Statistics

Problem Statement for "KingdomAndDice"

Problem Statement

King Dengklek has two N-sided dice. The dice are not necessarily equal. Each of the dice is fair: when rolled, each side will come up with probability 1/N. Some time ago, each side of each die was labeled by a positive integer between 1 and X, inclusive. The labels were all unique. In other words, exactly 2*N distinct integers were used to label the sides of the two dice.

King Dengklek has been playing with the first die for a long time. Therefore, some of its labels were scratched off. The corresponding sides of the die are now empty. The second die still has all of its labels.

The current labels on the first die are given in the int[] firstDie: if the i-th side has no label, firstDie[i] is 0, otherwise firstDie[i] is the label. The current labels on the second die are given in secondDie: the i-th side of the second die has the label secondDie[i].

In King Dengklek's favorite game, he takes one of the dice, his opponent takes the other, and they each roll the die they have. The one who throws a larger number is the winner. King Dengklek wants to fill in the missing labels on the first die. His goal is to fill them in such a way that his favorite game becomes as fair as possible.

When filling in the missing labels, King Dengklek wants to preserve the two properties mentioned above: first, each integer between 1 and X, inclusive, may only occur at most once on the two dice. Second, no other labels may be used. However, there is an exception to the second rule: King Dengklek is also allowed to use the label 0. Moreover, he may even use this label multiple times.

You are given the int[]s firstDie and secondDie, and the int X. For a particular way to fill in the missing labels, let P be the probability that the player with the first die wins in the king's game. Find the labeling that minimizes the value |P - 0.5| and return the corresponding value of P. If there are two possible solutions, return the smaller one.

Definition

Class:
KingdomAndDice
Method:
newFairness
Parameters:
int[], int[], int
Returns:
double
Method signature:
double newFairness(int[] firstDie, int[] secondDie, int X)
(be sure your method is public)

Notes

  • Your return value must have a relative or an absolute error of less than 1e-9.
  • |x| denotes the the absolute value of x. For example, |3| = |-3| = 3.

Constraints

  • firstDie and secondDie will contain the same number of elements, between 2 and 50, inclusive.
  • X will be between 2*N and 1,000,000,000, inclusive, where N is the number of elements in firstDie.
  • Each element of firstDie will be between 0 and X, inclusive.
  • Each element of secondDie will be between 1 and X, inclusive.
  • Each integer between 1 and X, inclusive, will occur at most once in firstDie and secondDie together.

Examples

  1. {0, 2, 7, 0}

    {6, 3, 8, 10}

    12

    Returns: 0.4375

    One possible solution is to relabel the first die into {4, 2, 7, 11}. The probability of winning against the second die will be 7/16.

  2. {0, 2, 7, 0}

    {6, 3, 8, 10}

    10

    Returns: 0.375

    One possible solution is to relabel the first die into {9, 2, 7, 5}. The probability of winning against the second die will be 3/8.

  3. {0, 0}

    {5, 8}

    47

    Returns: 0.5

    One possible solution is to relabel the first die into {10, 0}.

  4. {19, 50, 4}

    {26, 100, 37}

    1000

    Returns: 0.2222222222222222

    The first die does not have any missing labels.

  5. {6371, 0, 6256, 1852, 0, 0, 6317, 3004, 5218, 9012}

    {1557, 6318, 1560, 4519, 2012, 6316, 6315, 1559, 8215, 1561}

    10000

    Returns: 0.49

  6. {0, 2}

    {1, 3}

    4

    Returns: 0.25

  7. {0, 0}

    {1, 4}

    4

    Returns: 0.5

  8. {0, 0}

    {2, 4}

    4

    Returns: 0.25

  9. {0, 0}

    {1, 2}

    4

    Returns: 0.5

  10. {0, 0}

    {2, 4}

    5

    Returns: 0.5

  11. {0, 0, 0, 0}

    {5, 6, 7, 8}

    8

    Returns: 0.0

  12. {0, 0, 0, 0}

    {5, 6, 7, 8}

    9

    Returns: 0.25

  13. {0, 0, 0, 0}

    {5, 6, 7, 8}

    10

    Returns: 0.5

  14. {0, 0, 0, 0, 0}

    {1, 2, 3, 4, 5}

    10

    Returns: 0.4

  15. {0, 3, 6}

    {1, 4, 7}

    7

    Returns: 0.4444444444444444

  16. {1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990, 999999989, 999999988, 999999987, 999999986, 999999985, 999999984, 999999983, 999999982, 999999981, 999999980, 999999979, 999999978, 999999977, 999999976, 999999975, 999999974, 999999973, 999999972, 999999971, 999999970, 999999969, 999999968, 999999967, 999999966, 999999965, 999999964, 999999963, 999999962, 999999961, 999999960, 999999959, 999999958, 999999957, 999999956, 999999955, 999999954, 999999953, 999999952, 999999951}

    {999999950, 999999949, 999999948, 999999947, 999999946, 999999945, 999999944, 999999943, 999999942, 999999941, 999999940, 999999939, 999999938, 999999937, 999999936, 999999935, 999999934, 999999933, 999999932, 999999931, 999999930, 999999929, 999999928, 999999927, 999999926, 999999925, 999999924, 999999923, 999999922, 999999921, 999999920, 999999919, 999999918, 999999917, 999999916, 999999915, 999999914, 999999913, 999999912, 999999911, 999999910, 999999909, 999999908, 999999907, 999999906, 999999905, 999999904, 999999903, 999999902, 999999901}

    1000000000

    Returns: 1.0

  17. {999999950, 999999949, 999999948, 0, 999999946, 999999945, 0, 999999943, 999999942, 999999941, 999999940, 999999939, 999999938, 0, 999999936, 999999935, 999999934, 999999933, 0, 999999931, 0, 0, 999999928, 999999927, 999999926, 999999925, 999999924, 0, 0, 0, 0, 999999919, 999999918, 999999917, 999999916, 999999915, 0, 999999913, 0, 999999911, 0, 999999909, 0, 999999907, 999999906, 999999905, 999999904, 999999903, 0, 999999901}

    {1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990, 999999989, 999999988, 999999987, 999999986, 999999985, 999999984, 999999983, 999999982, 999999981, 999999980, 999999979, 999999978, 999999977, 999999976, 999999975, 999999974, 999999973, 999999972, 999999971, 999999970, 999999969, 999999968, 999999967, 999999966, 999999965, 999999964, 999999963, 999999962, 999999961, 999999960, 999999959, 999999958, 999999957, 999999956, 999999955, 999999954, 999999953, 999999952, 999999951}

    1000000000

    Returns: 0.0

  18. {259459975, 0, 0, 0, 0, 445850634, 287828435, 0, 11491506, 580197746, 0, 213259370, 451161373, 0, 0, 0, 0, 0, 0, 246308416, 0, 0, 0, 0, 0, 110097462, 0, 319028681, 30490980, 0, 0, 222982953, 0, 135611117}

    {404533979, 441107160, 207318154, 460329684, 15560111, 453934779, 40955192, 99574481, 289311781, 326154469, 410902148, 140254530, 91121427, 418817385, 11792150, 474496493, 102153269, 33952707, 554627, 333460927, 313402065, 508256967, 31214224, 343893045, 135709087, 297065442, 180216750, 358692039, 126533314, 12698873, 98937489, 531067293, 453806032, 306255642}

    584039327

    Returns: 0.5

  19. {583580964, 0, 0, 0, 0, 0, 0, 0, 549353893, 0, 0, 0, 255995577, 0, 0, 161064041, 0}

    {96185108, 124390413, 518950998, 108883980, 116516829, 70613296, 455878940, 27406803, 82605278, 583284951, 157082497, 28741378, 119415043, 66963096, 65882888, 361932014, 177433896}

    637444863

    Returns: 0.4982698961937716

  20. {22237969, 21086083, 0, 0, 20499604, 0, 0, 0, 19193784, 0, 0, 0, 5745362, 21344371, 1432274, 12292859, 0, 0, 14965190, 0, 7540295, 17645678, 8307861, 15626012, 3150902, 0, 866717, 0, 22854463, 11240592, 0, 0, 3424049, 0, 12020448}

    {7197896, 12316986, 15296439, 1556756, 20317264, 19123408, 20230973, 20892646, 13310099, 14610142, 14416670, 21617959, 13563036, 23077769, 9111344, 16713937, 4840796, 12679437, 17580654, 7714099, 12174806, 10203696, 15518992, 16450485, 15549882, 22104334, 18251953, 18973930, 17009371, 7555869, 762957, 17242354, 12907943, 16059395, 11834198}

