935, 1052679,
    1593367, 1028323, 815117, 913421, 1159239, 1445929, 2584925, 1200391, 929895, 1839183, 1642585,
    1888263, 979071, 364617, 520301, 4133525, 4714863, 3510373, 3535449, 2281935, 790629, 1724799,
    3363279, 3150287, 1355829, 2043957, 4059165, 569475, 1888603, 618627, 274485, 1028233, 667695,
    274463, 1626363, 3100901, 2454075, 217129, 397335, 1298485, 806915, 1110087, 1151085, 1642569,
    4182525, 413733, 2085231, 1028289, 987285, 1200265, 569397, 438331, 1896587, 2797941, 618507,
    913599, 2281475, 1282221, 3518661, 3002625, 1896453, 1896699, 1101987, 4059263, 1913059,
    3617157, 2454007, 1200339, 299069, 2626077, 1134611, 1273917, 1569025, 3265155, 3535675,
    1151059, 3494019, 3494345, 978987, 299019, 2429415, 864453, 1798247, 2339057, 323607, 2060727,
    6836295, 1773669, 667721, 1839547, 978949, 667661, 1101933, 1200169, 3879775, 2241021, 2216177,
    2699611, 1446181, 1593397, 3371121, 684139, 684073, 806949, 2281845, 733273, 1446001, 618519,
    1839231, 2633837, 4223419, 4297153, 438315, 2240823, 2428989, 462901, 618555, 3715119, 438303,
    1077307, 938115, 987239, 782349, 4969091, 1593457, 2306547, 2404357, 1675311, 1101937, 4084065,
    708661, 2330815, 1200187, 1257485, 979125, 274485, 1724723, 3002789, 1274127, 2044187, 1675277,
    2461979, 1101855, 4304957, 1765567, 2625777, 2011143, 1593555, 790541, 1028197, 741429, 462957,
    2404575, 2084977, 5575515, 790685, 1110227, 1200327, 3903601, 806979, 3494579, 1298605,
    2240541, 790635, 741435, 1527935, 4518067, 4543533, 2134083, 1724429, 1675661, 3732063,
    2830617, 2510909, 1134773, 1962445, 1298511, 3026991, 4453085, 2535867, 4174311, 4133451,
    1028293, 1470775, 3313971, 2453523, 610387, 1888353, 561279, 2536025, 1134615, 2216019, 790545,
    1298449, 4026715, 782445, 1470715, 2339027, 569475, 708619, 2011495, 667757, 3395825, 1962235,
    790559, 1568805, 815285, 2527335, 3002807, 2142359, 1626285, 987177, 2707569, 790533, 2535573,
    462901, 1568949, 2486379, 741507, 4837755, 929821, 1257755, 2757255, 561265, 1200225, 413719,
    1552415, 2486375, 5624007, 1798575, 3395985, 929835, 1356005, 684115, 290875, 4477317, 667715,
    364575, 4518139, 864455, 1028295, 1765413, 3510781, 1028115, 4796747, 1380411, 1421643,
    2945413, 1110045, 1052689, 1724817, 2306229, 3837963, 987173, 2699643, 151559, 1814631,
    2871957, 708679, 815271, 979045, 1200229, 2699545, 3043441, 2216193, 3437035, 3150023, 3371087,
    249899, 4174821, 5255517, 4026909, 1528001, 643115, 1151055, 2626155, 4714999, 3510631,
    1110195, 2904137, 167949, 1528049, 94225, 8655567, 913467, 151575, 1626291, 1814769, 2625549,
    339981, 241707, 2625693, 2216165, 2535591, 126989, 2584689, 1028253, 5337521, 1421439, 561205,
    2134503, 1380581, 1052709, 6189349, 4059755, 2535887, 864365, 667721, 2338953, 3879193,
    2306197, 1716307, 2453773, 815283, 1110179, 3494699, 2707713, 3076599, 618557, 1552487,
    2510927, 1814929, 6608415, 1101981, 2585177, 5239611, 1503455, 217135, 1200277, 667651, 290877,
    2461823, 5656589, 929919, 2134495, 446487, 3003077, 1380383, 2486315, 1642669, 340009, 2871607,
    2404791, 1593613, 2142561, 1995201, 4469545, 1888489, 4174647, 2011347, 2011239, 913557,
