Statistics

Problem Statement for "Halving"

Problem Statement

You have a collection of sticks. The length of each stick is a positive integer.

You want to have a collection of sticks in which all the sticks have the same length. You may alter your current collection by performing zero or more steps. Each step must look as follows:

  1. You choose one of your sticks. The chosen stick must have length at least 2.
  2. Let L be the length of the chosen stick.
  3. If L is even, cut the stick into two sticks of length L/2 each. Otherwise, cut it into sticks of lengths (L-1)/2 and (L+1)/2.
  4. Keep one of the two new sticks and throw away the other one.

It can be proved that any collection of sticks can be turned into a collection of sticks that all have the same length. You are given the current lengths of your sticks in the int[] a. Compute and return the smallest number of steps needed to reach your goal.

Definition

Class:
Halving
Method:
minSteps
Parameters:
int[]
Returns:
int
Method signature:
int minSteps(int[] a)
(be sure your method is public)

Constraints

  • a will contain between 2 and 50 elements, inclusive.
  • Each element of a will be between 1 and 109, inclusive.

Examples

  1. {11, 4}

    Returns: 3

    One optimal solution is: Pick the stick of length 11, cut it into sticks of lengths 5 and 6 and keep the part of length 5. Pick the stick of length 4, cut it into two sticks of length 2 and keep the part of length 2. Pick the stick of length 5, cut it into sticks of lengths 2 and 3 and keep the part of length 2. In the end, you'll have two sticks of length 2.

  2. {1000000000, 1000000000, 1000000000, 1000000000}

    Returns: 0

    All your sticks have the same length, no steps are needed.

  3. {1, 2, 3, 4, 5, 6, 7}

    Returns: 10

  4. {13, 13, 7, 11, 13, 11}

    Returns: 11

  5. {1, 1}

    Returns: 0

  6. {120405662, 698919604}

    Returns: 53

  7. {688307902, 172980724}

    Returns: 40

  8. {145897674, 152327620, 923531516, 227186712, 168504900, 4990177, 214655554, 191808208, 614864559, 267082849, 500359371, 129377264, 79950503, 341049060, 692356806, 571056304, 212145108, 484550895, 428922052, 74552152, 575706117, 486948166, 11440435, 714299831, 161926558, 634964944, 153179645, 303247109, 240764668, 377208093, 466622027, 233794446, 48472839, 247852183, 171900522, 815916004, 297945319, 40565574, 525610953, 245744056, 910202069, 370787649, 478477091, 4968540, 755532814, 541885359, 507599538, 2938576, 129953250, 326419829}

    Returns: 1308

  9. {315461279, 447297969, 153123822, 526780548, 378920322, 677297622, 429962081, 251944383, 377920255, 485550273, 445055383, 568926630, 338867875, 713954131, 605216012, 75920122, 313865306, 283308000, 91172709, 284341083, 22942201, 223336115, 474895734, 93321486, 713112215, 365877280, 51064304, 165150259, 608585843, 19868569, 71352895, 760461001, 557972562, 28980741, 252788794, 500061803, 286156050, 606077588, 149820544, 113652026, 270852241, 239904480, 197007221, 18514433, 67973989, 623225738, 316399714, 412859854, 799480216, 415643240}

    Returns: 1322

  10. {773498190, 670693202, 21122386, 962376887, 363001157, 154885741, 937765906, 883370172, 586055020, 951458831, 694438087, 998765425, 265895229, 798272929, 742408116, 502963659, 673961519, 456805379, 51099292, 366780327, 387932824, 573511511, 933195096, 774855165, 77514828, 312711573, 250539689, 845644471, 852463521, 616112617, 787218045, 597629376, 333185562, 222888273, 327728734, 832176053, 909704907, 816246052, 580819526, 569608972, 629765623, 384147659, 801720389, 432234792, 779364678, 710009025, 475884084, 844565586, 132558595, 559319060}