    23266508

    Returns: 0.4995918367346939

  21. {10513907, 0, 0, 0, 779690, 35111390, 23571472, 35023847, 0}

    {16868556, 10563831, 17569493, 14999524, 14227024, 25794435, 16882064, 24260721, 21487401}

    35642680

    Returns: 0.49382716049382713

  22. {600422104, 0, 0, 416081521, 0, 0, 0, 116545911, 0, 0, 0, 80598597}

    {522462300, 690995055, 293835844, 152997281, 561069289, 152430460, 384422853, 32505765, 590146042, 258723719, 116449587, 574540481}

    717552847

    Returns: 0.5

  23. {0, 243196107, 47435728, 0, 0, 79842716, 520326888, 402132894, 0, 0, 0, 228146431, 0, 0, 0, 0, 53188609, 98973129, 0, 0, 375318521, 0, 0, 407979309, 0, 0, 0, 263527863, 0, 0, 0, 441802073, 49357377, 430196072, 0, 318807186, 0, 184860182, 135771520, 0, 0, 424105269, 0, 0}

    {169523618, 104197718, 333854078, 157543320, 100309931, 41996210, 447019988, 363837793, 367370435, 488763031, 74987650, 536055105, 395249589, 373019073, 50096967, 488181787, 267899631, 329674637, 208787347, 51391302, 97854594, 300372892, 238325347, 458686401, 438218275, 524232521, 236815249, 201383706, 410948412, 392336480, 127258475, 43082651, 496534198, 461112553, 200625970, 61528614, 503108762, 112330444, 425366407, 335163683, 65777960, 500354056, 335903273, 461027548}

    537389378

    Returns: 0.5

  24. {145178052, 161901973, 0, 0, 0, 0, 288567440, 54231080, 222834418, 156430427, 0, 543006658, 0, 0, 583021208, 0, 0, 0, 0, 0, 0, 0, 525551962, 0, 536307429, 0, 0, 0, 0, 675224032, 0, 167006606, 0, 0, 0, 0, 0, 0, 0, 227928516, 0, 0, 915865789, 112423041, 0, 0, 941150194, 0, 0, 959647693}

    {562581057, 714799137, 409754231, 649344250, 391854598, 744451666, 639192016, 407714697, 152668442, 2902450, 580005222, 440801847, 9495491, 297133833, 124847261, 720499754, 373915842, 391913883, 255311816, 912492430, 309611100, 347550668, 873768965, 725209331, 488251861, 410723182, 517044447, 671446938, 89957313, 845186991, 481779554, 501391863, 410671051, 891533784, 152567541, 802525648, 486670372, 791759557, 60925267, 639338813, 643515500, 640930488, 81972089, 501864484, 938064320, 55672843, 73049161, 162665084, 447586725, 328360976}

    998168571

    Returns: 0.5

  25. {44244956, 14848426, 698990018, 636581069, 0, 0, 50166537, 0, 458743552, 0, 519668818, 0, 0}

    {405232860, 305248993, 141152593, 193982102, 360921835, 214201753, 356647185, 171757802, 29998409, 282489621, 416391306, 311961419, 326734576}

    755366445

    Returns: 0.4970414201183432

  26. {2008566, 0, 0, 0, 0, 0, 0, 0, 6722285, 64815398, 0, 0, 0, 0, 8453367, 0, 0, 0, 16457963, 80358931, 14923697, 0, 0, 14404974, 0, 11768058, 0, 17294411, 0, 0, 0, 36780774, 0, 0, 0, 50237482, 0, 46033881, 0, 0, 0, 0, 0, 0, 0, 0, 61722499, 0, 44999317}

    {2869819, 1020553, 3369147, 30844016, 7419899, 2776614, 10678463, 27774202, 80187785, 36564173, 19872355, 15683121, 21421829, 32729186, 65920602, 33737021, 43144319, 18882934, 44210279, 18790055, 465938, 71141498, 21220980, 51512809, 47629131, 27680536, 26360331, 27175145, 62945786, 4717762, 61279397, 65815604, 77019734, 64648543, 3588072, 2263148, 67425156, 3371470, 19142285, 54541392, 39935642, 28119575, 70224512, 50462406, 49953696, 53968629, 73304363, 10921531, 61956498}

    82176484

    Returns: 0.4997917534360683

  27. {0, 1943958}

    {1476036, 1875829}

    1947210

    Returns: 0.5

  28. {0, 0, 0, 0, 0, 7287108, 18873315, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11990496, 0, 0, 0, 0, 20042160, 13390394, 21671505, 2747037, 4579172, 0, 20211304, 347734, 15740306, 8188505, 0, 0, 0, 0}

    {7341302, 18248155, 21295448, 4306309, 3433641, 11668731, 4592019, 11213468, 13584372, 2187250, 14134127, 4527838, 16258707, 20780143, 2137039, 3980255, 12266338, 6716210, 3153677, 7840177, 11902026, 15969170, 15609350, 9452435, 16683987, 21491137, 17640939, 17195685, 8829546, 18254556, 11079770, 16170848, 21477222, 17349729, 5451668, 2463934, 13992971, 17465127, 21098841, 5130415}

    22446928

    Returns: 0.5

  29. {0, 0, 115722564, 176685469, 0, 165021409, 80575185, 223034204, 0, 0, 0, 79212563, 25200173, 178536410, 177836676, 0, 0, 0, 0, 132587905, 0, 0, 0, 58961234, 131608143, 0, 21251611, 75771601, 0, 0, 130865695, 0, 210078258, 0, 245542323, 0, 0, 0}

    {243724326, 24036570, 98626025, 291637705, 152217901, 231213930, 64173069, 95456571, 6032344, 19095744, 154417804, 73543687, 150703886, 49189811, 32100425, 171955497, 118588304, 144511703, 233141492, 99003383, 50418712, 51989569, 147939619, 305667175, 298707504, 210999297, 274098193, 268871886, 177217445, 277528251, 104855326, 145563830, 26186880, 203481350, 161823595, 178404780, 159317339, 225996663}

    312017618

    Returns: 0.5

  30. {0, 0, 0, 0, 0}

    {142283780, 310440974, 467347253, 286795482, 360165647}

    514006988

    Returns: 0.48

  31. {0, 0, 0, 0, 244881576, 0, 0, 111788183, 0, 0, 42464793, 247400851, 89897415, 0, 0, 0, 262210432, 0, 0, 0, 179108606, 0, 0, 173017128, 0, 0, 0, 176441600, 0, 0, 0, 148033829, 140748748, 0, 124323900, 0, 0, 95728473}

    {48789426, 135398493, 94113207, 206748893, 4477960, 61301927, 253881743, 183586565, 74308124, 25365662, 61991333, 210447188, 173925564, 30429421, 36455303, 107531411, 206871021, 121908117, 159290263, 77367287, 18445351, 6620330, 158878432, 159194098, 160240887, 67977883, 19692300, 114177279, 30096685, 40190805, 209905751, 78886110, 175589297, 40193259, 21809304, 143189193, 64617122, 238812983}

    263825698

    Returns: 0.5

  32. {0, 23767844, 8959878, 0, 0, 0, 76569858, 0, 53797753, 16750926, 45595040, 0, 0, 39755965, 10214571, 66031054, 0, 0, 0, 0, 16623638, 0, 35899873, 0, 96123019, 0, 2451344, 0, 0, 0}

    {78232303, 39766191, 101262795, 3544418, 85361230, 100827955, 98273420, 54514105, 34045071, 12134409, 64728675, 50733810, 73673855, 59874485, 2025653, 85805943, 90685147, 68513143, 382340, 77485060, 78700697, 31790605, 20444092, 88864912, 25866383, 74847632, 43548696, 28317726, 99282182, 63381707}

    102047240

    Returns: 0.5

  33. {220199902, 587714870, 780585305, 446521046, 0, 809504088, 768448038, 0, 236250624, 0, 0, 0, 358614190, 18152874, 0, 0, 0, 295231891, 312550196, 0, 532750097}

    {752976813, 394282257, 741131592, 298396117, 226240824, 275334990, 474340782, 820552111, 761990723, 5137013, 353834147, 644496182, 234022626, 590084770, 278773942, 458798971, 280937892, 106014664, 817413160, 100389857, 124167537}

    912317647

    Returns: 0.4988662131519274

  34. {0, 0, 182075576, 0, 0, 119560762, 0, 0, 0, 182725802, 0, 206624847, 116187008, 3882133, 0, 0, 196320232, 30530609, 112740817, 94380774, 0, 0, 86313354, 0, 0, 0, 100711460, 0, 209831780, 0, 0, 179332352, 208221282, 34663790}

