use deterministic_trigonometry::DTrig; #[test] fn main() { // Assigns 10,000 random numbers between -100,000 and 100,000 let random_array_1 = random_array_1(); // Assigns 10,000 random numbers between -100,000 and 100,000 let random_array_2 = random_array_2(); let d_trig = DTrig::initialize(); for numerator in random_array_1.iter() { for denominator in random_array_2.iter() { test_all_functions(*numerator, *denominator, &d_trig); } } for numerator in -10000..10001 { for denominator in 1..10001 { test_all_functions(numerator, denominator, &d_trig); } } // A variable that in intentionally never read. let mut _not_read; // This part just makes sure that none of these operations cause panics. _not_read = d_trig.sine((i32::MAX, 1)); _not_read = d_trig.sine((i32::MIN, 1)); _not_read = d_trig.cosine((i32::MAX, 1)); _not_read = d_trig.cosine((i32::MIN, 1)); _not_read = d_trig.tangent((i32::MAX, 1)); _not_read = d_trig.tangent((i32::MIN, 1)); _not_read = d_trig.arctangent((i32::MAX, 1)); _not_read = d_trig.arctangent((i32::MIN, 1)); } fn test_all_functions(numerator: i32, denominator: i32, d_trig: &DTrig) { let mut test: bool; let fraction_as_f64 = (numerator as f64) / (denominator as f64); /* This captures that sine is accurate to the nearest 1/1000 from 0 to 2 PI with a denominator that is factor of 1000 and accurate to +/- 1/1000 otherwise. */ if fraction_as_f64 >= 0.0 && fraction_as_f64 <= 2.0 * std::f64::consts::PI && 1000 % denominator == 0 { if ((fraction_as_f64.sin() * 1000.0).round() as i32) == d_trig.sine((numerator, denominator)).0 { test = true; } else { test = false; } } else { if ( ((fraction_as_f64.sin() * 1000.0).round() as i32) - d_trig.sine((numerator, denominator)).0 ).abs() <= 1 { test = true; } else { test = false; } } assert!(test == true); /* This captures that cosine is accurate to the nearest 1/1000 from 0 to 2 PI with a denominator that is factor of 1000 and accurate to +/- 1/1000 otherwise. */ if fraction_as_f64 >= 0.0 && fraction_as_f64 <= 2.0 * std::f64::consts::PI && 1000 % denominator == 0 { if ((fraction_as_f64.cos() * 1000.0).round() as i32) == d_trig.cosine((numerator, denominator)).0 { test = true; } else { test = false; } } else { if ( ((fraction_as_f64.cos() * 1000.0).round() as i32) - d_trig.cosine((numerator, denominator)).0 ).abs() <= 1 { test = true; } else { test = false; } } assert!(test == true); /* This captures that tangent is accurate to the nearest 1/1000 from 0 to 2 PI with a denominator that is factor of 1000 and accurate to +/- 1/1000 or +/- 2% otherwise unless it is close to an asymptote. */ if fraction_as_f64 >= 0.0 && fraction_as_f64 <= 2.0 * std::f64::consts::PI && 1000 % denominator == 0 { if ((fraction_as_f64.tan() * 1000.0).round() as i32) == d_trig.tangent((numerator, denominator)).0 { test = true; } else { test = false; } } else { // If it is farther than .2 from an asymptote, then it should be within .001 or 2% if ((fraction_as_f64 - std::f64::consts::PI / 2.0) % std::f64::consts::PI).abs() >= 0.2 && ((fraction_as_f64 - std::f64::consts::PI / 2.0) % std::f64::consts::PI).abs() <= std::f64::consts::PI - 0.2 { if ( ((fraction_as_f64.tan() * 1000.0).round() as i32) - d_trig.tangent((numerator, denominator)).0 ).abs() <= 1 || ( (fraction_as_f64.tan() * 1000.0).round() - (d_trig.tangent((numerator, denominator)).0 as f64) ).abs() / (fraction_as_f64.tan() * 1000.0).round() < 0.02 { test = true; } else { test = false; } // If it is between .2 and .02 of a asymptote it should be within 10%. } else if (fraction_as_f64 - std::f64::consts::PI / 2.0) % std::f64::consts::PI >= 0.02 && ((fraction_as_f64 - std::f64::consts::PI / 2.0) % std::f64::consts::PI).abs() <= std::f64::consts::PI - 0.02 { if ( (fraction_as_f64.tan() * 1000.0).round() - (d_trig.tangent((numerator, denominator)).0 as f64) ).abs() / (fraction_as_f64.tan() * 1000.0).round() < 0.1 { test = true; } else { test = false; } // If it is any closer than .02 to an asymptote, all bets are off. } else { test = true; } } assert!(test == true); /* This captures that arcsine is accurate to the nearest 1/1000 if the denominator is a factor of 1000 or is accurate to +/- 1/1000 if it is between -0.9 and 0.9 */ if fraction_as_f64 >= -1.0 && fraction_as_f64 <= 1.0 && 1000 % denominator == 0 { if ((fraction_as_f64.asin() * 1000.0).round() as i32) == d_trig.arcsine((numerator, denominator)).0 { test = true; } else { test = false; } } else if fraction_as_f64 >= -0.9 && fraction_as_f64 <= 0.9 { if ( ((fraction_as_f64.asin() * 1000.0).round() as i32) - d_trig.arcsine((numerator, denominator)).0 ).abs() <= 2 { test = true; } else { test = false; } } else { // Arcsine incorrectly gives -PI/2 or PI/2 on purpose if the domain is out of the allowed range. // If the fraction is below -.9 or above .9 and the denominator is not a factor of 1000 all bets are off. test = true; } assert!(test == true); /* This captures that arccosine is accurate to the nearest 1/1000 if the denominator is a factor of 1000 or is accurate to +/- 1/1000 if it is between -0.9 and 0.9 */ if fraction_as_f64 >= -1.0 && fraction_as_f64 <= 1.0 && 1000 % denominator == 0 { if ((fraction_as_f64.acos() * 1000.0).round() as i32) == d_trig.arccosine((numerator, denominator)).0 { test = true; } else { test = false; } } else if fraction_as_f64 >= -0.9 && fraction_as_f64 <= 0.9 { if ( ((fraction_as_f64.acos() * 1000.0).round() as i32) - d_trig.arccosine((numerator, denominator)).0 ).abs() <= 2 { test = true; } else { test = false; } } else { // Arccosine incorrectly gives -PI/2 or PI/2 on purpose if the domain is out of the allowed range. // If the fraction is below -.9 or above .9 and the denominator is not a factor of 1000 all bets are off. test = true; } assert!(test == true); /* This captures that arctangent is accurate to the nearest +/- 1/1000 if the denominator is a factor of 1000 and the input fraction is between -4 and 4 and to the nearest +/- 2/1000 otherwise */ if fraction_as_f64 >= -4.0 && fraction_as_f64 <= 4.0 && 1000 % denominator == 0 { if ( ((fraction_as_f64.atan() * 1000.0).round() as i32) - d_trig.arctangent((numerator, denominator)).0 ).abs() <= 1 { test = true; } else { test = false; } } else { if ( ((fraction_as_f64.atan() * 1000.0).round() as i32) - d_trig.arctangent((numerator, denominator)).0 ).abs() <= 2 { test = true; } else { test = false; } } assert!