    Returns: 1366

  11. {470606301, 303641739, 5050478, 317612083, 239477559, 235373415, 453658740, 591714712, 34143923, 405023898, 493822714, 541050090, 283201504, 143277167, 266712079, 51412177, 581525001, 653332397, 622491635, 652104135, 540510104, 637718673, 313900994, 417498811, 142244679, 295466351, 29818805, 289454114, 54578297, 205261577, 256599318, 50971976, 597453018, 438126638, 557171883, 458720233, 102760064, 324104133, 276071601, 550607975, 591140559, 278839265, 307417611, 139465598, 274937102, 272938857, 333251626, 232136871, 662175641, 453355011}

    Returns: 1299

  12. {306496179, 182982120, 654180110, 707468111, 708841078, 627652724, 271924548, 398582509, 153549264, 349867964, 38964592, 4416356, 80117993, 572639049, 352978767, 170741855, 798720016, 772762490, 171885253, 191217478, 386891368, 399367984, 310548128, 634967908, 755076157, 139890161, 667037266, 333342421, 335554910, 287374283, 145060969, 38327399, 381530702, 144143701, 292678630, 585367790, 639076604, 345457333, 540814911, 331465287, 572570159, 377380607, 546270642, 616224197, 782471691, 723964262, 619274, 619065389, 186261472, 600831556}

    Returns: 1288

  13. {828821695, 448120266, 433347696, 970801523, 805763903, 923910506, 518777568, 437628085, 830087156, 853749069, 807851727, 460326689, 110167445, 873831268, 929742262, 224234254, 945301207, 30545137, 127052686, 886709511, 499174860, 455567560, 533588455, 252427416, 526289069, 227193127, 483676459, 108797678, 921249459, 436047410, 530329403, 823532401, 415163695, 970240240, 858997183, 410028559, 822279684, 214806224, 133215042, 478748836, 993631160, 476106081, 444414771, 259455386, 457128417, 985884571, 862731698, 993108470, 132733377, 987269409}

    Returns: 1302

  14. {357232223, 669630030, 660843410, 708688506, 313686988, 10723324, 314816064, 182824420, 328614717, 707953113, 163935772, 720828214, 322099926, 712034948, 312323249, 617292424, 631367366, 44729186, 326014765, 156417993, 644360712, 608602653, 657877796, 624927734, 619690178, 659525799, 310362773, 359814252, 334764185, 604421927, 314468267, 347460277, 170510751, 339012707, 171934306, 690289582, 80239907, 175928479, 180015465, 88531154, 364233117, 733801785, 646136781, 77831787, 335753117, 356188249, 179293367, 686378656, 668445229, 177332257}

    Returns: 1247

  15. {58328767, 26271672, 459908892, 840494245, 874435264, 921479355, 887694774, 893334748, 233156634, 101107622, 869598402, 461875647, 859194254, 433281522, 432672448, 896267276, 28315660, 815460149, 847767261, 412680667, 909054539, 415462770, 911178135, 114784254, 443056878, 828520933, 872439814, 883121819, 938845645, 434607587, 924197628, 857306429, 836190986, 446500113, 813431111, 932563986, 895145952, 859356667, 868041831, 843465558, 829645268, 936714192, 201496967, 892129013, 816456077, 927613480, 103732336, 230191347, 413688809, 894811751}

    Returns: 1261

  16. {653089360, 660141537, 656536335, 164675603, 658123382, 341878140, 645433857, 344435701, 343817430, 692600788, 661333242, 666700762, 42337676, 320649838, 690536183, 337212651, 683527775, 665010127, 684501072, 686048488, 327094501, 330774332, 692270000, 704470987, 43233969, 699339352, 662193266, 692965705, 671591788, 40891599, 337482879, 166056907, 699338860, 639963193, 653104345, 165704490, 676219185, 688858835, 330300581, 159995670, 334753062, 347164550, 319823612, 675768444, 697238101, 337876707, 673806890, 10420047, 84045779, 673771923}

