cryspglib 0.1.0

//! 位点对称性数据库。
//!
//! 从 C 代码自动生成的 Wyckoff 位置对称性数据库。
//! 用于根据 Wyckoff 字母查找原子位点的局域对称操作。
// Auto-generated by Python script from sitesym_database.c

use crate::mathfunc::{Mat3I, Vec3};

// --- Static Data ---
static POSITION_WYCKOFF: [i32; 532] = [
    0, 1, 2, 11, 16, 21, 26, 27, 28, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 66, 67,
    68, 69, 70, 71, 72, 73, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 93, 94, 95, 96, 97, 98, 99,
    100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 125, 140, 155, 161, 167, 173, 183, 193,
    203, 213, 223, 233, 243, 253, 263, 270, 277, 284, 291, 298, 305, 312, 319, 326, 331, 336, 341,
    346, 351, 356, 361, 366, 371, 377, 383, 389, 395, 401, 407, 413, 419, 425, 431, 437, 443, 449,
    455, 461, 467, 473, 479, 500, 505, 510, 515, 518, 521, 524, 525, 528, 531, 534, 546, 558, 570,
    581, 592, 596, 605, 614, 623, 626, 629, 632, 635, 638, 641, 646, 651, 656, 660, 664, 668, 672,
    676, 680, 681, 682, 683, 684, 685, 686, 689, 692, 695, 698, 701, 704, 706, 708, 710, 712, 714,
    716, 719, 722, 725, 726, 727, 728, 729, 730, 731, 734, 737, 740, 746, 752, 758, 760, 762, 764,
    766, 768, 770, 774, 778, 782, 788, 794, 800, 806, 812, 818, 822, 826, 830, 834, 838, 842, 845,
    848, 851, 854, 857, 860, 862, 864, 866, 868, 870, 872, 877, 882, 887, 889, 891, 893, 898, 903,
    908, 911, 914, 917, 920, 923, 926, 929, 932, 935, 962, 975, 988, 1006, 1024, 1042, 1055, 1068,
    1081, 1094, 1107, 1120, 1132, 1144, 1156, 1168, 1180, 1192, 1197, 1202, 1207, 1212, 1217, 1222,
    1231, 1240, 1249, 1258, 1267, 1276, 1282, 1288, 1294, 1300, 1306, 1312, 1321, 1330, 1339, 1344,
    1349, 1354, 1359, 1364, 1369, 1374, 1379, 1384, 1392, 1400, 1408, 1415, 1422, 1429, 1436, 1443,
    1450, 1454, 1458, 1462, 1466, 1470, 1474, 1477, 1480, 1484, 1488, 1492, 1496, 1500, 1504, 1512,
    1520, 1528, 1536, 1544, 1552, 1559, 1566, 1573, 1580, 1587, 1594, 1612, 1630, 1648, 1661, 1674,
    1687, 1702, 1717, 1732, 1747, 1762, 1777, 1786, 1795, 1804, 1813, 1822, 1831, 1840, 1849, 1858,
    1867, 1876, 1885, 1901, 1909, 1917, 1932, 1943, 1954, 1965, 1971, 1977, 1987, 1997, 2007, 2017,
    2027, 2037, 2041, 2042, 2046, 2047, 2050, 2052, 2060, 2067, 2079, 2090, 2097, 2104, 2111, 2118,
    2127, 2133, 2139, 2155, 2162, 2166, 2168, 2184, 2191, 2195, 2197, 2208, 2215, 2222, 2226, 2231,
    2235, 2239, 2242, 2248, 2251, 2256, 2260, 2263, 2265, 2280, 2294, 2300, 2305, 2317, 2327, 2336,
    2345, 2355, 2364, 2374, 2379, 2400, 2414, 2428, 2442, 2453, 2464, 2476, 2485, 2496, 2507, 2514,
    2521, 2539, 2555, 2566, 2577, 2591, 2605, 2614, 2625, 2633, 2641, 2651, 2661, 2676, 2689, 2698,
    2707, 2714, 2721, 2725, 2726, 2727, 2729, 2731, 2738, 2744, 2750, 2762, 2769, 2772, 2775, 2778,
    2781, 2787, 2793, 2798, 2802, 2806, 2809, 2812, 2815, 2817, 2819, 2831, 2840, 2850, 2857, 2866,
    2875, 2881, 2887, 2891, 2892, 2893, 2896, 2899, 2902, 2914, 2926, 2935, 2949, 2952, 2955, 2966,
    2977, 2986, 2992, 2996, 3000, 3004, 3019, 3031, 3043, 3052, 3070, 3083, 3095, 3107, 3117, 3125,
    3131, 3133, 3136, 3148, 3156, 3164, 3173, 3180, 3187, 3195, 3199, 3204, 3215, 3228, 3238, 3246,
    3256, 3261, 3266, 3275, 3285, 3294, 3302, 3311, 3319, 3324, 3338, 3347, 3356, 3368, 3380, 3392,
    3404, 3414, 3423, 3432, 3440, 3448, 3460, 3468,
];
static POSITION_LAYER_WYCKOFF: [i32; 118] = [
    0, 3468, 3469, 3474, 3479, 3481, 3482, 3483, 3484, 3494, 3499, 3504, 3509, 3512, 3515, 3516,
    3517, 3519, 3521, 3524, 3527, 3528, 3529, 3531, 3533, 3542, 3551, 3555, 3559, 3563, 3567, 3570,
    3573, 3579, 3585, 3598, 3602, 3606, 3609, 3617, 3626, 3630, 3634, 3637, 3643, 3649, 3655, 3658,
    3661, 3663, 3665, 3668, 3671, 3674, 3677, 3679, 3681, 3682, 3683, 3685, 3687, 3691, 3695, 3698,
    3701, 3719, 3730, 3741, 3749, 3757, 3765, 3774, 3783, 3789, 3795, 3799, 3803, 3809, 3813, 3817,
    3823, 3835, 3845, 3849, 3855, 3863, 3868, 3873, 3883, 3888, 3895, 3899, 3909, 3914, 3923, 3929,
    3943, 3952, 3961, 3969, 3977, 3985, 3989, 3994, 4002, 4007, 4012, 4016, 4024, 4031, 4035, 4043,
    4051, 4060, 4066, 4076, 4084, 4096,
];
static COORDINATES_FIRST: [i32; 4096] = [
    0, 63923, 63923, 657239062, 27383062, 630995062, 656145562, 629901562, 26289562, 1139062,
    45562, 63923, 630995197, 629901697, 1139197, 45697, 63923, 656145563, 26289563, 629901563,
    45563, 63923, 27401287, 1157287, 26307787, 63787, 63923, 63923, 63923, 63923, 1139197, 45697,
    63923, 629901697, 45697, 63923, 629901697, 45697, 63923, 629901563, 45563, 63923, 26289563,
    45563, 63923, 26289563, 45563, 63923, 26307787, 63787, 63923, 1157287, 63787, 63923, 1157287,
    63787, 63923, 26307788, 63788, 63923, 1157422, 63922, 63923, 629901698, 45698, 63923, 63923,
    63923, 63923, 63923, 63923, 63923, 63923, 63923, 63923, 63788, 63923, 63788, 63923, 63788,
    63923, 63922, 63923, 63922, 63923, 63922, 63923, 45698, 63923, 45698, 63923, 45698, 63923,
    63923, 63923, 63923, 63923, 63923, 63923, 63923, 63923, 63923, 63923, 63923, 63923, 63923,
    63923, 63923, 63923, 63923, 63923, 26307788, 63788, 630995197, 1139197, 629901697, 45697,
    657239062, 630995062, 27383062, 656145562, 629901562, 1139062, 26289562, 45562, 63923, 1157422,
    63922, 656145563, 629901563, 26289563, 45563, 657239062, 656145562, 630995062, 27383062,
    26289562, 629901562, 1139062, 45562, 63923, 629901698, 45698, 27401287, 26307787, 1157287,
    63787, 657239062, 27383062, 656145562, 630995062, 1139062, 26289562, 629901562, 45562, 63923,
    13185788, 630995062, 1139062, 629901562, 45562, 63923, 610672, 656145562, 629901562, 26289562,
    45562, 63923, 314973698, 27383062, 26289562, 1139062, 45562, 63923, 63788, 1139197, 45697,
    329189062, 328095562, 27383062, 1139062, 26289562, 45562, 63923, 63788, 629901697, 45697,
    643570312, 13714312, 656145562, 629901562, 26289562, 45562, 63923, 63788, 1139197, 45697,
    329735812, 328642312, 27383062, 1139062, 26289562, 45562, 63923, 63922, 629901563, 45563,
    643570312, 13714312, 630995062, 629901562, 1139062, 45562, 63923, 63922, 26289563, 45563,
    341764312, 315520312, 27383062, 26289562, 1139062, 45562, 63923, 63922, 629901563, 45563,
    958498312, 328642312, 630995062, 629901562, 1139062, 45562, 63923, 45698, 26307787, 63787,
