Statistics

Problem Statement

Definition

Class:

Parabola

Method:

estimate

Parameters:

int[]

Returns:

int[]

Method signature:

int[] estimate(int[] Y)

(be sure your method is public)

Notes

• It can be shown that the answer is always well-defined and that for the optimal answer C always fits into a signed 32-bit integer variable.
• Note that the total badness of a function may overflow a signed 32-bit integer variable.

Constraints

• Y will have between 1 and 1,000 elements, inclusive.
• Each element of Y will be between -10^8 and 10^8, inclusive.

Examples

1. {0, 1, 4, 9, 16, 25, 36, 49}

   Returns: {1, 0, 0 }

   The parabola 1*x*x + 0*x + 0 is clearly the only perfect fit.

2. {10000, 10030, 10120, 10269, 10482, 10750, 11077, 11471}

   Returns: {30, 0, 10000 }

   This time there is some noise, but still obviously the best fit is the parabola 30*x*x + 0*x + 10000. This parabola has values 10000, 10030, 10120, 10270, 10480, 10750, 11080, 11470. Thus, the badness of the individual point estimates is 0, 0, 0, 1, 2, 0, 3, and 1, and hence the total badness of this parabola is 0+0+0+1+2+0+3+1 = 7.

3. {47}

   Returns: {1, -50, 47 }

   With just a single data point any parabola with C = Y[0] fits, so the one with the smallest A and B was picked.

4. {-10000, -9990, -9960, -9910, -9838, -9748, -9638, -9508}

   Returns: {10, 0, -10000 }

   The badness of the returned parabola is 0 + 0 + 0 + 0 + 2 + 2 + 2 + 2 = 8. The parabolas 10*x*x + (-9999) and 10*x*x + (-9998) also have the same badness as the returned parabola but their C is bigger.

5. {-123, 456, -78, 901234, -5678, 901, -234567}

   Returns: {1, -50, 18 }

6. {530, 486, 449, 415, 389, 370, 357, 347, 346, 349, 359, 377, 398, 427, 459, 499, 545, 597, 655, 721, 790, 865, 947, 1035, 1129, 1231, 1335, 1448, 1566, 1689}