(test == true); } fn random_array_1() -> [i32; 10000] { return [ 8923, 91750, 605, -68668, 97699, 29935, -66713, -39775, 53832, 7895, 74098, -77044, -74520, 37135, 34322, -37124, 23092, 28608, -48531, -99352, 40755, 82624, 3822, 55985, 18778, -2047, 52702, -35875, 12418, -94292, 76534, 49648, -70531, 54128, -93940, 87198, -23824, -89023, -77919, 65182, -63407, -19773, 19719, 65411, 3419, 98485, 13050, -6207, 42316, 24442, 79193, 79185, 25819, 62479, 59394, -26958, -24100, 42946, 47703, -36440, 18778, 1279, 32444, 31609, -66195, -70644, 50274, 92380, 29319, -58891, 60012, 13321, -66167, 63592, 1300, 65268, 14061, -26998, 28473, 44569, 75482, 55166, 6784, 32637, -64661, -52588, 56282, 52334, -45681, -28425, -77928, 87398, 61966, 91458, 34750, 5998, 93782, 8822, 1285, 70236, -1134, 20734, -61163, 62785, 5979, 22929, 34653, -98085, 7100, 37373, 86385, 88848, 98878, 46922, 97131, 9387, -76827, 14224, 46161, 31150, 61547, 61608, 14375, 69857, 41082, 60377, -3121, 22958, 58847, -54050, -9852, 97188, -36702, 21312, -59883, -25471, 66191, 2107, -83653, 71019, 35989, -16880, 99192, -81395, 41017, 46448, 88030, -46373, 13835, 13274, 80676, -92737, 37929, 84357, -6736, 38446, -72147, 77017, 77908, 83727, 54591, -56992, 40692, 45394, -87642, 81118, 86382, -91021, 62341, -96199, 29599, -50719, 82507, 68786, 64374, 4329, 37147, 29235, 36145, 1447, 79255, 62669, 34765, 54161, 48969, 34671, 24618, 24178, -69645, -30720, 15704, 11256, 45225, 59789, -48440, 7963, 29539, -11113, -93481, 33467, 30951, 79944, 31652, -44575, 72138, 37239, 26517, 36806, 10183, 78912, -71468, 33862, 76211, 54060, -66060, 22054, -59872, -9875, 56503, 9748, 94597, 19110, -91835, -81956, 36814, 18180, 37255, 77418, 73744, 38114, 56643, 7060, 73182, 83210, 47122, 47315, 70903, -68883, -46618, 86294, 73129, 57454, -17620, 69043, 34136, 75275, -10242, -70319, 44476, 95228, 80277, 96401, 14378, -21752, 91680, 73255, 52184, 62519, 73662, -66856, 36687, 39025, -40952, 16274, 16785, 34269, -8731, -18414, 5975, 52297, 81821, 38486, -29806, 19874, 12911, -94071, 86461, -73688, 85671, 29404, -31785, 86574, 6516, -81705, 34509, -2442, 46438, 87886, 6699, 71089, -48395, 70040, 15873, 62989, -60564, -8672, 43199, 54674, 44709, 43809, 67059, -13043, -48921, -12082, 47145, -84323, 28892, 68892, 87138, 54214, 53878, -39974, 87812, -32134, 87223, 32933, 18759, 94908, -16882, 68979, 81726, 74465, 37106, 85623, 75341, 74765, 18327, -11111, 92120, 86748, 29901, 20780, 57787, 97962, 46075, 2767, 64872, -89906, 28302, 40174, 25558, 482, 34751, 78962, 23352, 87907, -64165, 66517, 59026, 58435, 85335, -38390, 94170, 65770, 2683, -27799, 91285, 37895, -33708, -34372, 9951, 4835, 70547, 27778, 59247, 70136, 60767, 8457, 44290, 78463, 60066, 30687, 91076, 