/*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package io.airlift.stats.cardinality;
// These tables are generated empirically by running several thousand experiments and computing the average error for each cardinality
// TODO: check in the code for generating the tables
class BiasCorrection
{
// bias correction tables starting at p = 4
public static final double[][] RAW_ESTIMATES = {
{11.238823092354272, 11.725363299909107, 12.222487291610099, 12.735431957728302, 13.270736917504793, 13.822501301508458, 14.391255094466214, 14.969524108237062,
15.56691362087194, 16.175198427092205, 16.7981527546064, 17.448134120729758, 18.097592087776068, 18.759433618300417, 19.450004708799035, 20.156932338684754,
20.875136059898335, 21.60835330066454, 22.351989350566974, 23.113857534769974, 23.90429312484887, 24.67713081912686, 25.49420317767964, 26.309863939212107,
27.126802013148428, 27.972605647700796, 28.820451945782686, 29.67281734661721, 30.53644672326387, 31.39668010644774, 32.27870983729891, 33.14771510141357,
34.05425420817575, 34.97509016051461, 35.8818490065124, 36.792441662708065, 37.70780466307142, 38.62317635261747, 39.55502952281605, 40.49619871344004,
41.44603403431558, 42.42092766507492, 43.3709558040624, 44.327316505552744, 45.29307979619073, 46.24997474501817, 47.201710877073786, 48.18726977279131,
49.14448219007698, 50.137421167014054, 51.104818781406934, 52.10820437202683, 53.10052633157516, 54.0725395290788, 55.03295380938293, 56.033147332017876,
57.00397278312336, 58.062370314420136, 59.0227246094072, 60.00043177933829, 61.006867272215594, 61.97490128147253, 63.01903209306433, 63.971348060146816,
64.91162631773415, 65.85294872512344, 66.84339832519024, 67.79984837197942, 68.75333942356372, 69.77448114087566, 70.76918920249851, 71.77758462099953,
72.81907388775971, 73.82988285948488, 74.80625898013463, 75.79911363341205, 76.71741012222735, 77.6987982563626, 78.63348046315684, 79.62908902169245},
{22.77932649294573, 23.261115695867563, 23.751159067226258, 24.24915910631809, 24.75476648688801, 25.26732497026536, 25.786578222898626, 26.310905487923645,
26.839927196274342, 27.387865333182482, 27.94149546391533, 28.497249235818824, 29.059912306269123, 29.636802183334773, 30.22131848480806, 30.813233117380097,
31.406254563377363, 32.01114372186672, 32.61633519216477, 33.23200121019319, 33.8545001677627, 34.484029809476574, 35.124634639543416, 35.763358479018244,
36.42375698997327, 37.08614917999027, 37.768999116479655, 38.461184231325056, 39.14991724989846, 39.83535010437971, 40.53198877923012, 41.233663012500315,
41.95148310122916, 42.68221857875466, 43.403434589772075, 44.13934054539383, 44.88238280732905, 45.643917737439786, 46.394616846716765, 47.14524158486915,
47.904357522212386, 48.682141938915976, 49.4613425771598, 50.23246528465661, 51.00507853817475, 51.79679890970103, 52.59367935848412, 53.40124729599998,
54.21205142080146, 55.034610026416765, 55.86466243417469, 56.70015425059533, 57.54401311390876, 58.39385821257159, 59.22521021058371, 60.089290769757376,
60.95894725053715, 61.81542007186899, 62.666961224851526, 63.55349195818499, 64.42481374851235, 65.2840538099318, 66.15558862021457, 67.04972089567735,
67.93390957080265, 68.83079228437437, 69.7186239565501, 70.61074424926983, 71.51511208737145, 72.42924058054682, 73.3331481037979, 74.25178751536052,
75.15461273650473, 76.0794699409806, 77.00401813021591, 77.92067007066713, 78.82758185775968, 79.7585425145911, 80.6387463303789, 81.56851600227802, 82.51327204772852,
83.45797121387919, 84.41117650756297, 85.33285965326263, 86.2783412507562, 87.25064175559649, 88.1951944417447, 89.12771088513622, 90.10362358308917,
91.06182558116019, 92.002863892934, 92.94517201025293, 93.93458324321051, 94.87779889452023, 95.8536022538649, 96.83723858115665, 97.82095580229137, 98.82362070900676,
99.77944951035852, 100.77602256431138, 101.75167760375842, 102.71093796308753, 103.7028366449849, 104.67223583073061, 105.65029327904286, 106.63886770280547,
107.6237034396032, 108.58712460552255, 109.54762987179726, 110.53874105930242, 111.52920835619366, 112.55779104517525, 113.54361236488315, 114.51142338265662,