   Returns: {3, -47, 529 }

7. {5301250, 5301238, 5301283, 5301415, 5301608, 5301888, 5302223, 5302637, 5303112, 5303650, 5304278, 5304966, 5305711, 5306543, 5307451, 5308406, 5309447, 5310563, 5311733, 5312987, 5314307, 5315702, 5317151, 5318683, 5320279, 5321949, 5323688, 5325486, 5327362, 5329322, 5331326, 5333418, 5335579, 5337800, 5340102, 5342465, 5344923, 5347414, 5350001, 5352647, 5355364, 5358144, 5361005, 5363940, 5366945, 5370001, 5373138, 5376341, 5379629, 5382975, 5386402, 5389890, 5393438, 5397059, 5400768, 5404531, 5408380, 5412271, 5416254, 5420316, 5424418, 5428605, 5432866, 5437209, 5441598, 5446068, 5450609, 5455209, 5459880, 5464627, 5469465, 5474353, 5479307, 5484332, 5489425, 5494594, 5499843, 5505151, 5510519, 5515967, 5521484, 5527063, 5532739, 5538450, 5544262, 5550124, 5556053, 5562065, 5568149, 5574298, 5580514, 5586800, 5593162, 5599579, 5606083, 5612655, 5619293, 5626008, 5632769, 5639628, 5646547, 5653527, 5660600, 5667728, 5674924, 5682175, 5689521, 5696941, 5704417, 5711965, 5719578, 5727268, 5735022, 5742858, 5750748, 5758724, 5766747, 5774865, 5783035, 5791288, 5799609, 5808003, 5816461, 5824988, 5833580, 5842253, 5850984, 5859788, 5868668, 5877610, 5886642, 5895718, 5904881, 5914110, 5923400, 5932774, 5942213, 5951727, 5961303, 5970941, 5980664, 5990449, 6000318, 6010233, 6020240, 6030296, 6040450, 6050655, 6060926, 6071275, 6081698, 6092186, 6102737, 6113372, 6124077, 6134826, 6145667, 6156580, 6167558, 6178603, 6189718, 6200906, 6212162, 6223508, 6234895, 6246356, 6257897, 6269519, 6281190, 6292936, 6304751, 6316650, 6328604, 6340632, 6352717, 6364901, 6377135, 6389440, 6401823, 6414261, 6426778, 6439364, 6452026, 6464763, 6477554, 6490421, 6503372, 6516375, 6529439, 6542607, 6555812, 6569111, 6582462, 6595889, 6609385, 6622947, 6636598, 6650306, 6664070, 6677922, 6691850, 6705829, 6719893, 6734012, 6748224, 6762475, 6776821, 6791222, 6805718, 6820266, 6834878, 6849571, 6864315, 6879143, 6894052, 6909006, 6924051, 6939151, 6954347, 6969597, 6984909, 7000283, 7015748, 7031278, 7046879, 7062551, 7078293, 7094096, 7109967, 7125914, 7141937, 7158014, 7174181, 7190409, 7206699, 7223074, 7239516, 7256027, 7272600, 7289238, 7305971, 7322747, 7339620, 7356538, 7373536, 7390612, 7407748, 7424951, 7442234, 7459572, 7476985, 7494482, 7512049, 7529678, 7547361, 7565129, 7582980, 7600889, 7618866, 7636906, 7655028, 7673206, 7691481, 7709792, 7728195, 7746668, 7765210, 7783806, 7802498, 7821241, 7840052, 7858940, 7877897, 7896922, 7916035, 7935189, 7954426, 7973731, 7993126, 8012574, 8032094, 8051672, 8071338, 8091054, 8110855, 8130734, 8150653, 8170670, 8190751, 8210897, 8231116, 8251408, 8271765, 8292194, 8312680, 8333263, 8353889, 8374598, 8395369, 8416220, 8437144, 8458131, 8479187, 8500310, 8521524, 8542784, 8564119, 8585522, 8607017, 8628558, 8650183, 8671865, 8693630, 8715456, 8737344, 8759307, 8781353, 8803461, 8825629, 8847895, 8870208, 8892602, 8915057, 8937571, 8960187, 8982850, 9005585, 9028386, 9051267, 9074226, 9097226, 9120323, 9143473, 9166718, 9189998, 9213366, 9236807, 9260315, 9283897, 9307541, 9331268, 9355063, 9378911, 9402849, 9426827, 9450897, 9475052, 9499249, 9523533, 9547869, 9572302, 9596784, 9621338, 9645964, 9670661, 9695427, 9720264, 9745174, 9770150, 9795214, 9820332, 9845507, 9870777, 9896094, 9921493, 9946967, 9972501, 9998114, 10023780, 10049538, 10075347, 10101248, 10127206, 10153222, 10179324, 10205504, 10231738, 10258032, 10284413, 10310863, 10337387, 10363982, 10390625, 10417357, 10444149, 10471028, 10497968, 10524972, 10552049, 10579200, 10606415, 10633707, 10661069, 10688488, 10715996, 10743565, 10771195, 10798898, 10826689, 10854519, 10882443, 10910426, 10938481, 10966612, 10994821, 11023081, 11051424, 11079827, 11108312, 11136855, 11165467, 11194156, 11222927, 11251741, 11280644, 11309625, 11338656, 11367765, 11396936, 11426190, 11455510, 11484888, 11514342, 11543882, 11573483, 11603135, 11632873, 11662690, 11692574, 11722522, 11752535, 11782620, 11812791, 11843003, 11873309, 11903675, 11934123, 11964615, 11995205, 12025840, 12056555, 12087353, 12118209, 12149141, 12180131, 12211204, 12242341, 12273543, 12304820, 12336173, 12367604, 12399082, 12430638, 12462262, 12493968, 12525730, 12557578, 12589473, 12621455, 12653511, 12685625, 12717817, 12750073, 12782406, 12814798, 12847260, 12879802, 12912403, 12945094, 12977832, 13010660, 13043535, 13076491, 13109538, 13142637, 13175785, 13209029, 13242334, 13275729, 13309161, 13342683, 13376272, 13409936, 13443664, 13477459, 13511317, 13545261, 13579265, 13613345, 13647496, 13681709, 13715999, 13750353, 13784793, 13819294, 13853845, 13888490, 13923192, 13957979, 13992822, 14027743, 14062738, 14097801, 14132914, 14168127, 14203379, 14238731, 14274136, 14309615, 14345162, 14380781, 14416461, 14452218, 14488046, 14523947, 14559907, 14595959, 