    Returns: 1208

  17. {388864750, 5801584, 23444913, 187513623, 47140092, 744786453, 97323146, 782838427, 751915641, 98855881, 762684661, 777322030, 743687496, 50257031, 768770331, 804266205, 98681959, 741975988, 785059104, 762503594, 795985094, 761667444, 196147091, 392203271, 23418063, 390332279, 740082200, 197355052, 389674772, 752770452, 384220804, 373364943, 753611212, 372287720, 775011306, 785199344, 773758965, 794667147, 743844346, 199793580, 24470701, 23108006, 189808528, 24641491, 745218410, 96520314, 767637711, 94899581, 190905182, 785503926}

    Returns: 1176

  18. {708534101, 712372637, 89398483, 705654995, 345126908, 694371392, 703163990, 176738029, 178513559, 45085465, 351095950, 699989282, 690370335, 178881842, 352591453, 703773047, 718386549, 5547997, 179431765, 718455417, 89031614, 348045498, 351336940, 177867575, 703233960, 714629992, 720166867, 690023, 710795919, 43437160, 90004541, 174447974, 358278381, 350067397, 43876887, 177352396, 44492469, 350428933, 357958096, 691891152, 688327702, 355237467, 173411941, 695865768, 351269127, 691310889, 711274265, 705208173, 713527111, 357883938}

    Returns: 1130

  19. {162573446, 325967256, 646076721, 324127036, 639235431, 652641142, 160948079, 648380281, 639122567, 647121085, 320422066, 648240939, 638955014, 638776594, 645594994, 160128997, 650232867, 650102999, 81105813, 81201681, 161254600, 651435255, 645646867, 319599342, 651388128, 319263565, 645634103, 326774397, 159804290, 652815330, 642605318, 645911212, 324417449, 159518507, 163563359, 653108231, 646753862, 324205256, 80826269, 654283548, 649037021, 319818500, 319238488, 648211148, 162687106, 640662758, 325570662, 81652046, 644803879, 647442199}

    Returns: 1111

  20. {517025677, 519329090, 128154089, 511885538, 32485876, 519420030, 513672986, 258156960, 64911988, 32039901, 16251760, 518067871, 129664993, 517809333, 513714630, 259285531, 516669870, 257240307, 258532035, 64782474, 517619368, 64546427, 256186191, 514129426, 519287492, 258576845, 258124406, 128268738, 516759071, 512892264, 259679827, 514705768, 514717600, 260014645, 516097656, 259770214, 518869236, 128919233, 257236642, 515070480, 127959141, 517393669, 32450047, 514578989, 514364945, 64040684, 515105928, 258269527, 515322326, 64163165}

    Returns: 1046

  21. {323664275, 323311135, 161733638, 646899004, 323253321, 646799738, 646974513, 323475874, 647072853, 323224925, 647221476, 161623171, 647355477, 647012262, 161789714, 647346661, 80842854, 161856434, 40430282, 646723717, 323451625, 323524447, 646539770, 646608917, 80913181, 323558984, 646994550, 646459535, 647145631, 646948362, 646703059, 323408183, 647216861, 40438825, 647147932, 646579448, 646617822, 161848430, 323658146, 647379770, 323340930, 646478051, 323568700, 646454604, 646718954, 646788457, 40416520, 161663725, 646802784, 647273341}

    Returns: 908

  22. {202270988, 404514203, 101128191, 809071504, 404548373, 50564176, 101132245, 404528482, 809069022, 809032607, 809048655, 809042038, 809039131, 808984793, 404530451, 809015967, 809096978, 404524634, 101138408, 809031815, 101129411, 809051105, 809044558, 808977810, 202274229, 809077364, 809071325, 404545936, 202274597, 809036383, 809102505, 404547979, 808986815, 809102038, 202266533, 202260063, 404510262, 202262155, 809025400, 809083357, 50561784, 809028863, 202275332, 809091504, 809042484, 50561349, 202259114, 809076047, 202261885, 404497348}

    Returns: 749

  23. {505677876, 505673800, 505679704, 505674300, 505671997, 252837380, 63209769, 252837824, 505676606, 505677689, 505678819, 505674891, 252838258, 505672819, 505676525, 126419907, 505679226, 252837396, 252838591, 505674772, 505676239, 63209496, 505672260, 252837072, 505677245, 505676006, 126419710, 252839209, 63209011, 252836674, 252836808, 126417946, 252839764, 505678133, 31604490, 252837304, 252839393, 15802471, 505676986, 505673096, 505675677, 126419316, 126418987, 252838848, 505675187, 505677752, 505672463, 252838617, 126418311, 252836977}