    {37927979, 78121651, 30414358, 146408617, 55185414, 87846350, 176939225, 17717497, 200587166, 53870048, 157179302, 87951103, 191816393, 148298174, 174264457, 118406408, 129448872, 126161129, 114012193, 55984895, 74140303, 169694842, 46560206, 142422659, 14671388, 98742472, 147579574, 111353813, 132788317, 94748060, 146017602, 170716295, 217950742, 2256524}

    219256468

    Returns: 0.5

  35. {0, 159348060, 0, 217566588, 172143235, 0, 0, 0, 12498611, 0, 0, 298709279, 196516752, 296781778, 250559043, 0, 102105513, 0, 0, 227097076, 194464908, 0, 0, 310467338, 0, 164393331, 281487000}

    {37764959, 221719447, 293985611, 25148779, 306782593, 86153392, 85677855, 264230509, 44489942, 184624429, 242795045, 193075908, 197003269, 115967696, 120603881, 299108781, 82230790, 167121822, 165290615, 71147663, 213639709, 121575320, 203366612, 181325453, 213298361, 195616708, 128397582}

    318217241

    Returns: 0.4993141289437586

  36. {0, 0, 0, 0, 339338103, 0, 0, 19242999, 0, 0, 216243764, 458042777, 0, 0, 143959388, 176853661, 0, 263869945, 16761438, 631008841}

    {292013708, 221306410, 223008917, 605093227, 142721002, 545853498, 24805980, 609368528, 550005286, 363493972, 477987042, 569248284, 312104337, 536709532, 402198306, 528348100, 479697597, 229286149, 748845417, 38087576}

    758264357

    Returns: 0.5

  37. {19222813, 0, 0, 0, 20113926, 0, 9082972, 0, 0, 16213888, 1946490, 273630, 0, 0, 12441926, 12855011, 0, 19553878, 0, 8804199, 14801203, 0, 0, 9404593, 0, 0, 0, 19283403, 0, 2504666}

    {7304425, 1105109, 9202423, 14093411, 1378738, 11255187, 3963653, 5040018, 3582768, 4911483, 2531951, 20070337, 18175708, 1971483, 14977459, 7854987, 10775681, 8918479, 7293111, 18688347, 12191340, 17493962, 12729861, 5578135, 7580048, 3560688, 20079136, 11500372, 19516837, 7714240}

    20114345

    Returns: 0.5

  38. {0, 0, 0, 65663059, 0, 0, 0, 0, 0, 0, 0, 0, 0, 77097752, 0, 28439154, 32608562, 0, 0, 0, 43044903, 82108240, 0, 0, 20493166, 104212150, 52426318, 0, 0, 52236362}

    {81595198, 41486101, 71402785, 29712780, 22383795, 156742861, 13014441, 130404456, 13881495, 105633470, 117048890, 46490056, 112451381, 10512205, 16392926, 111303742, 53557108, 29665688, 35436016, 42846894, 71409183, 75892250, 63340059, 151968532, 86308309, 125003448, 110598759, 126027718, 2362069, 75650195}

    157975966

    Returns: 0.5

  39. {37249876, 0, 0, 422858970, 0, 0, 135101464, 379332996, 0, 194362340, 325147794, 0, 396556976, 0, 0, 0, 0, 0, 330434450, 0, 311267581, 0, 0, 0, 48522493, 0, 0, 247296091, 0}

    {187146271, 294390662, 223455372, 219286315, 402380501, 417817711, 191509842, 436401171, 228029276, 68281830, 77741891, 148796665, 210872184, 364656575, 7735164, 340167554, 164929727, 338169613, 220052935, 376482540, 358310070, 272900266, 181950000, 415700401, 384976620, 403434500, 385795111, 164695688, 282517300}

    464089131

    Returns: 0.4994054696789536

  40. {0, 214637138, 0, 350145872, 238194727, 0, 307118470, 86815916, 0, 153492641, 0, 0, 158025782, 0, 66484954, 0, 469919453, 432083744, 17870355, 0, 172499666, 0, 456018650, 134205221, 0, 0, 16715502, 322835763, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33283609, 0, 0, 429504577, 191149373, 0}

    {58168752, 107794506, 267838156, 358257625, 307958623, 63035733, 19555566, 17555656, 106479547, 38522666, 34271157, 95224474, 361358429, 184598194, 245240275, 108925021, 142922917, 139480308, 203582744, 3418889, 136254642, 406522799, 403307094, 169538250, 403943632, 71445660, 86962736, 104686398, 209712002, 22257576, 454565568, 12026221, 130052081, 249496444, 370283845, 182156172, 56677644, 389839411, 199711827, 163157191, 172507544, 233982983, 258381664}

    472907279

    Returns: 0.49972958355868036

  41. {0, 305619587, 334634698, 0, 741187470, 0, 416339317, 780003338, 0, 0, 0, 20913106, 0, 0, 0, 0, 0, 438076035, 116270706, 0, 0, 0, 0, 308311326, 0, 0, 139323191, 73953016, 0, 0, 0, 0, 538500686, 260740582, 828076699, 335871484, 229778666, 0, 667854700, 0}

    {333552904, 138274600, 540725829, 254927770, 608694341, 452855167, 90361790, 74553191, 170813551, 260430507, 213876382, 668158793, 698809387, 228271942, 183908323, 243347106, 189245478, 6783884, 781847791, 159105900, 631950330, 621393361, 149879427, 731876175, 484387539, 423398463, 124351669, 63112075, 640680661, 319329063, 358057305, 501356258, 457603662, 425905827, 283406722, 228994831, 405883688, 373768511, 303548021, 103819932}

    837303171

    Returns: 0.5

  42. {387253791, 0, 0, 0, 16916318, 0, 648866647, 662598399, 0, 0, 0, 0, 0, 514243075, 873306143, 0, 274862534, 0, 0, 0, 0, 337075448, 154474078, 358576642, 44749656, 0, 0, 0, 0, 0, 0, 152742966}

    {276313636, 461594434, 347656978, 557173047, 449761330, 861900052, 767759615, 57434154, 70046127, 138618692, 332296687, 842557545, 299144443, 168814595, 563889347, 179707138, 122107054, 285221086, 334181215, 462653303, 260014739, 204099056, 123619971, 179448442, 474716202, 724158018, 202628093, 512349665, 309847011, 504623154, 665092630, 586160647}

    881850330

    Returns: 0.5

  43. {0, 609016340, 195030067, 0, 0, 0, 0, 299608675, 879147273, 0, 0, 142302425, 0, 253172710, 613760741, 199306758, 0, 332896609, 0, 0}

    {20731192, 259936319, 485405441, 158327105, 510669040, 759832127, 889673569, 805948517, 278277489, 138617319, 678152220, 83117608, 79942375, 206895570, 67664865, 666941197, 173393414, 538926746, 809243622, 387156311}

    894600015

    Returns: 0.5

  44. {0, 0, 0, 731508997, 0, 0, 0, 603985286, 0, 404028772, 0, 0, 913848530, 117019528, 21112009, 0, 687509767, 0, 35969376, 0, 0, 167379288, 0, 349758785, 0, 0, 0, 0, 221045682, 0, 0, 0, 0, 819513399, 250105081, 0, 885089317, 0, 0, 0, 0, 0}

    {539340848, 140597686, 412652946, 34736005, 558671225, 346581609, 896482020, 953176658, 696340394, 156968994, 888723951, 230590086, 296577182, 519849516, 451635767, 806720031, 938673191, 591999244, 763875139, 274929742, 454496130, 100699563, 525034822, 83953289, 44658779, 219657002, 458088345, 60746902, 164424746, 562716655, 349003882, 703765594, 469863716, 761656828, 505050974, 71518428, 151221924, 444516482, 67678573, 614111693, 601485475, 722951899}

    957016512

    Returns: 0.5

  45. {631725432, 0, 559112562, 0, 487753668, 228297181, 153278578, 0, 0, 0, 0, 175931428, 346053511, 0, 0, 0, 0, 0, 279004111, 602544072, 99165162, 272559785, 0, 0, 328996549, 501166592, 174377137, 0, 0, 386346689, 0, 0, 658666993, 0, 0, 0, 500306910, 422195491, 0, 521360735, 0}

    {144166301, 620525896, 373010372, 416726085, 43539471, 243620255, 430139009, 218888710, 189700211, 113046179, 502857748, 210430038, 660064703, 632810745, 153259024, 228151970, 450934197, 182611913, 337041144, 291341768, 476399277, 127371716, 32517765, 56800553, 627678625, 103198293, 325348734, 35670976, 452882931, 28450046, 46207397, 443401922, 648975942, 419217769, 41868585, 27903299, 662838023, 472007593, 93144699, 34278812, 431406462}