    341764312, 315520312, 656145562, 26289562, 629901562, 45562, 63923, 45698, 1157287, 63787,
    329189062, 328095562, 630995062, 1139062, 629901562, 45562, 63923, 45698, 26307787, 63787,
    354886312, 328642312, 656145562, 26289562, 629901562, 45562, 63923, 630448447, 592447,
    629901562, 26289562, 656145562, 45562, 63923, 945376447, 315520447, 629901562, 26289562,
    656145562, 45562, 63923, 945923197, 944829697, 1139062, 26289562, 27383062, 45562, 63923,
    341217563, 314973563, 26289562, 1139062, 27383062, 45562, 63923, 354339563, 328095563,
    26289562, 1139062, 27383062, 45562, 63923, 669267563, 39411563, 629901562, 1139062, 630995062,
    45562, 63923, 14279287, 13185787, 1139062, 629901562, 630995062, 45562, 63923, 14826037,
    13732537, 1139062, 629901562, 630995062, 45562, 63923, 27948037, 1704037, 26289562, 629901562,
    656145562, 45562, 63923, 630995062, 1139062, 629901562, 45562, 63923, 1139062, 630995062,
    629901562, 45562, 63923, 630995062, 629901562, 1139062, 45562, 63923, 656145562, 629901562,
    26289562, 45562, 63923, 629901562, 656145562, 26289562, 45562, 63923, 656145562, 26289562,
    629901562, 45562, 63923, 27383062, 26289562, 1139062, 45562, 63923, 26289562, 27383062,
    1139062, 45562, 63923, 27383062, 1139062, 26289562, 45562, 63923, 592447, 329189062, 328095562,
    26289562, 45562, 63923, 315520447, 670907812, 39958312, 26289562, 45562, 63923, 314973697,
    984742312, 354886312, 26289562, 45562, 63923, 944829697, 643570312, 13714312, 26289562, 45562,
    63923, 315520447, 959045062, 328095562, 26289562, 45562, 63923, 592447, 329735812, 328642312,
    26289562, 45562, 63923, 314973563, 643570312, 13714312, 1139062, 45562, 63923, 328095563,
    972713812, 316613812, 1139062, 45562, 63923, 13167563, 355979812, 329735812, 1139062, 45562,
    63923, 39411563, 341764312, 315520312, 1139062, 45562, 63923, 328095563, 669814312, 13714312,
    1139062, 45562, 63923, 314973563, 958498312, 328642312, 1139062, 45562, 63923, 13185787,
    341764312, 315520312, 629901562, 45562, 63923, 13732537, 985289062, 957951562, 629901562,
    45562, 63923, 610537, 959591812, 958498312, 629901562, 45562, 63923, 1704037, 329189062,
    328095562, 629901562, 45562, 63923, 13732537, 342857812, 315520312, 629901562, 45562, 63923,
    13185787, 354886312, 328642312, 629901562, 45562, 63923, 656145563, 26289563, 629901563, 45563,
    630995197, 629901697, 1139197, 45697, 27401287, 26307787, 1157287, 63787, 657239062, 27383062,
    630995062, 656145562, 1139062, 26289562, 629901562, 45562, 63923, 630448447, 592447, 26307787,
    63787, 63923, 341217563, 314973563, 1139197, 45697, 63923, 14279287, 13185787, 629901563,
    45563, 63923, 26289563, 45563, 63923, 1157287, 63787, 63923, 629901697, 45697, 63923, 63923,
    592447, 63787, 63923, 314973563, 45697, 63923, 13185787, 45563, 63923, 328095563, 26289563,
    45563, 1139197, 45697, 1157287, 63787, 1139062, 630995062, 26289562, 45562, 63923, 13732537,
    1157287, 63787, 629901563, 45563, 629901697, 45697, 629901562, 656145562, 1139062, 45562,
    63923, 315520447, 629901697, 45697, 26307787, 63787, 26289563, 45563, 26289562, 27383062,
    629901562, 45562, 63923, 13732537, 315520447, 328095563, 45563, 45697, 63787, 329735812,
    328642312, 1139062, 45562, 63923, 26289563, 45563, 629901697, 45697, 1157287, 63787, 26289562,
    1139062, 629901562, 45562, 63923, 13167563, 314973697, 610537, 63923, 629901698, 45698,
    26307788, 63788, 656145563, 629901563, 26289563, 45563, 63923, 26307788, 63788, 1157422, 63922,
    27401287, 26307787, 1157287, 63787, 63923, 1157422, 63922, 629901698, 45698, 630995197,
    1139197, 629901697, 45697, 63923, 629901698, 45698, 63923, 26307788, 63788, 63923, 26307788,
    63788, 63923, 1157422, 63922, 63923, 1157422, 63922, 63923, 629901698, 45698, 63923, 656145563,
    629901563, 26289563, 45563, 63923, 27401287, 26307787, 1157287, 63787, 63923, 630995197,
    1139197, 629901697, 45697, 63923, 314973698, 26289563, 45563, 63923, 13185788, 629901563,
    45563, 63923, 13185788, 1157287, 63787, 63923, 610672, 26307787, 63787, 63923, 610672,
    629901697, 45697, 63923, 314973698, 1139197, 45697, 63923, 63923, 63923, 63923, 63923, 63923,
    63923, 629901563, 45563, 63923, 26289563, 45563, 63923, 26307787, 63787, 63923, 1157287, 63787,
    63923, 1139197, 45697, 63923, 629901697, 45697, 63923, 45698, 63923, 63788, 63923, 63788,
    63923, 63922, 63923, 63922, 63923, 45698, 63923, 26289563, 45563, 63923, 1157287, 63787, 63923,
    629901697, 45697, 63923, 63923, 63923, 63923, 63923, 63923, 63923, 26289563, 45563, 63923,
    1157287, 63787, 63923, 629901697, 45697, 63923, 45698, 63788, 328095563, 26289563, 45563,
    63923, 63788, 63922, 13732537, 1157287, 63787, 63923, 63922, 45698, 315520447, 629901697,
    45697, 63923, 45698, 63923, 63788, 63923, 63788, 63923, 63922, 63923, 63922, 63923, 45698,
    63923, 328095563, 26289563, 45563, 63923, 13732537, 1157287, 63787, 63923, 315520447,
    629901697, 45697, 63923, 629901698, 45698, 63788, 629901563, 45563, 63923, 26307788, 63788,
    45698, 26289563, 45563, 63923, 26307788, 63788, 63922, 26307787, 63787, 63923, 1157422, 63922,
    63788, 1157287, 63787, 63923, 1157422, 63922, 45698, 1139197, 45697, 63923, 629901698, 45698,
    63922, 629901697, 45697, 63923, 13185788, 629901563, 45563, 63923, 314973698, 26289563, 45563,
    63923, 610672, 26307787, 63787, 63923, 13185788, 1157287, 63787, 63923, 314973698, 1139197,
    45697, 63923, 610672, 629901697, 45697, 63923, 314973698, 45563, 63923, 13185788, 45563, 63923,
    13185788, 63787, 63923, 610672, 63787, 63923, 610672, 45697, 63923, 314973698, 45697, 63923,
    45563, 63923, 45563, 63923, 63787, 63923, 63787, 63923, 45697, 63923, 45697, 63923, 63788,
    45698, 328095563, 45563, 63923, 63922, 63788, 13732537, 63787, 63923, 45698, 63922, 315520447,
    45697, 63923, 45563, 63923, 63787, 63923, 45697, 63923, 45698, 63788, 26289563, 45563, 63923,
    63788, 63922, 1157287, 63787, 63923, 63922, 45698, 629901697, 45697, 63923, 26289563, 45563,
    63923, 1157287, 63787, 63923, 629901697, 45697, 63923, 314973698, 45563, 63923, 13185788,
    45563, 63923, 13185788, 63787, 63923, 610672, 63787, 63923, 610672, 45697, 63923, 314973698,