14632060, 14668244, 14704477, 14740806, 14777188, 14813659, 14850180, 14886774, 14923447, 14960177, 14996986, 15033865, 15070818, 15107831, 15144926, 15182076, 15219313, 15256603, 15293981, 15331415, 15368911, 15406497, 15444139, 15481865, 15519647, 15557516, 15595433, 15633427, 15671510, 15709643, 15747848, 15786135, 15824467, 15862902, 15901383, 15939942, 15978559, 16017273, 16056042, 16094877, 16133791, 16172752, 16211798, 16250924, 16290106, 16329364, 16368698, 16408107, 16447570, 16487109, 16526717, 16566384, 16606146, 16645957, 16685843, 16725807, 16765837, 16805936, 16846099, 16886330, 16926643, 16967029, 17007463, 17047984, 17088579, 17129227, 17169953, 17210760, 17251617, 17292567, 17333562, 17374656, 17415804, 17457025, 17498293, 17539653, 17581082, 17622586, 17664154, 17705799, 17747501, 17789285, 17831123, 17873035, 17915037, 17957090, 17999217, 18041413, 18083681, 18126018, 18168421, 18210903, 18253456, 18296082, 18338757, 18381512, 18424342, 18467243, 18510222, 18553256, 18596351, 18639543, 18682785, 18726100, 18769485, 18812954, 18856480, 18900072, 18943738, 18987479, 19031281, 19075169, 19119110, 19163129, 19207229, 19251391, 19295603, 19339915, 19384266, 19428705, 19473231, 19517790, 19562455, 19607165, 19651951, 19696815, 19741740, 19786742, 19831812, 19876936, 19922150, 19967424, 20012772, 20058187, 20103677, 20149235, 20194865, 20240573, 20286341, 20332176, 20378087, 20424066, 20470097, 20516219, 20562403, 20608680, 20655001, 20701406, 20747855, 20794405, 20841021, 20887681, 20934435, 20981259, 21028145, 21075109, 21122122, 21169237, 21216397, 21263623, 21310936, 21358328, 21405775, 21453289, 21500882, 21548537, 21596262, 21644049, 21691925, 21739858, 21787865, 21835950, 21884096, 21932319, 21980596, 22028952, 22077379, 22125891, 22174458, 22223102, 22271807, 22320588, 22369434, 22418353, 22467323, 22516385, 22565510, 22614721, 22663987, 22713333, 22762740, 22812206, 22861766, 22911379, 22961072, 23010814, 23060639, 23110551, 23160507, 23210549, 23260670, 23310831, 23361089, 23411409, 23461785, 23512258, 23562781, 23613373, 23664052, 23714784, 23765597, 23816473, 23867414, 23918443, 23969529, 24020682, 24071906, 24123206, 24174578, 24226012, 24277525, 24329107, 24380747, 24432474, 24484246, 24536112, 24588044, 24640029, 24692111, 24744236, 24796448, 24848731, 24901070, 24953485, 25005983, 25058541, 25111161, 25163872, 25216642, 25269478, 25322384, 25375352, 25428411, 25481533, 25534711, 25587979, 25641289, 25694706, 25748170, 25801699, 25855310, 25908981, 25962732, 26016549, 26070438, 26124407, 26178437, 26232521, 26286690, 26340935, 26395236, 26449615, 26504060, 26558591, 26613182, 26667827, 26722559, 26777351, 26832230, 26887159, 26942181, 26997254, 27052393, 27107609, 27162906, 27218256, 27273697, 27329196, 27384761, 27440383, 27496099, 27551877, 27607729, 27663642, 27719637, 27775682, 27831822, 27888012, 27944286, 28000614, 28057032, 28113517, 28170051, 28226683, 28283368, 28340131, 28396943, 28453837, 28510810, 28567843, 28624968, 28682140, 28739382, 28796697, 28854088, 28911559, 28969088, 29026678, 29084348, 29142075, 29199886, 29257767, 29315725, 29373734, 29431825, 29489976, 29548202, 29606515, 29664878, 29723308, 29781811, 29840406, 29899040, 29957775, 30016560, 30075414, 30134343, 30193344, 30252403, 30311538, 30370755, 30430033, 30489383, 30548799, 30608293, 30667847, 30727462, 30787162, 30846945, 30906777, 30966685, 31026660, 31086717, 31146833, 31207012, 31267276, 31327596, 31388007, 31448471, 31508994, 31569602, 31630291, 31691029, 31751848, 31812734, 31873693, 31934729, 31995835, 32056991, 32118224, 32179532, 32240928, 32302365, 32363885, 32425475, 32487126, 32548853, 32610652, 32672519, 32734466, 32796472, 32858541, 32920687, 32982915, 33045210, 33107562, 33169995, 33232479, 33295047, 33357692, 33420406, 33483187, 33546034, 33608938, 33671939, 33734985, 33798116, 33861309, 33924591, 33987917, 34051327, 34114811, 34178366, 34241971, 34305669, 34369426, 34433246, 34497142, 34561105, 34625160, 34689262, 34753431, 34817677, 34882010, 34946402, 35010861, 35075385, 35139986, 35204655, 35269389, 35334185, 35399071, 35464017, 35529041, 35594120, 35659289, 35724511, 35789799, 35855175, 35920605, 35986126, 36051703, 36117346, 36183063, 36248860, 36314708, 36380630, 36446629, 36512709, 36578849, 36645053, 36711322, 36777672, 36844097, 36910590, 36977136, 37043767, 37110473, 37177245, 37244071, 37310984, 37377962, 37445007, 37512128, 37579321, 37646579, 37713907, 37781292, 37848765, 37916302, 37983904, 38051580, 38119344, 38187161, 38255041, 38323007, 38391038, 38459137, 38527302, 38595530, 38663840, 38732221, 38800674, 38869177, 38937770, 39006426, 39075164, 39143960, 39212818, 39281759, 39350772, 39419859, 39489006, 39558220, 39627503, 39696857, 39766295, 39835790, 39905352, 39974985, 40044710, 40114488, 40184331}