    664612113

    Returns: 0.4997025580011898

  46. {0, 0, 11945964, 91162037, 0, 0, 567420388, 806484995, 0, 0, 0, 0, 0}

    {6253913, 458717962, 58894048, 81679306, 304385182, 100762632, 865256282, 148963782, 663831790, 49079993, 847854706, 185917264, 736144003}

    909320987

    Returns: 0.4970414201183432

  47. {0, 6563924, 43730097, 0, 0, 20579196, 0, 0, 63730211, 27340527, 50796887, 0, 66900338, 0, 0, 24704515, 0, 0, 0, 0, 0, 22007422, 0, 0, 123848805, 72973363, 0, 30667678, 0, 0, 0, 0, 0, 8980690, 0, 0, 74503, 26366488, 0, 128413531, 0, 87536164, 57428575, 129498062, 0, 60174563}

    {6664325, 22433653, 58826145, 22188525, 120503873, 2258846, 47813185, 29267331, 9421758, 123362767, 95658739, 85804991, 56536932, 128785630, 24345797, 124013977, 37653255, 50712284, 81348256, 38627937, 116240935, 109733873, 67552421, 73489675, 96187749, 62096115, 120148380, 32513507, 105978787, 2206127, 29803189, 49758232, 24639779, 88629333, 9061876, 82258771, 28003299, 56875060, 111526102, 104827599, 117352946, 14012537, 60345166, 111004997, 12510743, 84690963}

    130287423

    Returns: 0.5

  48. {157558990, 4509410, 81457897, 0, 0, 0, 0, 107243799, 0, 0, 0, 0, 0, 63915783, 84448378, 0, 75312313, 30836845, 0, 191852763, 0, 150602944, 0, 155112354, 0, 0, 0, 0, 118475164}

    {157848452, 150814430, 125656451, 7208009, 219489927, 177795169, 117445213, 40450866, 77059463, 176281596, 208101775, 151453988, 117533210, 118762599, 138813691, 148370054, 187513310, 180645027, 175571328, 104219137, 222476306, 78320251, 178483953, 58879857, 68781116, 98613709, 224595324, 245885249, 237890238}

    247854020

    Returns: 0.4994054696789536

  49. {96141541, 86468088, 0, 0, 0, 16816112, 0, 47523206, 0, 97598969, 0, 0, 85396396, 0}

    {43381461, 75907456, 73833936, 90365688, 67846274, 7796157, 87220328, 85990839, 29841340, 11505365, 17732406, 78021190, 10691270, 51339166}

    107922527

    Returns: 0.5

  50. {0, 361046937, 446763674, 0, 188105352, 0, 0, 0, 182458312, 0, 0, 0, 0, 0, 0, 353924299, 0, 0, 0, 474204553, 0, 461294819, 491229743, 0, 0, 52366682, 261061818, 0, 0, 0, 23543185, 0, 0, 0, 0, 0, 280259892, 212379740, 108034710, 230949976, 313547531, 0, 202522978, 0, 0}

    {570320408, 102346916, 199445512, 50367718, 261044348, 29981795, 484691165, 466053296, 441493829, 154646823, 489596481, 103331372, 7060792, 243734298, 179256958, 409082114, 279737939, 28991314, 524611933, 492117678, 232649969, 60327271, 189666820, 33074409, 200808, 72688816, 272381258, 778641, 275211793, 232268879, 350792380, 415006665, 476409630, 119712356, 34848848, 165134607, 291487986, 519540012, 200662367, 160662444, 101867464, 259733312, 405787651, 250722091, 503467609}

    572319371

    Returns: 0.4997530864197531

  51. {0, 66054454, 99396759, 0, 132471167, 102553580, 0, 0, 0, 0, 19205847, 221649327, 0, 0, 0, 187751300, 131174694, 0, 0, 0, 0, 152618021, 0, 0}

    {218672474, 28978169, 197405120, 145562217, 58842933, 16622366, 184659867, 77421308, 106466032, 25044177, 140177921, 82028245, 14974046, 159383767, 21254186, 7344656, 129463256, 123859896, 91711271, 15221813, 82332479, 21731570, 62421302, 71259657}

    229278716

    Returns: 0.5

  52. {0, 283682187, 172308714, 0, 0, 299632968, 0, 0, 0, 144518322, 290439874, 0, 0, 128795560, 133878624, 0, 0, 153888365, 224670898, 0, 161486335, 201993386, 263798457, 43557477, 0, 0, 240363293, 0, 85336926, 321048924}

    {14343731, 186306962, 107812548, 304182563, 315102521, 290418283, 97742879, 324564031, 22202652, 162868110, 138134087, 102121670, 47220699, 300421663, 180869487, 229821794, 112677541, 21429804, 313557246, 36157689, 34298835, 16796414, 57610755, 103627778, 19668550, 297974047, 2845056, 214694359, 42992664, 46580656}

    361433068

    Returns: 0.5

  53. {0, 38005679, 0, 57297323, 0, 0, 0, 0, 69952219, 0, 0, 62514224, 55987050, 59702690, 0, 0, 21097466, 0, 0, 0, 0, 26465329, 0, 15897914, 0, 29571977, 41304148, 0, 31037476, 34158336, 0, 38455214, 60640256, 0, 0, 0, 0, 0, 35730453, 21371051}

    {78451234, 78451233, 78451232, 7587014, 78451231, 33125912, 37007832, 9241719, 78451230, 10978864, 78451229, 78451228, 78451227, 78451226, 29667487, 11870359, 78451225, 26503345, 64206262, 78451224, 78451223, 27306411, 78451222, 48144683, 42123502, 5008141, 43437465, 19302791, 78451221, 981324, 1660172, 32189133, 78451220, 61997676, 20780699, 78451219, 78451218, 11701392, 23244701, 8252091}

    78451234

    Returns: 0.5

  54. {459429879, 0, 0, 0, 0, 145358528, 0, 0, 743825909, 0, 0}

    {164474086, 327985446, 50345153, 301569030, 496770901, 243957078, 14246731, 886860371, 527344174, 886860370, 74863452}

    886860371

    Returns: 0.49586776859504134

  55. {0, 0, 2931029}

    {655001, 1539792, 3117950}

    4478864

    Returns: 0.4444444444444444

  56. {0, 170051912, 133315046, 266833883, 17065731, 3214524, 0, 143661133, 19768262, 9896138, 17244196, 92216312, 0, 0, 124346817, 0, 0, 0, 0, 266088527, 11143512, 181945618, 0, 157778753, 0, 0, 111340638, 11223394, 0, 0, 0, 276669095, 0, 75454392, 0, 166610443, 0, 274892847, 0, 115984447, 0, 127127958, 32821801, 49122399, 0, 218976888, 117469667, 0, 0, 12228936}

    {293431014, 293431013, 11596371, 270885871, 293431012, 293431011, 279989144, 32060582, 150760987, 293431010, 201601634, 160542136, 93086556, 293431009, 293431008, 241708322, 293431007, 293431006, 293431005, 246013465, 223607359, 293431004, 293431003, 293431002, 293431001, 293431000, 119472008, 293430999, 293430998, 28339674, 293430997, 293430996, 63342217, 171158035, 81013842, 293430995, 293430994, 293430993, 194893093, 293430992, 293430991, 293430990, 293430989, 221647653, 249460122, 198681539, 293430988, 293430987, 225109331, 293430986}

    293431014

    Returns: 0.2616

  57. {0, 0, 83101507, 0, 254259541, 279161842, 451874034, 415072294, 146398851, 508758742, 0, 0, 0, 28969514, 0, 148078941, 458994610, 0, 348096412, 214089358, 323672223, 0, 494876015, 0, 0, 388347039, 91641713, 510281282, 0, 0, 0, 163160129, 0, 0, 401831545, 0, 350022109, 45261460, 442281639, 537195951, 354520418, 0, 0}

    {573389924, 273247111, 64928754, 573389923, 13720333, 525098886, 224592790, 146689426, 395718872, 240580289, 543865869, 552408593, 573389922, 421300307, 304125093, 119868189, 573389921, 573389920, 573389919, 395760478, 171470671, 451035754, 573389918, 573389917, 573389916, 376509073, 461485773, 573389915, 519067011, 130758594, 45736702, 224042531, 249839740, 262866983, 109258489, 47101258, 573389914, 573389913, 387872787, 573389912, 411594664, 113123857, 470123323}

    573389924

    Returns: 0.49972958355868036

  58. {0, 0, 0, 112875242, 84887508, 0, 0, 114210011, 105094483, 335644762, 0, 0, 0, 0, 0, 354801251, 213425404, 244618562, 298793664, 2416601, 218333303, 0, 0, 158780690, 135797205, 275141571, 0, 0, 356595869, 65145390}