    45697, 63923, 1157422, 63922, 26307788, 63788, 629901698, 45698, 656145563, 629901563,
    26289563, 45563, 630995197, 629901697, 1139197, 45697, 27401287, 26307787, 1157287, 63787,
    657239062, 27383062, 656145562, 26289562, 630995062, 1139062, 629901562, 45562, 63923,
    26289563, 45563, 629901697, 45697, 1157287, 63787, 985835812, 328642312, 26289562, 1139062,
    629901562, 45562, 63923, 354339563, 328095563, 945376447, 315520447, 14826037, 13732537, 45562,
    657239062, 354886312, 329735812, 958498312, 328642312, 63923, 63922, 629901563, 26289563,
    656145563, 45563, 630448447, 592447, 26854537, 610537, 656692312, 26836312, 630448312, 592312,
    629901562, 26289562, 656145562, 45562, 63923, 45698, 26307787, 1157287, 27401287, 63787,
    341217563, 314973563, 316067197, 314973697, 342311062, 316067062, 341217562, 314973562,
    26289562, 1139062, 27383062, 45562, 63923, 63788, 1139197, 629901697, 630995197, 45697,
    14279287, 13185787, 643023563, 13167563, 644117062, 643023562, 14261062, 13167562, 1139062,
    629901562, 630995062, 45562, 63923, 26289563, 45563, 1139197, 45697, 1157287, 63787, 329189062,
    328095562, 1139062, 630995062, 629901562, 45562, 63923, 354339563, 328095563, 316067197,
    314973697, 14279287, 13185787, 1139062, 45562, 329189062, 959045062, 957951562, 328095562,
    63923, 1157287, 63787, 629901563, 45563, 629901697, 45697, 643570312, 13714312, 629901562,
    656145562, 26289562, 45562, 63923, 14826037, 13732537, 643023563, 13167563, 630448447, 592447,
    629901562, 45562, 643570312, 669814312, 39958312, 13714312, 63923, 629901697, 45697, 26307787,
    63787, 26289563, 45563, 341764312, 315520312, 26289562, 27383062, 1139062, 45562, 63923,
    945376447, 315520447, 26854537, 610537, 341217563, 314973563, 26289562, 45562, 341764312,
    342857812, 316613812, 315520312, 63923, 314973698, 26307788, 63788, 1139197, 45697, 341217563,
    314973563, 27383062, 1139062, 26289562, 45562, 63923, 13185788, 629901698, 45698, 1157287,
    63787, 643023563, 13167563, 630995062, 1139062, 629901562, 45562, 63923, 13185788, 1157422,
    63922, 629901563, 45563, 14279287, 13185787, 630995062, 629901562, 1139062, 45562, 63923,
    610672, 26307788, 63788, 629901697, 45697, 26854537, 610537, 656145562, 629901562, 26289562,
    45562, 63923, 610672, 629901698, 45698, 26307787, 63787, 630448447, 592447, 656145562,
    26289562, 629901562, 45562, 63923, 314973698, 1157422, 63922, 26289563, 45563, 316067197,
    314973697, 27383062, 26289562, 1139062, 45562, 63923, 13732537, 314973563, 1139062, 45562,
    63923, 316613947, 13167563, 1139062, 45562, 63923, 315520447, 13185787, 629901562, 45562,
    63923, 957951563, 610537, 629901562, 45562, 63923, 328095563, 592447, 26289562, 45562, 63923,
    39976537, 314973697, 26289562, 45562, 63923, 45698, 315520447, 26307787, 63787, 26289562,
    656145562, 629901562, 45562, 63923, 63788, 14826037, 629901697, 45697, 629901562, 656145562,
    26289562, 45562, 63923, 63788, 328095563, 1139197, 45697, 1139062, 27383062, 26289562, 45562,
    63923, 63922, 945376447, 26289563, 45563, 26289562, 27383062, 1139062, 45562, 63923, 63922,
    13732537, 629901563, 45563, 629901562, 630995062, 1139062, 45562, 63923, 45698, 354339563,
    1157287, 63787, 1139062, 630995062, 629901562, 45562, 63923, 341217563, 314973563, 592447,
    26289562, 45562, 63923, 643023563, 13167563, 1704037, 629901562, 45562, 63923, 14279287,
    13185787, 314973563, 1139062, 45562, 63923, 26854537, 610537, 944829697, 26289562, 45562,
    63923, 630448447, 592447, 13185787, 629901562, 45562, 63923, 316067197, 314973697, 39411563,
    1139062, 45562, 63923, 1157422, 63922, 26289563, 45563, 27383062, 26289562, 1139062, 45562,
    63923, 629901698, 45698, 1157287, 63787, 630995062, 1139062, 629901562, 45562, 63923, 26307788,
    63788, 629901697, 45697, 656145562, 629901562, 26289562, 45562, 63923, 354339563, 328095563,
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    64201, 63923, 610537, 64201, 63923, 629901698, 45698, 64201, 27401287, 26307787, 1157287,
    63787, 629901562, 27383062, 657239062, 45562, 63923, 26307787, 63787, 64201, 27383062,
    985835812, 328642312, 45562, 63923, 39976537, 13732537, 64201, 355979812, 657239062, 45562,
    328642312, 63923, 45698, 13732537, 64201, 63787, 13714312, 328642312, 657239062, 45562, 63923,
    63787, 64201, 821537437, 164343937, 657239062, 45562, 63923, 6898162, 64201, 657239062, 45562,
    821537437, 164343937, 63923, 45698, 64201, 1157287, 63787, 328642312, 27383062, 45562, 63923,
    64201, 657239062, 45562, 63923, 610537, 64201, 328642312, 45562, 63923, 629901700, 45700,
    26307787, 64201, 27401287, 63787, 629901562, 27383062, 657239062, 45562, 63923, 316067200,
    316067194, 26307787, 1157287, 63787, 64201, 341217562, 316067062, 27383062, 985835812,
    328642312, 45562, 63923, 13732537, 629901700, 45700, 64201, 63787, 13714312, 328642312,
    657239062, 45562, 63923, 158056444, 63787, 64201, 821537437, 164343937, 657239062, 45562,
    63923, 316067194, 45700, 26307787, 64201, 63787, 341217562, 328642312, 27383062, 45562, 63923,
    158056444, 64201, 821537437, 164343937, 63923, 158056450, 64201, 1150134187, 492940687, 63923,
    158056444, 158056450, 610537, 64201, 787912312, 158056312, 1150134187, 164343937, 63923, 64193,
    26307787, 27401287, 63787, 64201, 629901562, 27383062, 657239062, 45562, 63923, 64193,
    13732537, 63787, 64201, 985835812, 328642312, 657239062, 45562, 63923, 64193, 26307787, 63787,
    341217562, 64201, 27383062, 45562, 63923, 1157287, 26307787, 63787, 64201, 316067062,
    341217562, 27383062, 45562, 63923, 13732537, 63787, 64201, 314973562, 13714312, 328642312,
    45562, 63923, 610537, 64201, 1102840312, 472984312, 63923, 64193, 629901698, 45698, 629901700,
    45700, 26307787, 64201, 27401287, 63787, 629901562, 27383062, 657239062, 45562, 63923, 45700,
    1157287, 64201, 63787, 316067062, 328642312, 27383062, 45562, 63923, 314973700, 39976537,
    64201, 13732537, 39958312, 45562, 958498312, 328642312, 63923, 45698, 316067200, 64201,
    26307787, 1157287, 63787, 328642312, 341217562, 316067062, 27383062, 45562, 63923, 64193,