   Returns: {35, -47, 5301245 }

8. {10, 78, 190}

   Returns: {22, 46, 10 }

9. {30, 35}

   Returns: {1, 4, 30 }

10. {30, 9470}

    Returns: {50, 50, 30 }

11. {30, -9470}

    Returns: {1, -50, -9421 }

12. {-872, -119, 133, -71, 168, -297, -473, 49, -209, -197, 260, -917, 628, -143, 348}

    Returns: {5, -50, -74 }

13. {960, -791, -999, -460}

    Returns: {50, -50, -791 }

14. {482, 119, -982, 878, 670, 840, -354, 162, -125, -529, -514, 71, 52, -265, -95, 961, -505, -932, 148}

    Returns: {1, -50, 409 }

15. {467, 408, -277, 230, -300, 142, 177, 560, -599, -512, 615, 721, 493, 873, 915}

    Returns: {7, -50, 243 }

16. {-743, -317, -800, -257, 184}

    Returns: {50, 12, -743 }

17. {41, 106, 664, -483, -802, 328, 785, 804, -536, 898, 431, 731, -315, -553, -36, 524}

    Returns: {1, 14, 89 }

18. {583, -147, 238, -277, 382, 786, -414}

    Returns: {1, -50, 334 }

19. {657, 137, 888, -465, -269, 90, 157, -918, -9, -361, 152}

    Returns: {3, -50, 199 }

20. {-468, 934, 495, 63, 637, -548, 241, -767, 284, 723, -576, -223, -6, -482, 970, 236}

    Returns: {3, -50, 186 }

21. {-91, -969, -652, 120, 284, 647, 559, -831}

    Returns: {11, 47, -120 }

22. {-456, 47, 664, 274, 119, -25}

    Returns: {1, 19, 27 }

23. {-252, 881, 554, -933, 244, -458, 841, 319, 246, 58, 932, 380, 862, -34, 872, 450, 307}

    Returns: {1, 0, 228 }

24. {698, -955, 181, -503, -568, -292, -117, 962, 775, 416, -624, -639, -38, 886}

    Returns: {3, -40, 10 }

25. {-739, -799, -721, 495, 607, 166, -296, 80, -197, -779}

    Returns: {1, 50, -661 }

26. {-91, -1000, 336, -750, -152, -863, -244, -958, -459, -915, -713, -629}

    Returns: {1, -50, -313 }

27. {711, 5, -589, 603, 582, 662, 13, 81, -72, 154, 161, -980, 423, -849, -642, 711, -692, 887, 112, -308}

    Returns: {1, -50, 382 }

28. {797, 273, -520, 458, -875}

    Returns: {1, -50, 322 }

29. {-748, -955, -819, -381, -890, 800, 122, -370, -511, 254, 835, 503, 95, -691, 126, 187}

    Returns: {1, 49, -756 }

30. {267, 757, 169, -835, 152, 6, -299, 139, -894, 952, -766, -154}

    Returns: {1, -50, 265 }

31. {-276, 856, -380, 155, 729, 555, 1, 224, -714, -870, 988, 40, -761, 849, -56, 337, 611}

    Returns: {4, -50, 187 }

32. {18677350, 18889771, 18902566, 18495455, 18632828, 18745121, 18723045, 18550908, 18860948, 18399648, 18478955, 18857836, 18858997, 18666385, 18947602, 18401214, 18963752, 18574893, 18677486, 18419439, 18652699, 18945330, 18882957, 18779265, 18448813, 18491456, 18923396, 18877847, 18940707, 18757122, 18704538, 18809940, 18592779, 18473980, 18485900, 18915656, 18698334, 18803429, 18727747, 18944160, 18756765, 18493401, 18477194, 18826489, 18757884, 18432710, 18746984, 18439622, 18791490, 18661724, 18647690, 18602048, 18685217, 18601002, 18869441, 18696138, 18849175, 18844380, 18715640, 18440438, 18546069, 18886498, 18384393, 18412863, 18827540, 18864146, 18930285, 18844211, 18655579, 18693858, 18493386, 18703984, 18516342, 18564766, 18830711, 18740384, 18909378, 18834683, 18634207, 18916433, 18927116, 18665158, 18717801, 18971683, 18414469, 18788371, 18875231, 18976757, 18579897, 18787365, 18437275, 18583224, 18583414, 18475231, 18902403, 18825259, 18457860, 18630374, 18879599, 18580302, 18813471, 18401338, 18542914, 18473804, 18985305, 18806339, 18399543, 18802223, 18923200, 18877288, 18791828, 18529381, 18937479, 18821789, 18509379, 18492991, 18843948, 18835676, 18981432, 18513994, 18588473, 18928421, 18905040, 18867207, 18505399, 18822340, 18958128, 18938842, 18752458, 18863268, 18616395, 18742481, 18827665, 18490006, 18551282, 18924181, 18762661, 18523908, 18679289, 18924130, 18512862, 18790722, 18447965, 18831075, 18503215, 18653656, 18959964, 18640724, 18952762, 18691093, 18742966, 18946463, 18541981, 19012795, 18489434, 18725415, 18611080, 18937824, 18679501, 18851115, 18924841, 18435819, 18848038, 18676382, 19011672, 18823297, 18543590, 18786624, 18500453, 18598422, 18545433, 18685680, 18627905, 18520329, 18585770, 18977869, 18614899, 18612737, 18520993, 18537918, 18573518, 18855090, 18808140, 18571354, 18879191, 18754323, 19021806, 18676832, 18811146, 18542613, 18778315, 18556532, 18487962, 18662839, 19038236, 18594827, 18799809, 18549661, 18789988, 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    Returns: {2, -50, 18704184 }