    {246255318, 116851072, 383307890, 88344432, 383307889, 383307888, 383307887, 239380100, 124350886, 383307886, 342684188, 151146222, 367902332, 146083200, 306124210, 186833169, 292292058, 253133918, 270841521, 131751859, 362712420, 383307885, 383307884, 383307883, 71767290, 383307882, 196118175, 369062151, 313871269, 87199961}

    383307890

    Returns: 0.47888888888888886

  59. {671092147, 0, 0}

    {703554709, 461271406, 703554708}

    703554709

    Returns: 0.3333333333333333

  60. {0, 38887532, 0, 0, 139122951, 161671836}

    {341604047, 268928532, 476172205, 7750176, 476172204, 476172203}

    476172205

    Returns: 0.3333333333333333

  61. {144039374, 0, 51875600, 11842846, 168651230}

    {205889833, 261143122, 261143121, 171945551, 169000514}

    261143122

    Returns: 0.12

  62. {167343868, 0, 153439354, 0, 97382471, 114106237, 190536238, 0, 0, 0, 215990906}

    {207979583, 282833045, 132720306, 124064784, 57330780, 6438271, 133033386, 62530982, 47257642, 282833044, 65862210}

    282833045

    Returns: 0.49586776859504134

  63. {0, 0, 0, 0, 0, 0, 0, 31905265, 0, 2002218}

    {40387038, 80545070, 80545069, 80545068, 11018991, 26478491, 25290414, 69777728, 22915410, 10105167}

    80545070

    Returns: 0.5

  64. {0, 0, 0, 0, 0, 675643720, 616254500, 0, 652107621, 628599358, 284635012, 0, 0, 0, 0, 372485426, 636926116, 253424615, 0, 344074851, 0, 0, 9741162, 0, 316874075, 315989656, 559494221, 0, 0, 0, 412819368, 418783367, 298356695}

    {830136369, 187691702, 852144867, 852144866, 422164010, 132910021, 852144865, 852144864, 852144863, 852144862, 852144861, 852144860, 120360148, 136403404, 100989736, 308763898, 346922528, 303609137, 50454808, 852144859, 852144858, 293656692, 852144857, 852144856, 787264953, 852144855, 68030107, 251551632, 236074643, 852144854, 56488390, 852144853, 852144852}

    852144867

    Returns: 0.4508723599632691

  65. {55972811, 0, 0, 85256967, 0, 206013582, 0, 118315645, 174403982, 0, 191425352, 0, 73009405, 0, 35973113, 0, 0, 222186519}

    {256747861, 228632258, 256747860, 191104309, 112043511, 137109050, 59571562, 184953559, 111189655, 187514337, 3834123, 90662654, 256747859, 256747858, 118769113, 185428802, 256747857, 57366699}

    256747861

    Returns: 0.5

  66. {0, 0}

    {48592805, 83042800}

    83042800

    Returns: 0.5

  67. {0, 0, 0, 106474560, 0, 0, 0, 7356358, 0, 0, 0, 51995350, 0, 0, 38938253, 0, 78267084, 34070773, 81628977, 18942451, 0, 0, 0, 0, 0, 0, 6439440, 0}

    {88485610, 144641908, 23440116, 144641907, 144641906, 144641905, 82116275, 128019695, 144641904, 113686002, 59047444, 127485151, 141600786, 144641903, 79861826, 31346034, 116968514, 130908053, 78307417, 483528, 120336842, 144641902, 52876621, 144641901, 144641900, 144641899, 98748281, 144641898}

    144641908

    Returns: 0.45535714285714285

  68. {0, 241195906, 165750082, 0, 0, 160515871, 248811044, 314916249, 242452806, 0, 120439397, 0, 0, 0, 0, 12618356, 0, 52477309, 0, 0, 0, 113774466, 0, 279532240, 0, 306988689, 0}

    {108665913, 283833346, 314328782, 320214915, 287598015, 320214914, 144996345, 320214913, 24340196, 320214912, 320214911, 80604640, 86837185, 320214910, 320214909, 115031297, 159928975, 194303155, 42433206, 123195259, 320214908, 368347, 111989065, 320214907, 320214906, 108825905, 227814513}

    320214915

    Returns: 0.4993141289437586

  69. {2921402, 0, 0, 680644, 238083, 0, 0, 9735463, 2339473, 686269, 14278171, 11168406, 0, 0, 11992890, 0, 0, 0, 4128622, 14290998, 14212055, 0, 3853429, 0, 0, 0, 0, 0}

    {6884235, 7514836, 9678971, 4390340, 8490173, 16647737, 16647736, 700520, 6980934, 8330553, 3684834, 12780902, 5697644, 16647735, 16647734, 4161356, 3399740, 14443879, 13950486, 16647733, 16647732, 16647731, 16647730, 16647729, 16647728, 10141850, 12629336, 16647727}

    16647737

    Returns: 0.4451530612244898

  70. {369210996, 904146839, 0, 657581125}

    {236241139, 950747775, 676971613, 488667241}

    950747775

    Returns: 0.5

  71. {5386078, 7046154, 5898677, 0, 0, 0}

    {18289515, 18289514, 18289513, 11877024, 1948188, 18289512}

    18289515

    Returns: 0.25

  72. {91769378, 4056982, 78316512, 94597093, 0, 0, 63196080, 160990945, 0, 152686330, 34865872, 0, 22070964, 0, 0, 0, 0, 134194330, 54614526, 0, 0, 0, 10372895, 51402047, 101537766, 0, 13038219, 0, 0, 14471097, 0, 0, 5847252, 0, 27918216, 132227822, 131136124}

    {221465646, 221465645, 25421582, 221465644, 171805484, 73904929, 142452541, 193163901, 75879683, 221465643, 67177630, 221465642, 38159010, 221465641, 111179073, 221465640, 139097288, 139134553, 218185383, 213857220, 221465639, 110356532, 221465638, 221465637, 221465636, 221465635, 122393920, 221465634, 132880272, 221465633, 208942141, 138236690, 127541510, 221465632, 17254937, 187957180, 8129742}

    221465646

    Returns: 0.35865595325054783

  73. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {1000000,2000000,3000000,4000000,5000000,6000000,7000000,8000000,9000000,10000000,11000000,12000000,13000000,14000000,15000000,16000000,17000000,18000000,19000000,20000000,21000000,22000000,23000000,24000000,25000000,26000000,27000000,28000000,29000000,30000000,31000000,32000000,33000000,34000000,35000000,36000000,37000000,38000000,39000000,40000000,41000000,42000000,43000000,44000000,45000000,46000000,47000000,48000000,49000000,50000000}

    1000000000

    Returns: 0.5

  74. {111,0,0,4,78,79,96,39,0}

    {10,82,74,106,1,105,83,24,110}

    111

    Returns: 0.49382716049382713

  75. {999991087,999996234,0,0,999923781,3860500,8092387,19,892322953,999998862,1000000000,999999020,969677542,998470619,999999217,0,998995153,0,998960737,999999985,999999998,80,999999120,0,952840206,0,32854894,9033170,5479917,8777488,287445,30,999989880,999963908,910433750,999429288,999999963,0,0}

    {996408791,7333,997656436,208112,151,2,80049886,485762158,44943,292340299,999999119,22086181,6348,22225540,65789230,999999932,646,1,3479760,4039,12214188,15384,999999943,90700,999999950,44108004,982322052,999999988,217937,148,132,999998323,999999523,12,150,8365457,35069,997939753,32039}

    1000000000

    Returns: 0.5489809335963182

  76. {36171694,1158,999803038,999802999,988671211,1037946,0,951709561,142585856,695964,674,57,999803053,1,0,999318574,376859,0,1164,991427936,999802816,27763,999803055,3279343,999799870,999801567,972921101,0,0,56,36255018,999695474,0,31,158094,999802733,22657616,22081511,920220257}

    {25,4,3206507,3132331,11,6,1151,29872584,12,998894418,59,365,999802930,1531520,1882783,16591095,999803060,747515203,50,947532182,7,3,999803048,16157,999803061,12539481,998875380,999803006,876391765,745537229,472708,999802825,999757173,999621256,35,8179,997870511,919095840,7114}

    999803062

    Returns: 0.4996712689020381

  77. {2758,1,3238,3134,3232,0,2723,3218,2897,3237,3228,1471,3216,130,3217,502,220,58,3074,2236,4,2,3226,3196,14,3234,0,0,3164,0,482,0,3174,3}

    {7,23,3224,1812,10,3230,3235,12,2911,3163,6,1958,73,440,1676,112,3179,3096,3202,3190,2137,15,425,1236,3212,30,405,442,3233,292,1223,445,191,2273}