115.49447666964366, 116.46507922964537, 117.43881734646392, 118.42968165038685, 119.42983356803025, 120.4601306876298, 121.45059523184032, 122.41649774138901,
123.39336589514583, 124.4049044729134, 125.3842953165607, 126.32063285027671, 127.28967873110413, 128.28266606917657, 129.25532262489594, 130.23933874898773,
131.25819523494158, 132.24090748038762, 133.2297629541157, 134.22534951364486, 135.22035867773053, 136.1678562665769, 137.12796347528385, 138.1340270095745,
139.1189380526937, 140.0537398375486, 141.07634390152796, 142.073110720766, 143.040795363473, 143.98192941463194, 144.96284196892032, 145.90561111080373,
146.95345755896653, 147.93678120623173, 148.9334165695148, 149.97317687889736, 150.98329126343938, 152.0347759146844, 153.00198765200474, 153.98235642430805,
154.97860226311164, 155.9697402149397, 156.96609109521634, 157.96284964484528, 158.91621843372602, 159.91708349191092},
{45.854533130412854, 47.31072242086501, 48.29929645296603, 49.80832079609545, 51.34888741647967, 53.45748177790311, 54.53342031818346, 55.62364530505762,
56.727805614623165, 58.98144360990141, 60.129787381154244, 61.293268346875685, 62.4709700350214, 64.2558361487712, 65.46421418969446, 67.29074416313107,
68.54355767689897, 70.4484221038948, 73.04105149253134, 73.70633117479629, 74.35497376545588, 75.01433813755582, 75.68724740562939, 76.37270066728811,
77.71796857261704, 79.07420144916753, 80.46115952175705, 82.57276076341451, 83.28898515261109, 84.70515072297304, 86.15237381333378, 87.61636104566209,
88.3600325345711, 89.82859541233302, 92.81272268755218, 94.31452129789375, 95.828760992489, 98.13160585081147, 98.92531949856895, 100.45711178024001,
102.03257131914106, 102.80234262759095, 105.15407838273727, 108.3655629752791, 109.15674736027415, 109.98589195510806, 112.39568935298358, 113.18575147060288,
114.03210278299062, 114.84116444407297, 115.66992694946393, 116.51167865680164, 117.33947404522743, 120.69267241138799, 121.50962008913476, 122.39226298256881,
124.94113081205148, 126.61150006264253, 127.49441369308887, 129.20157709573363, 130.0736343105852, 132.63769264486032, 133.47709162353496, 136.9962659564278,
140.48806609662918, 141.3863940441779, 143.1421855702465, 144.07336753364896, 144.980256109538, 146.77132820906183, 148.60038943868207, 149.48687678895365,
154.07471141192576, 155.01192277049543, 155.93069311527395, 156.86576895230874, 158.6925567655158, 159.62510014648623, 161.46779181331155, 163.36541856542576,
166.14411192248377, 167.11031113384806, 168.04975878592248, 168.95334510813785, 172.7224138950209, 174.59448376951818, 176.534466878692, 177.48563687422936,
178.4168373486183, 179.404453087958, 180.33714343007378, 181.29285656479732, 182.26413531364435, 184.1633825009286, 185.16536877967062, 189.05517521763838,
190.0647637904211, 191.97763714868236, 192.89671599080265, 194.80425704458005, 195.8051727860706, 197.68986510910162, 199.58861448928957, 200.59802676257644,
201.57194705405402, 204.452991143457, 206.39210296776724, 207.3985192699964, 209.331879540886, 210.315622249521, 211.26215728343084, 213.24765174223248,
215.1661627983063, 216.1738131044242, 218.10156102540725, 220.11524137527718, 221.0977093643887, 223.0284016977248, 223.97671016352066, 224.90491286823328,
225.91294490677927, 226.8522139881627, 227.8192445919417, 228.80497857170414, 229.77581769142353, 231.76122478346318, 232.72808375870122, 233.73269877506553,
234.68168723472496, 235.6775151290225, 236.70685583728832, 237.69208889988715, 240.6035756939352, 241.58696164500378, 242.53514941402875, 243.5136136866957,
245.5439336931616, 246.53264782794383, 247.4795684383069, 249.4218388868179, 250.3673552957724, 251.40832089717136, 252.3278484642049, 253.28522589571384,
254.26386350912614, 255.22664403458154, 256.28403711913927, 258.18688976302906, 259.24067272852307, 260.2462607367207, 262.21642614291045, 263.2405506324472,
265.21263550393434, 266.1483824353132, 267.1661088158451, 268.11092541090835, 270.1216470331842, 271.0705615945983, 272.0964411533475, 273.05618962855823,
274.03169645727434, 275.05406801670085, 276.0208348825076, 277.0115775293853, 277.969551652295, 278.9999638142669, 279.9799929658816, 280.98287126005556,