    1765503, 3436587, 1028259, 1101891, 5035137, 2085343, 1814709, 2650755, 1503413, 3535041,
    815261, 815211, 3396341, 249869, 323601, 2134243, 667653, 1298473, 569347, 2773665, 954541,
    2625849, 2281873, 3634015, 733255, 3117393, 1110273, 217111, 913619, 5403577, 864297, 1356053,
    2535933, 2626105, 2281581, 1765539, 2404621, 1814791, 3437271, 1052683, 2584815, 1134833,
    421967, 930015, 1134611, 2634065, 274469, 176141, 2871897, 2404525, 340047, 1355847, 1552607,
    1593525, 864323, 790595, 2330887, 1200181, 782503, 1200319, 684061, 2011315, 1274067, 1110207,
    397317, 1282341, 1421353, 1282155, 667785, 1298445, 1675371, 5042277, 1150989, 782403, 1724445,
    462877, 2945631, 1052685, 2674915, 979003, 684091, 2363529, 1773605, 4600667, 3961505, 3608713,
    6435735, 5828901, 2461935, 1642563, 954477, 815285, 1503333, 569481, 2699763, 77837, 1159367,
    4223115, 1839315, 4379103, 1273879, 864285, 2773261, 4001839, 954411, 1052809, 1765387,
    1134597, 2633985, 3002411, 2699391, 438285, 1356053, 1470573, 1839477, 2584787, 1912863,
    1626221, 1724817, 3100739, 3535509, 929971, 1159271, 421893, 2535591, 1994925, 2240735,
    1421581, 643185, 421955, 1896557, 643155, 1503291, 2240705, 2486523, 1355859, 1569115, 1503383,
    1896579, 1282157, 1716405, 3076559, 2339199, 1028109, 2044155, 1642879, 618605, 1896785,
    2584965, 1052811, 1552445, 643169, 1994925, 520197, 2134329, 1798527, 2306187, 1962381,
    1568917, 1814545, 5329665, 1380591, 4723485, 1503389, 3396185, 1675487, 5313729, 938093,
    864339, 2510945, 1716465, 1282121, 2650263, 1274113, 2756619, 1724421, 815235, 1765669,
    1773605, 3535207, 2404501, 3617445, 1896561, 1159269, 3436795, 2142287, 3363429, 1552565,
    5328927, 3838305, 913607, 3879709, 1110209, 1445995, 4059777, 1995003, 1675403, 667805,
    2330653, 2756865, 815285, 782377, 1445917, 1101921, 413709, 1446165, 3764765, 4231941, 913571,
    2216043, 2625549, 2585055, 1814707, 1716555, 2306437, 1273873, 2363703, 3805911, 1052923,
    4256267, 2281821, 397329, 864365, 2634041, 1470745, 2339213, 1552413, 2871957, 1200141,
    4452915, 913565, 790631, 2043965, 1028179, 1101955, 3395691, 3314383, 4887567, 1675395, 741449,
    1429661, 1298463, 536637, 1839127, 1568917, 421901, 1888603, 2797989, 782515, 610365, 4354071,
    1913071, 2453547, 1028175, 938111, 1134821, 397317, 1675311, 1626381, 2240745, 610333, 1888315,
    4297581, 1675283, 1569061, 1724649, 1421509, 1798191, 290875, 397401, 397401, 2633979, 1814791,
    3223709, 807075, 3027575, 1773819, 3166249, 4600847, 954435, 3117069, 1200355, 2699767,
    1101861, 1298671, 438303, 3322443, 1593625, 913481, 1675391, 4026705, 1995083, 790551, 1675661,
    1765689, 1200217, 2134299, 741479, 2085027, 1470757, 438345, 2011399, 2363649, 815177, 2134465,
    3002831, 1839135, 1593675, 913589, 1159187, 2363835, 741381, 1028245, 733225, 5231149, 667689,
    864269, 217117, 3387501, 2699497, 569445, 446565, 1052719, 536617, 569481, 3855159, 438325,
    1716307, 118803, 1675463, 3396063, 1429635, 4887547, 3764229, 1150987, 987243, 3395693, 954471,
    299051, 1298599, 1429841, 2708057, 3510655, 2978369, 274443, 1626471, 2240525, 733189, 1626275,