    Returns: 555

  24. {9876534, 316049101, 79012319, 632098695, 316049277, 632098308, 632098542, 632098242, 632098590, 632098426, 316049256, 632098671, 632098180, 316049092, 316049066, 632098349, 39506115, 632098781, 632098129, 632098116, 316049001, 632098085, 158024559, 9876541, 632098258, 39506124, 158024487, 316048947, 632098631, 158024594, 632098485, 632098453, 632098418, 316049310, 632098154, 632098183, 158024554, 632098099, 632098794, 316049270, 632098209, 316049110, 632098558, 316049197, 158024680, 632098596, 316049138, 158024595, 632098324, 632098258}

    Returns: 403

  25. {790123359, 790123398, 790123446, 197530837, 395061712, 395061682, 790123359, 790123442, 395061672, 395061724, 790123450, 790123447, 790123420, 49382715, 790123438, 790123374, 395061706, 790123396, 395061719, 790123362, 395061699, 790123438, 790123415, 790123439, 395061717, 790123436, 790123410, 790123350, 790123362, 790123427, 395061719, 790123354, 98765430, 395061718, 790123383, 395061727, 790123425, 790123400, 790123342, 395061673, 197530841, 98765418, 790123384, 395061725, 395061721, 790123430, 790123341, 790123427, 98765422, 197530850}

    Returns: 267

  26. {987654307, 987654319, 987654307, 987654319, 987654315, 987654311, 493827159, 987654306, 493827158, 493827158, 987654306, 987654316, 493827157, 987654312, 987654318, 987654311, 246913579, 493827159, 987654308, 246913579, 987654308, 123456789, 493827154, 987654316, 987654312, 493827158, 493827154, 987654314, 987654315, 987654306, 493827153, 493827153, 987654316, 987654309, 246913579, 987654316, 987654309, 493827157, 987654318, 987654306, 987654316, 246913577, 493827156, 987654308, 987654317, 493827153, 246913577, 493827158, 493827157, 246913577}

    Returns: 120

  27. {1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000}

    Returns: 0

  28. {500000000, 500000000, 500000000, 500000000, 1000000000, 500000000, 500000000, 500000000, 500000000, 1000000000, 1000000000, 1000000000, 999999999, 500000000, 1000000000, 999999999, 1000000000, 500000000, 1000000000, 500000000, 500000000, 500000000, 500000000, 1000000000, 999999999, 500000000, 1000000000, 999999999, 500000000, 999999999, 500000000, 999999999, 999999999, 999999999, 1000000000, 1000000000, 999999999, 500000000, 999999999, 500000000, 1000000000, 1000000000, 500000000, 500000000, 500000000, 999999999, 999999999, 500000000, 999999999, 999999999}

    Returns: 27

  29. {999999999, 999999999, 499999999, 999999997, 499999999, 999999997, 999999997, 999999998, 999999998, 999999998, 999999997, 499999999, 999999998, 999999997, 499999999, 999999998, 499999999, 999999999, 999999997, 499999999, 499999999, 999999998, 499999999, 999999998, 999999999, 499999999, 999999998, 499999999, 999999997, 499999999, 999999998, 999999999, 999999999, 999999997, 999999998, 999999997, 999999998, 499999999, 499999999, 999999997, 999999998, 999999998, 999999997, 999999998, 999999997, 999999997, 999999998, 999999999, 499999999, 499999999}

    Returns: 35

  30. {500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001}

    Returns: 0

  31. {551747708, 139633970, 486476711, 573274841, 134721384, 508403642, 569126914, 488954834, 578484901, 547436442, 572077687, 134634759, 145226722, 514981273, 476898832, 484194262, 475439374, 477636088, 549987524, 520646151, 586760284, 256201649, 240622148, 119032296, 242082922, 286665276, 547141828, 499818041, 34687796, 139404533, 71153239, 492864579, 564606593, 1911701, 500865287, 485259955, 268124775, 260682644, 480125570, 292547066, 500635860, 15412827, 128190006, 525677087, 60721015, 540390273, 473594896, 273971377, 8357828, 578096742}