282.00456073135956, 282.98056535711294, 283.92235039303756, 284.91021860071606, 285.87048062164644, 286.84504410520015, 288.8595648237398, 289.81725855585887,
290.83361431690116, 291.80346949982095, 292.8365748309084, 293.79543488205104, 294.7995300177809, 295.75879331855447, 296.7647579184519, 297.82327398609283,
299.88319977442654, 301.8192945473352, 302.7516120171321, 303.7170521590099, 304.70328058450764, 305.7265573935557, 306.7015824476859, 307.7681334511439,
308.79405871690483, 309.7927984031691, 310.82086592021955, 311.81302301639863, 312.7534065395336, 314.7314765664714, 318.7116483648745, 319.74022867571614},
{92.03509566514494, 95.44497621836193, 97.93301152406725, 101.49180819872358, 105.65088450234082, 108.85980426212826, 111.58262041691164, 114.89455607870187,
119.43589024787555, 122.9163500097106, 127.06844359764042, 133.15351467381302, 135.01434491448396, 140.03077953204075, 142.57666354443413, 147.1137322595245,
151.74047957549945, 157.10442156072784, 162.58661616787234, 166.11422992616212, 167.50059641687366, 174.57847260909153, 178.90812903222218, 181.14036108332618,
182.5874117423085, 186.29078057530805, 189.29180315613382, 190.06376255308078, 195.33339289317792, 199.93670232968688, 204.59875004573706, 211.69353304653652,
214.1198533744616, 216.49257080996975, 218.9291577595253, 222.13007153901384, 225.3744241940457, 232.74210823831666, 235.23609687001905, 237.69361835143724,
241.08227796296825, 246.94489397557123, 247.75746494849855, 253.71303781724143, 256.29223072991454, 257.1256563823788, 261.4104754480469, 264.89566266433127,
266.6066523441263, 267.4944657102422, 269.20548961801046, 272.6806568652068, 273.58775510581694, 278.0092433761338, 282.39035649809506, 285.93674833532117,
295.8717004999003, 296.80399910166705, 298.5856421631121, 299.44467791257523, 307.5764827262699, 311.265142372392, 312.1449164399839, 314.8918999386731,
319.5321947704583, 322.26784577559096, 323.2182290670821, 324.1084885976447, 325.0733490300525, 326.9011347180376, 334.43539804303094, 338.1219818790606,
339.09961258235774, 344.76990450335796, 349.40232414085364, 350.3649522738527, 351.27982886318995, 355.10091445982414, 356.9305444893733, 362.676501927006,
365.4642266327095, 366.4474671476038, 367.3811973912587, 373.1158185497122, 377.76318134159203, 379.691143475922, 380.6132140385909, 381.58525961273887,
384.4026011502023, 387.306800451803, 389.2880919170236, 393.1512923955702, 394.142794801798, 395.0831210884745, 397.07125280297316, 399.9890133687759,
402.9730157913189, 404.9022652657989, 406.787491691716, 411.6679919664327, 415.4654621194505, 418.3709129215508, 420.42887377878924, 422.4176233665061,
425.3331847363532, 426.36321246158343, 437.93628451839226, 439.91911509671985, 440.86735691778847, 442.8291946737918, 451.52643079284906, 454.3502543187279,
457.2401348625619, 459.09880791177426, 460.10765606172384, 462.0433915143628, 464.02746424732607, 464.97894580697556, 465.98728235286296, 466.9457042355389,
467.9716493224284, 469.952895126153, 470.90205041356137, 471.8978141263659, 472.850818800059, 477.8969098904873, 479.7860743487078, 483.7512013081145,
484.7784990127453, 488.7330076075651, 489.67603349280984, 491.63572616272523, 493.72339144570026, 495.67534091041233, 499.7271092833366, 503.6412797374585,
505.5002945337613, 506.50992558916954, 508.4526985990731, 509.48313241565353, 511.41278098184745, 512.4546865922741, 513.3888394758542, 514.4288551293096,
518.3016895767877, 519.3395550920872, 522.2366044843038, 523.2519954165105, 525.1552988364048, 528.1428483253017, 530.1812920462645, 531.1493210844883,
534.1320123491877, 537.1801316512037, 538.1518025075683, 540.1830626803153, 543.124710980792, 548.0945584787735, 550.1464423508572, 552.1387813848073,
553.1906718144394, 555.1053998600016, 556.0131373229553, 558.9257829854911, 561.9134152379364, 562.8560972469294, 565.7911652042748, 568.8317823911899,
569.8150593887624, 570.8505248140114, 571.829369147002, 577.8982662683503, 578.8806962929154, 579.9137998702437, 583.9135058785267, 584.8446491655831,
586.8235811012087, 589.8878837974004, 590.8513701890881, 594.8798420329019, 595.8248678596194, 597.7965508706933, 599.8575486844194, 603.7405554194753,