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-51846654, -51768460, -51690188, -51611821, -51533359, -51454826, -51376199, -51297497}

    Returns: {43, -24, -87354920 }

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    Returns: {37, -50, 38782588 }

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    Returns: {12, 8, -61880298 }

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    Returns: {26, 46, -80784996 }

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    Returns: {19, 50, -8725198 }

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    Returns: {33, -25, -69159990 }

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47148477, 47334532, 47289806, 47285999, 47423030, 47093962, 47606280, 47601867, 47806045, 47644359, 47655032, 47810754, 48413146, 48237308, 48427704, 48274543, 48478115, 48292852, 48403625, 48348196, 48696264, 48921003, 48947516, 49325759, 49496157, 49544294, 49576764, 49437919, 49119782, 49198707, 49775385, 50069216, 50117619, 50281727}

    Returns: {48, 50, 5485825 }

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-9660689, -9635052, -9609637, -9584105, -9558457, -9532930, -9507374, -9481649}

    Returns: {14, -38, -21219370 }

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    Returns: {30, 23, -85309619 }

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    Returns: {6, 3, -60684768 }

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    Returns: {11, -35, -75979663 }

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    Returns: {33, -39, 5177058 }

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-40583004, -40536821, -40454199}

    Returns: {38, -40, -71952851 }

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    Returns: {29, 26, -39916502 }

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    Returns: {24, 25, -82528166 }

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    Returns: {46, -28, -27816880 }

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    Returns: {42, 48, -35213142 }

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    Returns: {44, 18, 39126713 }

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29308482, 29519971, 29592508, 29442965, 29364195, 29587670, 29390591, 29818887, 29653342, 29865411}

    Returns: {28, -11, 4397533 }

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-47479255, -47435591, -47391883, -47348092, -47304249, -47260411, -47216472, -47172478}

    Returns: {24, 24, -67331829 }

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3912993, 3723810, 3456273, 4258415, 4245393, 4686870, 3409901, 3598314, 4713728, 4425248, 5212648, 5219172, 5361131}

    Returns: {18, -50, -10594637 }

54. {-48149254, -48151716, -48145580, -48156927, -48130722, -48156571, -48143893, -48128315, -48140319, -48144065, -48139444, -48135750, -48133642, -48149817, -48151779, -48130679, -48128814, -48127492, -48120176, -48122920, -48124338, -48122366, -48118686, -48113877, -48121342, -48141208, -48123177, -48109835, -48113594, -48108084, -48130879, -48117420, -48109249, -48102316, -48124255, -48105043, -48106148, -48100447, -48097887, -48093041, -48110842, -48113081, -48098204, -48104583, -48077373, -48073997, -48074493, -48080680, -48092471, -48087600, -48074762, -48074632, -48076880, -48071474, -48064769, -48054415, -48069431, -48069279, -48048830, -48064828, -48061092, -48044160, -48045875, -48034168, -48044370, -48022570, -48041135, -48033013, -48007469, -48003604, -48018018, -48017020, -47989983, -48009906, -48000562, -47984506, -47996467, -47980303, -47974601, -47979561, -47983964, -47981748, -47966805, -47969782, -47950097, -47960477, -47930743, -47952080, -47926004, -47920563, 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    Returns: {27, -11, -48143198 }

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23853635, 23946608, 24039671, 24132844, 24226100, 24319460, 24412912, 24506466, 24600111, 24693860, 24787689, 24881629, 24975650, 25069786, 25164002, 25258325, 25352737, 25447241, 25541846, 25636560, 25731356, 25826251}

    Returns: {48, -2, -21121584 }

56. {-83423373, -83423398, -83423437, -83423456, -83423451, -83423476, -83423498, -83423486, -83423508, -83423530, -83423510, -83423521, -83423513, -83423515, -83423505, -83423497, -83423525, -83423484, -83423468, -83423485, -83423461, -83423453, -83423430, -83423416, -83423396, -83423335, -83423342, -83423300, -83423269, -83423215, -83423209, -83423146, -83423103, -83423076, -83423036, -83422974, -83422941, -83422878, -83422843, -83422792, -83422751, -83422679, -83422626, -83422563, -83422479, -83422433, -83422364, -83422316, -83422229, -83422135, -83422089, -83422001, -83421918, -83421858, -83421744, -83421672, -83421573, -83421503, -83421398, -83421324, -83421225, -83421127, -83421011, -83420917, -83420825, -83420717, -83420599, -83420510, -83420392, -83420273, -83420139, -83420034, -83419924, -83419787, -83419685, -83419541, -83419442, -83419299, -83419148, -83419026, -83418888, -83418750, -83418613, -83418498, -83418321, -83418210, -83418060, -83417895, -83417758, -83417574, 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-82618898, -82617106, -82615308, -82613508, -82611730, -82609921, -82608117}

    Returns: {1, -24, -83423378 }

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    Returns: {19, 39, -56344015 }