    Returns: 1249

  32. {101447715, 819479947, 815596463, 808853690, 808737217, 410517456, 51003874, 404134884, 817274008, 405028180, 817638233, 808336522, 409564168, 812569176, 405982051, 404070536, 809283751, 816818059, 201903041, 817408683, 814746697, 808979425, 811990135, 807701053, 805718615, 102147762, 408156285, 812071515, 409442651, 405383861, 205417695, 818506921, 819856291, 202151471, 404334776, 815852594, 814215961, 810544833, 817117121, 814669542, 403272785, 813453158, 819773989, 202731099, 814287493, 407340845, 819268147, 405489327, 403036543, 410583051}

    Returns: 1117

  33. {521002481, 522518232, 520954147, 523645441, 260979675, 260048183, 261520077, 522628222, 522643434, 523866870, 65437496, 522480147, 65517798, 260904785, 65454170, 130173774, 260178518, 260501668, 523450676, 522494865, 521270854, 260174343, 260804146, 261996668, 524020382, 521326110, 521669260, 130327282, 261542860, 16256601, 521243859, 523178362, 520637941, 522921448, 520876628, 522767560, 521714594, 260296751, 511023, 261225552, 32660114, 520906152, 521277508, 524193322, 522859323, 523743072, 261458508, 523721963, 523647045, 261776304}

    Returns: 1004

  34. {649471505, 649502462, 81183609, 324708485, 40589976, 649423110, 649432382, 324713978, 649519668, 649527044, 649440300, 649419702, 324702456, 649411553, 649422893, 649471051, 324742337, 324732855, 649411022, 649479737, 649471230, 649481014, 649518889, 649473559, 649431256, 649427263, 649400417, 649439481, 324719693, 324711630, 81185232, 649482715, 649507852, 649412079, 649519919, 649457537, 649523905, 649517223, 649429350, 324706546, 649490979, 81181501, 324730986, 649512941, 81179411, 649399785, 649473086, 324761464, 162356497, 324760614}

    Returns: 771

  35. {27317889, 54635464, 874177028, 54633903, 27317078, 874163637, 874152151, 874155426, 109269938, 874161293, 218536546, 13658384, 27316693, 874140739, 874140160, 437063700, 874170093, 874124198, 218533262, 437086622, 874180974, 874147445, 218531189, 874170401, 218537047, 874137538, 437090053, 874133361, 437088552, 109267324, 437061622, 109271696, 437063084, 874168540, 437066263, 874131098, 437078157, 874133740, 218542698, 437085121, 874149697, 437083047, 874173495, 874133285, 27316545, 874180565, 437071334, 218544922, 874173617, 874174155}

    Returns: 684

  36. {710852157, 177712186, 710852193, 88856212, 710849238, 177712411, 710849780, 44428200, 355424847, 44428067, 177712539, 710849801, 710852517, 177712965, 355426245, 177713057, 710850000, 710848595, 710850801, 177712249, 177712186, 710852492, 710851624, 710848866, 710851033, 710852277, 710852447, 710851541, 710852169, 22214023, 710849795, 710851526, 710851522, 88856167, 355425792, 355424488, 710849019, 710849769, 710849230, 710852148, 710848624, 710848840, 710851104, 710851367, 177712479, 710850218, 355425569, 88856230, 710852196, 710849148}

    Returns: 507

  37. {607620976, 303810526, 303810515, 607620943, 607620942, 303810494, 75952618, 607620942, 151905247, 151905263, 75952629, 303810478, 303810466, 607621041, 607621028, 303810526, 607621001, 151905254, 607621042, 303810497, 607620962, 607620960, 607620957, 607621000, 607620971, 303810504, 607620991, 75952621, 607621022, 607620952, 303810527, 607620935, 607621002, 607620949, 607621004, 607620984, 151905253, 607620983, 303810524, 607621017, 607621028, 607621045, 151905252, 607620957, 607620994, 151905237, 303810508, 303810491, 607621005, 607621053}