    3238

    Returns: 0.5060553633217993

  78. {0,125219,7184,999935586,60733,999957916,2198898,0,1618401,999956346,488447773,694058555,999929085,8,999957432,946933067,12612,222172659,999958096,1,249,999958088,999958086,4,472,6926,999958090,999958074,0,419275935,999958085,932363531,999956363,42125080,999958095,0,6469414,999737653,0,999958040}

    {635129,468,52,999947170,999957161,999947793,999958094,128,918779760,961392816,1245,2,179450,6762,999955267,986138729,413,980613804,8217592,850523940,89,108,999929661,204735631,31032350,16,18146056,999958092,995956577,4862,3538,123058,87065509,71206541,2022,990774817,996635099,584020903,999718388,999958063}

    999958096

    Returns: 0.52375

  79. {2,30,8,92,55,67,74,0,104,1,102,80,99,91,43,75,57,0}

    {89,10,16,103,64,15,61,97,3,70,53,96,18,82,19,95,12,13}

    104

    Returns: 0.5

  80. {76981527,0,10,76989745,5236,3405,76986514,1,0,1466958,13965,76983549,75671056,76989789,76989755,76989088,76967743,76467849,4,0,76959915,247,76989780,0,76986433,76989500,76989793,0,60965,0,73918290,76981137,76797614,76989762,76989309,35,76989593,76989722,191,6}

    {3,76989422,23375,440,86,429,7590876,76987490,75176,241,76989749,636699,76924674,309392,234,76915024,76104154,727,63368377,6468566,76983435,76986052,229642,7696612,81,76610932,3500683,76989710,5887,76970635,76989591,76058633,76891093,22,76989747,17,177,503,76989419,1679}

    76989793

    Returns: 0.52

  81. {6,0,154,127,151,126,136,152,15,20,0,153,129,30,155,1,69,120,135,141,72,2,4,0,149,28,63,16,150,71,0,0,7,140,93,10,0,123}

    {107,13,38,26,130,12,5,147,3,14,104,27,33,144,8,112,139,109,124,115,119,19,11,80,101,21,32,22,53,146,54,51,70,64,82,58,134,96}

    155

    Returns: 0.5006925207756233

  82. {12973,0,12967,12950,0,37,12366,0,1,45,10068,12951,0,12,7116,12929,2,12498,444,11623,12744,199,613,12972,10368,11181,12963,113}

    {3046,12919,12460,254,5,12938,55,242,11308,12958,4805,12960,11424,445,11572,1214,12970,3690,11,12968,82,32,74,38,4,28,12971,8}

    12973

    Returns: 0.5

  83. {6660375,4485114,0,3865,0,6665473,813,2422018}

    {47,1667,1,6562783,6614305,429325,1100,277345}

    6665474

    Returns: 0.53125

  84. {3678,0,1961,2549,5644,10782,70,10952,0,0,9492,2,18,32,10956,9340,653,0,10779,11040,11042,11030,2969,11014,11041,10923,3,3632,11026,0,9133,4395,375,207}

    {7453,1,10729,11036,2279,31,10677,6,10859,55,10831,9247,146,10210,174,63,15,11020,11012,11037,10035,11,91,1229,1653,17,1721,8,8990,637,6246,10325,9663,5091}

    11042

    Returns: 0.5086505190311419

  85. {0,983956848,983957379,31,0,0,983938195,0,0}

    {5,811565146,944625879,186228881,933549118,734454931,983926879,10537959,581}

    983957382

    Returns: 0.49382716049382713

  86. {2,435897349,0,868409748,999712074,0,0,999999833,0,43,999999986,999149159,0,0,0,604,1516,16851947,0,543917,22664,758022296,131423497,13349696,998953064,634252871,999977556,300506856,1,611550268,0,411041,983888553,0,383,922,999999769}

    {2528,16,519518620,999869386,386628297,3351,999924390,999998627,89593,13741737,19455536,53628,164371914,999984046,2194,3,999999985,999969881,999999621,63,999999984,999980095,15,38,979837254,5,999999954,1014,5036794,251,999999983,56819009,999999592,899373157,5985,577864697,998606928}

    999999986

    Returns: 0.4996347699050402

  87. {237366,0,0,0,0,106,4363,0,237363,41,0,236969,206861,19,0,10824,46,237286,1,237199,856,179924,1981,77133,0,0,187347,0,80987,198,235558,96796,237336,0,0,0,363,182774,44660,237316,0,3327,235775,234134,19098}

    {150401,2193,237365,236348,1387,237357,237112,237361,237353,237320,216250,182043,236029,237324,236980,237359,237342,4,231400,237282,236773,341,237352,176210,2,3,1769,32,1030,12,282,7,237364,237346,237362,7297,4061,140255,3418,235877,197,235636,128385,1042,217413}

    237366

    Returns: 0.4997530864197531

  88. {93890562,722640,0,15,90127740,93890470,2611,13345763,119940,1,2,93809165,93890368,86782779,0,91626490,5,93739311,11455746,5801350,87216}

    {235028,93343139,325991,1785,90227659,11912060,18405,975,54,18,93872258,19,86310156,93890421,974407,38183388,93163944,15732749,2938259,93890560,1309617}

    93890563

    Returns: 0.4988662131519274

  89. {0,999962756,0,0,0,0,0,0,0,0,0,0,226435,0,0,0,0,0,0,0,999999961}

    {999999621,10258,236,4,341278,3,999999452,999999814,1615834,572620,984515944,774172530,11196,999999963,908444286,999987132,999988277,999999878,1517421,999999978,999999967}

    999999978

    Returns: 0.4988662131519274

  90. {999584844,0,995921961,671,0,0,999995192,999995196,0,0,0,0,85668}

    {993499085,1,998251205,999852693,18457,999107612,999995133,999994027,2,111526257,28,999995086,999943050}

    999995210

    Returns: 0.4970414201183432

  91. {2,0,999993451,0,0,0,95434,999957503,782126440,0,999997286,0,754427347,999965426,999782308,999909927,4031926,0,96291,63309719,999943496,0,999787946,0,0,999994971,21713396,0,0,999991407,0,1,0,10932,640613023,875058164,988948813,0,325,0,0,182071,29999,999997316,792197017}

    {123,3,153,2971316,8,306181,939126811,489414,2693932,26992,999937577,999997368,999979380,999753688,7,1512451,1665,968901086,46376,590,1413082,997612058,999986955,999160997,17,999997388,999758579,998518473,106,999997360,999120304,999997324,999638786,999982188,43651,999968657,993246702,998356296,12,999695085,999991177,999997377,811082017,999997391,989107592}

    999997391

    Returns: 0.4997530864197531

  92. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {8249,56,8369,55,8254,8372,8371,2829,1,90,8367,6,3,602,5,7438,8288,7813,4468,51,77,2,8095,9,1512,8101,1984,8200,1424,8361,1870,363,2366}

    8372

    Returns: 0.4995408631772268

  93. {999237492,0,0,0,0,994230280,23,0,4,0,0,999236206,110046768,999237476,999232808,230144,2}

    {999010438,1,1046866,1045654,137576007,1729,999222300,996879135,16121480,999237426,999237466,999229592,23464823,999225276,999236625,995354790,999237490}

    999237492

    Returns: 0.4982698961937716

  94. {16787592,802,0,0,999959864,1,0,0,0,997940127,0,16,0,0,0,506387041,0,0,0,0,0,994379736,0,890910,0,0,0}

    {6080925,137,71208815,999997958,135747,999997687,12242,748,26064512,999999969,6710572,997329688,999999911,9228,6159558,6086780,999999898,999998995,12084839,999533714,999999875,999999775,960301305,999998269,21158,7750066,999735214}

    999999969

    Returns: 0.4993141289437586

  95. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {7173610,504299,863666270,52397895,8446398,994022319,992328475,994022258,994022266,5681,3,133935423,11925820,128370587,994021377,3908336,993450415,994021682,3733}

    994022319

    Returns: 0.4986149584487535

  96. {0,8017082,0,999586343,1,18583281,999951916,664829142,471,15604647,0,260,999641866,752009,15282277,999959769,529717,0,0,4042783,999961837,999961849,0,3,2574,573134,22,157390278,3967,999961696,149,999961077}

    {430234315,999961822,440,1213,15935483,999961801,999961728,999733493,100663,999961739,999703594,33171761,999960422,2012,999961834,8,999961847,956392483,999197097,15443,999961732,999961785,1182,992523503,996155601,919898,998206207,5519,465325,999961846,999933499,49985}

    999961849

    Returns: 0.48828125

  97. {212261581,0,11032,1404900,0,212722417,0,0,2252926,8597,338,212699631,205740327,209217867,4,212721756,3434573,2082,9930,0,19738161,490,0,675110,5892961,37687,196035439,33118,892,212568608,208493774}