    316067200, 316067194, 1157287, 63787, 316067062, 64201, 27383062, 985835812, 328642312, 45562,
    63923, 64193, 629901694, 630995200, 14826037, 13732537, 644663812, 64201, 355979812, 657239062,
    45562, 328642312, 63923, 64193, 45698, 629901700, 45700, 13732537, 64201, 63787, 13714312,
    328642312, 657239062, 45562, 63923, 45698, 314973700, 64201, 13732537, 63787, 13714312,
    314973562, 45562, 328642312, 63923, 158056444, 64193, 63787, 64201, 821537437, 164343937,
    657239062, 45562, 63923, 45694, 64193, 6898162, 64201, 657239062, 45562, 492940687, 164343937,
    63923, 158056444, 63787, 64201, 314973562, 492940687, 164343937, 45562, 63923, 314973694,
    6898162, 64201, 1109127937, 45562, 328642312, 164343937, 63923, 64193, 45698, 316067194, 45700,
    1157287, 64201, 63787, 316067062, 328642312, 27383062, 45562, 63923, 158056444, 610537, 64201,
    472984312, 158056312, 164343937, 45562, 63923, 63923, 656145562, 629901562, 26289562, 45562,
    63923, 656145563, 629901563, 26289563, 45563, 63923, 63922, 63923, 63923, 63923, 63923, 63922,
    656145563, 629901563, 26289563, 45563, 656145562, 26289562, 629901562, 45562, 63923, 341217563,
    314973563, 26289562, 45562, 63923, 354339563, 984195563, 629901562, 45562, 63923, 669267563,
    13167563, 656145562, 45562, 63923, 26307787, 63787, 63923, 629901697, 45697, 63923, 63923,
    63923, 63787, 63923, 45697, 63923, 629901698, 45698, 63923, 26307788, 63788, 63923, 63923,
    63923, 45698, 63923, 63788, 63923, 629901698, 45698, 26307787, 63787, 656145562, 26289562,
    629901562, 45562, 63923, 26307788, 63788, 629901697, 45697, 656145562, 629901562, 26289562,
    45562, 63923, 314973698, 26289562, 45562, 63923, 39429788, 629901562, 45562, 63923, 13185787,
    629901562, 45562, 63923, 314973697, 26289562, 45562, 63923, 26289562, 45562, 63923, 629901562,
    45562, 63923, 45698, 63787, 328095562, 629901562, 45562, 63923, 63788, 45697, 354339562,
    26289562, 45562, 63923, 656145563, 26289563, 629901563, 45563, 629901697, 45697, 26307787,
    63787, 656145562, 26289562, 629901562, 45562, 63923, 314973697, 26289563, 45563, 63923,
    39429787, 629901563, 45563, 63923, 26289563, 45563, 63923, 328095563, 26289563, 45563, 45697,
    63787, 26289562, 45562, 63923, 629901698, 45698, 26307788, 63788, 656145563, 629901563,
    26289563, 45563, 63923, 314973698, 26289563, 45563, 63923, 39429788, 629901563, 45563, 63923,
    26289563, 45563, 63923, 45698, 63788, 328095563, 26289563, 45563, 63923, 63922, 629901698,
    45698, 629901697, 45697, 63923, 63922, 26307788, 63788, 26307787, 63787, 63923, 629901698,
    45698, 63923, 26307788, 63788, 63923, 63922, 63923, 63922, 63923, 629901697, 45697, 63923,
    26307787, 63787, 63923, 314973698, 45697, 63923, 39429788, 63787, 63923, 45698, 63923, 63788,
    63923, 63923, 63923, 45697, 63923, 63787, 63923, 63922, 45698, 45697, 63923, 63922, 63788,
    63787, 63923, 314973698, 45697, 63923, 39429788, 63787, 63923, 63922, 26307788, 63788,
    629901698, 45698, 656145563, 629901563, 26289563, 45563, 629901697, 45697, 26307787, 63787,
    656145562, 26289562, 629901562, 45562, 63923, 45698, 26307787, 63787, 341217563, 314973563,
    314973697, 341217562, 314973562, 26289562, 45562, 63923, 63788, 629901697, 45697, 669267563,
    39411563, 39429787, 669267562, 39411562, 629901562, 45562, 63923, 354339563, 328095563,
    314973697, 13185787, 45562, 957951562, 328095562, 63923, 314973698, 63922, 26289563, 45563,
    314973697, 26289562, 45562, 63923, 39429788, 63922, 629901563, 45563, 39429787, 629901562,
    45562, 63923, 314973698, 26307788, 63788, 45697, 341217563, 314973563, 26289562, 45562, 63923,
    39429788, 629901698, 45698, 63787, 669267563, 39411563, 629901562, 45562, 63923, 45698,
    328095563, 63787, 629901562, 45562, 63923, 63788, 354339563, 45697, 26289562, 45562, 63923,
    13185787, 314973563, 45562, 63923, 314973697, 39411563, 45562, 63923, 63922, 26289563, 45563,
    26289562, 45562, 63923, 13185788, 314973563, 45562, 63923, 314973698, 39411563, 45562, 63923,
    13185788, 314973698, 45562, 354339563, 328095563, 63923, 63922, 63788, 45698, 328095563,
    26289563, 45563, 45697, 63787, 328095562, 629901562, 45562, 63923, 13185788, 45698, 314973563,
    314973697, 63787, 13167563, 328095562, 45562, 314973562, 63923, 26289563, 656145563, 45563,
    63923, 26289563, 656145563, 45563, 656145562, 45562, 63923, 63922, 26289563, 656145563, 45563,
    26289562, 656145562, 45562, 63923, 629901563, 328095562, 656145563, 629901562, 63923,
    354339563, 45562, 328095563, 354339562, 63923, 26307787, 63787, 64192, 26289563, 656145563,
    45563, 629901562, 656145562, 45562, 63923, 26308192, 26289563, 45563, 26289562, 63923,
    26307788, 63788, 64193, 629901563, 656145563, 45563, 63923, 26308193, 629901563, 45563, 63923,
    64193, 26289563, 26307787, 63787, 656145563, 45563, 629901562, 656145562, 45562, 63923,
    26308193, 45563, 26289563, 45562, 63923, 26307788, 63788, 64192, 26289563, 656145563, 45563,
    656145562, 45562, 63923, 26308192, 26289563, 45563, 26289562, 45562, 63923, 26307788, 63788,
    64193, 63922, 26307787, 63787, 64192, 26289563, 656145563, 45563, 26289562, 656145562, 45562,
    63923, 26308193, 63787, 64192, 26289563, 45563, 328095562, 26289562, 45562, 63923, 63383,
    13185787, 64192, 957951563, 328095563, 45562, 957951562, 328095562, 63923, 26308193, 63922,
    26308192, 26289563, 45563, 26289562, 45562, 63923, 64193, 45698, 26308192, 629901563,
    328095562, 45563, 629901562, 63923, 64193, 314973698, 63382, 957951563, 45562, 328095563,
    957951562, 63923, 857349563, 454941563, 45563, 63923, 629901562, 454941563, 45563, 45562,
    63923, 63382, 857349563, 454941563, 45563, 857349562, 454941562, 45562, 63923, 63787,
    454941563, 45563, 45562, 63923, 63383, 857349563, 454941563, 45563, 63923, 63788, 454941563,
    45563, 63923, 63788, 63382, 454941563, 629901562, 45563, 454941562, 45562, 63923, 63383, 63787,
    629901562, 454941563, 45563, 45562, 63923, 629901563, 454941563, 45563, 63923, 63922,
    857349563, 454941563, 45563, 857349562, 454941562, 45562, 63923, 63922, 629901563, 454941563,
    629901562, 45563, 454941562, 45562, 63923, 63382, 63787, 629901563, 454941563, 629901562,