    Returns: 267

  38. {586550988, 586550979, 586550991, 146637742, 586550971, 36659436, 293275486, 293275492, 293275492, 146637745, 293275488, 586550989, 586550978, 586550984, 73318872, 73318873, 146637746, 586550966, 586550977, 146637746, 293275481, 586550974, 146637745, 586550985, 586550988, 586550971, 73318873, 293275494, 586550969, 146637743, 586550963, 586550975, 586550968, 146637747, 586550975, 293275485, 293275486, 586550964, 586550962, 586550970, 586550968, 586550965, 586550991, 293275488, 586550990, 586550977, 293275494, 293275487, 293275481, 586550971}

    Returns: 161

  39. {979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913, 979863913}

    Returns: 0

  40. {1000000000, 1000000000}

    Returns: 0

  41. {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    Returns: 0

  42. {1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000}

    Returns: 0

  43. {1000000000, 999999999, 999999999, 999999999, 999999999, 1000000000, 999999999, 999999999, 99999999, 999999999, 346346734, 346346734, 346346734, 346346733, 346346731, 346346735, 346346737, 346346739, 346346734, 346346734, 346346734, 346346733, 346346731, 346346735, 346346737, 346436739, 876543543, 876543541, 876543545, 876543547, 876543549, 876543551, 876543551, 876543553, 876543555, 876543557, 876543559, 876543561, 876543563, 876543565, 876543567, 876543567, 876543569, 32426, 754445, 2349832, 823567, 293845, 3252635, 2356461 }

    Returns: 1311

  44. {3, 9 }

    Returns: 2

  45. {999999997, 999998310, 999999421, 999997574, 999998245, 999998561, 999998950, 999997313, 999997532, 999997761, 999999478, 999997424, 999997869, 999998460, 999999089, 999999956, 999999726, 999998907, 999999559, 999999503, 999997035, 999998663, 999999643, 999999986, 999999974, 999998867, 999998406, 999998287, 999998195, 999998179, 999999502, 999998011, 999998648, 999998944, 999999829, 999998177, 999997651, 999997593, 999998441, 999999095, 999997373, 999997820, 999997133, 999997223, 999998382, 999999573, 999998614, 999999295, 999997414, 999999372 }

    Returns: 600

  46. {536870911, 536870911, 536870911, 536870911, 536870911, 536870911, 536870911, 536870911, 536870911, 536870911, 536870911, 536870911, 536870911, 1 }

    Returns: 364

  47. {499211613, 581869303, 890346735, 586334586, 545404205, 161255392, 922919430, 949333986, 715962299, 323567404, 418932836, 350294566, 196140741, 809094427, 348838240, 264392721, 112460520, 279768805, 144164698, 156218107, 676943010, 117454610, 168664244, 213834040, 111000747, 471852627, 84672537, 427838554, 437178461, 275731772, 609397213, 20544910, 811450930, 483031419, 933054127, 747762696, 402504554, 772830894, 120988588, 163214729, 816384845, 427077307, 153380496, 551745921, 646982598, 910208077, 11470446, 926416935, 915145308, 16 }

    Returns: 1341

  48. {6, 21 }

    Returns: 2

  49. {2, 3 }

    Returns: 1

  50. {1, 125387416, 407456958, 681542493, 913057001, 194544296, 332513754, 972751016, 145906011, 378686835, 10987091, 226480213, 543106121, 125036298, 438929287, 192254391, 161710939, 147414552, 320499865, 495099010, 446149916, 659038814, 408656647, 699392023, 559675251, 537119683, 183238762, 224309097, 686974156, 903636290, 705043005, 391127256, 392574100, 410713327, 22946130, 551606640, 991039580, 787152820, 636677434, 509369540, 235531669, 264912905, 588932169, 806630974, 42842696, 237668475, 709011804, 878568074, 739551429, 145972960 }

    Returns: 1364

  51. {3, 2 }

    Returns: 1

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