77978, 38622, 86289, 17981, 36049, 18250, 35032, 70013, 65057, 80046, -43953, 92454, 91766, 50021, 87334, -69611, -98370, -2010, 27459, 76868, 85083, 77816, -669, -78229, 77094, 43554, -63598, 94189, 47620, 50508, 94517, 7714, -29039, 99142, 15861, 15445, -34344, 99706, 45590, 77265, -20091, -84247, 32760, -73108, 93147, 27366, 13491, -17941, 3284, 82054, 70607, 79248, 22936, 55652, 60902, 64356, 69834, 43601, 65840, 95632, 79415, -68560, 71751, -22080, 45529, 98288, 59916, 52627, -56148, 66096, 29015, 40327, -84476, 14372, -66391, 29546, 63238, 17490, 31337, 38063, 98861, 93984, 5400, 66794, 7696, 12031, 34031, 6704, -99927, -53970, 80117, 52437, -5797, 57382, 17208, 79977, 35349, 72907, 78329, 17445, 4736, 84370, -56689, -43173, -61428, 79948, 48761, 78488, 7118, 89431, 31001, 67466, 62145, 62395, 68597, 15649, 38228, 23002, -17130, 35179, 83575, 13929, 7683, -46530, 78925, 78835, 80167, -75423, 6407, -68414, 18708, 22986, -31595, 75050, -88824, -31073, 42370, -96939, -95920, 76130, 94247, -60436, 73245, 29865, 93531, 77410, 18482, 21078, 15134, -99400, 24607, -40732, 63656, 12026, 77440, -89409, 15441, 1464, 6393, -69408, 48308, 18294, 19993, 8252, -33291, -54852, 91008, -78542, -99215, 27005, 52591, 99641, 40219, 86388, -96720, 71479, 82776, -53837, -84813, -71748, 36802, 39027, 33272, -43411, 4541, 17995, 11964, 33849, -46478, 39073, 73180, 67622, 63742, -21836, 96758, 79187, 5158, 18927, 34844, 61533, 13101, -54889, 40825, -27137, 64229, 6827, 87430, 48652, 92455, -23645, 60691, 39717, 74080, 65628, 831, 31962, -65926, 55992, 338, -77494, 28977, -83392, 53680, 37403, 50853, 27479, 43045, -1582, 779, 61037, 27453, 39675, 26057, 52362, 43373, 33676, -50734, 53849, 66016, 7065, 55991, -61380, 39466, 83289, 49844, -1609, -57658, -45507, 60731, 48317, 46603, 42875, 28895, -5514, -28551, -75835, 23947, 49362, 74466, 85888, -31763, 37387, -8051, -98564, 15628, 96529, -77468, 78378, 61897, 98170, 24766, 95294, 38540, 86522, 69228, 98844, 41684, 6035, 27106, 4446, 44734, 24895, 61604, -12534, -21393, 511, 12521, 56386, 92674, 64913, -27697, 990, -78521, 60861, -2138, -7738, 30547, 66965, -11328, 82937, 91758, -80936, 83118, 92289, 12530, 96793, 88492, 42657, -87664, -36828, -73461, 86981, 38639, -95038, 18603, 1663, 72624, 53139, -4701, 49961, 23881, 28904, -48067, -35418, -27967, 52158, 98586, 66437, -51990, 50119, -12338, 9145, 80941, 12724, 99740, 99630, 27076, 91046, 2781, 26633, -4591, 58830, 61531, -41133, 29400, 25486, 3772, -17732, 51109, 33360, 30390, 92453, -17471, 80366, 91903, 33727, 74509, 48030, 47166, 48389, 86304, 70560, 15195, 98687, -76087, 16441, 95399, -85885, -53757, -98910, 70358, -79246, -77684, 94242, 88938, 59428, -34811, 17151, 90944, 4860, 51245, 77537, -57475, 5066, -99724, 48858, -12195, 7792, 36443, 78362, 65540, 16581, -1515, 37221, 86081, 56213, 47148, 39953, 68199, 42203, -14054, -75806, 61176, -92656, 73590, 61443, -84163, -4543, -78754, 73897, 67653, 1509, 73122, 99445, 83583, 56704, 97464, 52438, 53362, -64441, 63116, -90457, -13747, 