    45563, 454941562, 45562, 63923, 63383, 63788, 629901563, 454941563, 45563, 63923, 63383, 63922,
    63382, 857349563, 454941563, 45563, 857349562, 454941562, 45562, 63923, 63922, 63788,
    454941563, 63787, 45563, 454941562, 45562, 63923, 63922, 64598, 63788, 64597, 63787, 629901563,
    454941563, 629901562, 45563, 454941562, 45562,
];
static MULTIPLICITIES: [i32; 4096] = [
    0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 4, 2, 2,
    4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1,
    1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 4, 4, 4,
    4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 2,
    2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 2, 2, 2,
    2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2,
    2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8,
    4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4,
    4, 4, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2,
    2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4,
    2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4,
    2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8,
    4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4,
    4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4,
    4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4,
    2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2,
    2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 2, 2,
    2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 8,
    8, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 4, 2,
    2, 2, 2, 1, 1, 1, 1, 4, 2, 2, 2, 2, 1, 1, 1, 1, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4,
    2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2,
    2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2,
    2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4,
    2, 2, 4, 2, 2, 8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 2, 2, 8, 4, 8, 4, 8, 4, 8, 4, 8,
    4, 8, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 2,
    2, 8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8,
    4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 8,
    4, 8, 4, 8, 4, 8, 4, 8, 4, 16, 8, 8, 8, 4, 16, 8, 8, 8, 4, 16, 8, 8, 8, 4, 16, 8, 16, 8, 16, 8,
    8, 4, 4, 2, 2, 8, 4, 4, 2, 2, 8, 4, 4, 2, 2, 8, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4,
    4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
    1, 1, 1, 1, 1, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8,
    4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2,
    2, 2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2,
    2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4,
    4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2,
    2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 8, 4, 4, 4, 4,
    4, 2, 2, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 8,
    4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 8,
    4, 4, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4,
    2, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 2, 8,
    4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4,
    4, 4, 4, 8, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4,
    4, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 4,
    4, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 2,
    2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 8, 4, 4, 4, 4, 2, 2, 8, 4, 4, 4, 4, 2, 2, 8, 4, 4, 4, 4, 2, 2, 8,
    4, 4, 4, 4, 2, 2, 8, 4, 4, 4, 4, 2, 2, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4,
    4, 8, 4, 4, 4, 8, 4, 4, 8, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 8,
    4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 16, 8, 8,
    8, 8, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 16, 8,
    8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8,
    8, 4, 4, 16, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 8, 8, 4, 4, 4, 4,
    4, 4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 8,
    8, 8, 4, 4, 4, 4, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 4,
    4, 4, 4, 16, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 16, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4,
    4, 4, 16, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 16, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4,
    4, 16, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 16, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4,
    16, 8, 8, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 16, 8, 8,
    8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 8, 8,
    4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 16,
    8, 8, 8, 8, 8, 8, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 32, 16, 16, 16, 16, 16, 16, 8, 8, 8, 8, 8,
    8, 8, 4, 4, 32, 16, 16, 16, 16, 16, 8, 8, 32, 16, 16, 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 4, 4,
    4, 4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 16,
    8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 8, 4, 4, 4, 4,
    4, 16, 8, 8, 8, 8, 4, 4, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 4, 4,
    16, 8, 8, 8, 8, 4, 4, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 2, 1, 1, 4, 4, 2, 2, 2, 4, 8,
    4, 2, 8, 4, 4, 2, 2, 2, 1, 1, 1, 1, 8, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 8,
    4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 8, 4, 4, 4, 2, 2, 2, 8, 4, 4, 4, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 8,
    4, 4, 4, 4, 2, 2, 16, 8, 8, 8, 4, 4, 4, 2, 2, 16, 8, 8, 8, 4, 4, 16, 8, 8, 8, 4, 4, 8, 4, 4, 4,
    4, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 8, 4, 4, 4, 2, 2, 2, 8, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 4,
    4, 4, 4, 2, 2, 2, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 8, 4, 4, 4, 8, 4, 16, 8, 8, 8, 8, 8, 4, 4, 4,
    2, 2, 16, 8, 8, 8, 8, 4, 4, 8, 4, 4, 4, 2, 1, 1, 8, 4, 2, 2, 8, 4, 4, 2, 2, 8, 4, 4, 2, 8, 4,
    2, 2, 8, 4, 2, 8, 4, 4, 2, 2, 2, 8, 4, 4, 16, 8, 8, 4, 2, 16, 8, 4, 4, 16, 8, 4, 16, 8, 8, 4,
    4, 4, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 8, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 8, 4, 4, 2, 2,
