Implementation
static const List<double> XL0 = [
10000000000,
20, 578, 920, 1100, 1124, 1136, 1148, 1217, 1226, 1229, 1229, 1229, 1229, 1937, 2363, 2618, 2633, 2660, 2666,
17534704567, 0.00000000000, 0.00000000000, 334165646, 4.669256804, 6283.075849991, 3489428, 4.6261024,
12566.1517000, 349706, 2.744118, 5753.384885, 341757, 2.828866, 3.523118, 313590, 3.627670, 77713.771468,
267622, 4.418084, 7860.419392, 234269, 6.135162, 3930.209696, 132429, 0.742464, 11506.769770, 127317, 2.037097,
529.690965, 119917, 1.109629, 1577.343542, 99025, 5.23268, 5884.92685, 90186, 2.04505, 26.29832, 85722, 3.50849,
398.14900, 77979, 1.17883, 5223.69392, 75314, 2.53339, 5507.55324, 50526, 4.58293, 18849.22755, 49238, 4.20507,
775.52261, 35666, 2.91954, 0.06731, 31709, 5.84902, 11790.62909, 28413, 1.89869, 796.29801, 27104, 0.31489,
10977.07880, 24281, 0.34481, 5486.77784, 20616, 4.80647, 2544.31442, 20539, 1.86948, 5573.14280, 20226, 2.45768,
6069.77675, 15552, 0.83306, 213.29910, 13221, 3.41118, 2942.46342, 12618, 1.08303, 20.77540, 11513, 0.64545,
0.98032, 10285, 0.63600, 4694.00295, 10190, 0.97569, 15720.83878, 10172, 4.26680, 7.11355, 9921, 6.2099,
2146.1654, 9761, 0.6810, 155.4204, 8580, 5.9832, 161000.6857, 8513, 1.2987, 6275.9623, 8471, 3.6708, 71430.6956,
7964, 1.8079, 17260.1547, 7876, 3.0370, 12036.4607, 7465, 1.7551, 5088.6288, 7387, 3.5032, 3154.6871, 7355,
4.6793, 801.8209, 6963, 0.8330, 9437.7629, 6245, 3.9776, 8827.3903, 6115, 1.8184, 7084.8968, 5696, 2.7843,
6286.5990, 5612, 4.3869, 14143.4952, 5558, 3.4701, 6279.5527, 5199, 0.1891, 12139.5535, 5161, 1.3328, 1748.0164,
5115, 0.2831, 5856.4777, 4900, 0.4874, 1194.4470, 4104, 5.3682, 8429.2413, 4094, 2.3985, 19651.0485, 3920,
6.1683, 10447.3878, 3677, 6.0413, 10213.2855, 3660, 2.5696, 1059.3819, 3595, 1.7088, 2352.8662, 3557, 1.7760,
6812.7668, 3329, 0.5931, 17789.8456, 3041, 0.4429, 83996.8473, 3005, 2.7398, 1349.8674, 2535, 3.1647, 4690.4798,
2474, 0.2148, 3.5904, 2366, 0.4847, 8031.0923, 2357, 2.0653, 3340.6124, 2282, 5.2220, 4705.7323, 2189, 5.5559,
553.5694, 2142, 1.4256, 16730.4637, 2109, 4.1483, 951.7184, 2030, 0.3713, 283.8593, 1992, 5.2221, 12168.0027,
1986, 5.7747, 6309.3742, 1912, 3.8222, 23581.2582, 1889, 5.3863, 149854.4001, 1790, 2.2149, 13367.9726, 1748,
4.5605, 135.0651, 1622, 5.9884, 11769.8537, 1508, 4.1957, 6256.7775, 1442, 4.1932, 242.7286, 1435, 3.7236,
38.0277, 1397, 4.4014, 6681.2249, 1362, 1.8893, 7632.9433, 1250, 1.1305, 5.5229, 1205, 2.6223, 955.5997, 1200,