    {212623817,205774514,212711872,211871128,211843572,212722374,196961887,212722413,7207,215058,17,212722416,211000073,237,1432078,212721965,5647,15044982,2,210822642,170882756,212675446,73832296,212722411,212529184,495,212714206,212722219,212722084,1326696,212658537}

    212722417

    Returns: 0.4547346514047867

  98. {993122712,36608,555483030,995529955,0,865653385,995061219,997120626,0,116,124,34008,68,29379,166221085,997120454,996862155,38,34,27054,0,0,15,1823782,5,0,552883,17,7711211,575776,26194929,1327,958979871,228757,0,930232906,1919818}

    {968277357,997108720,603685,141,113729096,997039820,25,815199083,740,5794,50301865,997120621,98,997120567,997120610,8,997117701,997120630,1000,1,997110357,997120629,991663346,10256512,997105092,14,40781584,997117386,997107353,995938718,12541,989797991,997120604,997119225,46,997120618,997090974}

    997120630

    Returns: 0.4426588750913075

  99. {1,2431352,262,0,2431259,44,594,33,241,1015495,2431383,0,2,2423737,16064,3,2430455,6,861,2431393,2431359,2779,2431170,2595,57,74313,2108,2430788,616731,2429289,2366939,7,0,2381313,1478047,2431041,159,10,2431394,2431391,14512,123084,2431395,34886}

    {2424144,2431384,2431390,2329937,258085,444365,2431396,2431333,2045,2428653,2356424,2408400,2430454,136,2431382,64,2420999,65331,2431260,3084,823,1696303,9048,2015,867471,4,104156,1262308,522199,2430503,2431374,446562,2431375,2095217,12966,2324076,27,2430929,2366413,5047,176337,2431387,2427701,2431377}

    2431396

    Returns: 0.44163223140495866

  100. {4,1,997387544,994880859,999968461,999972085,111092558,6958456,149259}

    {999964938,999971995,399819406,887379381,993450878,191306,999971573,997159412,999971130}

    999972097

    Returns: 0.32098765432098764

  101. {511719,15,29317,730,1,510978,315889,5,21,511250,3635,511777,43,243,4423,271794,4,11,511770,509557}

    {510381,510571,1243,511757,97403,20,7736,509316,511755,484204,1135,511062,511776,487097,501993,511694,287837,511702,511762,26}

    511777

    Returns: 0.315

  102. {1,120,18,0}

    {2,525,572,394}

    572

    Returns: 0.3125

  103. {857,78881}

    {999005031,29528}

    999005031

    Returns: 0.25

  104. {71655,39418}

    {994659874,993257381}

    994659878

    Returns: 0.0

  105. {0,0,0,999999938,0,0,999999977,0,0,0,0,20318,999303521}

    {4753573,999992431,978201023,12,999591544,1,999999872,3698949,999945514,999999982,999999997,999427435,725317951}

    1000000000

    Returns: 0.4970414201183432

  106. {0,0,0,207074265,64624,0,999983953,999986798,999986518,0,0,0,0,999972177,146445,0,0,0,999983067,0,0,0,7665528,0,998440555,999986779,303550974,48,0,0,999935430,0,0,11,0,0,133206996,468,1720,0,238291671,999960805}

    {2,2113491,12,999986775,999986664,999986790,999242472,999981835,998411394,4549,997864498,978109347,988124476,999986684,999986283,992314696,411633810,999985348,205,975072654,25,32,999983354,10541,999975704,342580369,61239726,10104534,194,39763,999986777,107648665,983493896,999986378,999986432,2842853,999986797,950633151,999982606,991174328,999922412,999986796}

    999986798

    Returns: 0.5

  107. {17,23399692,0,31671,2356113,999994255,999785698,1756329,51,494525423,1115,228452281}

    {2066,5,999994250,7,14,160,998401278,21,642209387,999126718,999994232,6}

    999994257

    Returns: 0.5486111111111112

  108. {183815570,0,999942750,999966006,999966522,99484770,22}

    {2,971168315,10,12288782,999947249,17134532,951100554}

    999966846

    Returns: 0.6122448979591837

  109. {998336511,19446873,999991754,971919973,494119,999294243}

    {5,999991904,2,174352298,999991567,124}

    999991904

    Returns: 0.6388888888888888

  110. {999996376,999999969,1479749,999999889,593018528,855659,246378,0,990814744,999998583,999999957,992485981,999999994,999995253,999970559,992695867,6036898,999999991}

    {866708296,20695,309,442105699,3649101,975485215,34171575,247881823,999999990,1686,999991971,2577291,999972360,28,18726363,705,973,999948003}

    1000000000

    Returns: 0.7191358024691358

  111. {999999857,999200513,12753442,16356271,999998731}

    {972918884,1773331,67277,181388,476081740}

    999999888

    Returns: 0.84

  112. {16885755,16988805}

    {478,16869706}

    16988805

    Returns: 1.0

  113. {0, 0 }

    {1, 2 }

    4

    Returns: 0.5

  114. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000, 110000, 120000, 130000, 140000, 150000, 160000, 170000, 180000, 190000, 200000, 210000, 220000, 230000, 240000, 250000, 260000, 270000, 280000, 290000, 300000, 310000, 320000, 330000, 340000, 350000, 360000, 370000, 380000, 390000, 400000, 410000, 420000, 430000, 440000, 450000, 460000, 470000, 480000, 490000, 500000 }

    1000000000

    Returns: 0.5

  115. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {553004783, 509477451, 647624790, 543942796, 232933658, 307388835, 555943838, 730591586, 336528454, 879934640, 179609727, 537702473, 348355566, 154440638, 464181750, 709957421, 574781586, 242785155, 520972417, 950184923, 293378838, 319791637, 465199851, 983962854, 140866409, 191181893, 149288522, 262536245, 194889062, 726089973, 911535331, 877740453, 455750376, 235026154, 4041835, 851470536, 73449187, 554727749, 328118644, 721864951, 559269015, 685294237, 991454444, 30968851, 942961769, 503573891, 453989707, 24091315, 319010551, 305157555 }

    1000000000

    Returns: 0.5

  116. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {371573083, 358468430, 753279639, 403284478, 22520933, 546434282, 723065755, 97982478, 597550363, 203560713, 81330621, 543641108, 57098389, 12634333, 66187368, 937262530, 384608944, 963854098, 851368768, 143301033, 871463024, 484956169, 814505425, 115058638, 953290510, 762745379, 898150191, 938583634, 965839424, 557715566, 657172063, 745037327, 658451581, 241637281, 607360350, 613891659, 522401615, 267830711, 510312492, 983671210, 770824049, 438251859, 241953920, 66953349, 361421856, 295628926, 860415599, 590096173, 331499242 }

    1000000000

    Returns: 0.4997917534360683

  117. {0, 0 }

    {3, 4 }

    5

    Returns: 0.5

  118. {1, 2, 3, 4, 5, 70, 7, 8, 9, 0, 0, 0, 13, 14, 0, 16, 0, 18, 19, 20, 21, 0, 0, 24, 25, 26, 27, 28, 29, 30, 0, 32, 0, 34, 35, 0, 37, 0, 0, 0, 0, 42, 43, 0, 0, 0, 0, 0, 0, 0 }

    {765934, 377744, 216263, 391530, 669701, 475509, 349753, 887257, 417257, 158120, 699712, 268352, 772844, 78706, 754109, 546394, 118331, 137367, 932170, 957933, 226918, 669848, 937973, 32869, 206981, 706224, 638550, 567593, 488165, 776170, 126552, 950428, 516191, 542625, 40636, 604921, 427945, 719311, 269863, 998485, 937364, 643302, 914711, 267237, 351877, 750432, 579930, 560398, 500676, 970492 }

    1000000000

    Returns: 0.42

  119. {19, 50, 4 }

    {26, 100, 37 }

    1000

    Returns: 0.2222222222222222

  120. {1, 2, 3, 4, 0 }

    {5, 6, 7, 8, 9 }

    10

    Returns: 0.2

  121. {0, 0, 0, 0, 0 }

    {3, 5, 6, 8, 9 }

    10

    Returns: 0.36

  122. {3, 4 }

    {1, 2 }

    8

    Returns: 1.0

  123. {3, 4 }

    {1, 2 }

    4

    Returns: 1.0

  124. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 3100, 3200, 3300, 3400, 3500, 3600, 3700, 3800, 3900, 4000, 4100, 4200, 4300, 4400, 4500, 4600, 4700, 4800, 4900, 5000 }

    1000000000

    Returns: 0.5

  125. {16678006, 16737860, 16986736, 16684400, 16930234, 16900595, 16718745, 0, 16957505, 0, 17188383, 16798616, 16979811, 16916109, 0, 0, 0, 0, 17028676, 17164640 }