606.7405042295918, 608.6761993025847, 610.713326324779, 612.6976510769083, 613.7664643765897, 614.677083249776, 620.7255511251976, 626.7135644233679,
628.6482693710398, 629.6570105099962, 631.7400311199661, 632.7118891638025, 635.7923587859781, 636.7709992391547, 637.8175487128655, 639.845112431125},
{184.3579859401234, 192.15443283236525, 196.64802549992893, 201.73378884943716, 209.52358084097227, 216.97691752635689, 224.0657993482173, 231.2862994438282,
238.6625730493835, 242.12408374656806, 249.15561782714988, 256.86471818361053, 263.5319594189586, 269.69586545849444, 275.31692514546455, 280.37778290772025,
291.9478638244543, 300.513497637161, 311.19794713029614, 316.63338160003235, 326.2836213329782, 333.96927781514285, 343.90841349102305, 355.4321905415327,
361.252430896053, 376.8323797468785, 387.39565954837866, 388.95387120776206, 394.25069503908753, 406.5751476081739, 412.0255709668396, 423.0368620509097,
427.85241248994515, 436.56670992765095, 448.6292975576179, 462.4971762699291, 465.0181329297163, 473.23028532363463, 494.21821330177335, 500.2434993554995,
513.0014139242118, 522.496114486894, 523.3168928943005, 531.9670562412849, 532.8711506150325, 544.1597408165791, 549.5100029267074, 552.1042259223233,
563.6853804561397, 573.3721908171308, 585.9698197341706, 588.5887838237893, 593.0741324403267, 606.7892991240519, 608.5480547483602, 624.0489334691753,
636.0119530229101, 638.7069486891311, 647.0702912092839, 653.45853792942, 658.1066220021323, 660.9695512159882, 670.2482611345346, 672.0439958533756,
688.8620623207361, 689.837601476221, 694.467443510656, 698.3050483874695, 709.5286091001703, 711.4958669465436, 712.4011920599339, 713.3956516374291,
715.2578337301354, 721.94146846189, 741.8317347736604, 743.677216267255, 757.0396508112627, 761.6854715358696, 763.643985916227, 770.2833878742357, 771.1795755249319,
777.925639149453, 783.6420677560948, 787.5911979357787, 789.4782206160799, 791.4862054664015, 803.9390536356827, 813.6647304995123, 823.192909529516,
828.1613375497931, 829.0784558301758, 831.1108351357013, 833.9435567609042, 842.7825840977509, 851.4847821767731, 855.4492099065142, 861.1528386263293,
863.1477431250398, 868.9580084279557, 874.6575284645011, 882.5505042589203, 883.4520422270363, 886.4264765324858, 887.3390667109261, 891.3824519702691,
899.1866593259443, 905.8205127765627, 911.8339813322575, 921.7265292754852, 926.5688610573277, 932.5099164592001, 935.6170179874478, 941.4892642985235,
943.5076114706833, 946.3928437680761, 950.4036796364679, 952.3284855397286, 956.3867546637368, 960.162538945685, 962.2535585402532, 966.1194868652601,
971.1132262837799, 975.0123521444228, 975.9241245963434, 978.8364299502302, 982.8490322233816, 991.6844199868463, 995.7058814734006, 997.626983124524,
1001.7054416129671, 1007.6703305966038, 1010.5779494726818, 1018.6353254890861, 1019.5704413811535, 1027.6061631316975, 1031.50270141741, 1040.5587129300611,
1042.4956826155196, 1043.5398720559738, 1052.4157045189665, 1056.2006012480815, 1073.035130227522, 1077.1008964464959, 1082.0138853699345, 1085.093949128817,
1089.9631741079747, 1096.965754582916, 1099.886063523516, 1104.9144828217911, 1105.848979511025, 1107.8634448066625, 1110.7459978156887, 1111.7669136568938,
1121.4995513078188, 1124.554675004647, 1127.5203486727237, 1130.3681660562618, 1137.3411610436212, 1143.1601815334398, 1147.1715966924762, 1148.1052085805802,
1154.069027187493, 1159.127039195876, 1165.93250135203, 1170.0025626733925, 1173.9247902934667, 1174.974155518286, 1181.9556455070372, 1184.0097986698054,
1184.9625590230953, 1194.0877760519652, 1195.0336743851974, 1197.0938050828192, 1206.0613724898317, 1207.1367604041764, 1212.0612351981104, 1213.1379974106208,
1216.048195019326, 1221.1112797216022, 1223.005557645146, 1227.0391903379211, 1227.9854774610744, 1235.9642503261903, 1238.0326284684475, 1251.8117078014764,
1252.8603727887098, 1261.7356816439792, 1263.6430445292704, 1265.64932015684, 1267.7456479627224, 1273.8219604039284, 1275.7683805978327, 1277.8750726888861,
1283.8893465472297, 1284.9620788769657, 1287.8214884938702, 1290.7770876742688, 1293.852039971248, 1297.6156557963761, 1300.5406066066353},