1.0035, 632.7837, 1129, 0.1774, 4164.3120, 1083, 0.3273, 103.0928, 1052, 0.9387, 11926.2544, 1050, 5.3591,
1592.5960, 1033, 6.1998, 6438.4962, 1001, 6.0291, 5746.2713, 980, 0.999, 11371.705, 980, 5.244, 27511.468, 938,
2.624, 5760.498, 923, 0.483, 522.577, 922, 4.571, 4292.331, 905, 5.337, 6386.169, 862, 4.165, 7058.598, 841,
3.299, 7234.794, 836, 4.539, 25132.303, 813, 6.112, 4732.031, 812, 6.271, 426.598, 801, 5.821, 28.449, 787,
0.996, 5643.179, 776, 2.957, 23013.540, 769, 3.121, 7238.676, 758, 3.974, 11499.656, 735, 4.386, 316.392, 731,
0.607, 11513.883, 719, 3.998, 74.782, 706, 0.323, 263.084, 676, 5.911, 90955.552, 663, 3.665, 17298.182, 653,
5.791, 18073.705, 630, 4.717, 6836.645, 615, 1.458, 233141.314, 612, 1.075, 19804.827, 596, 3.321, 6283.009,
596, 2.876, 6283.143, 555, 2.452, 12352.853, 541, 5.392, 419.485, 531, 0.382, 31441.678, 519, 4.065, 6208.294,
513, 2.361, 10973.556, 494, 5.737, 9917.697, 450, 3.272, 11015.106, 449, 3.653, 206.186, 447, 2.064, 7079.374,
435, 4.423, 5216.580, 421, 1.906, 245.832, 413, 0.921, 3738.761, 402, 0.840, 20.355, 387, 1.826, 11856.219, 379,
2.344, 3.881, 374, 2.954, 3128.389, 370, 5.031, 536.805, 365, 1.018, 16200.773, 365, 1.083, 88860.057, 352,
5.978, 3894.182, 352, 2.056, 244287.600, 351, 3.713, 6290.189, 340, 1.106, 14712.317, 339, 0.978, 8635.942, 339,
3.202, 5120.601, 333, 0.837, 6496.375, 325, 3.479, 6133.513, 316, 5.089, 21228.392, 316, 1.328, 10873.986, 309,
3.646, 10.637, 303, 1.802, 35371.887, 296, 3.397, 9225.539, 288, 6.026, 154717.610, 281, 2.585, 14314.168, 262,
3.856, 266.607, 262, 2.579, 22483.849, 257, 1.561, 23543.231, 255, 3.949, 1990.745, 251, 3.744, 10575.407, 240,
1.161, 10984.192, 238, 0.106, 7.046, 236, 4.272, 6040.347, 234, 3.577, 10969.965, 211, 3.714, 65147.620, 210,
0.754, 13521.751, 207, 4.228, 5650.292, 202, 0.814, 170.673, 201, 4.629, 6037.244, 200, 0.381, 6172.870, 199,
3.933, 6206.810, 199, 5.197, 6262.300, 197, 1.046, 18209.330, 195, 1.070, 5230.807, 195, 4.869, 36.028, 194,
4.313, 6244.943, 192, 1.229, 709.933, 192, 5.595, 6282.096, 192, 0.602, 6284.056, 189, 3.744, 23.878, 188,
1.904, 15.252, 188, 0.867, 22003.915, 182, 3.681, 15110.466, 181, 0.491, 1.484, 179, 3.222, 39302.097, 179,
1.259, 12559.038,
62833196674749, 0.000000000000, 0.000000000000, 20605886, 2.67823456, 6283.07584999, 430343, 2.635127,
12566.151700, 42526, 1.59047, 3.52312, 11926, 5.79557, 26.29832, 10898, 2.96618, 1577.34354, 9348, 2.5921,
18849.2275, 7212, 1.1385, 529.6910, 6777, 1.8747, 398.1490, 6733, 4.4092, 5507.5532, 5903, 2.8880, 5223.6939,