88412, 30185, 32588, 36944, -39523, 57291, 23182, 90933, 79850, 85481, -35160, 29881, -25239, 80569, 3114, 9447, -36371, 31069, 67019, -78977, 84184, 63742, -53254, -97638, 15211, -55689, 12412, 78305, -65424, 20598, 89103, 96143, -17575, 19119, 37050, 13102, 6282, 3028, 95739, -74377, 11836, 60996, -78800, 28531, -52680, -66197, 99509, 69545, -9395, -56320, 61223, 88381, 17635, 56897, 54924, 93163, 80432, 61863, 27391, -19035, -46462, 67072, 841, -97188, 57470, 43633, 30739, -38246, 76530, 31338, 4503, 60009, 76604, -96014, 83766, 70386, 80266, 13762, 99393, -35476, -46270, -63596, 80693, 29287, 42036, 46712, 58988, -62246, 15699, 54604, -27574, -51493, 19170, 11064, 93865, 94680, 89941, 64222, 55720, -54014, 23492, 31748, 11306, -38109, 60659, -79090, 22294, 77574, 77678, 21975, 46874, 76612, 53154, 70563, -82308, 55193, 58436, 98215, 87769, 29730, 36209, 30046, 79232, 24648, -32522, 54104, 63495, -68409, 72343, -71911, 72638, 43147, 8765, 95752, 88862, 34681, 78807, 59967, 91338, -95890, -4228, 66069, 37709, -24900, 38482, 83269, 51189, 56669, 70584, -42951, 58247, 14948, 98791, 54154, 11218, 6062, 27255, 705, 41666, 11525, 37265, -12902, 15532, 68115, -87872, -43385, 17632, -37710, -51274, -56911, 27375, 46209, 97287, -38385, 70722, 98323, 12524, 80912, 19207, 67302, 89424, 98466, 88047, 47094, 75024, -38968, -83808, 52317, 23053, 1432, 45682, 37108, 18118, -53402, -40576, 73222, 46057, 42035, 49151, 9539, 60215, 93741, -29050, 30479, 50253, 94111, 72033, 52052, 26993, 19101, -63921, -65880, 58486, 2687, -15255, 46690, 39935, 30227, 76870, -51100, -93040, 63027, 30974, 82310, -48730, 35565, 4513, 74812, 72471, 44237, -36679, 98077, 16257, -75884, 69412, 33769, -33704, 18725, 35172, 79520, 68539, 89378, 62946, -91046, 11918, 84509, 97852, -34002, 19910, 55420, 7721, 73848, 54239, -86634, 71093, 216, -15330, 68273, 34480, -60872, 97377, -21617, 70247, 306, 42300, 39225, 76445, 8567, 67478, -69277, 40372, 59097, 23137, -81065, 80226, 84957, -8100, -41097, 1623, 50674, 49100, 88649, 90046, 69409, 73409, -36806, -68878, 74130, 27022, 52510, 62352, 17617, -71609, 87743, -4054, 77853, 27728, -42379, 94272, 81779, 92564, 29805, -72413, 62341, 22514, 1003, 29018, 30136, 38682, 59206, 64347, 5191, 2415, 47222, 90098, 98662, 23726, 80931, 47101, 83148, 71181, 18078, 39802, -77132, 75180, -33297, 59367, -88360, 70127, 42763, -76588, 79074, 38815, 51921, 21956, 33529, 13346, 66598, -90199, -77948, 21045, 12950, 42943, 16408, 10637, 10584, 17832, 58086, 68549, 56253, 22773, 54255, 86196, 35993, -402, -62399, 63718, 57866, 55137, 70498, 6061, -44909, 69520, 16299, 14304, -87348, -2976, 33261, 1653, 38850, 17994, 80342, 60290, 80044, 37213, -37150, 87239, 21061, -64061, 88179, 70623, 92003, 81235, 93886, 58253, 28858, -66611, 18729, 73468, 75336, -27540, -53755, 14874, 48697, 62421, -87394, 32281, 82606, -57140, 55278, 38235, -66551, 60769, -82621, 94810, -42829, -75454, -87653, 64325, 59790, 38055, 25202, 4358, -95833, 34880, 14991, -84104, -15084, -99049, -86288, 11624, 33070, 17708, 