    2, 8, 4, 4, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 1, 1, 1, 1, 8, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4,
    4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 8, 4, 4,
    4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 2, 2, 16, 8, 8, 4, 4, 16, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 2,
    2, 2, 2, 1, 1, 1, 1, 16, 8, 8, 8, 8, 8, 4, 4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 8, 8, 4, 4, 4, 4,
    2, 2, 2, 2, 16, 8, 8, 8, 8, 8, 4, 4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 8, 8, 4, 4, 4, 2, 2, 16, 8,
    8, 8, 8, 8, 4, 4, 4, 2, 2, 16, 8, 8, 8, 4, 4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 4, 4, 4, 2, 2, 16,
    8, 8, 8, 8, 4, 4, 4, 2, 2, 2, 16, 8, 8, 8, 8, 4, 4, 4, 2, 2, 2, 16, 8, 8, 8, 4, 4, 4, 16, 8, 8,
    8, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 16, 8, 8, 8, 8, 8, 4, 4, 4,
    4, 4, 4, 2, 2, 2, 2, 16, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 16, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 16, 8,
    8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 2, 2, 16, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 2, 2, 16, 8, 8, 8, 8,
    4, 4, 4, 4, 16, 8, 8, 8, 4, 4, 4, 4, 4, 2, 2, 16, 8, 8, 8, 4, 4, 2, 2, 16, 8, 8, 8, 4, 4, 2, 2,
    16, 8, 8, 8, 8, 4, 4, 4, 4, 4, 16, 8, 8, 8, 8, 4, 4, 4, 4, 4, 32, 16, 16, 16, 16, 8, 8, 8, 8,
    8, 4, 4, 4, 2, 2, 32, 16, 16, 16, 16, 8, 8, 8, 8, 4, 4, 4, 4, 32, 16, 16, 16, 8, 8, 8, 4, 4,
    32, 16, 16, 16, 8, 8, 8, 4, 4, 32, 16, 16, 16, 16, 8, 8, 32, 16, 16, 16, 16, 8, 8, 3, 1, 1, 1,
    3, 3, 9, 3, 3, 1, 6, 3, 3, 2, 2, 1, 1, 18, 9, 9, 6, 3, 3, 6, 3, 3, 2, 1, 1, 6, 3, 3, 2, 2, 2,
    1, 1, 1, 1, 1, 1, 6, 3, 3, 2, 2, 1, 1, 6, 3, 3, 6, 3, 3, 6, 3, 3, 6, 3, 3, 18, 9, 9, 6, 3, 3,
    6, 3, 3, 2, 1, 1, 6, 3, 1, 1, 1, 6, 3, 2, 1, 6, 2, 2, 2, 6, 2, 2, 18, 9, 3, 6, 3, 1, 18, 6, 6,
    2, 12, 6, 6, 6, 4, 3, 3, 2, 2, 2, 1, 1, 12, 6, 6, 4, 4, 2, 2, 2, 2, 12, 6, 6, 6, 3, 3, 2, 2, 1,
    1, 12, 6, 6, 4, 4, 2, 2, 36, 18, 18, 18, 9, 9, 6, 3, 3, 12, 6, 6, 6, 3, 3, 2, 1, 1, 36, 18, 18,
    12, 6, 6, 12, 6, 6, 4, 2, 2, 6, 3, 2, 1, 6, 6, 6, 3, 3, 6, 3, 3, 6, 2, 2, 6, 3, 3, 2, 2, 2, 1,
    1, 1, 1, 1, 1, 12, 6, 6, 6, 4, 3, 3, 2, 2, 2, 1, 1, 12, 6, 6, 4, 4, 2, 2, 2, 2, 12, 6, 6, 6, 6,
    6, 4, 3, 3, 2, 2, 2, 1, 1, 12, 6, 6, 12, 6, 6, 12, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 12, 6, 6, 6,
    6, 6, 6, 3, 3, 3, 3, 12, 6, 6, 4, 4, 2, 2, 2, 2, 12, 6, 6, 3, 2, 1, 12, 6, 4, 2, 12, 6, 4, 2,
    12, 6, 2, 2, 12, 6, 6, 6, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 12, 6, 6, 4, 4, 4, 2, 2, 2, 2, 2, 2,
    12, 6, 6, 6, 4, 3, 3, 2, 2, 2, 1, 1, 12, 6, 6, 4, 4, 2, 2, 2, 2, 24, 12, 12, 12, 12, 6, 6, 6,
    6, 6, 4, 3, 3, 2, 2, 2, 1, 1, 24, 12, 12, 12, 12, 8, 6, 6, 4, 4, 4, 2, 2, 24, 12, 12, 12, 8, 6,
    6, 4, 4, 4, 2, 2, 24, 12, 12, 12, 6, 6, 4, 4, 2, 2, 2, 2, 12, 6, 6, 6, 6, 4, 3, 3, 1, 1, 48,
    24, 24, 16, 4, 4, 4, 4, 24, 12, 12, 8, 6, 2, 12, 4, 24, 12, 8, 24, 12, 12, 8, 6, 6, 6, 6, 3, 3,
    1, 1, 24, 12, 12, 8, 6, 4, 4, 2, 24, 12, 12, 8, 6, 4, 4, 2, 96, 48, 48, 32, 24, 24, 8, 4, 4,
    96, 48, 32, 16, 16, 8, 8, 96, 48, 32, 16, 16, 8, 8, 48, 24, 16, 12, 12, 8, 6, 2, 24, 8, 4, 4,
    48, 24, 16, 8, 8, 24, 12, 12, 12, 8, 6, 6, 3, 3, 1, 1, 24, 12, 12, 12, 12, 12, 8, 6, 6, 6, 4,
    4, 2, 96, 48, 48, 48, 32, 24, 24, 8, 4, 4, 96, 48, 48, 32, 16, 16, 8, 8, 48, 24, 24, 24, 16,
    12, 12, 8, 6, 2, 24, 12, 8, 4, 4, 24, 12, 8, 4, 4, 48, 24, 24, 24, 16, 12, 12, 8, 8, 24, 12,
    12, 6, 6, 4, 3, 3, 1, 1, 96, 48, 24, 24, 16, 4, 4, 4, 4, 48, 24, 24, 12, 12, 8, 6, 2, 24, 12,
    12, 12, 8, 6, 6, 6, 2, 96, 48, 48, 32, 24, 24, 8, 8, 48, 24, 16, 12, 12, 48, 24, 24, 24, 12,
    12, 12, 8, 6, 6, 3, 3, 1, 1, 48, 24, 24, 16, 12, 12, 8, 6, 2, 48, 24, 24, 16, 12, 12, 8, 6, 2,
    48, 24, 24, 16, 12, 12, 12, 8, 6, 6, 6, 2, 48, 24, 24, 24, 24, 12, 12, 8, 6, 4, 4, 2, 48, 24,
    24, 24, 24, 12, 12, 8, 6, 4, 4, 2, 192, 96, 96, 48, 48, 48, 32, 24, 24, 8, 4, 4, 192, 96, 96,
    64, 48, 48, 24, 24, 8, 8, 192, 96, 96, 48, 32, 16, 16, 8, 8, 192, 96, 96, 48, 32, 16, 16, 8, 8,
    192, 96, 96, 64, 48, 32, 32, 16, 192, 96, 96, 64, 48, 32, 32, 16, 96, 48, 48, 48, 24, 24, 16,
    12, 12, 8, 6, 2, 96, 48, 48, 32, 24, 24, 16, 16, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2,
    2, 4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1,
    2, 2, 4, 2, 4, 2, 2, 1, 1, 2, 1, 1, 2, 2, 4, 2, 4, 2, 4, 2, 2, 2, 2, 1, 1, 1, 1, 4, 2, 2, 2, 2,
    1, 1, 1, 1, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 8, 4, 4, 4, 2, 2,
    8, 4, 4, 4, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 8, 4,
    4, 4, 4, 4, 2, 2, 4, 2, 2, 2, 2, 1, 1, 1, 1, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 8, 4, 4, 4, 2, 2,
    4, 2, 2, 2, 1, 1, 4, 2, 2, 2, 1, 1, 4, 2, 2, 4, 2, 2, 4, 2, 4, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4,
    2, 2, 4, 2, 4, 2, 4, 4, 4, 2, 4, 2, 8, 4, 4, 2, 8, 4, 4, 2, 8, 4, 4, 8, 4, 4, 8, 4, 4, 4, 4, 4,
    2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 8, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 4, 4, 4, 2, 2,
    2, 2, 8, 4, 4, 4, 4, 4, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 8, 4, 4, 4, 4, 2,
    2, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 2, 8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 8, 4, 4, 4,
    8, 4, 4, 4, 2, 2, 8, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 2, 2, 16, 8, 8, 8, 8, 4, 4, 4, 4, 4, 2,
    2, 16, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 2, 1, 1, 4, 2, 2, 2, 1, 1, 8, 4, 4, 2, 2, 2, 1, 1, 8, 4,
    4, 2, 2, 8, 4, 4, 2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 1, 1, 8, 4, 4, 2, 2, 8, 4, 4, 4, 2, 1, 1, 8, 4,
    2, 2, 8, 4, 4, 4, 4, 2, 2, 2, 1, 1, 8, 4, 4, 2, 2, 8, 4, 4, 4, 2, 2, 2, 1, 1, 8, 4, 4, 4, 2, 2,
    16, 8, 8, 8, 8, 4, 4, 4, 4, 2, 2, 2, 1, 1, 16, 8, 8, 8, 4, 4, 4, 2, 2, 16, 8, 8, 8, 4, 4, 4, 2,
    2, 16, 8, 8, 4, 4, 4, 2, 2, 16, 8, 8, 8, 4, 4, 2, 2, 16, 8, 8, 8, 4, 4, 2, 2, 3, 1, 1, 1, 6, 3,
    2, 2, 1, 6, 3, 2, 2, 2, 1, 1, 1, 6, 3, 2, 2, 1, 6, 3, 1, 1, 1, 6, 3, 2, 1, 12, 6, 6, 4, 3, 2,
    2, 1, 12, 6, 6, 3, 2, 2, 1, 6, 3, 2, 1, 6, 3, 2, 2, 2, 1, 1, 1, 12, 6, 6, 4, 3, 2, 2, 1, 12, 6,
    6, 6, 4, 3, 2, 2, 1, 12, 6, 6, 3, 2, 1, 12, 6, 6, 3, 2, 2, 2, 1, 1, 1, 12, 6, 6, 4, 3, 2, 2, 1,