{369.0069786460945, 380.1669746478074, 387.57806250005774, 396.090322539455, 404.7421424771744, 414.5521582364457, 428.78572659222965, 437.9224700071899,
451.03092190250413, 465.5372251526111, 476.90434126302773, 490.8138580868185, 510.3126805745858, 524.1926000432966, 536.4847337664372, 549.5681955159181,
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16354.912672034006, 16586.075089726073, 16748.719292822258, 17116.725679190713, 17398.180206007823, 17622.83368123115, 17915.310612311896, 18124.78989034852,
18478.365872098464, 18686.39467076671, 18919.374167920923, 19143.728494715226, 19200.009025233103, 19644.645785970046, 20074.328247628582, 20378.206928445088,
20743.522644574154, 21198.004591356348, 21242.00817486205, 21426.25502500753, 21667.272151756748, 22058.323138287244, 22115.71353092448, 22297.409263294103,
22548.694442926266, 22861.1443558341, 23248.01485493211, 23553.305445219346, 23819.757377434315, 24226.244753341656, 24515.433999725345, 24885.875745174097,
24973.46835655312, 25381.900404589378, 25588.739691491806, 25678.711548179417, 25729.1116240537, 25804.650006005242, 25912.156929503897, 26050.34578599577,
26287.93157176747, 26387.143463641012, 26453.505676956192, 26939.46152960968, 27028.270481680316, 27316.021412339585, 27347.601211282647, 27630.879728915188,
28002.150642323373, 28181.756937479182, 28327.383147924767, 28497.546000816084, 28694.23576729056, 29161.022870229965, 29348.395979549303, 29702.69103114622,
29818.841708815187, 29941.210700447165, 29965.407188077148, 30248.182859493125, 30653.36529594024, 30807.255592353897, 30870.578318898024, 31051.657439803505,
31184.253544716303, 31734.914842800677, 31815.2497357844, 31972.371043585692, 32008.466202896245, 32183.85823452268, 32301.746718424758, 32355.460794891544,
32558.079516419606, 32652.492707533576, 32710.392787660683, 32999.33986704946, 33032.586402050736, 33277.68140336112, 33305.824369330614, 33573.74693349188,
33817.14460961934, 33863.38026556199, 34014.93184650621, 34142.25345854573, 34257.82231528342, 34471.74397148778, 34619.29237775281, 34696.3533555786,
34978.35787219777, 35147.645705015864, 35189.885671230346, 35248.86663235365, 35423.92670346899, 35611.231338911566, 35642.602646917585, 35796.60367187511,
36207.20817570764, 36291.657483091265, 36323.05484388122, 36400.16857425642, 36642.17224643523, 36652.48001529269, 37000.59281167143, 37452.803750730265,
37589.27269888348, 37719.50056087664, 37885.04885383869, 38153.96707060569, 38374.37355212518, 38506.026579471625, 38557.25901637052, 38847.80072468681,
38899.82583915901, 39096.631007015945, 39190.37843588755, 39289.54191563119, 39434.644869254524, 39525.3749844504, 39695.61107690911, 39741.98033953684,
39916.68948038638, 39961.166799407, 40471.59928849396, 40596.153694295455, 40689.14167424357, 40945.26204340346, 41144.54487142977, 41204.08393118228,
41234.612296106374, 41269.183253739866, 41565.23191335165, 41663.463643446186, 41733.45429816502, 42011.07895808608},
{11817.48284814069, 12025.030152959966, 12248.464195296252, 12405.01818427126, 12617.778358464597, 12847.438540703668, 13007.265038320045, 13235.073605058598,
13405.0579491439, 13663.553132655054, 13853.986296820434, 14092.167685994842, 14316.680466515418, 14538.619141937597, 14685.019452482671, 14930.993807382209,
15107.906198997342, 15266.122881636436, 15512.492951696953, 15795.566797500669, 15951.1720654472, 16095.899273870584, 16321.465032255444, 16607.815822100183,
16801.463180656727, 16992.851950260214, 17297.447163103196, 17509.257909147327, 17816.456537123406, 18042.777641744804, 18163.262466408913, 18517.3435549237,
18656.573047168997, 18903.57415031232, 19159.063881387796, 19301.084603672418, 19499.226683644727, 19851.737489572584, 20186.20199316548, 20329.79570413158,
20573.494383877598, 20809.03649523294, 21000.9292932581, 21248.87214778442, 21655.87886127781, 21981.282573777742, 22374.74539610225, 22585.99825438857,
22965.094229314134, 23276.898428752178, 23585.295459186844, 24032.233494191812, 24274.28256622153, 24673.854146868754, 25088.080246181093, 25337.77906428822,
25539.50873836242, 25897.8036273155, 26149.575348286624, 26513.59516189047, 26736.999651484835, 27286.716708715434, 27774.918948749575, 28043.02192718279,