    2904671, 5354439, 1593357, 1052709, 3371207, 413733, 2338973, 1028253, 1593607, 569445, 979173,
    1101855, 4985961, 1257753, 176141, 3879411, 2511297, 1134759, 815271, 938015, 2699697, 1724439,
    1052865, 1429817, 864383, 3076805, 1257665, 1913043, 1134785, 938091, 733189, 1839451, 53251,
    536703, 2339247, 5042483, 4624893, 3223589, 2085325, 520293, 806925, 3166441, 4599975, 3387433,
    954559, 3765083, 1159445, 1028127, 643091, 1445893, 3027323, 1421589, 4133057, 3617001,
    2044197, 2527329, 3117747, 4027251, 4796649, 1839277, 3617429, 3961505, 1052761, 3363205,
    69643, 708711, 1995003, 1716555, 2527471, 4354227, 782343, 561235, 1298595, 2871369, 2650611,
    913455, 1470517, 1052901, 790541, 2904107, 2650165, 643085, 790531, 1503465, 1421629, 1765513,
    2281575, 3027083, 323627, 6788253, 3764313, 2044185, 2429259, 1675535, 1274133, 2281479,
    2363465, 1642509, 1151215, 2216135, 2945173, 1445997, 1052799, 2527581, 1872321, 1593405,
    421967, 1798185, 1028329, 217105, 987365, 2011449, 1675461, 2331091, 954429, 561195, 815157,
    667757, 618645, 667749, 1593349, 2511449, 2339295, 1446085, 610405, 1593661, 118801, 3002931,
    2461827, 979041, 5328963, 1994943, 1765605, 2871837, 1355817, 2453727, 1896891, 1151127,
    2486793, 1552607, 618585, 3592271, 192517, 1200351, 5869861, 2535675, 1380581, 3002789,
    1798475, 274445, 2511111, 462945, 1675283, 4231521, 2461889, 913539, 4920173, 1159251, 5230815,
    249903, 3043375, 3043375, 3314425, 1871961, 290875, 3002871, 1052785, 2945467, 1896479,
    2363429, 937997, 1569037, 569405, 3002877, 2650375, 4083779, 3043501, 1503585, 643211, 1028199,
    1110057, 2429221, 979143, 2462139, 2281543, 1765735, 2773231, 6321299, 1134863, 3960837,
    3166617, 569349, 3608769, 3117115, 3314311, 2674785, 2871559, 1568847, 1872021, 1642539,
    913451, 2043947, 1421595, 667751, 1888405, 1356045, 1912845, 1839375, 438301, 4149861, 1503429,
    1552665, 1527989, 5255359, 864269, 2634305, 5066951, 3510471, 2281975, 3322595, 2674693,
    2527653, 2486303, 536679, 2675131, 2527515, 1110099, 2240823, 782349, 3363535, 3764277,
    1716481, 3314037, 1429677, 3387565, 1282215, 643109, 2650305, 3100979, 4763755, 733189, 987273,
    2773623, 1642647, 2060451, 2978411, 126999, 1593717, 643115, 3264931, 2453755, 2584803,
    3224061, 2773221, 1896687, 4231215, 2330803, 618645, 1626351, 2535527, 2511425, 3396323,
    2281831, 7467699, 1642575, 2650115, 413775, 1527813, 2044071, 815241, 782437, 3731469, 4174581,
    192525, 3387649, 618569, 987179, 4862781, 1134651, 2142699, 1503459, 2142491, 2281503, 6346163,
    3633939, 815255, 2699613, 979045, 2757267, 790595, 1110245, 2707913, 979167, 3494429, 7278965,
    3076433, 2674759, 217111, 438313, 1200141, 3150093, 192517, 3117499, 1102053, 2216109, 913607,
    3617045, 1724483, 1552421, 1527813, 1724517, 741525, 733281, 807043, 536629, 1839231, 2486535,
    1913071, 1913095, 364617, 1282239, 1642695, 5870031, 167959, 1446157, 2633961, 1446201, 413793,
    1552523, 2060559, 3960837, 3592301, 913439, 2216127, 741527, 4886629, 118807, 2044301, 1257561,
    2626137, 2650153, 299045, 790659, 1257653, 806953, 1282341, 610307, 2085223, 3494117, 364567,
    3002375, 3510513, 5239553, 2871435, 3879709, 1380533, 733291, 2797969, 2650659, 1159307,