    {17355908, 17152485, 17080002, 16700407, 16766918, 16695477, 17268762, 16866471, 16893978, 17295366, 17047868, 17233436, 17213681, 17377940, 17013129, 17227187, 17324651, 17237341, 17406523, 17108153 }

    999999997

    Returns: 0.4575

  126. {0, 132262568, 87040238, 51497359, 0, 169142565, 56147172, 17211071, 167697194, 164720946, 252305969, 0, 245335747, 259393484, 30806936, 43450878, 251514692, 111008162, 10739176, 22326414, 0, 132838554, 184128855, 21791398, 247587898, 167297261, 115255435, 193931864, 219076752, 77001069, 194074183 }

    {151975576, 169822846, 33217564, 39719391, 92003691, 212230914, 138417192, 196438573, 103212460, 84618709, 232259095, 80370900, 39798453, 138461731, 232246058, 41298920, 57299232, 121456370, 248938284, 35032531, 77862645, 228470681, 192302163, 8187421, 120113357, 10107235, 38444317, 146624126, 106552096, 185067290, 150195034 }

    265550123

    Returns: 0.4994797086368366

  127. {1, 0 }

    {2, 3 }

    4

    Returns: 0.5

  128. {6, 0, 0 }

    {2, 3, 5 }

    6

    Returns: 0.5555555555555556

  129. {0, 0 }

    {500000000, 1000000000 }

    1000000000

    Returns: 0.5

  130. {0, 0, 6, 7, 8 }

    {1, 2, 3, 4, 5 }

    10

    Returns: 0.6

  131. {207579013, 0, 0, 0, 762888636, 98152103, 0, 0, 9580639, 0, 178509023, 0, 0, 558212775, 26389630, 0, 925801173, 0, 656585276, 902071051, 727123763, 0, 0, 0, 520690250, 0, 799313373, 789204467, 0, 0, 0, 806956092, 0, 0, 158398860, 0, 0, 0, 0, 882264705, 877444310, 0, 0, 0, 775142615, 0, 0, 0, 0, 590064714 }

    {506507264, 909420688, 489726670, 55434271, 793692317, 210461043, 901329639, 537850353, 29523792, 614794872, 570497240, 905203770, 706091348, 904237002, 118054687, 337246325, 307178253, 150625750, 896162464, 644505509, 271356543, 1738704, 865692963, 226102989, 593986004, 122173998, 807688148, 583502198, 468916698, 747545899, 468884929, 620479532, 675026050, 541326149, 747075168, 203959041, 191528802, 491192255, 104714246, 101365768, 179252, 960570656, 244081265, 440998363, 674385237, 484916146, 641913151, 917826070, 670850119, 607465477 }

    1000000000

    Returns: 0.5

  132. {2, 4 }

    {1, 3 }

    4

    Returns: 0.75

  133. {74, 56, 36, 5, 104, 34, 1, 6, 80, 10, 28, 95, 73, 32, 85, 89, 13, 75, 11, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {67, 84, 24, 107, 88, 101, 60, 17, 100, 94, 110, 35, 91, 33, 106, 58, 29, 66, 92, 63, 42, 22, 111, 70, 4, 78, 12, 57, 54, 26, 86, 15, 38, 62, 52, 2, 3, 99, 93, 30, 37, 109, 31, 39, 23, 97, 103, 40, 79, 71 }

    111

    Returns: 0.5016

  134. {0, 217, 11, 457, 105, 277, 467, 229, 0, 0, 207, 317, 142, 0, 146, 470, 45, 99, 115, 101, 488, 433, 258, 267, 0, 29, 400, 237, 314, 10, 0, 284, 74, 294, 454, 0, 77, 88, 0, 0, 463, 222, 202, 57, 219, 262, 471, 0, 27, 203 }

    {218, 465, 187, 63, 311, 328, 477, 278, 360, 298, 414, 373, 209, 296, 416, 214, 166, 497, 441, 372, 449, 355, 403, 419, 135, 349, 319, 255, 103, 272, 38, 464, 265, 376, 469, 226, 324, 250, 185, 56, 248, 438, 89, 149, 411, 75, 435, 153, 392, 341 }

    500

    Returns: 0.4928

  135. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {1, 18000001, 36000001, 54000001, 72000001, 90000001, 108000001, 126000001, 144000001, 162000001, 180000001, 198000001, 216000001, 234000001, 252000001, 270000001, 288000001, 306000001, 324000001, 342000001, 360000001, 378000001, 396000001, 414000001, 432000001, 450000001, 468000001, 486000001, 504000001, 522000001, 540000001, 558000001, 576000001, 594000001, 612000001, 630000001, 648000001, 666000001, 684000001, 702000001, 720000001, 738000001, 756000001, 774000001, 792000001, 810000001, 828000001, 846000001, 864000001, 882000001 }

    1000000000

    Returns: 0.5

  136. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22 }

    {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 14, 16, 17, 18, 23 }

    53

    Returns: 0.49691358024691357

  137. {14, 0, 0, 70, 8, 64, 0, 0, 34, 28, 36, 46, 0, 66, 0, 0, 144, 68, 0, 63, 137, 0, 24, 50, 41, 88, 10, 127, 57, 31, 0, 124, 0, 43, 71, 61, 13, 173, 47, 0, 170, 65, 1, 49, 17, 45, 72, 172, 26, 18 }

    {139, 108, 107, 98, 138, 83, 159, 182, 999999999, 194, 167, 122, 115, 150, 198, 103, 156, 100, 116, 146, 89, 151, 13371337, 106, 200, 141, 183, 168, 176, 177, 77, 93, 189, 187, 110, 133, 80, 152, 193, 113, 84, 92, 148, 136, 87, 191, 169, 119, 131, 155 }

    1000000000

    Returns: 0.3176

  138. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 3100, 3200, 3300, 3400, 3500, 3600, 3700, 3800, 3900, 4000, 4100, 4200, 4300, 4400, 4500, 4600, 4700, 4800, 4900, 5000 }

    6000

    Returns: 0.5

  139. {0, 0, 0, 0 }

    {1, 2, 3, 10 }

    11

    Returns: 0.4375

  140. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {1000, 2000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000, 110000, 120000, 130000, 140000, 150000, 160000, 170000, 180000, 190000, 200000, 210000, 220000, 230000, 240000, 250000, 260000, 270000, 280000, 290000, 300000, 310000, 320000, 330000, 340000, 350000, 360000, 370000, 380000, 390000, 400000, 410000, 420000, 430000, 440000, 450000, 460000, 470000, 480000, 490000, 500000 }

    5550000

    Returns: 0.5

  141. {0, 0, 0, 0, 0 }

    {900000000, 900000001, 900000002, 900000003, 900000004 }

    1000000000

    Returns: 0.4

  142. {4, 5, 0 }

    {1, 3, 2 }

    50

    Returns: 0.6666666666666666

  143. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 3100, 3200, 3300, 3400, 3500, 3600, 3700, 3800, 3900, 4000, 4100, 4200, 4300, 4400, 4500, 4600, 4700, 4800, 4900, 5000 }

    1000000

    Returns: 0.5

  144. {0, 0, 7, 8 }

    {1, 2, 3, 4 }

    8

    Returns: 0.5

  145. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999, 1111111, 2222222, 3333333, 4444444, 5555555, 6666666, 7777777, 8888888, 9999999, 11111111, 22222222, 33333333, 44444444, 55555555, 66666666, 77777777, 88888888, 99999999, 111111111, 222222222, 333333333, 444444444, 555555555, 666666666, 777777777, 888888888, 12345678, 87654321, 123456789, 987654321, 32768, 766794 }

    1000000000

    Returns: 0.5

  146. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    {1000002, 1000004, 1000005, 1000006, 1000008, 1000009, 1000010, 1000011, 1000012, 1000013, 1000015, 1000017, 1000019, 1000021, 1000023, 1000025, 1000027, 1000028, 1000030, 1000031, 1000033, 1000034, 1000035, 1000037, 1000038, 1000039, 1000041, 1000042, 1000043, 1000045, 1000047, 1000048, 1000050, 1000051, 1000053, 1000054, 1000056, 1000058, 1000060, 1000061, 1000063, 1000065, 1000066, 1000068, 1000070, 1000071, 1000073, 1000075, 1000077, 1000078 }

    1000090

    Returns: 0.5

  147. {11, 12, 0, 0, 0 }

    {1, 2, 3, 4, 8 }

    12

    Returns: 0.56

  148. {1, 4, 0, 0 }

    {8, 5, 3, 2 }

    15

    Returns: 0.5

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