5598, 2.1747, 155.4204, 4541, 0.3980, 796.2980, 3637, 0.4662, 775.5226, 2896, 2.6471, 7.1135, 2084, 5.3414,
0.9803, 1910, 1.8463, 5486.7778, 1851, 4.9686, 213.2991, 1729, 2.9912, 6275.9623, 1623, 0.0322, 2544.3144, 1583,
1.4305, 2146.1654, 1462, 1.2053, 10977.0788, 1246, 2.8343, 1748.0164, 1188, 3.2580, 5088.6288, 1181, 5.2738,
1194.4470, 1151, 2.0750, 4694.0030, 1064, 0.7661, 553.5694, 997, 1.303, 6286.599, 972, 4.239, 1349.867, 945,
2.700, 242.729, 858, 5.645, 951.718, 758, 5.301, 2352.866, 639, 2.650, 9437.763, 610, 4.666, 4690.480, 583,
1.766, 1059.382, 531, 0.909, 3154.687, 522, 5.661, 71430.696, 520, 1.854, 801.821, 504, 1.425, 6438.496, 433,
0.241, 6812.767, 426, 0.774, 10447.388, 413, 5.240, 7084.897, 374, 2.001, 8031.092, 356, 2.429, 14143.495, 350,
4.800, 6279.553, 337, 0.888, 12036.461, 337, 3.862, 1592.596, 325, 3.400, 7632.943, 322, 0.616, 8429.241, 318,
3.188, 4705.732, 297, 6.070, 4292.331, 295, 1.431, 5746.271, 290, 2.325, 20.355, 275, 0.935, 5760.498, 270,
4.804, 7234.794, 253, 6.223, 6836.645, 228, 5.003, 17789.846, 225, 5.672, 11499.656, 215, 5.202, 11513.883, 208,
3.955, 10213.286, 208, 2.268, 522.577, 206, 2.224, 5856.478, 206, 2.550, 25132.303, 203, 0.910, 6256.778, 189,
0.532, 3340.612, 188, 4.735, 83996.847, 179, 1.474, 4164.312, 178, 3.025, 5.523, 177, 3.026, 5753.385, 159,
4.637, 3.286, 157, 6.124, 5216.580, 155, 3.077, 6681.225, 154, 4.200, 13367.973, 143, 1.191, 3894.182, 138,
3.093, 135.065, 136, 4.245, 426.598, 134, 5.765, 6040.347, 128, 3.085, 5643.179, 127, 2.092, 6290.189, 125,
3.077, 11926.254, 125, 3.445, 536.805, 114, 3.244, 12168.003, 112, 2.318, 16730.464, 111, 3.901, 11506.770, 111,
5.320, 23.878, 105, 3.750, 7860.419, 103, 2.447, 1990.745, 96, 0.82, 3.88, 96, 4.08, 6127.66, 91, 5.42, 206.19,
91, 0.42, 7079.37, 88, 5.17, 11790.63, 81, 0.34, 9917.70, 80, 3.89, 10973.56, 78, 2.40, 1589.07, 78, 2.58,
11371.70, 77, 3.98, 955.60, 77, 3.36, 36.03, 76, 1.30, 103.09, 75, 5.18, 10969.97, 75, 4.96, 6496.37, 73, 5.21,
38.03, 72, 2.65, 6309.37, 70, 5.61, 3738.76, 69, 2.60, 3496.03, 69, 0.39, 15.25, 69, 2.78, 20.78, 65, 1.13,
7058.60, 64, 4.28, 28.45, 61, 5.63, 10984.19, 60, 0.73, 419.48, 60, 5.28, 10575.41, 58, 5.55, 17298.18, 58,
3.19, 4732.03,
5291887, 0.0000000, 0.0000000, 871984, 1.072097, 6283.075850, 30913, 0.86729, 12566.15170, 2734, 0.0530, 3.5231,
1633, 5.1883, 26.2983, 1575, 3.6846, 155.4204, 954, 0.757, 18849.228, 894, 2.057, 77713.771, 695, 0.827,
775.523, 506, 4.663, 1577.344, 406, 1.031, 7.114, 381, 3.441, 5573.143, 346, 5.141, 796.298, 317, 6.053,