    618501, 913565, 1134803, 2060299, 1765473, 938195, 1871913, 2536001, 913419, 1896837, 1298659,
    1200391, 1814757, 2085285, 2650753, 1962343, 3838749, 2084869, 1773581, 684091, 1429541,
    2634215, 1888563, 561163, 733225, 3150425, 1503545, 1888269, 1028245, 3321945, 6140731,
    2428975, 2773651, 3731647, 69645, 3150213, 1765615, 4174401, 1552731, 561283, 929989, 1273927,
    2978315, 536581, 446505, 954561, 1421485, 938021, 1298461, 1102075, 3002835, 643179, 561165,
    4059141, 2339303, 192525, 3150023, 4059645, 733203, 790707, 2281545, 2830995, 1077261, 2453821,
    2085265, 1896611, 807085, 4625487, 2510915, 1298605, 1503465, 1134759, 741477, 6115525, 192549,
    1282317, 3977413, 397343, 3609453, 1724495, 569357, 1380383, 815231, 1913143, 1765603, 2527569,
    1814727, 413755, 733227, 708735, 3961463, 733189, 462957, 520229, 864365, 446469, 536613,
    2756627, 3592809, 610365, 3388135, 126983, 1077357, 2756621, 1257713, 6190003, 1773635,
    3027225, 5771301, 1028127, 8532021, 2454051, 782433, 3076289, 3510309, 1569061, 2773585,
    1593475, 2281921, 2757029, 1355855, 4543107, 1052755, 2650117, 2363565, 1429851, 987237,
    1642647, 340029, 5010237, 4182633, 4232055, 929905, 913421, 1626201, 2675301, 1110255, 1282325,
    1593475, 2429419, 2240549, 1773899, 1724483, 667659, 2306053, 1159275, 1052725, 3100725,
    1282061, 2429239, 2331087, 3879795, 2306239, 913455, 2871567, 3166591, 790719, 1765489,
    3371451, 2797611, 610315, 2330713, 2756627, 4305725, 2535603, 1871913, 2011525, 4297587,
    4059993, 1593615, 2871669, 3043869, 1503459, 438303, 1052691, 4174507, 2330671, 2625607,
    1421341, 2674801, 2363585, 1716573, 2281821, 5402803, 2510907, 1503321, 2699877, 4452579,
    929919, 929797, 290827, 667719, 1765437, 684051, 569457, 2429419, 913451, 1716327, 3150015,
    2535987, 987237, 167949, 569453, 1429635, 4256571, 1077459, 1626305, 1765773, 2453733, 2240685,
    3519191, 864309, 446469, 2945307, 790607, 3076529, 2486529, 2216219, 1274149, 2462127, 684103,
    2699575, 2830745, 2215949, 3027543, 930015, 1773849, 987287, 5279749, 1298745, 2215983,
    1052709, 1429635, 4379033, 3313827, 2904171, 1675575, 2142587, 3264523, 4083903, 364627,
    1527947, 3043789, 364561, 741513, 1355829, 1675323, 741473, 438277, 3609085, 2707527, 2142471,
    1626243, 643079, 1159401, 1527881, 733267, 1552641, 2707899, 3805935, 954535, 979177, 1839121,
    1675305, 2339109, 2625759, 3903561, 733215, 4002123, 3117409, 1888593, 929959, 2462007,
    1110077, 643151, 3371011, 1159257, 3732027, 2044283, 1552403, 536587, 1593625, 2904243,
    1445917, 4477961, 2830997, 4355045, 167953, 1675445, 438375, 2510909, 4133685, 4969067,
    2462183, 2535845, 4378763, 1568791, 1503525, 3395603, 2011141, 1355987, 4223167, 979143,
    913547, 2084953, 1552697, 667695, 937995, 364549, 1888519, 643223, 4305363, 741533, 733333,
    5231049, 1872095, 667707, 569471, 4297675, 4026985, 2773593, 3371027, 1896629, 3609267,
    3371681, 1429617, 1052703, 290883, 1994789, 1896905, 1446055, 667761, 1994765, 241675, 1675307,
    1470705, 643151, 1150989, 2756757, 3437283, 806955, 5411693, 69643, 1675575, 2363661, 1716283,
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];