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    Returns: {30, -31, -84241253 }

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37588806, 37601331, 37613926, 37626535, 37639316, 37651886, 37664554, 37677252, 37689956, 37702740, 37715335, 37728125, 37740883, 37753745}

    Returns: {7, 8, 31924171 }

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    Returns: {39, -12, 16249777 }

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    Returns: {32, -34, 11964178 }

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    Returns: {25, 40, -28182195 }

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    Returns: {36, -46, -55751806 }

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    Returns: {27, -33, -76802002 }

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    Returns: {49, 31, -44824722 }

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    Returns: {42, -24, -21502436 }

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    Returns: {40, -7, 27742186 }

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    Returns: {33, -14, -52195225 }

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    Returns: {26, -49, 9176806 }

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    Returns: {35, 10, -32852092 }

71. {-24349726, -24351277, -24351098, -24351115, -24350939, -24348055, -24347436, -24348904, -24347832, -24348431, -24348402, -24345671, -24345282, -24344239, -24345106, -24344366, -24340274, -24341056, -24340579, -24339536, -24337138, -24336326, -24333187, -24334389, -24332251, -24329697, -24328393, -24328867, -24327245, -24322586, -24320419, -24320374, -24319320, -24317678, -24315895, -24310663, -24308357, -24308834, -24303439, -24301339, -24299641, -24296146, -24295882, -24294340, -24290344, -24288859, -24284746, -24280982, -24279359, -24276346, -24273500, -24269731, -24266308, -24262996, -24259951, -24255435, -24254460, -24248752, -24244637, -24241478, -24238365, -24233152, -24230123, -24228113, -24223785, -24218790, -24215607, -24209444, -24208144, -24202903, -24196303, -24193446, -24187992, -24184663, -24181359, -24177449, -24171698, -24165242, -24159630, -24156905, -24151520, -24148177, -24141319, -24136146, -24129969, -24127685, -24121232, -24115787, -24109957, -24105423, 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3039860, 3098921, 3155230, 3214340, 3272563, 3332117, 3392412, 3450779, 3506978, 3565916, 3624349, 3683741, 3745495, 3801210, 3861972, 3919187, 3979444, 4038417, 4098551, 4158456, 4216250, 4276620, 4335791, 4396377, 4457106, 4515924, 4577247, 4635949, 4695005, 4757780, 4817041, 4876218, 4936449, 4995204, 5058780, 5118168, 5177151, 5239158, 5298504, 5360318, 5421646, 5482759, 5543537, 5603437, 5664341, 5725634, 5785572, 5846594, 5909249, 5969917, 6030993, 6093937, 6155102, 6216715, 6277670, 6339500, 6402337, 6462509}

    Returns: {31, -2, -24349829 }

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    Returns: {28, 13, -1904338 }

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    Returns: {32, -26, 20898376 }

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    Returns: {5, -19, -8756804 }

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    Returns: {23, -50, 36827170 }

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    Returns: {18, -7, -88967873 }

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    Returns: {2, -18, 730287 }

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    Returns: {45, -20, 17500643 }

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46402617, 46762506, 46584235}

    Returns: {30, 50, 22317859 }

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62484263}

    Returns: {47, 36, 15626987 }

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    Returns: {28, 2, 21573203 }

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    Returns: {9, 50, -6874208 }

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    Returns: {1, -50, 3690687 }

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    Returns: {11, -50, -7292803 }

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    Returns: {4, -50, -560956 }

86. {89989527, 77921953, -52415531, -83803464, 69236368, 504877, 7669173, 63980280, -83298131, 11723275, -38006061, 75563329, -22316847, -29340065, -25127443, -28583955, 74986832, -10169749, 95325804, -31281166, 32751182, 22130690, -68756039, 51294519, 80595090, -56905151, -22960353, 72661528, -32376980, -12269581, -17432210, -26766036, 93304254, 69884528, 44399539, 49508510, -75695131, -63897265, -14250766, -92728517, -32774358, -62373391, 79319608, 73100770, 81053988, 14868122, 46176544, -57498834, 17334763, -70387314, 52635948, -988926, -7292397, 90052844, -10138558, 16153266, -88271945, -10113502, 77079718, -3837152, 95083895, 35853544, 9114840, 96546088, 80845038, 85839119, 96354556, 95477350, -3582698, -10993719, 13132513, -59580893, 28083913, -84620505, -42309338, -36868406, 17500092, 14445026, 11439294, -86984154, -30512938, 73910840, -50882164, 43283354, 91473330, 99986580, 47671424, -42660, 66275789, -6362690, -73787449, 89967234, -6167379, 61496287, 95571143, 29796302, 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    Returns: {10, -50, 2711822 }

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    Returns: {1, -50, -2724915 }

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    Returns: {1, -50, -2902405 }

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    Returns: {1, 50, 5372099 }

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    Returns: {4, -50, 4951920 }

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    Returns: {7, 50, -7517785 }

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    Returns: {31, 50, -684226 }

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    Returns: {31, -50, 634495 }

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    Returns: {15, -50, 945654 }

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    Returns: {20, 50, -201318 }