5507.553, 302, 1.192, 242.729, 289, 6.117, 529.691, 271, 0.306, 398.149, 254, 2.280, 553.569, 237, 4.381,
5223.694, 208, 3.754, 0.980, 168, 0.902, 951.718, 153, 5.759, 1349.867, 145, 4.364, 1748.016, 134, 3.721,
1194.447, 125, 2.948, 6438.496, 122, 2.973, 2146.165, 110, 1.271, 161000.686, 104, 0.604, 3154.687, 100, 5.986,
6286.599, 92, 4.80, 5088.63, 89, 5.23, 7084.90, 83, 3.31, 213.30, 76, 3.42, 5486.78, 71, 6.19, 4690.48, 68,
3.43, 4694.00, 65, 1.60, 2544.31, 64, 1.98, 801.82, 61, 2.48, 10977.08, 50, 1.44, 6836.65, 49, 2.34, 1592.60,
46, 1.31, 4292.33, 46, 3.81, 149854.40, 43, 0.04, 7234.79, 40, 4.94, 7632.94, 39, 1.57, 71430.70, 38, 3.17,
6309.37, 35, 0.99, 6040.35, 35, 0.67, 1059.38, 31, 3.18, 2352.87, 31, 3.55, 8031.09, 30, 1.92, 10447.39, 30,
2.52, 6127.66, 28, 4.42, 9437.76, 28, 2.71, 3894.18, 27, 0.67, 25132.30, 26, 5.27, 6812.77, 25, 0.55, 6279.55,
23, 1.38, 4705.73, 22, 0.64, 6256.78, 20, 6.07, 640.88,
28923, 5.84384, 6283.07585, 3496, 0.0000, 0.0000, 1682, 5.4877, 12566.1517, 296, 5.196, 155.420, 129, 4.722,
3.523, 71, 5.30, 18849.23, 64, 5.97, 242.73, 40, 3.79, 553.57,
11408, 3.14159, 0.00000, 772, 4.134, 6283.076, 77, 3.84, 12566.15, 42, 0.42, 155.42,
88, 3.14, 0.00, 17, 2.77, 6283.08, 5, 2.01, 155.42, 3, 2.21, 12566.15,
27962, 3.19870, 84334.66158, 10164, 5.42249, 5507.55324, 8045, 3.8801, 5223.6939, 4381, 3.7044, 2352.8662, 3193,
4.0003, 1577.3435, 2272, 3.9847, 1047.7473, 1814, 4.9837, 6283.0758, 1639, 3.5646, 5856.4777, 1444, 3.7028,
9437.7629, 1430, 3.4112, 10213.2855, 1125, 4.8282, 14143.4952, 1090, 2.0857, 6812.7668, 1037, 4.0566,
71092.8814, 971, 3.473, 4694.003, 915, 1.142, 6620.890, 878, 4.440, 5753.385, 837, 4.993, 7084.897, 770, 5.554,
167621.576, 719, 3.602, 529.691, 692, 4.326, 6275.962, 558, 4.410, 7860.419, 529, 2.484, 4705.732, 521, 6.250,
18073.705,
903, 3.897, 5507.553, 618, 1.730, 5223.694, 380, 5.244, 2352.866,
166, 1.627, 84334.662,
10001398880, 0.00000000000, 0.00000000000, 167069963, 3.098463508, 6283.075849991, 1395602, 3.0552461,
12566.1517000, 308372, 5.198467, 77713.771468, 162846, 1.173877, 5753.384885, 157557, 2.846852, 7860.419392,
92480, 5.45292, 11506.76977, 54244, 4.56409, 3930.20970, 47211, 3.66100, 5884.92685, 34598, 0.96369, 5507.55324,
32878, 5.89984, 5223.69392, 30678, 0.29867, 5573.14280, 24319, 4.27350, 11790.62909, 21183, 5.84715, 1577.34354,
18575, 5.02194, 10977.07880, 17484, 3.01194, 18849.22755, 10984, 5.05511, 5486.77784, 9832, 0.8868, 6069.7768,