38376, 30866, -9903, 94392, 93516, 59833, 31634, -56421, 56293, 41788, 12389, 91104, 40189, -28551, 72616, -43145, 79076, 6728, 11888, 70093, -70574, -18076, -78097, 61653, 48993, 10995, -10161, 98404, 28900, 44581, 76476, -2205, 83786, -10873, 33958, -73574, 95646, 56738, 21300, 57623, 7834, 54518, -91655, 24209, 68416, 63245, -39482, 551, 35991, 56236, 6476, 20618, 20602, 45879, -46268, -28529, 57923, 73471, 1366, 52576, -87568, 55499, 58780, 66573, 56806, 9230, 4239, 86534, 95464, 54217, -12082, 28875, 34936, -81785, 19481, -630, 29741, 1010, 55510, 42188, 42367, 86241, 48364, 64254, 23438, -37863, 71964, -57947, 3175, 53327, 86430, 52433, 79232, -25969, -26918, 48085, 774, 63613, 2217, -48803, -80464, 52314, 43935, 65326, 32936, 50523, 89130, 85436, 94654, 39847, -39180, -39065, -1896, 57119, 2913, 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-69410, 92921, 77546, 71958, 59431, 50050, 32408, 3257, 94501, -82290, 51335, 97587, 96443, 50479, -52823, -13592, 20115, 96206, 54501, 94831, -40078, -87163, 59740, -95426, 89533, -56789, 35269, 71462, 4721, 85472, -65480, -24785, 36849, 24672, 72306, 82389, 66023, -87415, 12832, -53433, -70402, 99158, 47004, 26458, 65212, -43435, 55674, -91957, 58954, 59368, -52119, -99049, -32648, -52622, 27762, 66010, 76178, 24590, 3154, 70769, 45834, 89262, 72184, -88726, 43461, 83598, 51542, 50424, 17706, 73144, 1828, 65280, 89012, 6613, 49307, -65584, 21333, -60722, 23865, 58549, 23315, 69734, 86770, 63364, 50730, 97252, 54754, 89406, 65326, 80324, 30914, 36696, 11213, -12862, -3565, -5674, 83245, -6700, 50390, 5955, 23844, 87953, -34088, 64643, 94904, 35792, 87113, 24532, 71775, 46428, 10751, -46894, 14067, -55580, 14762, 7403, 45805, -29657, 75611, 65716, 55573, 30585, -99115, 64430, -2745, 26527, 39848, 13241, 496, 29997, 88295, 42861, 55603, -11476, -5653, 35918, 3297, 89960, 64167, 48239, -119, 61847, 42619, 95000, 9364, 30270, 68290, 68997, -48165, -65453, -7641, 32683, 82618, 13385, 4516, 25273, -62248, 40229, 23773, -78064, 8011, 50472, 60975, 91985, 27431, -20014, 98932, 19686, 47980, -47046, 6323, 68819, 48200, 30583, 12070, 91698, -36844, -24835, 20556, 41318, 27095, 35570, 56797, -20419, 41591, 24952, 41567, 30895, 71282, 56888, 96736, 54248, 26746, 2556, -73328, 44901, 69838, 85829, -69232, 94509, -43465, -29558, -18527, 29435, 47919, 63874, 99608, 26874, 48507, 46790, 95659, 60266, -15327, 22369, -37826, 96883, -73193, -19004, 22589, 5109, 39966, 68497, 15477, 15844, 86415, 90811, 59124, -22423, 76331, 26827, 55579, 40240, -29559, 57763, 5761, 3656, 8438, 71013, 66461, 24802, 16483, -87538, 42300, 54751, 67380, 29426, 15314, -8021, 41619, 44310, 70273, 43209, 73117, 54295, 79041, -86182, 19121, 36364, 45656, -14063, 37041, 34912, 45353, -18756, 79772, 89423, 58694, -12381, 43649, -81149, 43239, 90213, 35891, ]; } fn random_array_2() -> [i32; 10000] { return [ 17448, 78363, -28250, 81820, -16365, 53384, -85473, 41082, 90083, 45939, -63826, 17726, -26015, 95822, -55159, -42804, 73709, -18174, 46068, -98185, 25827, 