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    Returns: {29, -50, -388926 }

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    Returns: {44, -50, 203754 }

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14692201, 6045963, 22808573, 14083293, 7968508, 17847623, 15403916, 16281363}

    Returns: {15, 50, 468563 }

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14299857, 4414072, 8005173, 17141502, 12807668, 5172546, 7330535, 8397701, 3312491, 8133534, 5726418, 14672135, 16792616, 13948828, 9384648, 7854957, 1282593, 2281446, 3180249, 6889069, 15531774, 5882308, 6386060, 13310538, 4079372, 3279467, 3709560, 4156675, 7761223, 6859626, 1001802, 18972611, 18932700, 9130899, 17595659}

    Returns: {11, -27, -331151 }

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     Returns: {22, -50, -252894 }

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22308111, 22857813, 9928103, 27855462}

     Returns: {24, -50, -699532 }

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11130971, 13509732, 9707088, 5622714, 3818947, 20105559, 15047029, 7346266, 11684907, 12144508, 16483312, 21153794, 12270909}

     Returns: {14, -50, 127636 }

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     Returns: {12, -50, 541718 }

104. {-2993990, -2453594, -9460195, -4341266, 8321932, 9842670, 4699523, -5353423, 1928398, -471184, -8745192, -6264954, -627563, 5651046, -3146849, -6769510, 1992971, -8364552, -5644591, -302640, -9512529, -5894169, 8700040, 2645519, -7224354, 7168058, -3871, -6576194, -2028634, -883476, 8872574, 7804683, -462125, 2672355, 6806838, 8460484, -5559102, 5830449, 2026210, 7190935, -2111426, -9539478, -2864685, -9079609, -8308984, 4666024, 4533073, 4904144, -3290980, 9453807, 2861870, 385496, -759067, -4780450, 6681659, 4705185, 7205534, -3252430, 8580313, 1046691, -868326, 8057050, -548386, 7260876, -7082084, -2491011, 8113170, -1917398, 1457426, -2213473, -512299, -6591786, 6491917, -9496904, 4540196, -6586346, 8486177, -4872732, 4956757, -5827714, 7604728, 9696407, -251599, -7133572, -3502596, -8012265, 170453, 9596727, 6403893, -6385093, -3059888, -5078686, 4268629, -4622424, -9560225, -1522329, -3762402, -1813200, 826073, -1786265, -4849527, -3631282, -3821461, -624314, 9724180, 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32191662, 38071098, 30993564, 34260873, 35329087, 42175539}

     Returns: {36, 50, 462067 }

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30994420, 43565678, 28216132, 30606896, 43572627, 38768480, 29397235, 33246509, 44593739, 44164852, 35760256, 45959836, 35770899, 30891498}

     Returns: {42, 50, 440400 }

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     Returns: {34, -50, -57288 }

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     Returns: {28, 50, 258430 }

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     Returns: {6, 50, -176661 }

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     Returns: {41, -50, 573629 }

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23621347, 23696216, 21402762, 29854294, 20505714, 36323260, 37220359, 34595713, 29472958, 26252669, 31525054, 32198072, 21910980, 31883433, 38785121, 38981085, 29063654, 26841030, 27311169, 36732300, 33302272, 22906649, 36561162, 22927208, 37214576, 22971759, 38875250, 24751898, 35624591, 29270620, 39824160, 37980384, 20981519, 38294568, 35648298, 33595614, 27392169, 31365817, 38645644, 25072830, 29521554, 38095463}

     Returns: {33, -50, -380085 }

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17680472, 5045255, 12963228, 14878820, 10783206, 12654937, 12512979, 7269983, 22187049, 15025778, 20394319, 15046087, 21441321, 3679057, 14245123, 20179603, 20469334, 17299061, 14743215, 3896180, 10495150, 16255861, 16141157, 11106385, 5944672, 3850557, 16566438, 22421359, 22483358, 4530092, 19216483, 11664338, 6093704, 4721221, 7551029, 16718198, 6235964, 4941155, 16556560, 12654044, 19502754, 20787186, 10524746, 6409830, 16917215, 17227619, 5064045, 6945775, 13989991, 10428686, 10265638, 22035163, 23090479}

     Returns: {16, -50, 357404 }

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     Returns: {50, 50, -100000000 }

113. {12345678, -23456795, 12345680, -23456765, 12345738, -23456679, 12345852, -23456537, 12346022, -23456339, 12346248, -23456085, 12346530, -23455775, 12346868, -23455409, 12347262, -23454987, 12347712, -23454509, 12348218, -23453975, 12348780, -23453385, 12349398, -23452739, 12350072, -23452037, 12350802, -23451279, 12351588, -23450465, 12352430, -23449595, 12353328, -23448669, 12354282, -23447687, 12355292, -23446649, 12356358, -23445555, 12357480, -23444405, 12358658, -23443199, 12359892, -23441937, 12361182, -23440619, 12362528, -23439245, 12363930, -23437815, 12365388, -23436329, 12366902, -23434787, 12368472, -23433189, 12370098, -23431535, 12371780, -23429825, 12373518, -23428059, 12375312, -23426237, 12377162, -23424359, 12379068, -23422425, 12381030, -23420435, 12383048, -23418389, 12385122, -23416287, 12387252, -23414129, 12389438, -23411915, 12391680, -23409645, 12393978, -23407319, 12396332, -23404937, 12398742, -23402499, 12401208, -23400005, 12403730, -23397455, 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     Returns: {1, -50, -17431820 }