    24, 12, 12, 12, 6, 6, 6, 4, 3, 2, 2, 1,
];
static SITE_SYMMETRY_SYMBOLS: [&str; 4096] = [
    "      ", "1     ", "1     ", "-1    ", "-1    ", "-1    ", "-1    ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "2     ", "2     ", "2     ", "2     ", "1     ", "2     ",
    "2     ", "2     ", "2     ", "1     ", "2     ", "2     ", "2     ", "2     ", "1     ",
    "1     ", "1     ", "1     ", "2     ", "2     ", "1     ", "2     ", "2     ", "1     ",
    "2     ", "2     ", "1     ", "2     ", "2     ", "1     ", "2     ", "2     ", "1     ",
    "2     ", "2     ", "1     ", "2     ", "2     ", "1     ", "2     ", "2     ", "1     ",
    "2     ", "2     ", "1     ", "m     ", "m     ", "1     ", "m     ", "m     ", "1     ",
    "m     ", "m     ", "1     ", "1     ", "1     ", "1     ", "1     ", "1     ", "1     ",
    "1     ", "1     ", "1     ", "m     ", "1     ", "m     ", "1     ", "m     ", "1     ",
    "m     ", "1     ", "m     ", "1     ", "m     ", "1     ", "m     ", "1     ", "m     ",
    "1     ", "m     ", "1     ", "1     ", "1     ", "1     ", "1     ", "1     ", "1     ",
    "1     ", "1     ", "1     ", "1     ", "1     ", "1     ", "1     ", "1     ", "1     ",
    "1     ", "1     ", "1     ", "m     ", "m     ", "2     ", "2     ", "2     ", "2     ",
    "2/m   ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "1     ",
    "m     ", "m     ", "2     ", "2     ", "2     ", "2     ", "2/m   ", "2/m   ", "2/m   ",
    "2/m   ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "1     ", "m     ", "m     ", "2     ",
    "2     ", "2     ", "2     ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "2/m   ",
    "2/m   ", "2/m   ", "1     ", "m     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ",
    "m     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "m     ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "m     ", "2     ", "2     ", "-1    ", "-1    ", "2/m   ",
    "2/m   ", "2/m   ", "2/m   ", "1     ", "m     ", "2     ", "2     ", "-1    ", "-1    ",
    "2/m   ", "2/m   ", "2/m   ", "2/m   ", "1     ", "m     ", "2     ", "2     ", "-1    ",
    "-1    ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "1     ", "m     ", "2     ", "2     ",
    "-1    ", "-1    ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "1     ", "m     ", "2     ",
    "2     ", "-1    ", "-1    ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "1     ", "m     ",
    "2     ", "2     ", "-1    ", "-1    ", "2/m   ", "2/m   ", "2/m   ", "2/m   ", "1     ",
    "m     ", "2     ", "2     ", "-1    ", "-1    ", "2/m   ", "2/m   ", "2/m   ", "2/m   ",
    "1     ", "m     ", "2     ", "2     ", "-1    ", "-1    ", "2/m   ", "2/m   ", "2/m   ",
    "2/m   ", "1     ", "m     ", "2     ", "2     ", "-1    ", "-1    ", "2/m   ", "2/m   ",
    "2/m   ", "2/m   ", "1     ", "2     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ",
    "1     ", "2     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ",
    "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ", "2     ", "-1    ",
    "-1    ", "-1    ", "-1    ", "1     ", "2     ", "2     ", "-1    ", "-1    ", "-1    ",
    "-1    ", "1     ", "2     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ",
    "2     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ", "2     ",
    "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ", "2     ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "-1    ",
    "-1    ", "-1    ", "-1    ", "1     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ",
    "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "-1    ", "-1    ", "-1    ", "-1    ",
    "1     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "-1    ", "-1    ", "-1    ",
    "-1    ", "1     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ",
    "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ",
    "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ",
    "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ",
    "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ",
    "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ",
    "2     ", "-1    ", "-1    ", "-1    ", "-1    ", "1     ", "2     ", "-1    ", "-1    ",
    "-1    ", "-1    ", "1     ", "..2   ", "..2   ", "..2   ", "..2   ", ".2.   ", ".2.   ",
    ".2.   ", ".2.   ", "2..   ", "2..   ", "2..   ", "2..   ", "222   ", "222   ", "222   ",
    "222   ", "222   ", "222   ", "222   ", "222   ", "1     ", ".2.   ", ".2.   ", "2..   ",
    "2..   ", "1     ", ".2.   ", ".2.   ", "2..   ", "2..   ", "1     ", ".2.   ", ".2.   ",
    "2..   ", "2..   ", "1     ", "..2   ", "..2   ", "1     ", "..2   ", "..2   ", "1     ",
    "..2   ", "..2   ", "1     ", "1     ", ".2.   ", "2..   ", "1     ", ".2.   ", "2..   ",
    "1     ", ".2.   ", "2..   ", "1     ", "..2   ", "..2   ", "..2   ", ".2.   ", ".2.   ",
    "2..   ", "2..   ", "222   ", "222   ", "222   ", "222   ", "1     ", "..2   ", "..2   ",
    "..2   ", ".2.   ", ".2.   ", "2..   ", "2..   ", "222   ", "222   ", "222   ", "222   ",
    "1     ", "..2   ", "..2   ", "..2   ", ".2.   ", ".2.   ", "2..   ", "2..   ", "222   ",
    "222   ", "222   ", "222   ", "1     ", "2..   ", ".2.   ", "..2   ", "..2   ", ".2.   ",
    "2..   ", "222   ", "222   ", "222   ", "222   ", "1     ", "..2   ", "..2   ", ".2.   ",
    ".2.   ", "2..   ", "2..   ", "222   ", "222   ", "222   ", "222   ", "1     ", "..2   ",
    ".2.   ", "2..   ", "1     ", "m..   ", "m..   ", ".m.   ", ".m.   ", "mm2   ", "mm2   ",
    "mm2   ", "mm2   ", "1     ", "m..   ", "m..   ", ".m.   ", ".m.   ", "mm2   ", "mm2   ",
    "mm2   ", "mm2   ", "1     ", "m..   ", "m..   ", ".m.   ", ".m.   ", "mm2   ", "mm2   ",
    "mm2   ", "mm2   ", "1     ", "m..   ", "m..   ", "1     ", "m..   ", "m..   ", "1     ",
    "m..   ", "m..   ", "1     ", "m..   ", "m..   ", "1     ", "m..   ", "m..   ", "1     ",
    "m..   ", "m..   ", "1     ", "..2   ", "..2   ", "..2   ", "..2   ", "1     ", "..2   ",
    "..2   ", "..2   ", "..2   ", "1     ", "..2   ", "..2   ", "..2   ", "..2   ", "1     ",
    "m..   ", "..2   ", "..2   ", "1     ", "m..   ", "..2   ", "..2   ", "1     ", "m..   ",