39115, 18620, 90270, -74808, 13047, 52921, 5507, 64924, 22151, 64004, 82256, -66928, 89030, -42724, 20915, 16645, 64689, 86651, 88657, 81378, 12294, -69734, 55241, -89950, 33145, 96829, 24670, 2861, -53671, 21822, 38700, 97948, 52477, -82141, 42469, -22581, -52821, -56552, 7255, -56081, -40086, 95057, -77623, 20213, -73874, -41590, -75568, 26920, 18364, -38780, 61293, 84701, -47850, -3068, 62569, 5839, 18501, 5813, -24988, 41130, 85875, -21916, 23479, -38034, 86032, -24533, -60043, 41955, -82533, 62561, 74076, 21691, -60579, 63243, -94961, 34179, -68575, 37682, 485, 3383, -4206, 58299, -11662, 78165, 52216, 39192, -22474, 2818, 32503, -13101, 67001, -69098, 52448, 53540, 15298, -49080, -16763, 76436, 50124, 96632, 45897, 46602, -30364, 29903, 45474, 56675, -73368, 55462, 23522, 63646, -42556, 15987, 81073, 35902, 44793, 70291, 1036, 3982, 34015, 75784, 32226, 11012, 66419, -9085, 45875, -83040, 78278, 68236, 92840, 62249, -20819, -23784, 80297, 79115, 45888, 19398, 65465, 69071, -4034, 35599, -23860, 24740, 36132, -58958, 95606, 27590, 99385, 67502, 38683, -62042, -22480, 81982, 37863, 28767, 43900, -92636, 86669, -75462, -22473, 49760, 19890, 66753, -8993, 90185, 87015, 23128, 21238, 80093, -2124, 7342, 29883, -24485, 62344, -11737, 89354, 23958, 45167, 71583, -41738, 82141, 46010, 79346, 74934, 31660, 60045, 77080, -21189, -4385, -82937, -44205, 33454, 12937, 63298, 28429, 35596, 38082, 69153, 50276, 35586, 42247, 1104, -11583, -56791, -49288, -53505, 22595, 98568, 59398, 62045, 54499, 2942, 98771, 33503, -78505, 94706, 96664, 30505, -22849, 99790, 41515, 429, 33097, 88913, 12016, -11602, 31898, -71866, 14512, 20292, 75198, 32519, 32738, 50152, 85016, -66667, -68509, 62759, 28441, 7941, 35609, 74452, 51517, 57281, 34554, 90836, 29672, 61316, 14601, -16839, -51629, -20012, 24222, 70300, 40737, 51584, 8912, 25524, 21110, 12956, 38677, 82122, 72847, 46520, -24014, 46697, 59205, 60722, -57623, 38891, 53739, 34697, 87996, 69965, 13668, 58843, 42346, -1342, 34479, 41009, 85951, 32808, 26132, 4763, -5007, -28913, 20545, 4553, -17433, 38218, 95352, -99390, -17003, 6347, 40855, 71798, 76369, -19798, 26185, 94958, 44674, 20520, 22296, 94036, -77288, -26227, 64872, 38337, 92915, 93826, -19834, 68696, 67807, 47513, 83826, 80929, -17993, 69270, 2837, 78269, 45093, 37992, 76262, 99954, 4953, 96210, 70806, -51644, -38729, 22312, 35481, 84535, 58064, -70572, -74205, -57922, 37114, -7202, 32718, 73940, 64493, 78688, 57259, 60931, 2449, -41367, 75026, -63896, -85360, 32948, 55490, -96763, 56481, -14180, 97315, 77932, -79193, 33697, 69469, 18886, 1186, 7782, 27247, 53194, -2806, 50966, 39677, 53529, -56084, 61338, 37501, 68808, 1470, 43050, 69868, 69792, 58994, 81058, 37980, 99204, -54795, -84307, 65596, -84402, 24723, 63436, 70289, -42934, 45733, 26690, -23458, 94305, -57280, 4616, 77519, 88392, -6738, -41136, 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65101, 98284, 26122, -6737, 21554, -4991, 98076, -1642, 29536, -34391, 49133, 93878, 90655, 97483, 63363, 62146, 94233, 50165, 