28497.97818804517, 28930.615790815693, 29200.57022600932, 29690.509486080784, 29988.056297845756, 30645.991905586507, 30956.22246920247, 31289.775764778133,
31853.030105629456, 32271.36518453615, 32468.709057878063, 32977.72567643425, 33414.11888603862, 33808.27381333534, 34491.79693257003, 34845.74081192588,
35250.83830143174, 35516.921246488644, 35924.268480323604, 36347.164696462045, 36751.299562693486, 37206.531027200544, 37681.97395311277, 37986.59665367647,
38603.64723512325, 39267.56997034544, 39766.35419539569, 40527.8087854173, 41392.330207790656, 41592.92201033885, 41995.92453925431, 42693.315471461196,
43096.8897773028, 44019.16655363803, 44280.74832842459, 44444.70012666934, 45312.54980893415, 45668.9683099376, 46388.39412925136, 47852.35671903567,
48467.710122297285, 49648.733946069115, 50254.84010255284, 50836.71911226846, 51012.14372539943, 52302.73320661809, 52436.744044789244, 52816.77539587083,
53019.52898984149, 53117.36670282434, 53571.557319694024, 54198.008560948474, 54414.065926819516, 54608.66450125954, 55615.64930325156, 55920.93685839912,
56016.66214267581, 57578.93540077729, 57626.48398308241, 57784.23044622798, 58071.82492909185, 58314.960914047944, 58890.70676439089, 58962.52052038851,
59540.03831282236, 59745.033985631075, 60555.68226396474, 60783.35250874083, 60871.007684026874, 62144.40878205181, 62374.66449999, 63964.79392626599,
64544.72520432804, 65405.94160988867, 65609.38341029624, 65855.34324611587, 66347.12847265646, 66438.28362352039, 66541.81045314795, 66827.0338341525,
67191.34725376232, 67975.66207241916, 68138.16033626764, 68191.3896865123, 68801.20624550495, 69120.67046147799, 69166.18743358155, 69700.7730015856,
70124.27048156314, 70308.16410238993, 70537.69539100963, 70782.83755356305, 70888.57881951089, 72004.40138912469, 72389.70910055735, 72745.81512322256,
73107.6979157422, 73383.12241293085, 73511.26718852727, 73804.4157033782, 74208.63609802125, 74396.66300781416, 74624.80579761098, 75014.35929611747,
75660.38284719188, 76050.14791912262, 76346.26464865675, 76459.62688375934, 76898.95858165064, 76962.54562456123, 77101.11100936931, 77283.4448464156,
77398.37363132581, 77651.39533049139, 77995.03476855856, 78282.26115372841, 78389.93225444441, 78493.36065919467, 78756.67315839021, 79147.05195488808,
79913.64068416048, 80199.60853142221, 80407.14576880759, 80928.45933381062, 81140.92495826371, 81557.77030919166, 82074.87361430205, 82504.03981365131,
82740.33776350027, 83123.46518537514, 83211.8208441617, 83400.26917127652, 83439.77357849317, 83471.01660312648, 83652.03382005985, 84025.10834292526},
{23635.26250432443, 23794.30602789379, 24064.553615582015, 24338.874224687228, 24729.936018665605, 25002.147594322778, 25366.773977533063, 25625.019386813325,
25849.2088781992, 26099.033387656782, 26329.71202427824, 26661.656582902724, 26944.65570467436, 27270.612021644745, 27628.77114870539, 27916.56360543604,
28215.635684759884, 28628.085034890395, 28853.29367269045, 29191.854806354302, 29520.18481438468, 29780.368754225954, 30228.908137565988, 30688.584076924686,
31016.762623592538, 31390.327245706572, 31782.14355523691, 32049.73877380041, 32436.011288994898, 32662.201797771224, 33116.413890907694, 33441.42588576025,
33808.186418903104, 34233.867116267924, 34565.75413627513, 34862.18635669768, 35148.80149106708, 35609.56276733607, 36018.751950549995, 36563.41394184721,
36852.70351784452, 37182.372367484495, 37608.12144325968, 38077.444637455534, 38549.955251495856, 38954.88592082942, 39417.20505074357, 39719.21837290385,
40125.8042792429, 40724.961968813164, 41164.446272483015, 41812.49813492699, 42224.63331218628, 42696.16521971619, 43122.731069360976, 43799.471345968566,
44197.703964797154, 44646.15197543685, 45355.273930893854, 45824.229860239706, 46444.4887234516, 47134.91510550991, 47505.61346218054, 48093.25864686965,
48463.17322173295, 49202.644495571345, 49866.369538109204, 50307.0209373876, 50846.60775977639, 51577.42823677959, 52130.304148016454, 52691.69511085835,
53250.59897519543, 53967.63275140123, 54700.274430892474, 55372.01112053795, 55968.06987639319, 56867.35031473779, 57451.79982367642, 58303.09723544275,