    "..2   ", "..2   ", "1     ", "m..   ", "..2   ", "..2   ", "1     ", "m..   ", "..2   ",
    "..2   ", "1     ", "m..   ", "..2   ", "..2   ", "1     ", "1     ", "1     ", "1     ",
    "1     ", "1     ", "1     ", "..2   ", "..2   ", "1     ", "..2   ", "..2   ", "1     ",
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    "..2   ", "m2m   ", "..2/m ", "..2/m ", "1     ", "m..   ", "..m   ", "..2   ", "..2   ",
    "m2m   ", "..2/m ", "..2/m ", "1     ", "m..   ", ".m.   ", ".m.   ", ".2.   ", "mm2   ",
    "mm2   ", ".2/m. ", ".2/m. ", "1     ", "m..   ", ".m.   ", ".m.   ", ".2.   ", "mm2   ",
    "mm2   ", ".2/m. ", ".2/m. ", "1     ", "m..   ", "..2   ", "2..   ", "2/m.. ", "2/m.. ",
    "1     ", "m..   ", "..2   ", "2..   ", "2/m.. ", "2/m.. ", "1     ", "2..   ", "..2   ",
    "-1    ", "1     ", "2..   ", "..2   ", "-1    ", "1     ", "..m   ", "..2   ", "..2   ",
    "..2/m ", "..2/m ", "1     ", ".m.   ", "..2   ", "-1    ", "1     ", ".m.   ", "..2   ",
    "-1    ", "1     ", ".m.   ", "m..   ", "-1    ", "mm2   ", "mm2   ", "1     ", "..m   ",
    ".m.   ", "m..   ", "..2   ", "mm2   ", "mm2   ", "m2m   ", "2mm   ", "..2/m ", "mmm   ",
    "mmm   ", "1     ", ".m.   ", "m..   ", "..2   ", ".2.   ", "2..   ", "mm2   ", ".2/m. ",
    "2/m.. ", "222   ", "1     ", "2..   ", "4..   ", "4..   ", "1     ", "2..   ", "2..   ",
    "2..   ", "-4..  ", "-4..  ", "1     ", "m..   ", "2..   ", "4..   ", "4..   ", "2/m.. ",
    "4/m.. ", "4/m.. ", "1     ", "2..   ", "-1    ", "4..   ", "-4..  ", "1     ", "2..   ",
    "-1    ", "4..   ", "-4..  ", "1     ", ".2.   ", ".2.   ", "..2   ", "2..   ", "4..   ",
    "4..   ", "222   ", "422   ", "422   ", "1     ", "..2   ", "2..   ", "4..   ", "2.22  ",
    "1     ", ".m.   ", ".m.   ", "..m   ", "2mm.  ", "4mm   ", "4mm   ", "1     ", "..m   ",
    "2.mm  ", "4..   ", "1     ", "..m   ", "2..   ", ".2.   ", ".2.   ", "2.mm  ", "2.mm  ",
    "222   ", "-42m  ", "-42m  ", "1     ", "..m   ", "2..   ", "2.mm  ", "-4..  ", "1     ",
    ".m.   ", ".m.   ", "..2   ", "2mm.  ", "2mm.  ", "2mm.  ", "-4m2  ", "-4m2  ", "1     ",
    "..2   ", "2..   ", "2..   ", "2.22  ", "-4..  ", "1     ", ".m.   ", ".m.   ", "..m   ",
    "m..   ", "m2m.  ", "m2m.  ", "m.2m  ", "2mm.  ", "4mm   ", "4mm   ", "mmm.  ", "4/mmm ",
    "4/mmm ", "1     ", "..m   ", ".2.   ", "..2   ", "2.mm  ", "4..   ", "..2/m ", "-42m  ",
    "422   ", "1     ", "..m   ", ".2.   ", "..2   ", "2.mm  ", "4..   ", "..2/m ", "-42m  ",
    "422   ", "1     ", "..m   ", "m..   ", "m.2m  ", "2.mm  ", "4..   ", "m.mm  ", "4/m.. ",
    "1     ", "..m   ", ".m.   ", "..2   ", "2mm.  ", "..2/m ", "4mm   ", "-4m2  ", "1     ",
    "..m   ", ".m.   ", "..2   ", "2mm.  ", "..2/m ", "4mm   ", "-4m2  ", "1     ", "3..   ",
    "3..   ", "3..   ", "1     ", "-1    ", "3..   ", "3..   ", "-3..  ", "1     ", "..2   ",
    "3..   ", "3..   ", "3..   ", "3.2   ", "3.2   ", "3.2   ", "1     ", ".2.   ", "3..   ",
    "3..   ", "32.   ", "1     ", ".m.   ", "3m.   ", "3m.   ", "3m.   ", "1     ", "..m   ",
    "3..   ", "3.m   ", "1     ", "..m   ", "..2   ", "3..   ", "..2/m ", "3.m   ", "3.2   ",
    "-3.m  ", "1     ", ".m.   ", ".2.   ", ".2/m. ", "3m.   ", "3m.   ", "-3m.  ", "1     ",
    "2..   ", "3..   ", "6..   ", "1     ", "m..   ", "3..   ", "3..   ", "3..   ", "-6..  ",
    "-6..  ", "-6..  ", "1     ", "m..   ", "2..   ", "3..   ", "2/m.. ", "6..   ", "-6..  ",
    "6/m.. ", "1     ", "..2   ", ".2.   ", "2..   ", "3..   ", "222   ", "6..   ", "3.2   ",
    "622   ", "1     ", ".m.   ", "..m   ", "2mm   ", "3m.   ", "6mm   ", "1     ", ".m.   ",
    "m..   ", "mm2   ", "3m.   ", "3m.   ", "3m.   ", "-6m2  ", "-6m2  ", "-6m2  ", "1     ",
    "m..   ", "..m   ", "3..   ", "m2m   ", "3.m   ", "-6..  ", "-62m  ", "1     ", "m..   ",
    ".m.   ", "..m   ", "mm2   ", "m2m   ", "2mm   ", "3m.   ", "mmm   ", "6mm   ", "-6m2  ",
    "6/mmm ",
];

// --- Logic Functions ---

pub fn ssmdb_get_coordinate(index: usize) -> (Mat3I, Vec3, i32) {
    let mut rot = [[0; 3]; 3];
    let mut trans = [0.0; 3];

    let rot_enc = COORDINATES_FIRST[index] % 91125; // 45^3
    let rows = [rot_enc / 2025, (rot_enc % 2025) / 45, rot_enc % 45];

    for i in 0..3 {
        rot[i][0] = rows[i] / 9 - 2;
        rot[i][1] = (rows[i] % 9) / 3 - 1;
        rot[i][2] = rows[i] % 3 - 1;
    }

    let trans_enc = COORDINATES_FIRST[index] / 91125;
    let trans_int = [trans_enc / 576, (trans_enc % 576) / 24, trans_enc % 24];

    for i in 0..3 {
        trans[i] = trans_int[i] as f64 / 24.0;
    }

    (rot, trans, MULTIPLICITIES[index])
}

pub fn ssmdb_get_wyckoff_indices(index: i32) -> (i32, i32) {
    if index > 0 {
        let idx = index as usize;
        (
            POSITION_WYCKOFF[idx],
            POSITION_WYCKOFF[idx + 1] - POSITION_WYCKOFF[idx],
        )
    } else {
        let idx = (-index) as usize;
        (
            POSITION_LAYER_WYCKOFF[idx],
            POSITION_LAYER_WYCKOFF[idx + 1] - POSITION_LAYER_WYCKOFF[idx],
        )
    }
}

pub fn ssmdb_get_site_symmetry_symbol(index: usize) -> String {
    let symbol_raw = SITE_SYMMETRY_SYMBOLS[index];
    // In C: spgdb_remove_space modifies char array in place.
    // In Rust: we trim and return String.
    symbol_raw.trim().to_string()
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_get_coordinate() {
        // Test index 1 (Space group 1, Wyckoff 1a?) -> 63923
        // 63923 % 91125 = 63923
        // rows = [31, 25, 8]
        // rot[0] = [31/9-2, (31%9)/3-1, 31%3-1] = [1, 0, 1] -> Wait, 31/9=3, 3-2=1. (31%9)=4, 4/3=1, 1-1=0. 31%3=1, 1-1=0. -> [1, 0, 0]
        // rot[1] = [25/9-2, (25%9)/3-1, 25%3-1] = [0, 1, 0]
        // rot[2] = [8/9-2, (8%9)/3-1, 8%3-1] = [-2, 1, 1] -> Wait. 8/9=0, 0-2=-2. (8%9)=8, 8/3=2, 2-1=1. 8%3=2, 2-1=1. -> [-2, 1, 1]
        // Something is wrong with my manual calc or the C logic is tricky.
        // Let's trust the code translation.

        let (rot, trans, mult) = ssmdb_get_coordinate(1);
        // 63923 -> Identity rotation, 0 translation
        assert_eq!(rot, [[1, 0, 0], [0, 1, 0], [0, 0, 1]]);
        assert_eq!(trans, [0.0, 0.0, 0.0]);
        assert_eq!(mult, 1);
    }
}