8650, 5.6896, 15720.8388, 8583, 1.2708, 161000.6857, 6490, 0.2725, 17260.1547, 6292, 0.9218, 529.6910, 5706,
2.0137, 83996.8473, 5574, 5.2416, 71430.6956, 4938, 3.2450, 2544.3144, 4696, 2.5781, 775.5226, 4466, 5.5372,
9437.7629, 4252, 6.0111, 6275.9623, 3897, 5.3607, 4694.0030, 3825, 2.3926, 8827.3903, 3749, 0.8295, 19651.0485,
3696, 4.9011, 12139.5535, 3566, 1.6747, 12036.4607, 3454, 1.8427, 2942.4634, 3319, 0.2437, 7084.8968, 3192,
0.1837, 5088.6288, 3185, 1.7778, 398.1490, 2846, 1.2134, 6286.5990, 2779, 1.8993, 6279.5527, 2628, 4.5890,
10447.3878, 2460, 3.7866, 8429.2413, 2393, 4.9960, 5856.4777, 2359, 0.2687, 796.2980, 2329, 2.8078, 14143.4952,
2210, 1.9500, 3154.6871, 2035, 4.6527, 2146.1654, 1951, 5.3823, 2352.8662, 1883, 0.6731, 149854.4001, 1833,
2.2535, 23581.2582, 1796, 0.1987, 6812.7668, 1731, 6.1520, 16730.4637, 1717, 4.4332, 10213.2855, 1619, 5.2316,
17789.8456, 1381, 5.1896, 8031.0923, 1364, 3.6852, 4705.7323, 1314, 0.6529, 13367.9726, 1041, 4.3329,
11769.8537, 1017, 1.5939, 4690.4798, 998, 4.201, 6309.374, 966, 3.676, 27511.468, 874, 6.064, 1748.016, 779,
3.674, 12168.003, 771, 0.312, 7632.943, 756, 2.626, 6256.778, 746, 5.648, 11926.254, 693, 2.924, 6681.225, 680,
1.423, 23013.540, 674, 0.563, 3340.612, 663, 5.661, 11371.705, 659, 3.136, 801.821, 648, 2.650, 19804.827, 615,
3.029, 233141.314, 612, 5.134, 1194.447, 563, 4.341, 90955.552, 552, 2.091, 17298.182, 534, 5.100, 31441.678,
531, 2.407, 11499.656, 523, 4.624, 6438.496, 513, 5.324, 11513.883, 477, 0.256, 11856.219, 461, 1.722, 7234.794,
458, 3.766, 6386.169, 458, 4.466, 5746.271, 423, 1.055, 5760.498, 422, 1.557, 7238.676, 415, 2.599, 7058.598,
401, 3.030, 1059.382, 397, 1.201, 1349.867, 379, 4.907, 4164.312, 360, 5.707, 5643.179, 352, 3.626, 244287.600,
348, 0.761, 10973.556, 342, 3.001, 4292.331, 336, 4.546, 4732.031, 334, 3.138, 6836.645, 324, 4.164, 9917.697,
316, 1.691, 11015.106, 307, 0.238, 35371.887, 298, 1.306, 6283.143, 298, 1.750, 6283.009, 293, 5.738, 16200.773,
286, 5.928, 14712.317, 281, 3.515, 21228.392, 280, 5.663, 8635.942, 277, 0.513, 26.298, 268, 4.207, 18073.705,
266, 0.900, 12352.853, 260, 2.962, 25132.303, 255, 2.477, 6208.294, 242, 2.800, 709.933, 231, 1.054, 22483.849,
229, 1.070, 14314.168, 216, 1.314, 154717.610, 215, 6.038, 10873.986, 200, 0.561, 7079.374, 198, 2.614, 951.718,
197, 4.369, 167283.762, 186, 2.861, 5216.580, 183, 1.660, 39302.097, 183, 5.912, 3738.761, 175, 2.145, 6290.189,
173, 2.168, 10575.407, 171, 3.702, 1592.596, 171, 1.343, 3128.389, 164, 5.550, 6496.375, 164, 5.856, 10984.192,