58922.8114712268, 59778.29071557835, 60439.80336735719, 61070.38087021157, 62150.70579251569, 62506.2400896546, 63285.862270972764, 63649.8611841696,
64726.87956382803, 65193.53374374984, 65935.18078656228, 66478.24328217992, 67629.98753672457, 68075.27010430768, 69145.32377943303, 69879.54466395514,
70696.55103333302, 71654.7944444127, 72568.83597503215, 73543.6436505053, 74275.19928173361, 75061.84521541459, 76269.7516604588, 77463.51204693466, 78305.1789992632,
79411.95751984186, 80449.48391667801, 81867.38287662473, 82620.18603676399, 82944.96919543215, 83662.72836443047, 84043.33839954434, 85409.69753521914,
85971.29046297049, 87086.74165015959, 88481.83407147469, 89605.47221179189, 91526.81443755922, 92312.68978050741, 93643.31323778773, 94767.15504944729,
95911.9688314506, 96207.94226957098, 96557.98902011877, 97863.26429671576, 98690.18988085617, 100232.32087194078, 101282.92635004457, 102170.33744450907,
103419.96173645303, 105806.54240375882, 106885.7372462029, 108126.24266870097, 108352.78687260809, 109374.55719880741, 109985.82712955638, 111547.30250090164,
112219.54254045247, 112524.56181491369, 114222.13331339943, 115463.91211497717, 116301.28073471365, 116568.80752773283, 117545.88479743751, 118842.59674462846,
121251.37569304225, 122225.69118269537, 122553.41921701186, 124328.21439674891, 125911.04853568034, 126332.67981340272, 126778.59316507734, 128133.6364062359,
128940.7315370688, 129869.8564397216, 130816.27189549909, 131565.61592123925, 132335.19109727684, 133541.2433914402, 134856.99530451663, 135793.35514701836,
137660.8903957349, 139129.9766200432, 141240.50028465324, 142358.38109197514, 144220.28479912528, 144701.31459441246, 145687.72698996292, 145843.2784935425,
147261.06000399432, 148146.63163076664, 148589.9698039796, 150013.94834580386, 150484.86664524925, 151451.4972291893, 151508.11546051747, 152429.0542690752,
152871.364127855, 153370.06021153688, 153641.78862003674, 154849.60962490333, 155790.46469390494, 156281.4865058937, 156977.02901953223, 157472.55296719086,
158192.49607328785, 158315.9914360443, 158613.02078164357, 159256.1275360414, 159485.63731920972, 160649.9507699145, 162065.77879570262, 164040.82836848975,
164253.15745128618, 164518.2295916837, 166264.35692674396, 166346.1241747027, 166484.73418291975, 167760.38706816608, 168046.91179316072},
{47270.82162542315, 47612.6003882724, 48124.97050889209, 48806.865950659325, 49291.150790504194, 49650.72287078281, 50095.72289876183, 50683.79936198399,
51149.38583946996, 51872.735586218005, 52343.42234611583, 52856.607978855645, 53473.73273307313, 53915.84077838252, 54473.502474986155, 54875.45821700446,
55307.911888649345, 55748.46589845833, 56425.49354484362, 57081.95468276005, 57518.46926949399, 58141.93048815492, 58856.519215375396, 59226.33416256713,
59791.207615602456, 60605.46226322718, 61134.21447993713, 61955.6571271055, 62747.68309023563, 63492.31174488727, 64194.0102460736, 64717.92677240835,
65279.272353442255, 66083.5282114963, 66969.78133703033, 67481.44617127757, 68012.69112191009, 68522.32009313258, 69469.37420253527, 70067.0898301875, 70887.178675695,
71478.88697056568, 72114.21966790121, 72701.43984369676, 73483.68558111228, 74488.55779008688, 75251.09256181798, 75645.71752692231, 76494.64678387501,
77191.55832127016, 77939.89153744273, 78910.77240837885, 79478.67426548121, 80527.12129378975, 81387.53565899115, 81957.84389966795, 82800.12446947607,
83534.17895192992, 84228.82972175677, 84971.82746636451, 85784.87233481342, 86480.71285935756, 87672.98366678407, 88985.97998457833, 89601.12954041036,
90531.50899412342, 91738.90306102768, 92557.56817985185, 93868.73584377483, 94918.44039124223, 96223.49372440959, 97074.91249303488, 97889.69455412764,
98889.2755267402, 99531.97647523394, 100154.1509511274, 101257.82237326172, 102253.32717065712, 102960.96420645724, 104159.17673686496, 105012.09095103221,
105691.55194967844, 106488.91239032547, 107368.75917403684, 108407.15730746115, 109100.1200746079, 110021.99347326191, 110698.45139902468, 111675.67510622002,
112877.73286103945, 114309.50840195913, 115841.72362104406, 116634.5786915186, 117532.9162393803, 118776.33209454716, 120241.77401333873, 121254.5863858341,