114. {1234567, -2345684, 1234569, -2345654, 1234627, -2345568, 1234741, -2345426, 1234911, -2345228, 1235137, -2344974, 1235419, -2344664, 1235757, -2344298, 1236151, -2343876, 1236601, -2343398, 1237107, -2342864, 1237669, -2342274, 1238287, -2341628, 1238961, -2340926, 1239691, -2340168, 1240477, -2339354, 1241319, -2338484, 1242217, -2337558, 1243171, -2336576, 1244181, -2335538, 1245247, -2334444, 1246369, -2333294, 1247547, -2332088, 1248781, -2330826, 1250071, -2329508, 1251417, -2328134, 1252819, -2326704, 1254277, -2325218, 1255791, -2323676, 1257361, -2322078, 1258987, -2320424, 1260669, -2318714, 1262407, -2316948, 1264201, -2315126, 1266051, -2313248, 1267957, -2311314, 1269919, -2309324, 1271937, -2307278, 1274011, -2305176, 1276141, -2303018, 1278327, -2300804, 1280569, -2298534, 1282867, -2296208, 1285221, -2293826, 1287631, -2291388, 1290097, -2288894, 1292619, -2286344, 1295197, -2283738, 1297831, -2281076, 1300521, -2278358, 1303267, -2275584, 1306069, -2272754, 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     Returns: {4, -50, 685288 }

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     Returns: {7, -50, -197604 }

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     Returns: {7, -49, 12417 }

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     Returns: {7, -16, 652 }

118. {3033873, 9239062, 7194669, 6374331, 9000196, 2557924, 1796956, 3673290, 4278969, 1188663, 5800783, 7598111, 1361013, 2277947, 8991470, 9536506, 5369601, 6436020, 3342218, 4778591, 8942616, 143529, 9085765, 2886034, 2439045, 470330, 7432402, 2749529, 7479105, 602274, 1132425, 9104021, 7916155, 5727779, 140792, 8383598, 1640151, 5507209, 1936763, 7540962, 8410818, 3054446, 4719932, 9562441, 8127956, 7469661, 692750, 5838841, 1183810, 6852926, 5718778, 9704359, 8171311, 3883522, 9227034, 3100970, 1468371, 882983, 1165777, 563571, 6964764, 8793828, 9314999, 6818634, 1056356, 9029567, 2239254, 9643526, 5183261, 4281809, 6948343, 7681960, 5544371, 6385249, 2997865, 4841472, 914106, 1241053, 7768213, 5294734, 6058458, 6979419, 7990707, 4318780, 1658113, 1227697, 9671654, 9369895, 9358275, 9629716, 2864613, 6304846, 1021395, 2909371, 3271175, 4396710, 2988225, 7964453, 319692, 3224988, 5834263, 2130178, 4630680, 7998192, 3358013, 8755245, 322485, 9797079, 8547875, 3257200, 9270698, 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4293021, 1445835, 1782569, 9215839, 8204707, 9626997, 8589242, 1289025, 9665838, 3166890, 905212, 7182485, 6782237, 7566260, 1590414, 363923, 4875941, 5960440, 5426306, 7988380, 3343666, 3910955, 3444487, 3569822, 1453374, 9067423, 9755116, 975440, 8553618, 4696511, 241175, 8690914, 690809, 6627657, 6511651, 5004636, 9673267, 839445, 9153188, 7645543, 4940681, 5821473, 4787815, 353871, 4804667, 7573348, 4007083, 6844147, 5183363, 688869, 9260955, 772426, 325771, 447694, 53487, 8748776, 7113942, 8352678, 8470007, 1684587, 3041457, 6494188, 8614719, 4695348, 701370, 3481276, 3865103, 3771499, 5300618, 5550640, 8027709, 2286189, 7401610, 1620783, 648893, 7470200, 7674162, 4671442, 928221, 4942839, 9581038, 2326408, 8464666, 2825929, 5633548, 9256971, 4771344, 1757349, 5806131, 7124591, 8497677, 5765826, 6511123, 5118134, 632758, 1153406, 1992669, 4325833, 7613582, 6584792, 81512, 8132171, 8720795 }

     Returns: {1, -50, 4439017 }

119. {-10000, -9990, -9960, -9910, -9838, -9748, -9638, -9508 }

     Returns: {10, 0, -10000 }

120. {100000000, -100000000 }

     Returns: {1, -50, -99999951 }

121. {100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 100000000, -100000000, 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     Returns: {1, -50, -99999375 }

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     Returns: {19, 50, -10175908 }

123. {10000, 10030, 10120, 10269, 10482, 10750, 11077, 11471 }

     Returns: {30, 0, 10000 }