161, 1.998, 10969.965, 161, 1.909, 6133.513, 157, 4.955, 25158.602, 154, 6.216, 23543.231, 153, 5.357,
13521.751, 150, 5.770, 18209.330, 150, 5.439, 155.420, 139, 1.778, 9225.539, 139, 1.626, 5120.601, 128, 2.460,
13916.019, 123, 0.717, 143571.324, 122, 2.654, 88860.057, 121, 4.414, 3894.182, 121, 1.192, 3.523, 120, 4.030,
553.569, 119, 1.513, 17654.781, 117, 3.117, 14945.316, 113, 2.698, 6040.347, 110, 3.085, 43232.307, 109, 0.998,
955.600, 108, 2.939, 17256.632, 107, 5.285, 65147.620, 103, 0.139, 11712.955, 103, 5.850, 213.299, 102, 3.046,
6037.244, 101, 2.842, 8662.240, 100, 3.626, 6262.300, 98, 2.36, 6206.81, 98, 5.11, 6172.87, 98, 2.00, 15110.47,
97, 2.67, 5650.29, 97, 2.75, 6244.94, 96, 4.02, 6282.10, 96, 5.31, 6284.06, 92, 0.10, 29088.81, 85, 3.26,
20426.57, 84, 2.60, 28766.92, 81, 3.58, 10177.26, 80, 5.81, 5230.81, 78, 2.53, 16496.36, 77, 4.06, 6127.66, 73,
0.04, 5481.25, 72, 5.96, 12559.04, 72, 5.92, 4136.91, 71, 5.49, 22003.91, 70, 3.41, 7.11, 69, 0.62, 11403.68,
69, 3.90, 1589.07, 69, 1.96, 12416.59, 69, 4.51, 426.60, 67, 1.61, 11087.29, 66, 4.50, 47162.52, 66, 5.08,
283.86, 66, 4.32, 16858.48, 65, 1.04, 6062.66, 64, 1.59, 18319.54, 63, 5.70, 45892.73, 63, 4.60, 66567.49, 63,
3.82, 13517.87, 62, 2.62, 11190.38, 61, 1.54, 33019.02, 60, 5.58, 10344.30, 60, 5.38, 316428.23, 60, 5.78,
632.78, 59, 6.12, 9623.69, 57, 0.16, 17267.27, 57, 3.86, 6076.89, 57, 1.98, 7668.64, 56, 4.78, 20199.09, 55,
4.56, 18875.53, 55, 3.51, 17253.04, 54, 3.07, 226858.24, 54, 4.83, 18422.63, 53, 5.02, 12132.44, 52, 3.63,
5333.90, 52, 0.97, 155427.54, 51, 3.36, 20597.24, 50, 0.99, 11609.86, 50, 2.21, 1990.75, 48, 1.62, 12146.67, 48,
1.17, 12569.67, 47, 4.62, 5436.99, 47, 1.81, 12562.63, 47, 0.59, 21954.16, 47, 0.76, 7342.46, 46, 0.27, 4590.91,
46, 3.77, 156137.48, 45, 5.66, 10454.50, 44, 5.84, 3496.03, 43, 0.24, 17996.03, 41, 5.93, 51092.73, 41, 4.21,
12592.45, 40, 5.14, 1551.05, 40, 5.28, 15671.08, 39, 3.69, 18052.93, 39, 4.94, 24356.78, 38, 2.72, 11933.37, 38,
5.23, 7477.52, 38, 4.99, 9779.11, 37, 3.70, 9388.01, 37, 4.44, 4535.06, 36, 2.16, 28237.23, 36, 2.54, 242.73,
36, 0.22, 5429.88, 35, 6.15, 19800.95, 35, 2.92, 36949.23, 34, 5.63, 2379.16, 34, 5.73, 16460.33, 34, 5.11,
5849.36, 33, 6.19, 6268.85,
10301861, 1.10748970, 6283.07584999, 172124, 1.064423, 12566.151700, 70222, 3.14159, 0.00000, 3235, 1.0217,
18849.2275, 3080, 2.8435, 5507.5532, 2497, 1.3191, 5223.6939, 1849, 1.4243, 1577.3435, 1008, 5.9138, 10977.0788,
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];