122307.38549659493, 123634.50403331353, 125185.71812610143, 127142.1178438596, 128550.10176251282, 129884.3808381802, 131116.79696994726, 132610.6839630497,
133846.10045950869, 135325.1717496334, 136824.957907786, 138064.16125512627, 139325.70086610343, 141564.40387324974, 142639.3255128661, 143959.2859309,
145257.03781513628, 147027.1333823731, 149067.05354282158, 151711.81274094107, 153038.19819248506, 155398.6201218249, 157458.14779339853, 159849.27434453266,
161374.9352159001, 162857.97985592482, 164769.11720744925, 166147.99633650604, 167577.98001603963, 170419.56777390657, 171941.58288474844, 173559.62865373245,
175876.81962667927, 177802.64760756906, 179403.25887214657, 182141.4447441623, 184157.2619806166, 185987.52384298953, 189532.5628119443, 192618.02407572692,
196868.76513427327, 199421.25423186316, 202909.09836376304, 204841.88315899466, 208160.2163544678, 212184.63308609757, 214460.84505382317, 216393.99988388436,
219981.91491706518, 225902.8174322498, 230016.95609678063, 231119.78613955065, 232784.49405840438, 236847.35730770032, 238300.2762582974, 240745.73813290277,
242342.50925377544, 244465.1937314753, 245160.11078883402, 249534.3165309213, 253286.29488829247, 253624.37480595623, 257650.01444310325, 260673.3535187715,
261582.10369184543, 266650.47108694474, 266795.4791610051, 267799.86174038623, 268054.0422243958, 269830.37320485315, 270457.0307620312, 270675.32191205537,
272791.814343606, 275214.80167340493, 277188.203275372, 283831.16339052055, 284993.80190333363, 286750.54324496986, 290000.3170697107, 291023.1314566506,
293173.73961718613, 293533.353780165, 295035.15811863565, 300147.81524280395, 304257.82900497457, 309062.3647832776, 310936.55125602294, 313342.5459188892,
314743.20487610216, 316994.84273719386, 318215.3943710811, 321101.43468237336, 323603.30094258615, 324278.270774957, 327699.72886823973, 328182.1147374806,
330525.8316341028, 331706.8112985908, 332177.6565437824, 332485.42023789266, 333915.48719946627, 334468.9826006183, 336062.0295492246}};
public static final double[][] BIAS = {
{10.238823092354272, 9.725363299909107, 9.222487291610099, 8.735431957728302, 8.270736917504793, 7.822501301508534, 7.391255094466184, 6.969524108237091,
6.566913620871893, 6.175198427092166, 5.798152754606432, 5.4481341207297564, 5.097592087776076, 4.759433618300469, 4.450004708799128, 4.156932338684772,
3.8751360598984688, 3.6083533006645165, 3.35198935056703, 3.113857534769951, 2.904293124848894, 2.6771308191268623, 2.494203177679573, 2.309863939212093,
2.1268020131484757, 1.9726056477009326, 1.820451945782651, 1.6728173466173288, 1.536446723263771, 1.3966801064477672, 1.2787098372986367, 1.1477151014137548,
1.054254208175691, 0.9750901605149008, 0.8818490065123549, 0.792441662708069, 0.7078046630714576, 0.6231763526174284, 0.5550295228159745, 0.4961987134400305,
0.4460340343155875, 0.42092766507493157, 0.3709558040625834, 0.32731650555261926, 0.2930797961906953, 0.24997474501807215, 0.20171087707374413, 0.1872697727911162,
0.14448219007693647, 0.13742116701404872, 0.1048187814070875, 0.10820437202685436, 0.10052633157509167, 0.07253952907892267, 0.032953809383083635,
0.033147332017672955, 0.003972783123437948, 0.06237031442010072, 0.02272460940724239, 4.3177933812619325E-4, 0.006867272215557697, -0.02509871852774808,
0.019032093064211296, -0.02865193985317796, -0.0883736822658644, -0.14705127487667033, -0.15660167481003034, -0.20015162802077294, -0.246660576435814,
-0.22551885912460168, -0.23081079750132674, -0.22241537900060998, -0.1809261122402105, -0.17011714051528953, -0.19374101986580122, -0.2008863665881389,
-0.2825898777727797, -0.3012017436374525, -0.3665195368432668, -0.37091097830764735},
{21.77932649294573, 21.261115695867563, 20.751159067226258, 20.24915910631809, 19.75476648688801, 19.26732497026536, 18.786578222898626, 18.310905487923645,
17.839927196274342, 17.387865333182482, 16.94149546391533, 16.497249235818824, 16.059912306269123, 15.636802183334744, 15.221318484808126, 14.813233117380165,
14.406254563377503, 14.011143721866615, 13.61633519216458, 13.232001210193262, 12.85450016776248, 12.48402980947681, 12.124634639543544, 11.763358479018141,
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