46407, 65047, -44055, -61093, -74990, -51146, 25950, -27698, 68264, 45010, 49401, 81470, 18001, 62807, -23366, -68130, 82301, 5982, 3849, 7927, 79555, -14303, 35605, 50849, 2476, 14780, 19126, -25734, 8722, 95345, 46805, 85605, 13557, 88549, 23871, 69158, 40770, 63380, 15773, -64921, -53961, 98252, 80291, 25129, 41527, 78658, 43867, 75503, 30920, 47955, 96341, 45747, -34685, 99087, 68044, 96958, -28137, 2267, -77544, 1404, 54414, -61736, 24344, -24956, 23736, 76751, 93016, 65302, 30886, -33446, -2919, 1221, 14689, 21713, 17462, -54941, 19524, 65527, 15792, 51915, 60845, 25508, 51927, 11586, 159, 21455, 86129, 90582, 19887, 72601, 64109, 31863, 31178, 61868, 16304, 44311, 10169, -72072, 45653, 75896, 86251, 55948, 52246, -59387, -76531, 49090, -42196, -15423, 67786, 6133, 37989, 17104, -35909, -91004, 92295, 10180, -78462, 40106, -10452, 73943, 25393, 82453, 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-63152, 48575, -12177, 28693, 66133, 21831, 18168, -57051, 42620, 96719, 90491, 29150, -50036, 85872, 69045, 13044, 8346, 15303, 36493, 40653, 62671, 27049, 87918, 35629, 6461, -69269, 52174, 22577, 95932, 60422, 28570, 50894, -19951, 87636, 54675, 16813, 72465, 30031, 92515, -72092, 51116, 42434, -8674, 21005, -86198, -71238, 63269, -50597, 31759, -55163, 61190, 22507, 12514, 57416, -96915, -10681, 13829, 66468, -41057, 18969, -87341, -76180, 15738, 91307, 7252, -50337, -69899, -11942, 51059, 89450, 62546, 58934, 30987, 28892, 21143, 48349, 62290, 22704, 25900, 5522, -95003, 43973, -53476, -90220, 73805, 73736, 5600, 48095, 88531, -95879, -5029, 30195, -58646, 27358, 97679, 40447, 96763, 44901, -28927, -98383, -12763, 80068, 75111, 15079, 81467, -98912, 33798, 15417, -95886, -77756, 3203, 61291, 41663, -77064, 67921, 82181, 75275, -50901, -56841, 51251, 70612, -82647, 40219, 41573, 20831, 60662, 25857, 77655, 48002, 4446, -99602, 38839, 98465, 9415, 28495, -88067, 7090, 5119, 26974, 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7851, 97401, 37723, 42558, -82535, 46283, 38288, 74616, 64297, 68384, 40939, 22476, 71417, -5846, -60956, 72014, -46435, -27631, 48271, 30608, -73379, 13299, 66125, 4336, 37102, 61713, 86226, 40365, 6415, 47483, -14556, 38906, -76653, 59371, 9138, -9890, 35526, -34572, 78674, 96824, -78318, -27193, 76764, -56417, 57592, 21929, 96897, 73147, 18500, -63911, 21740, 63339, -13370, 4427, 18430, 56378, 17281, 78031, 81856, 38059, 95477, 12785, 182, 62253, 58572, 32495, 90013, 44394, 54764, 97422, -27607, 65508, 15681, -77617, 70608, 24393, -28123, 50193, 83304, 34323, 4910, 45290, 55979, 4375, 35842, -10378, 75761, 55105, 93692, 23301, 59739, 73323, 51848, 67874, -45688, 57798, 8226, 14007, -13240, 62709, -7282, 13126, -63676, 17522, 3036, 6817, -87798, -12397, 87678, 440, 50667, 79714, 98094, 70065, 30623, 35514, 14395, 51031, 14435, 4875, -56103, -63147, 34478, 11683, 78433, 74512, 93856, 1290, -47230, 3261, 85215, 60438, -56517, 51497, 871, 43887, -74744, 98890, 89649, 67602, 28697, 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